diff options
| author | Michael Kruse <llvm-project@meinersbur.de> | 2025-01-03 10:22:51 +0100 |
|---|---|---|
| committer | Michael Kruse <llvm-project@meinersbur.de> | 2025-01-03 10:22:51 +0100 |
| commit | 38500d63e14ce340236840f60d356cdefb56a52c (patch) | |
| tree | 17edbec446ce9b50d2f215a483b83afb293a635d /libc/docs/math/index.rst | |
| parent | 1a3d5daaef7a6a63448a497da3eff7fc9e23df26 (diff) | |
| parent | 27f30029741ecf023baece7b3dde1ff9011ffefc (diff) | |
Merge branch 'main' into users/meinersbur/flang_runtime_split-headersusers/meinersbur/flang_runtime_split-headers
Diffstat (limited to 'libc/docs/math/index.rst')
| -rw-r--r-- | libc/docs/math/index.rst | 459 |
1 files changed, 0 insertions, 459 deletions
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst deleted file mode 100644 index 4934e93ccb16..000000000000 --- a/libc/docs/math/index.rst +++ /dev/null @@ -1,459 +0,0 @@ -.. _math: - -============== -Math Functions -============== - -.. include:: ../check.rst - -.. raw:: html - - <style> .green {color:green} </style> - -.. role:: green - -.. toctree:: - :hidden: - - log.rst - stdfix.rst - - -.. contents:: Table of Contents - :depth: 4 - :local: - -Source Locations -================ - -- The main source is located at: `libc/src/math <https://github.com/llvm/llvm-project/tree/main/libc/src/math>`_. -- The tests are located at: `libc/test/src/math <https://github.com/llvm/llvm-project/tree/main/libc/test/src/math>`_. -- The floating point utilities are located at: `libc/src/__support/FPUtil <https://github.com/llvm/llvm-project/tree/main/libc/src/__support/FPUtil>`_. - -Implementation Requirements / Goals -=================================== - -* The highest priority is to be as accurate as possible, according to the C and - IEEE 754 standards. By default, we will aim to be correctly rounded for `all rounding modes <https://en.cppreference.com/w/c/numeric/fenv/FE_round>`_. - The current rounding mode of the floating point environment is used to perform - computations and produce the final results. - - - To test for correctness, we compare the outputs with other correctly rounded - multiple-precision math libraries such as the `GNU MPFR library <https://www.mpfr.org/>`_ - or the `CORE-MATH library <https://core-math.gitlabpages.inria.fr/>`_. - -* Our next requirement is that the outputs are consistent across all platforms. - Notice that the consistency requirement will be satisfied automatically if the - implementation is correctly rounded. - -* Our last requirement for the implementations is to have good and predicable - performance: - - - The average performance should be comparable to other ``libc`` - implementations. - - The worst case performance should be within 10X-20X of the average. - - Platform-specific implementations or instructions could be added whenever it - makes sense and provides significant performance boost. - -* For other use cases that have strict requirements on the code size, memory - footprint, or latency, such as embedded systems, we will aim to be as accurate - as possible within the memory or latency budgets, and consistent across all - platforms. - - -Add a new math function to LLVM libc -==================================== - -* To add a new math function, follow the steps at: `libc/src/math/docs/add_math_function.md <https://github.com/llvm/llvm-project/tree/main/libc/src/math/docs/add_math_function.md>`_. - -Implementation Status -===================== - -* To check math functions enabled for Linux: - - - `linux-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/x86_64/entrypoints.txt>`_ - - - `linux-aarch64 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/aarch64/entrypoints.txt>`_ - - - `linux-aarch32 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/arm/entrypoints.txt>`_ - - - `linux-riscv and linux-riscv32 <https://github.com/llvm/llvm-project/tree/main/libc/config/linux/riscv/entrypoints.txt>`_ - -* To check math functions enabled for Windows: - - - `windows-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/windows/entrypoints.txt>`_ - - - windows-aarch64 - to be added - -* To check math functions enabled for macOS: - - - `darwin-x86_64 <https://github.com/llvm/llvm-project/tree/main/libc/config/darwin/x86_64/entrypoints.txt>`_ - - - `darwin-aarch64 <https://github.com/llvm/llvm-project/tree/main/libc/config/darwin/arm/entrypoints.txt>`_ - -* To check math functions enabled for GPU: - - - `gpu-entrypoints <https://github.com/llvm/llvm-project/tree/main/libc/config/gpu/entrypoints.txt>`_ - -* To check math functions enabled for embedded system: - - - `baremetal-aarch32 <https://github.com/llvm/llvm-project/tree/main/libc/config/baremetal/arm/entrypoints.txt>`_ - - - baremetal-riscv32 - to be added - - -Basic Operations -================ - -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section | -+==================+==================+=================+========================+======================+========================+========================+============================+ -| ceil | |check| | |check| | |check| | |check| | |check| | 7.12.9.1 | F.10.6.1 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| canonicalize | |check| | |check| | |check| | |check| | |check| | 7.12.11.7 | F.10.8.7 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| copysign | |check| | |check| | |check| | |check| | |check| | 7.12.11.1 | F.10.8.1 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| dadd | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.1 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ddiv | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.4 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| dfma | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.5 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| dmul | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.3 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| dsub | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.2 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16add | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.1 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16div | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.4 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16fma | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.5 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16mul | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.5 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16sub | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.2 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fabs | |check| | |check| | |check| | |check| | |check| | 7.12.7.3 | F.10.4.3 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fadd | N/A | |check| | |check| | N/A | |check| | 7.12.14.1 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fdim | |check| | |check| | |check| | |check| | |check| | 7.12.12.1 | F.10.9.1 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fdiv | N/A | |check| | |check| | N/A | |check|\* | 7.12.14.4 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ffma | N/A | |check| | |check| | N/A | |check|\* | 7.12.14.5 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| floor | |check| | |check| | |check| | |check| | |check| | 7.12.9.2 | F.10.6.2 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmax | |check| | |check| | |check| | |check| | |check| | 7.12.12.2 | F.10.9.2 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmaximum | |check| | |check| | |check| | |check| | |check| | 7.12.12.4 | F.10.9.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmaximum_mag | |check| | |check| | |check| | |check| | |check| | 7.12.12.6 | F.10.9.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmaximum_mag_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.10 | F.10.9.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmaximum_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.8 | F.10.9.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmin | |check| | |check| | |check| | |check| | |check| | 7.12.12.3 | F.10.9.3 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fminimum | |check| | |check| | |check| | |check| | |check| | 7.12.12.5 | F.10.9.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fminimum_mag | |check| | |check| | |check| | |check| | |check| | 7.12.12.7 | F.10.9.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fminimum_mag_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.11 | F.10.9.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fminimum_num | |check| | |check| | |check| | |check| | |check| | 7.12.12.9 | F.10.9.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmod | |check| | |check| | |check| | |check| | |check| | 7.12.10.1 | F.10.7.1 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fmul | N/A | |check| | |check| | N/A | |check|\* | 7.12.14.3 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| frexp | |check| | |check| | |check| | |check| | |check| | 7.12.6.7 | F.10.3.7 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fromfp | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fromfpx | |check| | |check| | |check| | |check| | |check| | 7.12.9.11 | F.10.6.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fsub | N/A | |check| | |check| | N/A | |check|\* | 7.12.14.2 | F.10.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| getpayload | |check| | |check| | |check| | |check| | |check| | F.10.13.1 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ilogb | |check| | |check| | |check| | |check| | |check| | 7.12.6.8 | F.10.3.8 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| iscanonical | |check| | |check| | |check| | |check| | |check| | 7.12.3.2 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| issignaling | |check| | |check| | |check| | |check| | |check| | 7.12.3.8 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ldexp | |check| | |check| | |check| | |check| | |check| | 7.12.6.9 | F.10.3.9 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| llogb | |check| | |check| | |check| | |check| | |check| | 7.12.6.10 | F.10.3.10 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| llrint | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| llround | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| logb | |check| | |check| | |check| | |check| | |check| | 7.12.6.17 | F.10.3.17 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| lrint | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| lround | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| modf | |check| | |check| | |check| | |check| | |check| | 7.12.6.18 | F.10.3.18 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nan | |check| | |check| | |check| | |check| | |check| | 7.12.11.2 | F.10.8.2 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nearbyint | |check| | |check| | |check| | |check| | |check| | 7.12.9.3 | F.10.6.3 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nextafter | |check| | |check| | |check| | |check| | |check| | 7.12.11.3 | F.10.8.3 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nextdown | |check| | |check| | |check| | |check| | |check| | 7.12.11.6 | F.10.8.6 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nexttoward | |check| | |check| | |check| | |check| | N/A | 7.12.11.4 | F.10.8.