[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'.

1 files changed, 1 insertions, 0 deletions

diff --git a/libc/config/linux/arm/entrypoints.txt b/libc/config/linux/arm/entrypoints.txt
index 00df445..53cdcc3 100644
--- a/libc/config/linux/arm/entrypoints.txt
+++ b/libc/config/linux/arm/entrypoints.txt
@@ -354,6 +354,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.scalbnf
     libc.src.math.scalbnl
     libc.src.math.sincosf
+    libc.src.math.sin
     libc.src.math.sinf
     libc.src.math.sinhf
     libc.src.math.sqrt