============== Math Functions

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log.rst stdfix.rst

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Source Locations

The main source is located at: libc/src/math.
The tests are located at: libc/test/src/math.
The floating point utilities are located at: 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. 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 or the CORE-MATH library.
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.

Implementation Status

To check math functions enabled for Linux:
To check math functions enabled for Windows:
- windows-x86_64
- windows-aarch64 - to be added
To check math functions enabled for macOS:
- darwin-x86_64
- darwin-aarch64
To check math functions enabled for GPU:
- gpu-entrypoints
To check math functions enabled for embedded system:
- baremetal-aarch32
- baremetal-riscv32 - to be added

Basic Operations

+------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | | <Func_f> (float) | (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 | | N/A | | 7.12.14.1 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | ddiv | N/A | N/A | | N/A | | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | dfma | N/A | N/A | | N/A | | 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 | | N/A | | 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 | | | N/A | | 7.12.14.4 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | ffma | N/A | | | N/A | | 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 | | | N/A | | 7.12.14.2 | F.10.11 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | getpayload | | | | |check| | | F.10.13.1 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | ilogb | |check| | |check| | |check| | |check| | |check| | 7.12.6.8 | F.10.3.8 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | 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| | | 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| | | 7.12.6.19 | F.10.3.19 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | scalbn | |check| | |check| | |check| | |check| | |check| | 7.12.6.19 | F.10.3.19 | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | setpayload | | | | |check| | | F.10.13.2 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | setpayloadsig | | | | |check| | | F.10.13.3 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | totalorder | | | | |check| | | F.10.12.1 | N/A | +------------------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | totalordermag | | | | |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_f> (float) | (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| | | | | | 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| | | | | | 7.12.5.4 | F.10.2.4 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | cospi | |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| | | | | 7.12.6.1 | F.10.3.1 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | exp10 | |check| | |check| | | | | 7.12.6.2 | F.10.3.2 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | exp10m1 | | | | | | 7.12.6.3 | F.10.3.3 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | exp2 | |check| | |check| | | | | 7.12.6.4 | F.10.3.4 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | exp2m1 | |check| | | | | | 7.12.6.5 | F.10.3.5 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | expm1 | |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| | | | | 7.12.6.11 | F.10.3.11 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | log10 | |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| | | | | 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| | | | | | 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| | | | | 7.12.4.6 | F.10.1.6 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | sincos | |check| | |check| | | | | | | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | sinh | |check| | | | | | 7.12.5.5 | F.10.2.5 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | sinpi | |check| | | | | | 7.12.4.13 | F.10.1.13 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | sqrt | |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| | | | | | 7.12.5.6 | F.10.2.6 | +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+ | tanpi | | | | | | 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.
We also use the perf tool from the CORE-MATH project: link. 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 on Linux). Fmod performance results obtained with "performance_testing".

+--------------+-------------------------------+-------------------------------+-------------------------------------+----------------------------------------------------------------------+ | | 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 | +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+