dragonbox-master/0000775000175000017500000000000015060737600013004 5ustar renerenedragonbox-master/CMakeLists.txt0000664000175000017500000000731115060737600015546 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(dragonbox VERSION 1.1.3 LANGUAGES CXX) # ---- Includes ---- include(CMakePackageConfigHelpers) include(GNUInstallDirs) # ---- Warning guard ---- # Protect dependents from this project's warnings if the guard isn't disabled set(dragonbox_warning_guard "SYSTEM") if(dragonbox_INCLUDE_WITHOUT_SYSTEM) set(dragonbox_warning_guard "") endif() # ---- Declare library (dragonbox) ---- set(dragonbox_headers include/dragonbox/dragonbox.h) if (CMAKE_VERSION VERSION_GREATER_EQUAL "3.19.0") add_library(dragonbox INTERFACE ${dragonbox_headers}) else() add_library(dragonbox INTERFACE) endif() add_library(dragonbox::dragonbox ALIAS dragonbox) target_include_directories(dragonbox ${dragonbox_warning_guard} INTERFACE "$") target_compile_features(dragonbox INTERFACE cxx_std_17) # ---- Declare library (dragonbox_to_chars) ---- if (CMAKE_VERSION VERSION_GREATER_EQUAL "3.19.0") set(dragonbox_to_chars_headers include/dragonbox/dragonbox_to_chars.h) else() set(dragonbox_to_chars_headers ${dragonbox_headers} include/dragonbox/dragonbox_to_chars.h) endif() set(dragonbox_to_chars_sources source/dragonbox_to_chars.cpp) add_library(dragonbox_to_chars STATIC ${dragonbox_to_chars_headers} ${dragonbox_to_chars_sources}) add_library(dragonbox::dragonbox_to_chars ALIAS dragonbox_to_chars) target_include_directories(dragonbox_to_chars ${dragonbox_warning_guard} PUBLIC "$") target_link_libraries(dragonbox_to_chars PUBLIC dragonbox) target_compile_features(dragonbox_to_chars PUBLIC cxx_std_17) # ---- Install ---- option(DRAGONBOX_INSTALL_TO_CHARS "When invoked with --install, dragonbox_to_chars.h/.cpp are installed along with dragonbox.h" On) set(dragonbox_directory "dragonbox-${PROJECT_VERSION}") set(dragonbox_include_directory "${CMAKE_INSTALL_INCLUDEDIR}/${dragonbox_directory}") set(dragonbox_install_targets "dragonbox") if (DRAGONBOX_INSTALL_TO_CHARS) set(dragonbox_install_targets ${dragonbox_install_targets} dragonbox_to_chars) endif() install(TARGETS ${dragonbox_install_targets} EXPORT dragonboxTargets ARCHIVE # DESTINATION "${CMAKE_INSTALL_LIBDIR}" COMPONENT dragonbox_Development INCLUDES # DESTINATION "${dragonbox_include_directory}") set(dragonbox_install_cmakedir "${CMAKE_INSTALL_LIBDIR}/cmake/${dragonbox_directory}") write_basic_package_version_file( dragonboxConfigVersion.cmake VERSION ${PROJECT_VERSION} COMPATIBILITY SameMajorVersion ARCH_INDEPENDENT) install(EXPORT dragonboxTargets NAMESPACE dragonbox:: DESTINATION "${dragonbox_install_cmakedir}") install(FILES "${PROJECT_SOURCE_DIR}/cmake/dragonboxConfig.cmake" "${PROJECT_BINARY_DIR}/dragonboxConfigVersion.cmake" DESTINATION "${dragonbox_install_cmakedir}") if (DRAGONBOX_INSTALL_TO_CHARS) install(FILES ${dragonbox_to_chars_headers} DESTINATION "${dragonbox_include_directory}/dragonbox") else() install(FILES ${dragonbox_headers} DESTINATION "${dragonbox_include_directory}/dragonbox") endif() # ---- Subproject ---- option(DRAGONBOX_ENABLE_SUBPROJECT "Build subproject as well" OFF) if (DRAGONBOX_ENABLE_SUBPROJECT) add_subdirectory("subproject/benchmark") add_subdirectory("subproject/meta") add_subdirectory("subproject/test") endif() # ---- MSVC Specifics ---- if (MSVC) # /permissive- is required (see https://github.com/jk-jeon/dragonbox/pull/74#issuecomment-3247531231) target_compile_options(dragonbox INTERFACE /permissive-) endif()dragonbox-master/.gitignore0000664000175000017500000002145315060737600015001 0ustar renerene# TODO: clean # VS generated CMake settings CMakeSettings.json # CMake build directory build/ # Ignore CLion build folder everywhere **/cmake-build-*/ # Created by https://www.toptal.com/developers/gitignore/api/clion+all,visualstudio # Edit at https://www.toptal.com/developers/gitignore?templates=clion+all,visualstudio ### CLion+all ### # Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider # Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839 # User-specific stuff .idea/**/workspace.xml .idea/**/tasks.xml .idea/**/usage.statistics.xml .idea/**/dictionaries .idea/**/shelf # Generated files .idea/**/contentModel.xml # Sensitive or high-churn files .idea/**/dataSources/ .idea/**/dataSources.ids .idea/**/dataSources.local.xml .idea/**/sqlDataSources.xml .idea/**/dynamic.xml .idea/**/uiDesigner.xml .idea/**/dbnavigator.xml # Gradle .idea/**/gradle.xml .idea/**/libraries # Gradle and Maven with auto-import # When using Gradle or Maven with auto-import, you should exclude module files, # since they will be recreated, and may cause churn. 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Dragonbox is a float-to-string conversion algorithm based on a beautiful algorithm [Schubfach](https://drive.google.com/file/d/1IEeATSVnEE6TkrHlCYNY2GjaraBjOT4f/edit), developed by Raffaello Giulietti in 2017-2018. Dragonbox is further inspired by [Grisu](https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf) and [Grisu-Exact](https://github.com/jk-jeon/Grisu-Exact). # Introduction Dragonbox generates a pair of integers from a floating-point number: the decimal significand and the decimal exponent of the input floating-point number. These integers can then be used for string generation of decimal representation of the input floating-point number, the procedure commonly called ````ftoa```` or ````dtoa````. The algorithm guarantees three things: 1) It has the roundtrip guarantee; that is, a correct parser interprets the generated output string as the original input floating-point number. (See [here](https://github.com/jk-jeon/dragonbox/blob/master/README.md#precise-meaning-of-roundtrip-gurantee) for some explanation on this.) 2) The output is of the shortest length; that is, no other output strings that are interpreted as the input number can contain less number of significand digits than the output of Dragonbox. 3) The output is correctly rounded: the number generated by Dragonbox is the closest to the actual value of the input number among possible outputs of minimum number of digits. # About the Name "Dragonbox" The core idea of Schubfach, which Dragonbox is based on, is a continuous analogue of discrete [pigeonhole principle](https://en.wikipedia.org/wiki/Pigeonhole_principle). The name *Schubfach* is coming from the German name of the pigeonhole principle, *Schubfachprinzip*, meaning "drawer principle". Since another name of the pigeonhole principle is *Dirichlet's box principle*, I decided to call my algorithm "Dragonbox" to honor its origins: Schubfach (box) and Grisu (dragon). # How to Use Although Dragonbox is intended for float-to-string conversion routines, the actual string generation is not officially a part of the algorithm. Dragonbox just outputs two integers (the decimal significand/exponent) that can be consumed by a string generation procedure. The header file [`include/dragonbox/dragonbox.h`](include/dragonbox/dragonbox.h) includes everything needed for this (it is header-only). Nevertheless, a string generation procedure is included in the library. There are two additional files needed for that: [`include/dragonbox/dragonbox_to_chars.h`](include/dragonbox/dragonbox_to_chars.h) and [`source/dragonbox_to_chars.cpp`](source/dragonbox_to_chars.cpp). Since there are only three files, it should be not difficult to set up this library manually if you want, but you can also use it via CMake as explained below. If you are not familiar with CMake, I recommend you to have a look at [this](https://cliutils.gitlab.io/modern-cmake/) wonderful introduction. ## Installing Dragonbox The following will create platform-specific build files on your directory: ``` git clone https://github.com/jk-jeon/dragonbox cd dragonbox mkdir build cd build cmake .. ``` If you only want [`dragonbox.h`](include/dragonbox/dragonbox.h) but not [`dragonbox_to_chars.h`](include/dragonbox/dragonbox_to_chars.h)/[`.cpp`](source/dragonbox_to_chars.cpp), you can do the following to install [`dragonbox.h`](include/dragonbox/dragonbox.h) into your system: ``` cmake .. -DDRAGONBOX_INSTALL_TO_CHARS=OFF cmake --install . ``` If you want the string generation part as well, build the generated files using platform-specific build tools (`make` or Visual Studio for example) and then perform ``` cmake --install . ``` on the `build` directory. ## Including Dragonbox into CMake project The easiest way to include Dragonbox in a CMake project is to do the following: ```cmake include(FetchContent) FetchContent_Declare( dragonbox GIT_REPOSITORY https://github.com/jk-jeon/dragonbox ) FetchContent_MakeAvailable(dragonbox) target_link_libraries(my_target dragonbox::dragonbox) # or dragonbox::dragonbox_to_chars ``` Or, if you already have installed Dragonbox in your system, you can include it with: ```cmake find_package(dragonbox) target_link_libraries(my_target dragonbox::dragonbox) # or dragonbox::dragonbox_to_chars ``` # Language Standard The library requires C++11 or higher. Since C++20, every function provided is `constexpr`. # Usage Examples (Simple string generation from `float/double`) ```cpp #include "dragonbox/dragonbox_to_chars.h" constexpr int buffer_length = 1 + // for '\0' jkj::dragonbox::max_output_string_length; double x = 1.234; // Also works for float char buffer[buffer_length]; // Null-terminate the buffer and return the pointer to the null character // Hence, the length of the string is (end_ptr - buffer) // buffer is now { '1', '.', '2', '3', '4', 'E', '0', '\0', (garbages) } char* end_ptr = jkj::dragonbox::to_chars(x, buffer); // Does not null-terminate the buffer; returns the next-to-end pointer // buffer is now { '1', '.', '2', '3', '4', 'E', '0', (garbages) } // you can wrap the buffer with things like std::string_view end_ptr = jkj::dragonbox::to_chars_n(x, buffer); ``` (Direct use of `jkj::dragonbox::to_decimal`) ```cpp #include "dragonbox/dragonbox.h" double x = 1.234; // Also works for float // Here, x should be a nonzero finite number! // The return value v is a struct with three members: // significand : decimal significand (1234 in this case); // it is of type std::uint64_t for double, std::uint32_t for float // exponent : decimal exponent (-3 in this case); it is of type int // is_negative : as the name suggests; it is of type bool auto v = jkj::dragonbox::to_decimal(x); ``` By default, `jkj::dragonbox::to_decimal` returns a struct with three members (`significand`, `exponent`, and `is_negative`). But the return type and the return value can change if you specify policy parameters. See [below](https://github.com/jk-jeon/dragonbox#policies). ***Important.*** `jkj::dragonbox::to_decimal` is designed to ***work only with finite nonzero*** inputs. The behavior of it when given with infinities/NaN's/`+0`/`-0` is undefined. `jkj::dragonbox::to_chars` and `jkj::dragonbox::to_chars_n` work fine for any inputs. # To people wanting to port the algorithm Those who want to port the algorithm into other languages or re-implement it from scratch are recommended to look at the [simpler implementation](https://github.com/jk-jeon/dragonbox/tree/master/subproject/simple) first rather than the main implementation, since the main implementation is riddled with template indirections obscuring the core logic of the algorithm. The simpler implementation offers less flexibility and somewhat slower performance, but is much more straightforward so it should be easier to understand. # Policies Dragonbox provides several policies that the user can select. Most of the time the default policies will be sufficient, but for some situation this customizability might be useful. There are currently five different kinds of policies that you can specify: sign policy, trailing zero policy, decimal-to-binary (parsing) rounding policy, binary-to-decimal (formatting) rounding policy, and cache policy. Those policies live in the namespace `jkj::dragonbox::policy`. You can provide the policies as additional parameters to `jkj::dragonbox::to_decimal` or `jkj::dragonbox::to_chars` or `jkj::dragonbox::to_chars_n`. Here is an example usage: ```cpp #include "dragonbox/dragonbox.h" auto v = jkj::dragonbox::to_decimal(x, jkj::dragonbox::policy::sign::ignore, jkj::dragonbox::policy::cache::compact); ``` In this example, the `ignore` sign policy and the `compact` cache policy are specified. The return value will not include the member `is_negative`, and `jkj::dragonbox::to_decimal` will internally use the compressed cache for the computation, rather than the full cache. There is no particular order for policy parameters; you can give them in any order. Default policies will be chosen if you do not explicitly specify any. In the above example, for instance, `nearest_to_even` decimal-to-binary rounding mode policy is chosen, which is the default decimal-to-binary rounding mode policy. If you provide two or more policies of the same kind, or if you provide an invalid policy parameter, then the compliation will fail. Policy parameters (e.g., `jkj::dragonbox::policy::sign::ignore` in the above example) are of different types, so different combinations of policies generally result in separate template instantiations, which might cause binary bloat. (However, it is only the combination that matters; giving the same parameter combination in a different order will usually not generate a separate binary.) ## Sign policy Determines whether or not `jkj::dragonbox::to_decimal` will extract and return the sign of the input parameter. - `jkj::dragonbox::policy::sign::ignore`: There is no `is_negative` member in the returned struct and the sign of the input is not returned. A string generation routine might anyway need to deal with the sign by itself, so often this member will not be needed. In that case, omitting `is_negative` member can reduce some overhead. `jkj::dragonbox::to_chars` and `jkj::dragonbox::to_chars_n` use this policy internally. In the implementation of `jkj::dragonbox::to_decimal`, the sign of the input is relevant only for deciding the rounding interval under certain rounding mode policies. Under the default rounding mode policies, the sign is completely ignored. - `jkj::dragonbox::policy::sign::return_sign`: **This is the default policy.** The sign of the input will be written in the `is_negative` member of the returned struct. You cannot specify sign policy to `jkj::dragonbox::to_chars`/`jkj::dragonbox::to_chars_n`. ## Trailing zero policy Determines what `jkj::dragonbox::to_decimal` will do with possible trailing decimal zeros. - `jkj::dragonbox::policy::trailing_zero::ignore`: Do not care about trailing zeros; the output significand may contain trailing zeros. Since trailing zero removal is a relatively heavy operation involving lots of divisions, and a string generation routine will need to perform divisions anyway, it would be possible to get a better overall performance by omitting trailing zero removal from `jkj::dragonbox::to_decimal` and taking care of that in other places. - `jkj::dragonbox::policy::trailing_zero::remove`: **This is the default policy.** Remove all trailing zeros in the output. `jkj::dragonbox::to_chars` and `jkj::dragonbox::to_chars_n` use this policy internally for IEEE-754 binary32 format (aka `float`). - `jkj::dragonbox::policy::trailing_zero::report`: The output significand may contain trailing zeros, but such possibility will be reported in the additional member `may_have_trailing_zeros` of the returned struct. This member will be set to `true` if there might be trailing zeros, and it will be set to `false` if there should be no trailing zero. By how the algorithm works, it is guaranteed that whenever there might be trailing zeros, the maximum number of trailing zeros is 7 for binary32 and 15 for binary64. You cannot specify trailing zero policy to `jkj::dragonbox::to_chars`/`jkj::dragonbox::to_chars_n`. ## Decimal-to-binary rounding policy Dragonbox provides a roundtrip guarantee. This means that if we convert the output of Dragonbox back to IEEE-754 binary floating-point format, the result should be equal to the original input to Dragonbox. However, converting the decimal output of Dragonbox back into binary floating-point number requires a rounding, so in order to ensure the roundtrip guarantee, Dragonbox must assume which kind of rounding will be performed for *the inverse, decimal-to-binary conversion*. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_even`: **This is the default policy.** Use *round-to-nearest, tie-to-even* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_odd`: Use *round-to-nearest, tie-to-odd* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_plus_infinity`: Use *round-to-nearest, tie-toward-plus-infinity* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_minus_infinity`: Use *round-to-nearest, tie-toward-minus-infinity* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_zero`: Use *round-to-nearest, tie-toward-zero* rounding mode. This will produce the fastest code among all *round-to-nearest* rounding modes. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_away_from_zero`: Use *round-to-nearest, tie-away-from-zero* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_even_static_boundary`: Use *round-to-nearest, tie-to-even* rounding mode, but there will be completely independent code paths for even inputs and odd inputs. This will produce a bigger binary, but might run faster than `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_even` for some situation. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_odd_static_boundary`: Use *round-to-nearest, tie-to-odd* rounding mode, but there will be completely independent code paths for even inputs and odd inputs. This will produce a bigger binary, but might run faster than `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_odd` for some situation. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_plus_infinity_static_boundary`: Use *round-to-nearest, tie-toward-plus-infinity* rounding mode, but there will be completely independent code paths for positive inputs and negative inputs. This will produce a bigger binary, but might run faster than `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_plus_infinity` for some situation. - `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_minus_infinity_static_boundary`: Use *round-to-nearest, tie-toward-plus-infinity* rounding mode, but there will be completely independent code paths for positive inputs and negative inputs. This will produce a bigger binary, but might run faster than `jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_toward_minus_infinity` for some situation. - `jkj::dragonbox::policy::decimal_to_binary_rounding::toward_plus_infinity`: Use *round-toward-plus-infinity* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::toward_minus_infinity`: Use *round-toward-minus-infinity* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::toward_zero`: Use *round-toward-zero* rounding mode. - `jkj::dragonbox::policy::decimal_to_binary_rounding::away_from_zero`: Use *away-from-zero* rounding mode. All of these policies can be specified also to `jkj::dragonbox::to_chars`/`jkj::dragonbox::to_chars_n`. ## Binary-to-decimal rounding policy Determines what `jkj::dragonbox::to_decimal` will do when rounding tie occurs while obtaining the decimal significand. This policy will be completely ignored if the specified binary-to-decimal rounding policy is not one of the round-to-nearest policies (because for other policies rounding tie simply doesn't exist). - `jkj::dragonbox::policy::binary_to_decimal_rounding::do_not_care`: Do not care about correct rounding at all and just find any shortest output with the correct roundtrip. It will produce a faster code, but the performance difference will not be big. - `jkj::dragonbox::policy::binary_to_decimal_rounding::to_even`: **This is the default policy.** Choose the even number when rounding tie occurs. - `jkj::dragonbox::policy::binary_to_decimal_rounding::to_odd`: Choose the odd number when rounding tie occurs. - `jkj::dragonbox::policy::binary_to_decimal_rounding::away_from_zero`: Choose the number with the bigger absolute value when rounding tie occurs. - `jkj::dragonbox::policy::binary_to_decimal_rounding::toward_zero`: Choose the number with the smaller absolute value when rounding tie occurs. All of these policies can be specified also to `jkj::dragonbox::to_chars`/`jkj::dragonbox::to_chars_n`. ## Cache policy Choose between the full cache table and the compressed one. Using the compressed cache will result in about 20% slower code, but it can significantly reduce the amount of required static data. It currently has no effect for binary32 (`float`) inputs. For binary64 (`double`) inputs, `jkj::dragonbox::cache_policy::full` will cause `jkj::dragonbox::to_decimal` to use `619*16 = 9904` bytes of static data table, while the corresponding amount for `jkj::dragonbox::cache_policy::compact` is `23*16 + 27*8 = 584` bytes. - `jkj::dragonbox::policy::cache::full`: **This is the default policy.** Use the full table. - `jkj::dragonbox::policy::cache::compact`: Use the compressed table. All of these policies can be specified also to `jkj::dragonbox::to_chars`/`jkj::dragonbox::to_chars_n`. # Performance In my machine (Intel Core i7-7700HQ 2.80GHz, Windows 10), it defeats or is on par with other contemporary algorithms including Grisu-Exact, Ryu, and Schubfach. The following benchmark result (performed on 03/30/2024) is obtained using Milo's dtoa benchmark framework ([https://github.com/miloyip/dtoa-benchmark](https://github.com/miloyip/dtoa-benchmark)). The complete source code for the benchmark below is available [here](https://github.com/jk-jeon/dtoa-benchmark). ![corei7_7700hq@2.80_win64_vc2019_randomdigit_time](other_files/unknown_win64_vc2019_randomdigit_time.png) ![corei7_7700hq@2.80_win64_vc2019_randomdigit_time](other_files/unknown_win64_vc2019_randomdigit_timedigit.png) Note 1: `dragonbox` is the performance of Dragonbox with the full cache table, and `dragonbox_comp` is the performance of Dragonbox with the compact cache table. Note 2: [`fmt`](https://github.com/fmtlib/fmt) internally uses Dragonbox with an implementation almost identical to that in this repository. There is also a benchmark done by myself (also performed on 03/30/2024): (top: benchmark for ````float```` data, bottom: benchmark for ````double```` data; solid lines are the averages, dashed lines are the medians, and the shaded regions show 30%, 50%, and 70% percentiles): (Clang) ![digits_benchmark_binary32](subproject/benchmark/results/digits_benchmark_binary32_clang.png) ![digits_benchmark_binary64](subproject/benchmark/results/digits_benchmark_binary64_clang.png) (MSVC) ![digits_benchmark_binary32](subproject/benchmark/results/digits_benchmark_binary32_msvc.png) ![digits_benchmark_binary64](subproject/benchmark/results/digits_benchmark_binary64_msvc.png) Here is another performance plot with uniformly randomly generated ````float````(top) or ````double````(bottom) data: (Clang) ![uniform_benchmark_binary32](subproject/benchmark/results/uniform_benchmark_binary32_clang.png) ![uniform_benchmark_binary64](subproject/benchmark/results/uniform_benchmark_binary64_clang.png) (MSVC) ![uniform_benchmark_binary32](subproject/benchmark/results/uniform_benchmark_binary32_msvc.png) ![uniform_benchmark_binary64](subproject/benchmark/results/uniform_benchmark_binary64_msvc.png) (Note: the comparison with Schubfach is not completely fair, since the implementation I benchmarked against uses a digit generation procedure with a different set of constraints. More fair comparison is available in [this repository](https://github.com/abolz/Drachennest).) # Comprehensive Explanation of the Algorithm Please see [this](other_files/Dragonbox.pdf) paper. # How to Run Tests, Benchmark, and Others There are four subprojects contained in this repository: 1. [`common`](subproject/common): The subproject that other subprojects depend on. 2. [`benchmark`](subproject/benchmark): Runs benchmark. 3. [`test`](subproject/test): Runs tests. 4. [`meta`](subproject/meta): Generates static data that the main library uses. ## Build each subproject independently All subprojects including tests and benchmark are standalone, which means that you can build and run each of them independently. For example, you can do the following to run tests: ``` git clone https://github.com/jk-jeon/dragonbox cd dragonbox mkdir -p build/subproject/test cd build/subproject/test cmake ../../../subproject/test cmake --build . ctest . ``` (You might need to pass the configuration option to `cmake` and `ctest` if you use multi-configuration generators like Visual Studio.) ## Build all subprojects from the root directory It is also possible to build all subprojects from the root directory by passing the option `-DDRAGONBOX_ENABLE_SUBPROJECT=On` to `cmake`: ``` git clone https://github.com/jk-jeon/dragonbox cd dragonbox mkdir build cd build cmake .. -DDRAGONBOX_ENABLE_SUBPROJECT=On cmake --build . ``` ## Notes on working directory Some executable files require the correct working directory to be set. For example, the executable for [`benchmark`](subproject/benchmark) runs some MATLAB scripts provided in [`subproject/benchmark/matlab`](subproject/benchmark/matlab) directory, which will fail to execute if the working directory is not set to [`subproject/benchmark`](subproject/benchmark). If you use the provided `CMakeLists.txt` files to generate a Visual Studio solution, the debugger's working directory is automatically set to the corresponding source directory. For example, the working directory is set to [`subproject/benchmark`](subproject/benchmark) for the benchmark subproject. However, other generators of cmake are not able to set the debugger's working directory, so in that case you need to manually set the correct working directory when running the executables in order to make them work correctly. # Notes ## Correctness of the algorithm The [paper](other_files/Dragonbox.pdf) provides a mathematical proof of the correctness of the algorithm, with the aid of verification programs in [`test`](test) and [`meta`](meta) directories. In addition to that, I did a fair amount of uniformly random tests against Ryu (which is extremely heavily tested in its own), and I also ran a joint test of Dragonbox with a binary-to-decimal floating-point conversion routine I developed, and confirmed correct roundtrip for all possible IEEE-754 binary32-encoded floating-point numbers (aka `float`) with the round-to-nearest, tie-to-even rounding mode. Therefore, I am pretty confident about the correctness of both of the algorithms. ## Precise meaning of roundtrip guarantee The precise meaning of roundtrip guarantee might be tricky, as it depends on the notion of "correct parsers". For example, given that `significand` and `exponent` are the outputs of Dragonbox with respect to an input floating-point number `x` of, say, type `double`, then things like `x == significand * pow(10.0, exponent)` might or might not be the case, because each of the floating-point operations in the expression `significand * pow(10.0, exponent)` can introduce rounding errors that can accumulate to a bigger error. What a correct parser should do is to precisely compute the floating-point number from the given expression according to the assumed rounding rule, and the result must be "correctly rounded" in the sense that only the minimum possible rounding error is allowed. Implementing a correct parser is indeed a very nontrivial job, so you may need additional libraries (like [Ryu](https://github.com/ulfjack/ryu) or [double-conversion](https://github.com/google/double-conversion)) if you want to check this roundtrip guarantee by yourself. # License All code, except for those belong to third-party libraries (code in [`subproject/3rdparty`](subproject/3rdparty)), is licensed under either of * Apache License Version 2.0 with LLVM Exceptions ([LICENSE-Apache2-LLVM](LICENSE-Apache2-LLVM) or https://llvm.org/foundation/relicensing/LICENSE.txt) or * Boost Software License Version 1.0 ([LICENSE-Boost](LICENSE-Boost) or https://www.boost.org/LICENSE_1_0.txt). dragonbox-master/LICENSE-Apache2-LLVM0000664000175000017500000002774615060737600016042 0ustar renerene Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. 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C0e7OGdE&N`H CbH#ƪ.{C=~qL,s_w P_6i'gܓ~ӸG2/C'C yl{n)em _N&N,ZK4/cg^jӹ\H~W"?x7!MSh$yXHh-L=vOO,VWQy*cWby:5^j3mvPF5!ࡳ5.cdN?rLzۅ^ֶEg?ru@gSKr"Qq`^M߼ 2C[K!|Dx4v(RY$g^CzL8rWk560jÈqNbNVF yF~zOg/ ?a@x7:_?;;!@0~TjubÓ&u#7?S]|e?}~{߼׾\)r?O__oW1WvJ]MǧgF@:eN!>Pzr endstream endobj 524 0 obj << /Type /ObjStm /N 100 /First 886 /Length 2193 /Filter /FlateDecode >> stream xZs_x2#[NZk"O֓(l%RGG_*I>/}naq&3)1Iěa9 FJ3tM.~C1%\x>`1(`'ƀVcd% ' +x- yか|֕`H8C(Px% Τ@\DQ)8c؆}ԓb@7`Cqd'  E1 bL&xT ARń0HQe"T^Nϕ bE`8=fdnSBOB@{Xad#)A,R`I.*`3$b(NAzXGR1%p0ALRd)&@IHWG"R{qx''}Ϯh4,N`%_u=&ѯ'ȠMG5#]}0RY̓E=YXjr6MkX_/1ơ .3VNJ9vxX47Ojιj zfBs=î lN/.߼}Φ-0 ~tgՍ!}K+0_r('.}7Ϸ]pnT\oU/ƣ~2^'צxr: k?w"n)zk/)`(loGjK-qj4^tg3R}&m9[ҜX#9PQ_@,HV+/fLr֡`!RBF&;m5/,h8M[.˶t'Wtaz2/XeoUqtx)`H!KX׳|yRGy 2J)l]i+R>KS[y,~sA!h㖮[9-Gyvc(Qn;> stream x+2T0BC]c]C#\.}\K|@.e~ endstream endobj 572 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (c:/Users/jjk/source/repos/jk-jeon/study_log/Applied\040Mathematics/Dragonbox_old/digits_benchmark_binary64.pdf) 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0 R /GS198 993 0 R /GS199 994 0 R /GS200 995 0 R /GS201 996 0 R /GS202 997 0 R /GS203 998 0 R /GS204 999 0 R /GS205 1000 0 R /GS206 1001 0 R /GS207 1002 0 R /GS208 1003 0 R /GS209 1004 0 R /GS210 1005 0 R /GS211 1006 0 R /GS212 1007 0 R /GS213 1008 0 R /GS214 1009 0 R /GS215 1010 0 R /GS216 1011 0 R /GS217 1012 0 R /GS218 1013 0 R /GS219 1014 0 R /GS220 1015 0 R /GS221 1016 0 R /GS222 1017 0 R /GS223 1018 0 R /GS224 1019 0 R /GS225 1020 0 R /GS226 1021 0 R /GS227 1022 0 R /GS228 1023 0 R /GS229 1024 0 R /GS230 1025 0 R /GS231 1026 0 R /GS232 1027 0 R /GS233 1028 0 R /GS234 1029 0 R /GS235 1030 0 R /GS236 1031 0 R /GS237 1032 0 R /GS238 1033 0 R /GS239 1034 0 R /GS240 1035 0 R /GS241 1036 0 R /GS242 1037 0 R /GS243 1038 0 R /GS244 1039 0 R /GS245 1040 0 R /GS246 1041 0 R /GS247 1042 0 R /GS248 1043 0 R /GS249 1044 0 R /GS250 1045 0 R /GS251 1046 0 R /GS252 1047 0 R /GS253 1048 0 R /GS254 1049 0 R /GS255 1050 0 R /GS256 1051 0 R /GS257 1052 0 R /GS258 1053 0 R /GS259 1054 0 R /GS260 1055 0 R /GS261 1056 0 R /GS262 1057 0 R /GS263 1058 0 R /GS264 1059 0 R /GS265 1060 0 R /GS266 1061 0 R /GS267 1062 0 R /GS268 1063 0 R /GS269 1064 0 R /GS270 1065 0 R /GS271 1066 0 R /GS272 1067 0 R /GS273 1068 0 R /GS274 1069 0 R /GS275 1070 0 R /GS276 1071 0 R /GS277 1072 0 R /GS278 1073 0 R /GS279 1074 0 R /GS280 1075 0 R /GS281 1076 0 R /GS282 1077 0 R /GS283 1078 0 R /GS284 1079 0 R /GS285 1080 0 R /GS286 1081 0 R /GS287 1082 0 R /GS288 1083 0 R /GS289 1084 0 R /GS290 1085 0 R /GS291 1086 0 R /GS292 1087 0 R /GS293 1088 0 R /GS294 1089 0 R /GS295 1090 0 R /GS296 1091 0 R /GS297 1092 0 R /GS298 1093 0 R /GS299 1094 0 R /GS300 1095 0 R /GS301 1096 0 R /GS302 1097 0 R /GS303 1098 0 R /GS304 1099 0 R /GS305 1100 0 R /GS306 1101 0 R /GS307 1102 0 R /GS308 1103 0 R /GS309 1104 0 R /GS310 1105 0 R /GS311 1106 0 R /GS312 1107 0 R >>>> /Length 22489 /Filter /FlateDecode >> stream xKd[n8_q1,P=(2%X o{E5:IE~|/~|Bտ[n)ykow!xn;tqat_kҠ>f~Yӗۿ?|/?2W?4\x>bngc 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1493 0 R /GS214 1494 0 R /GS215 1495 0 R >>>> /Length 19834 /Filter /FlateDecode >> stream x}K%mE-E;2 0<0 Z%Wh0~ 1ϩuP edƃA~|ǧ={}STjT.ӥjOi%˖|DXOi>Z*}o۶>qe?~ OD,ק~OUssZ+GFi'tOKO`ϴe?俏񿧿|n2|ɯ|/mW(aWrKk0?+)1_mCJmr=A07+u 9_Qˑ!!?/ 0Gr&>x1o ?J= 8C_+\ !YZ9ø"9 }1$ǙZYSL Yj_Ҹ)rœ V~i!k] gWX47LJ6H%lߖ7VcM;%XyR~i"}GV^oDߏ7l[6c ;2yi|Gf^md߸4"^b! 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M5stx]!,FdfK3nb`I-n@[nFF_#5Vw%< ?הk| Wnb@q%Y˫,!c3jc'xD?5`PEu´ҝvjpM+ -.@y_H[ZUZFcPc}Ԥǧم98}{i t'uZ/b[ҫ&)~3WPov+ޖ3AАz9Z)mQ dS4wz{9W&WR.ke]w4r͠)ޱ鑎.^^y/!ysII.Rtëb>Qe-Y$TtlSigw/kCj Z-N+/^ln<`kAPmI׼Y:4 A%e=m]\38; .JZNc'n;.!ntX2? 03E]rMH]Hbծ)bܥΦ qɧTg6XʝKA%uWVl!JRõ:oNuZ?\m?̿>z=IF,gL3D{s'n1>`_ g_ǖW=ݡe!?΄i|B'x~o&OɅmoo={,M EM#[w"p`lL]szg_Ӌ?o0IbaA҈pfx:r85?o0^F:tno|5?@ǻR ͬܓ%b endstream endobj 810 0 obj << /Length 812 0 R /Filter /FlateDecode >> stream x]j y9n=@Rȡ4SQ1搷N,tGGY:gU u:엨D ڪ{4Ieq KI7s+4u#K?8K)N^ιi=g\BM9HQ+9[Sכj0[ƃ6d8p܏Ǎ;ˡcnގ(O>_܊ endstream endobj 814 0 obj << /Length1 4032 /Length 816 0 R /Filter /FlateDecode >> stream xW P~%!. 0Gt$!$m0 9$N4nt2d<'qL*ӤI۩uNiSMdtԙ3\r#j߾}Ǿo 6`e[#c.@r;fg-G?MGyk Cqy@U ?/Q`ί #7`?Htfc2>1gpد'o3P4fwH'“wq*H<0?~%O3'94 opbppDa":Za#uPnpʡP qpw[9b5f >Ir'wC$Jj| uZ s#xexF[ 5`amG{d[jЎBhL}NIRcJ KKjY6:c`2Tw+MĒL1Hb_?0F,FB1ƈcRH<-utb9 kۺd5͑`l `kWan voʥOs˥kߥL诿o?UXZj9n]\j1H_cjic_& 1Vg4(-i$ ݱ\e2֜ vw8ɏ"QK6e[-bSjhXr x2K~)FBf0_GW-Zp( vZlVE>7YataE<4"ʉXc<ԧ4tTNf%`Oӻh*`hDml|[57Ǔѥouyoq\cЧW3&hm05F 5F ": N 4HEZY,6 MElmIgp˶{LHW:Y/[S+TdÉU+{K*Nt쨿GzY}Otx&7}2ɾBwA_ХǿYƛ:h׎ 9 ֋X_}ɂ5P[Mh)R%%!pZP]z!;8f3WdHU qdjR>˙YrTm5]R .oW[%dbI/v/ t)H& _MV-nʴ%'*Vr+YWL:5:2yDu%2R カ-r*G %yKJ@?E"soOrަooR~;dƱm{߷[ ZuuVAw !kpܴKSx4]CW <5VK1XŦoosdPBR8IJ8o meµd_KqíU"uUnJK^r$SqA |BГ~ryTjrzޑ;xK[1;%xzN߻fzRΉwwm<|ss ]3L>%7agcg" y,$L^Z3\̪(nj.(W ZO2Xmokrk͓ߍTzJZ%r{kiъ#xv)8tJ*s\J?s†sߛOMŘ> stream xk`r endstream endobj 736 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (./digits_benchmark_binary64.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 818 0 R /BBox [0 0 732 337] /Resources << /Font << /F427 819 0 R/F1 820 0 R>> /ProcSet [ /PDF /ImageB /ImageC /Text ] /ExtGState << /GS1 821 0 R /GS2 822 0 R /GS3 823 0 R /GS4 824 0 R /GS5 825 0 R /GS6 826 0 R /GS7 827 0 R /GS8 828 0 R /GS9 829 0 R /GS10 830 0 R /GS11 831 0 R /GS12 832 0 R /GS13 833 0 R /GS14 834 0 R /GS15 835 0 R /GS16 836 0 R /GS17 837 0 R /GS18 838 0 R /GS19 839 0 R /GS20 840 0 R /GS21 841 0 R /GS22 842 0 R /GS23 843 0 R /GS24 844 0 R /GS25 845 0 R /GS26 846 0 R /GS27 847 0 R /GS28 848 0 R /GS29 849 0 R /GS30 850 0 R /GS31 851 0 R /GS32 852 0 R /GS33 853 0 R /GS34 854 0 R /GS35 855 0 R /GS36 856 0 R >>>> /Length 5824 /Filter /FlateDecode >> stream xڽ][l7~_яW|H@CHvH{Z^= vukd/{Gx/_}|2uqmϧ .[r%]9[KG|d.>/1 Z|,ﶗ!+|ӟnO?(?b(!?+~7=$?|T=P-ozkEH@ˍ)³聃kE'A@I~(~.}۷|)& ;oW;()yRQa_rN B{7oeܻ(rw_r6 B{woE Io_VgkgK]V%BUvy.0PgøSt=:x]leBMzC 9CL?^4TY#]&A&_?t^ޔL7MMǹR;|g} k, MC/bLdN<\ -\&W}º$gJpBu>M>cFą(AȾW?i>e9XeZ)@6%{xDDd1 b4j^Ir%Sׁ4\/ú^0䥖cKT>gZbr ,`rӲe@B>#&(zW y:V$㖌p -V+p%LZP6#jWCH )\ Ph#A! l! pe%D[*,\C$% -YU-^znz@\$= \wȘHMQ U/q6qG,K)J>ULŇi 5azϵzPOB_5fxoZW`xDy{eÁFVz} tN% )U`RF,'eyX-v$eY Ǜ Bg PC "Eg 0 `.]]\ýaO{ӳKҿd{Kdk8yք&>F(hE `\C@cI {le ±c蛁H"l sd "֤IOEqs:^ @d D@CޭpZ3`QQH-渨HO]9YШŔhE8 #ppy;؊X<ثkp#?+՝5 -(H[ ED%jV z8 3tYۢ[ LZpP.1\7|&3r'@%ǖ^,em- Kҵ,h?BI z(S;f(S09#U:XvHbG_XL:5n,̎0$FdG#;b"n;`IYwqyۛ <8Kt\7GjASt\HxJXc0vhoXdŜD"kc^5m&lJ1ұ&ȵ,_a+(`֙_`.x-1fx6+[*΁*aDtG1! X!RQ#'rk] T"H SMS_|mT]TsѬK1Fx5kWcK[YBq9G2D!m-Rv1Xt;;!8 !)I+eœ[}ydp,/bnDsV*v ʯdJc9\ v_6=񺹃;_m-45UfhgdGZ|@C8CDDXDly2~S1CYwCOcL?LB,hܿ|LTc:L1:"]*ͱQ9j0=t(|As2Qhh¡NBr|9 Kh-Å\H \(D%jWj8¿3pYDϷ|}ר"#LoWm&P|v[,UV s̑]k_dWD4kD'$JbU F^dxc;%Ze7"O7H)cjv_+Z{r/v]wQbm!zEqyqa`3E-4pfmB/Qo*S[50"FV9e‡4i6R.^i$_5(f&U`wJE%3l߳a,ҮnI" 'j5ڟjo>+]Qmq%:&YW,[ܕZ!wڜS@Y ^;oq7 Rj2g/uV\[7$R*ފ"3"V VP6F#ʈ,6ʗ_㮫y}VGJ!pC%m?~Ufv 5XSDlXvjO[KCc>ЈA}5" y"/ &3\W`#Pdqe;I.;սMR\|YET\ST[LKDr5SW}cH[hkۈ`;tUKˢB~%Z)@Xt0O 8,;]öfh]ȾmNkpwk9ooI#طᇸUCmD8 ]i`(l";" @ԍTzwu򧰢AYQPo5xb OPXŜzE6kthœNBMzjRY~5sz>sYsyB5nZ(T"hq-H1KTբ%ӊm2o f gI +ch.-.CW],yzvKj&N/Ej ~_^P#.wou2cs~~Dj*DWV*GZ!DzR$ǁF0 |TҠM9vjP S((42+QF{DOt+w~,[~M^,fׁ; Kb ޓ4XUCLzq#K^&/1ڛw*:Rz:qe{}P"qL4p18-֡ ,oǗqOB?լZ\gtšhvSac\%N@@1JOWtϮ.eS8=Q?|O~/ӾxbT"_\F~izm ڴ?O_~W]1g qgsI3T{CJ3GBrKC endstream endobj 857 0 obj << /Length 859 0 R /Filter /FlateDecode >> stream x]j y9n=@Rȡ4SQ1搷N,tGGY:gU u:엨D ڪ{4Ieq KI7s+4u#K?8K)N^ιi=g\BM9HQ+9[Sכj0[ƃ6d8p܏Ǎ;ˡcnގ(O>_܊ endstream endobj 861 0 obj << /Length1 4032 /Length 863 0 R /Filter /FlateDecode >> stream xW P~%!. 0Gt$!$m0 9$N4nt2d<'qL*ӤI۩uNiSMdtԙ3\r#j߾}Ǿo 6`e[#c.@r;fg-G?MGyk Cqy@U ?/Q`ί #7`?Htfc2>1gpد'o3P4fwH'“wq*H<0?~%O3'94 opbppDa":Za#uPnpʡP qpw[9b5f >Ir'wC$Jj| uZ s#xexF[ 5`amG{d[jЎBhL}NIRcJ KKjY6:c`2Tw+MĒL1Hb_?0F,FB1ƈcRH<-utb9 kۺd5͑`l `kWan voʥOs˥kߥL诿o?UXZj9n]\j1H_cjic_& 1Vg4(-i$ ݱ\e2֜ vw8ɏ"QK6e[-bSjhXr x2K~)FBf0_GW-Zp( vZlVE>7YataE<4"ʉXc<ԧ4tTNf%`Oӻh*`hDml|[57Ǔѥouyoq\cЧW3&hm05F 5F ": N 4HEZY,6 MElmIgp˶{LHW:Y/[S+TdÉU+{K*Nt쨿GzY}Otx&7}2ɾBwA_ХǿYƛ:h׎ 9 ֋X_}ɂ5P[Mh)R%%!pZP]z!;8f3WdHU qdjR>˙YrTm5]R .oW[%dbI/v/ t)H& _MV-nʴ%'*Vr+YWL:5:2yDu%2R カ-r*G %yKJ@?E"soOrަooR~;dƱm{߷[ ZuuVAw !kpܴKSx4]CW <5VK1XŦoosdPBR8IJ8o meµd_KqíU"uUnJK^r$SqA |BГ~ryTjrzޑ;xK[1;%xzN߻fzRΉwwm<|ss ]3L>%7agcg" y,$L^Z3\̪(nj.(W ZO2Xmokrk͓ߍTzJZ%r{kiъ#xv)8tJ*s\J?s†sߛOMŘ> stream xk`r endstream endobj 768 0 obj << /Type /ObjStm /N 100 /First 882 /Length 1346 /Filter /FlateDecode >> stream xX[OG~_1oUHc$Pk.)~gibUZ#9{;=s G,E$gob T];db[5ElJYqZ=D-Z: bk ʧwElltv>Ħ-k6)ߛON.^379p|q[®&6 );גs ^v=$Iv[v4FQUӲax ahă̗ƶ4:jXxt]sNs"U[_10lE"5"Eex4#c UZ6o>OSK}'m귚wlGǴ8ΚilK?b1t\0NFQwnEW7eǾ@vNQgisշti ϟ,k1ga0ILcr'XHjut$w,,ODe"4崻%˗G,Oݏg!9s燝YmފlECv(?o X P@(?ݢѕqPjy.dH7tݑJW-/G].T^\|<=K0sOY endstream endobj 868 0 obj << /Length 2018 /Filter /FlateDecode >> stream xY[o7~G /öi  61P`>XP"+}('!]fΕr׆(fƷ_YU84md'BzS]vZ0 K\ljov_U65-x_Bb8&4+?(ct{hcLy؄v\߅)`(  /-li)]7j54,Qo_ΘQ F Pi d-`pxM(yq[WAw״}gêjQ̺*Z%-QK$+ gηLDsL_ 6[gA8JgVE x02u,W !N,X.5Z$r:q!@)f&v..FUX{W.9]|X2p~s loٻSþBpC=tl\r=Lgh2F. ܻ&sDyTP^zwķ#v. `"f:oɕiʚpnJWtT,f23rYN•T".#\0DG)EqzjW+D8|#A(SE\ŕ29UwLȌN,DJWzhLir0\8EE32peEEܕ<rl+#wH9Q^iI{!XuW ?|#5&xGOR2'U$+@}iՉ!x dە?\PL`΍n!gY/afZu#vG,N‰YlJSRiL;T 2sH%rFa+b$ى_ϊ`&<'յ2gU08P3;q(}h$e!& l06m pjZiA[tϑ@;G'StފIyjޤau,oC0Tm}xXӧocRdDx{$, B},,+aϘ~"x@#%:W1XGw<ǘsyqJr꓎BK/E!S9Q&`[2- |θ"EzП3K g}Bqak01xLBЇ~{5PZ2R@riH =NHa5&n>5U5e!vcڸ=hXG{'-qё`7 T:~,iYV-^UeCᦓH1WQЀ!`~巐6@Dnwi"e~y1|WvU &11 ,Їeqf!ZM| VM[w0Z\\=H)g L6cPuOUIAnCT̻l.a!i7:߄ pKBuq_mm}uИlwe} :Mܘ xۈ"C&v`ZÝazQ]*L}7mlXl|O݉kzd'O&ɑaCTo0:> /ProcSet [ /PDF /ImageB /ImageC /Text ] /ExtGState << /GS1 877 0 R /GS2 878 0 R /GS3 879 0 R /GS4 880 0 R /GS5 881 0 R /GS6 882 0 R /GS7 883 0 R >>>> /Length 319784 /Filter /FlateDecode >> stream xĽKv˒4?bAUY7 1H{f{6F}qӇc]*3232C->~_9HcW4zZG?.??Yu?Fÿ} |׍+? ~Pow۟=fo}sOEWݿJY_%lٸ_}|ZYjU~RZɣޯ}|)?|_͟E/`ǣE$osZQS}>֓}/K^X_w`TZj_ew_,2-o7 I5Y_o^oA@}PɸO:a O'<\K_ǔ/@ϥ&WFF>5$seo?g?7?{V Ls w[A_o* O*/UUV į }l'~&\A"uHY53B͙GQZ׿\ ⋏?+^PE?/ !!"~6O/A_ &ň'!~_½RSub{ǟt_so?2+9f}od 3f}ǿ+#jg} G+x3xE>yoP}NNi!Q#[G@npIϠOQ>|99hn:(k,6"܅p|?ف {܌G1ѭ 7\ԉ{XŊ~c>|z>(3[WtBKcW!J`2VNx;9 =J3j{ujDBb9(Ai y |w+"P6-T{[EG\&5O)~+.̨[sep.^|RO KB͌N(#hx ?dlB:p,[yW T@^;ےppWu4@B|܌3OPd9k wXm}%!6CndBr@ZP-ᗯ 1k>޽sByT0IDFdGt?ON$h~ Vrw0f\{h#+w2Fue{ r`s݄#>Y8FTJF.mdVMd!" }Z<;!h~CpMrcZM"+?;Tw M;%JPˬO MPEfx? `;,%\$Ӯ gZ V(Pg/JxFx 3.Ԋ$ BƧտHxVG<")iejԺ#2:!&IhPc hXq0w-̖F>d-x'I %r=ȐVD ,/"#"}9zgƜgn<\)"rh u7-ޏWۜP& ":ayj,ɳl" `;[wIyf 70KAJ֕<;9}hV َp1Sۺ * YyV\(J si`<)E A} ܢ'sl`\2A!jdFdgY2]/E#稯I+2B_Wqo9dB8w% AN[܊ r  w)|}  7ĦzppvW0SgM8@#DXOYRRuS]* V Z^n(3gJ̸+ڟѮAy3 q-τcP2WoZΖ jHHKT_ p[>m0= ;:f@d{GE s=DE\A6k7xߺAx:z%7S%F_0^;*\nRz~ FeLtxGUIiV|3f< ̕:"[v TG ?^k@p #rAY\tGD=sdEfzP`cޑ{Ukr$^k]K+3bޘ{8zgϱ nbNc?!*\kԊr 8 3u-*vً;;p \PNI% Za VࡎϢ2-65jHͼax^צ6&'Qǚ*)w!. 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K2XE?iڝ]]TʵHrS0QOKx&Z=1>bqb0q&d'H1[Q/c0&տp*I(kÆ2$l/#A cΘ :X"^fF~NK rJ_dP !@+MTH`ԩ3NE7kfBqxIA2Gs6AEYe/O3рI?kM'WGff@$%~S s셑(wr͂n"&}7dXz s)d?X~`5`?؈`cMv~+5k6c?؜` -d?diCNa\`͡2 ~DSim@]Yd8|pJ endstream endobj 1166 0 obj << /Length 739 /Filter /FlateDecode >> stream xmUMo0WxvHUdC۪TBb A!Gp?gxYOTm$|՜s_Iss :L;268{zb/}WUjWm?fd}Oi=7gRx=7i'Էf[7̖s ~ts[(:0p l:5m_-tB}W{X8 jw]lj'OC=6}Ӿ|< D0,6;96ݕq4L MUWqS~Ӿ |Ҳ\Khv7RKs|*Z -1 b[d08A  i$C#.CZ\wF|TT<\`Gc)y ,<$g v1a粳[ RHדL1>g~8 䔷5 B{ $.  3qdAEBu7js"ܨF)EYQУ.?yRmTy'oOz>OZOyʄS&}/6>zչ{ZkZs}=?Fey endstream endobj 1167 0 obj << /Length 740 /Filter /FlateDecode >> stream xmUMo0WxvH UdC۪TBb B8߯{ .@=/ۙڽs{K;K.k6/k+[M'ҷ>dyӔKe'$cS`vfSfK}fƁVGGf\bu<19w|擬CTAW $rG]IyMsh$aW7y̟u? sK-`θtJ!'c83?NaO<Dg!;IX 0z)rЃ@kpBQ]^Z7! / U <ɉ#W m/%]cX! gȀhID8QN~ACT/sQQRs 穅ύ>7: F+}n4eE=zG~<6OɈy2kLd>O&y2ϓQ>OfdV>OF<dR'<>O)yJS*}𗏿tx>z{O->tՍ]*3>cC~ endstream endobj 1168 0 obj << /Length 739 /Filter /FlateDecode >> stream xmUMo0WxvHUdC۪TBb A!Gp?gxYOTm$|՜s_Iss :L;268{zb/}WUjWm?fd}Oi=7gRd{nCN8oͰof-%6'&9Pu`L/"tkں(a[ duS $xqa MN{}m}gىx` tw8y*sύ }nFE>7*QύR>7G];~<6OIyktg>O:yұϓN|I/|yIg>O:y҅ϓ.}2 L> stream xmUMo:W5?$R. d9M eCkmCp;;w~>|3E_?O]5߶w]Occ]=~?}Oyh9%?۹׬B|Ɯ>);vw%g43>\ 6 EJ78 1{~`W(-;]%=xe_,b+-O;q\L}UI--=BKE1p[! 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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. dragonbox-master/cmake/0000775000175000017500000000000015060737600014064 5ustar renerenedragonbox-master/cmake/dragonboxConfig.cmake0000664000175000017500000000007415060737600020200 0ustar renereneinclude("${CMAKE_CURRENT_LIST_DIR}/dragonboxTargets.cmake") dragonbox-master/subproject/0000775000175000017500000000000015060737600015164 5ustar renerenedragonbox-master/subproject/benchmark/0000775000175000017500000000000015060737600017116 5ustar renerenedragonbox-master/subproject/benchmark/CMakeLists.txt0000664000175000017500000000364115060737600021662 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(benchmark LANGUAGES CXX) include(FetchContent) if (NOT TARGET dragonbox) FetchContent_Declare(dragonbox SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../..") FetchContent_MakeAvailable(dragonbox) endif() if (NOT TARGET common) FetchContent_Declare(common SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../common") FetchContent_MakeAvailable(common) endif() if (NOT TARGET ryu) FetchContent_Declare(ryu SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../3rdparty/ryu") FetchContent_MakeAvailable(ryu) endif() if (NOT TARGET schubfach) FetchContent_Declare(schubfach SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../3rdparty/schubfach") FetchContent_MakeAvailable(schubfach) endif() if (NOT TARGET grisu_exact) FetchContent_Declare(grisu_exact SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../3rdparty/grisu_exact") FetchContent_MakeAvailable(grisu_exact) endif() set(benchmark_headers include/benchmark.h) set(benchmark_sources source/dragonbox.cpp source/grisu_exact.cpp source/benchmark.cpp source/ryu.cpp source/schubfach.cpp) add_executable(benchmark ${benchmark_headers} ${benchmark_sources}) target_compile_features(benchmark PRIVATE cxx_std_17) target_include_directories(benchmark PRIVATE $) target_link_libraries(benchmark PRIVATE ryu::ryu dragonbox::common dragonbox::dragonbox_to_chars grisu_exact::grisu_exact schubfach::schubfach) # ---- MSVC Specifics ---- if (MSVC) # /permissive- is required (see https://github.com/jk-jeon/dragonbox/pull/74#issuecomment-3247531231) target_compile_options(benchmark PUBLIC /permissive-) # See https://gitlab.kitware.com/cmake/cmake/-/issues/16478 set_target_properties(benchmark PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${CMAKE_CURRENT_LIST_DIR}") endif()dragonbox-master/subproject/benchmark/matlab/0000775000175000017500000000000015060737600020356 5ustar renerenedragonbox-master/subproject/benchmark/matlab/plot_uniform_benchmark.m0000664000175000017500000000627715060737600025277 0ustar renerene% Copyright 2020-2021 Junekey Jeon % % The contents of this file may be used under the terms of % the Apache License v2.0 with LLVM Exceptions. % % (See accompanying file LICENSE-Apache or copy at % https://llvm.org/foundation/relicensing/LICENSE.txt) % % Alternatively, the contents of this file may be used under the terms of % the Boost Software License, Version 1.0. % (See accompanying file LICENSE-Boost or copy at % https://www.boost.org/LICENSE_1_0.txt) % % Unless required by applicable law or agreed to in writing, this software % is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY % KIND, either express or implied. function [] = plot_uniform_benchmark( filename, bits ) output_filename = replace(filename, '.csv', '.pdf'); samples = csvread(filename,0,1,[0 1 0 1]); table = readtable(filename); number_of_algorithms = size(table,1) / samples; names = string(zeros(number_of_algorithms, 1)); for i=1:number_of_algorithms names(i) = string(table{samples * i,1}); end % algorithm index, measured_time measured_times = zeros(number_of_algorithms, samples); for algorithm_idx=1:number_of_algorithms offset = (algorithm_idx-1) * samples; measured_times(algorithm_idx,:) = table{offset+1:offset+samples, 3}; end bit_representations = sscanf(strjoin(string(table{1:samples, 2})', ' '), '%lu'); color_array = {[.8 .06 .1],[.1 .7 .06],[.06 .1 .8],[.6 .2 .8],[.8 .9 0],[.5 .6 .7],[.8 .2 .6]}; % compute statistics av = mean(measured_times'); st = std(measured_times'); me = median(measured_times'); decorated_names = names; for algorithm_idx=1:number_of_algorithms decorated_names(algorithm_idx) = sprintf('%s (avg: %.2f, std: %.2f, med: %.2f)', ... names(algorithm_idx), av(algorithm_idx), st(algorithm_idx), me(algorithm_idx)); end % sample data for plot maximum_plot_size = 10000; if samples > maximum_plot_size plot_size = maximum_plot_size; unit = floor(samples / maximum_plot_size); sampled_br = bit_representations(1:unit:unit*plot_size); sampled_mt = measured_times(:,1:unit:unit*plot_size); else plot_size = samples; sampled_br = bit_representations; sampled_mt = measured_times; end % plot fig = figure('Color','w'); fig_handles = zeros(number_of_algorithms,1); hold on sz = ones(plot_size, 1) * 0.4; for algorithm_idx=1:number_of_algorithms fig_handles(algorithm_idx) = scatter(sampled_br, ... sampled_mt(algorithm_idx,:), sz, '+', ... 'MarkerEdgeColor', color_array{algorithm_idx}, 'LineWidth', 0.1); end legend(fig_handles,decorated_names); xlabel('Bit representation'); ylabel('Time (ns)'); range = prctile(measured_times(:), 99.9); axis([0 uint64(2)^bits 0 range(1)]); if bits==32 xticks([0 uint64(2)^30 uint64(2)^31 3*uint64(2)^30 uint64(2)^32]); xticklabels({'$0$','$2^{30}$','$2^{31}$','$3\times2^{30}$','$2^{32}$'}); elseif bits==64 xticks([0 uint64(2)^62 uint64(2)^63 3*uint64(2)^62 uint64(2)^64]); xticklabels({'$0$','$2^{62}$','$2^{63}$','$3\times2^{62}$','$2^{64}$'}); end h = gca; h.XGrid = 'off'; h.YGrid = 'on'; set(gca,'TickLabelInterpreter', 'latex'); set(gcf, 'Position', [100 100 1200 500]); orient(fig,'landscape'); exportgraphics(fig, output_filename, 'BackgroundColor', 'none'); hold off end dragonbox-master/subproject/benchmark/matlab/plot_benchmarks.m0000664000175000017500000000175015060737600023712 0ustar renerene% Copyright 2020-2021 Junekey Jeon % % The contents of this file may be used under the terms of % the Apache License v2.0 with LLVM Exceptions. % % (See accompanying file LICENSE-Apache or copy at % https://llvm.org/foundation/relicensing/LICENSE.txt) % % Alternatively, the contents of this file may be used under the terms of % the Boost Software License, Version 1.0. % (See accompanying file LICENSE-Boost or copy at % https://www.boost.org/LICENSE_1_0.txt) % % Unless required by applicable law or agreed to in writing, this software % is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY % KIND, either express or implied. addpath('../../3rdparty/shaded_plots'); plot_uniform_benchmark('../results/uniform_benchmark_binary32.csv', 32); plot_uniform_benchmark('../results/uniform_benchmark_binary64.csv', 64); avg32 = plot_digit_benchmark('../results/digits_benchmark_binary32.csv'); avg64 = plot_digit_benchmark('../results/digits_benchmark_binary64.csv');dragonbox-master/subproject/benchmark/matlab/plot_digit_benchmark.m0000664000175000017500000000530215060737600024704 0ustar renerene% Copyright 2020-2021 Junekey Jeon % % The contents of this file may be used under the terms of % the Apache License v2.0 with LLVM Exceptions. % % (See accompanying file LICENSE-Apache or copy at % https://llvm.org/foundation/relicensing/LICENSE.txt) % % Alternatively, the contents of this file may be used under the terms of % the Boost Software License, Version 1.0. % (See accompanying file LICENSE-Boost or copy at % https://www.boost.org/LICENSE_1_0.txt) % % Unless required by applicable law or agreed to in writing, this software % is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY % KIND, either express or implied. function [avg] = plot_digit_benchmark( filename ) output_filename = replace(filename, '.csv', '.pdf'); samples_per_digits = csvread(filename,0,1,[0 1 0 1]); table = readtable(filename); max_digits = table{size(table,1),2}; number_of_algorithms = size(table,1) / samples_per_digits / max_digits; names = string(zeros(number_of_algorithms, 1)); for i=1:number_of_algorithms names(i) = string(table{samples_per_digits * i * max_digits,1}); end % algorithm index, digits, measured_time data = zeros(number_of_algorithms, max_digits, samples_per_digits); for algorithm_idx=1:number_of_algorithms for digits_idx=1:max_digits offset = ((algorithm_idx-1) * max_digits + (digits_idx-1)) * samples_per_digits; data(algorithm_idx, digits_idx,:) = table{offset+1:offset+samples_per_digits, 4}; end end color_array = {[.8 .06 .1],[.1 .7 .06],[.06 .1 .8],[.6 .2 .8],[.8 .9 0],[.5 .6 .7],[.8 .2 .6]}; avg = zeros(number_of_algorithms, max_digits); for algorithm_idx=1:number_of_algorithms for digits_idx=1:max_digits avg(algorithm_idx,digits_idx) = mean(data(algorithm_idx,digits_idx,:)); end end % we will call this function stdshade addpath(genpath('shaded_plots')); % plot fig = figure('Color','w'); fig_handles = zeros(number_of_algorithms,1); hold on for algorithm_idx=1:number_of_algorithms fig_handles(algorithm_idx) = plot(1:max_digits,squeeze(avg(algorithm_idx,:)), ... 