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math.h

src/third_party/llvm-libc/src/docs/headers/math/index.rst

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Original Source

.. _math:

====== math.h

.. include:: ../../check.rst

.. raw:: html

<style> .green {color:green} </style>

.. role:: green

.. toctree:: :hidden:

log.rst

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/aarch64/entrypoints.txt>_

  • To check math functions enabled for GPU:

    • amdgpu-entrypoints <https://github.com/llvm/llvm-project/tree/main/libc/config/gpu/amdgpu/entrypoints.txt>_

    • nvptx-entrypoints <https://github.com/llvm/llvm-project/tree/main/libc/config/gpu/nvptx/entrypoints.txt>_

  • To check math functions enabled for embedded system:

    • baremetal-aarch64 <https://github.com/llvm/llvm-project/tree/main/libc/config/baremetal/aarch64/entrypoints.txt>_

    • baremetal-aarch32 <https://github.com/llvm/llvm-project/tree/main/libc/config/baremetal/arm/entrypoints.txt>_

    • baremetal-riscv32 <https://github.com/llvm/llvm-project/tree/main/libc/config/baremetal/riscv/entrypoints.txt>_

Basic Operations

+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | <Func> | <Func_f> (float) | <Func> (double) | <Func_l> (long double) | <Func_f16> (float16) | <Func_f128> (float128) | <Func_bf16> (bfloat16) | C23 Definition Section | C23 Error Handling Section | +==================+==================+=================+========================+======================+========================+========================+========================+============================+ | ceil | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.1 | F.10.6.1 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | canonicalize | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.7 | F.10.8.7 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | copysign | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.1 | F.10.8.1 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | dadd | N/A | N/A | |check| | N/A | |check|* | N/A | 7.12.14.1 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ddiv | N/A | N/A | |check| | N/A | |check|* | N/A | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | dfma | N/A | N/A | |check| | N/A | |check|* | N/A | 7.12.14.5 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | dmul | N/A | N/A | |check| | N/A | |check|* | N/A | 7.12.14.3 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | dsub | N/A | N/A | |check| | N/A | |check|* | N/A | 7.12.14.2 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | f16add | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.1 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | f16div | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | f16fma | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.5 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | f16mul | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.3 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | f16sub | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.2 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | bf16add | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.1 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | bf16div | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | bf16fma | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.5 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | bf16mul | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.3 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | bf16sub | |check|* | |check|* | |check|* | N/A | |check| | N/A | 7.12.14.2 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fabs | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.7.3 | F.10.4.3 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fadd | N/A | |check| | |check| | N/A | |check| | N/A | 7.12.14.1 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fdim | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.1 | F.10.9.1 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fdiv | N/A | |check| | |check| | N/A | |check|* | N/A | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ffma | N/A | |check| | |check| | N/A | |check|* | N/A | 7.12.14.5 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | floor | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.2 | F.10.6.2 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmax | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.2 | F.10.9.2 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmaximum | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.4 | F.10.9.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmaximum_mag | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.6 | F.10.9.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmaximum_mag_num | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.10 | F.10.9.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmaximum_num | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.8 | F.10.9.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmin | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.3 | F.10.9.3 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fminimum | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.5 | F.10.9.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fminimum_mag | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.7 | F.10.9.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fminimum_mag_num | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.11 | F.10.9.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fminimum_num | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.12.9 | F.10.9.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmod | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.10.1 | F.10.7.1 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fmul | N/A | |check| | |check| | N/A | |check|* | N/A | 7.12.14.3 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | frexp | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.7 | F.10.3.7 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fromfp | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fromfpx | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.11 | F.10.6.