[all-commits] [llvm/llvm-project] ade502: [libc][math] Implement double precision asin corre...

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: ade502a8c46b8393e022b4eabcdd445af91a451c
      https://github.com/llvm/llvm-project/commit/ade502a8c46b8393e022b4eabcdd445af91a451c
  Author: lntue <lntue at google.com>
  Date:   2025-04-25 (Fri, 25 Apr 2025)

  Changed paths:
    M libc/config/darwin/arm/entrypoints.txt
    M libc/config/linux/aarch64/entrypoints.txt
    M libc/config/linux/arm/entrypoints.txt
    M libc/config/linux/riscv/entrypoints.txt
    M libc/config/linux/x86_64/entrypoints.txt
    M libc/config/windows/entrypoints.txt
    M libc/docs/headers/math/index.rst
    M libc/src/math/generic/CMakeLists.txt
    A libc/src/math/generic/asin.cpp
    A libc/src/math/generic/asin_utils.h
    M libc/test/src/math/CMakeLists.txt
    A libc/test/src/math/asin_test.cpp
    M libc/test/src/math/smoke/CMakeLists.txt
    A libc/test/src/math/smoke/asin_test.cpp

  Log Message:
  -----------
  [libc][math] Implement double precision asin correctly rounded for all rounding modes. (#134401)

Main algorithm:

The Taylor series expansion of `asin(x)` is:
```math
\begin{align*}
  asin(x) &= x + x^3 / 6 + 3x^5 / 40 + ... \\
       &= x \cdot P(x^2) \\
       &= x \cdot P(u) &\text{, where } u = x^2.
\end{align*}
```
For the fast path, we perform range reduction mod 1/64 and use degree-7
(minimax + Taylor) polynomials to approximate `P(x^2)`.

When `|x| >= 0.5`, we use the transformation:
```math
  u = \frac{1 + x}{2}
```
and apply half-angle formula to reduce `asin(x)` to:
```math
\begin{align*}
  asin(x) &= sign(x) \cdot \left( \frac{\pi}{2} - 2 \cdot asin(\sqrt{u}) \right) \\
       &= sign(x) \cdot \left( \frac{\pi}{2} - 2 \cdot \sqrt{u} \cdot P(u) \right).
\end{align*}
```
Since `0.5 <= |x| <= 1`, `|u| <= 0.5`. So we can reuse the polynomial
evaluation of `P(u)` when `|x| < 0.5`.

For the accurate path, we redo the computations in 128-bit precision
with degree-15 (minimax + Taylor) polynomials to approximate `P(u)`.



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