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[libc][math] Implement double precision sin correctly rounded to all …
…rounding modes. (llvm#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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