[libc][math] Implement erff function correctly rounded to all rounding modes.
Implement correctly rounded `erff` functions. For `x >= 4`, `erff(x) = 1` for `FE_TONEAREST` or `FE_UPWARD`, `0x1.ffffep-1` for `FE_DOWNWARD` or `FE_TOWARDZERO`. For `0 <= x < 4`, we divide into 32 sub-intervals of length `1/8`, and use a degree-15 odd polynomial to approximate `erff(x)` in each sub-interval: ``` erff(x) ~ x * (c0 + c1 * x^2 + c2 * x^4 + ... + c7 * x^14). ``` For `x < 0`, we can use the same formula as above, since the odd part is factored out. Performance tested with `perf.sh` tool from the CORE-MATH project on AMD Ryzen 9 5900X: Reciprocal throughput (clock cycles / op) ``` $ ./perf.sh erff --path2 GNU libc version: 2.35 GNU libc release: stable -- CORE-MATH reciprocal throughput -- with -march=native (with FMA instructions) [####################] 100 % Ntrial = 20 ; Min = 11.790 + 0.182 clc/call; Median-Min = 0.154 clc/call; Max = 12.255 clc/call; -- CORE-MATH reciprocal throughput -- with -marc...
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