'Color', color_array{algorithm_idx}, 'LineWidth', 1.2); end for algorithm_idx=1:number_of_algorithms plot_distribution_prctile(1:max_digits,squeeze(data(algorithm_idx,:,:))', ... 'Color', color_array{algorithm_idx}, 'Alpha', 0.05, ... 'Prctile', [30 50 70], 'LineWidth', 0.2); end legend(fig_handles,names); axis([1 max_digits -Inf Inf]); xlabel('Number of digits'); ylabel('Time (ns)'); h = gca; h.XTick = 1:max_digits; h.XGrid = 'on'; h.YGrid = 'on'; set(gca,'TickLabelInterpreter', 'latex'); set(gcf, 'Position', [100 100 1200 500]); orient(fig,'landscape'); exportgraphics(fig, output_filename, 'BackgroundColor', 'none'); hold off end dragonbox-master/subproject/benchmark/results/0000775000175000017500000000000015060737600020617 5ustar renerenedragonbox-master/subproject/benchmark/results/uniform_benchmark_binary64_clang.png0000664000175000017500000047244515060737600027720 0ustar renerenePNG  IHDRqr pHYs+tIME)z>$tEXtSoftwareMATLAB, The MathWorks, Inc. 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ϓO>~\(>nsK.-J? `|x\s#s1'xy''NK M5 <۴iӥ^ꏮyM7^zխ~cE6t|lSϦM>w}z `|o~sҤIҳp@CwW_}ϛ7/-Lgg>˗I{44 gy۽{\ٿGD㇟ `@z[{{{_wu{_ϗ gA0x&Nxxs[xqrmnz/Z{uŹs-x0PfΜ͏s=s4^{y}O<˗/[l͚5r0hh>Δ!/^tE+W7o޵^{~#[(1޽{[[[[n3<3/44qwE 7pYg]lͯyΝ;/R0hh>20Tz{{|}577ˉ0طoߖ-[z{{Ν;s̼29S pN)8er @29S &-U__inn>3>OqҥKsk׮_mw (:Q 'X)d޽/9 .|Wn|3o֏}c9 'ʸ  V~߼[nzg:Q~ڹs6JPM`@gZz뭷 룏>ꜛ7oޓO>k.___w#L2eʔ)wu'|`7wtt8ZZZZ[[-GyY6nܸsN;䮴bs=S7o.[`37zIN<߶m[SSy79믿iӦW^ySO?cVX(imڴ#8:jdɄe1ҥK_vvv?_9wW8֯_uؿ|_퓟ɓ_~yҤI?ԩSg>~=yO]]]GGo喩S[3_zh6?Os1~ycٻwory晇zꯜy晗\rO~~̙F8e`Hڵ'?ի_}sEΝ;W{KG}ϝ;ן́u::t`tSjCoA>}(-̞={ח_~90&N|#_Ʋnݺ~{z/_~iY/oqvm8e\\}0昘0(>9sŸPpBBk}_Ygo>~_o{N:餁ƶyN;mιs9/w=sՈO?s饗Gf׮]j4fuuu7n:j…Ո 20$_|yOvέ_G&溺~=е^s_|[ne#ι^{;UVutt,]tw]_[nݷoߣ>z-̘1ûB#O<9w 7o?=i$Y򓦥iӦ]qկo?]]]VڼyW^) ؂K0$nvίN;- pYfxgqF5vsW\qŤIn喟gιI&]ve+Vϟ>}?A1jժ?M:uÆ \se]|?Π~d|ժUַZ[[so}[;vq{:uj>O<~#ܛ+W^zU }}}y;#&*}gJһn*䓟ɓׯ_/>D^xgN:7_t{zz}3f8qI'4 5h U) L}ٜq c/ۗr @29S pN)8er @29S pN)8er KIENDB`dragonbox-master/subproject/benchmark/include/0000775000175000017500000000000015060737600020541 5ustar renerenedragonbox-master/subproject/benchmark/include/benchmark.h0000664000175000017500000000220715060737600022645 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_BENCHMARK #define JKJ_BENCHMARK #include struct register_function_for_benchmark { register_function_for_benchmark() = default; register_function_for_benchmark( std::string_view name, void(*func)(float, char*)); register_function_for_benchmark( std::string_view name, void(*func)(double, char*)); register_function_for_benchmark( std::string_view name, void(*func_float)(float, char*), void(*func_double)(double, char*)); }; #endif dragonbox-master/subproject/benchmark/source/0000775000175000017500000000000015060737600020416 5ustar renerenedragonbox-master/subproject/benchmark/source/ryu.cpp0000664000175000017500000000154615060737600021747 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "benchmark.h" #include "ryu/ryu.h" namespace { #if 1 auto dummy = []() -> register_function_for_benchmark { return {"Ryu", f2s_buffered, d2s_buffered}; }(); #endif } dragonbox-master/subproject/benchmark/source/schubfach.cpp0000664000175000017500000000205315060737600023050 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "benchmark.h" #include "schubfach_32.h" #include "schubfach_64.h" namespace { void schubfach_32(float x, char* buf) { *schubfach::Ftoa(buf, x) = '\0'; } void schubfach_64(double x, char* buf) { *schubfach::Dtoa(buf, x) = '\0'; } #if 1 auto dummy = []() -> register_function_for_benchmark { return {"Schubfach", schubfach_32, schubfach_64}; }(); #endif } dragonbox-master/subproject/benchmark/source/grisu_exact.cpp0000664000175000017500000000254015060737600023440 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "benchmark.h" #include "fp_to_chars.h" namespace { void grisu_exact_float_to_chars(float x, char* buffer) { jkj::fp_to_chars(x, buffer, jkj::grisu_exact_rounding_modes::nearest_to_even{}, jkj::grisu_exact_correct_rounding::tie_to_even{}); } void grisu_exact_double_to_chars(double x, char* buffer) { jkj::fp_to_chars(x, buffer, jkj::grisu_exact_rounding_modes::nearest_to_even{}, jkj::grisu_exact_correct_rounding::tie_to_even{}); } #if 1 auto dummy = []() -> register_function_for_benchmark { return {"Grisu-Exact", grisu_exact_float_to_chars, grisu_exact_double_to_chars}; }(); #endif } dragonbox-master/subproject/benchmark/source/benchmark.cpp0000664000175000017500000002335215060737600023061 0ustar renerene// Copyright 2020-2021 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "benchmark.h" #include "random_float.h" #include "dragonbox/dragonbox_to_chars.h" #include #include #include #include #include #include #include #include #include #include template class benchmark_holder { public: static constexpr auto max_digits = std::size_t(std::numeric_limits::max_digits10); static benchmark_holder& get_instance() { static benchmark_holder inst; return inst; } // Generate random samples void prepare_samples(std::size_t number_of_general_samples, std::size_t number_of_digits_samples_per_digits) { samples_[0].resize(number_of_general_samples); for (auto& sample : samples_[0]) sample = uniformly_randomly_generate_general_float(rg_); for (unsigned int digits = 1; digits <= max_digits; ++digits) { samples_[digits].resize(number_of_digits_samples_per_digits); for (auto& sample : samples_[digits]) sample = randomly_generate_float_with_given_digits(digits, rg_); } } // { "name" : [(digits, [(sample, measured_time)])] } // Results for general samples is stored at the position digits=0 using output_type = std::unordered_map>, max_digits + 1>>; void run(std::size_t number_of_iterations, std::string_view float_name, output_type& out) { assert(number_of_iterations >= 1); char buffer[40]; for (auto const& name_func_pair : name_func_pairs_) { auto [result_array_itr, is_inserted] = out.insert_or_assign( name_func_pair.first, std::array>, max_digits + 1>{}); for (unsigned int digits = 0; digits <= max_digits; ++digits) { (*result_array_itr).second[digits].resize(samples_[digits].size()); auto out_itr = (*result_array_itr).second[digits].begin(); if (digits == 0) { std::cout << "Benchmarking " << name_func_pair.first << " with uniformly random " << float_name << "'s...\n"; } else { std::cout << "Benchmarking " << name_func_pair.first << " with (approximately) uniformly random " << float_name << "'s of " << digits << " digits...\n"; } for (Float sample : samples_[digits]) { auto from = std::chrono::high_resolution_clock::now(); for (std::size_t i = 0; i < number_of_iterations; ++i) { name_func_pair.second(sample, buffer); } auto dur = std::chrono::high_resolution_clock::now() - from; *out_itr = { sample, double(std::chrono::duration_cast(dur).count()) / double(number_of_iterations)}; ++out_itr; } } } } output_type run(std::size_t number_of_iterations, std::string_view float_name) { output_type out; run(number_of_iterations, float_name, out); return out; } void register_function(std::string_view name, void (*func)(Float, char*)) { name_func_pairs_.emplace(name, func); } private: benchmark_holder() : rg_(generate_correctly_seeded_mt19937_64()) {} // Digits samples for [1] ~ [max_digits], general samples for [0] std::array, max_digits + 1> samples_; std::mt19937_64 rg_; std::unordered_map name_func_pairs_; }; register_function_for_benchmark::register_function_for_benchmark(std::string_view name, void (*func_float)(float, char*)) { benchmark_holder::get_instance().register_function(name, func_float); }; register_function_for_benchmark::register_function_for_benchmark(std::string_view name, void (*func_double)(double, char*)) { benchmark_holder::get_instance().register_function(name, func_double); }; register_function_for_benchmark::register_function_for_benchmark(std::string_view name, void (*func_float)(float, char*), void (*func_double)(double, char*)) { benchmark_holder::get_instance().register_function(name, func_float); benchmark_holder::get_instance().register_function(name, func_double); }; #define RUN_MATLAB #ifdef RUN_MATLAB #include void run_matlab() { struct launcher { ~launcher() { std::system("matlab -nosplash -r \"cd('matlab'); plot_benchmarks\""); } }; static launcher l; } #endif template static void benchmark_test(std::string_view float_name, std::size_t number_of_uniform_samples, std::size_t number_of_digits_samples_per_digits, std::size_t number_of_iterations) { auto& inst = benchmark_holder::get_instance(); std::cout << "Generating random samples...\n"; inst.prepare_samples(number_of_uniform_samples, number_of_digits_samples_per_digits); auto out = inst.run(number_of_iterations, float_name); std::cout << "Benchmarking done.\n" << "Now writing to files...\n"; // Write uniform benchmark results auto filename = std::string("results/uniform_benchmark_"); filename += float_name; filename += ".csv"; std::ofstream out_file{filename}; out_file << "number_of_samples," << number_of_uniform_samples << std::endl; ; out_file << "name,sample,bit_representation,time\n"; typename jkj::dragonbox::default_float_bit_carrier_conversion_traits::carrier_uint br; for (auto& name_result_pair : out) { for (auto const& data_time_pair : name_result_pair.second[0]) { std::memcpy(&br, &data_time_pair.first, sizeof(Float)); out_file << "\"" << name_result_pair.first << "\"," << "0x" << std::hex << std::setfill('0'); if constexpr (sizeof(Float) == 4) out_file << std::setw(8); else out_file << std::setw(16); out_file << br << std::dec << "," << data_time_pair.second << "\n"; } } out_file.close(); // Write digits benchmark results filename = std::string("results/digits_benchmark_"); filename += float_name; filename += ".csv"; out_file.open(filename); out_file << "number_of_samples_per_digits," << number_of_digits_samples_per_digits << std::endl; out_file << "name,digits,sample,time\n"; for (auto& name_result_pair : out) { for (unsigned int digits = 1; digits <= benchmark_holder::max_digits; ++digits) { for (auto const& data_time_pair : name_result_pair.second[digits]) { std::memcpy(&br, &data_time_pair.first, sizeof(Float)); out_file << "\"" << name_result_pair.first << "\"," << digits << "," << "0x" << std::hex << std::setfill('0'); if constexpr (sizeof(Float) == 4) out_file << std::setw(8); else out_file << std::setw(16); out_file << br << std::dec << "," << data_time_pair.second << "\n"; } } } out_file.close(); } int main() { constexpr bool benchmark_float = true; constexpr std::size_t number_of_uniform_benchmark_samples_float = 1000000; constexpr std::size_t number_of_digits_benchmark_samples_per_digits_float = 100000; constexpr std::size_t number_of_benchmark_iterations_float = 1000; constexpr bool benchmark_double = true; constexpr std::size_t number_of_uniform_benchmark_samples_double = 1000000; constexpr std::size_t number_of_digits_benchmark_samples_per_digits_double = 100000; constexpr std::size_t number_of_benchmark_iterations_double = 1000; if constexpr (benchmark_float) { std::cout << "[Running benchmark for binary32...]\n"; benchmark_test("binary32", number_of_uniform_benchmark_samples_float, number_of_digits_benchmark_samples_per_digits_float, number_of_benchmark_iterations_float); std::cout << "Done.\n\n\n"; } if constexpr (benchmark_double) { std::cout << "[Running benchmark for binary64...]\n"; benchmark_test("binary64", number_of_uniform_benchmark_samples_double, number_of_digits_benchmark_samples_per_digits_double, number_of_benchmark_iterations_double); std::cout << "Done.\n\n\n"; } #ifdef RUN_MATLAB run_matlab(); #endif }dragonbox-master/subproject/benchmark/source/dragonbox.cpp0000664000175000017500000000214115060737600023103 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "benchmark.h" #include "dragonbox/dragonbox_to_chars.h" namespace { void dragonbox_float_to_chars(float x, char* buffer) { jkj::dragonbox::to_chars(x, buffer); } void dragonbox_double_to_chars(double x, char* buffer) { jkj::dragonbox::to_chars(x, buffer); } #if 1 auto dummy = []() -> register_function_for_benchmark { return {"Dragonbox", dragonbox_float_to_chars, dragonbox_double_to_chars}; }(); #endif } dragonbox-master/subproject/simple/0000775000175000017500000000000015060737600016455 5ustar renerenedragonbox-master/subproject/simple/CMakeLists.txt0000664000175000017500000000106215060737600021214 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(dragonbox_simple LANGUAGES CXX) set(dragonbox_simple_headers include/simple_dragonbox.h) if (CMAKE_VERSION VERSION_GREATER_EQUAL "3.19.0") add_library(dragonbox_simple INTERFACE ${dragonbox_simple_headers}) else() add_library(dragonbox_simple INTERFACE) endif() add_library(dragonbox::simple ALIAS dragonbox_simple) target_include_directories(dragonbox_simple INTERFACE $) target_compile_features(dragonbox_simple INTERFACE cxx_std_17)dragonbox-master/subproject/simple/README.md0000664000175000017500000000535015060737600017737 0ustar renerene# Simple Dragonbox This is a simplified implementation of the algorithm, that closely follows the one in `include/dragonbox/dragonbox.h`, but aims to be shorter overall, use less C++ template indirection, and offer less flexibility and performance for the sake of simplicity. Following simplifications over the implementation in `include/dragonbox/dragonbox.h` are made: 1. No support of policies (always uses default policies). 2. `int` is assumed to be of at least 32-bits. 3. `float` and `double` are assumed to be of [IEEE-754 binary32](https://en.wikipedia.org/wiki/Single-precision_floating-point_format) and [IEEE-754 binary64](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) representations, respectively. 4. No use of compiler intrinsics for 128-bit arithmetics (always uses portable fallback implementations). 5. Straightforward digit character generation without any fancy tricks. 6. `if constexpr` is available (C++17). 7. No support of `constexpr`. 8. No `noexcept` annotations. 9. No forced inlining. 10. Modern compiler and standard library are assumed to be available. The points 4 and 5 have critical impact on the performance, so any serious port of Dragonbox that aims for excellent performance must re-address them. # Usage Examples Simple string generation from `float`/`double` (mirrors the interface and behavior of `jkj::dragonbox::to_chars`; see the [primary README](/README.md)): ```cpp #include "simple_dragonbox.h" constexpr int buffer_length = 1 + // for '\0' jkj::simple_dragonbox::max_output_string_length; double x = 1.234; // Also works for float char buffer[buffer_length]; // Null-terminate the buffer and return the pointer to the null character. // Hence, the length of the string is `end - buffer`. // `buffer` is now { '1', '.', '2', '3', '4', 'E', '0', '\0', (garbage) }. char* end = jkj::simple_dragonbox::to_chars(x, buffer); ``` Direct use of `jkj::simple_dragonbox::to_decimal` (mirrors the interface and behavior of `jkj::dragonbox::to_decimal`; see the [primary README](/README.md)): ```cpp #include "simple_dragonbox.h" double x = 1.234; // Also works for float // `x` must be a nonzero finite number. // `v` is a struct with three members: // significand : decimal significand (1234 in this case); // it is of type std::uint64_t for double, std::uint32_t for float // exponent : decimal exponent (-3 in this case); it is of type int // is_negative : as the name suggests; it is of type bool auto v = jkj::simple_dragonbox::to_decimal(x); ``` Like `jkj::dragonbox::to_decimal`, `jkj::simple_dragonbox::to_decimal` only works with finite nonzero inputs. Its behavior when given infinities, NaNs, and ±0 is undefined. `jkj::simple_dragonbox::to_chars` works fine for any inputs. dragonbox-master/subproject/simple/include/0000775000175000017500000000000015060737600020100 5ustar renerenedragonbox-master/subproject/simple/include/simple_dragonbox.h0000664000175000017500000027020415060737600023612 0ustar renerene// Copyright 2024-2025 Junekey Jeon, Toby Bell // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_SIMPLE_DRAGONBOX #define JKJ_HEADER_SIMPLE_DRAGONBOX #include #include #include #include #include namespace jkj { namespace simple_dragonbox { template struct decimal_fp { SignificandType significand; int exponent; bool is_negative; }; namespace detail { using std::int16_t; using std::int32_t; using std::size_t; using std::uint16_t; using std::uint32_t; using std::uint64_t; constexpr uint32_t rotr32(uint32_t n, unsigned r) { r &= 31; return (n >> r) | (n << ((32 - r) & 31)); } constexpr uint64_t rotr64(uint64_t n, unsigned r) { r &= 63; return (n >> r) | (n << ((64 - r) & 63)); } static_assert((int32_t(-1) >> 1) == int32_t(-1) && (int16_t(-1) >> 1) == int16_t(-1), "right-shift for signed integers must be arithmetic"); // For constexpr computation. // Returns -1 when n = 0. constexpr int floor_log2(uint64_t n) { int count = -1; while (n != 0) { ++count; n >>= 1; } return count; } // Followings assume int is of at least 32-bits. static_assert(std::numeric_limits::digits >= 31); constexpr int floor_log10_pow2(int e) { assert(-2620 <= e && e <= 2620); return (e * 315653) >> 20; } constexpr int floor_log2_pow10(int e) { // Formula itself holds on [-4003,4003]; [-1233,1233] is to ensure no overflow. assert(-1233 <= e && e <= 1233); return (e * 1741647) >> 19; } constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) { assert(-2985 <= e && e <= 2936); return (e * 631305 - 261663) >> 21; } constexpr int floor_log5_pow2(int e) { assert(-1831 <= e && e <= 1831); return (e * 225799) >> 19; } constexpr int floor_log5_pow2_minus_log5_3(int e) { assert(-3543 <= e && e <= 2427); return (e * 451597 - 715764) >> 20; } struct uint128 { uint64_t high; uint64_t low; constexpr uint128& operator+=(uint64_t n) { auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); high += (sum < low ? 1 : 0); low = sum; return *this; } }; constexpr uint64_t umul64(uint32_t x, uint32_t y) { return x * uint64_t(y); } // Get 128-bit result of multiplication of two 64-bit unsigned integers. constexpr uint128 umul128(uint64_t x, uint64_t y) { auto const a = uint32_t(x >> 32); auto const b = uint32_t(x); auto const c = uint32_t(y >> 32); auto const d = uint32_t(y); auto const ac = umul64(a, c); auto const bc = umul64(b, c); auto const ad = umul64(a, d); auto const bd = umul64(b, d); auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), (intermediate << 32) + uint32_t(bd)}; } // Get high half of the 128-bit result of multiplication of two 64-bit unsigned // integers. constexpr uint64_t umul128_upper64(uint64_t x, uint64_t y) { auto const a = uint32_t(x >> 32); auto const b = uint32_t(x); auto const c = uint32_t(y >> 32); auto const d = uint32_t(y); auto const ac = umul64(a, c); auto const bc = umul64(b, c); auto const ad = umul64(a, d); auto const bd = umul64(b, d); auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); } // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit // unsigned integer. constexpr uint128 umul192_upper128(uint64_t x, uint128 y) { auto r = umul128(x, y.high); r += umul128_upper64(x, y.low); return r; } // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit // unsigned integer. constexpr uint64_t umul96_upper64(uint32_t x, uint64_t y) { auto const yh = uint32_t(y >> 32); auto const yl = uint32_t(y); auto const xyh = umul64(x, yh); auto const xyl = umul64(x, yl); return xyh + (xyl >> 32); } // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit // unsigned integer. constexpr uint128 umul192_lower128(uint64_t x, uint128 y) { auto const high = x * y.high; auto const high_low = umul128(x, y.low); return {(high + high_low.high) & UINT64_C(0xffffffffffffffff), high_low.low}; } // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit // unsigned integer. constexpr uint64_t umul96_lower64(uint32_t x, uint64_t y) { return (x * y) & UINT64_C(0xffffffffffffffff); } template constexpr Int compute_power(Int a) { static_assert(k >= 0); int e = k; Int p = 1; while (e) { if (e % 2) p *= a; e /= 2; a *= a; } return p; } template struct compute_mul_result { Integer integer_part; bool is_integer; }; struct compute_mul_parity_result { bool parity; bool is_integer; }; template struct float_format; template <> struct float_format { using carrier_uint = uint32_t; static constexpr int total_bits = 32; static constexpr int significand_bits = 23; static constexpr int exponent_bits = 8; static constexpr int min_exponent = -126; static constexpr int max_exponent = 127; static constexpr int exponent_bias = -127; static constexpr int decimal_significand_digits = 9; static constexpr int decimal_exponent_digits = 2; static constexpr int cache_bits = 64; static constexpr int min_k = -31; static constexpr int max_k = 46; static constexpr void remove_trailing_zeros(uint32_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. // The idea of branchless search below is by reddit users r/pigeon768 and // r/TheoreticalDumbass. auto r = rotr32(uint32_t(significand * UINT32_C(184254097)), 4); auto b = r < UINT32_C(429497); auto s = size_t(b); significand = b ? r : significand; r = rotr32(uint32_t(significand * UINT32_C(42949673)), 2); b = r < UINT32_C(42949673); s = s * 2 + b; significand = b ? r : significand; r = rotr32(uint32_t(significand * UINT32_C(1288490189)), 1); b = r < UINT32_C(429496730); s = s * 2 + b; significand = b ? r : significand; exponent += int(s); } static constexpr compute_mul_result compute_mul(uint32_t u, uint64_t cache) { auto const r = umul96_upper64(u, cache); return {uint32_t(r >> 32), uint32_t(r) == 0}; } static constexpr uint32_t compute_delta(uint64_t cache, int beta) { return uint32_t(cache >> (cache_bits - 1 - beta)); } static constexpr compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, int beta) { assert(beta >= 1); assert(beta <= 32); auto const r = umul96_lower64(two_f, cache); return {((r >> (64 - beta)) & 1) != 0, (UINT32_C(0xffffffff) & (r >> (32 - beta))) == 0}; } static constexpr uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { return uint32_t((cache - (cache >> (significand_bits + 2))) >> (cache_bits - significand_bits - 1 - beta)); } static constexpr uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { return uint32_t((cache + (cache >> (significand_bits + 1))) >> (cache_bits - significand_bits - 1 - beta)); } static constexpr uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { return (uint32_t(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; } template static constexpr uint32_t divide_by_pow10(uint32_t n) { static_assert(N >= 0, ""); // Specialize for 32-bit division by 10. // Without the bound on n_max (which compilers these days never leverage), the // minimum needed amount of shift is larger than 32. Hence, this may generate better // code for 32-bit or smaller architectures. Even for 64-bit architectures, it seems // compilers tend to generate mov + mul instead of a single imul for an unknown // reason if we just write n / 10. if constexpr (N == 1 && n_max <= UINT32_C(1073741828)) { return uint32_t(umul64(n, UINT32_C(429496730)) >> 32); } // Specialize for 32-bit division by 100. // It seems compilers tend to generate mov + mul instead of a single imul for an // unknown reason if we just write n / 100. else if constexpr (N == 2) { return uint32_t(umul64(n, UINT32_C(1374389535)) >> 37); } else { return n / compute_power(uint32_t(10)); } } static constexpr uint64_t cache[78]{ UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; }; template <> struct float_format { using carrier_uint = uint64_t; static constexpr int total_bits = 64; static constexpr int significand_bits = 52; static constexpr int exponent_bits = 11; static constexpr int min_exponent = -1022; static constexpr int max_exponent = 1023; static constexpr int exponent_bias = -1023; static constexpr int decimal_significand_digits = 17; static constexpr int decimal_exponent_digits = 3; static constexpr int cache_bits = 128; static constexpr int min_k = -292; static constexpr int max_k = 326; static constexpr void remove_trailing_zeros(uint64_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. // The idea of branchless search below is by reddit users r/pigeon768 and // r/TheoreticalDumbass. auto r = rotr64(uint64_t(significand * UINT64_C(28999941890838049)), 8); auto b = r < UINT64_C(184467440738); auto s = size_t(b); significand = b ? r : significand; r = rotr64(uint64_t(significand * UINT64_C(182622766329724561)), 4); b = r < UINT64_C(1844674407370956); s = s * 2 + b; significand = b ? r : significand; r = rotr64(uint64_t(significand * UINT64_C(10330176681277348905)), 2); b = r < UINT64_C(184467440737095517); s = s * 2 + b; significand = b ? r : significand; r = rotr64(uint64_t(significand * UINT64_C(14757395258967641293)), 1); b = r < UINT64_C(1844674407370955162); s = s * 2 + b; significand = b ? r : significand; exponent += int(s); } static constexpr compute_mul_result compute_mul(uint64_t u, uint128 cache) { auto const r = umul192_upper128(u, cache); return {r.high, r.low == 0}; } static constexpr uint64_t compute_delta(uint128 cache, int beta) { return cache.high >> (total_bits - 1 - beta); } static constexpr compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, int beta) { assert(beta >= 1); assert(beta < 64); auto const r = umul192_lower128(two_f, cache); return {((r.high >> (64 - beta)) & 1) != 0, (((r.high << beta) & UINT64_C(0xffffffffffffffff)) | (r.low >> (64 - beta))) == 0}; } static constexpr uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { return (cache.high - (cache.high >> (significand_bits + 2))) >> (total_bits - significand_bits - 1 - beta); } static constexpr uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { return (cache.high + (cache.high >> (significand_bits + 1))) >> (total_bits - significand_bits - 1 - beta); } static constexpr uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { return ((cache.high >> (total_bits - significand_bits - 2 - beta)) + 1) / 2; } template static constexpr uint64_t divide_by_pow10(uint64_t n) { static_assert(N >= 0, ""); // Specialize for 64-bit division by 10. // Without the bound on n_max (which compilers these days never leverage), the // minimum needed amount of shift is larger than 64. if constexpr (N == 1 && n_max <= UINT64_C(4611686018427387908)) { return umul128_upper64(n, UINT64_C(1844674407370955162)); } // Specialize for 64-bit division by 1000. // Without the bound on n_max (which compilers these days never leverage), the // smallest magic number for this computation does not fit into 64-bits. else if constexpr (N == 3 && n_max <= UINT64_C(15534100272597517998)) { return umul128_upper64(n, UINT64_C(4722366482869645214)) >> 8; } else { return n / compute_power(uint64_t(10)); } } static constexpr uint128 cache[619] = { {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, {UINT64_C(0xd097ad07a71f26b2), 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UINT64_C(0x9c3b29620e29fc74)}, {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; }; template constexpr int count_factors(UInt n) { static_assert(a > 1); int c = 0; while (n % a == 0) { n /= a; ++c; } return c; } static constexpr uint32_t divide_magic_number[2]{6554, 656}; template static constexpr bool valid_float = std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2 && sizeof(T) == Size; static_assert(valid_float, "simple_dragonbox: float may not be IEEE-754 binary32"); static_assert(valid_float, "simple_dragonbox: double may not be IEEE-754 binary64"); constexpr void reverse(char* begin, char* end) { while (begin < --end) { char tmp = *begin; *begin++ = *end; *end = tmp; } } template struct impl { using format = float_format; using carrier_uint = typename format::carrier_uint; static_assert(sizeof(carrier_uint) == sizeof(Float)); static constexpr int min(int x, int y) { return x < y ? x : y; } static constexpr int max(int x, int y) { return x > y ? x : y; } static constexpr int min_exponent = format::min_exponent; static constexpr int max_exponent = format::max_exponent; static constexpr int significand_bits = format::significand_bits; static constexpr int carrier_bits = 8 * sizeof(carrier_uint); static constexpr int kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1; static constexpr int min_k = min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), -floor_log10_pow2(max_exponent - significand_bits) + kappa); // We do invoke shorter_interval_case for exponent == min_exponent case; // so we should not add 1 here. static constexpr int max_k = max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), -floor_log10_pow2(min_exponent - significand_bits) + kappa); static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2; static constexpr int case_shorter_interval_left_endpoint_upper_threshold = 2 + floor_log2( compute_power< count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) / 3); static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0; static constexpr int case_shorter_interval_right_endpoint_upper_threshold = 2 + floor_log2( compute_power< count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) / 3); static constexpr int shorter_interval_tie_lower_threshold = -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits; static constexpr int shorter_interval_tie_upper_threshold = -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits; static_assert(kappa >= 1); static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); static_assert(min_k >= format::min_k && max_k <= format::max_k); template static constexpr bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { // Make sure the computation for max_n does not overflow. static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); assert(n <= compute_power(carrier_uint(10))); constexpr auto magic_number = divide_magic_number[N - 1]; auto const prod = uint32_t(n * magic_number); constexpr auto mask = uint32_t((uint32_t(1) << 16) - 1); bool const result = ((prod & mask) < magic_number); n = carrier_uint(prod >> 16); return result; } // Compute floor(n / 10^N) for small n and N. // Precondition: n <= 10^(N+1) template static constexpr carrier_uint small_division_by_pow10(carrier_uint n) { // Make sure the computation for max_n does not overflow. static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); assert(n <= compute_power(carrier_uint(10))); return carrier_uint((n * divide_magic_number[N - 1]) >> 16); } struct binary_fp { carrier_uint significand; int exponent; bool is_negative; }; static binary_fp decompose_float(Float x) { carrier_uint bits; static_assert(sizeof(x) == sizeof(bits)); std::memcpy(&bits, &x, sizeof(x)); return {// significand carrier_uint(bits & ((carrier_uint(1) << format::significand_bits) - 1)), // exponent int(bits >> format::significand_bits & ((1u << format::exponent_bits) - 1)), // is_negative bool(bits >> (format::significand_bits + format::exponent_bits))}; } static constexpr bool is_finite(int binary_exponent) { return binary_exponent != (1u << format::exponent_bits) - 1; } // The main algorithm assumes the input is a normal/subnormal finite number. static constexpr decimal_fp to_decimal(carrier_uint binary_significand, int binary_exponent, bool is_negative) { bool is_even = binary_significand % 2 == 0; carrier_uint two_fc = binary_significand * 2; // Is the input a normal number? if (binary_exponent != 0) { binary_exponent += format::exponent_bias - format::significand_bits; // Shorter interval case; proceed like Schubfach. // One might think this condition is wrong, since when exponent_bits == // 1 and two_fc == 0, the interval is actually regular. However, it // turns out that this seemingly wrong condition is actually fine, // because the end result is anyway the same. // // [binary32] // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 // fc * 2^e = 1.175'494'35... * 10^-38 // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 // // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. // 1.175'494'3 * 10^-38 is also a correct shortest representation that // will be rejected if we assume shorter interval, but 1.175'494'4 * // 10^-38 is closer to the true value so it doesn't matter. // // [binary64] // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 // // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * // 10^-308. This is indeed of the shortest length, and it is the unique // one closest to the true value among valid representations of the same // length. // Shorter interval case. if (two_fc == 0) { // Compute k and beta. int const minus_k = floor_log10_pow2_minus_log10_4_over_3(binary_exponent); int const beta = binary_exponent + floor_log2_pow10(-minus_k); // Compute xi and zi. auto const cache = format::cache[-minus_k - format::min_k]; auto xi = format::compute_left_endpoint_for_shorter_interval_case(cache, beta); auto zi = format::compute_right_endpoint_for_shorter_interval_case(cache, beta); // If the left endpoint is not an integer, increase it. // (Both endpoints are always included since the significand is even.) if (!is_left_endpoint_integer_shorter_interval(binary_exponent)) { ++xi; } // Try bigger divisor. // zi is at most floor((f_c + 1/2) * 2^e * 10^k0). // Substituting f_c = 2^p and k0 = -floor(log10(3 * 2^(e-2))), we get // zi <= floor((2^(p+1) + 1) * 20/3) <= ceil((2^(p+1) + 1)/3) * 20. // This computation does not overflow for any of the formats I care about. carrier_uint decimal_significand = format::template divide_by_pow10< 1, (((carrier_uint(2) << significand_bits) + 1) / 3 + 1) * 20>(zi); // If succeed, remove trailing zeros if necessary and return. if (decimal_significand * 10 >= xi) { int decimal_exponent = minus_k + 1; format::remove_trailing_zeros(decimal_significand, decimal_exponent); return {decimal_significand, decimal_exponent, is_negative}; } // Otherwise, compute the round-up of y. decimal_significand = format::compute_round_up_for_shorter_interval_case(cache, beta); // When tie occurs, choose the even one. if (decimal_significand % 2 != 0 && binary_exponent >= shorter_interval_tie_lower_threshold && binary_exponent <= shorter_interval_tie_upper_threshold) { --decimal_significand; } else if (decimal_significand < xi) { ++decimal_significand; } return {decimal_significand, minus_k, is_negative}; } // Normal interval case. two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); } else { // Is the input a subnormal number? // Normal interval case. binary_exponent = min_exponent - format::significand_bits; } ////////////////////////////////////////////////////////////////////// // Step 1: Schubfach multiplier calculation. ////////////////////////////////////////////////////////////////////// // Compute k and beta. int const minus_k = floor_log10_pow2(binary_exponent) - kappa; auto const cache = format::cache[-minus_k - format::min_k]; int const beta = binary_exponent + floor_log2_pow10(-minus_k); // Compute zi and deltai. // 10^kappa <= deltai < 10^(kappa + 1) auto const deltai = format::compute_delta(cache, beta); // For the case of binary32, the result of integer check is not correct for // 29711844 * 2^-82 // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 // and 29711844 * 2^-81 // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, // and they are the unique counterexamples. However, since 29711844 is even, // this does not cause any problem for the endpoints calculations; it can only // cause a problem when we need to perform integer check for the center. // Fortunately, with these inputs, that branch is never executed, so we are // fine. auto const z_result = format::compute_mul(carrier_uint((two_fc | 1) << beta), cache); ////////////////////////////////////////////////////////////////////// // Step 2: Try larger divisor; remove trailing zeros if necessary. ////////////////////////////////////////////////////////////////////// constexpr auto big_divisor = compute_power(carrier_uint(10)); constexpr auto small_divisor = compute_power(carrier_uint(10)); // Using an upper bound on zi, we might be able to optimize the division // better than the compiler; we are computing zi / big_divisor here. carrier_uint decimal_significand = format::template divide_by_pow10< kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( z_result.integer_part); auto r = carrier_uint(z_result.integer_part - big_divisor * decimal_significand); do { if (r < deltai) { // Exclude the right endpoint if necessary. if ((r | carrier_uint(!z_result.is_integer) | carrier_uint(is_even)) == 0) { --decimal_significand; r = big_divisor; break; } } else if (r > deltai) { break; } else { // r == deltai; compare fractional parts. auto const x_result = format::compute_mul_parity(carrier_uint(two_fc - 1), cache, beta); if (!(x_result.parity | (x_result.is_integer & is_even))) { break; } } int decimal_exponent = minus_k + kappa + 1; format::remove_trailing_zeros(decimal_significand, decimal_exponent); return {decimal_significand, decimal_exponent, is_negative}; } while (false); ////////////////////////////////////////////////////////////////////// // Step 3: Find the significand with the smaller divisor. ////////////////////////////////////////////////////////////////////// decimal_significand *= 10; // delta is equal to 10^(kappa + elog10(2) - floor(elog10(2))), so dist cannot // be larger than r. auto dist = carrier_uint(r - (deltai / 2) + (small_divisor / 2)); bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; // Is dist divisible by 10^kappa? bool const divisible_by_small_divisor = check_divisibility_and_divide_by_pow10(dist); // Add dist / 10^kappa to the significand. decimal_significand += dist; if (divisible_by_small_divisor) { // Check z^(f) >= epsilon^(f). // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). // Since there are only 2 possibilities, we only need to care about the // parity. Also, zi and r should have the same parity since the divisor // is an even number. auto const y_result = format::compute_mul_parity(two_fc, cache, beta); if (y_result.parity != approx_y_parity) { --decimal_significand; } else { // If z^(f) >= epsilon^(f), we might have a tie // when z^(f) == epsilon^(f), or equivalently, when y is an integer. // When tie happens, always choose the even one. if ((decimal_significand % 2) & y_result.is_integer) { --decimal_significand; } } } return {decimal_significand, minus_k + kappa, is_negative}; } static constexpr bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; } static constexpr bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; } static char* to_chars_n(Float x, char* buffer) { binary_fp const decomposed = decompose_float(x); if (!is_finite(decomposed.exponent)) { if (decomposed.significand == 0) { if (decomposed.is_negative) { *buffer++ = '-'; } std::memcpy(buffer, "Infinity", 8); return buffer + 8; } else { buffer[0] = 'N'; buffer[1] = 'a'; buffer[2] = 'N'; return buffer + 3; } } if (decomposed.is_negative) { *buffer++ = '-'; } if (decomposed.significand == 0 && decomposed.exponent == 0) { buffer[0] = '0'; buffer[1] = 'E'; buffer[2] = '0'; return buffer + 3; } auto [dec_sig, dec_exp, dec_sign] = to_decimal(decomposed.significand, decomposed.exponent, decomposed.is_negative); if (dec_sig < 10) { *buffer++ = char('0' + dec_sig); } else { auto begin = buffer; do { *buffer++ = char('0' + dec_sig % 10); dec_sig /= 10; ++dec_exp; } while (dec_sig >= 10); *buffer++ = '.'; *buffer++ = char('0' + dec_sig); reverse(begin, buffer); } *buffer++ = 'E'; if (dec_exp < 0) { *buffer++ = '-'; dec_exp = -dec_exp; } auto begin = buffer; do { *buffer++ = char('0' + dec_exp % 10); dec_exp /= 10; } while (dec_exp); reverse(begin, buffer); return buffer; } }; } // namespace detail template auto to_decimal(Float x) { auto const decomposed = detail::impl::decompose_float(x); assert(detail::impl::is_finite(decomposed.exponent) && (decomposed.significand != 0 || decomposed.exponent != 0)); return detail::impl::to_decimal(decomposed.significand, decomposed.exponent, decomposed.is_negative); } // Null-terminate and bypass the return value of impl::to_chars_n. template char* to_chars(Float x, char* buffer) { auto ptr = detail::impl::to_chars_n(x, buffer); *ptr = '\0'; return ptr; } // Maximum required buffer size (excluding null-terminator) template static constexpr size_t max_output_string_length = // sign(1) + significand + decimal_point(1) + exp_marker(1) + exp_sign(1) + exp 1 + detail::float_format::decimal_significand_digits + 1 + 1 + 1 + detail::float_format::decimal_exponent_digits; } // namespace simple_dragonbox } // namespace jkj #endif dragonbox-master/subproject/meta/0000775000175000017500000000000015060737600016112 5ustar renerenedragonbox-master/subproject/meta/CMakeLists.txt0000664000175000017500000000261615060737600020657 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(dragonbox_meta LANGUAGES CXX) include(FetchContent) if (NOT TARGET dragonbox) FetchContent_Declare(dragonbox SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../..") FetchContent_MakeAvailable(dragonbox) endif() if (NOT TARGET common) FetchContent_Declare(common SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../common") FetchContent_MakeAvailable(common) endif() if (NOT TARGET ryu) FetchContent_Declare(ryu SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../3rdparty/ryu") FetchContent_MakeAvailable(ryu) endif() function(meta_exe NAME) add_executable(${NAME} source/${NAME}.cpp) target_compile_features(${NAME} PRIVATE cxx_std_17) target_link_libraries(${NAME} PRIVATE ${ARGN}) # ---- MSVC Specifics ---- if (MSVC) # /permissive- is required (see https://github.com/jk-jeon/dragonbox/pull/74#issuecomment-3247531231) target_compile_options(${NAME} PUBLIC /permissive-) # See https://gitlab.kitware.com/cmake/cmake/-/issues/16478 set_target_properties(${NAME} PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${CMAKE_CURRENT_LIST_DIR}") endif() endfunction() meta_exe(generate_cache dragonbox::common) meta_exe(live_test dragonbox::common dragonbox::dragonbox_to_chars ryu::ryu) meta_exe(perf_test dragonbox::common dragonbox::dragonbox_to_chars) meta_exe(sandbox dragonbox::common dragonbox::dragonbox_to_chars)dragonbox-master/subproject/meta/results/0000775000175000017500000000000015060737600017613 5ustar renerenedragonbox-master/subproject/meta/results/binary64_generated_cache.txt0000664000175000017500000011443315060737600025161 0ustar renerenestatic constexpr int min_k = -292; static constexpr int max_k = 326; static constexpr detail::array cache JKJ_STATIC_DATA_SECTION = { { {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, {UINT64_C(0x9436c0760c86e30b), 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UINT64_C(0x3d6a751f3b936244)}, {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)} } };dragonbox-master/subproject/meta/results/binary32_generated_cache.txt0000664000175000017500000000506615060737600025155 0ustar renerenestatic constexpr int min_k = -31; static constexpr int max_k = 46; static constexpr detail::array cache JKJ_STATIC_DATA_SECTION = { { UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f) } };dragonbox-master/subproject/meta/source/0000775000175000017500000000000015060737600017412 5ustar renerenedragonbox-master/subproject/meta/source/perf_test.cpp0000664000175000017500000000743215060737600022117 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "dragonbox/dragonbox_to_chars.h" #include "random_float.h" #include #include template static void uniform_random_perf_test(std::size_t number_of_tests) { std::cout << "Generating random samples...\n"; auto rg = generate_correctly_seeded_mt19937_64(); std::vector samples(number_of_tests); for (auto& sample : samples) { sample = uniformly_randomly_generate_general_float(rg); } std::cout << "Performing test...\n"; char buffer[41]; auto from = std::chrono::steady_clock::now(); for (auto& sample : samples) { jkj::dragonbox::to_chars(sample, buffer); } auto dur = std::chrono::steady_clock::now() - from; std::cout << "Average time: " << double(std::chrono::duration_cast(dur).count()) / number_of_tests << "ns\n"; } template static void digit_perf_test(unsigned int digits, std::size_t number_of_tests) { std::cout << "Generating random samples...\n"; auto rg = generate_correctly_seeded_mt19937_64(); std::vector samples(number_of_tests); for (auto& sample : samples) { sample = randomly_generate_float_with_given_digits(digits, rg); } std::cout << "Performing test...\n"; char buffer[41]; auto from = std::chrono::steady_clock::now(); for (auto& sample : samples) { jkj::dragonbox::to_chars(sample, buffer); } auto dur = std::chrono::steady_clock::now() - from; std::cout << "Average time: " << double(std::chrono::duration_cast(dur).count()) / number_of_tests << "ns\n"; } int main() { constexpr bool run_uniform_random_float = true; constexpr std::size_t number_of_uniform_random_perf_tests_float = 100000000; constexpr bool run_uniform_random_double = true; constexpr std::size_t number_of_uniform_random_perf_tests_double = 100000000; constexpr bool run_digit_float = false; constexpr unsigned int digits_for_perf_test_float = 6; constexpr std::size_t number_of_digit_perf_tests_float = 40000000; constexpr bool run_digit_double = false; constexpr static unsigned int digits_for_perf_test_double = 17; constexpr static std::size_t number_of_digit_perf_tests_double = 6000000; if (run_uniform_random_float) { std::cout << "[Running the algorithm with uniformly randomly generated float inputs...]\n"; uniform_random_perf_test(number_of_uniform_random_perf_tests_float); std::cout << "Done.\n\n\n"; } if (run_uniform_random_double) { std::cout << "[Running the algorithm with uniformly randomly generated double inputs...]\n"; uniform_random_perf_test(number_of_uniform_random_perf_tests_double); std::cout << "Done.\n\n\n"; } if (run_digit_float) { std::cout << "[Running the algorithm with float inputs of digits = " << digits_for_perf_test_float << "...]\n"; digit_perf_test(digits_for_perf_test_float, number_of_digit_perf_tests_float); std::cout << "Done.\n\n\n"; } if (run_digit_double) { std::cout << "[Running the algorithm with double inputs of digits = " << digits_for_perf_test_double << "...]\n"; digit_perf_test(digits_for_perf_test_double, number_of_digit_perf_tests_double); std::cout << "Done.