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accurate path is skipped. (#164522)
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LIBC_ERRNO_MODE_SYSTEM to be header-only. (#143187)
This is the first step in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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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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Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D148781
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floating point exceptions.
Switch math functions to use libc_errno and fix some errno and
floating point exceptions
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D145349
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This part of the effort to make all test related pieces into the `test`
directory. This helps is excluding test related pieces in a straight
forward manner if LLVM_INCLUDE_TESTS is OFF. Future patches will also move
the MPFR wrapper and testutils into the 'test' directory.
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Add a place-holder implementation for asin to unblock libc demo
examples.
Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D137105
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