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463dcc8749
Implement acosf function correctly rounded for all rounding modes. We perform range reduction as follows: - When `|x| < 2^(-10)`, we use cubic Taylor polynomial: ``` acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 / 6. ``` - When `2^(-10) <= |x| <= 0.5`, we use the same approximation that is used for `asinf(x)` when `|x| <= 0.5`: ``` acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 * P(x^2). ``` - When `0.5 < x <= 1`, we use the double angle formula: `cos(2y) = 1 - 2 * sin^2 (y)` to reduce to: ``` acos(x) = 2 * asin( sqrt( (1 - x)/2 ) ) ``` - When `-1 <= x < -0.5`, we reduce to the positive case above using the formula: ``` acos(x) = pi - acos(-x) ``` Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700: ``` $ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh acosf GNU libc version: 2.35 GNU libc release: stable CORE-MATH reciprocal throughput : 28.613 System LIBC reciprocal throughput : 29.204 LIBC reciprocal throughput : 24.271 $ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh asinf --latency GNU libc version: 2.35 GNU libc release: stable CORE-MATH latency : 55.554 System LIBC latency : 76.879 LIBC latency : 62.118 ``` Reviewed By: orex, zimmermann6 Differential Revision: https://reviews.llvm.org/D133550
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