\n\n\n"; } } dragonbox-master/subproject/meta/source/generate_cache.cpp0000664000175000017500000001150015060737600023030 0ustar renerene// Copyright 2020-2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "big_uint.h" #include "continued_fractions.h" #include "dragonbox/dragonbox.h" #include #include #include #include template auto generate_cache(std::size_t cache_bits) { using impl = jkj::dragonbox::detail::impl; std::vector results; jkj::unsigned_rational target_number; for (int k = impl::min_k; k <= impl::max_k; ++k) { // (2f_c +- 1) * 2^beta * (2^(k - e_k - Q) * 5^k) // e_k = floor(k log2(10)) - Q + 1, so // k - e_k - Q = k - floor(k log2(10)) - 1. int exp_2 = k - jkj::dragonbox::detail::log::floor_log2_pow10(k) - 1; target_number.numerator = 1; target_number.denominator = 1; if (k >= 0) { target_number.numerator = jkj::big_uint::pow(5, k); } else { target_number.denominator = jkj::big_uint::pow(5, -k); } if (exp_2 >= 0) { target_number.numerator *= jkj::big_uint::power_of_2(exp_2); } else { target_number.denominator *= jkj::big_uint::power_of_2(-exp_2); } auto div_res = div(jkj::big_uint::power_of_2(cache_bits) * target_number.numerator, target_number.denominator); auto m = std::move(div_res.quot); if (!div_res.rem.is_zero()) { m += 1; } // Recheck that m is in the correct range. if (m < jkj::big_uint::power_of_2(cache_bits - 1) || m >= jkj::big_uint::power_of_2(cache_bits)) { throw std::logic_error{"Generated cache entry is not in the correct range"}; } results.push_back(std::move(m)); } return results; } #include #include #include int main() { std::cout << "[Generating cache...]\n"; auto write_file = [](std::ofstream& out, std::size_t cache_bits, auto type_tag, auto&& ieee_754_type_name_string, auto&& element_printer) { using impl_type = jkj::dragonbox::detail::impl; auto const cache_array = generate_cache(cache_bits); out << "static constexpr int min_k = " << std::dec << impl_type::min_k << ";\n"; out << "static constexpr int max_k = " << std::dec << impl_type::max_k << ";\n"; out << "static constexpr detail::array cache JKJ_STATIC_DATA_SECTION = { {"; for (int k = impl_type::min_k; k < impl_type::max_k; ++k) { auto idx = std::size_t(k - impl_type::min_k); out << "\n\t"; element_printer(out, cache_array[idx]); out << ","; } out << "\n\t"; element_printer(out, cache_array.back()); out << "\n} };"; }; std::ofstream out; try { out.open("results/binary32_generated_cache.txt"); write_file(out, 64, jkj::dragonbox::ieee754_binary_traits{}, "binary32", [](std::ofstream& out, jkj::big_uint const& value) { out << "UINT64_C(0x" << std::hex << std::setw(16) << std::setfill('0') << value[0] << ")"; }); out.close(); out.open("results/binary64_generated_cache.txt"); write_file(out, 128, jkj::dragonbox::ieee754_binary_traits{}, "binary64", [](std::ofstream& out, jkj::big_uint const& value) { out << "{UINT64_C(0x" << std::hex << std::setw(16) << std::setfill('0') << value[1] << "), UINT64_C(0x" << std::hex << std::setw(16) << std::setfill('0') << value[0] << ")}"; }); out.close(); } catch (std::logic_error const& ex) { std::cout << ex.what() << "\n"; return -1; } std::cout << "Done.\n\n\n"; } dragonbox-master/subproject/meta/source/live_test.cpp0000664000175000017500000000523215060737600022116 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "dragonbox/dragonbox_to_chars.h" #include "random_float.h" #include "ryu/ryu.h" #include #include #include void reference_implementation(float x, char* buffer) { f2s_buffered(x, buffer); } void reference_implementation(double x, char* buffer) { d2s_buffered(x, buffer); } template static void live_test(std::streamsize hex_width) { char buffer1[41]; char buffer2[41]; while (true) { Float x; std::string x_str; while (true) { std::getline(std::cin, x_str); try { x = std_string_to_float{}(x_str); } catch (...) { std::cout << "Not a valid input; input again.\n"; continue; } break; } auto xx = jkj::dragonbox::make_float_bits(x); std::cout << " sign: " << (xx.is_negative() ? "-" : "+") << std::endl; std::cout << " exponent bits: " << "0x" << std::hex << std::setfill('0') << xx.extract_exponent_bits() << std::dec << " (value: " << xx.binary_exponent() << ")\n"; std::cout << " significand bits: " << "0x" << std::hex << std::setfill('0'); std::cout << std::setw(hex_width); std::cout << xx.extract_significand_bits() << " (value: 0x" << xx.binary_significand() << ")\n" << std::dec; jkj::dragonbox::to_chars(x, buffer1); reference_implementation(x, buffer2); std::cout << " Dragonbox output: " << buffer1 << "\n"; std::cout << " Reference output: " << buffer2 << "\n\n"; } } int main() { constexpr enum { test_float, test_double } test = test_float; if (test == test_float) { std::cout << "[Start live test for float's]\n"; live_test(8); } else if (test == test_double) { std::cout << "[Start live test for double's]\n"; live_test(16); } } dragonbox-master/subproject/meta/source/sandbox.cpp0000664000175000017500000000134315060737600021555 0ustar renerene// Copyright 2020-2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "dragonbox/dragonbox_to_chars.h" int main() {}dragonbox-master/subproject/3rdparty/0000775000175000017500000000000015060737600016734 5ustar renerenedragonbox-master/subproject/3rdparty/schubfach/0000775000175000017500000000000015060737600020662 5ustar renerenedragonbox-master/subproject/3rdparty/schubfach/CMakeLists.txt0000664000175000017500000000060615060737600023424 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(schubfach LANGUAGES CXX) add_library(schubfach STATIC schubfach_32.cc schubfach_32.h schubfach_64.cc schubfach_64.h) add_library(schubfach::schubfach ALIAS schubfach) target_compile_features(schubfach PUBLIC cxx_std_17) target_include_directories(schubfach PUBLIC $)dragonbox-master/subproject/3rdparty/schubfach/schubfach_64.cc0000664000175000017500000016001615060737600023434 0ustar renerene// Copyright 2020 Alexander Bolz // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) #include "schubfach_64.h" //-------------------------------------------------------------------------------------------------- // This file contains an implementation of the Schubfach algorithm as described in // // [1] Raffaello Giulietti, "The Schubfach way to render doubles", // https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN //-------------------------------------------------------------------------------------------------- #include #include #include #include #include #if _MSC_VER #include #endif #ifndef SF_ASSERT #define SF_ASSERT(X) assert(X) #endif //================================================================================================== // //================================================================================================== template static inline Dest ReinterpretBits(Source source) { static_assert(sizeof(Dest) == sizeof(Source), "size mismatch"); Dest dest; std::memcpy(&dest, &source, sizeof(Source)); return dest; } namespace { struct Double { static_assert(std::numeric_limits::is_iec559 && std::numeric_limits::digits == 53 && std::numeric_limits::max_exponent == 1024, "IEEE-754 double-precision implementation required"); using value_type = double; using bits_type = uint64_t; // static constexpr int32_t MaxDigits10 = std::numeric_limits::max_digits10; static constexpr int32_t SignificandSize = std::numeric_limits::digits; // = p (includes the hidden bit) static constexpr int32_t ExponentBias = std::numeric_limits::max_exponent - 1 + (SignificandSize - 1); // static constexpr int32_t MaxExponent = std::numeric_limits::max_exponent - 1 - (SignificandSize - 1); // static constexpr int32_t MinExponent = std::numeric_limits::min_exponent - 1 - (SignificandSize - 1); static constexpr bits_type MaxIeeeExponent = bits_type{2 * std::numeric_limits::max_exponent - 1}; static constexpr bits_type HiddenBit = bits_type{1} << (SignificandSize - 1); // = 2^(p-1) static constexpr bits_type SignificandMask = HiddenBit - 1; // = 2^(p-1) - 1 static constexpr bits_type ExponentMask = MaxIeeeExponent << (SignificandSize - 1); static constexpr bits_type SignMask = ~(~bits_type{0} >> 1); bits_type bits; explicit Double(bits_type bits_) : bits(bits_) {} explicit Double(value_type value) : bits(ReinterpretBits(value)) {} bits_type PhysicalSignificand() const { return bits & SignificandMask; } bits_type PhysicalExponent() const { return (bits & ExponentMask) >> (SignificandSize - 1); } bool IsFinite() const { return (bits & ExponentMask) != ExponentMask; } bool IsInf() const { return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) == 0; } bool IsNaN() const { return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) != 0; } bool IsZero() const { return (bits & ~SignMask) == 0; } bool SignBit() const { return (bits & SignMask) != 0; } }; } // namespace //================================================================================================== // //================================================================================================== // Returns floor(x / 2^n). // // Technically, right-shift of negative integers is implementation defined... // Should easily be optimized into SAR (or equivalent) instruction. static inline int32_t FloorDivPow2(int32_t x, int32_t n) { #if 0 return x < 0 ? ~(~x >> n) : (x >> n); #else return x >> n; #endif } // Returns floor(log_10(2^e)) // static inline int32_t FloorLog10Pow2(int32_t e) // { // SF_ASSERT(e >= -1500); // SF_ASSERT(e <= 1500); // return FloorDivPow2(e * 1262611, 22); // } // Returns floor(log_10(3/4 2^e)) // static inline int32_t FloorLog10ThreeQuartersPow2(int32_t e) // { // SF_ASSERT(e >= -1500); // SF_ASSERT(e <= 1500); // return FloorDivPow2(e * 1262611 - 524031, 22); // } // Returns floor(log_2(10^e)) static inline int32_t FloorLog2Pow10(int32_t e) { SF_ASSERT(e >= -1233); SF_ASSERT(e <= 1233); return FloorDivPow2(e * 1741647, 19); } //================================================================================================== // //================================================================================================== namespace { struct uint64x2 { uint64_t hi; uint64_t lo; }; } static inline uint64x2 ComputePow10_Double(int32_t k) { // There are unique beta and r such that 10^k = beta 2^r and // 2^127 <= beta < 2^128, namely r = floor(log_2 10^k) - 127 and // beta = 2^-r 10^k. // Let g = ceil(beta), so (g-1) 2^r < 10^k <= g 2^r, with the latter // value being a pretty good overestimate for 10^k. // NB: Since for all the required exponents k, we have g < 2^128, // all constants can be stored in 128-bit integers. static constexpr int32_t kMin = -292; static constexpr int32_t kMax = 324; static constexpr uint64x2 g[kMax - kMin + 1] = { {0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7B}, // -292 {0x9FAACF3DF73609B1, 0x77B191618C54E9AD}, // -291 {0xC795830D75038C1D, 0xD59DF5B9EF6A2418}, // -290 {0xF97AE3D0D2446F25, 0x4B0573286B44AD1E}, // -289 {0x9BECCE62836AC577, 0x4EE367F9430AEC33}, // -288 {0xC2E801FB244576D5, 0x229C41F793CDA740}, // -287 {0xF3A20279ED56D48A, 0x6B43527578C11110}, // -286 {0x9845418C345644D6, 0x830A13896B78AAAA}, // -285 {0xBE5691EF416BD60C, 0x23CC986BC656D554}, // -284 {0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA9}, // -283 {0x94B3A202EB1C3F39, 0x7BF7D71432F3D6AA}, // -282 {0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC54}, // -281 {0xE858AD248F5C22C9, 0xD1B3400F8F9CFF69}, // -280 {0x91376C36D99995BE, 0x23100809B9C21FA2}, // -279 {0xB58547448FFFFB2D, 0xABD40A0C2832A78B}, // -278 {0xE2E69915B3FFF9F9, 0x16C90C8F323F516D}, // -277 {0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E4}, // -276 {0xB1442798F49FFB4A, 0x99CD11CFDF41779D}, // -275 {0xDD95317F31C7FA1D, 0x40405643D711D584}, // -274 {0x8A7D3EEF7F1CFC52, 0x482835EA666B2573}, // -273 {0xAD1C8EAB5EE43B66, 0xDA3243650005EED0}, // -272 {0xD863B256369D4A40, 0x90BED43E40076A83}, // -271 {0x873E4F75E2224E68, 0x5A7744A6E804A292}, // -270 {0xA90DE3535AAAE202, 0x711515D0A205CB37}, // -269 {0xD3515C2831559A83, 0x0D5A5B44CA873E04}, // -268 {0x8412D9991ED58091, 0xE858790AFE9486C3}, // -267 {0xA5178FFF668AE0B6, 0x626E974DBE39A873}, // -266 {0xCE5D73FF402D98E3, 0xFB0A3D212DC81290}, // -265 {0x80FA687F881C7F8E, 0x7CE66634BC9D0B9A}, // -264 {0xA139029F6A239F72, 0x1C1FFFC1EBC44E81}, // -263 {0xC987434744AC874E, 0xA327FFB266B56221}, // -262 {0xFBE9141915D7A922, 0x4BF1FF9F0062BAA9}, // -261 {0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4AA}, // -260 {0xC4CE17B399107C22, 0xCB550FB4384D21D4}, // -259 {0xF6019DA07F549B2B, 0x7E2A53A146606A49}, // -258 {0x99C102844F94E0FB, 0x2EDA7444CBFC426E}, // -257 {0xC0314325637A1939, 0xFA911155FEFB5309}, // -256 {0xF03D93EEBC589F88, 0x793555AB7EBA27CB}, // -255 {0x96267C7535B763B5, 0x4BC1558B2F3458DF}, // -254 {0xBBB01B9283253CA2, 0x9EB1AAEDFB016F17}, // -253 {0xEA9C227723EE8BCB, 0x465E15A979C1CADD}, // -252 {0x92A1958A7675175F, 0x0BFACD89EC191ECA}, // -251 {0xB749FAED14125D36, 0xCEF980EC671F667C}, // -250 {0xE51C79A85916F484, 0x82B7E12780E7401B}, // -249 {0x8F31CC0937AE58D2, 0xD1B2ECB8B0908811}, // -248 {0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA16}, // -247 {0xDFBDCECE67006AC9, 0x67A791E093E1D49B}, // -246 {0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E1}, // -245 {0xAECC49914078536D, 0x58FAE9F773886E19}, // -244 {0xDA7F5BF590966848, 0xAF39A475506A899F}, // -243 {0x888F99797A5E012D, 0x6D8406C952429604}, // -242 {0xAAB37FD7D8F58178, 0xC8E5087BA6D33B84}, // -241 {0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A65}, // -240 {0x855C3BE0A17FCD26, 0x5CF2EEA09A550680}, // -239 {0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481F}, // -238 {0xD0601D8EFC57B08B, 0xF13B94DAF124DA27}, // -237 {0x823C12795DB6CE57, 0x76C53D08D6B70859}, // -236 {0xA2CB1717B52481ED, 0x54768C4B0C64CA6F}, // -235 {0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD0A}, // -234 {0xFE5D54150B090B02, 0xD3F93B35435D7C4D}, // -233 {0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DB0}, // -232 {0xC6B8E9B0709F109A, 0x359AB6419CA1091C}, // -231 {0xF867241C8CC6D4C0, 0xC30163D203C94B63}, // -230 {0x9B407691D7FC44F8, 0x79E0DE63425DCF1E}, // -229 {0xC21094364DFB5636, 0x985915FC12F542E5}, // -228 {0xF294B943E17A2BC4, 0x3E6F5B7B17B2939E}, // -227 {0x979CF3CA6CEC5B5A, 0xA705992CEECF9C43}, // -226 {0xBD8430BD08277231, 0x50C6FF782A838354}, // -225 {0xECE53CEC4A314EBD, 0xA4F8BF5635246429}, // -224 {0x940F4613AE5ED136, 0x871B7795E136BE9A}, // -223 {0xB913179899F68584, 0x28E2557B59846E40}, // -222 {0xE757DD7EC07426E5, 0x331AEADA2FE589D0}, // -221 {0x9096EA6F3848984F, 0x3FF0D2C85DEF7622}, // -220 {0xB4BCA50B065ABE63, 0x0FED077A756B53AA}, // -219 {0xE1EBCE4DC7F16DFB, 0xD3E8495912C62895}, // -218 {0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95D}, // -217 {0xB080392CC4349DEC, 0xBD8D794D96AACFB4}, // -216 {0xDCA04777F541C567, 0xECF0D7A0FC5583A1}, // -215 {0x89E42CAAF9491B60, 0xF41686C49DB57245}, // -214 {0xAC5D37D5B79B6239, 0x311C2875C522CED6}, // -213 {0xD77485CB25823AC7, 0x7D633293366B828C}, // -212 {0x86A8D39EF77164BC, 0xAE5DFF9C02033198}, // -211 {0xA8530886B54DBDEB, 0xD9F57F830283FDFD}, // -210 {0xD267CAA862A12D66, 0xD072DF63C324FD7C}, // -209 {0x8380DEA93DA4BC60, 0x4247CB9E59F71E6E}, // -208 {0xA46116538D0DEB78, 0x52D9BE85F074E609}, // -207 {0xCD795BE870516656, 0x67902E276C921F8C}, // -206 {0x806BD9714632DFF6, 0x00BA1CD8A3DB53B7}, // -205 {0xA086CFCD97BF97F3, 0x80E8A40ECCD228A5}, // -204 {0xC8A883C0FDAF7DF0, 0x6122CD128006B2CE}, // -203 {0xFAD2A4B13D1B5D6C, 0x796B805720085F82}, // -202 {0x9CC3A6EEC6311A63, 0xCBE3303674053BB1}, // -201 {0xC3F490AA77BD60FC, 0xBEDBFC4411068A9D}, // -200 {0xF4F1B4D515ACB93B, 0xEE92FB5515482D45}, // -199 {0x991711052D8BF3C5, 0x751BDD152D4D1C4B}, // -198 {0xBF5CD54678EEF0B6, 0xD262D45A78A0635E}, // -197 {0xEF340A98172AACE4, 0x86FB897116C87C35}, // -196 {0x9580869F0E7AAC0E, 0xD45D35E6AE3D4DA1}, // -195 {0xBAE0A846D2195712, 0x8974836059CCA10A}, // -194 {0xE998D258869FACD7, 0x2BD1A438703FC94C}, // -193 {0x91FF83775423CC06, 0x7B6306A34627DDD0}, // -192 {0xB67F6455292CBF08, 0x1A3BC84C17B1D543}, // -191 {0xE41F3D6A7377EECA, 0x20CABA5F1D9E4A94}, // -190 {0x8E938662882AF53E, 0x547EB47B7282EE9D}, // -189 {0xB23867FB2A35B28D, 0xE99E619A4F23AA44}, // -188 {0xDEC681F9F4C31F31, 0x6405FA00E2EC94D5}, // -187 {0x8B3C113C38F9F37E, 0xDE83BC408DD3DD05}, // -186 {0xAE0B158B4738705E, 0x9624AB50B148D446}, // -185 {0xD98DDAEE19068C76, 0x3BADD624DD9B0958}, // -184 {0x87F8A8D4CFA417C9, 0xE54CA5D70A80E5D7}, // -183 {0xA9F6D30A038D1DBC, 0x5E9FCF4CCD211F4D}, // -182 {0xD47487CC8470652B, 0x7647C32000696720}, // -181 {0x84C8D4DFD2C63F3B, 0x29ECD9F40041E074}, // -180 {0xA5FB0A17C777CF09, 0xF468107100525891}, // -179 {0xCF79CC9DB955C2CC, 0x7182148D4066EEB5}, // -178 {0x81AC1FE293D599BF, 0xC6F14CD848405531}, // -177 {0xA21727DB38CB002F, 0xB8ADA00E5A506A7D}, // -176 {0xCA9CF1D206FDC03B, 0xA6D90811F0E4851D}, // -175 {0xFD442E4688BD304A, 0x908F4A166D1DA664}, // -174 {0x9E4A9CEC15763E2E, 0x9A598E4E043287FF}, // -173 {0xC5DD44271AD3CDBA, 0x40EFF1E1853F29FE}, // -172 {0xF7549530E188C128, 0xD12BEE59E68EF47D}, // -171 {0x9A94DD3E8CF578B9, 0x82BB74F8301958CF}, // -170 {0xC13A148E3032D6E7, 0xE36A52363C1FAF02}, // -169 {0xF18899B1BC3F8CA1, 0xDC44E6C3CB279AC2}, // -168 {0x96F5600F15A7B7E5, 0x29AB103A5EF8C0BA}, // -167 {0xBCB2B812DB11A5DE, 0x7415D448F6B6F0E8}, // -166 {0xEBDF661791D60F56, 0x111B495B3464AD22}, // -165 {0x936B9FCEBB25C995, 0xCAB10DD900BEEC35}, // -164 {0xB84687C269EF3BFB, 0x3D5D514F40EEA743}, // -163 {0xE65829B3046B0AFA, 0x0CB4A5A3112A5113}, // -162 {0x8FF71A0FE2C2E6DC, 0x47F0E785EABA72AC}, // -161 {0xB3F4E093DB73A093, 0x59ED216765690F57}, // -160 {0xE0F218B8D25088B8, 0x306869C13EC3532D}, // -159 {0x8C974F7383725573, 0x1E414218C73A13FC}, // -158 {0xAFBD2350644EEACF, 0xE5D1929EF90898FB}, // -157 {0xDBAC6C247D62A583, 0xDF45F746B74ABF3A}, // -156 {0x894BC396CE5DA772, 0x6B8BBA8C328EB784}, // -155 {0xAB9EB47C81F5114F, 0x066EA92F3F326565}, // -154 {0xD686619BA27255A2, 0xC80A537B0EFEFEBE}, // -153 {0x8613FD0145877585, 0xBD06742CE95F5F37}, // -152 {0xA798FC4196E952E7, 0x2C48113823B73705}, // -151 {0xD17F3B51FCA3A7A0, 0xF75A15862CA504C6}, // -150 {0x82EF85133DE648C4, 0x9A984D73DBE722FC}, // -149 {0xA3AB66580D5FDAF5, 0xC13E60D0D2E0EBBB}, // -148 {0xCC963FEE10B7D1B3, 0x318DF905079926A9}, // -147 {0xFFBBCFE994E5C61F, 0xFDF17746497F7053}, // -146 {0x9FD561F1FD0F9BD3, 0xFEB6EA8BEDEFA634}, // -145 {0xC7CABA6E7C5382C8, 0xFE64A52EE96B8FC1}, // -144 {0xF9BD690A1B68637B, 0x3DFDCE7AA3C673B1}, // -143 {0x9C1661A651213E2D, 0x06BEA10CA65C084F}, // -142 {0xC31BFA0FE5698DB8, 0x486E494FCFF30A63}, // -141 {0xF3E2F893DEC3F126, 0x5A89DBA3C3EFCCFB}, // -140 {0x986DDB5C6B3A76B7, 0xF89629465A75E01D}, // -139 {0xBE89523386091465, 0xF6BBB397F1135824}, // -138 {0xEE2BA6C0678B597F, 0x746AA07DED582E2D}, // -137 {0x94DB483840B717EF, 0xA8C2A44EB4571CDD}, // -136 {0xBA121A4650E4DDEB, 0x92F34D62616CE414}, // -135 {0xE896A0D7E51E1566, 0x77B020BAF9C81D18}, // -134 {0x915E2486EF32CD60, 0x0ACE1474DC1D122F}, // -133 {0xB5B5ADA8AAFF80B8, 0x0D819992132456BB}, // -132 {0xE3231912D5BF60E6, 0x10E1FFF697ED6C6A}, // -131 {0x8DF5EFABC5979C8F, 0xCA8D3FFA1EF463C2}, // -130 {0xB1736B96B6FD83B3, 0xBD308FF8A6B17CB3}, // -129 {0xDDD0467C64BCE4A0, 0xAC7CB3F6D05DDBDF}, // -128 {0x8AA22C0DBEF60EE4, 0x6BCDF07A423AA96C}, // -127 {0xAD4AB7112EB3929D, 0x86C16C98D2C953C7}, // -126 {0xD89D64D57A607744, 0xE871C7BF077BA8B8}, // -125 {0x87625F056C7C4A8B, 0x11471CD764AD4973}, // -124 {0xA93AF6C6C79B5D2D, 0xD598E40D3DD89BD0}, // -123 {0xD389B47879823479, 0x4AFF1D108D4EC2C4}, // -122 {0x843610CB4BF160CB, 0xCEDF722A585139BB}, // -121 {0xA54394FE1EEDB8FE, 0xC2974EB4EE658829}, // -120 {0xCE947A3DA6A9273E, 0x733D226229FEEA33}, // -119 {0x811CCC668829B887, 0x0806357D5A3F5260}, // -118 {0xA163FF802A3426A8, 0xCA07C2DCB0CF26F8}, // -117 {0xC9BCFF6034C13052, 0xFC89B393DD02F0B6}, // -116 {0xFC2C3F3841F17C67, 0xBBAC2078D443ACE3}, // -115 {0x9D9BA7832936EDC0, 0xD54B944B84AA4C0E}, // -114 {0xC5029163F384A931, 0x0A9E795E65D4DF12}, // -113 {0xF64335BCF065D37D, 0x4D4617B5FF4A16D6}, // -112 {0x99EA0196163FA42E, 0x504BCED1BF8E4E46}, // -111 {0xC06481FB9BCF8D39, 0xE45EC2862F71E1D7}, // -110 {0xF07DA27A82C37088, 0x5D767327BB4E5A4D}, // -109 {0x964E858C91BA2655, 0x3A6A07F8D510F870}, // -108 {0xBBE226EFB628AFEA, 0x890489F70A55368C}, // -107 {0xEADAB0ABA3B2DBE5, 0x2B45AC74CCEA842F}, // -106 {0x92C8AE6B464FC96F, 0x3B0B8BC90012929E}, // -105 {0xB77ADA0617E3BBCB, 0x09CE6EBB40173745}, // -104 {0xE55990879DDCAABD, 0xCC420A6A101D0516}, // -103 {0x8F57FA54C2A9EAB6, 0x9FA946824A12232E}, // -102 {0xB32DF8E9F3546564, 0x47939822DC96ABFA}, // -101 {0xDFF9772470297EBD, 0x59787E2B93BC56F8}, // -100 {0x8BFBEA76C619EF36, 0x57EB4EDB3C55B65B}, // -99 {0xAEFAE51477A06B03, 0xEDE622920B6B23F2}, // -98 {0xDAB99E59958885C4, 0xE95FAB368E45ECEE}, // -97 {0x88B402F7FD75539B, 0x11DBCB0218EBB415}, // -96 {0xAAE103B5FCD2A881, 0xD652BDC29F26A11A}, // -95 {0xD59944A37C0752A2, 0x4BE76D3346F04960}, // -94 {0x857FCAE62D8493A5, 0x6F70A4400C562DDC}, // -93 {0xA6DFBD9FB8E5B88E, 0xCB4CCD500F6BB953}, // -92 {0xD097AD07A71F26B2, 0x7E2000A41346A7A8}, // -91 {0x825ECC24C873782F, 0x8ED400668C0C28C9}, // -90 {0xA2F67F2DFA90563B, 0x728900802F0F32FB}, // -89 {0xCBB41EF979346BCA, 0x4F2B40A03AD2FFBA}, // -88 {0xFEA126B7D78186BC, 0xE2F610C84987BFA9}, // -87 {0x9F24B832E6B0F436, 0x0DD9CA7D2DF4D7CA}, // -86 {0xC6EDE63FA05D3143, 0x91503D1C79720DBC}, // -85 {0xF8A95FCF88747D94, 0x75A44C6397CE912B}, // -84 {0x9B69DBE1B548CE7C, 0xC986AFBE3EE11ABB}, // -83 {0xC24452DA229B021B, 0xFBE85BADCE996169}, // -82 {0xF2D56790AB41C2A2, 0xFAE27299423FB9C4}, // -81 {0x97C560BA6B0919A5, 0xDCCD879FC967D41B}, // -80 {0xBDB6B8E905CB600F, 0x5400E987BBC1C921}, // -79 {0xED246723473E3813, 0x290123E9AAB23B69}, // -78 {0x9436C0760C86E30B, 0xF9A0B6720AAF6522}, // -77 {0xB94470938FA89BCE, 0xF808E40E8D5B3E6A}, // -76 {0xE7958CB87392C2C2, 0xB60B1D1230B20E05}, // -75 {0x90BD77F3483BB9B9, 0xB1C6F22B5E6F48C3}, // -74 {0xB4ECD5F01A4AA828, 0x1E38AEB6360B1AF4}, // -73 {0xE2280B6C20DD5232, 0x25C6DA63C38DE1B1}, // -72 {0x8D590723948A535F, 0x579C487E5A38AD0F}, // -71 {0xB0AF48EC79ACE837, 0x2D835A9DF0C6D852}, // -70 {0xDCDB1B2798182244, 0xF8E431456CF88E66}, // -69 {0x8A08F0F8BF0F156B, 0x1B8E9ECB641B5900}, // -68 {0xAC8B2D36EED2DAC5, 0xE272467E3D222F40}, // -67 {0xD7ADF884AA879177, 0x5B0ED81DCC6ABB10}, // -66 {0x86CCBB52EA94BAEA, 0x98E947129FC2B4EA}, // -65 {0xA87FEA27A539E9A5, 0x3F2398D747B36225}, // -64 {0xD29FE4B18E88640E, 0x8EEC7F0D19A03AAE}, // -63 {0x83A3EEEEF9153E89, 0x1953CF68300424AD}, // -62 {0xA48CEAAAB75A8E2B, 0x5FA8C3423C052DD8}, // -61 {0xCDB02555653131B6, 0x3792F412CB06794E}, // -60 {0x808E17555F3EBF11, 0xE2BBD88BBEE40BD1}, // -59 {0xA0B19D2AB70E6ED6, 0x5B6ACEAEAE9D0EC5}, // -58 {0xC8DE047564D20A8B, 0xF245825A5A445276}, // -57 {0xFB158592BE068D2E, 0xEED6E2F0F0D56713}, // -56 {0x9CED737BB6C4183D, 0x55464DD69685606C}, // -55 {0xC428D05AA4751E4C, 0xAA97E14C3C26B887}, // -54 {0xF53304714D9265DF, 0xD53DD99F4B3066A9}, // -53 {0x993FE2C6D07B7FAB, 0xE546A8038EFE402A}, // -52 {0xBF8FDB78849A5F96, 0xDE98520472BDD034}, // -51 {0xEF73D256A5C0F77C, 0x963E66858F6D4441}, // -50 {0x95A8637627989AAD, 0xDDE7001379A44AA9}, // -49 {0xBB127C53B17EC159, 0x5560C018580D5D53}, // -48 {0xE9D71B689DDE71AF, 0xAAB8F01E6E10B4A7}, // -47 {0x9226712162AB070D, 0xCAB3961304CA70E9}, // -46 {0xB6B00D69BB55C8D1, 0x3D607B97C5FD0D23}, // -45 {0xE45C10C42A2B3B05, 0x8CB89A7DB77C506B}, // -44 {0x8EB98A7A9A5B04E3, 0x77F3608E92ADB243}, // -43 {0xB267ED1940F1C61C, 0x55F038B237591ED4}, // -42 {0xDF01E85F912E37A3, 0x6B6C46DEC52F6689}, // -41 {0x8B61313BBABCE2C6, 0x2323AC4B3B3DA016}, // -40 {0xAE397D8AA96C1B77, 0xABEC975E0A0D081B}, // -39 {0xD9C7DCED53C72255, 0x96E7BD358C904A22}, // -38 {0x881CEA14545C7575, 0x7E50D64177DA2E55}, // -37 {0xAA242499697392D2, 0xDDE50BD1D5D0B9EA}, // -36 {0xD4AD2DBFC3D07787, 0x955E4EC64B44E865}, // -35 {0x84EC3C97DA624AB4, 0xBD5AF13BEF0B113F}, // -34 {0xA6274BBDD0FADD61, 0xECB1AD8AEACDD58F}, // -33 {0xCFB11EAD453994BA, 0x67DE18EDA5814AF3}, // -32 {0x81CEB32C4B43FCF4, 0x80EACF948770CED8}, // -31 {0xA2425FF75E14FC31, 0xA1258379A94D028E}, // -30 {0xCAD2F7F5359A3B3E, 0x096EE45813A04331}, // -29 {0xFD87B5F28300CA0D, 0x8BCA9D6E188853FD}, // -28 {0x9E74D1B791E07E48, 0x775EA264CF55347E}, // -27 {0xC612062576589DDA, 0x95364AFE032A819E}, // -26 {0xF79687AED3EEC551, 0x3A83DDBD83F52205}, // -25 {0x9ABE14CD44753B52, 0xC4926A9672793543}, // -24 {0xC16D9A0095928A27, 0x75B7053C0F178294}, // -23 {0xF1C90080BAF72CB1, 0x5324C68B12DD6339}, // -22 {0x971DA05074DA7BEE, 0xD3F6FC16EBCA5E04}, // -21 {0xBCE5086492111AEA, 0x88F4BB1CA6BCF585}, // -20 {0xEC1E4A7DB69561A5, 0x2B31E9E3D06C32E6}, // -19 {0x9392EE8E921D5D07, 0x3AFF322E62439FD0}, // -18 {0xB877AA3236A4B449, 0x09BEFEB9FAD487C3}, // -17 {0xE69594BEC44DE15B, 0x4C2EBE687989A9B4}, // -16 {0x901D7CF73AB0ACD9, 0x0F9D37014BF60A11}, // -15 {0xB424DC35095CD80F, 0x538484C19EF38C95}, // -14 {0xE12E13424BB40E13, 0x2865A5F206B06FBA}, // -13 {0x8CBCCC096F5088CB, 0xF93F87B7442E45D4}, // -12 {0xAFEBFF0BCB24AAFE, 0xF78F69A51539D749}, // -11 {0xDBE6FECEBDEDD5BE, 0xB573440E5A884D1C}, // -10 {0x89705F4136B4A597, 0x31680A88F8953031}, // -9 {0xABCC77118461CEFC, 0xFDC20D2B36BA7C3E}, // -8 {0xD6BF94D5E57A42BC, 0x3D32907604691B4D}, // -7 {0x8637BD05AF6C69B5, 0xA63F9A49C2C1B110}, // -6 {0xA7C5AC471B478423, 0x0FCF80DC33721D54}, // -5 {0xD1B71758E219652B, 0xD3C36113404EA4A9}, // -4 {0x83126E978D4FDF3B, 0x645A1CAC083126EA}, // -3 {0xA3D70A3D70A3D70A, 0x3D70A3D70A3D70A4}, // -2 {0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCD}, // -1 {0x8000000000000000, 0x0000000000000000}, // 0 {0xA000000000000000, 0x0000000000000000}, // 1 {0xC800000000000000, 0x0000000000000000}, // 2 {0xFA00000000000000, 0x0000000000000000}, // 3 {0x9C40000000000000, 0x0000000000000000}, // 4 {0xC350000000000000, 0x0000000000000000}, // 5 {0xF424000000000000, 0x0000000000000000}, // 6 {0x9896800000000000, 0x0000000000000000}, // 7 {0xBEBC200000000000, 0x0000000000000000}, // 8 {0xEE6B280000000000, 0x0000000000000000}, // 9 {0x9502F90000000000, 0x0000000000000000}, // 10 {0xBA43B74000000000, 0x0000000000000000}, // 11 {0xE8D4A51000000000, 0x0000000000000000}, // 12 {0x9184E72A00000000, 0x0000000000000000}, // 13 {0xB5E620F480000000, 0x0000000000000000}, // 14 {0xE35FA931A0000000, 0x0000000000000000}, // 15 {0x8E1BC9BF04000000, 0x0000000000000000}, // 16 {0xB1A2BC2EC5000000, 0x0000000000000000}, // 17 {0xDE0B6B3A76400000, 0x0000000000000000}, // 18 {0x8AC7230489E80000, 0x0000000000000000}, // 19 {0xAD78EBC5AC620000, 0x0000000000000000}, // 20 {0xD8D726B7177A8000, 0x0000000000000000}, // 21 {0x878678326EAC9000, 0x0000000000000000}, // 22 {0xA968163F0A57B400, 0x0000000000000000}, // 23 {0xD3C21BCECCEDA100, 0x0000000000000000}, // 24 {0x84595161401484A0, 0x0000000000000000}, // 25 {0xA56FA5B99019A5C8, 0x0000000000000000}, // 26 {0xCECB8F27F4200F3A, 0x0000000000000000}, // 27 {0x813F3978F8940984, 0x4000000000000000}, // 28 {0xA18F07D736B90BE5, 0x5000000000000000}, // 29 {0xC9F2C9CD04674EDE, 0xA400000000000000}, // 30 {0xFC6F7C4045812296, 0x4D00000000000000}, // 31 {0x9DC5ADA82B70B59D, 0xF020000000000000}, // 32 {0xC5371912364CE305, 0x6C28000000000000}, // 33 {0xF684DF56C3E01BC6, 0xC732000000000000}, // 34 {0x9A130B963A6C115C, 0x3C7F400000000000}, // 35 {0xC097CE7BC90715B3, 0x4B9F100000000000}, // 36 {0xF0BDC21ABB48DB20, 0x1E86D40000000000}, // 37 {0x96769950B50D88F4, 0x1314448000000000}, // 38 {0xBC143FA4E250EB31, 0x17D955A000000000}, // 39 {0xEB194F8E1AE525FD, 0x5DCFAB0800000000}, // 40 {0x92EFD1B8D0CF37BE, 0x5AA1CAE500000000}, // 41 {0xB7ABC627050305AD, 0xF14A3D9E40000000}, // 42 {0xE596B7B0C643C719, 0x6D9CCD05D0000000}, // 43 {0x8F7E32CE7BEA5C6F, 0xE4820023A2000000}, // 44 {0xB35DBF821AE4F38B, 0xDDA2802C8A800000}, // 45 {0xE0352F62A19E306E, 0xD50B2037AD200000}, // 46 {0x8C213D9DA502DE45, 0x4526F422CC340000}, // 47 {0xAF298D050E4395D6, 0x9670B12B7F410000}, // 48 {0xDAF3F04651D47B4C, 0x3C0CDD765F114000}, // 49 {0x88D8762BF324CD0F, 0xA5880A69FB6AC800}, // 50 {0xAB0E93B6EFEE0053, 0x8EEA0D047A457A00}, // 51 {0xD5D238A4ABE98068, 0x72A4904598D6D880}, // 52 {0x85A36366EB71F041, 0x47A6DA2B7F864750}, // 53 {0xA70C3C40A64E6C51, 0x999090B65F67D924}, // 54 {0xD0CF4B50CFE20765, 0xFFF4B4E3F741CF6D}, // 55 {0x82818F1281ED449F, 0xBFF8F10E7A8921A5}, // 56 {0xA321F2D7226895C7, 0xAFF72D52192B6A0E}, // 57 {0xCBEA6F8CEB02BB39, 0x9BF4F8A69F764491}, // 58 {0xFEE50B7025C36A08, 0x02F236D04753D5B5}, // 59 {0x9F4F2726179A2245, 0x01D762422C946591}, // 60 {0xC722F0EF9D80AAD6, 0x424D3AD2B7B97EF6}, // 61 {0xF8EBAD2B84E0D58B, 0xD2E0898765A7DEB3}, // 62 {0x9B934C3B330C8577, 0x63CC55F49F88EB30}, // 63 {0xC2781F49FFCFA6D5, 0x3CBF6B71C76B25FC}, // 64 {0xF316271C7FC3908A, 0x8BEF464E3945EF7B}, // 65 {0x97EDD871CFDA3A56, 0x97758BF0E3CBB5AD}, // 66 {0xBDE94E8E43D0C8EC, 0x3D52EEED1CBEA318}, // 67 {0xED63A231D4C4FB27, 0x4CA7AAA863EE4BDE}, // 68 {0x945E455F24FB1CF8, 0x8FE8CAA93E74EF6B}, // 69 {0xB975D6B6EE39E436, 0xB3E2FD538E122B45}, // 70 {0xE7D34C64A9C85D44, 0x60DBBCA87196B617}, // 71 {0x90E40FBEEA1D3A4A, 0xBC8955E946FE31CE}, // 72 {0xB51D13AEA4A488DD, 0x6BABAB6398BDBE42}, // 73 {0xE264589A4DCDAB14, 0xC696963C7EED2DD2}, // 74 {0x8D7EB76070A08AEC, 0xFC1E1DE5CF543CA3}, // 75 {0xB0DE65388CC8ADA8, 0x3B25A55F43294BCC}, // 76 {0xDD15FE86AFFAD912, 0x49EF0EB713F39EBF}, // 77 {0x8A2DBF142DFCC7AB, 0x6E3569326C784338}, // 78 {0xACB92ED9397BF996, 0x49C2C37F07965405}, // 79 {0xD7E77A8F87DAF7FB, 0xDC33745EC97BE907}, // 80 {0x86F0AC99B4E8DAFD, 0x69A028BB3DED71A4}, // 81 {0xA8ACD7C0222311BC, 0xC40832EA0D68CE0D}, // 82 {0xD2D80DB02AABD62B, 0xF50A3FA490C30191}, // 83 {0x83C7088E1AAB65DB, 0x792667C6DA79E0FB}, // 84 {0xA4B8CAB1A1563F52, 0x577001B891185939}, // 85 {0xCDE6FD5E09ABCF26, 0xED4C0226B55E6F87}, // 86 {0x80B05E5AC60B6178, 0x544F8158315B05B5}, // 87 {0xA0DC75F1778E39D6, 0x696361AE3DB1C722}, // 88 {0xC913936DD571C84C, 0x03BC3A19CD1E38EA}, // 89 {0xFB5878494ACE3A5F, 0x04AB48A04065C724}, // 90 {0x9D174B2DCEC0E47B, 0x62EB0D64283F9C77}, // 91 {0xC45D1DF942711D9A, 0x3BA5D0BD324F8395}, // 92 {0xF5746577930D6500, 0xCA8F44EC7EE3647A}, // 93 {0x9968BF6ABBE85F20, 0x7E998B13CF4E1ECC}, // 94 {0xBFC2EF456AE276E8, 0x9E3FEDD8C321A67F}, // 95 {0xEFB3AB16C59B14A2, 0xC5CFE94EF3EA101F}, // 96 {0x95D04AEE3B80ECE5, 0xBBA1F1D158724A13}, // 97 {0xBB445DA9CA61281F, 0x2A8A6E45AE8EDC98}, // 98 {0xEA1575143CF97226, 0xF52D09D71A3293BE}, // 99 {0x924D692CA61BE758, 0x593C2626705F9C57}, // 100 {0xB6E0C377CFA2E12E, 0x6F8B2FB00C77836D}, // 101 {0xE498F455C38B997A, 0x0B6DFB9C0F956448}, // 102 {0x8EDF98B59A373FEC, 0x4724BD4189BD5EAD}, // 103 {0xB2977EE300C50FE7, 0x58EDEC91EC2CB658}, // 104 {0xDF3D5E9BC0F653E1, 0x2F2967B66737E3EE}, // 105 {0x8B865B215899F46C, 0xBD79E0D20082EE75}, // 106 {0xAE67F1E9AEC07187, 0xECD8590680A3AA12}, // 107 {0xDA01EE641A708DE9, 0xE80E6F4820CC9496}, // 108 {0x884134FE908658B2, 0x3109058D147FDCDE}, // 109 {0xAA51823E34A7EEDE, 0xBD4B46F0599FD416}, // 110 {0xD4E5E2CDC1D1EA96, 0x6C9E18AC7007C91B}, // 111 {0x850FADC09923329E, 0x03E2CF6BC604DDB1}, // 112 {0xA6539930BF6BFF45, 0x84DB8346B786151D}, // 113 {0xCFE87F7CEF46FF16, 0xE612641865679A64}, // 114 {0x81F14FAE158C5F6E, 0x4FCB7E8F3F60C07F}, // 115 {0xA26DA3999AEF7749, 0xE3BE5E330F38F09E}, // 116 {0xCB090C8001AB551C, 0x5CADF5BFD3072CC6}, // 117 {0xFDCB4FA002162A63, 0x73D9732FC7C8F7F7}, // 118 {0x9E9F11C4014DDA7E, 0x2867E7FDDCDD9AFB}, // 119 {0xC646D63501A1511D, 0xB281E1FD541501B9}, // 120 {0xF7D88BC24209A565, 0x1F225A7CA91A4227}, // 121 {0x9AE757596946075F, 0x3375788DE9B06959}, // 122 {0xC1A12D2FC3978937, 0x0052D6B1641C83AF}, // 123 {0xF209787BB47D6B84, 0xC0678C5DBD23A49B}, // 124 {0x9745EB4D50CE6332, 0xF840B7BA963646E1}, // 125 {0xBD176620A501FBFF, 0xB650E5A93BC3D899}, // 126 {0xEC5D3FA8CE427AFF, 0xA3E51F138AB4CEBF}, // 127 {0x93BA47C980E98CDF, 0xC66F336C36B10138}, // 128 {0xB8A8D9BBE123F017, 0xB80B0047445D4185}, // 129 {0xE6D3102AD96CEC1D, 0xA60DC059157491E6}, // 130 {0x9043EA1AC7E41392, 0x87C89837AD68DB30}, // 131 {0xB454E4A179DD1877, 0x29BABE4598C311FC}, // 132 {0xE16A1DC9D8545E94, 0xF4296DD6FEF3D67B}, // 133 {0x8CE2529E2734BB1D, 0x1899E4A65F58660D}, // 134 {0xB01AE745B101E9E4, 0x5EC05DCFF72E7F90}, // 135 {0xDC21A1171D42645D, 0x76707543F4FA1F74}, // 136 {0x899504AE72497EBA, 0x6A06494A791C53A9}, // 137 {0xABFA45DA0EDBDE69, 0x0487DB9D17636893}, // 138 {0xD6F8D7509292D603, 0x45A9D2845D3C42B7}, // 139 {0x865B86925B9BC5C2, 0x0B8A2392BA45A9B3}, // 140 {0xA7F26836F282B732, 0x8E6CAC7768D7141F}, // 141 {0xD1EF0244AF2364FF, 0x3207D795430CD927}, // 142 {0x8335616AED761F1F, 0x7F44E6BD49E807B9}, // 143 {0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A7}, // 144 {0xCD036837130890A1, 0x36DBA887C37A8C10}, // 145 {0x802221226BE55A64, 0xC2494954DA2C978A}, // 146 {0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6D}, // 147 {0xC83553C5C8965D3D, 0x6F92829494E5ACC8}, // 148 {0xFA42A8B73ABBF48C, 0xCB772339BA1F17FA}, // 149 {0x9C69A97284B578D7, 0xFF2A760414536EFC}, // 150 {0xC38413CF25E2D70D, 0xFEF5138519684ABB}, // 151 {0xF46518C2EF5B8CD1, 0x7EB258665FC25D6A}, // 152 {0x98BF2F79D5993802, 0xEF2F773FFBD97A62}, // 153 {0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FB}, // 154 {0xEEAABA2E5DBF6784, 0x95BA2A53F983CF39}, // 155 {0x952AB45CFA97A0B2, 0xDD945A747BF26184}, // 156 {0xBA756174393D88DF, 0x94F971119AEEF9E5}, // 157 {0xE912B9D1478CEB17, 0x7A37CD5601AAB85E}, // 158 {0x91ABB422CCB812EE, 0xAC62E055C10AB33B}, // 159 {0xB616A12B7FE617AA, 0x577B986B314D600A}, // 160 {0xE39C49765FDF9D94, 0xED5A7E85FDA0B80C}, // 161 {0x8E41ADE9FBEBC27D, 0x14588F13BE847308}, // 162 {0xB1D219647AE6B31C, 0x596EB2D8AE258FC9}, // 163 {0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BC}, // 164 {0x8AEC23D680043BEE, 0x25DE7BB9480D5855}, // 165 {0xADA72CCC20054AE9, 0xAF561AA79A10AE6B}, // 166 {0xD910F7FF28069DA4, 0x1B2BA1518094DA05}, // 167 {0x87AA9AFF79042286, 0x90FB44D2F05D0843}, // 168 {0xA99541BF57452B28, 0x353A1607AC744A54}, // 169 {0xD3FA922F2D1675F2, 0x42889B8997915CE9}, // 170 {0x847C9B5D7C2E09B7, 0x69956135FEBADA12}, // 171 {0xA59BC234DB398C25, 0x43FAB9837E699096}, // 172 {0xCF02B2C21207EF2E, 0x94F967E45E03F4BC}, // 173 {0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F6}, // 174 {0xA1BA1BA79E1632DC, 0x6462D92A69731733}, // 175 {0xCA28A291859BBF93, 0x7D7B8F7503CFDCFF}, // 176 {0xFCB2CB35E702AF78, 0x5CDA735244C3D43F}, // 177 {0x9DEFBF01B061ADAB, 0x3A0888136AFA64A8}, // 178 {0xC56BAEC21C7A1916, 0x088AAA1845B8FDD1}, // 179 {0xF6C69A72A3989F5B, 0x8AAD549E57273D46}, // 180 {0x9A3C2087A63F6399, 0x36AC54E2F678864C}, // 181 {0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DE}, // 182 {0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D6}, // 183 {0x969EB7C47859E743, 0x9F644AE5A4B1B326}, // 184 {0xBC4665B596706114, 0x873D5D9F0DDE1FEF}, // 185 {0xEB57FF22FC0C7959, 0xA90CB506D155A7EB}, // 186 {0x9316FF75DD87CBD8, 0x09A7F12442D588F3}, // 187 {0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB30}, // 188 {0xE5D3EF282A242E81, 0x8F1668C8A86DA5FB}, // 189 {0x8FA475791A569D10, 0xF96E017D694487BD}, // 190 {0xB38D92D760EC4455, 0x37C981DCC395A9AD}, // 191 {0xE070F78D3927556A, 0x85BBE253F47B1418}, // 192 {0x8C469AB843B89562, 0x93956D7478CCEC8F}, // 193 {0xAF58416654A6BABB, 0x387AC8D1970027B3}, // 194 {0xDB2E51BFE9D0696A, 0x06997B05FCC0319F}, // 195 {0x88FCF317F22241E2, 0x441FECE3BDF81F04}, // 196 {0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C4}, // 197 {0xD60B3BD56A5586F1, 0x8A71E223D8D3B075}, // 198 {0x85C7056562757456, 0xF6872D5667844E4A}, // 199 {0xA738C6BEBB12D16C, 0xB428F8AC016561DC}, // 200 {0xD106F86E69D785C7, 0xE13336D701BEBA53}, // 201 {0x82A45B450226B39C, 0xECC0024661173474}, // 202 {0xA34D721642B06084, 0x27F002D7F95D0191}, // 203 {0xCC20CE9BD35C78A5, 0x31EC038DF7B441F5}, // 204 {0xFF290242C83396CE, 0x7E67047175A15272}, // 205 {0x9F79A169BD203E41, 0x0F0062C6E984D387}, // 206 {0xC75809C42C684DD1, 0x52C07B78A3E60869}, // 207 {0xF92E0C3537826145, 0xA7709A56CCDF8A83}, // 208 {0x9BBCC7A142B17CCB, 0x88A66076400BB692}, // 209 {0xC2ABF989935DDBFE, 0x6ACFF893D00EA436}, // 210 {0xF356F7EBF83552FE, 0x0583F6B8C4124D44}, // 211 {0x98165AF37B2153DE, 0xC3727A337A8B704B}, // 212 {0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5D}, // 213 {0xEDA2EE1C7064130C, 0x1162DEF06F79DF74}, // 214 {0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA9}, // 215 {0xB9A74A0637CE2EE1, 0x6D953E2BD7173693}, // 216 {0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0438}, // 217 {0x910AB1D4DB9914A0, 0x1D9C9892400A22A3}, // 218 {0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4C}, // 219 {0xE2A0B5DC971F303A, 0x2E44AE64840FD61E}, // 220 {0x8DA471A9DE737E24, 0x5CEAECFED289E5D3}, // 221 {0xB10D8E1456105DAD, 0x7425A83E872C5F48}, // 222 {0xDD50F1996B947518, 0xD12F124E28F7771A}, // 223 {0x8A5296FFE33CC92F, 0x82BD6B70D99AAA70}, // 224 {0xACE73CBFDC0BFB7B, 0x636CC64D1001550C}, // 225 {0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4F}, // 226 {0x8714A775E3E95C78, 0x65ACFAEC34810A72}, // 227 {0xA8D9D1535CE3B396, 0x7F1839A741A14D0E}, // 228 {0xD31045A8341CA07C, 0x1EDE48111209A051}, // 229 {0x83EA2B892091E44D, 0x934AED0AAB460433}, // 230 {0xA4E4B66B68B65D60, 0xF81DA84D56178540}, // 231 {0xCE1DE40642E3F4B9, 0x36251260AB9D668F}, // 232 {0x80D2AE83E9CE78F3, 0xC1D72B7C6B42601A}, // 233 {0xA1075A24E4421730, 0xB24CF65B8612F820}, // 234 {0xC94930AE1D529CFC, 0xDEE033F26797B628}, // 235 {0xFB9B7CD9A4A7443C, 0x169840EF017DA3B2}, // 236 {0x9D412E0806E88AA5, 0x8E1F289560EE864F}, // 237 {0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E3}, // 238 {0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DC}, // 239 {0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF2A}, // 240 {0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF4}, // 241 {0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B1}, // 242 {0x95F83D0A1FB69CD9, 0x4ABDAF101564F98F}, // 243 {0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F2}, // 244 {0xEA53DF5FD18D5513, 0x84C86189216DC5EE}, // 245 {0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB5}, // 246 {0xB7118682DBB66A77, 0x3FBC8C33221DC2A2}, // 247 {0xE4D5E82392A40515, 0x0FABAF3FEAA5334B}, // 248 {0x8F05B1163BA6832D, 0x29CB4D87F2A7400F}, // 249 {0xB2C71D5BCA9023F8, 0x743E20E9EF511013}, // 250 {0xDF78E4B2BD342CF6, 0x914DA9246B255417}, // 251 {0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548F}, // 252 {0xAE9672ABA3D0C320, 0xA184AC2473B529B2}, // 253 {0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741F}, // 254 {0x8865899617FB1871, 0x7E2FA67C7A658893}, // 255 {0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB8}, // 256 {0xD51EA6FA85785631, 0x552A74227F3EA566}, // 257 {0x8533285C936B35DE, 0xD53A88958F872760}, // 258 {0xA67FF273B8460356, 0x8A892ABAF368F138}, // 259 {0xD01FEF10A657842C, 0x2D2B7569B0432D86}, // 260 {0x8213F56A67F6B29B, 0x9C3B29620E29FC74}, // 261 {0xA298F2C501F45F42, 0x8349F3BA91B47B90}, // 262 {0xCB3F2F7642717713, 0x241C70A936219A74}, // 263 {0xFE0EFB53D30DD4D7, 0xED238CD383AA0111}, // 264 {0x9EC95D1463E8A506, 0xF4363804324A40AB}, // 265 {0xC67BB4597CE2CE48, 0xB143C6053EDCD0D6}, // 266 {0xF81AA16FDC1B81DA, 0xDD94B7868E94050B}, // 267 {0x9B10A4E5E9913128, 0xCA7CF2B4191C8327}, // 268 {0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F1}, // 269 {0xF24A01A73CF2DCCF, 0xBC633B39673C8CED}, // 270 {0x976E41088617CA01, 0xD5BE0503E085D814}, // 271 {0xBD49D14AA79DBC82, 0x4B2D8644D8A74E19}, // 272 {0xEC9C459D51852BA2, 0xDDF8E7D60ED1219F}, // 273 {0x93E1AB8252F33B45, 0xCABB90E5C942B504}, // 274 {0xB8DA1662E7B00A17, 0x3D6A751F3B936244}, // 275 {0xE7109BFBA19C0C9D, 0x0CC512670A783AD5}, // 276 {0x906A617D450187E2, 0x27FB2B80668B24C6}, // 277 {0xB484F9DC9641E9DA, 0xB1F9F660802DEDF7}, // 278 {0xE1A63853BBD26451, 0x5E7873F8A0396974}, // 279 {0x8D07E33455637EB2, 0xDB0B487B6423E1E9}, // 280 {0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA63}, // 281 {0xDC5C5301C56B75F7, 0x7641A140CC7810FC}, // 282 {0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9E}, // 283 {0xAC2820D9623BF429, 0x546345FA9FBDCD45}, // 284 {0xD732290FBACAF133, 0xA97C177947AD4096}, // 285 {0x867F59A9D4BED6C0, 0x49ED8EABCCCC485E}, // 286 {0xA81F301449EE8C70, 0x5C68F256BFFF5A75}, // 287 {0xD226FC195C6A2F8C, 0x73832EEC6FFF3112}, // 288 {0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAC}, // 289 {0xA42E74F3D032F525, 0xBA3E7CA8B77F5E56}, // 290 {0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EC}, // 291 {0x80444B5E7AA7CF85, 0x7980D163CF5B81B4}, // 292 {0xA0555E361951C366, 0xD7E105BCC3326220}, // 293 {0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA8}, // 294 {0xFA856334878FC150, 0xB14F98F6F0FEB952}, // 295 {0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D4}, // 296 {0xC3B8358109E84F07, 0x0A862F80EC4700C9}, // 297 {0xF4A642E14C6262C8, 0xCD27BB612758C0FB}, // 298 {0x98E7E9CCCFBD7DBD, 0x8038D51CB897789D}, // 299 {0xBF21E44003ACDD2C, 0xE0470A63E6BD56C4}, // 300 {0xEEEA5D5004981478, 0x1858CCFCE06CAC75}, // 301 {0x95527A5202DF0CCB, 0x0F37801E0C43EBC9}, // 302 {0xBAA718E68396CFFD, 0xD30560258F54E6BB}, // 303 {0xE950DF20247C83FD, 0x47C6B82EF32A206A}, // 304 {0x91D28B7416CDD27E, 0x4CDC331D57FA5442}, // 305 {0xB6472E511C81471D, 0xE0133FE4ADF8E953}, // 306 {0xE3D8F9E563A198E5, 0x58180FDDD97723A7}, // 307 {0x8E679C2F5E44FF8F, 0x570F09EAA7EA7649}, // 308 {0xB201833B35D63F73, 0x2CD2CC6551E513DB}, // 309 {0xDE81E40A034BCF4F, 0xF8077F7EA65E58D2}, // 310 {0x8B112E86420F6191, 0xFB04AFAF27FAF783}, // 311 {0xADD57A27D29339F6, 0x79C5DB9AF1F9B564}, // 312 {0xD94AD8B1C7380874, 0x18375281AE7822BD}, // 313 {0x87CEC76F1C830548, 0x8F2293910D0B15B6}, // 314 {0xA9C2794AE3A3C69A, 0xB2EB3875504DDB23}, // 315 {0xD433179D9C8CB841, 0x5FA60692A46151EC}, // 316 {0x849FEEC281D7F328, 0xDBC7C41BA6BCD334}, // 317 {0xA5C7EA73224DEFF3, 0x12B9B522906C0801}, // 318 {0xCF39E50FEAE16BEF, 0xD768226B34870A01}, // 319 {0x81842F29F2CCE375, 0xE6A1158300D46641}, // 320 {0xA1E53AF46F801C53, 0x60495AE3C1097FD1}, // 321 {0xCA5E89B18B602368, 0x385BB19CB14BDFC5}, // 322 {0xFCF62C1DEE382C42, 0x46729E03DD9ED7B6}, // 323 {0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D2}, // 324 }; SF_ASSERT(k >= kMin); SF_ASSERT(k <= kMax); return g[static_cast(k - kMin)]; } #if defined(__SIZEOF_INT128__) static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp) { __extension__ using uint128_t = unsigned __int128; const uint128_t x = uint128_t{cp} * g.lo; const uint128_t y = uint128_t{cp} * g.hi + static_cast(x >> 64); const uint64_t y0 = static_cast(y); const uint64_t y1 = static_cast(y >> 64); return y1 | (y0 > 1); } #elif defined(_MSC_VER) && defined(_M_X64) static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp) { uint64_t x1 = 0; uint64_t x0 = _umul128(g.lo, cp, &x1); uint64_t y1 = 0; uint64_t y0 = _umul128(g.hi, cp, &y1); static_cast(x0); // y0 += x1; // y1 += y0 < x1; _addcarry_u64(_addcarry_u64(0, y0, x1, &y0), y1, 0, &y1); return y1 | (y0 > 1); } #else static inline uint32_t Lo32(uint64_t x) { return static_cast(x); } static inline uint32_t Hi32(uint64_t x) { return static_cast(x >> 32); } static inline uint64x2 Mul128(uint64_t a, uint64_t b) { const uint64_t b00 = uint64_t{Lo32(a)} * Lo32(b); const uint64_t b01 = uint64_t{Lo32(a)} * Hi32(b); const uint64_t b10 = uint64_t{Hi32(a)} * Lo32(b); const uint64_t b11 = uint64_t{Hi32(a)} * Hi32(b); const uint64_t mid1 = b10 + Hi32(b00); const uint64_t mid2 = b01 + Lo32(mid1); const uint64_t hi = b11 + Hi32(mid1) + Hi32(mid2); const uint64_t lo = Lo32(b00) | uint64_t{Lo32(mid2)} << 32; return {hi, lo}; } static inline uint64_t RoundToOdd(uint64x2 g, uint64_t cp) { uint64_t x = Mul128(g.lo, cp).hi; uint64x2 y = Mul128(g.hi, cp); y.lo += x; y.hi += y.lo < x; return y.hi | (y.lo > 1); } #endif // Returns whether value is divisible by 2^e2 static inline bool MultipleOfPow2(uint64_t value, int32_t e2) { SF_ASSERT(e2 >= 0); SF_ASSERT(e2 <= 63); return (value & ((uint64_t{1} << e2) - 1)) == 0; } namespace { struct FloatingDecimal64 { uint64_t digits; // num_digits <= 17 int32_t exponent; }; } static inline FloatingDecimal64 ToDecimal64(uint64_t ieee_significand, uint64_t ieee_exponent) { uint64_t c; int32_t q; if (ieee_exponent != 0) { c = Double::HiddenBit | ieee_significand; q = static_cast(ieee_exponent) - Double::ExponentBias; if (0 <= -q && -q < Double::SignificandSize && MultipleOfPow2(c, -q)) { return {c >> -q, 0}; } } else { c = ieee_significand; q = 1 - Double::ExponentBias; } const bool is_even = (c % 2 == 0); const bool accept_lower = is_even; const bool accept_upper = is_even; const bool lower_boundary_is_closer = (ieee_significand == 0 && ieee_exponent > 1); // const int32_t qb = q - 2; const uint64_t cbl = 4 * c - 2 + lower_boundary_is_closer; const uint64_t cb = 4 * c; const uint64_t cbr = 4 * c + 2; // (q * 1262611 ) >> 22 == floor(log_10( 2^q)) // (q * 1262611 - 524031) >> 22 == floor(log_10(3/4 2^q)) SF_ASSERT(q >= -1500); SF_ASSERT(q <= 1500); const int32_t k = FloorDivPow2(q * 1262611 - (lower_boundary_is_closer ? 524031 : 0), 22); const int32_t h = q + FloorLog2Pow10(-k) + 1; SF_ASSERT(h >= 1); SF_ASSERT(h <= 4); const uint64x2 pow10 = ComputePow10_Double(-k); const uint64_t vbl = RoundToOdd(pow10, cbl << h); const uint64_t vb = RoundToOdd(pow10, cb << h); const uint64_t vbr = RoundToOdd(pow10, cbr << h); const uint64_t lower = vbl + !accept_lower; const uint64_t upper = vbr - !accept_upper; // See Figure 4 in [1]. // And the modifications in Figure 6. const uint64_t s = vb / 4; // NB: 4 * s == vb & ~3 == vb & -4 if (s >= 10) // vb >= 40 { const uint64_t sp = s / 10; // = vb / 40 const bool up_inside = lower <= 40 * sp; const bool wp_inside = 40 * sp + 40 <= upper; // if (up_inside || wp_inside) // NB: At most one of u' and w' is in R_v. if (up_inside != wp_inside) { return {sp + wp_inside, k + 1}; } } const bool u_inside = lower <= 4 * s; const bool w_inside = 4 * s + 4 <= upper; if (u_inside != w_inside) { return {s + w_inside, k}; } // NB: s & 1 == vb & 0x4 const uint64_t mid = 4 * s + 2; // = 2(s + t) const bool round_up = vb > mid || (vb == mid && (s & 1) != 0); return {s + round_up, k}; } //================================================================================================== // ToChars //================================================================================================== static inline void Utoa_2Digits(char* buf, uint32_t digits) { static constexpr char Digits100[200] = { '0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9', '1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9', '2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9', '3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9', '4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9', '5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9', '6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9', '7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9', '8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9', '9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9', }; SF_ASSERT(digits <= 99); std::memcpy(buf, &Digits100[2 * digits], 2 * sizeof(char)); } static inline int TrailingZeros_2Digits(uint32_t digits) { static constexpr int8_t TrailingZeros100[100] = { 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, }; SF_ASSERT(digits <= 99); return TrailingZeros100[digits]; } static inline int Utoa_8Digits_skip_trailing_zeros(char* buf, uint32_t digits) { SF_ASSERT(digits >= 1); SF_ASSERT(digits <= 99999999); const uint32_t q = digits / 10000; const uint32_t r = digits % 10000; const uint32_t qH = q / 100; const uint32_t qL = q % 100; Utoa_2Digits(buf + 0, qH); Utoa_2Digits(buf + 2, qL); if (r == 0) { return TrailingZeros_2Digits(qL == 0 ? qH : qL) + (qL == 0 ? 6 : 4); } else { const uint32_t rH = r / 100; const uint32_t rL = r % 100; Utoa_2Digits(buf + 4, rH); Utoa_2Digits(buf + 6, rL); return TrailingZeros_2Digits(rL == 0 ? rH : rL) + (rL == 0 ? 2 : 0); } } static inline int PrintDecimalDigitsBackwards(char* buf, uint64_t output64) { int tz = 0; // number of trailing zeros removed. int nd = 0; // number of decimal digits processed. // At most 17 digits remaining if (output64 >= 100000000) { const uint64_t q = output64 / 100000000; const uint32_t r = static_cast(output64 % 100000000); output64 = q; buf -= 8; if (r != 0) { tz = Utoa_8Digits_skip_trailing_zeros(buf, r); SF_ASSERT(tz >= 0); SF_ASSERT(tz <= 7); } else { tz = 8; } nd = 8; } // At most 9 digits remaining. SF_ASSERT(output64 <= UINT32_MAX); uint32_t output = static_cast(output64); if (output >= 10000) { const uint32_t q = output / 10000; const uint32_t r = output % 10000; output = q; buf -= 4; if (r != 0) { const uint32_t rH = r / 100; const uint32_t rL = r % 100; Utoa_2Digits(buf + 0, rH); Utoa_2Digits(buf + 2, rL); if (tz == nd) { tz += TrailingZeros_2Digits(rL == 0 ? rH : rL) + (rL == 0 ? 