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| nextup | |check| | |check| | |check| | |check| | |check| | 7.12.11.5 | F.10.8.5 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| remainder | |check| | |check| | |check| | |check| | |check| | 7.12.10.2 | F.10.7.2 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| remquo | |check| | |check| | |check| | |check| | |check| | 7.12.10.3 | F.10.7.3 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| rint | |check| | |check| | |check| | |check| | |check| | 7.12.9.4 | F.10.6.4 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| round | |check| | |check| | |check| | |check| | |check| | 7.12.9.6 | F.10.6.6 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| roundeven | |check| | |check| | |check| | |check| | |check| | 7.12.9.8 | F.10.6.8 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| scalbln | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| scalbn | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| setpayload | |check| | |check| | |check| | |check| | |check| | F.10.13.2 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| setpayloadsig | |check| | |check| | |check| | |check| | |check| | F.10.13.3 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| totalorder | |check| | |check| | |check| | |check| | |check| | F.10.12.1 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| totalordermag | |check| | |check| | |check| | |check| | |check| | F.10.12.2 | N/A | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| trunc | |check| | |check| | |check| | |check| | |check| | 7.12.9.9 | F.10.6.9 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ufromfp | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| ufromfpx | |check| | |check| | |check| | |check| | |check| | 7.12.9.11 | F.10.6.11 | -+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ - - -Higher Math Functions -===================== - -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | C23 Definition Section | C23 Error Handling Section | -+===========+==================+=================+========================+======================+========================+========================+============================+ -| acos | |check| | | | | | 7.12.4.1 | F.10.1.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| acosh | |check| | | | | | 7.12.5.1 | F.10.2.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| acospi | | | | | | 7.12.4.8 | F.10.1.8 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| asin | |check| | | | | | 7.12.4.2 | F.10.1.2 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| asinh | |check| | | | | | 7.12.5.2 | F.10.2.2 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| asinpi | | | | | | 7.12.4.9 | F.10.1.9 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| atan | |check| | | | | | 7.12.4.3 | F.10.1.3 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| atan2 | |check| | 1 ULP | | | | 7.12.4.4 | F.10.1.4 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| atan2pi | | | | | | 7.12.4.11 | F.10.1.11 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| atanh | |check| | | | | | 7.12.5.3 | F.10.2.3 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| atanpi | | | | | | 7.12.4.10 | F.10.1.10 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| cbrt | |check| | |check| | | | | 7.12.7.1 | F.10.4.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| compoundn | | | | | | 7.12.7.2 | F.10.4.2 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| cos | |check| | |check| | | | | 7.12.4.5 | F.10.1.5 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| cosh | |check| | | | |check| | | 7.12.5.4 | F.10.2.4 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| cospi | |check| | | | |check| | | 7.12.4.12 | F.10.1.12 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| dsqrt | N/A | N/A | |check| | N/A | |check|\* | 7.12.14.6 | F.10.11 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| erf | |check| | | | | | 7.12.8.1 | F.10.5.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| erfc | | | | | | 7.12.8.2 | F.10.5.2 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| exp | |check| | |check| | | |check| | | 7.12.6.1 | F.10.3.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| exp10 | |check| | |check| | | |check| | | 7.12.6.2 | F.10.3.2 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| exp10m1 | |check| | | | |check| | | 7.12.6.3 | F.10.3.3 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| exp2 | |check| | |check| | | |check| | | 7.12.6.4 | F.10.3.4 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| exp2m1 | |check| | | | |check| | | 7.12.6.5 | F.10.3.5 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| expm1 | |check| | |check| | | |check| | | 7.12.6.6 | F.10.3.6 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fma | |check| | |check| | | | | 7.12.13.1 | F.10.10.1 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| f16sqrt | |check|\* | |check|\* | |check|\* | N/A | |check| | 7.12.14.6 | F.10.11 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| fsqrt | N/A | |check| | |check| | N/A | |check|\* | 7.12.14.6 | F.10.11 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| hypot | |check| | |check| | | | | 7.12.7.4 | F.10.4.4 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| lgamma | | | | | | 7.12.8.3 | F.10.5.3 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log | |check| | |check| | | |check| | | 7.12.6.11 | F.10.3.11 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log10 | |check| | |check| | | |check| | | 7.12.6.12 | F.10.3.12 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log10p1 | | | | | | 7.12.6.13 | F.10.3.13 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log1p | |check| | |check| | | | | 7.12.6.14 | F.10.3.14 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log2 | |check| | |check| | | |check| | | 7.12.6.15 | F.10.3.15 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| log2p1 | | | | | | 7.12.6.16 | F.10.3.16 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| logp1 | | | | | | 7.12.6.14 | F.10.3.14 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| pow | |check| | 1 ULP | | | | 7.12.7.5 | F.10.4.5 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| powi\* | | | | | | | | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| pown | | | | | | 7.12.7.6 | F.10.4.6 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| powr | | | | | | 7.12.7.7 | F.10.4.7 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| rootn | | | | | | 7.12.7.8 | F.10.4.8 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| rsqrt | | | | | | 7.12.7.9 | F.10.4.9 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| sin | |check| | |check| | | |check| | | 7.12.4.6 | F.10.1.6 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| sincos | |check| | |check| | | | | | | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| sinh | |check| | | | |check| | | 7.12.5.5 | F.10.2.5 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| sinpi | |check| | | | |check| | | 7.12.4.13 | F.10.1.13 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| sqrt | |check| | |check| | |check| | |check| | |check| | 7.12.7.10 | F.10.4.10 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| tan | |check| | |check| | | | | 7.12.4.7 | F.10.1.7 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| tanh | |check| | | | |check| | | 7.12.5.6 | F.10.2.6 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| tanpi | | | | |check| | | 7.12.4.14 | F.10.1.14 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ -| tgamma | | | | | | 7.12.8.4 | F.10.5.4 | -+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ - -Legends: - -* |check| : correctly rounded for all 4 rounding modes. -* CR: correctly rounded for the default rounding mode (round-to-the-nearest, - tie-to-even). -* x ULPs: largest errors recorded. -* N/A: Not defined in the standard or will not be added. -* \*: LLVM libc extension. - -.. - TODO(lntue): Add a new page to discuss about the algorithms used in the - implementations and include the link here. - - -Performance -=========== - -* Simple performance testings are located at: `libc/test/src/math/performance_testing <https://github.com/llvm/llvm-project/tree/main/libc/test/src/math/performance_testing>`_. - -* We also use the *perf* tool from the `CORE-MATH <https://core-math.gitlabpages.inria.fr/>`_ - project: `link <https://gitlab.inria.fr/core-math/core-math/-/tree/master>`_. - The performance results from the CORE-MATH's perf tool are reported in the - table below, using the system library as reference (such as the `GNU C library <https://www.gnu.org/software/libc/>`_ - on Linux). Fmod performance results obtained with "performance_testing". - -+--------------+-------------------------------+-------------------------------+-------------------------------------+----------------------------------------------------------------------+ -| <Func> | Reciprocal throughput (clk) | Latency (clk) | Testing ranges | Testing configuration | -| +-----------+-------------------+-----------+-------------------+ +-------------+-------------------------+--------------+---------------+ -| | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) | | CPU | OS | Compiler | Special flags | -+==============+===========+===================+===========+===================+=====================================+=============+=========================+==============+===============+ -| acosf | 24 | 29 | 62 | 77 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| acoshf | 18 | 26 | 73 | 74 | :math:`[1, 21]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| asinf | 23 | 27 | 62 | 62 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| asinhf | 21 | 39 | 77 | 91 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| atanf | 27 | 29 | 79 | 68 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| atanhf | 18 | 66 | 68 | 133 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| cosf | 13 | 32 | 53 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| coshf | 14 | 20 | 50 | 48 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| expf | 9 | 7 | 44 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| exp10f | 10 | 8 | 40 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| exp2f | 9 | 6 | 35 | 31 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| expm1f | 9 | 44 | 42 | 121 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| fmodf | 73 | 263 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | | -| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| | 9 | 11 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| fmod | 595 | 3297 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | | -| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| | 14 | 13 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| hypotf | 25 | 15 | 64 | 49 | :math:`[-10, 10] \times [-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| logf | 12 | 10 | 56 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| log10f | 9 | 17 | 35 | 48 | :math:`[e^{-1}, e]` | Ryzen 5900X | Ubuntu 22.04 LTS x86_64 | Clang 15.0.6 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| log1pf | 16 | 33 | 61 | 97 | :math:`[e^{-0.5} - 1, e^{0.5} - 1]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| log2f | 13 | 10 | 57 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| sinf | 12 | 25 | 51 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| sincosf | 19 | 30 | 57 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| sinhf | 13 | 63 | 48 | 137 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| tanf | 16 | 50 | 61 | 107 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ -| tanhf | 13 | 55 | 57 | 123 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA | -+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+ - -Algorithms + Implementation Details -=================================== - -* :doc:`log` - -Fixed-point Arithmetics -======================= - -* :doc:`stdfix` - -References -========== - -* `CRLIBM <https://hal-ens-lyon.archives-ouvertes.fr/ensl-01529804/file/crlibm.pdf>`_. -* `RLIBM <https://people.cs.rutgers.edu/~sn349/rlibm/>`_. -* `Sollya <https://www.sollya.org/>`_. -* `The CORE-MATH Project <https://core-math.gitlabpages.inria.fr/>`_. -* `The GNU C Library (glibc) <https://www.gnu.org/software/libc/>`_. -* `The GNU MPFR Library <https://www.mpfr.org/>`_. |