[all-commits] [llvm/llvm-project] 463dcc: [libc][math] Implement acosf function correctly ro...

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: 463dcc8749ed713df858dd1738e472725c8b1b35
      https://github.com/llvm/llvm-project/commit/463dcc8749ed713df858dd1738e472725c8b1b35
  Author: Tue Ly <lntue at google.com>
  Date:   2022-09-09 (Fri, 09 Sep 2022)

  Changed paths:
    M libc/config/darwin/arm/entrypoints.txt
    M libc/config/linux/aarch64/entrypoints.txt
    M libc/config/linux/x86_64/entrypoints.txt
    M libc/config/windows/entrypoints.txt
    M libc/docs/math.rst
    M libc/spec/stdc.td
    M libc/src/math/CMakeLists.txt
    A libc/src/math/acosf.h
    M libc/src/math/generic/CMakeLists.txt
    A libc/src/math/generic/acosf.cpp
    M libc/src/math/generic/asinf.cpp
    M libc/src/math/generic/inv_trigf_utils.h
    M libc/test/src/math/CMakeLists.txt
    A libc/test/src/math/acosf_test.cpp
    M libc/test/src/math/exhaustive/CMakeLists.txt
    A libc/test/src/math/exhaustive/acosf_test.cpp
    M libc/test/src/math/exhaustive/asinf_test.cpp
    M libc/utils/MPFRWrapper/MPFRUtils.cpp
    M libc/utils/MPFRWrapper/MPFRUtils.h

  Log Message:
  -----------
  [libc][math] Implement acosf function correctly rounded for all rounding modes.

Implement acosf function correctly rounded for all rounding modes.

We perform range reduction as follows:

- When `|x| < 2^(-10)`, we use cubic Taylor polynomial:
```
  acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 / 6.
```
- When `2^(-10) <= |x| <= 0.5`, we use the same approximation that is used for `asinf(x)` when `|x| <= 0.5`:
```
  acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 * P(x^2).
```
- When `0.5 < x <= 1`, we use the double angle formula: `cos(2y) = 1 - 2 * sin^2 (y)` to reduce to:
```
  acos(x) = 2 * asin( sqrt( (1 - x)/2 ) )
```
- When `-1 <= x < -0.5`, we reduce to the positive case above using the formula:
```
  acos(x) = pi - acos(-x)
```

Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh acosf
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput   : 28.613
System LIBC reciprocal throughput : 29.204
LIBC reciprocal throughput        : 24.271

$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh asinf --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency   : 55.554
System LIBC latency : 76.879
LIBC latency        : 62.118
```

Reviewed By: orex, zimmermann6

Differential Revision: https://reviews.llvm.org/D133550