2 : 0); } } else { if (tz == nd) tz += 4; else std::memset(buf, '0', 4); // (actually not required...) } nd += 4; } // At most 5 digits remaining. if (output >= 100) { const uint32_t q = output / 100; const uint32_t r = output % 100; output = q; buf -= 2; Utoa_2Digits(buf, r); if (tz == nd) { tz += TrailingZeros_2Digits(r); } nd += 2; if (output >= 100) { const uint32_t q2 = output / 100; const uint32_t r2 = output % 100; output = q2; buf -= 2; Utoa_2Digits(buf, r2); if (tz == nd) { tz += TrailingZeros_2Digits(r2); } nd += 2; } } // At most 2 digits remaining. SF_ASSERT(output >= 1); SF_ASSERT(output <= 99); if (output >= 10) { const uint32_t q = output; buf -= 2; Utoa_2Digits(buf, q); if (tz == nd) { tz += TrailingZeros_2Digits(q); } // nd += 2; } else { const uint32_t q = output; SF_ASSERT(q >= 1); SF_ASSERT(q <= 9); *--buf = static_cast('0' + q); } return tz; } static inline int32_t DecimalLength(uint64_t v) { SF_ASSERT(v >= 1); SF_ASSERT(v <= 99999999999999999ull); if (static_cast(v >> 32) != 0) { if (v >= 10000000000000000ull) { return 17; } if (v >= 1000000000000000ull) { return 16; } if (v >= 100000000000000ull) { return 15; } if (v >= 10000000000000ull) { return 14; } if (v >= 1000000000000ull) { return 13; } if (v >= 100000000000ull) { return 12; } if (v >= 10000000000ull) { return 11; } return 10; } const uint32_t v32 = static_cast(v); if (v32 >= 1000000000u) { return 10; } if (v32 >= 100000000u) { return 9; } if (v32 >= 10000000u) { return 8; } if (v32 >= 1000000u) { return 7; } if (v32 >= 100000u) { return 6; } if (v32 >= 10000u) { return 5; } if (v32 >= 1000u) { return 4; } if (v32 >= 100u) { return 3; } if (v32 >= 10u) { return 2; } return 1; } static inline char* FormatDigits(char* buffer, uint64_t digits, int32_t decimal_exponent, bool force_trailing_dot_zero = false) { static constexpr int32_t MinFixedDecimalPoint = -6; static constexpr int32_t MaxFixedDecimalPoint = 17; static_assert(MinFixedDecimalPoint <= -1, "internal error"); static_assert(MaxFixedDecimalPoint >= 17, "internal error"); SF_ASSERT(digits >= 1); SF_ASSERT(digits <= 99999999999999999ull); SF_ASSERT(decimal_exponent >= -999); SF_ASSERT(decimal_exponent <= 999); int32_t num_digits = DecimalLength(digits); const int32_t decimal_point = num_digits + decimal_exponent; const bool use_fixed = MinFixedDecimalPoint <= decimal_point && decimal_point <= MaxFixedDecimalPoint; // Prepare the buffer. // Avoid calling memset/memcpy with variable arguments below... std::memset(buffer + 0, '0', 16); std::memset(buffer + 16, '0', 16); static_assert(MinFixedDecimalPoint >= -30, "internal error"); static_assert(MaxFixedDecimalPoint <= 32, "internal error"); int32_t decimal_digits_position; if (use_fixed) { if (decimal_point <= 0) { // 0.[000]digits decimal_digits_position = 2 - decimal_point; } else { // dig.its // digits[000] decimal_digits_position = 0; } } else { // dE+123 or d.igitsE+123 decimal_digits_position = 1; } char* digits_end = buffer + decimal_digits_position + num_digits; const int tz = PrintDecimalDigitsBackwards(digits_end, digits); digits_end -= tz; num_digits -= tz; // decimal_exponent += tz; // => decimal_point unchanged. if (use_fixed) { if (decimal_point <= 0) { // 0.[000]digits buffer[1] = '.'; buffer = digits_end; } else if (decimal_point < num_digits) { // dig.its #if defined(_MSC_VER) && !defined(__clang__) // VC does not inline the memmove call below. (Even if compiled with /arch:AVX2.) // However, memcpy will be inlined. uint8_t tmp[16]; char* const src = buffer + decimal_point; char* const dst = src + 1; std::memcpy(tmp, src, 16); std::memcpy(dst, tmp, 16); #else std::memmove(buffer + decimal_point + 1, buffer + decimal_point, 16); #endif buffer[decimal_point] = '.'; buffer = digits_end + 1; } else { // digits[000] buffer += decimal_point; if (force_trailing_dot_zero) { std::memcpy(buffer, ".0", 2); buffer += 2; } } } else { // Copy the first digit one place to the left. buffer[0] = buffer[1]; if (num_digits == 1) { // dE+123 ++buffer; } else { // d.igitsE+123 buffer[1] = '.'; buffer = digits_end; } const int32_t scientific_exponent = decimal_point - 1; // SF_ASSERT(scientific_exponent != 0); std::memcpy(buffer, scientific_exponent < 0 ? "e-" : "e+", 2); buffer += 2; const uint32_t k = static_cast(scientific_exponent < 0 ? -scientific_exponent : scientific_exponent); if (k < 10) { *buffer++ = static_cast('0' + k); } else if (k < 100) { Utoa_2Digits(buffer, k); buffer += 2; } else { const uint32_t q = k / 100; const uint32_t r = k % 100; *buffer++ = static_cast('0' + q); Utoa_2Digits(buffer, r); buffer += 2; } } return buffer; } static inline char* ToChars(char* buffer, double value, bool force_trailing_dot_zero = false) { const Double v(value); const uint64_t significand = v.PhysicalSignificand(); const uint64_t exponent = v.PhysicalExponent(); if (exponent != Double::MaxIeeeExponent) // [[likely]] { // Finite buffer[0] = '-'; buffer += v.SignBit(); if (exponent != 0 || significand != 0) // [[likely]] { // != 0 const auto dec = ToDecimal64(significand, exponent); return FormatDigits(buffer, dec.digits, dec.exponent, force_trailing_dot_zero); } else { std::memcpy(buffer, "0.0 ", 4); buffer += force_trailing_dot_zero ? 3 : 1; return buffer; } } if (significand == 0) { buffer[0] = '-'; buffer += v.SignBit(); std::memcpy(buffer, "inf ", 4); return buffer + 3; } else { std::memcpy(buffer, "nan ", 4); return buffer + 3; } } //================================================================================================== // //================================================================================================== char* schubfach::Dtoa(char* buffer, double value) { return ToChars(buffer, value); } dragonbox-master/subproject/3rdparty/schubfach/schubfach_32.h0000664000175000017500000000171315060737600023267 0ustar renerene// Copyright 2020 Alexander Bolz // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) #pragma once namespace schubfach { // char* output_end = Ftoa(buffer, value); // // Converts the given single-precision number into decimal form and stores the result in the given // buffer. // // The buffer must be large enough, i.e. >= FtoaMinBufferLength. // The output format is similar to printf("%g"). // The output is _not_ null-terminted. // // The output is optimal, i.e. the output string // 1. rounds back to the input number when read in (using round-to-nearest-even) // 2. is as short as possible, // 3. is as close to the input number as possible. // // Note: // This function may temporarily write up to FtoaMinBufferLength characters into the buffer. constexpr int FtoaMinBufferLength = 32; char* Ftoa(char* buffer, float value); } // namespace schubfach dragonbox-master/subproject/3rdparty/schubfach/schubfach_32.cc0000664000175000017500000005050615060737600023431 0ustar renerene// Copyright 2020 Alexander Bolz // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) #include "schubfach_32.h" //-------------------------------------------------------------------------------------------------- // This file contains an implementation of the Schubfach algorithm as described in // // [1] Raffaello Giulietti, "The Schubfach way to render doubles", // https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN //-------------------------------------------------------------------------------------------------- #include #include #include #include #include #if _MSC_VER #include #endif #ifndef SF_ASSERT #define SF_ASSERT(X) assert(X) #endif //================================================================================================== // //================================================================================================== template static inline Dest ReinterpretBits(Source source) { static_assert(sizeof(Dest) == sizeof(Source), "size mismatch"); Dest dest; std::memcpy(&dest, &source, sizeof(Source)); return dest; } namespace { struct Single { static_assert(std::numeric_limits::is_iec559 && std::numeric_limits::digits == 24 && std::numeric_limits::max_exponent == 128, "IEEE-754 single-precision implementation required"); using value_type = float; using bits_type = uint32_t; // static constexpr int32_t MaxDigits10 = std::numeric_limits::max_digits10; static constexpr int32_t SignificandSize = std::numeric_limits::digits; // = p (includes the hidden bit) static constexpr int32_t ExponentBias = std::numeric_limits::max_exponent - 1 + (SignificandSize - 1); // static constexpr int32_t MaxExponent = std::numeric_limits::max_exponent - 1 - (SignificandSize - 1); // static constexpr int32_t MinExponent = std::numeric_limits::min_exponent - 1 - (SignificandSize - 1); static constexpr bits_type MaxIeeeExponent = bits_type{2 * std::numeric_limits::max_exponent - 1}; static constexpr bits_type HiddenBit = bits_type{1} << (SignificandSize - 1); // = 2^(p-1) static constexpr bits_type SignificandMask = HiddenBit - 1; // = 2^(p-1) - 1 static constexpr bits_type ExponentMask = MaxIeeeExponent << (SignificandSize - 1); static constexpr bits_type SignMask = ~(~bits_type{0} >> 1); bits_type bits; explicit Single(bits_type bits_) : bits(bits_) {} explicit Single(value_type value) : bits(ReinterpretBits(value)) {} bits_type PhysicalSignificand() const { return bits & SignificandMask; } bits_type PhysicalExponent() const { return (bits & ExponentMask) >> (SignificandSize - 1); } bool IsFinite() const { return (bits & ExponentMask) != ExponentMask; } bool IsInf() const { return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) == 0; } bool IsNaN() const { return (bits & ExponentMask) == ExponentMask && (bits & SignificandMask) != 0; } bool IsZero() const { return (bits & ~SignMask) == 0; } bool SignBit() const { return (bits & SignMask) != 0; } }; } // namespace //================================================================================================== // //================================================================================================== // Returns floor(x / 2^n). // // Technically, right-shift of negative integers is implementation defined... // Should easily be optimized into SAR (or equivalent) instruction. static inline int32_t FloorDivPow2(int32_t x, int32_t n) { #if 0 return x < 0 ? ~(~x >> n) : (x >> n); #else return x >> n; #endif } // Returns floor(log_10(2^e)) // static inline int32_t FloorLog10Pow2(int32_t e) // { // SF_ASSERT(e >= -1500); // SF_ASSERT(e <= 1500); // return FloorDivPow2(e * 1262611, 22); // } // Returns floor(log_10(3/4 2^e)) // static inline int32_t FloorLog10ThreeQuartersPow2(int32_t e) // { // SF_ASSERT(e >= -1500); // SF_ASSERT(e <= 1500); // return FloorDivPow2(e * 1262611 - 524031, 22); // } // Returns floor(log_2(10^e)) static inline int32_t FloorLog2Pow10(int32_t e) { SF_ASSERT(e >= -1233); SF_ASSERT(e <= 1233); return FloorDivPow2(e * 1741647, 19); } //================================================================================================== // //================================================================================================== static inline uint64_t ComputePow10(int32_t k) { // There are unique beta and r such that 10^k = beta 2^r and // 2^63 <= beta < 2^64, namely r = floor(log_2 10^k) - 63 and // beta = 2^-r 10^k. // Let g = ceil(beta), so (g-1) 2^r < 10^k <= g 2^r, with the latter // value being a pretty good overestimate for 10^k. // NB: Since for all the required exponents k, we have g < 2^64, // all constants can be stored in 128-bit integers. static constexpr int32_t kMin = -31; static constexpr int32_t kMax = 45; static constexpr uint64_t g[kMax - kMin + 1] = { 0x81CEB32C4B43FCF5, // -31 0xA2425FF75E14FC32, // -30 0xCAD2F7F5359A3B3F, // -29 0xFD87B5F28300CA0E, // -28 0x9E74D1B791E07E49, // -27 0xC612062576589DDB, // -26 0xF79687AED3EEC552, // -25 0x9ABE14CD44753B53, // -24 0xC16D9A0095928A28, // -23 0xF1C90080BAF72CB2, // -22 0x971DA05074DA7BEF, // -21 0xBCE5086492111AEB, // -20 0xEC1E4A7DB69561A6, // -19 0x9392EE8E921D5D08, // -18 0xB877AA3236A4B44A, // -17 0xE69594BEC44DE15C, // -16 0x901D7CF73AB0ACDA, // -15 0xB424DC35095CD810, // -14 0xE12E13424BB40E14, // -13 0x8CBCCC096F5088CC, // -12 0xAFEBFF0BCB24AAFF, // -11 0xDBE6FECEBDEDD5BF, // -10 0x89705F4136B4A598, // -9 0xABCC77118461CEFD, // -8 0xD6BF94D5E57A42BD, // -7 0x8637BD05AF6C69B6, // -6 0xA7C5AC471B478424, // -5 0xD1B71758E219652C, // -4 0x83126E978D4FDF3C, // -3 0xA3D70A3D70A3D70B, // -2 0xCCCCCCCCCCCCCCCD, // -1 0x8000000000000000, // 0 0xA000000000000000, // 1 0xC800000000000000, // 2 0xFA00000000000000, // 3 0x9C40000000000000, // 4 0xC350000000000000, // 5 0xF424000000000000, // 6 0x9896800000000000, // 7 0xBEBC200000000000, // 8 0xEE6B280000000000, // 9 0x9502F90000000000, // 10 0xBA43B74000000000, // 11 0xE8D4A51000000000, // 12 0x9184E72A00000000, // 13 0xB5E620F480000000, // 14 0xE35FA931A0000000, // 15 0x8E1BC9BF04000000, // 16 0xB1A2BC2EC5000000, // 17 0xDE0B6B3A76400000, // 18 0x8AC7230489E80000, // 19 0xAD78EBC5AC620000, // 20 0xD8D726B7177A8000, // 21 0x878678326EAC9000, // 22 0xA968163F0A57B400, // 23 0xD3C21BCECCEDA100, // 24 0x84595161401484A0, // 25 0xA56FA5B99019A5C8, // 26 0xCECB8F27F4200F3A, // 27 0x813F3978F8940985, // 28 0xA18F07D736B90BE6, // 29 0xC9F2C9CD04674EDF, // 30 0xFC6F7C4045812297, // 31 0x9DC5ADA82B70B59E, // 32 0xC5371912364CE306, // 33 0xF684DF56C3E01BC7, // 34 0x9A130B963A6C115D, // 35 0xC097CE7BC90715B4, // 36 0xF0BDC21ABB48DB21, // 37 0x96769950B50D88F5, // 38 0xBC143FA4E250EB32, // 39 0xEB194F8E1AE525FE, // 40 0x92EFD1B8D0CF37BF, // 41 0xB7ABC627050305AE, // 42 0xE596B7B0C643C71A, // 43 0x8F7E32CE7BEA5C70, // 44 0xB35DBF821AE4F38C, // 45 }; SF_ASSERT(k >= kMin); SF_ASSERT(k <= kMax); return g[static_cast(k - kMin)]; } static inline uint32_t Lo32(uint64_t x) { return static_cast(x); } static inline uint32_t Hi32(uint64_t x) { return static_cast(x >> 32); } #if defined(__SIZEOF_INT128__) static inline uint32_t RoundToOdd(uint64_t g, uint32_t cp) { __extension__ using uint128_t = unsigned __int128; const uint128_t p = uint128_t{g} * cp; const uint32_t y1 = Lo32(static_cast(p >> 64)); const uint32_t y0 = Hi32(static_cast(p)); return y1 | (y0 > 1); } #elif defined(_MSC_VER) && defined(_M_X64) static inline uint32_t RoundToOdd(uint64_t g, uint32_t cpHi) { uint64_t p1 = 0; uint64_t p0 = _umul128(g, cpHi, &p1); const uint32_t y1 = Lo32(p1); const uint32_t y0 = Hi32(p0); return y1 | (y0 > 1); } #else static inline uint32_t RoundToOdd(uint64_t g, uint32_t cp) { const uint64_t b01 = uint64_t{Lo32(g)} * cp; const uint64_t b11 = uint64_t{Hi32(g)} * cp; const uint64_t hi = b11 + Hi32(b01); const uint32_t y1 = Hi32(hi); const uint32_t y0 = Lo32(hi); return y1 | (y0 > 1); } #endif // Returns whether value is divisible by 2^e2 static inline bool MultipleOfPow2(uint32_t value, int32_t e2) { SF_ASSERT(e2 >= 0); SF_ASSERT(e2 <= 31); return (value & ((uint32_t{1} << e2) - 1)) == 0; } namespace { struct FloatingDecimal32 { uint32_t digits; // num_digits <= 9 int32_t exponent; }; } static inline FloatingDecimal32 ToDecimal32(uint32_t ieee_significand, uint32_t ieee_exponent) { uint32_t c; int32_t q; if (ieee_exponent != 0) { c = Single::HiddenBit | ieee_significand; q = static_cast(ieee_exponent) - Single::ExponentBias; if (0 <= -q && -q < Single::SignificandSize && MultipleOfPow2(c, -q)) { return {c >> -q, 0}; } } else { c = ieee_significand; q = 1 - Single::ExponentBias; } const bool is_even = (c % 2 == 0); const bool accept_lower = is_even; const bool accept_upper = is_even; const bool lower_boundary_is_closer = (ieee_significand == 0 && ieee_exponent > 1); // const int32_t qb = q - 2; const uint32_t cbl = 4 * c - 2 + lower_boundary_is_closer; const uint32_t cb = 4 * c; const uint32_t cbr = 4 * c + 2; // (q * 1262611 ) >> 22 == floor(log_10( 2^q)) // (q * 1262611 - 524031) >> 22 == floor(log_10(3/4 2^q)) SF_ASSERT(q >= -1500); SF_ASSERT(q <= 1500); const int32_t k = FloorDivPow2(q * 1262611 - (lower_boundary_is_closer ? 524031 : 0), 22); const int32_t h = q + FloorLog2Pow10(-k) + 1; SF_ASSERT(h >= 1); SF_ASSERT(h <= 4); const uint64_t pow10 = ComputePow10(-k); const uint32_t vbl = RoundToOdd(pow10, cbl << h); const uint32_t vb = RoundToOdd(pow10, cb << h); const uint32_t vbr = RoundToOdd(pow10, cbr << h); const uint32_t lower = vbl + !accept_lower; const uint32_t upper = vbr - !accept_upper; // See Figure 4 in [1]. // And the modifications in Figure 6. const uint32_t s = vb / 4; // NB: 4 * s == vb & ~3 == vb & -4 if (s >= 10) // vb >= 40 { const uint32_t sp = s / 10; // = vb / 40 const bool up_inside = lower <= 40 * sp; const bool wp_inside = 40 * sp + 40 <= upper; // if (up_inside || wp_inside) // NB: At most one of u' and w' is in R_v. if (up_inside != wp_inside) { return {sp + wp_inside, k + 1}; } } const bool u_inside = lower <= 4 * s; const bool w_inside = 4 * s + 4 <= upper; if (u_inside != w_inside) { return {s + w_inside, k}; } // NB: s & 1 == vb & 0x4 const uint32_t mid = 4 * s + 2; // = 2(s + t) const bool round_up = vb > mid || (vb == mid && (s & 1) != 0); return {s + round_up, k}; } //================================================================================================== // ToChars //================================================================================================== static inline void Utoa_2Digits(char* buf, uint32_t digits) { static constexpr char Digits100[200] = { '0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9', '1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9', '2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9', '3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9', '4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9', '5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9', '6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9', '7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9', '8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9', '9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9', }; SF_ASSERT(digits <= 99); std::memcpy(buf, &Digits100[2 * digits], 2 * sizeof(char)); } static inline int TrailingZeros_2Digits(uint32_t digits) { static constexpr int8_t TrailingZeros100[100] = { 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, }; SF_ASSERT(digits <= 99); return TrailingZeros100[digits]; } static inline int PrintDecimalDigitsBackwards(char* buf, uint32_t output) { int tz = 0; // number of trailing zeros removed. int nd = 0; // number of decimal digits processed. // At most 9 digits remaining if (output >= 10000) { const uint32_t q = output / 10000; const uint32_t r = output % 10000; output = q; buf -= 4; if (r != 0) { const uint32_t rH = r / 100; const uint32_t rL = r % 100; Utoa_2Digits(buf + 0, rH); Utoa_2Digits(buf + 2, rL); tz = TrailingZeros_2Digits(rL == 0 ? rH : rL) + (rL == 0 ? 2 : 0); } else { tz = 4; } nd = 4; } // At most 5 digits remaining. if (output >= 100) { const uint32_t q = output / 100; const uint32_t r = output % 100; output = q; buf -= 2; Utoa_2Digits(buf, r); if (tz == nd) { tz += TrailingZeros_2Digits(r); } nd += 2; if (output >= 100) { const uint32_t q2 = output / 100; const uint32_t r2 = output % 100; output = q2; buf -= 2; Utoa_2Digits(buf, r2); if (tz == nd) { tz += TrailingZeros_2Digits(r2); } nd += 2; } } // At most 2 digits remaining. SF_ASSERT(output >= 1); SF_ASSERT(output <= 99); if (output >= 10) { const uint32_t q = output; buf -= 2; Utoa_2Digits(buf, q); if (tz == nd) { tz += TrailingZeros_2Digits(q); } // nd += 2; } else { const uint32_t q = output; SF_ASSERT(q >= 1); SF_ASSERT(q <= 9); *--buf = static_cast('0' + q); } return tz; } static inline int32_t DecimalLength(uint32_t v) { SF_ASSERT(v >= 1); SF_ASSERT(v <= 999999999u); if (v >= 100000000u) { return 9; } if (v >= 10000000u) { return 8; } if (v >= 1000000u) { return 7; } if (v >= 100000u) { return 6; } if (v >= 10000u) { return 5; } if (v >= 1000u) { return 4; } if (v >= 100u) { return 3; } if (v >= 10u) { return 2; } return 1; } static inline char* FormatDigits(char* buffer, uint32_t digits, int32_t decimal_exponent, bool force_trailing_dot_zero = false) { static constexpr int32_t MinFixedDecimalPoint = -4; static constexpr int32_t MaxFixedDecimalPoint = 9; static_assert(MinFixedDecimalPoint <= -1, "internal error"); static_assert(MaxFixedDecimalPoint >= 9, "internal error"); SF_ASSERT(digits >= 1); SF_ASSERT(digits <= 999999999u); SF_ASSERT(decimal_exponent >= -99); SF_ASSERT(decimal_exponent <= 99); int32_t num_digits = DecimalLength(digits); const int32_t decimal_point = num_digits + decimal_exponent; const bool use_fixed = MinFixedDecimalPoint <= decimal_point && decimal_point <= MaxFixedDecimalPoint; // Prepare the buffer. // Avoid calling memset/memcpy with variable arguments below... std::memset(buffer, '0', 16); static_assert(MinFixedDecimalPoint >= -14, "internal error"); static_assert(MaxFixedDecimalPoint <= 16, "internal error"); int32_t decimal_digits_position; if (use_fixed) { if (decimal_point <= 0) { // 0.[000]digits decimal_digits_position = 2 - decimal_point; } else { // dig.its // digits[000] decimal_digits_position = 0; } } else { // dE+123 or d.igitsE+123 decimal_digits_position = 1; } char* digits_end = buffer + decimal_digits_position + num_digits; const int tz = PrintDecimalDigitsBackwards(digits_end, digits); digits_end -= tz; num_digits -= tz; // decimal_exponent += tz; // => decimal_point unchanged. if (use_fixed) { if (decimal_point <= 0) { // 0.[000]digits buffer[1] = '.'; buffer = digits_end; } else if (decimal_point < num_digits) { // dig.its std::memmove(buffer + decimal_point + 1, buffer + decimal_point, 8); buffer[decimal_point] = '.'; buffer = digits_end + 1; } else { // digits[000] buffer += decimal_point; if (force_trailing_dot_zero) { std::memcpy(buffer, ".0", 2); buffer += 2; } } } else { buffer[0] = buffer[1]; if (num_digits == 1) { // dE+123 ++buffer; } else { // d.igitsE+123 buffer[1] = '.'; buffer = digits_end; } const int32_t scientific_exponent = decimal_point - 1; // SF_ASSERT(scientific_exponent != 0); std::memcpy(buffer, scientific_exponent < 0 ? "e-" : "e+", 2); buffer += 2; const uint32_t k = static_cast(scientific_exponent < 0 ? -scientific_exponent : scientific_exponent); if (k < 10) { *buffer++ = static_cast('0' + k); } else { Utoa_2Digits(buffer, k); buffer += 2; } } return buffer; } static inline char* ToChars(char* buffer, float value, bool force_trailing_dot_zero = false) { const Single v(value); const uint32_t significand = v.PhysicalSignificand(); const uint32_t exponent = v.PhysicalExponent(); if (exponent != Single::MaxIeeeExponent) // [[likely]] { // Finite buffer[0] = '-'; buffer += v.SignBit(); if (exponent != 0 || significand != 0) // [[likely]] { // != 0 const auto dec = ToDecimal32(significand, exponent); return FormatDigits(buffer, dec.digits, dec.exponent, force_trailing_dot_zero); } else { std::memcpy(buffer, "0.0 ", 4); buffer += force_trailing_dot_zero ? 3 : 1; return buffer; } } if (significand == 0) { buffer[0] = '-'; buffer += v.SignBit(); std::memcpy(buffer, "inf ", 4); return buffer + 3; } else { std::memcpy(buffer, "nan ", 4); return buffer + 3; } } //================================================================================================== // //================================================================================================== char* schubfach::Ftoa(char* buffer, float value) { return ToChars(buffer, value); } dragonbox-master/subproject/3rdparty/schubfach/schubfach_64.h0000664000175000017500000000171415060737600023275 0ustar renerene// Copyright 2020 Alexander Bolz // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt) #pragma once namespace schubfach { // char* output_end = Dtoa(buffer, value); // // Converts the given double-precision number into decimal form and stores the result in the given // buffer. // // The buffer must be large enough, i.e. >= DtoaMinBufferLength. // The output format is similar to printf("%g"). // The output is _not_ null-terminted. // // The output is optimal, i.e. the output string // 1. rounds back to the input number when read in (using round-to-nearest-even) // 2. is as short as possible, // 3. is as close to the input number as possible. // // Note: // This function may temporarily write up to DtoaMinBufferLength characters into the buffer. constexpr int DtoaMinBufferLength = 64; char* Dtoa(char* buffer, double value); } // namespace schubfach dragonbox-master/subproject/3rdparty/grisu_exact/0000775000175000017500000000000015060737600021251 5ustar renerenedragonbox-master/subproject/3rdparty/grisu_exact/CMakeLists.txt0000664000175000017500000000057215060737600024015 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(grisu_exact LANGUAGES CXX) add_library(grisu_exact STATIC fp_to_chars.h fp_to_chars.cpp grisu_exact.h) add_library(grisu_exact::grisu_exact ALIAS grisu_exact) target_compile_features(grisu_exact PUBLIC cxx_std_17) target_include_directories(grisu_exact PUBLIC $)dragonbox-master/subproject/3rdparty/grisu_exact/fp_to_chars.h0000664000175000017500000000527315060737600023720 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_FP_TO_CHARS #define JKJ_FP_TO_CHARS #include "grisu_exact.h" namespace jkj { namespace fp_to_chars_detail { char* float_to_chars(unsigned_fp_t v, char* buffer); char* double_to_chars(unsigned_fp_t v, char* buffer); } // Returns the next-to-end position template char* fp_to_chars_n(Float x, char* buffer, RoundingMode&& rounding_mode = {}, CorrectRoundingSearch&& crs = {}) { auto br = get_bit_representation(x); if (br.is_finite()) { if (br.is_negative()) { *buffer = '-'; ++buffer; } if (br.is_nonzero()) { if constexpr (sizeof(Float) == 4) { return fp_to_chars_detail::float_to_chars(grisu_exact(x, std::forward(rounding_mode), std::forward(crs)), buffer); } else { return fp_to_chars_detail::double_to_chars(grisu_exact(x, std::forward(rounding_mode), std::forward(crs)), buffer); } } else { std::memcpy(buffer, "0E0", 3); return buffer + 3; } } else { if ((br.f << (grisu_exact_detail::common_info::exponent_bits + 1)) != 0) { std::memcpy(buffer, "NaN", 3); return buffer + 3; } else { if (br.is_negative()) { *buffer = '-'; ++buffer; } std::memcpy(buffer, "Infinity", 8); return buffer + 8; } } } // Null-terminate and bypass the return value of fp_to_chars_n template char* fp_to_chars(Float x, char* buffer, RoundingMode&& rounding_mode = {}, CorrectRoundingSearch&& crs = {}) { auto ptr = fp_to_chars_n(x, buffer, std::forward(rounding_mode), std::forward(crs)); *ptr = '\0'; return ptr; } } #endif dragonbox-master/subproject/3rdparty/grisu_exact/fp_to_chars.cpp0000664000175000017500000002003515060737600024244 0ustar renerene// The contents of this file is based on contents of: // // https://github.com/ulfjack/ryu/blob/master/ryu/common.h, // https://github.com/ulfjack/ryu/blob/master/ryu/d2s.c, and // https://github.com/ulfjack/ryu/blob/master/ryu/f2s.c, // // which are distributed under the following terms: //-------------------------------------------------------------------------------- // Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. //-------------------------------------------------------------------------------- // Modifications Copyright 2020 Junekey Jeon // // Following modifications were made to the original contents: // - Put everything inside the namespace jkj::fp_to_chars_detail // - Combined decimalLength9 (from common.h) and decimalLength17 (from d2s.c) // into a single template function decimal_length // - Combined to_chars (from f2s.c) and to_chars (from d2s.c) into a // single template function fp_to_chars_impl // - Removed index counting statements; replaced them with pointer increments // - Removed usages of DIGIT_TABLE; replaced them with radix_100_table // // These modifications, together with other contents of this file may be used // under the same terms as the original contents. #include "fp_to_chars.h" namespace jkj { namespace fp_to_chars_detail { static constexpr char radix_100_table[] = { '0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9', '1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9', '2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9', '3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9', '4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9', '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9', '6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9', '7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9', '8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', '9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9' }; template static constexpr std::uint32_t decimal_length(UInt const v) { if constexpr (std::is_same_v) { // Function precondition: v is not a 10-digit number. // (f2s: 9 digits are sufficient for round-tripping.) // (d2fixed: We print 9-digit blocks.) assert(v < 1000000000); if (v >= 100000000) { return 9; } if (v >= 10000000) { return 8; } if (v >= 1000000) { return 7; } if (v >= 100000) { return 6; } if (v >= 10000) { return 5; } if (v >= 1000) { return 4; } if (v >= 100) { return 3; } if (v >= 10) { return 2; } return 1; } else { static_assert(std::is_same_v); // This is slightly faster than a loop. // The average output length is 16.38 digits, so we check high-to-low. // Function precondition: v is not an 18, 19, or 20-digit number. // (17 digits are sufficient for round-tripping.) assert(v < 100000000000000000L); if (v >= 10000000000000000L) { return 17; } if (v >= 1000000000000000L) { return 16; } if (v >= 100000000000000L) { return 15; } if (v >= 10000000000000L) { return 14; } if (v >= 1000000000000L) { return 13; } if (v >= 100000000000L) { return 12; } if (v >= 10000000000L) { return 11; } if (v >= 1000000000L) { return 10; } if (v >= 100000000L) { return 9; } if (v >= 10000000L) { return 8; } if (v >= 1000000L) { return 7; } if (v >= 100000L) { return 6; } if (v >= 10000L) { return 5; } if (v >= 1000L) { return 4; } if (v >= 100L) { return 3; } if (v >= 10L) { return 2; } return 1; } } template static char* fp_to_chars_impl(unsigned_fp_t v, char* buffer) { auto output = v.significand; auto const olength = decimal_length(output); // Print the decimal digits. // The following code is equivalent to: // for (uint32_t i = 0; i < olength - 1; ++i) { // const uint32_t c = output % 10; output /= 10; // result[index + olength - i] = (char) ('0' + c); // } // result[index] = '0' + output % 10; uint32_t i = 0; if constexpr (sizeof(Float) == 8) { // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. if ((output >> 32) != 0) { // Expensive 64-bit division. const uint64_t q = output / 100000000; uint32_t output2 = ((uint32_t)output) - 100000000 * ((uint32_t)q); output = q; const uint32_t c = output2 % 10000; output2 /= 10000; const uint32_t d = output2 % 10000; const uint32_t c0 = (c % 100) << 1; const uint32_t c1 = (c / 100) << 1; const uint32_t d0 = (d % 100) << 1; const uint32_t d1 = (d / 100) << 1; memcpy(buffer + olength - i - 1, radix_100_table + c0, 2); memcpy(buffer + olength - i - 3, radix_100_table + c1, 2); memcpy(buffer + olength - i - 5, radix_100_table + d0, 2); memcpy(buffer + olength - i - 7, radix_100_table + d1, 2); i += 8; } } auto output2 = (uint32_t)output; while (output2 >= 10000) { #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217 const uint32_t c = output2 - 10000 * (output2 / 10000); #else const uint32_t c = output2 % 10000; #endif output2 /= 10000; const uint32_t c0 = (c % 100) << 1; const uint32_t c1 = (c / 100) << 1; memcpy(buffer + olength - i - 1, radix_100_table + c0, 2); memcpy(buffer + olength - i - 3, radix_100_table + c1, 2); i += 4; } if (output2 >= 100) { const uint32_t c = (output2 % 100) << 1; output2 /= 100; memcpy(buffer + olength - i - 1, radix_100_table + c, 2); i += 2; } if (output2 >= 10) { const uint32_t c = output2 << 1; // We can't use memcpy here: the decimal dot goes between these two digits. buffer[olength - i] = radix_100_table[c + 1]; buffer[0] = radix_100_table[c]; } else { buffer[0] = (char)('0' + output2); } // Print decimal point if needed. if (olength > 1) { buffer[1] = '.'; buffer += olength + 1; } else { ++buffer; } // Print the exponent. *buffer = 'E'; ++buffer; int32_t exp = v.exponent + (int32_t)olength - 1; if (exp < 0) { *buffer = '-'; ++buffer; exp = -exp; } if constexpr (sizeof(Float) == 8) { if (exp >= 100) { const int32_t c = exp % 10; memcpy(buffer, radix_100_table + 2 * (exp / 10), 2); buffer[2] = (char)('0' + c); buffer += 3; } else if (exp >= 10) { memcpy(buffer, radix_100_table + 2 * exp, 2); buffer += 2; } else { *buffer = (char)('0' + exp); ++buffer; } } else { if (exp >= 10) { memcpy(buffer, radix_100_table + 2 * exp, 2); buffer += 2; } else { *buffer = (char)('0' + exp); ++buffer; } } return buffer; } char* float_to_chars(unsigned_fp_t v, char* buffer) { return fp_to_chars_impl(v, buffer); } char* double_to_chars(unsigned_fp_t v, char* buffer) { return fp_to_chars_impl(v, buffer); } } } dragonbox-master/subproject/3rdparty/grisu_exact/grisu_exact.h0000664000175000017500000030120515060737600023740 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_GRISU_EXACT #define JKJ_GRISU_EXACT //#include // We don't have C++20 yet #include // Payload of NaN's is of type std::bitset #include #include // std::size_t, etc #include // std::uint32_t, etc. #include // std::memcpy; not needed if C++20 std::bit_cast is used instead #include #include // std::remove_cv, etc #if defined(_MSC_VER) #include #include // Suppress additional buffer overrun check // I have no idea why MSVC thinks some functions here are vulnerable to the buffer overrun attacks // No, they aren't. #ifndef __clang__ #define JKJ_SAFEBUFFERS __declspec(safebuffers) #else #define JKJ_SAFEBUFFERS #endif #else #define JKJ_SAFEBUFFERS #endif namespace jkj { namespace grisu_exact_detail { //////////////////////////////////////////////////////////////////////////////////////// // Utilities for 128-bit arithmetic //////////////////////////////////////////////////////////////////////////////////////// // Get 128-bit result of multiplication of two 64-bit unsigned integers struct uint128 { uint128() = default; #if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__) unsigned __int128 internal_; constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept : internal_{ ((unsigned __int128)low) | (((unsigned __int128)high) << 64) } {} constexpr uint128(unsigned __int128 u) : internal_{ u } {} constexpr std::uint64_t high() const noexcept { return std::uint64_t(internal_ >> 64); } constexpr std::uint64_t low() const noexcept { return std::uint64_t(internal_); } #else std::uint64_t high_; std::uint64_t low_; constexpr uint128(std::uint64_t high, std::uint64_t low) noexcept : high_{ high }, low_{ low } {} constexpr std::uint64_t high() const noexcept { return high_; } constexpr std::uint64_t low() const noexcept { return low_; } #endif }; JKJ_SAFEBUFFERS inline uint128 umul128(std::uint64_t x, std::uint64_t y) noexcept { #if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__) return (unsigned __int128)(x) * (unsigned __int128)(y); #elif defined(_MSC_VER) && defined(_M_X64) uint128 result; result.low_ = _umul128(x, y, &result.high_); return result; #else constexpr auto mask = (std::uint64_t(1) << 32) - std::uint64_t(1); auto a = x >> 32; auto b = x & mask; auto c = y >> 32; auto d = y & mask; auto ac = a * c; auto bc = b * c; auto ad = a * d; auto bd = b * d; auto intermediate = (bd >> 32) + (ad & mask) + (bc & mask); return{ ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), (intermediate << 32) + (bd & mask) }; #endif } JKJ_SAFEBUFFERS inline std::uint64_t umul128_upper64(std::uint64_t x, std::uint64_t y) noexcept { #if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__) auto p = (unsigned __int128)(x) * (unsigned __int128)(y); return std::uint64_t(p >> 64); #elif defined(_MSC_VER) && defined(_M_X64) return __umulh(x, y); #else constexpr auto mask = (std::uint64_t(1) << 32) - std::uint64_t(1); auto a = x >> 32; auto b = x & mask; auto c = y >> 32; auto d = y & mask; auto ac = a * c; auto bc = b * c; auto ad = a * d; auto bd = b * d; auto intermediate = (bd >> 32) + (ad & mask) + (bc & mask); return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); #endif } // Get upper 64-bits of multiplication of a 64-bit unsigned integer and a 128-bit unsigned integer JKJ_SAFEBUFFERS inline std::uint64_t umul192_upper64(std::uint64_t x, uint128 y) noexcept { auto g0 = umul128(x, y.high()); auto g10 = umul128_upper64(x, y.low()); #if (defined(__GNUC__) || defined(__clang__)) && defined(__SIZEOF_INT128__) && defined(__x86_64__) return uint128{ g0.internal_ + g10 }.high(); #elif defined(_MSC_VER) && defined(_M_X64) std::uint64_t high, low; auto carry = _addcarry_u64(0, g0.low(), g10, &low); _addcarry_u64(carry, g0.high(), 0, &high); return high; #else auto intermediate = g0.low() + g10; return g0.high() + (intermediate < g10); #endif } // Get upper 32-bits of multiplication of a 32-bit unsigned integer and a 64-bit unsigned integer inline std::uint32_t umul96_upper32(std::uint32_t x, std::uint64_t y) noexcept { return std::uint32_t(umul128_upper64(x, y)); } // Compute b^e in compile-time template constexpr UInt compute_power(UInt b, unsigned int e) noexcept { UInt r = 1; for (unsigned int i = 0; i < e; ++i) { r *= b; } return r; } // Check if a number is a multiple of 2^exp template inline bool divisible_by_power_of_2(UInt x, int exp) noexcept { static_assert(std::is_same_v || std::is_same_v); assert(exp >= 1); assert(x != 0); #if (defined(__GNUC__) || defined(__clang__)) && defined(__x86_64__) int index; if constexpr (std::is_same_v) { if constexpr (sizeof(unsigned long) == 4) { index = __builtin_ctzl((unsigned long)x); } else { static_assert(sizeof(unsigned int) == 4, "jkj::grisu_exact: at least one of unsigned int and unsigned long should be 4 bytes long"); index = __builtin_ctz((unsigned int)x); } } else { static_assert(sizeof(unsigned long long) == 8, "jkj::grisu_exact: unsigned long long should be 8 bytes long"); index = __builtin_ctzll((unsigned long long)x); } return index >= exp; #elif defined(_MSC_VER) && defined(_M_X64) unsigned long index; if constexpr (std::is_same_v) { _BitScanForward(&index, x); } else { _BitScanForward64(&index, x); } return int(index) >= exp; #else if (exp >= int(sizeof(UInt) * 8)) { return false; } return x == ((x >> exp) << exp); #endif } // Check if a number is a multiple of 5^exp // Use the algorithm introduced in Section 9 of Granlund-Montgomery template constexpr UInt compute_modular_inverse_of_5() noexcept { // Use Euler's theorem // phi(p^k) = p^(k-1) * (p-1), so phi(2^n) = 2^(n-1). // Hence, we need to compute 5^(2^(n-1) - 1), which is equal to // 5^1 * 5^2 * 5^4 * 5^8 * ... * 5^(2^(n-2)), // which can be computed as: constexpr unsigned int n = std::numeric_limits::digits; UInt r = 5; for (unsigned int e = 1; e <= n - 2; ++e) { r = 5 * r * r; } return r; } template struct divisibility_test_table_entry { UInt max_quotient; UInt mod_inv; }; // std::array might be an overkill template struct divisibility_test_table { static constexpr auto size = N; divisibility_test_table_entry value[N]; }; template constexpr auto generate_divisibility_test_table() noexcept { using return_type = divisibility_test_table; return_type table{}; for (unsigned int i = 0; i < size; ++i) { table.value[i].max_quotient = std::numeric_limits::max() / compute_power(UInt(5), i); table.value[i].mod_inv = compute_power(compute_modular_inverse_of_5(), i); } return table; } template struct divisibility_test_table_holder { static constexpr auto table = generate_divisibility_test_table ? 12 : 24>(); }; template constexpr bool divisible_by_power_of_5(UInt x, unsigned int exp) noexcept { assert(exp < divisibility_test_table_holder::table.size); auto const& entry = divisibility_test_table_holder::table.value[exp]; return (x * entry.mod_inv) <= entry.max_quotient; } //////////////////////////////////////////////////////////////////////////////////////// // Fast and accurate log floor calculation //////////////////////////////////////////////////////////////////////////////////////// // This function is accurate if e is in the range [-1650,1650] template constexpr int floor_log10_pow2(int e) noexcept { if constexpr (should_assert) { assert(e >= -1650 && e <= 1650); } // The next 12 digits are 0xd27 constexpr std::int32_t log10_2_up_to_20 = 0x4d104; return int( // Calculate 0x0.4d104 * exp * 2^20 (std::int32_t(e) * log10_2_up_to_20) // Perform arithmetic-shift >> 20); } // This function is accurate if e is in the range [-642,642] template constexpr int floor_log2_pow10(int e) noexcept { if constexpr (should_assert) { assert(e >= -642 && e <= 642); } // The next 12 digits are 0x12f constexpr std::int32_t log2_5_over_4_up_to_20 = 0x35269e; return int( // Calculate 0x3.5269e * exp * 2^20 (std::int32_t(e) * log2_5_over_4_up_to_20) // Perform arithmetic-shift >> 20); } // This function is accurate if e is in the range [-65536,+65536] // This function is only executed at compile-time, // and never executed at runtime. template constexpr int floor_log5_pow2(int e) noexcept { if constexpr (should_assert) { assert(e >= -65536 && e <= 65536); } // The next 32 digits are 0x143dcb94 constexpr std::uint32_t log5_2_up_to_32 = 0x6e40d1a4; return int( // Calculate 0x0.6e40d1a4 * exp * 2^32 (std::int64_t(e) * log5_2_up_to_32) // Perform arithmetic-shift >> 32); } //////////////////////////////////////////////////////////////////////////////////////// // Collection of relevent information about IEEE-754 and precision settings //////////////////////////////////////////////////////////////////////////////////////// template struct common_info { using float_type = Float; static_assert(std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2 && (sizeof(Float) == 4 || sizeof(Float) == 8), "Grisu-Exact algorithm only applies to IEEE-754 binary32 and binary64 formats!"); static constexpr std::size_t precision = std::numeric_limits::digits - 1; using extended_significand_type = std::conditional_t< sizeof(Float) == 4, std::uint32_t, std::uint64_t>; static_assert(sizeof(extended_significand_type) == sizeof(Float)); static constexpr std::size_t extended_precision = sizeof(extended_significand_type) * std::numeric_limits::digits; static constexpr auto sign_bit_mask = (extended_significand_type(1) << (extended_precision - 1)); static constexpr std::size_t exponent_bits = extended_precision - precision - 1; static constexpr int exponent_bias = 1 - (1 << (exponent_bits - 1)); static constexpr auto exponent_bits_mask = ((extended_significand_type(1) << exponent_bits) - 1) << precision; static constexpr auto boundary_bit = (extended_significand_type(1) << (extended_precision - precision - 2)); static constexpr auto normal_interval_length = boundary_bit << 1; static constexpr auto edge_case_boundary_bit = boundary_bit >> 1; static constexpr int min_exponent = std::numeric_limits::min_exponent - int(extended_precision); static constexpr int max_exponent = std::numeric_limits::max_exponent - int(extended_precision); static_assert(min_exponent < 0 && max_exponent > 0 && -min_exponent >= max_exponent); static_assert(min_exponent == 1 + exponent_bias - int(extended_precision) + 1); static constexpr int alpha = sizeof(Float) == 4 ? -5 : -5; static constexpr int gamma = alpha + 3; static_assert(alpha >= -(int(extended_precision - precision) - 4) && gamma <= 0); static constexpr int min_kappa = -floor_log10_pow2(-(int(extended_precision - precision) - 3 + alpha)) - 1; static constexpr int max_kappa = -floor_log10_pow2(-(int(extended_precision) + gamma)) - 1; static_assert(0 <= min_kappa && min_kappa <= max_kappa); static constexpr int initial_kappa = sizeof(Float) == 4 ? 