| commit | 16903ace180755b7558234ff2b2e8d89b00dcb88 | [log] [tgz] |
|---|---|---|
| author | lntue <35648136+lntue@users.noreply.github.com> | Mon Jun 24 17:57:08 2024 -0400 |
| committer | GitHub <noreply@github.com> | Mon Jun 24 17:57:08 2024 -0400 |
| tree | 1158c0aef94cca9903d1238e0eef7abdf3e4cb91 | |
| parent | 5ae50698a0d6a3022af2e79d405a7eb6c8c790f0 [diff] |
[libc][math] Implement double precision sin correctly rounded to all rounding modes. (#95736)
- Algorithm:
- Step 1 - Range reduction: for a double precision input `x`, return `k`
and `u` such that
- k is an integer
- u = x - k * pi / 128, and |u| < pi/256
- Step 2 - Calculate `sin(u)` and `cos(u)` in double-double using Taylor
polynomials with errors < 2^-70 with FMA or < 2^-66 w/o FMA.
- Step 3 - Calculate `sin(x) = sin(k*pi/128) * cos(u) + cos(k*pi/128) *
sin(u)` using look-up table for `sin(k*pi/128)` and `cos(k*pi/128)`.
- Step 4 - Use Ziv's rounding test to decide if the result is correctly
rounded.
- Step 4' - If the Ziv's rounding test failed, redo step 1-3 using
128-bit precision.
- Currently, without FMA instructions, the large range reduction only
works correctly for the default rounding mode (FE_TONEAREST).
- Provide `LIBC_MATH` flag so that users can set `LIBC_MATH =
LIBC_MATH_SKIP_ACCURATE_PASS` to build the `sin` function without step 4
and 4'.
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