[libc] Add a status page for math functions.

[lntue]

Summary

Add a status page for math functions.

[lntue]

Remove redundant line in performance table.

[sivachandra]

libc/docs/math.rst

26

I think you want to say,

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 result.

You probably don't need to list the different rounding modes below.

229

The MPFR or the GNU C library are not referenced in the text. Why list them here? Perhaps you want to add a section about testing and talk about MPFR there.

[lntue]

Address comments.

[lntue]

Add link to C rounding modes.

[lntue]

libc/docs/math.rst

229

I added the reference to use MPFR for correctness testing and GNU C library for performance reference.

libc/docs/index.rst

.. toctree::
     api_test
     layering
     mechanics_of_public_api
     redirectors
     source_layout
     strings
     runtimes_build
     stdio
+    math

libc/docs/math.rst

+===========================
+Math Functions in LLVM-libc
+===========================
+
+.. role::  raw-html(raw)
+    :format: html
+
+.. |check| replace:: :raw-html:`&#x2705`
+
+.. contents:: Table of Contents
+  :depth: 4
+  :local:
+
+Summary
+=======
+
+* This document tracks the status of the implementation of math functions in
+  LLVM libc.
+
+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.
+
+
+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>`_.
+
+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
+=====================
+
+Basic Operations
+----------------
+
+============== ================ =============== ======================
+<Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
+============== ================ =============== ======================
+ceil           |check|          |check|         |check|  
+copysign       |check|          |check|         |check|  
+fabs           |check|          |check|         |check|  
+fdim           |check|          |check|         |check|  
+floor          |check|          |check|         |check|  
+fmax           |check|          |check|         |check|  
+fmin           |check|          |check|         |check|  
+fmod
+fpclassify
+frexp          |check|          |check|         |check|  
+ilogb          |check|          |check|         |check|  
+isfinite
+isgreater
+isgreaterequal
+isinf
+isless
+islessequal
+islessgreater
+isnan
+isnormal
+isubordered
+ldexp          |check|          |check|         |check|  
+llrint         |check|          |check|         |check|  
+llround        |check|          |check|         |check|  
+logb           |check|          |check|         |check|  
+lrint          |check|          |check|         |check|  
+lround         |check|          |check|         |check|  
+modf           |check|          |check|         |check|  
+nan
+nearbyint      |check|          |check|         |check|  
+nextafter      |check|          |check|         |check|  
+nexttoward
+remainder      |check|          |check|         |check|  
+remquo         |check|          |check|         |check|  
+rint           |check|          |check|         |check|  
+round          |check|          |check|         |check|  
+scalbn
+signbit
+trunc          |check|          |check|         |check|  
+============== ================ =============== ======================
+
+Higher Math Functions
+---------------------
+
+============== ================ =============== ======================
+<Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
+============== ================ =============== ======================
+acos
+acosh
+asin
+asinh
+atan
+atan2
+atanh
+cbrt
+cos            |check|          |check|
+cosh
+erf
+erfc
+exp            |check|
+exp2           |check|
+expm1          |check|
+fma            |check|          |check|
+hypot          |check|          |check|
+lgamma
+log            |check|
+log10          |check|
+log1p          |check|
+log2           |check|
+pow
+sin            |check|          |check|
+sincos         |check|          |check|
+sinh
+sqrt           |check|          |check|         |check|
+tan
+tanh
+tgamma
+============== ================ =============== ======================
+
+Accuracy of Higher Math Functions
+=================================
+
+============== ================ =============== ======================
+<Func>         <Func_f> (float) <Func> (double) <Func_l> (long double)
+============== ================ =============== ======================
+cos            0.776 ULPs       large
+exp            |check|
+exp2           |check|
+expm1          |check|
+fma            |check|          |check|
+hypot          |check|          |check|
+log            |check|
+log10          |check|
+log1p          |check|
+log2           |check|
+sin            0.561 ULPs       large
+sincos         0.776 ULPs       large
+sqrt           |check|          |check|         |check|
+============== ================ =============== ======================
+
+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.
+
+..
+  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/differential_testing <https://github.com/llvm/llvm-project/tree/main/libc/test/src/math/differential_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 is 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).
+
++--------------+-------------------------------+-------------------------------+-------------------------------------+---------------------------------------------------------------------+
+| <Func>       | Reciprocal throughput (ns)    | Latency (ns)                  | Testing ranges                      | Testing configuration                                               |
+|              +-----------+-------------------+-----------+-------------------+                                     +------------+-------------------------+--------------+---------------+
+|              | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) |                                     | CPU        | OS                      | Compiler     | Special flags |
++==============+===========+===================+===========+===================+=====================================+============+=========================+==============+===============+
+| cosf         |        37 |                32 |        73 |                72 | :math:`[0, 2\pi]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 |               |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+| expf         |        14 |                 9 |        58 |                42 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+| exp2f        |        25 |                 8 |        81 |                37 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+| expm1f       |        14 |                53 |        59 |               146 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+| 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       |        13 |                25 |        57 |                72 | :math:`[e^{-1}, e]`                 | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | 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         |        36 |                31 |        72 |                71 | :math:`[-\pi, \pi]`                 | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 |               |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
+
+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/>`_.