2 : 3; static_assert(min_kappa <= initial_kappa && initial_kappa <= max_kappa); // Ensure delta cannot overflow // delta is upper bounded by 2^(q-p-1+gamma), and // during the decreasing search, it would get multiplied by 10^(initial_kappa-min_kappa-1) static_assert(floor_log2_pow10(initial_kappa - min_kappa - 1) < 32 - int(extended_precision - precision - 1) - gamma); // Ensure 10^initial_kappa fits inside 32 bits static_assert(initial_kappa < floor_log10_pow2(32)); static constexpr int min_k = -floor_log10_pow2(max_exponent + 1 - alpha); static constexpr int max_k = -floor_log10_pow2(min_exponent + 1 - alpha); static constexpr std::size_t cache_precision = extended_precision * 2; using cache_entry_type = std::conditional_t< sizeof(Float) == 4, std::uint64_t, uint128>; static constexpr int integer_check_exponent_lower_bound_for_q_mp_m3 = floor_log5_pow2(-(int(extended_precision - precision) - 3 + alpha)) - (int(extended_precision - precision) - 3); static constexpr int integer_check_exponent_lower_bound_for_q_mp_m2 = floor_log5_pow2(-(int(extended_precision - precision) - 2 + alpha)) - (int(extended_precision - precision) - 2); static constexpr int integer_check_exponent_lower_bound_for_q_mp_m1 = floor_log5_pow2(-(int(extended_precision - precision) - 1 + alpha)) - (int(extended_precision - precision) - 1); static constexpr int integer_check_exponent_lower_bound_for_q_mp = floor_log5_pow2(-(int(extended_precision - precision) + alpha)) - (int(extended_precision - precision)); static constexpr int max_exponent_for_k_geq_0 = alpha + 2; static constexpr int max_exponent_for_k_geq_m1 = alpha + 5; static constexpr int integer_check_exponent_upper_bound_for_p_p2 = (alpha - 2) - floor_log2_pow10(-floor_log5_pow2(precision + 2) - 1); static constexpr int integer_check_exponent_upper_bound_for_p_p1 = (alpha - 2) - floor_log2_pow10(-floor_log5_pow2(precision + 1) - 1); // Ensure that fractional parts cannot vanish when exponent is the minimum static_assert(min_exponent < integer_check_exponent_lower_bound_for_q_mp_m3); static constexpr int zero_fractional_part_min_exponent_normal = floor_log5_pow2(-(int(extended_precision - precision) - 2 + alpha)) - (int(extended_precision - precision) - 2); static constexpr int zero_fractional_part_min_exponent_edge = floor_log5_pow2(-(int(extended_precision - precision) - 3 + alpha)) - (int(extended_precision - precision) - 3); static constexpr int zero_fractional_part_max_exponent_normal = alpha - 2 - floor_log2_pow10(-floor_log5_pow2(precision + 2) - 1); static constexpr int max_exponent_for_nonnegative_k = alpha + 2; static constexpr int zero_fractional_part_min_exponent_delta_normal = floor_log5_pow2(-(int(extended_precision - precision) - 1 + alpha)) - (int(extended_precision - precision) - 1); }; //////////////////////////////////////////////////////////////////////////////////////// // Computed cache entries // !! You SHOULD regenerate the cache if you modify alpha and gamma !! //////////////////////////////////////////////////////////////////////////////////////// template struct cache_holder; template <> struct cache_holder { static constexpr std::uint64_t cache[] = { 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f, 0xfd87b5f28300ca0e, 0x9e74d1b791e07e49, 0xc612062576589ddb, 0xf79687aed3eec552, 0x9abe14cd44753b53, 0xc16d9a0095928a28, 0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb, 0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a, 0xe69594bec44de15c, 0x901d7cf73ab0acda, 0xb424dc35095cd810, 0xe12e13424bb40e14, 0x8cbccc096f5088cc, 0xafebff0bcb24aaff, 0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd, 0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424, 0xd1b71758e219652c, 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b, 0xcccccccccccccccd, 0x8000000000000000, 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000, 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000, 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000, 0x9184e72a00000000, 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000, 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, 0xad78ebc5ac620000, 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, 0xd3c21bcecceda100, 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984, 0xa18f07d736b90be5, 0xc9f2c9cd04674ede, 0xfc6f7c4045812296, 0x9dc5ada82b70b59d, 0xc5371912364ce305, 0xf684df56c3e01bc6, 0x9a130b963a6c115c, 0xc097ce7bc90715b3, 0xf0bdc21abb48db20, 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd, 0x92efd1b8d0cf37be, 0xb7abc627050305ad, 0xe596b7b0c643c719, 0x8f7e32ce7bea5c6f, 0xb35dbf821ae4f38b, 0xe0352f62a19e306e }; }; template <> struct cache_holder { static constexpr uint128 cache[] = { { 0xc795830d75038c1d, 0xd59df5b9ef6a2418 }, { 0xf97ae3d0d2446f25, 0x4b0573286b44ad1e }, { 0x9becce62836ac577, 0x4ee367f9430aec33 }, { 0xc2e801fb244576d5, 0x229c41f793cda740 }, { 0xf3a20279ed56d48a, 0x6b43527578c11110 }, { 0x9845418c345644d6, 0x830a13896b78aaaa }, { 0xbe5691ef416bd60c, 0x23cc986bc656d554 }, { 0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9 }, { 0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa }, { 0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54 }, { 0xe858ad248f5c22c9, 0xd1b3400f8f9cff69 }, { 0x91376c36d99995be, 0x23100809b9c21fa2 }, { 0xb58547448ffffb2d, 0xabd40a0c2832a78b }, { 0xe2e69915b3fff9f9, 0x16c90c8f323f516d }, { 0x8dd01fad907ffc3b, 0xae3da7d97f6792e4 }, { 0xb1442798f49ffb4a, 0x99cd11cfdf41779d }, { 0xdd95317f31c7fa1d, 0x40405643d711d584 }, { 0x8a7d3eef7f1cfc52, 0x482835ea666b2573 }, { 0xad1c8eab5ee43b66, 0xda3243650005eed0 }, { 0xd863b256369d4a40, 0x90bed43e40076a83 }, { 0x873e4f75e2224e68, 0x5a7744a6e804a292 }, { 0xa90de3535aaae202, 0x711515d0a205cb37 }, { 0xd3515c2831559a83, 0x0d5a5b44ca873e04 }, { 0x8412d9991ed58091, 0xe858790afe9486c3 }, { 0xa5178fff668ae0b6, 0x626e974dbe39a873 }, { 0xce5d73ff402d98e3, 0xfb0a3d212dc81290 }, { 0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a }, { 0xa139029f6a239f72, 0x1c1fffc1ebc44e81 }, { 0xc987434744ac874e, 0xa327ffb266b56221 }, { 0xfbe9141915d7a922, 0x4bf1ff9f0062baa9 }, { 0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa }, { 0xc4ce17b399107c22, 0xcb550fb4384d21d4 }, { 0xf6019da07f549b2b, 0x7e2a53a146606a49 }, { 0x99c102844f94e0fb, 0x2eda7444cbfc426e }, { 0xc0314325637a1939, 0xfa911155fefb5309 }, { 0xf03d93eebc589f88, 0x793555ab7eba27cb }, { 0x96267c7535b763b5, 0x4bc1558b2f3458df }, { 0xbbb01b9283253ca2, 0x9eb1aaedfb016f17 }, { 0xea9c227723ee8bcb, 0x465e15a979c1cadd }, { 0x92a1958a7675175f, 0x0bfacd89ec191eca }, { 0xb749faed14125d36, 0xcef980ec671f667c }, { 0xe51c79a85916f484, 0x82b7e12780e7401b }, { 0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811 }, { 0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16 }, { 0xdfbdcece67006ac9, 0x67a791e093e1d49b }, { 0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1 }, { 0xaecc49914078536d, 0x58fae9f773886e19 }, { 0xda7f5bf590966848, 0xaf39a475506a899f }, { 0x888f99797a5e012d, 0x6d8406c952429604 }, { 0xaab37fd7d8f58178, 0xc8e5087ba6d33b84 }, { 0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65 }, { 0x855c3be0a17fcd26, 0x5cf2eea09a550680 }, { 0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f }, { 0xd0601d8efc57b08b, 0xf13b94daf124da27 }, { 0x823c12795db6ce57, 0x76c53d08d6b70859 }, { 0xa2cb1717b52481ed, 0x54768c4b0c64ca6f }, { 0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a }, { 0xfe5d54150b090b02, 0xd3f93b35435d7c4d }, { 0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0 }, { 0xc6b8e9b0709f109a, 0x359ab6419ca1091c }, { 0xf867241c8cc6d4c0, 0xc30163d203c94b63 }, { 0x9b407691d7fc44f8, 0x79e0de63425dcf1e }, { 0xc21094364dfb5636, 0x985915fc12f542e5 }, { 0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e }, { 0x979cf3ca6cec5b5a, 0xa705992ceecf9c43 }, { 0xbd8430bd08277231, 0x50c6ff782a838354 }, { 0xece53cec4a314ebd, 0xa4f8bf5635246429 }, { 0x940f4613ae5ed136, 0x871b7795e136be9a }, { 0xb913179899f68584, 0x28e2557b59846e40 }, { 0xe757dd7ec07426e5, 0x331aeada2fe589d0 }, { 0x9096ea6f3848984f, 0x3ff0d2c85def7622 }, { 0xb4bca50b065abe63, 0x0fed077a756b53aa }, { 0xe1ebce4dc7f16dfb, 0xd3e8495912c62895 }, { 0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d }, { 0xb080392cc4349dec, 0xbd8d794d96aacfb4 }, { 0xdca04777f541c567, 0xecf0d7a0fc5583a1 }, { 0x89e42caaf9491b60, 0xf41686c49db57245 }, { 0xac5d37d5b79b6239, 0x311c2875c522ced6 }, { 0xd77485cb25823ac7, 0x7d633293366b828c }, { 0x86a8d39ef77164bc, 0xae5dff9c02033198 }, { 0xa8530886b54dbdeb, 0xd9f57f830283fdfd }, { 0xd267caa862a12d66, 0xd072df63c324fd7c }, { 0x8380dea93da4bc60, 0x4247cb9e59f71e6e }, { 0xa46116538d0deb78, 0x52d9be85f074e609 }, { 0xcd795be870516656, 0x67902e276c921f8c }, { 0x806bd9714632dff6, 0x00ba1cd8a3db53b7 }, { 0xa086cfcd97bf97f3, 0x80e8a40eccd228a5 }, { 0xc8a883c0fdaf7df0, 0x6122cd128006b2ce }, { 0xfad2a4b13d1b5d6c, 0x796b805720085f82 }, { 0x9cc3a6eec6311a63, 0xcbe3303674053bb1 }, { 0xc3f490aa77bd60fc, 0xbedbfc4411068a9d }, { 0xf4f1b4d515acb93b, 0xee92fb5515482d45 }, { 0x991711052d8bf3c5, 0x751bdd152d4d1c4b }, { 0xbf5cd54678eef0b6, 0xd262d45a78a0635e }, { 0xef340a98172aace4, 0x86fb897116c87c35 }, { 0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1 }, { 0xbae0a846d2195712, 0x8974836059cca10a }, { 0xe998d258869facd7, 0x2bd1a438703fc94c }, { 0x91ff83775423cc06, 0x7b6306a34627ddd0 }, { 0xb67f6455292cbf08, 0x1a3bc84c17b1d543 }, { 0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94 }, { 0x8e938662882af53e, 0x547eb47b7282ee9d }, { 0xb23867fb2a35b28d, 0xe99e619a4f23aa44 }, { 0xdec681f9f4c31f31, 0x6405fa00e2ec94d5 }, { 0x8b3c113c38f9f37e, 0xde83bc408dd3dd05 }, { 0xae0b158b4738705e, 0x9624ab50b148d446 }, { 0xd98ddaee19068c76, 0x3badd624dd9b0958 }, { 0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7 }, { 0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d }, { 0xd47487cc8470652b, 0x7647c32000696720 }, { 0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074 }, { 0xa5fb0a17c777cf09, 0xf468107100525891 }, { 0xcf79cc9db955c2cc, 0x7182148d4066eeb5 }, { 0x81ac1fe293d599bf, 0xc6f14cd848405531 }, { 0xa21727db38cb002f, 0xb8ada00e5a506a7d }, { 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0x0a862f80ec4700c8 }, { 0xf4a642e14c6262c8, 0xcd27bb612758c0fa }, { 0x98e7e9cccfbd7dbd, 0x8038d51cb897789c }, { 0xbf21e44003acdd2c, 0xe0470a63e6bd56c3 }, { 0xeeea5d5004981478, 0x1858ccfce06cac74 }, { 0x95527a5202df0ccb, 0x0f37801e0c43ebc8 }, { 0xbaa718e68396cffd, 0xd30560258f54e6ba }, { 0xe950df20247c83fd, 0x47c6b82ef32a2069 }, { 0x91d28b7416cdd27e, 0x4cdc331d57fa5441 }, { 0xb6472e511c81471d, 0xe0133fe4adf8e952 }, { 0xe3d8f9e563a198e5, 0x58180fddd97723a6 }, { 0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648 }, { 0xb201833b35d63f73, 0x2cd2cc6551e513da }, { 0xde81e40a034bcf4f, 0xf8077f7ea65e58d1 }, { 0x8b112e86420f6191, 0xfb04afaf27faf782 }, { 0xadd57a27d29339f6, 0x79c5db9af1f9b563 }, { 0xd94ad8b1c7380874, 0x18375281ae7822bc }, { 0x87cec76f1c830548, 0x8f2293910d0b15b5 }, { 0xa9c2794ae3a3c69a, 0xb2eb3875504ddb22 }, { 0xd433179d9c8cb841, 0x5fa60692a46151eb }, { 0x849feec281d7f328, 0xdbc7c41ba6bcd333 }, { 0xa5c7ea73224deff3, 0x12b9b522906c0800 }, { 0xcf39e50feae16bef, 0xd768226b34870a00 }, { 0x81842f29f2cce375, 0xe6a1158300d46640 }, { 0xa1e53af46f801c53, 0x60495ae3c1097fd0 }, { 0xca5e89b18b602368, 0x385bb19cb14bdfc4 }, { 0xfcf62c1dee382c42, 0x46729e03dd9ed7b5 }, { 0x9e19db92b4e31ba9, 0x6c07a2c26a8346d1 }, { 0xc5a05277621be293, 0xc7098b7305241885 } }; }; template constexpr typename common_info::cache_entry_type const& get_cache(int k) noexcept { assert(k >= common_info::min_k && k <= common_info::max_k); return cache_holder::cache[std::size_t(k - common_info::min_k)]; } // Forward declaration of the main class template struct grisu_exact_impl; } //////////////////////////////////////////////////////////////////////////////////////// // DIY floating-point data type //////////////////////////////////////////////////////////////////////////////////////// template struct fp_t; template struct fp_t { using extended_significand_type = typename grisu_exact_detail::common_info::extended_significand_type; extended_significand_type significand; int exponent; }; template struct fp_t { using extended_significand_type = typename grisu_exact_detail::common_info::extended_significand_type; extended_significand_type significand; int exponent; bool is_negative; }; template using unsigned_fp_t = fp_t; template using signed_fp_t = fp_t; // In order to reduce the argument passing overhead, // this class should be as simple as possible. // (e.g., no inheritance, no private non-static data member, etc.; // this is an unfortunate fact about x64 calling convention.) template struct bit_representation_t { private: using common_info = grisu_exact_detail::common_info; static constexpr auto precision = common_info::precision; static constexpr auto extended_precision = common_info::extended_precision; static constexpr auto sign_bit_mask = common_info::sign_bit_mask; static constexpr auto exponent_bits = common_info::exponent_bits; static constexpr auto exponent_bias = common_info::exponent_bias; static constexpr auto exponent_bits_mask = common_info::exponent_bits_mask; public: using extended_significand_type = typename common_info::extended_significand_type; extended_significand_type f; //// Inspector methods Float as_ieee754() const noexcept { Float x; std::memcpy(&x, &f, sizeof(Float)); return x; } constexpr extended_significand_type extract_significand_bits() const noexcept { constexpr auto significand_bits_mask = (extended_significand_type(1) << precision) - 1; return f & significand_bits_mask; } constexpr std::uint32_t extract_exponent_bits() const noexcept { constexpr auto exponent_bits_mask = (std::uint32_t(1) << exponent_bits) - 1; return std::uint32_t(f >> precision) & exponent_bits_mask; } constexpr bool is_finite() const noexcept { return (f & exponent_bits_mask) != exponent_bits_mask; } constexpr bool is_nonzero() const noexcept { // vs (f & ~sign_bit_mask) != 0; // It seems that there is no AND instruction for 64-bit immediate value in x86, // thus (f & ~sign_bit_mask) != 0 generates 3 instructions (load, and, compare), // while this generates only two (shift, compare). return (f << 1) != 0; } // Allows positive and negative zeros constexpr bool is_subnormal() const noexcept { return (f & exponent_bits_mask) == 0; } // Allows negative zero and negative NaN's, but not allow positive zero constexpr bool is_negative() const noexcept { // vs (f & sign_bit_mask) != 0; // It seems that there is no AND instruction for 64-bit immediate value in x86, // thus (f & sign_bit_mask) != 0 generates 3 instructions (load, and, compare), // while this generates only two (shift, compare). return (f >> (extended_precision - 1)) != 0; } // Allows positive zero and positive NaN's, but not allow negative zero constexpr bool is_positive() const noexcept { // vs (f & sign_bit_mask) == 0; // Ditto return (f >> (extended_precision - 1)) == 0; } constexpr bool is_positive_infinity() const noexcept { constexpr auto positive_infinity = exponent_bits_mask; return f == positive_infinity; } constexpr bool is_negative_infinity() const noexcept { constexpr auto negative_infinity = exponent_bits_mask | sign_bit_mask; return f == negative_infinity; } // Allows both plus and minus infinities constexpr bool is_infinity() const noexcept { return is_positive_infinity() || is_negative_infinity(); } constexpr bool is_nan() const noexcept { return !is_finite() && (extract_significand_bits() != 0); } bool is_quiet_nan() const noexcept { if (!is_nan()) { return false; } auto quiet_or_signal_indicator = extended_significand_type(1) << (precision - 1); auto quiet_or_signal = f & quiet_or_signal_indicator; constexpr auto a_quiet_nan = std::numeric_limits::quiet_NaN(); extended_significand_type a_quiet_nan_bit_representation; std::memcpy(&a_quiet_nan_bit_representation, &a_quiet_nan, sizeof(Float)); return (a_quiet_nan_bit_representation & quiet_or_signal_indicator) == quiet_or_signal; } bool is_signaling_nan() const noexcept { return is_nan() && !is_quiet_nan(); } static constexpr std::size_t nan_payload_length = precision - 1; std::bitset get_nan_payload() const noexcept { constexpr auto payload_mask = (extended_significand_type(1) << (precision - 1)) - 1; return{ f & payload_mask }; } }; template bit_representation_t get_bit_representation(Float x) noexcept { bit_representation_t br; std::memcpy(&br.f, &x, sizeof(Float)); return br; } // Determine what to do about the correct rounding guarantee namespace grisu_exact_correct_rounding { enum tag_t { do_not_care_tag, tie_to_even_tag, tie_to_odd_tag, tie_to_up_tag, tie_to_down_tag }; // Do not perform correct rounding search struct do_not_care { static constexpr tag_t tag = do_not_care_tag; template fp_t delegate(bit_representation_t br, IntervalTypeProvider&&) const { return grisu_exact_detail::grisu_exact_impl::template compute>, do_not_care>(br); } }; // Perform correct rounding search; tie-to-even struct tie_to_even { static constexpr tag_t tag = tie_to_even_tag; template fp_t delegate(bit_representation_t br, IntervalTypeProvider&&) const { return grisu_exact_detail::grisu_exact_impl::template compute>, tie_to_even>(br); } }; // Perform correct rounding search; tie-to-odd struct tie_to_odd { static constexpr tag_t tag = tie_to_odd_tag; template fp_t delegate(bit_representation_t br, IntervalTypeProvider&&) const { return grisu_exact_detail::grisu_exact_impl::template compute>, tie_to_odd>(br); } }; // Perform correct rounding search; tie-to-up struct tie_to_up { static constexpr tag_t tag = tie_to_up_tag; template fp_t delegate(bit_representation_t br, IntervalTypeProvider&&) const { return grisu_exact_detail::grisu_exact_impl::template compute>, tie_to_up>(br); } }; // Perform correct rounding search; tie-to-down struct tie_to_down { static constexpr tag_t tag = tie_to_down_tag; template fp_t delegate(bit_representation_t br, IntervalTypeProvider&&) const { return grisu_exact_detail::grisu_exact_impl::template compute>, tie_to_down>(br); } }; } // Dispatch to the appropriate operator() overloading of grisu_exact_impl namespace grisu_exact_rounding_modes { enum tag_t { to_nearest_tag, left_closed_directed_tag, right_closed_directed_tag }; namespace interval_type { struct symmetric_boundary { static constexpr bool is_symmetric = true; bool is_closed; constexpr bool include_left_endpoint() const noexcept { return is_closed; } constexpr bool include_right_endpoint() const noexcept { return is_closed; } }; struct asymmetric_boundary { static constexpr bool is_symmetric = false; bool is_left_closed; constexpr bool include_left_endpoint() const noexcept { return is_left_closed; } constexpr bool include_right_endpoint() const noexcept { return !is_left_closed; } }; struct closed { static constexpr bool is_symmetric = true; static constexpr bool include_left_endpoint() noexcept { return true; } static constexpr bool include_right_endpoint() noexcept { return true; } }; struct open { static constexpr bool is_symmetric = true; static constexpr bool include_left_endpoint() noexcept { return false; } static constexpr bool include_right_endpoint() noexcept { return false; } }; struct left_closed_right_open { static constexpr bool is_symmetric = false; static constexpr bool include_left_endpoint() noexcept { return true; } static constexpr bool include_right_endpoint() noexcept { return false; } }; struct right_closed_left_open { static constexpr bool is_symmetric = false; static constexpr bool include_left_endpoint() noexcept { return false; } static constexpr bool include_right_endpoint() noexcept { return true; } }; } struct nearest_to_even { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::symmetric_boundary operator()(bit_representation_t br) const noexcept { return{ br.f % 2 == 0 }; } }; struct nearest_to_odd { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::symmetric_boundary operator()(bit_representation_t br) const noexcept { return{ br.f % 2 != 0 }; } }; struct nearest_toward_plus_infinity { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::asymmetric_boundary operator()(bit_representation_t br) const noexcept { return{ !br.is_negative() }; } }; struct nearest_toward_minus_infinity { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::asymmetric_boundary operator()(bit_representation_t br) const noexcept { return{ br.is_negative() }; } }; // This may generate the fastest code among nearest rounding modes struct nearest_toward_zero { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::right_closed_left_open operator()(bit_representation_t) const noexcept { return{}; } }; struct nearest_away_from_zero { static constexpr tag_t tag = to_nearest_tag; template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, *this); } template constexpr interval_type::left_closed_right_open operator()(bit_representation_t) const noexcept { return{}; } }; namespace detail { struct nearest_always_closed { static constexpr tag_t tag = to_nearest_tag; template constexpr interval_type::closed operator()(bit_representation_t) const noexcept { return{}; } }; struct nearest_always_open { static constexpr tag_t tag = to_nearest_tag; template constexpr interval_type::open operator()(bit_representation_t) const noexcept { return{}; } }; } // Same as nearest_to_even, but generate separate codes for // different boundary conditions; may produce faster (or slower) code, but bigger binary struct nearest_to_even_static_boundary { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.f % 2 == 0) { return std::forward(crs).template delegate( br, detail::nearest_always_closed{}); } else { return std::forward(crs).template delegate( br, detail::nearest_always_open{}); } } }; // Same as nearest_to_odd, but generate separate codes for // different boundary conditions; may produce faster (or slower) code, but bigger binary struct nearest_to_odd_static_boundary { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.f % 2 == 0) { return std::forward(crs).template delegate( br, detail::nearest_always_open{}); } else { return std::forward(crs).template delegate( br, detail::nearest_always_closed{}); } } }; // Same as nearest_toward_plus_infinity, but generate separate codes for // different boundary conditions; may produce faster (or slower) code, but bigger binary struct nearest_toward_plus_infinity_static_boundary { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.is_negative()) { return std::forward(crs).template delegate( br, nearest_toward_zero{}); } else { return std::forward(crs).template delegate( br, nearest_away_from_zero{}); } } }; // Same as nearest_toward_minus_infinity, but generate separate codes for // different boundary conditions; may produce faster (or slower) code, but bigger binary struct nearest_toward_minus_infinity_static_boundary { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.is_negative()) { return std::forward(crs).template delegate( br, nearest_away_from_zero{}); } else { return std::forward(crs).template delegate( br, nearest_toward_zero{}); } } }; namespace detail { struct left_closed_directed { static constexpr tag_t tag = left_closed_directed_tag; template constexpr interval_type::left_closed_right_open operator()(bit_representation_t) const noexcept { return{}; } }; struct right_closed_directed { static constexpr tag_t tag = right_closed_directed_tag; template constexpr interval_type::right_closed_left_open operator()(bit_representation_t) const noexcept { return{}; } }; } struct toward_plus_infinity { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.is_negative()) { return std::forward(crs).template delegate( br, detail::left_closed_directed{}); } else { return std::forward(crs).template delegate( br, detail::right_closed_directed{}); } } }; struct toward_minus_infinity { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { if (br.is_negative()) { return std::forward(crs).template delegate( br, detail::right_closed_directed{}); } else { return std::forward(crs).template delegate( br, detail::left_closed_directed{}); } } }; struct toward_zero { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, detail::left_closed_directed{}); } }; struct away_from_zero { template fp_t delegate(bit_representation_t br, CorrectRoundingSearch&& crs) const { return std::forward(crs).template delegate( br, detail::right_closed_directed{}); } }; } namespace grisu_exact_detail { //////////////////////////////////////////////////////////////////////////////////////// // The main algorithm //////////////////////////////////////////////////////////////////////////////////////// // Get sign/decimal significand/decimal exponent from // the bit representation of a floating-point number template struct grisu_exact_impl : private common_info { using extended_significand_type = typename common_info::extended_significand_type; using cache_entry_type = typename common_info::cache_entry_type; using common_info::precision; using common_info::extended_precision; using common_info::cache_precision; using common_info::sign_bit_mask; using common_info::exponent_bits; using common_info::exponent_bias; using common_info::exponent_bits_mask; using common_info::min_exponent; using common_info::boundary_bit; using common_info::normal_interval_length; using common_info::edge_case_boundary_bit; using common_info::alpha; using common_info::gamma; using common_info::min_kappa; using common_info::max_kappa; using common_info::initial_kappa; using common_info::integer_check_exponent_lower_bound_for_q_mp_m3; using common_info::integer_check_exponent_lower_bound_for_q_mp_m2; using common_info::integer_check_exponent_lower_bound_for_q_mp_m1; using common_info::integer_check_exponent_lower_bound_for_q_mp; using common_info::max_exponent_for_k_geq_0; using common_info::max_exponent_for_k_geq_m1; using common_info::integer_check_exponent_upper_bound_for_p_p2; using common_info::integer_check_exponent_upper_bound_for_p_p1; template static constexpr extended_significand_type power_of_10 = compute_power(extended_significand_type(10), e); //// The main algorithm assumes the input is a normal/subnormal finite number template JKJ_SAFEBUFFERS static fp_t compute(bit_representation_t br) noexcept { ////////////////////////////////////////////////////////////////////// // Step 1: integer promotion & Grisu multiplier calculation ////////////////////////////////////////////////////////////////////// fp_t ret_value; auto interval_type = IntervalTypeProvider{}(br); if constexpr (return_sign) { ret_value.is_negative = br.is_negative(); } auto significand = br.f << exponent_bits; auto exponent = int((br.f >> precision) & (exponent_bits_mask >> precision)); // Deal with normal/subnormal dichotomy if (exponent != 0) { significand |= sign_bit_mask; exponent = exponent + exponent_bias - int(extended_precision) + 1; } else { exponent = min_exponent; } // Compute the endpoints extended_significand_type fr; // For nearest rounding if constexpr (IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag) { fr = significand | boundary_bit; } // For left-closed directed rounding else if constexpr (IntervalTypeProvider::tag == grisu_exact_rounding_modes::left_closed_directed_tag) { fr = significand + normal_interval_length; } // For right-closed directed rounding else { fr = significand; } // Compute k and beta int const minus_k = floor_log10_pow2(exponent + 1 - alpha); int const minus_beta = -(exponent + floor_log2_pow10(-minus_k) + 1); assert(-minus_beta >= alpha && -minus_beta <= gamma); // Compute zi and deltai auto const cache = jkj::grisu_exact_detail::get_cache(-minus_k); extended_significand_type zi; if constexpr (IntervalTypeProvider::tag == grisu_exact_rounding_modes::left_closed_directed_tag) { // Take care of the case when overflow occurs if (fr == 0) { if constexpr (sizeof(Float) == 4) { zi = extended_significand_type(cache >> extended_precision >> minus_beta); } else { zi = cache.high() >> minus_beta; } } else { zi = compute_mul(fr, cache, minus_beta); } } else { zi = compute_mul(fr, cache, minus_beta); } auto deltai = compute_delta( significand == sign_bit_mask && exponent != min_exponent, cache, minus_beta); ////////////////////////////////////////////////////////////////////// // Step 2: Search for kappa ////////////////////////////////////////////////////////////////////// // Comparison of fractional parts is delayed auto zf_vs_deltaf = zf_vs_deltaf_t::not_compared_yet; // Compute s and r for initial kappa extended_significand_type divisor; ret_value.significand = zi / power_of_10; auto r = zi % power_of_10; ret_value.exponent = initial_kappa + minus_k; // We've got too much? or too less? if (r < deltai) { goto increasing_search_label; } else if (r == deltai) { if (is_zf_smaller_than_deltaf(significand, minus_beta, cache, interval_type, exponent, minus_k)) { zf_vs_deltaf = zf_vs_deltaf_t::zf_smaller; goto increasing_search_label; } zf_vs_deltaf = zf_vs_deltaf_t::zf_larger; } // Perform decreasing search // In the paper, we calculate 10^(kappa0 - kappa) * r_(kappa - lambda) instead of // r_(kappa-lambda), and 10^(kappa0 - kappa) * deltai instead of deltai, and // 10^kappa0 instead of 10^kappa, so that the search procedure can be iterated. // However, in this implementation we will not iterate decreasing search and // the search will be performed only once. Hence, we do not need to do that. { // This procedure strictly depends on our specific choice of these parameters: static_assert(initial_kappa - min_kappa <= 2); constexpr unsigned int lambda = 1; // We already know r < 10^initial_kappa < 2^32 auto const quotient = std::uint32_t(r) / std::uint32_t(power_of_10); auto const new_r = std::uint32_t(r) % std::uint32_t(power_of_10); // Check if the remainder is still greater than or equal to the delta // remainder should be strictly greater if the left boundary is contained if (new_r < deltai) { goto decrease_kappa_by_1_label; } else if (new_r == deltai) { // zf_vs_deltaf cannot be zf_smaller here if (zf_vs_deltaf == zf_vs_deltaf_t::not_compared_yet) { if (is_zf_smaller_than_deltaf(significand, minus_beta, cache, interval_type, exponent, minus_k)) { zf_vs_deltaf = zf_vs_deltaf_t::zf_smaller; goto decrease_kappa_by_1_label; } zf_vs_deltaf = zf_vs_deltaf_t::zf_larger; } } // Decrease kappa by 1 + lambda (lambda = 1) if constexpr (initial_kappa == 2) { // kappa = 0 ret_value.significand = zi; r = 0; } else { static_assert(initial_kappa == 3); // kappa = 1 ret_value.significand *= 100; ret_value.significand += 10 * quotient + (std::uint32_t(new_r) / 10); r = std::uint32_t(new_r) % 10; } ret_value.exponent -= 2; divisor = power_of_10; // Since kappa is already the smallest possible value, // we do not need to search for kappa' // (But still need to get away from the boundary for certain cases) if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag) { // For binary32 case, kappa == 0 case requires a separate correct rounding search if constexpr (min_kappa == 0) { goto correct_rounding_search_when_kappa_is_0_label; } else { goto correct_rounding_search_label; } } else { goto boundary_adjustment_label; } decrease_kappa_by_1_label: // Decrease kappa by 1 ret_value.significand *= 10; ret_value.significand += quotient; r = new_r; --ret_value.exponent; divisor = power_of_10; goto boundary_adjustment_label; } increasing_search_label: // Perform binary search divisor = power_of_10; if constexpr (sizeof(Float) == 4) { // This procedure strictly depends on our specific choice of these parameters: static_assert(max_kappa - initial_kappa < 8); increasing_search<4, IntervalTypeProvider::tag, true>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); increasing_search<2, IntervalTypeProvider::tag, false>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); increasing_search<1, IntervalTypeProvider::tag, false>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); } else { // This procedure strictly depends on our specific choice of these parameters: static_assert(max_kappa - initial_kappa < 16); increasing_search<8, IntervalTypeProvider::tag, true>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); increasing_search<4, IntervalTypeProvider::tag, false>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); increasing_search<2, IntervalTypeProvider::tag, false>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); increasing_search<1, IntervalTypeProvider::tag, false>(ret_value, interval_type, zf_vs_deltaf, exponent, minus_k, minus_beta, significand, r, divisor, deltai, cache); } ////////////////////////////////////////////////////////////////////// // Step 3: Dealing with the right endpoint (search for kappa') ////////////////////////////////////////////////////////////////////// boundary_adjustment_label: // If right endpoint is not included, we should check if z mod 10^kappa = 0 if (!interval_type.include_right_endpoint() && r == 0) { constexpr integer_check_case_id case_id = IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag ? integer_check_case_id::fc_pm_2_to_the_q_mp_m2_generic : integer_check_case_id::other; if (is_product_integer(fr, exponent, minus_k)) { // Decrease kappa until 10^kappa becomes smaller than delta // If left boundary is included, 10^kappa can also be equal to delta while (true) { if (divisor < deltai) { break; } else if (divisor == deltai) { // For nearest rounding only if constexpr (IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag) { // We need to decrease kappa if // (1) The left boundary is not included, and // (2) delta is exactly equal to 10^kappa. // For symmetric boundary conditions, the first condition is // always true because we already have checked it, // and otherwise it is always false. // The second condition is true if and only if e = -(q-p-1). if constexpr (decltype(interval_type)::is_symmetric) { if (exponent == -int(extended_precision - precision - 1)) { ret_value.significand *= 10; divisor /= 10; --ret_value.exponent; } } } break; } ret_value.significand *= 10; divisor /= 10; --ret_value.exponent; } if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::do_not_care_tag || IntervalTypeProvider::tag != grisu_exact_rounding_modes::to_nearest_tag) { --ret_value.significand; } if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::left_closed_directed_tag) { r = divisor; } // For binary32 case, kappa == 0 case requires a separate correct rounding search if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag && min_kappa == 0) { if (ret_value.exponent == minus_k) { goto correct_rounding_search_when_kappa_is_0_label; } } } } ////////////////////////////////////////////////////////////////////// // Step 4: Correct rounding search ////////////////////////////////////////////////////////////////////// // Just to silence "unused label" warnings goto correct_rounding_search_label; correct_rounding_search_label: if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::left_closed_directed_tag) { // We already know r is at most deltai deltai -= std::uint32_t(r); auto const approx_x = zi - deltai; auto const current_digit = ret_value.significand % 10; // Perform binary search to find the minimum auto steps = current_digit / 2; while (steps != 0) { auto const displacement = steps * divisor; if (displacement > deltai) { steps /= 2; } else if (displacement == deltai) { // Compare fractional parts // If zf <= deltaf, we can move to the left // Otherwise, we should back off by 1 // The function is_zf_smaller_than_deltaf relies on // several assumptions that are not true here. // Hence, we need to do the comparison more carefully, // by comparing the parity of approx_x and xi. // x = (zi - deltai) + (zf - deltaf) switch (zf_vs_deltaf) { case zf_vs_deltaf_t::not_compared_yet: // zf >= deltaf ? if ((compute_mul(significand, cache, minus_beta) & 1) == (approx_x & 1)) { // zf > deltaf ? if (!equal_fractional_parts( significand, exponent, minus_k)) { --steps; } } break; case zf_vs_deltaf_t::zf_larger: --steps; break; case zf_vs_deltaf_t::zf_smaller: break; } goto return_label; } else { ret_value.significand -= steps; deltai -= std::uint32_t(displacement); } } } else if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag) { // Should treat the case kappa == 0 separately assert(ret_value.exponent != minus_k); // Distribution of n' with uniformly random data: // [binary32] // -1: 48.0% 0: 32.9% 1: 5.7% 2: 8.7% // 3: 3.9% 4: 0.9% // [binary64] // -1: 51.9% 0: 31.9% 1: 10.2% 2: 4.5% // 3: 1.4% 4: 0.1% 5: 0.0% auto const displacement = (divisor / 2) + r; auto epsiloni = compute_delta( false, cache, minus_beta + 1); // n' + 1 >= 1? if (displacement <= epsiloni) { auto const approx_y = zi - epsiloni; std::uint8_t steps; epsiloni -= std::uint32_t(displacement); // At this point, we can be sure that divisor should be // at most 1'000'000'000, because // epsiloni < 4'294'967'296 < 5'000'000'000 = (10'000'000'000 / 2) // and epsiloni >= divisor / 2. // Hence, 2 * divisor can fit inside std::uint32_t. auto const divisor32 = std::uint32_t(divisor); // n' + 1 >= 2? if (divisor32 <= epsiloni) { epsiloni -= divisor32; // n' + 1 >= 4? if (2 * divisor32 <= epsiloni) { epsiloni -= 2 * divisor32; // n' + 1 >= 5? if (divisor32 <= epsiloni) { epsiloni -= divisor32; // For binary32, this implies that n' should be 4 if constexpr (sizeof(Float) == 4) { steps = 5; } // For binary64, there are inputs such that // n' = 5, though extremely rare else { // n' + 1 = 6? if (divisor32 <= epsiloni) { epsiloni -= divisor32; steps = 6; } // n' + 1 = 5 else { steps = 5; } } } // n' + 1 = 4 else { steps = 4; } } // n' + 1 = 2 or 3 else { // n' + 1 = 3? if (divisor32 <= epsiloni) { epsiloni -= divisor32; steps = 3; } // n' + 1 = 2 else { steps = 2; } } } // n' + 1 = 1 else { steps = 1; } // Check fractional if necessary if (epsiloni == 0) { auto const yi = compute_mul(significand, cache, minus_beta); // We have either yi == approx_y or yi == approx_y - 1 if (yi == approx_y) { if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_even_tag || CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_odd_tag) { // Compare round-up vs round-down // round-up : steps - 1 // round-down: steps - 1 if !is_product_integer, steps otherwise // If they differ, that is, if is_product_integer, // then prefer even/odd if (is_product_integer(significand, exponent, minus_k)) { // steps vs steps - 1 if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_even_tag) { steps = (ret_value.significand & 1) != extended_significand_type(steps & 1) ? steps - 1 : steps; } else { steps = (ret_value.significand & 1) == extended_significand_type(steps & 1) ? steps - 1 : steps; } } else { --steps; } } else if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_up_tag) { --steps; } else { if (!is_product_integer(significand, exponent, minus_k)) { --steps; } } } } // The calculated steps might be too much if the left endpoint is closer than usual if (steps == 1 && significand == sign_bit_mask) { // We know already r is at most deltai deltai -= std::uint32_t(r); if (divisor > deltai) { goto return_label; } else if (divisor == deltai) { // See the test result of verify_incorrect_rounding_removal.cpp if constexpr (sizeof(Float) == 4) { if (exponent == 59) { goto return_label; } } else { if (exponent == -203) { goto return_label; } } } } ret_value.significand -= steps; } } goto return_label; // Just to silence "unused label" warnings goto correct_rounding_search_when_kappa_is_0_label; correct_rounding_search_when_kappa_is_0_label: if constexpr (CorrectRoundingSearch::tag != grisu_exact_correct_rounding::do_not_care_tag && IntervalTypeProvider::tag == grisu_exact_rounding_modes::to_nearest_tag && min_kappa == 0) { // (floor(2y) + 1) / 2 for tie-to-up, ceil(2y) / 2 for tie-to-down // First, compute floor(2y) auto two_yi = compute_mul(significand, cache, minus_beta - 1); if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_even_tag || CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_odd_tag) { // Compare round-up vs round-down // round-up : (two_yi + 1) / 2 // round-down: (two_yi + 1) / 2 if !is_prodict_integer, two_yi / 2 otherwise // If they can differ, that is, if is_product_integer, // then prefer even/odd if (is_product_integer( significand, exponent, minus_k)) { if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_even_tag) { ret_value.significand = (two_yi / 2) % 2 == 1 ? (two_yi + 1) / 2 : two_yi / 2; } else { ret_value.significand = (two_yi / 2) % 2 == 0 ? (two_yi + 1) / 2 : two_yi / 2; } } else { ret_value.significand = (two_yi + 1) / 2; } } else if constexpr (CorrectRoundingSearch::tag == grisu_exact_correct_rounding::tie_to_up_tag) { ret_value.significand = (two_yi + 1) / 2; } else { if (!is_product_integer( significand, exponent, minus_k)) { ++two_yi; } ret_value.significand = two_yi / 2; } } return_label: return ret_value; } static extended_significand_type compute_mul( extended_significand_type f, cache_entry_type const& cache, int minus_beta) noexcept { if constexpr (sizeof(Float) == 4) { return umul96_upper32(f, cache) >> minus_beta; } else { return umul192_upper64(f, cache) >> minus_beta; } } template static std::uint32_t compute_delta([[maybe_unused]] bool is_edge_case, cache_entry_type const& cache, int minus_beta) noexcept { constexpr auto q_mp_m1 = extended_precision - precision - 1; constexpr auto intermediate_precision = sizeof(Float) == 4 ? cache_precision : extended_precision; using intermediate_type = std::conditional_t; intermediate_type r; if constexpr (sizeof(Float) == 4) { r = cache; } else { r = cache.high(); } // For nearest rounding if constexpr (tag == grisu_exact_rounding_modes::to_nearest_tag) { if (is_edge_case) { r = (r >> 1) + (r >> 2); } return std::uint32_t(r >> (intermediate_precision - q_mp_m1 + minus_beta)); } // For left-directed rounding else if constexpr (tag == grisu_exact_rounding_modes::left_closed_directed_tag) { return std::uint32_t(r >> (intermediate_precision - q_mp_m1 + minus_beta)); } // For right-directed rounding else { if (is_edge_case) { return std::uint32_t(r >> (intermediate_precision - (q_mp_m1 - 1) + minus_beta)); } else { return std::uint32_t(r >> (intermediate_precision - q_mp_m1 + minus_beta)); } } } static bool is_zf_strictly_smaller_than_deltaf( extended_significand_type fl, int minus_beta, cache_entry_type const& cache) noexcept { auto mul = compute_mul(fl, cache, minus_beta); return (mul & 1) != 0; } enum class integer_check_case_id { fc_minus_2_to_the_q_mp_m3_edge, fc_pm_2_to_the_q_mp_m2_generic, fc_pm_2_to_the_q_mp_m2_edge, two_times_fc, other }; template static bool is_product_integer([[maybe_unused]] extended_significand_type f, int exponent, [[maybe_unused]] int minus_k) noexcept { // Case I: f = fc - 2^(q-p-3), Fw = 1 and Ew != Emin if constexpr (case_id == integer_check_case_id::fc_minus_2_to_the_q_mp_m3_edge) { return exponent >= integer_check_exponent_lower_bound_for_q_mp_m3 && exponent <= max_exponent_for_k_geq_0; } // Case II: f = fc +- 2^(q-p-2), generic case else if constexpr (case_id == integer_check_case_id::fc_pm_2_to_the_q_mp_m2_generic) { if (exponent < integer_check_exponent_lower_bound_for_q_mp_m2) { return false; } // For k >= 0 else if (exponent <= max_exponent_for_k_geq_0) { return true; } // For k < 0 else if (exponent <= integer_check_exponent_upper_bound_for_p_p2) { assert((sizeof(Float) == 4 && 1 <= minus_k && minus_k <= 10) || (sizeof(Float) == 8 && 1 <= minus_k && minus_k <= 23)); return divisible_by_power_of_5(f, minus_k); } else { return false; } } // Case III: f = fc - 2^(q-p-2), Fw = 1 and Ew != Emin else if constexpr (case_id == integer_check_case_id::fc_pm_2_to_the_q_mp_m2_edge) { // For IEEE-754 binary32 if constexpr (sizeof(Float) == 4) { return exponent >= integer_check_exponent_lower_bound_for_q_mp_m2 && exponent <= max_exponent_for_k_geq_m1; } // For IEEE-754 binary64 else { return exponent >= integer_check_exponent_lower_bound_for_q_mp_m2 && exponent <= max_exponent_for_k_geq_0; } } // Case IV or V or VI: f = fc or fc +- 2^(q-p-1) else { constexpr auto exp_2_upper_bound = case_id == integer_check_case_id::two_times_fc ? integer_check_exponent_lower_bound_for_q_mp : integer_check_exponent_lower_bound_for_q_mp_m1; // Exponent for 2 is negative if (exponent < exp_2_upper_bound) { auto exp_2 = minus_k - exponent; if constexpr (case_id == integer_check_case_id::two_times_fc) { --exp_2; } return divisible_by_power_of_2(f, exp_2); } // Both exponents for 2 and 5 are nonnegative else if (exponent <= max_exponent_for_k_geq_0) { return true; } // Exponent for 5 is negative else if (exponent <= integer_check_exponent_upper_bound_for_p_p1) { assert((sizeof(Float) == 4 && 1 <= minus_k && minus_k <= 10) || (sizeof(Float) == 8 && 1 <= minus_k && minus_k <= 22)); return divisible_by_power_of_5(f, minus_k); } else { return false; } } } enum class zf_vs_deltaf_t : std::uint8_t { not_compared_yet = 0, zf_larger = 1, zf_smaller = 2 }; template static bool equal_fractional_parts([[maybe_unused]] extended_significand_type fl, [[maybe_unused]] int exponent, [[maybe_unused]] int minus_k) noexcept { if constexpr (tag == grisu_exact_rounding_modes::to_nearest_tag) { // Generic case if (fl != (sign_bit_mask - edge_case_boundary_bit)) { return is_product_integer( fl, exponent, minus_k); } // Edge case else { return is_product_integer( fl, exponent, minus_k); } } // For left-closed directed rounding else if constexpr (tag == grisu_exact_rounding_modes::left_closed_directed_tag) { // Returns zf_smaller if zf = deltaf return is_product_integer( fl, exponent, minus_k); } // For right-closed directed rounding else { // Since left endpoint is always not included, // we do not actually have to call this function at all return false; } } template static bool is_zf_smaller_than_deltaf(extended_significand_type fc, int minus_beta, cache_entry_type const& cache, IntervalType& interval_type, int exponent, int minus_k) noexcept { // Compute fl extended_significand_type fl; if constexpr (tag == grisu_exact_rounding_modes::to_nearest_tag) { fl = (fc == sign_bit_mask && exponent != min_exponent) ? sign_bit_mask - edge_case_boundary_bit : fc - boundary_bit; } // For left-closed directed rounding else if constexpr (tag == grisu_exact_rounding_modes::left_closed_directed_tag) { fl = fc; } // For right-closed directed rounding else { fl = (fc == sign_bit_mask && exponent != min_exponent) ? sign_bit_mask - boundary_bit : fc - normal_interval_length; } return is_zf_strictly_smaller_than_deltaf(fl, minus_beta, cache) || (interval_type.include_left_endpoint() && equal_fractional_parts(fl, exponent, minus_k)); } // Perform binary search to find kappa upward // Returns true if kappa + lambda is a possible candidate template static bool increasing_search( fp_t& ret_value, IntervalType& interval_type, zf_vs_deltaf_t& zf_vs_deltaf, int exponent, int minus_k, int minus_beta, extended_significand_type fc, extended_significand_type& r, extended_significand_type& divisor, std::uint32_t deltai, cache_entry_type const& cache) noexcept { auto const quotient = ret_value.significand / power_of_10; auto const new_r = r + divisor * (ret_value.significand % power_of_10); // Check if delta is still greater than or equal to the remainder // delta should be strictly greater if the left boundary is not contained if (new_r > deltai) { return false; } else if (new_r == deltai) { if constexpr (is_initial_search) { // zf_vs_deltaf cannot be zf_larger here if (zf_vs_deltaf == zf_vs_deltaf_t::not_compared_yet) { if (!is_zf_smaller_than_deltaf(fc, minus_beta, cache, interval_type, exponent, minus_k)) { zf_vs_deltaf = zf_vs_deltaf_t::zf_larger; return false; } zf_vs_deltaf = zf_vs_deltaf_t::zf_smaller; } } else { switch (zf_vs_deltaf) { case zf_vs_deltaf_t::not_compared_yet: if (!is_zf_smaller_than_deltaf(fc, minus_beta, cache, interval_type, exponent, minus_k)) { zf_vs_deltaf = zf_vs_deltaf_t::zf_larger; return false; } zf_vs_deltaf = zf_vs_deltaf_t::zf_smaller; break; case zf_vs_deltaf_t::zf_larger: return false; case zf_vs_deltaf_t::zf_smaller: // Do nothing; just to silence the warning break; } } } // Update kappa ret_value.significand = quotient; ret_value.exponent += lambda; r = new_r; divisor *= power_of_10; return true; } }; } // What to do with non-finite inputs? namespace grisu_exact_case_handlers { struct assert_finite { template void operator()([[maybe_unused]] bit_representation_t br) const { assert(br.is_finite()); } }; // This policy is mainly for debugging purpose struct ignore_special_cases { template void operator()(bit_representation_t) const { } }; } template fp_t grisu_exact(Float x, RoundingMode&& rounding_mode = {}, CorrectRoundingSearch&& crs = {}, CaseHandler&& case_handler = {}) { auto br = get_bit_representation(x); case_handler(br); return std::forward(rounding_mode).template delegate( br, std::forward(crs)); } } #undef JKJ_SAFEBUFFERS #endif dragonbox-master/subproject/3rdparty/ryu/0000775000175000017500000000000015060737600017553 5ustar renerenedragonbox-master/subproject/3rdparty/ryu/CMakeLists.txt0000664000175000017500000000071415060737600022315 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(ryu_cmake LANGUAGES C) add_library(ryu STATIC ryu/ryu.h ryu/common.h ryu/f2s.c ryu/d2s.c ryu/f2s_intrinsics.h ryu/f2s_full_table.h ryu/d2s_intrinsics.h ryu/d2s_full_table.h ryu/digit_table.h) add_library(ryu::ryu ALIAS ryu) target_compile_features(ryu PUBLIC cxx_std_17) target_include_directories(ryu PUBLIC $) dragonbox-master/subproject/3rdparty/ryu/ryu/0000775000175000017500000000000015060737600020372 5ustar renerenedragonbox-master/subproject/3rdparty/ryu/ryu/d2s_intrinsics.h0000664000175000017500000003132715060737600023506 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_D2S_INTRINSICS_H #define RYU_D2S_INTRINSICS_H #include #include // Defines RYU_32_BIT_PLATFORM if applicable. #include "ryu/common.h" // ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined. // Let's do the same for now. #if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) #define HAS_UINT128 #elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64) #define HAS_64_BIT_INTRINSICS #endif #if defined(HAS_UINT128) typedef __uint128_t uint128_t; #endif #if defined(HAS_64_BIT_INTRINSICS) #include static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) { return _umul128(a, b, productHi); } // Returns the lower 64 bits of (hi*2^64 + lo) >> dist, with 0 < dist < 64. static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) { // For the __shiftright128 intrinsic, the shift value is always // modulo 64. // In the current implementation of the double-precision version // of Ryu, the shift value is always < 64. (In the case // RYU_OPTIMIZE_SIZE == 0, the shift value is in the range [49, 58]. // Otherwise in the range [2, 59].) // However, this function is now also called by s2d, which requires supporting // the larger shift range (TODO: what is the actual range?). // Check this here in case a future change requires larger shift // values. In this case this function needs to be adjusted. assert(dist < 64); return __shiftright128(lo, hi, (unsigned char) dist); } #else // defined(HAS_64_BIT_INTRINSICS) static inline uint64_t umul128(const uint64_t a, const uint64_t b, uint64_t* const productHi) { // The casts here help MSVC to avoid calls to the __allmul library function. const uint32_t aLo = (uint32_t)a; const uint32_t aHi = (uint32_t)(a >> 32); const uint32_t bLo = (uint32_t)b; const uint32_t bHi = (uint32_t)(b >> 32); const uint64_t b00 = (uint64_t)aLo * bLo; const uint64_t b01 = (uint64_t)aLo * bHi; const uint64_t b10 = (uint64_t)aHi * bLo; const uint64_t b11 = (uint64_t)aHi * bHi; const uint32_t b00Lo = (uint32_t)b00; const uint32_t b00Hi = (uint32_t)(b00 >> 32); const uint64_t mid1 = b10 + b00Hi; const uint32_t mid1Lo = (uint32_t)(mid1); const uint32_t mid1Hi = (uint32_t)(mid1 >> 32); const uint64_t mid2 = b01 + mid1Lo; const uint32_t mid2Lo = (uint32_t)(mid2); const uint32_t mid2Hi = (uint32_t)(mid2 >> 32); const uint64_t pHi = b11 + mid1Hi + mid2Hi; const uint64_t pLo = ((uint64_t)mid2Lo << 32) | b00Lo; *productHi = pHi; return pLo; } static inline uint64_t shiftright128(const uint64_t lo, const uint64_t hi, const uint32_t dist) { // We don't need to handle the case dist >= 64 here (see above). assert(dist < 64); assert(dist > 0); return (hi << (64 - dist)) | (lo >> dist); } #endif // defined(HAS_64_BIT_INTRINSICS) #if defined(RYU_32_BIT_PLATFORM) // Returns the high 64 bits of the 128-bit product of a and b. static inline uint64_t umulh(const uint64_t a, const uint64_t b) { // Reuse the umul128 implementation. // Optimizers will likely eliminate the instructions used to compute the // low part of the product. uint64_t hi; umul128(a, b, &hi); return hi; } // On 32-bit platforms, compilers typically generate calls to library // functions for 64-bit divisions, even if the divisor is a constant. // // E.g.: // https://bugs.llvm.org/show_bug.cgi?id=37932 // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958 // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443 // // The functions here perform division-by-constant using multiplications // in the same way as 64-bit compilers would do. // // NB: // The multipliers and shift values are the ones generated by clang x64 // for expressions like x/5, x/10, etc. static inline uint64_t div5(const uint64_t x) { return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 2; } static inline uint64_t div10(const uint64_t x) { return umulh(x, 0xCCCCCCCCCCCCCCCDu) >> 3; } static inline uint64_t div100(const uint64_t x) { return umulh(x >> 2, 0x28F5C28F5C28F5C3u) >> 2; } static inline uint64_t div1e8(const uint64_t x) { return umulh(x, 0xABCC77118461CEFDu) >> 26; } static inline uint64_t div1e9(const uint64_t x) { return umulh(x >> 9, 0x44B82FA09B5A53u) >> 11; } static inline uint32_t mod1e9(const uint64_t x) { // Avoid 64-bit math as much as possible. // Returning (uint32_t) (x - 1000000000 * div1e9(x)) would // perform 32x64-bit multiplication and 64-bit subtraction. // x and 1000000000 * div1e9(x) are guaranteed to differ by // less than 10^9, so their highest 32 bits must be identical, // so we can truncate both sides to uint32_t before subtracting. // We can also simplify (uint32_t) (1000000000 * div1e9(x)). // We can truncate before multiplying instead of after, as multiplying // the highest 32 bits of div1e9(x) can't affect the lowest 32 bits. return ((uint32_t) x) - 1000000000 * ((uint32_t) div1e9(x)); } #else // defined(RYU_32_BIT_PLATFORM) static inline uint64_t div5(const uint64_t x) { return x / 5; } static inline uint64_t div10(const uint64_t x) { return x / 10; } static inline uint64_t div100(const uint64_t x) { return x / 100; } static inline uint64_t div1e8(const uint64_t x) { return x / 100000000; } static inline uint64_t div1e9(const uint64_t x) { return x / 1000000000; } static inline uint32_t mod1e9(const uint64_t x) { return (uint32_t) (x - 1000000000 * div1e9(x)); } #endif // defined(RYU_32_BIT_PLATFORM) static inline uint32_t pow5Factor(uint64_t value) { const uint64_t m_inv_5 = 14757395258967641293u; // 5 * m_inv_5 = 1 (mod 2^64) const uint64_t n_div_5 = 3689348814741910323u; // #{ n | n = 0 (mod 2^64) } = 2^64 / 5 uint32_t count = 0; for (;;) { assert(value != 0); value *= m_inv_5; if (value > n_div_5) break; ++count; } return count; } // Returns true if value is divisible by 5^p. static inline bool multipleOfPowerOf5(const uint64_t value, const uint32_t p) { // I tried a case distinction on p, but there was no performance difference. return pow5Factor(value) >= p; } // Returns true if value is divisible by 2^p. static inline bool multipleOfPowerOf2(const uint64_t value, const uint32_t p) { assert(value != 0); assert(p < 64); // __builtin_ctzll doesn't appear to be faster here. return (value & ((1ull << p) - 1)) == 0; } // We need a 64x128-bit multiplication and a subsequent 128-bit shift. // Multiplication: // The 64-bit factor is variable and passed in, the 128-bit factor comes // from a lookup table. We know that the 64-bit factor only has 55 // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit // factor only has 124 significant bits (i.e., the 4 topmost bits are // zeros). // Shift: // In principle, the multiplication result requires 55 + 124 = 179 bits to // represent. However, we then shift this value to the right by j, which is // at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64 // bits. This means that we only need the topmost 64 significant bits of // the 64x128-bit multiplication. // // There are several ways to do this: // 1. Best case: the compiler exposes a 128-bit type. // We perform two 64x64-bit multiplications, add the higher 64 bits of the // lower result to the higher result, and shift by j - 64 bits. // // We explicitly cast from 64-bit to 128-bit, so the compiler can tell // that these are only 64-bit inputs, and can map these to the best // possible sequence of assembly instructions. // x64 machines happen to have matching assembly instructions for // 64x64-bit multiplications and 128-bit shifts. // // 2. Second best case: the compiler exposes intrinsics for the x64 assembly // instructions mentioned in 1. // // 3. We only have 64x64 bit instructions that return the lower 64 bits of // the result, i.e., we have to use plain C. // Our inputs are less than the full width, so we have three options: // a. Ignore this fact and just implement the intrinsics manually. // b. Split both into 31-bit pieces, which guarantees no internal overflow, // but requires extra work upfront (unless we change the lookup table). // c. Split only the first factor into 31-bit pieces, which also guarantees // no internal overflow, but requires extra work since the intermediate // results are not perfectly aligned. #if defined(HAS_UINT128) // Best case: use 128-bit type. static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) { const uint128_t b0 = ((uint128_t) m) * mul[0]; const uint128_t b2 = ((uint128_t) m) * mul[1]; return (uint64_t) (((b0 >> 64) + b2) >> (j - 64)); } static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j, uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) { // m <<= 2; // uint128_t b0 = ((uint128_t) m) * mul[0]; // 0 // uint128_t b2 = ((uint128_t) m) * mul[1]; // 64 // // uint128_t hi = (b0 >> 64) + b2; // uint128_t lo = b0 & 0xffffffffffffffffull; // uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0]; // uint128_t vpLo = lo + (factor << 1); // *vp = (uint64_t) ((hi + (vpLo >> 64)) >> (j - 64)); // uint128_t vmLo = lo - (factor << mmShift); // *vm = (uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64)); // return (uint64_t) (hi >> (j - 64)); *vp = mulShift64(4 * m + 2, mul, j); *vm = mulShift64(4 * m - 1 - mmShift, mul, j); return mulShift64(4 * m, mul, j); } #elif defined(HAS_64_BIT_INTRINSICS) static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) { // m is maximum 55 bits uint64_t high1; // 128 const uint64_t low1 = umul128(m, mul[1], &high1); // 64 uint64_t high0; // 64 umul128(m, mul[0], &high0); // 0 const uint64_t sum = high0 + low1; if (sum < high0) { ++high1; // overflow into high1 } return shiftright128(sum, high1, j - 64); } static inline uint64_t mulShiftAll64(const uint64_t m, const uint64_t* const mul, const int32_t j, uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) { *vp = mulShift64(4 * m + 2, mul, j); *vm = mulShift64(4 * m - 1 - mmShift, mul, j); return mulShift64(4 * m, mul, j); } #else // !defined(HAS_UINT128) && !defined(HAS_64_BIT_INTRINSICS) static inline uint64_t mulShift64(const uint64_t m, const uint64_t* const mul, const int32_t j) { // m is maximum 55 bits uint64_t high1; // 128 const uint64_t low1 = umul128(m, mul[1], &high1); // 64 uint64_t high0; // 64 umul128(m, mul[0], &high0); // 0 const uint64_t sum = high0 + low1; if (sum < high0) { ++high1; // overflow into high1 } return shiftright128(sum, high1, j - 64); } // This is faster if we don't have a 64x64->128-bit multiplication. static inline uint64_t mulShiftAll64(uint64_t m, const uint64_t* const mul, const int32_t j, uint64_t* const vp, uint64_t* const vm, const uint32_t mmShift) { m <<= 1; // m is maximum 55 bits uint64_t tmp; const uint64_t lo = umul128(m, mul[0], &tmp); uint64_t hi; const uint64_t mid = tmp + umul128(m, mul[1], &hi); hi += mid < tmp; // overflow into hi const uint64_t lo2 = lo + mul[0]; const uint64_t mid2 = mid + mul[1] + (lo2 < lo); const uint64_t hi2 = hi + (mid2 < mid); *vp = shiftright128(mid2, hi2, (uint32_t) (j - 64 - 1)); if (mmShift == 1) { const uint64_t lo3 = lo - mul[0]; const uint64_t mid3 = mid - mul[1] - (lo3 > lo); const uint64_t hi3 = hi - (mid3 > mid); *vm = shiftright128(mid3, hi3, (uint32_t) (j - 64 - 1)); } else { const uint64_t lo3 = lo + lo; const uint64_t mid3 = mid + mid + (lo3 < lo); const uint64_t hi3 = hi + hi + (mid3 < mid); const uint64_t lo4 = lo3 - mul[0]; const uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3); const uint64_t hi4 = hi3 - (mid4 > mid3); *vm = shiftright128(mid4, hi4, (uint32_t) (j - 64)); } return shiftright128(mid, hi, (uint32_t) (j - 64 - 1)); } #endif // HAS_64_BIT_INTRINSICS #endif // RYU_D2S_INTRINSICS_H dragonbox-master/subproject/3rdparty/ryu/ryu/ryu.h0000664000175000017500000000252015060737600021361 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_H #define RYU_H #ifdef __cplusplus extern "C" { #endif #include int d2s_buffered_n(double f, char* result); void d2s_buffered(double f, char* result); char* d2s(double f); int f2s_buffered_n(float f, char* result); void f2s_buffered(float f, char* result); char* f2s(float f); int d2fixed_buffered_n(double d, uint32_t precision, char* result); void d2fixed_buffered(double d, uint32_t precision, char* result); char* d2fixed(double d, uint32_t precision); int d2exp_buffered_n(double d, uint32_t precision, char* result); void d2exp_buffered(double d, uint32_t precision, char* result); char* d2exp(double d, uint32_t precision); #ifdef __cplusplus } #endif #endif // RYU_H dragonbox-master/subproject/3rdparty/ryu/ryu/digit_table.h0000664000175000017500000000332115060737600023011 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_DIGIT_TABLE_H #define RYU_DIGIT_TABLE_H // A table of all two-digit numbers. This is used to speed up decimal digit // generation by copying pairs of digits into the final output. static const char DIGIT_TABLE[200] = { '0','0','0','1','0','2','0','3','0','4','0','5','0','6','0','7','0','8','0','9', '1','0','1','1','1','2','1','3','1','4','1','5','1','6','1','7','1','8','1','9', '2','0','2','1','2','2','2','3','2','4','2','5','2','6','2','7','2','8','2','9', '3','0','3','1','3','2','3','3','3','4','3','5','3','6','3','7','3','8','3','9', '4','0','4','1','4','2','4','3','4','4','4','5','4','6','4','7','4','8','4','9', '5','0','5','1','5','2','5','3','5','4','5','5','5','6','5','7','5','8','5','9', '6','0','6','1','6','2','6','3','6','4','6','5','6','6','6','7','6','8','6','9', '7','0','7','1','7','2','7','3','7','4','7','5','7','6','7','7','7','8','7','9', '8','0','8','1','8','2','8','3','8','4','8','5','8','6','8','7','8','8','8','9', '9','0','9','1','9','2','9','3','9','4','9','5','9','6','9','7','9','8','9','9' }; #endif // RYU_DIGIT_TABLE_H dragonbox-master/subproject/3rdparty/ryu/ryu/f2s.c0000664000175000017500000002601715060737600021236 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. // Runtime compiler options: // -DRYU_DEBUG Generate verbose debugging output to stdout. #include "ryu/ryu.h" #include #include #include #include #include #include #ifdef RYU_DEBUG #include #endif #include "ryu/common.h" #include "ryu/f2s_intrinsics.h" #include "ryu/digit_table.h" #define FLOAT_MANTISSA_BITS 23 #define FLOAT_EXPONENT_BITS 8 #define FLOAT_BIAS 127 // A floating decimal representing m * 10^e. typedef struct floating_decimal_32 { uint32_t mantissa; // Decimal exponent's range is -45 to 38 // inclusive, and can fit in a short if needed. int32_t exponent; } floating_decimal_32; static inline floating_decimal_32 f2d(const uint32_t ieeeMantissa, const uint32_t ieeeExponent) { int32_t e2; uint32_t m2; if (ieeeExponent == 0) { // We subtract 2 so that the bounds computation has 2 additional bits. e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2; m2 = ieeeMantissa; } else { e2 = (int32_t) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2; m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa; } const bool even = (m2 & 1) == 0; const bool acceptBounds = even; #ifdef RYU_DEBUG printf("-> %u * 2^%d\n", m2, e2 + 2); #endif // Step 2: Determine the interval of valid decimal representations. const uint32_t mv = 4 * m2; const uint32_t mp = 4 * m2 + 2; // Implicit bool -> int conversion. True is 1, false is 0. const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1; const uint32_t mm = 4 * m2 - 1 - mmShift; // Step 3: Convert to a decimal power base using 64-bit arithmetic. uint32_t vr, vp, vm; int32_t e10; bool vmIsTrailingZeros = false; bool vrIsTrailingZeros = false; uint8_t lastRemovedDigit = 0; if (e2 >= 0) { const uint32_t q = log10Pow2(e2); e10 = (int32_t) q; const int32_t k = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1; const int32_t i = -e2 + (int32_t) q + k; vr = mulPow5InvDivPow2(mv, q, i); vp = mulPow5InvDivPow2(mp, q, i); vm = mulPow5InvDivPow2(mm, q, i); #ifdef RYU_DEBUG printf("%u * 2^%d / 10^%u\n", mv, e2, q); printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm); #endif if (q != 0 && (vp - 1) / 10 <= vm / 10) { // We need to know one removed digit even if we are not going to loop below. We could use // q = X - 1 above, except that would require 33 bits for the result, and we've found that // 32-bit arithmetic is faster even on 64-bit machines. const int32_t l = FLOAT_POW5_INV_BITCOUNT + pow5bits((int32_t) (q - 1)) - 1; lastRemovedDigit = (uint8_t) (mulPow5InvDivPow2(mv, q - 1, -e2 + (int32_t) q - 1 + l) % 10); } if (q <= 9) { // The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well. // Only one of mp, mv, and mm can be a multiple of 5, if any. if (mv % 5 == 0) { vrIsTrailingZeros = multipleOfPowerOf5_32(mv, q); } else if (acceptBounds) { vmIsTrailingZeros = multipleOfPowerOf5_32(mm, q); } else { vp -= multipleOfPowerOf5_32(mp, q); } } } else { const uint32_t q = log10Pow5(-e2); e10 = (int32_t) q + e2; const int32_t i = -e2 - (int32_t) q; const int32_t k = pow5bits(i) - FLOAT_POW5_BITCOUNT; int32_t j = (int32_t) q - k; vr = mulPow5divPow2(mv, (uint32_t) i, j); vp = mulPow5divPow2(mp, (uint32_t) i, j); vm = mulPow5divPow2(mm, (uint32_t) i, j); #ifdef RYU_DEBUG printf("%u * 5^%d / 10^%u\n", mv, -e2, q); printf("%u %d %d %d\n", q, i, k, j); printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm); #endif if (q != 0 && (vp - 1) / 10 <= vm / 10) { j = (int32_t) q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT); lastRemovedDigit = (uint8_t) (mulPow5divPow2(mv, (uint32_t) (i + 1), j) % 10); } if (q <= 1) { // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits. // mv = 4 * m2, so it always has at least two trailing 0 bits. vrIsTrailingZeros = true; if (acceptBounds) { // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1. vmIsTrailingZeros = mmShift == 1; } else { // mp = mv + 2, so it always has at least one trailing 0 bit. --vp; } } else if (q < 31) { // TODO(ulfjack): Use a tighter bound here. vrIsTrailingZeros = multipleOfPowerOf2_32(mv, q - 1); #ifdef RYU_DEBUG printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif } } #ifdef RYU_DEBUG printf("e10=%d\n", e10); printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm); printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // Step 4: Find the shortest decimal representation in the interval of valid representations. int32_t removed = 0; uint32_t output; if (vmIsTrailingZeros || vrIsTrailingZeros) { // General case, which happens rarely (~4.0%). while (vp / 10 > vm / 10) { #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=23106 // The compiler does not realize that vm % 10 can be computed from vm / 10 // as vm - (vm / 10) * 10. vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0; #else vmIsTrailingZeros &= vm % 10 == 0; #endif vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) (vr % 10); vr /= 10; vp /= 10; vm /= 10; ++removed; } #ifdef RYU_DEBUG printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm); printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false"); #endif if (vmIsTrailingZeros) { while (vm % 10 == 0) { vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) (vr % 10); vr /= 10; vp /= 10; vm /= 10; ++removed; } } #ifdef RYU_DEBUG printf("%u %d\n", vr, lastRemovedDigit); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) { // Round even if the exact number is .....50..0. lastRemovedDigit = 4; } // We need to take vr + 1 if vr is outside bounds or we need to round up. output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5); } else { // Specialized for the common case (~96.0%). Percentages below are relative to this. // Loop iterations below (approximately): // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01% while (vp / 10 > vm / 10) { lastRemovedDigit = (uint8_t) (vr % 10); vr /= 10; vp /= 10; vm /= 10; ++removed; } #ifdef RYU_DEBUG printf("%u %d\n", vr, lastRemovedDigit); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // We need to take vr + 1 if vr is outside bounds or we need to round up. output = vr + (vr == vm || lastRemovedDigit >= 5); } const int32_t exp = e10 + removed; #ifdef RYU_DEBUG printf("V+=%u\nV =%u\nV-=%u\n", vp, vr, vm); printf("O=%u\n", output); printf("EXP=%d\n", exp); #endif floating_decimal_32 fd; fd.exponent = exp; fd.mantissa = output; return fd; } static inline int to_chars(const floating_decimal_32 v, const bool sign, char* const result) { // Step 5: Print the decimal representation. int index = 0; if (sign) { result[index++] = '-'; } uint32_t output = v.mantissa; const uint32_t olength = decimalLength9(output); #ifdef RYU_DEBUG printf("DIGITS=%u\n", v.mantissa); printf("OLEN=%u\n", olength); printf("EXP=%u\n", v.exponent + olength); #endif // Print the decimal digits. // The following code is equivalent to: // for (uint32_t i = 0; i < olength - 1; ++i) { // const uint32_t c = output % 10; output /= 10; // result[index + olength - i] = (char) ('0' + c); // } // result[index] = '0' + output % 10; uint32_t i = 0; while (output >= 10000) { #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217 const uint32_t c = output - 10000 * (output / 10000); #else const uint32_t c = output % 10000; #endif output /= 10000; const uint32_t c0 = (c % 100) << 1; const uint32_t c1 = (c / 100) << 1; memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); i += 4; } if (output >= 100) { const uint32_t c = (output % 100) << 1; output /= 100; memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2); i += 2; } if (output >= 10) { const uint32_t c = output << 1; // We can't use memcpy here: the decimal dot goes between these two digits. result[index + olength - i] = DIGIT_TABLE[c + 1]; result[index] = DIGIT_TABLE[c]; } else { result[index] = (char) ('0' + output); } // Print decimal point if needed. if (olength > 1) { result[index + 1] = '.'; index += olength + 1; } else { ++index; } // Print the exponent. result[index++] = 'E'; int32_t exp = v.exponent + (int32_t) olength - 1; if (exp < 0) { result[index++] = '-'; exp = -exp; } if (exp >= 10) { memcpy(result + index, DIGIT_TABLE + 2 * exp, 2); index += 2; } else { result[index++] = (char) ('0' + exp); } return index; } int f2s_buffered_n(float f, char* result) { // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. const uint32_t bits = float_to_bits(f); #ifdef RYU_DEBUG printf("IN="); for (int32_t bit = 31; bit >= 0; --bit) { printf("%u", (bits >> bit) & 1); } printf("\n"); #endif // Decode bits into sign, mantissa, and exponent. const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0; const uint32_t ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1); const uint32_t ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1); // Case distinction; exit early for the easy cases. if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) { return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa); } const floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent); return to_chars(v, ieeeSign, result); } void f2s_buffered(float f, char* result) { const int index = f2s_buffered_n(f, result); // Terminate the string. result[index] = '\0'; } char* f2s(float f) { char* const result = (char*) malloc(16); f2s_buffered(f, result); return result; } dragonbox-master/subproject/3rdparty/ryu/ryu/d2s.c0000664000175000017500000004247115060737600021236 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. // Runtime compiler options: // -DRYU_DEBUG Generate verbose debugging output to stdout. // // -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower, // depending on your compiler. // // -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every // required power of 5, only store every 26th entry, and compute // intermediate values with a multiplication. This reduces the lookup table // size by about 10x (only one case, and only double) at the cost of some // performance. Currently requires MSVC intrinsics. #include "ryu/ryu.h" #include #include #include #include #include #ifdef RYU_DEBUG #include #include #endif #include "ryu/common.h" #include "ryu/digit_table.h" #include "ryu/d2s_intrinsics.h" // Include either the small or the full lookup tables depending on the mode. #if defined(RYU_OPTIMIZE_SIZE) #include "ryu/d2s_small_table.h" #else #include "ryu/d2s_full_table.h" #endif #define DOUBLE_MANTISSA_BITS 52 #define DOUBLE_EXPONENT_BITS 11 #define DOUBLE_BIAS 1023 static inline uint32_t decimalLength17(const uint64_t v) { // This is slightly faster than a loop. // The average output length is 16.38 digits, so we check high-to-low. // Function precondition: v is not an 18, 19, or 20-digit number. // (17 digits are sufficient for round-tripping.) assert(v < 100000000000000000L); if (v >= 10000000000000000L) { return 17; } if (v >= 1000000000000000L) { return 16; } if (v >= 100000000000000L) { return 15; } if (v >= 10000000000000L) { return 14; } if (v >= 1000000000000L) { return 13; } if (v >= 100000000000L) { return 12; } if (v >= 10000000000L) { return 11; } if (v >= 1000000000L) { return 10; } if (v >= 100000000L) { return 9; } if (v >= 10000000L) { return 8; } if (v >= 1000000L) { return 7; } if (v >= 100000L) { return 6; } if (v >= 10000L) { return 5; } if (v >= 1000L) { return 4; } if (v >= 100L) { return 3; } if (v >= 10L) { return 2; } return 1; } // A floating decimal representing m * 10^e. typedef struct floating_decimal_64 { uint64_t mantissa; // Decimal exponent's range is -324 to 308 // inclusive, and can fit in a short if needed. int32_t exponent; } floating_decimal_64; static inline floating_decimal_64 d2d(const uint64_t ieeeMantissa, const uint32_t ieeeExponent) { int32_t e2; uint64_t m2; if (ieeeExponent == 0) { // We subtract 2 so that the bounds computation has 2 additional bits. e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; m2 = ieeeMantissa; } else { e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2; m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa; } const bool even = (m2 & 1) == 0; const bool acceptBounds = even; #ifdef RYU_DEBUG printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2); #endif // Step 2: Determine the interval of valid decimal representations. const uint64_t mv = 4 * m2; // Implicit bool -> int conversion. True is 1, false is 0. const uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1; // We would compute mp and mm like this: // uint64_t mp = 4 * m2 + 2; // uint64_t mm = mv - 1 - mmShift; // Step 3: Convert to a decimal power base using 128-bit arithmetic. uint64_t vr, vp, vm; int32_t e10; bool vmIsTrailingZeros = false; bool vrIsTrailingZeros = false; if (e2 >= 0) { // I tried special-casing q == 0, but there was no effect on performance. // This expression is slightly faster than max(0, log10Pow2(e2) - 1). const uint32_t q = log10Pow2(e2) - (e2 > 3); e10 = (int32_t) q; const int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t) q) - 1; const int32_t i = -e2 + (int32_t) q + k; #if defined(RYU_OPTIMIZE_SIZE) uint64_t pow5[2]; double_computeInvPow5(q, pow5); vr = mulShiftAll64(m2, pow5, i, &vp, &vm, mmShift); #else vr = mulShiftAll64(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift); #endif #ifdef RYU_DEBUG printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); #endif if (q <= 21) { // This should use q <= 22, but I think 21 is also safe. Smaller values // may still be safe, but it's more difficult to reason about them. // Only one of mp, mv, and mm can be a multiple of 5, if any. const uint32_t mvMod5 = ((uint32_t) mv) - 5 * ((uint32_t) div5(mv)); if (mvMod5 == 0) { vrIsTrailingZeros = multipleOfPowerOf5(mv, q); } else if (acceptBounds) { // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q // <=> true && pow5Factor(mm) >= q, since e2 >= q. vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q); } else { // Same as min(e2 + 1, pow5Factor(mp)) >= q. vp -= multipleOfPowerOf5(mv + 2, q); } } } else { // This expression is slightly faster than max(0, log10Pow5(-e2) - 1). const uint32_t q = log10Pow5(-e2) - (-e2 > 1); e10 = (int32_t) q + e2; const int32_t i = -e2 - (int32_t) q; const int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT; const int32_t j = (int32_t) q - k; #if defined(RYU_OPTIMIZE_SIZE) uint64_t pow5[2]; double_computePow5(i, pow5); vr = mulShiftAll64(m2, pow5, j, &vp, &vm, mmShift); #else vr = mulShiftAll64(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift); #endif #ifdef RYU_DEBUG printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q); printf("%u %d %d %d\n", q, i, k, j); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); #endif if (q <= 1) { // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits. // mv = 4 * m2, so it always has at least two trailing 0 bits. vrIsTrailingZeros = true; if (acceptBounds) { // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1. vmIsTrailingZeros = mmShift == 1; } else { // mp = mv + 2, so it always has at least one trailing 0 bit. --vp; } } else if (q < 63) { // TODO(ulfjack): Use a tighter bound here. // We want to know if the full product has at least q trailing zeros. // We need to compute min(p2(mv), p5(mv) - e2) >= q // <=> p2(mv) >= q && p5(mv) - e2 >= q // <=> p2(mv) >= q (because -e2 >= q) vrIsTrailingZeros = multipleOfPowerOf2(mv, q); #ifdef RYU_DEBUG printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif } } #ifdef RYU_DEBUG printf("e10=%d\n", e10); printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // Step 4: Find the shortest decimal representation in the interval of valid representations. int32_t removed = 0; uint8_t lastRemovedDigit = 0; uint64_t output; // On average, we remove ~2 digits. if (vmIsTrailingZeros || vrIsTrailingZeros) { // General case, which happens rarely (~0.7%). for (;;) { const uint64_t vpDiv10 = div10(vp); const uint64_t vmDiv10 = div10(vm); if (vpDiv10 <= vmDiv10) { break; } const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); vmIsTrailingZeros &= vmMod10 == 0; vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) vrMod10; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } #ifdef RYU_DEBUG printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false"); #endif if (vmIsTrailingZeros) { for (;;) { const uint64_t vmDiv10 = div10(vm); const uint32_t vmMod10 = ((uint32_t) vm) - 10 * ((uint32_t) vmDiv10); if (vmMod10 != 0) { break; } const uint64_t vpDiv10 = div10(vp); const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = (uint8_t) vrMod10; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } } #ifdef RYU_DEBUG printf("%" PRIu64 " %d\n", vr, lastRemovedDigit); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) { // Round even if the exact number is .....50..0. lastRemovedDigit = 4; } // We need to take vr + 1 if vr is outside bounds or we need to round up. output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5); } else { // Specialized for the common case (~99.3%). Percentages below are relative to this. bool roundUp = false; const uint64_t vpDiv100 = div100(vp); const uint64_t vmDiv100 = div100(vm); if (vpDiv100 > vmDiv100) { // Optimization: remove two digits at a time (~86.2%). const uint64_t vrDiv100 = div100(vr); const uint32_t vrMod100 = ((uint32_t) vr) - 100 * ((uint32_t) vrDiv100); roundUp = vrMod100 >= 50; vr = vrDiv100; vp = vpDiv100; vm = vmDiv100; removed += 2; } // Loop iterations below (approximately), without optimization above: // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% // Loop iterations below (approximately), with optimization above: // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% for (;;) { const uint64_t vpDiv10 = div10(vp); const uint64_t vmDiv10 = div10(vm); if (vpDiv10 <= vmDiv10) { break; } const uint64_t vrDiv10 = div10(vr); const uint32_t vrMod10 = ((uint32_t) vr) - 10 * ((uint32_t) vrDiv10); roundUp = vrMod10 >= 5; vr = vrDiv10; vp = vpDiv10; vm = vmDiv10; ++removed; } #ifdef RYU_DEBUG printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // We need to take vr + 1 if vr is outside bounds or we need to round up. output = vr + (vr == vm || roundUp); } const int32_t exp = e10 + removed; #ifdef RYU_DEBUG printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm); printf("O=%" PRIu64 "\n", output); printf("EXP=%d\n", exp); #endif floating_decimal_64 fd; fd.exponent = exp; fd.mantissa = output; return fd; } static inline int to_chars(const floating_decimal_64 v, const bool sign, char* const result) { // Step 5: Print the decimal representation. int index = 0; if (sign) { result[index++] = '-'; } uint64_t output = v.mantissa; const uint32_t olength = decimalLength17(output); #ifdef RYU_DEBUG printf("DIGITS=%" PRIu64 "\n", v.mantissa); printf("OLEN=%u\n", olength); printf("EXP=%u\n", v.exponent + olength); #endif // Print the decimal digits. // The following code is equivalent to: // for (uint32_t i = 0; i < olength - 1; ++i) { // const uint32_t c = output % 10; output /= 10; // result[index + olength - i] = (char) ('0' + c); // } // result[index] = '0' + output % 10; uint32_t i = 0; // We prefer 32-bit operations, even on 64-bit platforms. // We have at most 17 digits, and uint32_t can store 9 digits. // If output doesn't fit into uint32_t, we cut off 8 digits, // so the rest will fit into uint32_t. if ((output >> 32) != 0) { // Expensive 64-bit division. const uint64_t q = div1e8(output); uint32_t output2 = ((uint32_t) output) - 100000000 * ((uint32_t) q); output = q; const uint32_t c = output2 % 10000; output2 /= 10000; const uint32_t d = output2 % 10000; const uint32_t c0 = (c % 100) << 1; const uint32_t c1 = (c / 100) << 1; const uint32_t d0 = (d % 100) << 1; const uint32_t d1 = (d / 100) << 1; memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2); memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2); i += 8; } uint32_t output2 = (uint32_t) output; while (output2 >= 10000) { #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217 const uint32_t c = output2 - 10000 * (output2 / 10000); #else const uint32_t c = output2 % 10000; #endif output2 /= 10000; const uint32_t c0 = (c % 100) << 1; const uint32_t c1 = (c / 100) << 1; memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); i += 4; } if (output2 >= 100) { const uint32_t c = (output2 % 100) << 1; output2 /= 100; memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2); i += 2; } if (output2 >= 10) { const uint32_t c = output2 << 1; // We can't use memcpy here: the decimal dot goes between these two digits. result[index + olength - i] = DIGIT_TABLE[c + 1]; result[index] = DIGIT_TABLE[c]; } else { result[index] = (char) ('0' + output2); } // Print decimal point if needed. if (olength > 1) { result[index + 1] = '.'; index += olength + 1; } else { ++index; } // Print the exponent. result[index++] = 'E'; int32_t exp = v.exponent + (int32_t) olength - 1; if (exp < 0) { result[index++] = '-'; exp = -exp; } if (exp >= 100) { const int32_t c = exp % 10; memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2); result[index + 2] = (char) ('0' + c); index += 3; } else if (exp >= 10) { memcpy(result + index, DIGIT_TABLE + 2 * exp, 2); index += 2; } else { result[index++] = (char) ('0' + exp); } return index; } static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent, floating_decimal_64* const v) { const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa; const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS; if (e2 > 0) { // f = m2 * 2^e2 >= 2^53 is an integer. // Ignore this case for now. return false; } if (e2 < -52) { // f < 1. return false; } // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53. // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0. const uint64_t mask = (1ull << -e2) - 1; const uint64_t fraction = m2 & mask; if (fraction != 0) { return false; } // f is an integer in the range [1, 2^53). // Note: mantissa might contain trailing (decimal) 0's. // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17(). v->mantissa = m2 >> -e2; v->exponent = 0; return true; } int d2s_buffered_n(double f, char* result) { // Step 1: Decode the floating-point number, and unify normalized and subnormal cases. const uint64_t bits = double_to_bits(f); #ifdef RYU_DEBUG printf("IN="); for (int32_t bit = 63; bit >= 0; --bit) { printf("%d", (int) ((bits >> bit) & 1)); } printf("\n"); #endif // Decode bits into sign, mantissa, and exponent. const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0; const uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1); const uint32_t ieeeExponent = (uint32_t) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1)); // Case distinction; exit early for the easy cases. if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) { return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa); } floating_decimal_64 v; const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v); if (isSmallInt) { // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros. // For scientific notation we need to move these zeros into the exponent. // (This is not needed for fixed-point notation, so it might be beneficial to trim // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.) for (;;) { const uint64_t q = div10(v.mantissa); const uint32_t r = ((uint32_t) v.mantissa) - 10 * ((uint32_t) q); if (r != 0) { break; } v.mantissa = q; ++v.exponent; } } else { v = d2d(ieeeMantissa, ieeeExponent); } return to_chars(v, ieeeSign, result); } void d2s_buffered(double f, char* result) { const int index = d2s_buffered_n(f, result); // Terminate the string. result[index] = '\0'; } char* d2s(double f) { char* const result = (char*) malloc(25); d2s_buffered(f, result); return result; } dragonbox-master/subproject/3rdparty/ryu/ryu/f2s_intrinsics.h0000664000175000017500000001030615060737600023502 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_F2S_INTRINSICS_H #define RYU_F2S_INTRINSICS_H // Defines RYU_32_BIT_PLATFORM if applicable. #include "ryu/common.h" #if defined(RYU_FLOAT_FULL_TABLE) #include "ryu/f2s_full_table.h" #else #if defined(RYU_OPTIMIZE_SIZE) #include "ryu/d2s_small_table.h" #else #include "ryu/d2s_full_table.h" #endif #define FLOAT_POW5_INV_BITCOUNT (DOUBLE_POW5_INV_BITCOUNT - 64) #define FLOAT_POW5_BITCOUNT (DOUBLE_POW5_BITCOUNT - 64) #endif static inline uint32_t pow5factor_32(uint32_t value) { uint32_t count = 0; for (;;) { assert(value != 0); const uint32_t q = value / 5; const uint32_t r = value % 5; if (r != 0) { break; } value = q; ++count; } return count; } // Returns true if value is divisible by 5^p. static inline bool multipleOfPowerOf5_32(const uint32_t value, const uint32_t p) { return pow5factor_32(value) >= p; } // Returns true if value is divisible by 2^p. static inline bool multipleOfPowerOf2_32(const uint32_t value, const uint32_t p) { // __builtin_ctz doesn't appear to be faster here. return (value & ((1u << p) - 1)) == 0; } // It seems to be slightly faster to avoid uint128_t here, although the // generated code for uint128_t looks slightly nicer. static inline uint32_t mulShift32(const uint32_t m, const uint64_t factor, const int32_t shift) { assert(shift > 32); // The casts here help MSVC to avoid calls to the __allmul library // function. const uint32_t factorLo = (uint32_t)(factor); const uint32_t factorHi = (uint32_t)(factor >> 32); const uint64_t bits0 = (uint64_t)m * factorLo; const uint64_t bits1 = (uint64_t)m * factorHi; #if defined(RYU_32_BIT_PLATFORM) // On 32-bit platforms we can avoid a 64-bit shift-right since we only // need the upper 32 bits of the result and the shift value is > 32. const uint32_t bits0Hi = (uint32_t)(bits0 >> 32); uint32_t bits1Lo = (uint32_t)(bits1); uint32_t bits1Hi = (uint32_t)(bits1 >> 32); bits1Lo += bits0Hi; bits1Hi += (bits1Lo < bits0Hi); if (shift >= 64) { // s2f can call this with a shift value >= 64, which we have to handle. // This could now be slower than the !defined(RYU_32_BIT_PLATFORM) case. return (uint32_t)(bits1Hi >> (shift - 64)); } else { const int32_t s = shift - 32; return (bits1Hi << (32 - s)) | (bits1Lo >> s); } #else // RYU_32_BIT_PLATFORM const uint64_t sum = (bits0 >> 32) + bits1; const uint64_t shiftedSum = sum >> (shift - 32); assert(shiftedSum <= UINT32_MAX); return (uint32_t) shiftedSum; #endif // RYU_32_BIT_PLATFORM } static inline uint32_t mulPow5InvDivPow2(const uint32_t m, const uint32_t q, const int32_t j) { #if defined(RYU_FLOAT_FULL_TABLE) return mulShift32(m, FLOAT_POW5_INV_SPLIT[q], j); #elif defined(RYU_OPTIMIZE_SIZE) // The inverse multipliers are defined as [2^x / 5^y] + 1; the upper 64 bits from the double lookup // table are the correct bits for [2^x / 5^y], so we have to add 1 here. Note that we rely on the // fact that the added 1 that's already stored in the table never overflows into the upper 64 bits. uint64_t pow5[2]; double_computeInvPow5(q, pow5); return mulShift32(m, pow5[1] + 1, j); #else return mulShift32(m, DOUBLE_POW5_INV_SPLIT[q][1] + 1, j); #endif } static inline uint32_t mulPow5divPow2(const uint32_t m, const uint32_t i, const int32_t j) { #if defined(RYU_FLOAT_FULL_TABLE) return mulShift32(m, FLOAT_POW5_SPLIT[i], j); #elif defined(RYU_OPTIMIZE_SIZE) uint64_t pow5[2]; double_computePow5(i, pow5); return mulShift32(m, pow5[1], j); #else return mulShift32(m, DOUBLE_POW5_SPLIT[i][1], j); #endif } #endif // RYU_F2S_INTRINSICS_H dragonbox-master/subproject/3rdparty/ryu/ryu/d2s_full_table.h0000664000175000017500000010330515060737600023426 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_D2S_FULL_TABLE_H #define RYU_D2S_FULL_TABLE_H // These tables are generated by PrintDoubleLookupTable. #define DOUBLE_POW5_INV_BITCOUNT 125 #define DOUBLE_POW5_BITCOUNT 125 #define DOUBLE_POW5_INV_TABLE_SIZE 342 #define DOUBLE_POW5_TABLE_SIZE 326 static const uint64_t DOUBLE_POW5_INV_SPLIT[DOUBLE_POW5_INV_TABLE_SIZE][2] = { { 1u, 2305843009213693952u }, { 11068046444225730970u, 1844674407370955161u }, { 5165088340638674453u, 1475739525896764129u }, { 7821419487252849886u, 1180591620717411303u }, { 8824922364862649494u, 1888946593147858085u }, { 7059937891890119595u, 1511157274518286468u }, { 13026647942995916322u, 1208925819614629174u }, { 9774590264567735146u, 1934281311383406679u }, { 11509021026396098440u, 1547425049106725343u }, { 16585914450600699399u, 1237940039285380274u }, { 15469416676735388068u, 1980704062856608439u }, { 16064882156130220778u, 1584563250285286751u }, { 9162556910162266299u, 1267650600228229401u }, { 7281393426775805432u, 2028240960365167042u }, { 16893161185646375315u, 1622592768292133633u }, { 2446482504291369283u, 1298074214633706907u }, { 7603720821608101175u, 2076918743413931051u }, { 2393627842544570617u, 1661534994731144841u }, { 16672297533003297786u, 1329227995784915872u }, { 11918280793837635165u, 2126764793255865396u }, { 5845275820328197809u, 1701411834604692317u }, { 15744267100488289217u, 1361129467683753853u }, { 3054734472329800808u, 2177807148294006166u }, { 17201182836831481939u, 1742245718635204932u }, { 6382248639981364905u, 1393796574908163946u }, { 2832900194486363201u, 2230074519853062314u }, { 5955668970331000884u, 1784059615882449851u }, { 1075186361522890384u, 1427247692705959881u }, { 12788344622662355584u, 2283596308329535809u }, { 13920024512871794791u, 1826877046663628647u }, { 3757321980813615186u, 1461501637330902918u }, { 10384555214134712795u, 1169201309864722334u }, { 5547241898389809503u, 1870722095783555735u }, { 4437793518711847602u, 1496577676626844588u }, { 10928932444453298728u, 1197262141301475670u }, { 17486291911125277965u, 1915619426082361072u }, { 6610335899416401726u, 1532495540865888858u }, { 12666966349016942027u, 1225996432692711086u }, { 12888448528943286597u, 1961594292308337738u }, { 17689456452638449924u, 1569275433846670190u }, { 14151565162110759939u, 1255420347077336152u }, { 7885109000409574610u, 2008672555323737844u }, { 9997436015069570011u, 1606938044258990275u }, { 7997948812055656009u, 1285550435407192220u }, { 12796718099289049614u, 2056880696651507552u }, { 2858676849947419045u, 1645504557321206042u }, { 13354987924183666206u, 1316403645856964833u }, { 17678631863951955605u, 2106245833371143733u }, { 3074859046935833515u, 1684996666696914987u }, { 13527933681774397782u, 1347997333357531989u }, { 10576647446613305481u, 2156795733372051183u }, { 15840015586774465031u, 1725436586697640946u }, { 8982663654677661702u, 1380349269358112757u }, { 18061610662226169046u, 2208558830972980411u }, { 10759939715039024913u, 1766847064778384329u }, { 12297300586773130254u, 1413477651822707463u }, { 15986332124095098083u, 2261564242916331941u }, { 9099716884534168143u, 1809251394333065553u }, { 14658471137111155161u, 1447401115466452442u }, { 4348079280205103483u, 1157920892373161954u }, { 14335624477811986218u, 1852673427797059126u }, { 7779150767507678651u, 1482138742237647301u }, { 2533971799264232598u, 1185710993790117841u }, { 15122401323048503126u, 1897137590064188545u }, { 12097921058438802501u, 1517710072051350836u }, { 5988988032009131678u, 1214168057641080669u }, { 16961078480698431330u, 1942668892225729070u }, { 13568862784558745064u, 1554135113780583256u }, { 7165741412905085728u, 1243308091024466605u }, { 11465186260648137165u, 1989292945639146568u }, { 16550846638002330379u, 1591434356511317254u }, { 16930026125143774626u, 1273147485209053803u }, { 4951948911778577463u, 2037035976334486086u }, { 272210314680951647u, 1629628781067588869u }, { 3907117066486671641u, 1303703024854071095u }, { 6251387306378674625u, 2085924839766513752u }, { 16069156289328670670u, 1668739871813211001u }, { 9165976216721026213u, 1334991897450568801u }, { 7286864317269821294u, 2135987035920910082u }, { 16897537898041588005u, 1708789628736728065u }, { 13518030318433270404u, 1367031702989382452u }, { 6871453250525591353u, 2187250724783011924u }, { 9186511415162383406u, 1749800579826409539u }, { 11038557946871817048u, 1399840463861127631u }, { 10282995085511086630u, 2239744742177804210u }, { 8226396068408869304u, 1791795793742243368u }, { 13959814484210916090u, 1433436634993794694u }, { 11267656730511734774u, 2293498615990071511u }, { 5324776569667477496u, 1834798892792057209u }, { 7949170070475892320u, 1467839114233645767u }, { 17427382500606444826u, 1174271291386916613u }, { 5747719112518849781u, 1878834066219066582u }, { 15666221734240810795u, 1503067252975253265u }, { 12532977387392648636u, 1202453802380202612u }, { 5295368560860596524u, 1923926083808324180u }, { 4236294848688477220u, 1539140867046659344u }, { 7078384693692692099u, 1231312693637327475u }, { 11325415509908307358u, 1970100309819723960u }, { 9060332407926645887u, 1576080247855779168u }, { 14626963555825137356u, 1260864198284623334u }, { 12335095245094488799u, 2017382717255397335u }, { 9868076196075591040u, 1613906173804317868u }, { 15273158586344293478u, 1291124939043454294u }, { 13369007293925138595u, 2065799902469526871u }, { 7005857020398200553u, 1652639921975621497u }, { 16672732060544291412u, 1322111937580497197u }, { 11918976037903224966u, 2115379100128795516u }, { 5845832015580669650u, 1692303280103036413u }, { 12055363241948356366u, 1353842624082429130u }, { 841837113407818570u, 2166148198531886609u }, { 4362818505468165179u, 1732918558825509287u }, { 14558301248600263113u, 1386334847060407429u }, { 12225235553534690011u, 2218135755296651887u }, { 2401490813343931363u, 1774508604237321510u }, { 1921192650675145090u, 1419606883389857208u }, { 17831303500047873437u, 2271371013423771532u }, { 6886345170554478103u, 1817096810739017226u }, { 1819727321701672159u, 1453677448591213781u }, { 16213177116328979020u, 1162941958872971024u }, { 14873036941900635463u, 1860707134196753639u }, { 15587778368262418694u, 1488565707357402911u }, { 8780873879868024632u, 1190852565885922329u }, { 2981351763563108441u, 1905364105417475727u }, { 13453127855076217722u, 1524291284333980581u }, { 7073153469319063855u, 1219433027467184465u }, { 11317045550910502167u, 1951092843947495144u }, { 12742985255470312057u, 1560874275157996115u }, { 10194388204376249646u, 1248699420126396892u }, { 1553625868034358140u, 1997919072202235028u }, { 8621598323911307159u, 1598335257761788022u }, { 17965325103354776697u, 1278668206209430417u }, { 13987124906400001422u, 2045869129935088668u }, { 121653480894270168u, 1636695303948070935u }, { 97322784715416134u, 1309356243158456748u }, { 14913111714512307107u, 2094969989053530796u }, { 8241140556867935363u, 1675975991242824637u }, { 17660958889720079260u, 1340780792994259709u }, { 17189487779326395846u, 2145249268790815535u }, { 13751590223461116677u, 1716199415032652428u }, { 18379969808252713988u, 1372959532026121942u }, { 14650556434236701088u, 2196735251241795108u }, { 652398703163629901u, 1757388200993436087u }, { 11589965406756634890u, 1405910560794748869u }, { 7475898206584884855u, 2249456897271598191u }, { 2291369750525997561u, 1799565517817278553u }, { 9211793429904618695u, 1439652414253822842u }, { 18428218302589300235u, 2303443862806116547u }, { 7363877012587619542u, 1842755090244893238u }, { 13269799239553916280u, 1474204072195914590u }, { 10615839391643133024u, 1179363257756731672u }, { 2227947767661371545u, 1886981212410770676u }, { 16539753473096738529u, 1509584969928616540u }, { 13231802778477390823u, 1207667975942893232u }, { 6413489186596184024u, 1932268761508629172u }, { 16198837793502678189u, 1545815009206903337u }, { 5580372605318321905u, 1236652007365522670u }, { 8928596168509315048u, 1978643211784836272u }, { 18210923379033183008u, 1582914569427869017u }, { 7190041073742725760u, 1266331655542295214u }, { 436019273762630246u, 2026130648867672343u }, { 7727513048493924843u, 1620904519094137874u }, { 9871359253537050198u, 1296723615275310299u }, { 4726128361433549347u, 2074757784440496479u }, { 7470251503888749801u, 1659806227552397183u }, { 13354898832594820487u, 1327844982041917746u }, { 13989140502667892133u, 2124551971267068394u }, { 14880661216876224029u, 1699641577013654715u }, { 11904528973500979224u, 1359713261610923772u }, { 4289851098633925465u, 2175541218577478036u }, { 18189276137874781665u, 1740432974861982428u }, { 3483374466074094362u, 1392346379889585943u }, { 1884050330976640656u, 2227754207823337509u }, { 5196589079523222848u, 1782203366258670007u }, { 15225317707844309248u, 1425762693006936005u }, { 5913764258841343181u, 2281220308811097609u }, { 8420360221814984868u, 1824976247048878087u }, { 17804334621677718864u, 1459980997639102469u }, { 17932816512084085415u, 1167984798111281975u }, { 10245762345624985047u, 1868775676978051161u }, { 4507261061758077715u, 1495020541582440929u }, { 7295157664148372495u, 1196016433265952743u }, { 7982903447895485668u, 1913626293225524389u }, { 10075671573058298858u, 1530901034580419511u }, { 4371188443704728763u, 1224720827664335609u }, { 14372599139411386667u, 1959553324262936974u }, { 15187428126271019657u, 1567642659410349579u }, { 15839291315758726049u, 1254114127528279663u }, { 3206773216762499739u, 2006582604045247462u }, { 13633465017635730761u, 1605266083236197969u }, { 14596120828850494932u, 1284212866588958375u }, { 4907049252451240275u, 2054740586542333401u }, { 236290587219081897u, 1643792469233866721u }, { 14946427728742906810u, 1315033975387093376u }, { 16535586736504830250u, 2104054360619349402u }, { 5849771759720043554u, 1683243488495479522u }, { 15747863852001765813u, 1346594790796383617u }, { 10439186904235184007u, 2154551665274213788u }, { 15730047152871967852u, 1723641332219371030u }, { 12584037722297574282u, 1378913065775496824u }, { 9066413911450387881u, 2206260905240794919u }, { 10942479943902220628u, 1765008724192635935u }, { 8753983955121776503u, 1412006979354108748u }, { 10317025513452932081u, 2259211166966573997u }, { 874922781278525018u, 1807368933573259198u }, { 8078635854506640661u, 1445895146858607358u }, { 13841606313089133175u, 1156716117486885886u }, { 14767872471458792434u, 1850745787979017418u }, { 746251532941302978u, 