tree 62b6f1d3c772dd48681797b178d22d609ae25ca7
parent db2d5762ebf61b95b0e414b461db68ac49d06b8c
author lntue <lntue@google.com> 1746760989 -0600
committer GitHub <noreply@github.com> 1746760989 -0400
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[libc][math] Implement double precision acos correctly rounded for all rounding modes. (#138308)

We reduce computation of `acos` to `asin` as follow:

When `|x| < 0.5`:
```math
acos(x) = \frac{\pi}{2} - asin(x).
```
For `0.5 <= |x| < 1`, let
```math
u = \frac{1 - \left| x \right|}{2},
```
then
```math
acos(x) = \begin{cases}
  2 \cdot asin \left( \sqrt{u} \right) &, 0.5 \leq x < 1 \\
  \pi - 2 \cdot asin \left( \sqrt{u} \right) &, -1 < x \leq 0.5 
\end{cases}
```