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | fsub | N/A | |check| | |check| | N/A | |check|* | N/A | 7.12.14.2 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | getpayload | |check| | |check| | |check| | |check| | |check| | |check| | F.10.13.1 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ilogb | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.8 | F.10.3.8 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | iscanonical | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.3.2 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | issignaling | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.3.8 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ldexp | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.9 | F.10.3.9 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | llogb | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.10 | F.10.3.10 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | llrint | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | llround | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | logb | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.17 | F.10.3.17 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | lrint | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.5 | F.10.6.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | lround | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.7 | F.10.6.7 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | modf | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.18 | F.10.3.18 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nan | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.2 | F.10.8.2 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nearbyint | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.3 | F.10.6.3 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nextafter | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.3 | F.10.8.3 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nextdown | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.6 | F.10.8.6 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nexttoward | |check| | |check| | |check| | |check| | N/A | |check| | 7.12.11.4 | F.10.8.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | nextup | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.11.5 | F.10.8.5 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | remainder | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.10.2 | F.10.7.2 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | remquo | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.10.3 | F.10.7.3 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | rint | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.4 | F.10.6.4 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | round | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.6 | F.10.6.6 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | roundeven | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.8 | F.10.6.8 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | scalbln | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | scalbn | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | setpayload | |check| | |check| | |check| | |check| | |check| | |check| | F.10.13.2 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | setpayloadsig | |check| | |check| | |check| | |check| | |check| | |check| | F.10.13.3 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | totalorder | |check| | |check| | |check| | |check| | |check| | |check| | F.10.12.1 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | totalordermag | |check| | |check| | |check| | |check| | |check| | |check| | F.10.12.2 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | trunc | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.9 | F.10.6.9 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ufromfp | |check| | |check| | |check| | |check| | |check| | |check| | 7.12.9.10 | F.10.6.10 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | ufromfpx | |check| | |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) | <Func_bf16> (bfloat16) | C23 Definition Section | C23 Error Handling Section | +===========+==================+=================+========================+======================+========================+========================+========================+============================+ | acos | |check| | |check| | | |check| | | | 7.12.4.1 | F.10.1.1 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | acosh | |check| | | | |check| | | | 7.12.5.1 | F.10.2.1 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | acospi | | | | |check| | | | 7.12.4.8 | F.10.1.8 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | asin | |check| | |check| | | |check| | | |check| | 7.12.4.2 | F.10.1.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | asinh | |check| | | | |check| | | | 7.12.5.2 | F.10.2.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | asinpi | |check| | |check| | | |check| | | | 7.12.4.9 | F.10.1.9 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | atan | |check| | 1 ULP | | |check| | | |check| | 7.12.4.3 | F.10.1.3 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | atan2 | |check| | 1 ULP | | |check| | 1 ULP | | 7.12.4.4 | F.10.1.4 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | atan2pi | | | | | | | 7.12.4.11 | F.10.1.11 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | atanh | |check| | | | |check| | | | 7.12.5.3 | F.10.2.3 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | atanpi | | | | |check| | | | 7.12.4.10 | F.10.1.10 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | cbrt | |check| | |check| | | | | |check| | 7.12.7.1 | F.10.4.1 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | compoundn | | | | | | | 7.12.7.2 | F.10.4.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | cos | |check| | |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| | | |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| | | |check| | | |check| | 7.12.7.4 | F.10.4.4 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | lgamma | | | | | | | 7.12.8.3 | F.10.5.3 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | log | |check| | |check| | | |check| | | |check| ? | 7.12.6.11 | F.10.3.11 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | log10 | |check| | |check| | | |check| | | | 7.12.6.12 | F.10.3.12 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | log10p1 | | | | |check| | | | 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 | | | | |check| | | | 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 | |check| | | | |check| | | | 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| | |check| | 7.12.7.10 | F.10.4.10 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | tan | |check| | |check| | | |check| | | | 7.12.4.7 | F.10.1.7 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | tanh | |check| | | | |check| | | | 7.12.5.6 | F.10.2.6 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+------------------------+----------------------------+ | tanpi | |check| | | | |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.
  • ? Because of a conflict between float16 logb function and bfloat16 log function, the latter is implemented as log_bf16.