1480596630383213935u }, { 597001226353042382u, 1184477304306571148u }, { 15712597221132509104u, 1895163686890513836u }, { 8880728962164096960u, 1516130949512411069u }, { 10793931984473187891u, 1212904759609928855u }, { 17270291175157100626u, 1940647615375886168u }, { 2748186495899949531u, 1552518092300708935u }, { 2198549196719959625u, 1242014473840567148u }, { 18275073973719576693u, 1987223158144907436u }, { 10930710364233751031u, 1589778526515925949u }, { 12433917106128911148u, 1271822821212740759u }, { 8826220925580526867u, 2034916513940385215u }, { 7060976740464421494u, 1627933211152308172u }, { 16716827836597268165u, 1302346568921846537u }, { 11989529279587987770u, 2083754510274954460u }, { 9591623423670390216u, 1667003608219963568u }, { 15051996368420132820u, 1333602886575970854u }, { 13015147745246481542u, 2133764618521553367u }, { 3033420566713364587u, 1707011694817242694u }, { 6116085268112601993u, 1365609355853794155u }, { 9785736428980163188u, 2184974969366070648u }, { 15207286772667951197u, 1747979975492856518u }, { 1097782973908629988u, 1398383980394285215u }, { 1756452758253807981u, 2237414368630856344u }, { 5094511021344956708u, 1789931494904685075u }, { 4075608817075965366u, 1431945195923748060u }, { 6520974107321544586u, 2291112313477996896u }, { 1527430471115325346u, 1832889850782397517u }, { 12289990821117991246u, 1466311880625918013u }, { 17210690286378213644u, 1173049504500734410u }, { 9090360384495590213u, 1876879207201175057u }, { 18340334751822203140u, 1501503365760940045u }, { 14672267801457762512u, 1201202692608752036u }, { 16096930852848599373u, 1921924308174003258u }, { 1809498238053148529u, 1537539446539202607u }, { 12515645034668249793u, 1230031557231362085u }, { 1578287981759648052u, 1968050491570179337u }, { 12330676829633449412u, 1574440393256143469u }, { 13553890278448669853u, 1259552314604914775u }, { 3239480371808320148u, 2015283703367863641u }, { 17348979556414297411u, 1612226962694290912u }, { 6500486015647617283u, 1289781570155432730u }, { 10400777625036187652u, 2063650512248692368u }, { 15699319729512770768u, 1650920409798953894u }, { 16248804598352126938u, 1320736327839163115u }, { 7551343283653851484u, 2113178124542660985u }, { 6041074626923081187u, 1690542499634128788u }, { 12211557331022285596u, 1352433999707303030u }, { 1091747655926105338u, 2163894399531684849u }, { 4562746939482794594u, 1731115519625347879u }, { 7339546366328145998u, 1384892415700278303u }, { 8053925371383123274u, 2215827865120445285u }, { 6443140297106498619u, 1772662292096356228u }, { 12533209867169019542u, 1418129833677084982u }, { 5295740528502789974u, 2269007733883335972u }, { 15304638867027962949u, 1815206187106668777u }, { 4865013464138549713u, 1452164949685335022u }, { 14960057215536570740u, 1161731959748268017u }, { 9178696285890871890u, 1858771135597228828u }, { 14721654658196518159u, 1487016908477783062u }, { 4398626097073393881u, 1189613526782226450u }, { 7037801755317430209u, 1903381642851562320u }, { 5630241404253944167u, 1522705314281249856u }, { 814844308661245011u, 1218164251424999885u }, { 1303750893857992017u, 1949062802279999816u }, { 15800395974054034906u, 1559250241823999852u }, { 5261619149759407279u, 1247400193459199882u }, { 12107939454356961969u, 1995840309534719811u }, { 5997002748743659252u, 1596672247627775849u }, { 8486951013736837725u, 1277337798102220679u }, { 2511075177753209390u, 2043740476963553087u }, { 13076906586428298482u, 1634992381570842469u }, { 14150874083884549109u, 1307993905256673975u }, { 4194654460505726958u, 2092790248410678361u }, { 18113118827372222859u, 1674232198728542688u }, { 3422448617672047318u, 1339385758982834151u }, { 16543964232501006678u, 2143017214372534641u }, { 9545822571258895019u, 1714413771498027713u }, { 15015355686490936662u, 1371531017198422170u }, { 5577825024675947042u, 2194449627517475473u }, { 11840957649224578280u, 1755559702013980378u }, { 16851463748863483271u, 1404447761611184302u }, { 12204946739213931940u, 2247116418577894884u }, { 13453306206113055875u, 1797693134862315907u }, { 3383947335406624054u, 1438154507889852726u }, { 16482362180876329456u, 2301047212623764361u }, { 9496540929959153242u, 1840837770099011489u }, { 11286581558709232917u, 1472670216079209191u }, { 5339916432225476010u, 1178136172863367353u }, { 4854517476818851293u, 1885017876581387765u }, { 3883613981455081034u, 1508014301265110212u }, { 14174937629389795797u, 1206411441012088169u }, { 11611853762797942306u, 1930258305619341071u }, { 5600134195496443521u, 1544206644495472857u }, { 15548153800622885787u, 1235365315596378285u }, { 6430302007287065643u, 1976584504954205257u }, { 16212288050055383484u, 1581267603963364205u }, { 12969830440044306787u, 1265014083170691364u }, { 9683682259845159889u, 2024022533073106183u }, { 15125643437359948558u, 1619218026458484946u }, { 8411165935146048523u, 1295374421166787957u }, { 17147214310975587960u, 2072599073866860731u }, { 10028422634038560045u, 1658079259093488585u }, { 8022738107230848036u, 1326463407274790868u }, { 9147032156827446534u, 2122341451639665389u }, { 11006974540203867551u, 1697873161311732311u }, { 5116230817421183718u, 1358298529049385849u }, { 15564666937357714594u, 2173277646479017358u }, { 1383687105660440706u, 1738622117183213887u }, { 12174996128754083534u, 1390897693746571109u }, { 8411947361780802685u, 2225436309994513775u }, { 6729557889424642148u, 1780349047995611020u }, { 5383646311539713719u, 1424279238396488816u }, { 1235136468979721303u, 2278846781434382106u }, { 15745504434151418335u, 1823077425147505684u }, { 16285752362063044992u, 1458461940118004547u }, { 5649904260166615347u, 1166769552094403638u }, { 5350498001524674232u, 1866831283351045821u }, { 591049586477829062u, 1493465026680836657u }, { 11540886113407994219u, 1194772021344669325u }, { 18673707743239135u, 1911635234151470921u }, { 14772334225162232601u, 1529308187321176736u }, { 8128518565387875758u, 1223446549856941389u }, { 1937583260394870242u, 1957514479771106223u }, { 8928764237799716840u, 1566011583816884978u }, { 14521709019723594119u, 1252809267053507982u }, { 8477339172590109297u, 2004494827285612772u }, { 17849917782297818407u, 1603595861828490217u }, { 6901236596354434079u, 1282876689462792174u }, { 18420676183650915173u, 2052602703140467478u }, { 3668494502695001169u, 1642082162512373983u }, { 10313493231639821582u, 1313665730009899186u }, { 9122891541139893884u, 2101865168015838698u }, { 14677010862395735754u, 1681492134412670958u }, { 673562245690857633u, 1345193707530136767u } }; static const uint64_t DOUBLE_POW5_SPLIT[DOUBLE_POW5_TABLE_SIZE][2] = { { 0u, 1152921504606846976u }, { 0u, 1441151880758558720u }, { 0u, 1801439850948198400u }, { 0u, 2251799813685248000u }, { 0u, 1407374883553280000u }, { 0u, 1759218604441600000u }, { 0u, 2199023255552000000u }, { 0u, 1374389534720000000u }, { 0u, 1717986918400000000u }, { 0u, 2147483648000000000u }, { 0u, 1342177280000000000u }, { 0u, 1677721600000000000u }, { 0u, 2097152000000000000u }, { 0u, 1310720000000000000u }, { 0u, 1638400000000000000u }, { 0u, 2048000000000000000u }, { 0u, 1280000000000000000u }, { 0u, 1600000000000000000u }, { 0u, 2000000000000000000u }, { 0u, 1250000000000000000u }, { 0u, 1562500000000000000u }, { 0u, 1953125000000000000u }, { 0u, 1220703125000000000u }, { 0u, 1525878906250000000u }, { 0u, 1907348632812500000u }, { 0u, 1192092895507812500u }, { 0u, 1490116119384765625u }, { 4611686018427387904u, 1862645149230957031u }, { 9799832789158199296u, 1164153218269348144u }, { 12249790986447749120u, 1455191522836685180u }, { 15312238733059686400u, 1818989403545856475u }, { 14528612397897220096u, 2273736754432320594u }, { 13692068767113150464u, 1421085471520200371u }, { 12503399940464050176u, 1776356839400250464u }, { 15629249925580062720u, 2220446049250313080u }, { 9768281203487539200u, 1387778780781445675u }, { 7598665485932036096u, 1734723475976807094u }, { 274959820560269312u, 2168404344971008868u }, { 9395221924704944128u, 1355252715606880542u }, { 2520655369026404352u, 1694065894508600678u }, { 12374191248137781248u, 2117582368135750847u }, { 14651398557727195136u, 1323488980084844279u }, { 13702562178731606016u, 1654361225106055349u }, { 3293144668132343808u, 2067951531382569187u }, { 18199116482078572544u, 1292469707114105741u }, { 8913837547316051968u, 1615587133892632177u }, { 15753982952572452864u, 2019483917365790221u }, { 12152082354571476992u, 1262177448353618888u }, { 15190102943214346240u, 1577721810442023610u }, { 9764256642163156992u, 1972152263052529513u }, { 17631875447420442880u, 1232595164407830945u }, { 8204786253993389888u, 1540743955509788682u }, { 1032610780636961552u, 1925929944387235853u }, { 2951224747111794922u, 1203706215242022408u }, { 3689030933889743652u, 1504632769052528010u }, { 13834660704216955373u, 1880790961315660012u }, { 17870034976990372916u, 1175494350822287507u }, { 17725857702810578241u, 1469367938527859384u }, { 3710578054803671186u, 1836709923159824231u }, { 26536550077201078u, 2295887403949780289u }, { 11545800389866720434u, 1434929627468612680u }, { 14432250487333400542u, 1793662034335765850u }, { 8816941072311974870u, 2242077542919707313u }, { 17039803216263454053u, 1401298464324817070u }, { 12076381983474541759u, 1751623080406021338u }, { 5872105442488401391u, 2189528850507526673u }, { 15199280947623720629u, 1368455531567204170u }, { 9775729147674874978u, 1710569414459005213u }, { 16831347453020981627u, 2138211768073756516u }, { 1296220121283337709u, 1336382355046097823u }, { 15455333206886335848u, 1670477943807622278u }, { 10095794471753144002u, 2088097429759527848u }, { 6309871544845715001u, 1305060893599704905u }, { 12499025449484531656u, 1631326116999631131u }, { 11012095793428276666u, 2039157646249538914u }, { 11494245889320060820u, 1274473528905961821u }, { 532749306367912313u, 1593091911132452277u }, { 5277622651387278295u, 1991364888915565346u }, { 7910200175544436838u, 1244603055572228341u }, { 14499436237857933952u, 1555753819465285426u }, { 8900923260467641632u, 1944692274331606783u }, { 12480606065433357876u, 1215432671457254239u }, { 10989071563364309441u, 1519290839321567799u }, { 9124653435777998898u, 1899113549151959749u }, { 8008751406574943263u, 1186945968219974843u }, { 5399253239791291175u, 1483682460274968554u }, { 15972438586593889776u, 1854603075343710692u }, { 759402079766405302u, 1159126922089819183u }, { 14784310654990170340u, 1448908652612273978u }, { 9257016281882937117u, 1811135815765342473u }, { 16182956370781059300u, 2263919769706678091u }, { 7808504722524468110u, 1414949856066673807u }, { 5148944884728197234u, 1768687320083342259u }, { 1824495087482858639u, 2210859150104177824u }, { 1140309429676786649u, 1381786968815111140u }, { 1425386787095983311u, 1727233711018888925u }, { 6393419502297367043u, 2159042138773611156u }, { 13219259225790630210u, 1349401336733506972u }, { 16524074032238287762u, 1686751670916883715u }, { 16043406521870471799u, 2108439588646104644u }, { 803757039314269066u, 1317774742903815403u }, { 14839754354425000045u, 1647218428629769253u }, { 4714634887749086344u, 2059023035787211567u }, { 9864175832484260821u, 1286889397367007229u }, { 16941905809032713930u, 1608611746708759036u }, { 2730638187581340797u, 2010764683385948796u }, { 10930020904093113806u, 1256727927116217997u }, { 18274212148543780162u, 1570909908895272496u }, { 4396021111970173586u, 1963637386119090621u }, { 5053356204195052443u, 1227273366324431638u }, { 15540067292098591362u, 1534091707905539547u }, { 14813398096695851299u, 1917614634881924434u }, { 13870059828862294966u, 1198509146801202771u }, { 12725888767650480803u, 1498136433501503464u }, { 15907360959563101004u, 1872670541876879330u }, { 14553786618154326031u, 1170419088673049581u }, { 4357175217410743827u, 1463023860841311977u }, { 10058155040190817688u, 1828779826051639971u }, { 7961007781811134206u, 2285974782564549964u }, { 14199001900486734687u, 1428734239102843727u }, { 13137066357181030455u, 1785917798878554659u }, { 11809646928048900164u, 2232397248598193324u }, { 16604401366885338411u, 1395248280373870827u }, { 16143815690179285109u, 1744060350467338534u }, { 10956397575869330579u, 2180075438084173168u }, { 6847748484918331612u, 1362547148802608230u }, { 17783057643002690323u, 1703183936003260287u }, { 17617136035325974999u, 2128979920004075359u }, { 17928239049719816230u, 1330612450002547099u }, { 17798612793722382384u, 1663265562503183874u }, { 13024893955298202172u, 2079081953128979843u }, { 5834715712847682405u, 1299426220705612402u }, { 16516766677914378815u, 1624282775882015502u }, { 11422586310538197711u, 2030353469852519378u }, { 11750802462513761473u, 1268970918657824611u }, { 10076817059714813937u, 1586213648322280764u }, { 12596021324643517422u, 1982767060402850955u }, { 5566670318688504437u, 1239229412751781847u }, { 2346651879933242642u, 1549036765939727309u }, { 7545000868343941206u, 1936295957424659136u }, { 4715625542714963254u, 1210184973390411960u }, { 5894531928393704067u, 1512731216738014950u }, { 16591536947346905892u, 1890914020922518687u }, { 17287239619732898039u, 1181821263076574179u }, { 16997363506238734644u, 1477276578845717724u }, { 2799960309088866689u, 1846595723557147156u }, { 10973347230035317489u, 1154122327223216972u }, { 13716684037544146861u, 1442652909029021215u }, { 12534169028502795672u, 1803316136286276519u }, { 11056025267201106687u, 2254145170357845649u }, { 18439230838069161439u, 1408840731473653530u }, { 13825666510731675991u, 1761050914342066913u }, { 3447025083132431277u, 2201313642927583642u }, { 6766076695385157452u, 1375821026829739776u }, { 8457595869231446815u, 1719776283537174720u }, { 10571994836539308519u, 2149720354421468400u }, { 6607496772837067824u, 1343575221513417750u }, { 17482743002901110588u, 1679469026891772187u }, { 17241742735199000331u, 2099336283614715234u }, { 15387775227926763111u, 1312085177259197021u }, { 5399660979626290177u, 1640106471573996277u }, { 11361262242960250625u, 2050133089467495346u }, { 11712474920277544544u, 1281333180917184591u }, { 10028907631919542777u, 1601666476146480739u }, { 7924448521472040567u, 2002083095183100924u }, { 14176152362774801162u, 1251301934489438077u }, { 3885132398186337741u, 1564127418111797597u }, { 9468101516160310080u, 1955159272639746996u }, { 15140935484454969608u, 1221974545399841872u }, { 479425281859160394u, 1527468181749802341u }, { 5210967620751338397u, 1909335227187252926u }, { 17091912818251750210u, 1193334516992033078u }, { 12141518985959911954u, 1491668146240041348u }, { 15176898732449889943u, 1864585182800051685u }, { 11791404716994875166u, 1165365739250032303u }, { 10127569877816206054u, 1456707174062540379u }, { 8047776328842869663u, 1820883967578175474u }, { 836348374198811271u, 2276104959472719343u }, { 7440246761515338900u, 1422565599670449589u }, { 13911994470321561530u, 1778206999588061986u }, { 8166621051047176104u, 2222758749485077483u }, { 2798295147690791113u, 1389224218428173427u }, { 17332926989895652603u, 1736530273035216783u }, { 17054472718942177850u, 2170662841294020979u }, { 8353202440125167204u, 1356664275808763112u }, { 10441503050156459005u, 1695830344760953890u }, { 3828506775840797949u, 2119787930951192363u }, { 86973725686804766u, 1324867456844495227u }, { 13943775212390669669u, 1656084321055619033u }, { 3594660960206173375u, 2070105401319523792u }, { 2246663100128858359u, 1293815875824702370u }, { 12031700912015848757u, 1617269844780877962u }, { 5816254103165035138u, 2021587305976097453u }, { 5941001823691840913u, 1263492066235060908u }, { 7426252279614801142u, 1579365082793826135u }, { 4671129331091113523u, 1974206353492282669u }, { 5225298841145639904u, 1233878970932676668u }, { 6531623551432049880u, 1542348713665845835u }, { 3552843420862674446u, 1927935892082307294u }, { 16055585193321335241u, 1204959932551442058u }, { 10846109454796893243u, 1506199915689302573u }, { 18169322836923504458u, 1882749894611628216u }, { 11355826773077190286u, 1176718684132267635u }, { 9583097447919099954u, 1470898355165334544u }, { 11978871809898874942u, 1838622943956668180u }, { 14973589762373593678u, 2298278679945835225u }, { 2440964573842414192u, 1436424174966147016u }, { 3051205717303017741u, 1795530218707683770u }, { 13037379183483547984u, 2244412773384604712u }, { 8148361989677217490u, 1402757983365377945u }, { 14797138505523909766u, 1753447479206722431u }, { 13884737113477499304u, 2191809349008403039u }, { 15595489723564518921u, 1369880843130251899u }, { 14882676136028260747u, 1712351053912814874u }, { 9379973133180550126u, 2140438817391018593u }, { 17391698254306313589u, 1337774260869386620u }, { 3292878744173340370u, 1672217826086733276u }, { 4116098430216675462u, 2090272282608416595u }, { 266718509671728212u, 1306420176630260372u }, { 333398137089660265u, 1633025220787825465u }, { 5028433689789463235u, 2041281525984781831u }, { 10060300083759496378u, 1275800953740488644u }, { 12575375104699370472u, 1594751192175610805u }, { 1884160825592049379u, 1993438990219513507u }, { 17318501580490888525u, 1245899368887195941u }, { 7813068920331446945u, 1557374211108994927u }, { 5154650131986920777u, 1946717763886243659u }, { 915813323278131534u, 1216698602428902287u }, { 14979824709379828129u, 1520873253036127858u }, { 9501408849870009354u, 1901091566295159823u }, { 12855909558809837702u, 1188182228934474889u }, { 2234828893230133415u, 1485227786168093612u }, { 2793536116537666769u, 1856534732710117015u }, { 8663489100477123587u, 1160334207943823134u }, { 1605989338741628675u, 1450417759929778918u }, { 11230858710281811652u, 1813022199912223647u }, { 9426887369424876662u, 2266277749890279559u }, { 12809333633531629769u, 1416423593681424724u }, { 16011667041914537212u, 1770529492101780905u }, { 6179525747111007803u, 2213161865127226132u }, { 13085575628799155685u, 1383226165704516332u }, { 16356969535998944606u, 1729032707130645415u }, { 15834525901571292854u, 2161290883913306769u }, { 2979049660840976177u, 1350806802445816731u }, { 17558870131333383934u, 1688508503057270913u }, { 8113529608884566205u, 2110635628821588642u }, { 9682642023980241782u, 1319147268013492901u }, { 16714988548402690132u, 1648934085016866126u }, { 11670363648648586857u, 2061167606271082658u }, { 11905663298832754689u, 1288229753919426661u }, { 1047021068258779650u, 1610287192399283327u }, { 15143834390605638274u, 2012858990499104158u }, { 4853210475701136017u, 1258036869061940099u }, { 1454827076199032118u, 1572546086327425124u }, { 1818533845248790147u, 1965682607909281405u }, { 3442426662494187794u, 1228551629943300878u }, { 13526405364972510550u, 1535689537429126097u }, { 3072948650933474476u, 1919611921786407622u }, { 15755650962115585259u, 1199757451116504763u }, { 15082877684217093670u, 1499696813895630954u }, { 9630225068416591280u, 1874621017369538693u }, { 8324733676974063502u, 1171638135855961683u }, { 5794231077790191473u, 1464547669819952104u }, { 7242788847237739342u, 1830684587274940130u }, { 18276858095901949986u, 2288355734093675162u }, { 16034722328366106645u, 1430222333808546976u }, { 1596658836748081690u, 1787777917260683721u }, { 6607509564362490017u, 2234722396575854651u }, { 1823850468512862308u, 1396701497859909157u }, { 6891499104068465790u, 1745876872324886446u }, { 17837745916940358045u, 2182346090406108057u }, { 4231062170446641922u, 1363966306503817536u }, { 5288827713058302403u, 1704957883129771920u }, { 6611034641322878003u, 2131197353912214900u }, { 13355268687681574560u, 1331998346195134312u }, { 16694085859601968200u, 1664997932743917890u }, { 11644235287647684442u, 2081247415929897363u }, { 4971804045566108824u, 1300779634956185852u }, { 6214755056957636030u, 1625974543695232315u }, { 3156757802769657134u, 2032468179619040394u }, { 6584659645158423613u, 1270292612261900246u }, { 17454196593302805324u, 1587865765327375307u }, { 17206059723201118751u, 1984832206659219134u }, { 6142101308573311315u, 1240520129162011959u }, { 3065940617289251240u, 1550650161452514949u }, { 8444111790038951954u, 1938312701815643686u }, { 665883850346957067u, 1211445438634777304u }, { 832354812933696334u, 1514306798293471630u }, { 10263815553021896226u, 1892883497866839537u }, { 17944099766707154901u, 1183052186166774710u }, { 13206752671529167818u, 1478815232708468388u }, { 16508440839411459773u, 1848519040885585485u }, { 12623618533845856310u, 1155324400553490928u }, { 15779523167307320387u, 1444155500691863660u }, { 1277659885424598868u, 1805194375864829576u }, { 1597074856780748586u, 2256492969831036970u }, { 5609857803915355770u, 1410308106144398106u }, { 16235694291748970521u, 1762885132680497632u }, { 1847873790976661535u, 2203606415850622041u }, { 12684136165428883219u, 1377254009906638775u }, { 11243484188358716120u, 1721567512383298469u }, { 219297180166231438u, 2151959390479123087u }, { 7054589765244976505u, 1344974619049451929u }, { 13429923224983608535u, 1681218273811814911u }, { 12175718012802122765u, 2101522842264768639u }, { 14527352785642408584u, 1313451776415480399u }, { 13547504963625622826u, 1641814720519350499u }, { 12322695186104640628u, 2052268400649188124u }, { 16925056528170176201u, 1282667750405742577u }, { 7321262604930556539u, 1603334688007178222u }, { 18374950293017971482u, 2004168360008972777u }, { 4566814905495150320u, 1252605225005607986u }, { 14931890668723713708u, 1565756531257009982u }, { 9441491299049866327u, 1957195664071262478u }, { 1289246043478778550u, 1223247290044539049u }, { 6223243572775861092u, 1529059112555673811u }, { 3167368447542438461u, 1911323890694592264u }, { 1979605279714024038u, 1194577431684120165u }, { 7086192618069917952u, 1493221789605150206u }, { 18081112809442173248u, 1866527237006437757u }, { 13606538515115052232u, 1166579523129023598u }, { 7784801107039039482u, 1458224403911279498u }, { 507629346944023544u, 1822780504889099373u }, { 5246222702107417334u, 2278475631111374216u }, { 3278889188817135834u, 1424047269444608885u }, { 8710297504448807696u, 1780059086805761106u } }; #endif // RYU_D2S_FULL_TABLE_H dragonbox-master/subproject/3rdparty/ryu/ryu/f2s_full_table.h0000664000175000017500000000625115060737600023432 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_F2S_FULL_TABLE_H #define RYU_F2S_FULL_TABLE_H // This table is generated by PrintFloatLookupTable. #define FLOAT_POW5_INV_BITCOUNT 59 #define FLOAT_POW5_BITCOUNT 61 static uint64_t FLOAT_POW5_INV_SPLIT[55] = { 576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u, 472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u, 386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u, 316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u, 519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u, 425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u, 348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u, 570899077082383953u, 456719261665907162u, 365375409332725730u, 292300327466180584u, 467680523945888934u, 374144419156711148u, 299315535325368918u, 478904856520590269u, 383123885216472215u, 306499108173177772u, 490398573077084435u, 392318858461667548u, 313855086769334039u, 502168138830934462u, 401734511064747569u, 321387608851798056u, 514220174162876889u, 411376139330301511u, 329100911464241209u, 526561458342785934u, 421249166674228747u, 336999333339382998u, 539198933343012796u, 431359146674410237u, 345087317339528190u, 552139707743245103u, 441711766194596083u }; static const uint64_t FLOAT_POW5_SPLIT[47] = { 1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u, 1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u, 1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u, 2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u, 1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u, 1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u, 1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u, 1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u, 1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u, 1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u, 2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u, 1292469707114105741u, 1615587133892632177u, 2019483917365790221u }; #endif // RYU_F2S_FULL_TABLE_H dragonbox-master/subproject/3rdparty/ryu/ryu/common.h0000664000175000017500000000710015060737600022031 0ustar renerene// Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef RYU_COMMON_H #define RYU_COMMON_H #include #include #include #if defined(_M_IX86) || defined(_M_ARM) #define RYU_32_BIT_PLATFORM #endif // Returns the number of decimal digits in v, which must not contain more than 9 digits. static inline uint32_t decimalLength9(const uint32_t v) { // Function precondition: v is not a 10-digit number. // (f2s: 9 digits are sufficient for round-tripping.) // (d2fixed: We print 9-digit blocks.) assert(v < 1000000000); if (v >= 100000000) { return 9; } if (v >= 10000000) { return 8; } if (v >= 1000000) { return 7; } if (v >= 100000) { return 6; } if (v >= 10000) { return 5; } if (v >= 1000) { return 4; } if (v >= 100) { return 3; } if (v >= 10) { return 2; } return 1; } // Returns e == 0 ? 1 : [log_2(5^e)]; requires 0 <= e <= 3528. static inline int32_t log2pow5(const int32_t e) { // This approximation works up to the point that the multiplication overflows at e = 3529. // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater // than 2^9297. assert(e >= 0); assert(e <= 3528); return (int32_t) ((((uint32_t) e) * 1217359) >> 19); } // Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528. static inline int32_t pow5bits(const int32_t e) { // This approximation works up to the point that the multiplication overflows at e = 3529. // If the multiplication were done in 64 bits, it would fail at 5^4004 which is just greater // than 2^9297. assert(e >= 0); assert(e <= 3528); return (int32_t) (((((uint32_t) e) * 1217359) >> 19) + 1); } // Returns e == 0 ? 1 : ceil(log_2(5^e)); requires 0 <= e <= 3528. static inline int32_t ceil_log2pow5(const int32_t e) { return log2pow5(e) + 1; } // Returns floor(log_10(2^e)); requires 0 <= e <= 1650. static inline uint32_t log10Pow2(const int32_t e) { // The first value this approximation fails for is 2^1651 which is just greater than 10^297. assert(e >= 0); assert(e <= 1650); return (((uint32_t) e) * 78913) >> 18; } // Returns floor(log_10(5^e)); requires 0 <= e <= 2620. static inline uint32_t log10Pow5(const int32_t e) { // The first value this approximation fails for is 5^2621 which is just greater than 10^1832. assert(e >= 0); assert(e <= 2620); return (((uint32_t) e) * 732923) >> 20; } static inline int copy_special_str(char * const result, const bool sign, const bool exponent, const bool mantissa) { if (mantissa) { memcpy(result, "NaN", 3); return 3; } if (sign) { result[0] = '-'; } if (exponent) { memcpy(result + sign, "Infinity", 8); return sign + 8; } memcpy(result + sign, "0E0", 3); return sign + 3; } static inline uint32_t float_to_bits(const float f) { uint32_t bits = 0; memcpy(&bits, &f, sizeof(float)); return bits; } static inline uint64_t double_to_bits(const double d) { uint64_t bits = 0; memcpy(&bits, &d, sizeof(double)); return bits; } #endif // RYU_COMMON_H dragonbox-master/subproject/3rdparty/shaded_plots/0000775000175000017500000000000015060737600021405 5ustar renerenedragonbox-master/subproject/3rdparty/shaded_plots/plot_distribution_prctile.m0000664000175000017500000000774415060737600027076 0ustar renerenefunction plot_distribution_prctile(varargin) % PLOT_DISTRIBUTION_PRCTILE(X,Y) - Plots the median with percentile errors as a shaded region in the open % figure window. % Inputs: % X: vector of n domain values (the x-axis). % Y: mxn matrix of distribution of range values (the y-axis), where m % corresponds to the number of data samples for each value n. % % PLOT_DISTRIBUTION_PRCTILE(X,Y,...) % Parameter options include: % 'Alpha': the alpha value of the shaded region, default 0.15. % 'Color': the shaded region color. % 'LineWidth': the contour line width, default = 2.0. % 'Prctile': the percentile values to plot, default [50] (the middle % 50 percentile, or inter-quartile range). % [X,Y,prctile_value,color_value,alpha_value,line_width] = parseinputs(varargin{:}); p_value = 0.5*(100-sort(prctile_value)); hold on % Create the polygons for the shaded region %%%% This part is modified by Junekey Jeon %%%% % for j=1:numel(p_value) % Ptop = prctile(Y,100-p_value(j)); % Pbot = prctile(Y,p_value(j)); % for i=1:numel(X)-1 % Px = [X(i) X(i+1) X(i+1) X(i)]; % Py = [Ptop(i) Ptop(i+1) Pbot(i+1) Pbot(i)]; % fill(Px,Py,color_value,'FaceAlpha',alpha_value,'EdgeColor','none'); % end % end % plot(X,median(Y),'LineWidth',line_width,'Color',color_value); Ptop = prctile(Y,100-p_value(1)); Pbot = prctile(Y,p_value(1)); block_alpha_value = 1- (1-alpha_value)^numel(p_value); for i=1:numel(X)-1 Px = [X(i) X(i+1) X(i+1) X(i)]; Py = [Ptop(i) Ptop(i+1) Pbot(i+1) Pbot(i)]; fill(Px,Py,color_value,'FaceAlpha',block_alpha_value,'EdgeColor','none'); end for j=2:numel(p_value) Ptop1 = prctile(Y,100-p_value(j)); Ptop2 = prctile(Y,100-p_value(j-1)); Pbot1 = prctile(Y,p_value(j)); Pbot2 = prctile(Y,p_value(j-1)); block_alpha_value = 1- (1-alpha_value)^(numel(p_value) - j + 1); for i=1:numel(X)-1 Px = [X(i) X(i+1) X(i+1) X(i)]; Py = [Ptop1(i) Ptop1(i+1) Ptop2(i+1) Ptop2(i)]; fill(Px,Py,color_value,'FaceAlpha',block_alpha_value,'EdgeColor','none'); Px = [X(i) X(i+1) X(i+1) X(i)]; Py = [Pbot1(i) Pbot1(i+1) Pbot2(i+1) Pbot2(i)]; fill(Px,Py,color_value,'FaceAlpha',block_alpha_value,'EdgeColor','none'); end end plot(X,median(Y),'--','LineWidth',line_width,'Color',color_value); hold off end function [X,Y,prctile_value,color_value,alpha_value,line_width] = parseinputs(varargin) % Check the number of input args minargs = 2; numopts = 4; maxargs = minargs + 2*numopts; narginchk(minargs,maxargs); ax = gca; % Set the defaults prctile_value = 50; alpha_value = 0.15; color_value = ax.ColorOrder(ax.ColorOrderIndex,:); line_width = 2.0; % Get the inputs and check them X = varargin{1}; validateattributes(X,{'numeric'},{'vector','nonnan','finite'},mfilename,'X',2); Y = varargin{2}; validateattributes(Y,{'numeric'},{'2d','nonnan','finite','ncols',numel(X)},mfilename,'Y',2); if nargin > minargs for i=3:2:nargin PNAME = varargin{i}; PVALUE = varargin{i+1}; PNAME = validatestring(PNAME,{'Alpha','Color','LineWidth','Prctile'},... mfilename,'ParameterName',i); switch PNAME case 'Alpha' validateattributes(PVALUE,{'numeric'},{'scalar','nonnan','finite','nonnegative','<=',1.0},mfilename,PNAME,i+1); alpha_value = PVALUE; case 'Color' validateattributes(PVALUE,{'numeric'},{'real','nonnegative','nonempty','vector','numel',3,'<=',1.0},mfilename,PNAME,i+1); color_value = PVALUE; case 'LineWidth' validateattributes(PVALUE,{'numeric'},{'scalar','finite','nonnegative'},... mfilename,PNAME,i+1); line_width = PVALUE; case 'Prctile' validateattributes(PVALUE,{'numeric'},{'vector','finite','nonnan','nonnegative','<=',100},... mfilename,PNAME,i+1); prctile_value = PVALUE; end end end end dragonbox-master/subproject/3rdparty/shaded_plots/license.txt0000664000175000017500000000271415060737600023574 0ustar renereneCopyright (c) 2018, John A. Onofrey All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution * Neither the name of Yale University nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. dragonbox-master/subproject/3rdparty/shaded_plots/plot_distribution.m0000664000175000017500000000467215060737600025351 0ustar renerenefunction plot_distribution(varargin) % PLOT_DISTRIBUTION(X,Y) - Plots the mean with standard deviation errors as a shaded region in the open % figure window. % Inputs: % X: vector of n domain values (the x-axis). % Y: mxn matrix of distribution of range values (the y-axis), where m % corresponds to the number of data samples for each value n. % % PLOT_DISTRIBUTION(X,Y,...) % Parameter options include: % 'Alpha': the alpha value of the shaded region, default 0.15. % 'Color': the shaded region color. % 'LineWidth': the contour line width, default = 2.0. [X,Y,color_value,alpha_value,line_width] = parseinputs(varargin{:}); MU = mean(Y); SIGMA = std(Y); hold on % Create the polygons for the shaded region Ptop = MU+SIGMA; Pbot = MU-SIGMA; for i=1:numel(X)-1 Px = [X(i) X(i+1) X(i+1) X(i)]; Py = [Ptop(i) Ptop(i+1) Pbot(i+1) Pbot(i)]; fill(Px,Py,color_value,'FaceAlpha',alpha_value,'EdgeColor','none'); end plot(X,MU,'LineWidth',line_width,'Color',color_value); hold off end function [X,Y,color_value,alpha_value,line_width] = parseinputs(varargin) % Check the number of input args minargs = 2; numopts = 3; maxargs = minargs + 2*numopts; narginchk(minargs,maxargs); ax = gca; % Set the defaults alpha_value = 0.15; color_value = ax.ColorOrder(ax.ColorOrderIndex,:); line_width = 2.0; % Get the inputs and check them X = varargin{1}; validateattributes(X,{'numeric'},{'vector','nonnan','finite'},mfilename,'X',2); Y = varargin{2}; validateattributes(Y,{'numeric'},{'2d','nonnan','finite','ncols',numel(X)},mfilename,'Y',2); if nargin > minargs for i=(minargs+1):2:nargin PNAME = varargin{i}; PVALUE = varargin{i+1}; PNAME = validatestring(PNAME,{'Alpha','Color','LineWidth','Prctile'},... mfilename,'ParameterName',i); switch PNAME case 'Alpha' validateattributes(PVALUE,{'numeric'},{'scalar','nonnan','finite','nonnegative','<=',1.0},mfilename,PNAME,i+1); alpha_value = PVALUE; case 'Color' validateattributes(PVALUE,{'numeric'},{'real','nonnegative','nonempty','vector','numel',3,'<=',1.0},mfilename,PNAME,i+1); color_value = PVALUE; case 'LineWidth' validateattributes(PVALUE,{'numeric'},{'scalar','finite','nonnegative'},... mfilename,PNAME,i+1); line_width = PVALUE; end end end end dragonbox-master/subproject/3rdparty/shaded_plots/plot_shaded.m0000664000175000017500000000475015060737600024057 0ustar renerenefunction plot_shaded(varargin) % PLOT_SHADED(X,Y) - Plots the line with pretty shaded region under the line in the open % figure window. % Inputs: % X: vector of domain values. % Y: vector or range values. % % PLOT_SHADED(X,Y,...) % Parameter options include: % 'Alpha': the alpha value of the shaded region, default 0.15. % 'Color': the shaded region color. % 'LineWidth': the contour line width, default = 2.0. [X,Y,color_value,alpha_value,line_width] = parseinputs(varargin{:}); y_min = min(Y); y_max = max(Y); V_alpha = alpha_value*((Y-y_min)/y_max); F = [1 2 3 4]; hold on % Create patches for the shaded region for i=1:numel(X)-1 V = [ X(i) y_min ; X(i) Y(i); X(i+1) Y(i+1); X(i+1) y_min ]; A = [0,V_alpha(i),V_alpha(i+1),0]'; patch('Faces',F,'Vertices',V,'FaceColor',color_value,... 'EdgeColor','none',... 'FaceVertexAlphaData',A,'FaceAlpha','interp','AlphaDataMapping','none'); end plot(X,Y,'LineWidth',line_width,'Color',color_value); hold off end function [X,Y,color_value,alpha_value,line_width] = parseinputs(varargin) % Check the number of input args minargs = 2; numopts = 3; maxargs = minargs + 2*numopts; narginchk(minargs,maxargs); ax = gca; % Set the defaults alpha_value = 0.15; color_value = ax.ColorOrder(ax.ColorOrderIndex,:); line_width = 2.0; % Get the inputs and check them X = varargin{1}; validateattributes(X,{'numeric'},{'vector','nonnan','finite'},mfilename,'X',2); Y = varargin{2}; validateattributes(Y,{'numeric'},{'vector','nonnan','finite','numel',numel(X)},mfilename,'Y',2); % Ensure that X and Y are column vectors X = X(:); Y = Y(:); if nargin > minargs for i=(minargs+1):2:nargin PNAME = varargin{i}; PVALUE = varargin{i+1}; PNAME = validatestring(PNAME,{'Alpha','Color','LineWidth','Prctile'},... mfilename,'ParameterName',i); switch PNAME case 'Alpha' validateattributes(PVALUE,{'numeric'},{'scalar','nonnan','finite','nonnegative','<=',1.0},mfilename,PNAME,i+1); alpha_value = PVALUE; case 'Color' validateattributes(PVALUE,{'numeric'},{'real','nonnegative','nonempty','vector','numel',3,'<=',1.0},mfilename,PNAME,i+1); color_value = PVALUE; case 'LineWidth' validateattributes(PVALUE,{'numeric'},{'scalar','finite','nonnegative'},... mfilename,PNAME,i+1); line_width = PVALUE; end end end end dragonbox-master/subproject/3rdparty/shaded_plots/example_shaded_plots.m0000664000175000017500000000241515060737600025751 0ustar renerene%% Shaded line plot % Example showing the difference between the standard plot routine and the % shaded routine x = -2*pi:pi/100:2*pi; fx = sin(x); figure('Color','w'); subplot(1,2,1); hold on plot(x,fx); plot(2*x+pi/2,0.5*fx+0.1*x); hold off title('plot'); subplot(1,2,2); hold on plot_shaded(x,fx); plot_shaded(2*x+pi/2,0.5*fx+0.1*x); hold off title('plot\_shaded'); %% Histogram plot % Plots two histograms for two different distributions X1 = 3 + 2.0*randn([100000,1]); X2 = 12 + 4.0*randn([100000,1]); figure('Color','w'); hold on plot_histogram_shaded(X1,'Alpha',0.3); plot_histogram_shaded(X2); hold off title('plot\_histogram\_shaded'); %% Distribution plots % Show different plot routines to visualize measurement errors/noise X = 1:0.25:10; Y = sin(X)+0.25*X; Y_error = randn(1000,numel(Y)); Y_noisy = Y+Y_error.*repmat(0.1*X,[size(Y_error,1) 1]); figure('Color','w'); subplot(3,1,1); plot(X,Y,'LineWidth',1.5); title('plot (True value y=f(x))'); ylim([-1 5]); subplot(3,1,2); hold on plot(X,Y,'LineWidth',1.5); plot_distribution(X,Y_noisy); hold off title('plot\_distribution'); ylim([-1 5]); subplot(3,1,3); hold on plot(X,Y,'LineWidth',1.5); plot_distribution_prctile(X,Y_noisy,'Prctile',[25 50 75 90]); hold off title('plot\_distribution\_prctile'); ylim([-1 5]); dragonbox-master/subproject/3rdparty/shaded_plots/plot_histogram_shaded.m0000664000175000017500000000611415060737600026130 0ustar renerenefunction [bin_centers,hist_values,bin_edges] = plot_histogram_shaded(varargin) % [C,V,E] = PLOT_HISTOGRAM_SHADED(X) - Plots the histogram as a shaded line plot instead of bar plot. % Outputs: % C: the histogram bin centers. % V: the histogram values at each bin. % E: the histogram bin edges values. % % [C,V,E] = PLOT_HISTOGRAM_SHADED(X,_) % Optional values: % 'alpha': alpha value of the shaded region, default 0.2. % 'bins': number of bins, default []. % 'color': color of the plot, default [0 0 1]. % 'edges': the bins edges to use, default []. % 'normalization': the normalization type to use (see histogram doc), % default 'probability' % [X,n_bins,bin_edges,color_value,alpha_value,norm_type] = parseinputs(varargin{:}); if isempty(n_bins) && isempty(bin_edges) [hist_values,bin_edges] = histcounts(X,'Normalization',norm_type); else bin_param = n_bins; if ~isempty(bin_edges) bin_param = bin_edges; end [hist_values,bin_edges] = histcounts(X,bin_param,'Normalization',norm_type); end x_cat = cat(1,bin_edges,circshift(bin_edges,-1)); x_mean = mean(x_cat,1); bin_centers = x_mean(1:end-1); fprintf(1,'Plotting histogram with %d bins\n',numel(bin_centers)); % Use a shaded plot plot_shaded(bin_centers,hist_values,'Alpha',alpha_value,'Color',color_value,'LineWidth',1.5); end function [X,n_bins,bin_edges,color_value,alpha_value,norm_type] = parseinputs(varargin) % Get the number of input args minargs = 1; maxargs = minargs+5*2; narginchk(minargs,maxargs); ax = gca; % Set the defaults n_bins = []; bin_edges = []; color_value = ax.ColorOrder(ax.ColorOrderIndex,:); alpha_value = 0.2; norm_type = 'probability'; % Get the inputs and check them X = varargin{1}; validateattributes(X,{'numeric'},{'nonnan','finite'},mfilename,'X',1); if nargin > 1 for i=2:2:nargin PNAME = varargin{i}; PVALUE = varargin{i+1}; PNAME = validatestring(PNAME,... {'alpha','bins','color','edges','normalization'},... mfilename,'ParameterName',i); switch PNAME case 'alpha' validateattributes(PVALUE,{'numeric'},{'real','nonnegative','finite','scalar'},... mfilename,PNAME,i+1); alpha_value = PVALUE; case 'bins' if ~isempty(PVALUE) validateattributes(PVALUE,{'numeric'},{'integer','positive','finite','scalar'},... mfilename,PNAME,i+1); n_bins = PVALUE; end case 'color' validateattributes(PVALUE,{'numeric'},{'real','nonnegative','nonempty','vector','numel',3,'<=',1.0},mfilename,PNAME,i+1); color_value = PVALUE; case 'edges' validateattributes(PVALUE,{'numeric'},{'real','nonempty','vector','nonnan'},mfilename,PNAME,i+1); bin_edges = PVALUE; case 'normalization' validateattributes(PVALUE,{'char'},{'nonempty'},mfilename,PNAME,i+1); norm_type = PVALUE; end end end end dragonbox-master/subproject/common/0000775000175000017500000000000015060737600016454 5ustar renerenedragonbox-master/subproject/common/CMakeLists.txt0000664000175000017500000000222515060737600021215 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(dragonbox_common LANGUAGES CXX) include(FetchContent) if (NOT TARGET dragonbox) FetchContent_Declare(dragonbox SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../..") FetchContent_MakeAvailable(dragonbox) endif() set(dragonbox_common_headers include/big_uint.h include/continued_fractions.h include/rational_continued_fractions.h include/best_rational_approx.h include/good_rational_approx.h include/random_float.h) set(dragonbox_common_sources source/big_uint.cpp) add_library(dragonbox_common STATIC ${dragonbox_common_headers} ${dragonbox_common_sources}) add_library(dragonbox::common ALIAS dragonbox_common) target_include_directories(dragonbox_common PUBLIC $) target_compile_features(dragonbox_common PUBLIC cxx_std_17) target_link_libraries(dragonbox_common PUBLIC dragonbox::dragonbox) # ---- MSVC Specifics ---- if (MSVC) # /permissive- is required (see https://github.com/jk-jeon/dragonbox/pull/74#issuecomment-3247531231) target_compile_options(dragonbox_common PUBLIC /permissive-) endif()dragonbox-master/subproject/common/include/0000775000175000017500000000000015060737600020077 5ustar renerenedragonbox-master/subproject/common/include/good_rational_approx.h0000664000175000017500000002547215060737600024474 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_GOOD_RATIONAL_APPROX #define JKJ_HEADER_GOOD_RATIONAL_APPROX #include "continued_fractions.h" #include #include #include namespace jkj { // Find all denominators of rational approximations from below of denominators no more than // denominator_upper_bound for the given number x whose error in the strong sense is at most // error_threshold. The returned list might contain several different denominators of the same // rational number. template std::vector find_all_good_rational_approx_from_below_denoms(PositiveNumberX const& x, UInt const& denominator_upper_bound, PositiveNumberEpsilon const& error_threshold) { assert(denominator_upper_bound > 0); using uint_type = typename ContinuedFractionsImpl::uint_type; std::vector results; if (error_threshold >= PositiveNumberEpsilon(1)) { for (UInt i = 1; i <= denominator_upper_bound; ++i) { results.push_back(i); } return results; } // Initialize a continued fractions calculator. ContinuedFractionsImpl cf{x}; // We will find the first even semiconvergent whose error is at most the threshold. // If such semiconvergent has the denominator strictly bigger than the // denominator_upper_bound, then there is no n such that nx - floor(nx) <= epsilon. unsigned_rational previous_convergent; // even unsigned_rational current_convergent; // odd uint_type semiconvergent_coeff = 0; unsigned_rational semiconvergent; auto perfect_approx_possible = [&] { // If there is no more convergent, we already obtained the perfect approximation. // This means that x = p/q is rational with q <= denominator_upper_bound. // In this case, just return q, 2q, 3q, ... up to denominator_upper_bound. auto denominator = cf.current_denominator(); while (denominator <= denominator_upper_bound) { results.push_back(denominator); denominator += cf.current_denominator(); } }; auto update_semiconvergent = [&] { semiconvergent.numerator = previous_convergent.numerator + semiconvergent_coeff * current_convergent.numerator; semiconvergent.denominator = previous_convergent.denominator + semiconvergent_coeff * current_convergent.denominator; }; auto gcd = [&](auto a, auto b) { decltype(a) t; while (b != 0) { t = b; b = a % b; a = static_cast(t); } return a; }; auto subroutine_for_each_semiconvergent = [&] { auto push_all_multiples = [&](auto const& candidate) { auto error = candidate.denominator * x - candidate.numerator; auto error_multiple = error; auto denominator_multiple = candidate.denominator; while (error_multiple < error_threshold && denominator_multiple <= denominator_upper_bound) { results.push_back(denominator_multiple); error_multiple += error; denominator_multiple += candidate.denominator; } }; push_all_multiples(semiconvergent); auto b_max = uint_type(denominator_upper_bound) / semiconvergent.denominator; for (decltype(b_max) b = 2; b <= b_max; ++b) { unsigned_rational candidate{b * semiconvergent.numerator, b * semiconvergent.denominator}; auto a_max = (uint_type(denominator_upper_bound) - candidate.denominator) / current_convergent.denominator; for (decltype(a_max) a = 1; a <= a_max && a < b; ++a) { candidate.numerator += current_convergent.numerator; candidate.denominator += current_convergent.denominator; // If a and b are not coprime, skip. if (gcd(a, b) != 1) { continue; } push_all_multiples(candidate); } } }; while (true) { // Currently, cf.current_index() is odd. // Obtain the next convergent. if (!cf.update()) { perfect_approx_possible(); // The last convergent is of odd index, and we are looking for semiconvergents after // the last even convergent. These semiconvergents should have the same error // with the last even convergent, and since the last even convergent has been // confirmed to have error worse than the threshold, there is nothing left to do. return results; } // Now, cf.current_index() is even. if (cf.current_denominator() * x - cf.current_numerator() < error_threshold) { // In this case, we should look at semiconvergents. if (cf.current_index() == 0) { // In this case, the semiconvergent we are looking for is the 0th convergent. break; } else { while (true) { ++semiconvergent_coeff; update_semiconvergent(); if (semiconvergent.denominator > denominator_upper_bound) { // This means there is no semiconvergent satisfying the condition. return results; } if (semiconvergent_coeff == cf.current_coefficient()) { // Found the first semiconvergent, which is the next convergent. break; } if (semiconvergent.denominator * x - semiconvergent.numerator < error_threshold) { // Found the first semiconvergent. // Iterate until reaching the next convergent. while (true) { subroutine_for_each_semiconvergent(); ++semiconvergent_coeff; update_semiconvergent(); if (semiconvergent.denominator > denominator_upper_bound) { return results; } if (semiconvergent_coeff == cf.current_coefficient()) { break; } } break; } } } break; } if (cf.current_denominator() > denominator_upper_bound) { // In this case, we haven't found any convergent that has better error than the // threshold, which means there is no n satisfying nx - floor(nx) <= epsilon. return results; } // Currently, cf.current_index() is even. // Obtain the next convergent. if (!cf.update()) { // In this case, there is no n satisfying nx - floor(nx) <= epsilon // other than those making x an integer. perfect_approx_possible(); return results; } // Now, cf.current_index() is odd. if (cf.current_denominator() > denominator_upper_bound) { // In this case, we haven't found any convergent that has better error than the // threshold, which means there is no n satisfying nx - floor(nx) <= epsilon. return results; } previous_convergent = cf.previous_convergent(); current_convergent = cf.current_convergent(); } // We have found the first even semiconvergent with a good enough error. assert(cf.current_index() % 2 == 0); // Now, iterate over all subsequent convergents. while (true) { if (!cf.update()) { perfect_approx_possible(); break; } // Now, cf.current_index() is odd. previous_convergent = cf.previous_convergent(); current_convergent = cf.current_convergent(); semiconvergent_coeff = 0; update_semiconvergent(); subroutine_for_each_semiconvergent(); if (cf.current_denominator() > denominator_upper_bound) { break; } // Obtain the next even convergent. if (!cf.update()) { perfect_approx_possible(); // The last convergent is of odd index, and we are looking for semiconvergents // after the last even convergent. while (true) { ++semiconvergent_coeff; update_semiconvergent(); if (semiconvergent.denominator > denominator_upper_bound) { break; } subroutine_for_each_semiconvergent(); } return results; } // Iterate over all semiconvergents. for (semiconvergent_coeff = 1; semiconvergent_coeff < cf.current_coefficient(); ++semiconvergent_coeff) { update_semiconvergent(); if (semiconvergent.denominator > denominator_upper_bound) { return results; } subroutine_for_each_semiconvergent(); } } return results; } } #endifdragonbox-master/subproject/common/include/continued_fractions.h0000664000175000017500000001623615060737600024320 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_CONTINUED_FRACTIONS #define JKJ_HEADER_CONTINUED_FRACTIONS namespace jkj { // Continued fractions calculator for positive numbers. template struct unsigned_rational { UInt numerator = 0; UInt denominator = 0; unsigned_rational() = default; unsigned_rational(UInt const& numerator) : numerator{numerator}, denominator{1} {} unsigned_rational(UInt&& numerator) : numerator{static_cast(numerator)}, denominator{1} {} unsigned_rational(UInt const& numerator, UInt const& denominator) : numerator{numerator}, denominator{denominator} {} unsigned_rational(UInt&& numerator, UInt const& denominator) : numerator{static_cast(numerator)}, denominator{denominator} {} unsigned_rational(UInt const& numerator, UInt&& denominator) : numerator{numerator}, denominator{static_cast(denominator)} {} unsigned_rational(UInt&& numerator, UInt&& denominator) : numerator{static_cast(numerator)}, denominator{ static_cast(denominator)} {} friend bool operator<(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator < y.numerator * x.denominator; } friend bool operator<=(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator <= y.numerator * x.denominator; } friend bool operator>(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator > y.numerator * x.denominator; } friend bool operator>=(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator >= y.numerator * x.denominator; } friend bool operator==(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator == y.numerator * x.denominator; } friend bool operator!