.. TODO(lntue): Add a new page to discuss about the algorithms used in the implementations and include the link here.

GPU Conformance

  • Conformance tests are located at: offload/unittests/Conformance <https://github.com/llvm/llvm-project/tree/main/offload/unittests/Conformance>_.

  • The math functions for GPUs are compiled with the following optimization options: LIBC_MATH_SKIP_ACCURATE_PASS, LIBC_MATH_INTERMEDIATE_COMP_IN_FLOAT, LIBC_MATH_SMALL_TABLES, LIBC_MATH_NO_ERRNO, and LIBC_MATH_NO_EXCEPT.

  • The conformance test results for higher math functions on GPUs are reported in the table below. The results show the maximum observed ULP distance when comparing a given GPU implementation against the corresponding correctly rounded implementation from LLVM libc, which is computed on the host CPU and serves as the reference. For comparison purposes, results for CUDA Math and HIP Math against the same reference are also included.

+------------------------+-------------+---------------+-----------------------------------------------------------------------------------+ | Function | Test Method | ULP Tolerance | Max ULP Distance | | | | +--------------------+--------------------+--------------------+--------------------+ | | | | LLVM libc | LLVM libc | CUDA Math | HIP Math | | | | | (AMDGPU) | (CUDA) | (CUDA) | (AMDGPU) | +========================+=============+===============+====================+====================+====================+====================+ | acos | Randomized | 4 | 6 (FAILED) | 6 (FAILED) | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | acosf | Exhaustive | 4 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | acosf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | acoshf | Exhaustive | 4 | 1 | 1 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | acoshf16 | Exhaustive | 2 | 0 | 0 | | 0 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | acospif16 | Exhaustive | 2 | 0 | 0 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | asin | Randomized | 4 | 6 (FAILED) | 6 (FAILED) | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | asinf | Exhaustive | 4 | 1 | 1 | 1 | 3 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | asinf16 | Exhaustive | 2 | 0 | 0 | | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | asinhf | Exhaustive | 4 | 1 | 1 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | asinhf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | atanf | Exhaustive | 5 | 0 | 0 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | atanf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | atan2f | Randomized | 6 | 1 | 1 | 2 | 3 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | atanhf | Exhaustive | 5 | 0 | 0 | 3 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | atanhf16 | Exhaustive | 2 | 0 | 0 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cbrt | Randomized | 2 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cbrtf | Exhaustive | 2 | 0 | 0 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cos | Randomized | 4 | 1 | 1 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cosf | Exhaustive | 4 | 1 | 1 | 2 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cosf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | coshf | Exhaustive | 4 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | coshf16 | Exhaustive | 2 | 1 | 0 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cospif | Exhaustive | 4 | 0 | 0 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | cospif16 | Exhaustive | 2 | 0 | 0 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | erff | Exhaustive | 16 | 0 | 0 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | expf | Exhaustive | 3 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | expf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp10 | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp10f | Exhaustive | 3 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp10f16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp2 | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp2f | Exhaustive | 3 | 1 | 1 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | exp2f16 | Exhaustive | 2 | 1 | 1 | | 0 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | expm1 | Randomized | 3 | 0 | 0 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | expm1f | Exhaustive | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | expm1f16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | hypot | Randomized | 4 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | hypotf | Randomized | 4 | 0 | 0 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | hypotf16 | Exhaustive | 2 | 0 | 0 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | logf | Exhaustive | 3 | 1 | 1 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | logf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log10 | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log10f | Exhaustive | 3 | 1 | 1 | 2 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log10f16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log1p | Randomized | 2 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log1pf | Exhaustive | 2 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log2 | Randomized | 3 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log2f | Exhaustive | 3 | 0 | 0 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | log2f16 | Exhaustive | 2 | 1 | 1 | | 0 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | powf (integer exp.) | Randomized | 16 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | powf (real exp.) | Randomized | 16 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sin | Randomized | 4 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinf | Exhaustive | 4 | 1 | 1 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sincos (cos part) | Randomized | 4 | 1 | 1 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sincos (sin part) | Randomized | 4 | 1 | 1 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sincosf (cos part) | Exhaustive | 4 | 1 | 1 | 2 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sincosf (sin part) | Exhaustive | 4 | 1 | 1 | 1 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinhf | Exhaustive | 4 | 1 | 1 | 3 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinhf16 | Exhaustive | 2 | 1 | 1 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinpif | Exhaustive | 4 | 0 | 0 | 1 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | sinpif16 | Exhaustive | 2 | 0 | 0 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tan | Randomized | 5 | 2 | 2 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanf | Exhaustive | 5 | 0 | 0 | 3 | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanf16 | Exhaustive | 2 | 1 | 1 | | 2 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanhf | Exhaustive | 5 | 0 | 0 | 2 | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanhf16 | Exhaustive | 2 | 0 | 0 | | 1 | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanpif | Exhaustive | 6 | 0 | 0 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+ | tanpif16 | Exhaustive | 2 | 1 | 1 | | | +------------------------+-------------+---------------+--------------------+--------------------+--------------------+--------------------+

Notes:

  • Exhaustive tests check every representable point in the input space. This method is used for half-precision functions and single-precision univariate functions.
  • Randomized tests check a large, deterministic subset of the input space, typically using 2\ :sup:32 samples. This method is used for functions with larger input spaces, such as single-precision bivariate and double-precision functions.
  • ULP tolerances are based on The Khronos Group, The OpenCL C Specification v3.0.19 <https://registry.khronos.org/OpenCL/specs/3.0-unified/html/OpenCL_C.html>_, Sec. 7.4, Khronos Registry [July 10, 2025].
  • The AMD GPU used for testing is AMD Radeon RX 6950 XT.
  • The NVIDIA GPU used for testing is NVIDIA RTX 4000 SFF Ada Generation.

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/>_.
  • C++23 Standard <https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/n4950.pdf>_.
  • BFloat16 <https://en.wikipedia.org/wiki/Bfloat16_floating-point_format>_.