=(unsigned_rational const& x, unsigned_rational const& y) { return x.numerator * y.denominator != y.numerator * x.denominator; } // Performs no reduction. friend unsigned_rational operator+(unsigned_rational const& x, unsigned_rational const& y) { return {x.numerator * y.denominator + y.numerator * x.denominator, x.denominator * y.denominator}; } // Performs no reduction. unsigned_rational& operator+=(unsigned_rational const& y) & { numerator *= y.denominator; numerator += y.numerator * denominator; denominator *= y.denominator; return *this; } // Performs no reduction. friend unsigned_rational operator-(unsigned_rational const& x, unsigned_rational const& y) { return {x.numerator * y.denominator - y.numerator * x.denominator, x.denominator * y.denominator}; } // Performs no reduction. unsigned_rational& operator-=(unsigned_rational const& y) & { numerator *= y.denominator; numerator -= y.numerator * denominator; denominator *= y.denominator; return *this; } // Performs no reduction. friend unsigned_rational operator*(unsigned_rational const& x, unsigned_rational const& y) { return {x.numerator * y.numerator, x.denominator * y.denominator}; } // Performs no reduction. unsigned_rational& operator*=(unsigned_rational const& y) & { numerator *= y.numerator; denominator *= y.denominator; return *this; } // Performs no reduction. friend unsigned_rational operator/(unsigned_rational const& x, unsigned_rational const& y) { return {x.numerator * y.denominator, x.denominator * y.numerator}; } // Performs no reduction. unsigned_rational& operator/=(unsigned_rational const& y) & { numerator *= y.denominator; denominator *= y.numerator; return *this; } }; template class continued_fractions { // The (-1)st coefficient is assumed to be 0. UInt current_coefficient_{0}; unsigned_rational current_convergent_{1, 0}; unsigned_rational previous_convergent_{0, 1}; int current_index_ = -1; bool terminated_ = false; protected: void set_terminate_flag() noexcept { terminated_ = true; } public: using uint_type = UInt; int current_index() const noexcept { return current_index_; } UInt const& current_coefficient() const noexcept { return current_coefficient_; } unsigned_rational const& current_convergent() const noexcept { return current_convergent_; } UInt const& current_numerator() const noexcept { return current_convergent().numerator; } UInt const& current_denominator() const noexcept { return current_convergent().denominator; } unsigned_rational const& previous_convergent() const noexcept { return previous_convergent_; } UInt const& previous_numerator() const noexcept { return previous_convergent().numerator; } UInt const& previous_denominator() const noexcept { return previous_convergent().denominator; } bool is_terminated() const noexcept { return terminated_; } // Do nothing if the procedure is terminated. // Returns true if the update is done, // and returns false if the procedure is already terminated. bool update() { if (!is_terminated()) { unsigned_rational new_output; current_coefficient_ = static_cast(*this).compute_next_coefficient(); unsigned_rational new_convergent{ previous_numerator() + current_coefficient_ * current_numerator(), previous_denominator() + current_coefficient_ * current_denominator()}; previous_convergent_ = static_cast&&>(current_convergent_); current_convergent_ = static_cast&&>(new_convergent); ++current_index_; return true; } else { return false; } } }; } #endifdragonbox-master/subproject/common/include/rational_continued_fractions.h0000664000175000017500000000357615060737600026214 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_RATIONAL_CONTINUED_FRACTIONS #define JKJ_HEADER_RATIONAL_CONTINUED_FRACTIONS #include "continued_fractions.h" #include #include namespace jkj { template class rational_continued_fractions : public continued_fractions, UInt> { using crtp_base = continued_fractions, UInt>; friend crtp_base; UInt prev_error_; UInt curr_error_; UInt compute_next_coefficient() { using std::div; auto div_result = div(prev_error_, curr_error_); prev_error_ = static_cast(curr_error_); curr_error_ = static_cast(div_result.rem); if (curr_error_ == 0) { crtp_base::set_terminate_flag(); } return static_cast(div_result.quot); } public: rational_continued_fractions(unsigned_rational r) : prev_error_{static_cast(r.numerator)}, curr_error_{static_cast( r.denominator)} { assert(curr_error_ != 0); } }; } #endifdragonbox-master/subproject/common/include/big_uint.h0000664000175000017500000001734115060737600022056 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_BIG_UINT #define JKJ_HEADER_BIG_UINT #include #include #include #include #include namespace jkj { class big_uint { public: using element_type = std::uint64_t; static constexpr std::size_t element_number_of_bits = 64; private: // Least significant element first. std::vector elements; public: // elements is empty if and only if it represents 0. big_uint() = default; big_uint(element_type n) { if (n != 0) { elements.push_back(n); } } // Remove leading zeros. explicit big_uint(std::initializer_list list) : big_uint(list.begin(), list.end()) {} // Remove leading zeros. template ::iterator_category> big_uint(Iter first, Iter last) : elements(first, last) { auto effective_size = elements.size(); while (effective_size > 0) { if (elements[effective_size - 1] != 0) { break; } --effective_size; } elements.resize(effective_size); } element_type operator[](std::size_t idx) const { return elements[idx]; } bool is_zero() const noexcept { return elements.empty(); } bool is_even() const noexcept { if (elements.empty()) { return true; } else { return elements[0] % 2 == 0; } } friend std::size_t log2p1(big_uint const& n) noexcept; static big_uint power_of_2(std::size_t k); static big_uint pow(big_uint base, std::size_t k); // Repeat multiplying 2 until the number becomes bigger than or equal to the given number. // Returns the number of multiplications, which is ceil(log2(n/*this)). // Precondition: *this is not zero and n should be bigger than or equal to the current // number. Note that this function need not require &n != this. std::size_t multiply_2_until(big_uint const& n); // Repeat multiplying 2 while the number becomes less than or equal to the given number. // Returns the number of multiplications, which is floor(log2(n/*this)). // Precondition: *this is not zero and n should be bigger than or equal to the current // number. Note that this function need not require &n != this. std::size_t multiply_2_while(big_uint const& n); void multiply_2() &; void multiply_5() &; bool operator==(big_uint const& n) const noexcept { return elements == n.elements; } bool operator!=(big_uint const& n) const noexcept { return elements != n.elements; } bool operator==(element_type n) const noexcept { return (elements.size() == 0 && n == 0) || (elements.size() == 1 && elements[0] == n); } bool operator!=(element_type n) const noexcept { return (elements.size() == 0 && n != 0) || (elements.size() == 1 && elements[0] != n) || (elements.size() > 1); } private: int comparison_common(big_uint const& n) const noexcept; public: bool operator<(big_uint const& n) const noexcept { return comparison_common(n) < 0; } bool operator<=(big_uint const& n) const noexcept { return comparison_common(n) <= 0; } bool operator>(big_uint const& n) const noexcept { return comparison_common(n) > 0; } bool operator>=(big_uint const& n) const noexcept { return comparison_common(n) >= 0; } bool operator<(element_type n) const noexcept { return (elements.size() == 0 && n != 0) || (elements.size() == 1 && elements[0] < n); } bool operator<=(element_type n) const noexcept { return (elements.size() == 0 && n == 0) || (elements.size() == 1 && elements[0] <= n); } bool operator>(element_type n) const noexcept { return (elements.size() == 1 && elements[0] > n) || (elements.size() > 1); } bool operator>=(element_type n) const noexcept { return (elements.size() == 0 && n == 0) || (elements.size() == 1 && elements[0] >= n) || (elements.size() > 1); } big_uint& operator+=(big_uint const& n) &; big_uint& operator+=(element_type n) &; template big_uint operator+(T const& n) const { auto r = *this; return r += n; } friend big_uint operator+(element_type n, big_uint const& m) { return m + n; } big_uint& operator++() & { *this += 1; return *this; } big_uint operator++(int) & { auto temp = *this; *this += 1; return temp; } // Precondition: n should be strictly smaller than or equal to the current number big_uint& operator-=(big_uint const& n) &; big_uint operator-(big_uint const& n) const { auto r = *this; return r -= n; } // Precondition: *this should be nonzero big_uint& operator--() &; big_uint& operator*=(element_type n) &; big_uint operator*(element_type n) { auto r = *this; return r *= n; } friend big_uint operator*(big_uint const& x, big_uint const& y); big_uint& operator*=(big_uint const& y) & { auto result = *this * y; *this = result; return *this; } // Perform long division // *this becomes the remainder, returns the quotient // Precondition: n != 0 big_uint long_division(big_uint const& n); big_uint operator/(big_uint const& n) const { auto temp = *this; return temp.long_division(n); } big_uint operator/(element_type n) const { auto temp = *this; return temp.long_division(n); } big_uint operator%(big_uint const& n) const { auto temp = *this; temp.long_division(n); return temp; } big_uint operator%(element_type n) const { auto temp = *this; temp.long_division(n); return temp; } // Convert the number into decimal, and returns the // array of (at most) 19 digits. std::vector to_decimal() const; }; std::size_t log2p1(big_uint const& n) noexcept; big_uint operator*(big_uint const& x, big_uint const& y); struct big_uint_div_t { big_uint quot; big_uint rem; }; inline big_uint_div_t div(big_uint const& x, big_uint const& y) { big_uint_div_t ret; ret.rem = x; ret.quot = ret.rem.long_division(y); return ret; } inline big_uint_div_t div(big_uint&& x, big_uint const& y) { big_uint_div_t ret; ret.rem = static_cast(x); ret.quot = ret.rem.long_division(y); return ret; } } #endifdragonbox-master/subproject/common/include/random_float.h0000664000175000017500000001614415060737600022723 0ustar renerene// Copyright 2020-2021 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_RANDOM_FLOAT #define JKJ_HEADER_RANDOM_FLOAT #include "dragonbox/dragonbox.h" #include #include #include #include #include #include // For correct seeding class repeating_seed_seq { public: using result_type = std::uint32_t; repeating_seed_seq() : stored_values{0} {} template repeating_seed_seq(InputIterator first, InputIterator last) : stored_values(first, last) {} template repeating_seed_seq(std::initializer_list list) : stored_values(list) {} repeating_seed_seq(std::random_device&& rd, std::size_t count) { stored_values.resize(count); for (auto& elem : stored_values) elem = rd(); } template void generate(RandomAccessIterator first, RandomAccessIterator last) { auto count = last - first; auto q = count / stored_values.size(); for (std::size_t i = 0; i < q; ++i) { std::copy_n(stored_values.cbegin(), stored_values.size(), first); first += stored_values.size(); } count -= q * stored_values.size(); std::copy_n(stored_values.cbegin(), count, first); } std::size_t size() const noexcept { return stored_values.size(); } template void param(OutputIterator first) const { std::copy(stored_values.begin(), stored_values.end(), first); } private: std::vector stored_values; }; inline std::mt19937_64 generate_correctly_seeded_mt19937_64() { repeating_seed_seq seed_seq{std::random_device{}, std::mt19937_64::state_size * std::mt19937_64::word_size / (sizeof(std::uint32_t) * 8)}; return std::mt19937_64{seed_seq}; } template Float uniformly_randomly_generate_finite_float(RandGen& rg) { using default_float_bit_carrier_conversion_traits = jkj::dragonbox::default_float_bit_carrier_conversion_traits; using format = typename default_float_bit_carrier_conversion_traits::format; using carrier_uint = typename default_float_bit_carrier_conversion_traits::carrier_uint; using format_traits = jkj::dragonbox::ieee754_binary_traits; using uniform_distribution = std::uniform_int_distribution; // Generate sign bit auto sign_bit = uniform_distribution{0, 1}(rg); // Generate exponent bits auto exponent_bits = uniform_distribution{0, (carrier_uint(1) << format::exponent_bits) - 2}(rg); // Generate significand bits auto significand_bits = uniform_distribution{0, (carrier_uint(1) << format_traits::significand_bits) - 1}(rg); auto bit_representation = (sign_bit << (format_traits::carrier_bits - 1)) | (exponent_bits << (format_traits::significand_bits)) | significand_bits; return default_float_bit_carrier_conversion_traits::carrier_to_float(bit_representation); } template Float uniformly_randomly_generate_general_float(RandGen& rg) { using default_float_bit_carrier_conversion_traits = jkj::dragonbox::default_float_bit_carrier_conversion_traits; using carrier_uint = typename default_float_bit_carrier_conversion_traits::carrier_uint; using uniform_distribution = std::uniform_int_distribution; // Generate sign bit auto bit_representation = uniform_distribution{0, std::numeric_limits::max()}(rg); return default_float_bit_carrier_conversion_traits::carrier_to_float(bit_representation); } template struct std_string_to_float; template <> struct std_string_to_float { float operator()(std::string const& str) const { return std::stof(str); } }; template <> struct std_string_to_float { double operator()(std::string const& str) const { return std::stod(str); } }; // This function tries to uniformly randomly generate a float number with the // given number of decimal digits, and the end-result is not perfectly bias-free. // However, I don't think there is an easy way to do it correctly. template Float randomly_generate_float_with_given_digits(unsigned int digits, RandGen& rg) { using conversion_traits = jkj::dragonbox::default_float_bit_carrier_conversion_traits; using carrier_uint = typename conversion_traits::carrier_uint; using signed_int_t = std::make_signed_t; assert(digits >= 1); assert(digits <= conversion_traits::format::decimal_significand_digits); // Generate sign uniformly randomly signed_int_t sign = std::uniform_int_distribution{0, 1}(rg) == 0 ? 1 : -1; // Try to generate significand uniformly randomly Float result; signed_int_t from = 0, to = 9; if (digits > 1) { from = 1; for (unsigned int e = 1; e < digits - 1; ++e) { from *= 10; } to = from * 10 - 1; } while (true) { auto significand = std::uniform_int_distribution{from, to}(rg); if (digits > 1) { significand *= 10; significand += std::uniform_int_distribution{1, 9}(rg); } // Generate exponent uniformly randomly auto exp = std::uniform_int_distribution{ std::numeric_limits::min_exponent10 - (int(digits) - 1), std::numeric_limits::max_exponent10 - (int(digits) - 1)}(rg); // Cook up auto str = std::to_string(sign * significand) + 'e' + std::to_string(exp); try { result = std_string_to_float{}(str); } catch (...) { continue; } if (!std::isfinite(result)) { continue; } // Discard if a shorter representation exists // We don't need to care about sign and correct rounding here if (from != 0) { auto roundtrip = jkj::dragonbox::to_decimal( result, jkj::dragonbox::policy::sign::ignore, jkj::dragonbox::policy::decimal_to_binary_rounding::nearest_to_even, jkj::dragonbox::policy::binary_to_decimal_rounding::do_not_care); if (roundtrip.significand <= carrier_uint(from * 10)) { continue; } } break; } return result; } #endif dragonbox-master/subproject/common/include/best_rational_approx.h0000664000175000017500000000747615060737600024505 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #ifndef JKJ_HEADER_BEST_RATIONAL_APPROX #define JKJ_HEADER_BEST_RATIONAL_APPROX #include "continued_fractions.h" #include #include namespace jkj { template struct best_rational_approx_output { unsigned_rational below; unsigned_rational above; }; // Find the best rational approximations from below and from above of denominators no more than // denominator_upper_bound for the given number x. template best_rational_approx_output find_best_rational_approx(PositiveNumber const& x, UInt const& denominator_upper_bound) { assert(denominator_upper_bound > 0); using uint_type = typename ContinuedFractionsImpl::uint_type; best_rational_approx_output ret_value; // Initialize a continued fractions calculator. ContinuedFractionsImpl cf{x}; // First, find the last convergent whose denominator is bounded above by the given upper // bound. unsigned_rational previous_convergent; unsigned_rational current_convergent; do { previous_convergent = cf.previous_convergent(); current_convergent = cf.current_convergent(); // Obtain the next convergent. if (!cf.update()) { // If there is no more convergents, we already obtained the perfect approximation. ret_value.below = cf.current_convergent(); ret_value.above = cf.current_convergent(); return ret_value; } } while (cf.current_denominator() <= denominator_upper_bound); // If the current convergent is of even index, // then the current convergent is the best approximation from below, // and the best approximation from above is the last semiconvergent. // If the current convergent is of odd index, then the other way around. // Note that cf.current_index() is one larger than the index of the current convergent, // so we need to reverse the parity. auto compute_bounds = [&](auto& major, auto& minor) { // The current convergent is the best approximation from below. major = current_convergent; // The best approximation from above is the last semiconvergent. using std::div; auto semiconvergent_coeff = div(denominator_upper_bound - previous_convergent.denominator, current_convergent.denominator) .quot; minor.numerator = previous_convergent.numerator + semiconvergent_coeff * current_convergent.numerator; minor.denominator = previous_convergent.denominator + semiconvergent_coeff * current_convergent.denominator; }; if (cf.current_index() % 2 == 1) { compute_bounds(ret_value.below, ret_value.above); } else { compute_bounds(ret_value.above, ret_value.below); } return ret_value; } } #endifdragonbox-master/subproject/common/source/0000775000175000017500000000000015060737600017754 5ustar renerenedragonbox-master/subproject/common/source/big_uint.cpp0000664000175000017500000005064715060737600022274 0ustar renerene// Copyright 2022 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "big_uint.h" #include "dragonbox/dragonbox.h" #include #include namespace jkj { static constexpr std::size_t log2p1(std::uint64_t x) noexcept { // C++20 std::log2p1 is not yet supported // return std::log2p1(x); std::size_t ret = 0; auto inspect = [&x, &ret](int shft) { if ((x >> shft) != 0) { x >>= shft; ret += shft; } }; inspect(32); inspect(16); inspect(8); inspect(4); inspect(2); inspect(1); return ret + x; } std::size_t log2p1(big_uint const& n) noexcept { if (n.is_zero()) { return 0; } return (n.elements.size() - 1) * big_uint::element_number_of_bits + log2p1(n.elements.back()); } big_uint big_uint::power_of_2(std::size_t k) { auto number_of_elmts = k / element_number_of_bits + 1; big_uint ret_val; ret_val.elements.resize(number_of_elmts, 0); ret_val.elements.back() = (element_type(1) << (k % element_number_of_bits)); return ret_val; } big_uint big_uint::pow(big_uint base, std::size_t k) { big_uint result{1}; while (true) { if (k % 2 != 0) { result *= base; } k /= 2; if (k == 0) { break; } base *= base; } return result; } std::size_t big_uint::multiply_2_until(big_uint const& n) { assert(elements.size() != 0); std::size_t number_of_multiplications = 0; // Perform left-shift to match the leading-1 position. // Perform element-wise shift first. assert(elements.size() <= n.elements.size()); auto element_pos_offset = n.elements.size() - elements.size(); if (element_pos_offset > 0) { number_of_multiplications = element_pos_offset * element_number_of_bits; auto old_size = elements.size(); elements.resize(n.elements.size()); std::move_backward(std::begin(elements), std::begin(elements) + old_size, std::begin(elements) + elements.size()); std::fill_n(std::begin(elements), element_pos_offset, 0); } // And then perform bit-wise shift. auto new_bit_pos = log2p1(elements.back()); auto bit_pos_offset = std::ptrdiff_t(log2p1(n.elements.back())) - std::ptrdiff_t(new_bit_pos); assert(element_pos_offset > 0 || (element_pos_offset == 0 && bit_pos_offset >= 0)); number_of_multiplications += bit_pos_offset; if (bit_pos_offset > 0) { // Left-shfit auto shft = std::size_t(bit_pos_offset); auto remaining_bits = element_number_of_bits - shft; for (auto idx = elements.size() - 1; idx > 0; --idx) { auto bits_to_transfer = elements[idx - 1] >> remaining_bits; elements[idx] <<= shft; elements[idx] |= bits_to_transfer; } elements[0] <<= shft; } else if (bit_pos_offset < 0) { // Right-shift auto shft = std::size_t(-bit_pos_offset); auto remaining_bits = element_number_of_bits - shft; elements[0] >>= shft; for (std::size_t idx = 1; idx < elements.size(); ++idx) { auto bits_to_transfer = elements[idx] << remaining_bits; elements[idx - 1] |= bits_to_transfer; elements[idx] >>= shft; } } // Compare the shifted number with the given number. bool is_bigger_than_or_equal_to = true; for (auto idx = std::ptrdiff_t(elements.size()) - 1; idx >= 0; --idx) { if (elements[idx] > n.elements[idx]) break; else if (elements[idx] < n.elements[idx]) { is_bigger_than_or_equal_to = false; break; } } // If our number is still less, if (!is_bigger_than_or_equal_to) { // Shift one more bit. ++number_of_multiplications; if (new_bit_pos == element_number_of_bits) { elements.resize(elements.size() + 1); } constexpr auto remaining_bits = element_number_of_bits - 1; for (auto idx = elements.size() - 1; idx > 0; --idx) { elements[idx] <<= 1; elements[idx] |= (elements[idx - 1] >> remaining_bits); } elements[0] <<= 1; } return number_of_multiplications; } std::size_t big_uint::multiply_2_while(big_uint const& n) { assert(elements.size() != 0); std::size_t number_of_multiplications = 0; // Perform left-shift to match the leading-1 position. // Perform element-wise shift first. assert(elements.size() <= n.elements.size()); auto element_pos_offset = n.elements.size() - elements.size(); if (element_pos_offset > 0) { number_of_multiplications = element_pos_offset * element_number_of_bits; auto old_size = elements.size(); elements.resize(n.elements.size()); std::move_backward(std::begin(elements), std::begin(elements) + old_size, std::begin(elements) + elements.size()); std::fill_n(std::begin(elements), element_pos_offset, 0); } // And then perform bit-wise shift. auto new_bit_pos = log2p1(elements.back()); auto bit_pos_offset = std::ptrdiff_t(log2p1(n.elements.back())) - std::ptrdiff_t(new_bit_pos); assert(element_pos_offset > 0 || (element_pos_offset == 0 && bit_pos_offset >= 0)); number_of_multiplications += bit_pos_offset; if (bit_pos_offset > 0) { // Left-shfit auto shft = std::size_t(bit_pos_offset); auto remaining_bits = element_number_of_bits - shft; for (auto idx = elements.size() - 1; idx > 0; --idx) { auto bits_to_transfer = elements[idx - 1] >> remaining_bits; elements[idx] <<= shft; elements[idx] |= bits_to_transfer; } elements[0] <<= shft; } else if (bit_pos_offset < 0) { // Right-shift auto shft = std::size_t(-bit_pos_offset); auto remaining_bits = element_number_of_bits - shft; elements[0] >>= shft; for (std::size_t idx = 1; idx < elements.size(); ++idx) { auto bits_to_transfer = elements[idx] << remaining_bits; elements[idx - 1] |= bits_to_transfer; elements[idx] >>= shft; } } // Compare the shifted number with the given number. bool is_strictly_bigger = true; for (auto idx = std::ptrdiff_t(elements.size()) - 1; idx >= 0; --idx) { if (elements[idx] > n.elements[idx]) break; else if (elements[idx] <= n.elements[idx]) { is_strictly_bigger = false; break; } } // If our number is strictly bigger, if (is_strictly_bigger) { // Shift one bit back. assert(number_of_multiplications > 0); --number_of_multiplications; constexpr auto remaining_bits = element_number_of_bits - 1; for (auto idx = 0; idx < elements.size() - 1; ++idx) { elements[idx] >>= 1; elements[idx] |= (elements[idx + 1] << remaining_bits); } elements.back() >>= 1; if (elements.back() == 0) { elements.pop_back(); } } return number_of_multiplications; } void big_uint::multiply_2() & { // Shift to left by 1. element_type carry = 0; for (std::size_t idx = 0; idx < elements.size(); ++idx) { auto new_element = (elements[idx] << 1) | carry; // Keep the carry. carry = (elements[idx] >> (element_number_of_bits - 1)); elements[idx] = new_element; } if (carry != 0) { elements.push_back(1); } } void big_uint::multiply_5() & { if (elements.size() == 0) { return; } element_type upper_2_bits = 0; element_type carry = 0; for (std::size_t idx = 0; idx < elements.size(); ++idx) { auto times_4 = (elements[idx] << 2) | upper_2_bits; upper_2_bits = (elements[idx] >> (element_number_of_bits - 2)); element_type new_carry = 0; // Add *this with *this * 4. elements[idx] += times_4; // If carry happens, if (elements[idx] < times_4) { new_carry = 1; // Add the carry from the previous element. elements[idx] += carry; } // If no carry happens, else { // Add the carry from the previous element. elements[idx] += carry; // If carry happens, if (elements[idx] < carry) { new_carry = 1; } } carry = new_carry; } upper_2_bits += carry; if (upper_2_bits != 0) { elements.push_back(upper_2_bits); } } int big_uint::comparison_common(big_uint const& n) const noexcept { if (elements.size() < n.elements.size()) { return -1; } else if (elements.size() > n.elements.size()) { return +1; } else { for (auto idx_p1 = elements.size(); idx_p1 > 0; --idx_p1) { if (elements[idx_p1 - 1] < n.elements[idx_p1 - 1]) { return -1; } else if (elements[idx_p1 - 1] > n.elements[idx_p1 - 1]) { return +1; } } return 0; } } big_uint& big_uint::operator+=(big_uint const& n) & { std::size_t min_size; if (elements.size() >= n.elements.size()) { min_size = n.elements.size(); } else { min_size = elements.size(); elements.insert(elements.cend(), n.elements.cbegin() + min_size, n.elements.cend()); } unsigned int carry = 0; for (std::size_t idx = 0; idx < min_size; ++idx) { auto with_carry = elements[idx] + carry; unsigned int first_carry = (with_carry < elements[idx]) ? 1 : 0; auto n_element = n.elements[idx]; elements[idx] = with_carry + n_element; carry = first_carry | ((elements[idx] < n_element) ? 1 : 0); } if (carry != 0) { for (std::size_t idx = min_size; idx < elements.size(); ++idx) { ++elements[idx]; if (elements[idx] != 0) { return *this; } } elements.push_back(1); } return *this; } big_uint& big_uint::operator+=(element_type n) & { if (is_zero()) { elements.push_back(n); return *this; } elements[0] += n; // If carry happens, if (elements[0] < n) { // Propagate carry. for (std::size_t idx = 1; idx < elements.size(); ++idx) { ++elements[idx]; if (elements[idx] != 0) { return *this; } } elements.push_back(1); } return *this; } big_uint& big_uint::operator-=(big_uint const& n) & { // Underflow! assert(elements.size() >= n.elements.size()); unsigned int borrow = 0; for (std::size_t idx = 0; idx < n.elements.size(); ++idx) { auto with_borrow = elements[idx] - borrow; unsigned int first_borrow = (with_borrow > elements[idx]) ? 1 : 0; auto n_element = n.elements[idx]; elements[idx] = with_borrow - n_element; borrow = first_borrow | ((elements[idx] > with_borrow) ? 1 : 0); } if (borrow != 0) { for (std::size_t idx = n.elements.size(); idx < elements.size(); ++idx) { --elements[idx]; if (elements[idx] != std::numeric_limits::max()) { goto remove_leading_zeros; } } // Underflow! assert(elements.back() != std::numeric_limits::max()); } remove_leading_zeros: auto itr = elements.end(); for (; itr != elements.begin(); --itr) { if (*(itr - 1) != 0) { break; } } elements.erase(itr, elements.end()); return *this; } big_uint& big_uint::operator--() & { // Underflow! assert(!is_zero()); for (std::size_t idx = 0; idx < elements.size(); ++idx) { --elements[idx]; if (elements[idx] != std::numeric_limits::max()) { break; } } // Remove leading zeros auto itr = elements.end(); for (; itr != elements.begin(); --itr) { if (*(itr - 1) != 0) { break; } } elements.erase(itr, elements.end()); return *this; } big_uint& big_uint::operator*=(element_type n) & { if (n == 0) { elements.clear(); return *this; } element_type carry = 0; for (std::size_t idx = 0; idx < elements.size(); ++idx) { auto mul = jkj::dragonbox::detail::wuint::umul128(elements[idx], n); elements[idx] = mul.low() + carry; carry = mul.high() + (elements[idx] < mul.low() ? 1 : 0); } if (carry != 0) { elements.push_back(carry); } return *this; } big_uint operator*(big_uint const& x, big_uint const& y) { if (x.is_zero() || y.is_zero()) { return big_uint(); } big_uint result; result.elements.resize(x.elements.size() + y.elements.size(), 0); decltype(x.elements) temp(x.elements.size()); for (std::size_t y_idx = 0; y_idx < y.elements.size(); ++y_idx) { // Compute y.elements[y_idx] * x and accumulate it into the result for (std::size_t x_idx = 0; x_idx < x.elements.size(); ++x_idx) { auto mul = jkj::dragonbox::detail::wuint::umul128(x.elements[x_idx], y.elements[y_idx]); // Add the first half result.elements[x_idx + y_idx] += mul.low(); unsigned int carry = result.elements[x_idx + y_idx] < mul.low() ? 1 : 0; // Add the second half auto with_carry = mul.high() + carry; carry = with_carry < mul.high() ? 1 : 0; result.elements[x_idx + y_idx + 1] += with_carry; // If there is carry, if (result.elements[x_idx + y_idx + 1] < with_carry) { // Propagate. assert(x_idx + y_idx + 2 < result.elements.size()); for (auto idx = x_idx + y_idx + 2; idx < result.elements.size(); ++idx) { ++result.elements[idx]; if (result.elements[idx] != 0) { break; } } } } } // Remove the last element if it is zero. if (result.elements.back() == 0) { result.elements.pop_back(); } return result; } big_uint big_uint::long_division(big_uint const& n) { assert(!n.is_zero()); if (this == &n) { elements.clear(); return big_uint(1); } big_uint quotient; big_uint n_shifted; while (true) { // Break if *this is smaller than n. if (elements.size() < n.elements.size()) { break; } // Shift n element-wise first. n_shifted.elements.resize(elements.size()); std::fill_n(n_shifted.elements.begin(), (elements.size() - n.elements.size()), 0); std::copy(n.elements.cbegin(), n.elements.cend(), n_shifted.elements.begin() + (elements.size() - n.elements.size())); std::size_t total_shift_amount = element_number_of_bits * (elements.size() - n.elements.size()); // Shift n bit-wise to match the leading 1 position. auto leading_1_pos = log2p1(elements.back()); auto n_leading_1_pos = log2p1(n_shifted.elements.back()); if (leading_1_pos > n_leading_1_pos) { // Shift left. auto shift_amount = leading_1_pos - n_leading_1_pos; total_shift_amount += shift_amount; element_type carry = 0; for (std::size_t idx = elements.size() - n.elements.size(); idx < elements.size(); ++idx) { auto new_element = (n_shifted.elements[idx] << shift_amount) | carry; carry = (n_shifted.elements[idx] >> (element_number_of_bits - shift_amount)); n_shifted.elements[idx] = new_element; } assert(carry == 0); } else if (leading_1_pos < n_leading_1_pos) { // Break if *this is smaller than n. if (total_shift_amount == 0) { break; } // Shift right. auto shift_amount = n_leading_1_pos - leading_1_pos; assert(total_shift_amount > shift_amount); total_shift_amount -= shift_amount; for (std::size_t idx = elements.size() - n.elements.size(); idx < elements.size(); ++idx) { n_shifted.elements[idx - 1] |= (n_shifted.elements[idx] << (element_number_of_bits - shift_amount)); n_shifted.elements[idx] >>= shift_amount; } } // Check if n_shifted is bigger than *this; if that's the case, shift one bit to right. if (n_shifted > *this) { // If we actually didn't shift anything, if (total_shift_amount == 0) { // *this is smaller than n. break; } // Shift right. --total_shift_amount; n_shifted.elements[0] >>= 1; for (std::size_t idx = 1; idx < elements.size(); ++idx) { n_shifted.elements[idx - 1] |= (n_shifted.elements[idx] << (element_number_of_bits - 1)); n_shifted.elements[idx] >>= 1; } } // Subtract n_shifted from *this. *this -= n_shifted; // Update the quotient. auto quotient_element_idx = total_shift_amount / element_number_of_bits; auto quotient_bit_idx = total_shift_amount % element_number_of_bits; if (quotient.elements.size() <= quotient_element_idx) { quotient.elements.resize(quotient_element_idx + 1); } quotient.elements[quotient_element_idx] |= (element_type(1) << quotient_bit_idx); } return quotient; } std::vector big_uint::to_decimal() const { std::vector ret; auto n = *this; auto divisor = big_uint{1000'0000'0000'0000'0000ull}; do { auto quotient = n.long_division(divisor); ret.push_back(n.is_zero() ? 0 : n[0]); n = quotient; } while (!n.is_zero()); return ret; } }dragonbox-master/subproject/test/0000775000175000017500000000000015060737600016143 5ustar renerenedragonbox-master/subproject/test/CMakeLists.txt0000664000175000017500000000444415060737600020711 0ustar renerenecmake_minimum_required(VERSION 3.14 FATAL_ERROR) project(dragonboxTests LANGUAGES CXX) # ---- Add dependencies ---- # We want warnings in tests set(dragonbox_INCLUDE_WITHOUT_SYSTEM ON CACHE INTERNAL "") include(FetchContent) if (NOT TARGET dragonbox) FetchContent_Declare(dragonbox SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../..") FetchContent_MakeAvailable(dragonbox) endif() if (NOT TARGET common) FetchContent_Declare(common SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../common") FetchContent_MakeAvailable(common) endif() if (NOT TARGET simple) FetchContent_Declare(simple SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../simple") FetchContent_MakeAvailable(simple) endif() if (NOT TARGET ryu) FetchContent_Declare(ryu SOURCE_DIR "${CMAKE_CURRENT_LIST_DIR}/../3rdparty/ryu") FetchContent_MakeAvailable(ryu) endif() # ---- Tests ---- enable_testing() function(add_test NAME) cmake_parse_arguments(TEST "TO_CHARS;RYU" "NAME" "" ${ARGN}) if(TEST_TO_CHARS) set(dragonbox dragonbox::dragonbox_to_chars) else() set(dragonbox dragonbox::dragonbox) endif() add_executable(${NAME} source/${NAME}.cpp) target_link_libraries(${NAME} PRIVATE ${dragonbox} dragonbox::common dragonbox::simple) if(TEST_RYU) target_link_libraries(${NAME} PRIVATE ryu::ryu) endif() target_compile_features(${NAME} PRIVATE cxx_std_17) _add_test(NAME ${NAME} COMMAND ${NAME}) # ---- MSVC Specifics ---- if (MSVC) # /permissive- is required (see https://github.com/jk-jeon/dragonbox/pull/74#issuecomment-3247531231) target_compile_options(${NAME} PUBLIC /permissive-) # See https://gitlab.kitware.com/cmake/cmake/-/issues/16478 set_target_properties(${NAME} PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${CMAKE_CURRENT_LIST_DIR}") endif() endfunction() add_test(verify_cache_precision) add_test(test_all_shorter_interval_cases TO_CHARS RYU) add_test(uniform_random_test TO_CHARS RYU) add_test(verify_compressed_cache) add_test(verify_fast_multiplication) add_test(verify_log_computation) add_test(verify_magic_division) option(DRAGONBOX_ENABLE_CONSTEXPR_TEST "Build constexpr test" OFF) if (DRAGONBOX_ENABLE_CONSTEXPR_TEST) add_test(constexpr) set_target_properties(constexpr PROPERTIES CXX_STANDARD 20 CXX_STANDARD_REQUIRED ON ) endif() dragonbox-master/subproject/test/results/0000775000175000017500000000000015060737600017644 5ustar renerenedragonbox-master/subproject/test/results/binary32.csv0000664000175000017500000000531215060737600022013 0ustar renerenee,bits_for_multiplication,bits_for_integer_check -149,50,61 -148,54,60 -147,55,59 -146,48,57 -145,54,57 -144,54,56 -143,54,57 -142,56,56 -141,56,56 -140,56,57 -139,46,58 -138,53,60 -137,53,60 -136,52,63 -135,52,63 -134,52,63 -133,52,63 -132,50,63 -131,50,63 -130,53,62 -129,52,62 -128,53,61 -127,53,60 -126,48,53 -125,48,53 -124,61,57 -123,61,56 -122,52,59 -121,55,58 -120,61,57 -119,54,57 -118,54,57 -117,54,59 -116,51,59 -115,53,58 -114,55,57 -113,55,60 -112,55,57 -111,55,57 -110,55,58 -109,51,60 -108,54,59 -107,54,58 -106,52,60 -105,53,59 -104,53,58 -103,54,57 -102,50,60 -101,55,59 -100,55,58 -99,52,59 -98,54,58 -97,54,57 -96,51,59 -95,51,58 -94,52,57 -93,52,59 -92,52,59 -91,52,58 -90,54,58 -89,50,56 -88,54,59 -87,55,58 -86,51,58 -85,52,58 -84,52,58 -83,50,57 -82,53,58 -81,53,66 -80,53,66 -79,52,59 -78,52,58 -77,52,57 -76,52,58 -75,54,58 -74,54,58 -73,45,56 -72,45,55 -71,45,55 -70,54,57 -69,52,58 -68,52,58 -67,52,58 -66,49,58 -65,49,57 -64,49,57 -63,47,56 -62,47,57 -61,47,61 -60,47,60 -59,45,57 -58,45,60 -57,45,60 -56,42,58 -55,42,58 -54,42,57 -53,40,59 -52,40,59 -51,40,58 -50,40,57 -49,38,58 -48,38,58 -47,38,57 -46,35,57 -45,35,57 -44,35,60 -43,33,59 -42,33,58 -41,33,60 -40,33,59 -39,31,57 -38,31,57 -37,31,57 -36,28,57 -35,28,56 -34,28,55 -33,26,55 -32,26,54 -31,26,53 -30,26,52 -29,24,52 -28,24,51 -27,24,50 -26,21,50 -25,21,49 -24,21,48 -23,19,48 -22,19,47 -21,19,46 -20,19,45 -19,17,45 -18,17,44 -17,17,43 -16,14,43 -15,14,42 -14,14,41 -13,12,41 -12,12,40 -11,12,39 -10,12,38 -9,10,38 -8,10,37 -7,10,36 -6,7,36 -5,7,35 -4,7,34 -3,5,34 -2,5,33 -1,5,32 0,3,32 1,3,32 2,3,32 3,3,32 4,1,32 5,1,32 6,1,32 7,31,35 8,31,35 9,32,35 10,31,37 11,33,37 12,33,37 13,33,37 14,36,39 15,36,39 16,36,39 17,37,42 18,38,42 19,40,42 20,38,44 21,41,44 22,41,44 23,43,44 24,41,46 25,44,46 26,44,46 27,41,49 28,41,49 29,46,49 30,46,51 31,47,51 32,47,51 33,47,51 34,50,53 35,50,53 36,52,53 37,51,56 38,51,56 39,53,56 40,52,58 41,54,58 42,54,57 43,54,56 44,54,57 45,54,57 46,54,60 47,51,63 48,52,62 49,52,61 50,51,59 51,54,58 52,57,57 53,57,57 54,52,58 55,52,57 56,55,62 57,52,64 58,52,64 59,53,63 60,50,57 61,53,58 62,53,58 63,56,58 64,51,57 65,51,59 66,55,58 67,52,55 68,52,54 69,52,53 70,51,56 71,51,55 72,51,55 73,54,64 74,49,59 75,49,59 76,49,59 77,50,62 78,50,62 79,50,62 80,51,62 81,51,62 82,51,62 83,51,62 84,50,62 85,50,62 86,50,62 87,51,62 88,51,62 89,51,62 90,50,62 91,51,61 92,51,60 93,51,59 94,49,59 95,56,58 96,56,57 97,52,58 98,54,57 99,54,58 100,50,58 101,50,58 102,54,57 103,48,60 104,48,59 dragonbox-master/subproject/test/results/plot_required_bits.m0000664000175000017500000000104415060737600023720 0ustar renerenefunction [] = plot_required_bits(filename) table = readtable(filename); fig = figure('Color','w'); hold on mul_fig_handle = plot(table{:,1}, table{:,2}); int_fig_handle = plot(table{:,1}, table{:,3}); legend([mul_fig_handle int_fig_handle], ... ["For multiplication", "For integer check"]); axis([min(table{:,1}) max(table{:,1}) min(min(table{:,2:3})) max(max(table{:,2:3}))]); xlabel('$e$', 'Interpreter', 'latex'); ylabel('Upper bound on required number of bits'); h = gca; h.YTick = 0:8:max(max(table{:,2:3})); h.YGrid = 'on'; hold off enddragonbox-master/subproject/test/results/binary64.csv0000664000175000017500000006517015060737600022030 0ustar renerenee,bits_for_multiplication,bits_for_integer_check -1074,115,118 -1073,115,118 -1072,115,119 -1071,115,118 -1070,115,119 -1069,115,119 -1068,115,119 -1067,115,118 -1066,112,119 -1065,112,119 -1064,115,119 -1063,108,120 -1062,110,119 -1061,115,118 -1060,115,118 -1059,113,117 -1058,113,116 -1057,113,115 -1056,113,118 -1055,113,117 -1054,113,118 -1053,114,118 -1052,114,121 -1051,115,120 -1050,116,119 -1049,114,119 -1048,114,121 -1047,116,121 -1046,112,117 -1045,112,118 -1044,118,118 -1043,110,118 -1042,115,118 -1041,115,118 -1040,117,121 -1039,111,118 -1038,115,118 -1037,115,117 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916,117,119 917,111,120 918,111,119 919,115,118 920,115,120 921,111,120 922,113,119 923,113,119 924,109,120 925,114,119 926,117,119 927,115,118 928,115,117 929,115,116 930,115,118 931,114,120 932,114,120 933,116,119 934,115,119 935,115,118 936,115,117 937,112,117 938,112,117 939,112,117 940,112,117 941,115,119 942,115,118 943,116,119 944,115,117 945,115,118 946,122,118 947,120,118 948,120,118 949,120,118 950,120,118 951,112,121 952,112,121 953,115,120 954,116,118 955,116,119 956,116,119 957,114,119 958,114,119 959,114,119 960,115,119 961,114,122 962,114,122 963,114,121 964,110,117 965,116,118 966,116,118 967,111,116 968,114,119 969,114,118 970,116,119 971,114,121 dragonbox-master/subproject/test/source/0000775000175000017500000000000015060737600017443 5ustar renerenedragonbox-master/subproject/test/source/verify_log_computation.cpp0000664000175000017500000002307515060737600024745 0ustar renerene// Copyright 2020 Junekey Jeon // // The contents of this file may be used under the terms of // the Apache License v2.0 with LLVM Exceptions. // // (See accompanying file LICENSE-Apache or copy at // https://llvm.org/foundation/relicensing/LICENSE.txt) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. #include "big_uint.h" #include "dragonbox/dragonbox.h" #include #include static std::int_least32_t floor_log10_pow2_precise(std::int_least32_t e) { using namespace jkj::dragonbox::detail::log; bool is_negative; if (e < 0) { is_negative = true; e = -e; } else { is_negative = false; } auto power_of_2 = jkj::big_uint::power_of_2(std::size_t(e)); auto power_of_10 = jkj::big_uint(1); std::int_least32_t k = 0; while (power_of_10 <= power_of_2) { power_of_10.multiply_5(); power_of_10.multiply_2(); ++k; } return is_negative ? -k : k - 1; } static std::int_least32_t floor_log10_pow2_minus_log10_4_over_3_precise(std::int_least32_t e) { e -= 2; if (e < 0) { e = -e; auto power_of_2 = jkj::big_uint::power_of_2(std::size_t(e)); auto power_of_10_times_3 = jkj::big_uint(3); std::int_least32_t k = 0; while (power_of_10_times_3 < power_of_2) { power_of_10_times_3.multiply_5(); power_of_10_times_3.multiply_2(); ++k; } return -k; } else { auto power_of_2_times_3 = jkj::big_uint::power_of_2(std::size_t(e)) * 3; auto power_of_10 = jkj::big_uint(1); std::int_least32_t k = 0; while (power_of_10 <= power_of_2_times_3) { power_of_10.multiply_5(); power_of_10.multiply_2(); ++k; } return k - 1; } } static std::int_least32_t floor_log2_pow10_precise(std::int_least32_t e) { bool is_negative; if (e < 0) { is_negative = true; e = -e; } else { is_negative = false; } auto power_of_10 = jkj::big_uint(1); for (std::int_least32_t i = 0; i < e; ++i) { power_of_10.multiply_5(); power_of_10.multiply_2(); } auto k = std::int_least32_t(log2p1(power_of_10)); return is_negative ? -k : k - 1; } static std::int_least32_t floor_log2_pow5_precise(std::int_least32_t e) { return floor_log2_pow10_precise(e) - e; } static std::int_least32_t floor_log5_pow2_precise(std::int_least32_t e) { bool is_negative; if (e < 0) { is_negative = true; e = -e; } else { is_negative = false; } auto power_of_2 = jkj::big_uint::power_of_2(std::size_t(e)); auto power_of_5 = jkj::big_uint(1); std::int_least32_t k = 0; while (power_of_5 <= power_of_2) { power_of_5.multiply_5(); ++k; } return is_negative ? -k : k - 1; } static std::int_least32_t floor_log5_pow2_minus_log5_3_precise(std::int_least32_t e) { if (e >= 0) { auto power_of_2 = jkj::big_uint::power_of_2(std::size_t(e)); auto power_of_5_times_3 = jkj::big_uint(3); std::int_least32_t k = 0; while (power_of_5_times_3 <= power_of_2) { power_of_5_times_3.multiply_5(); ++k; } return k - 1; } else { e = -e; auto power_of_2_times_3 = jkj::big_uint::power_of_2(std::size_t(e)) * 3; auto power_of_5 = jkj::big_uint(1); std::int_least32_t k = 0; while (power_of_5 < power_of_2_times_3) { power_of_5.multiply_5(); ++k; } return -k; } } struct verify_result { std::int_least32_t min_exponent; std::int_least32_t max_exponent; }; template static verify_result verify(std::string_view name, std::size_t tier, PreciseCalculator&& precise_calculator) { // Compute the maximum possible exponent for ensuring no overflow. using info = FastCalculatorInfo; using intermediate_type = decltype(info::multiply); using return_type = typename info::default_return_type; constexpr auto max_intermediate_value = std::min( std::numeric_limits::max(), intermediate_type( (std::min(static_cast(std::numeric_limits::max()), intermediate_type(std::numeric_limits::max() >> info::shift)) * (intermediate_type(1) << info::shift)) + ((intermediate_type(1) << info::shift) - 1))); constexpr auto no_overflow_max_exponent = (max_intermediate_value + std::min(info::subtract, intermediate_type(0))) / info::multiply; constexpr auto min_intermediate_value = std::max(std::numeric_limits::min(), intermediate_type( (std::max(static_cast(std::numeric_limits::min()), intermediate_type((std::numeric_limits::min() + (intermediate_type(1) << (info::shift + 1)) - 2) >> info::shift)) * (intermediate_type(1) << info::shift)) - ((intermediate_type(1) << info::shift) - 1))); constexpr auto no_overflow_min_exponent = (min_intermediate_value + std::max(info::subtract, intermediate_type(0))) / info::multiply; // (negative) / (positive) computes the ceiling in C/C++. verify_result result{std::int_least32_t(no_overflow_min_exponent), std::int_least32_t(no_overflow_max_exponent)}; bool reach_upper_bound = false; bool reach_lower_bound = false; for (std::int_least32_t e = 0; e <= std::max(-no_overflow_min_exponent, no_overflow_max_exponent); ++e) { if (!reach_upper_bound) { auto true_value = precise_calculator(e); auto computed_value = (e * info::multiply - info::subtract) >> info::shift; if (computed_value != true_value) { std::cout << " - error with positive e (" << "e: " << e << ", true value: " << true_value << ", computed value: " << computed_value << ")\n"; reach_upper_bound = true; result.max_exponent = e - 1; } } if (!reach_lower_bound) { auto true_value = precise_calculator(-e); auto computed_value = static_cast( static_cast((-e * info::multiply - info::subtract) >> info::shift)); if (computed_value != true_value) { std::cout << " - error with negative e (" << "e: " << -e << ", true value: " << true_value << ", computed value: " << computed_value << ")\n"; reach_lower_bound = true; result.min_exponent = -e + 1; } } if (reach_upper_bound && reach_lower_bound) { break; } } std::cout << name << " (tier: " << tier << ") is correct for e in [" << result.min_exponent << ", " << result.max_exponent << "]\n\n"; return result; } template