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Commit 15b9380d authored by Tue Ly's avatar Tue Ly
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[libc] Change sinf range reduction to mod pi/16 to be shared with cosf.

Change `sinf` range reduction to mod pi/16 to be shared with `cosf`.

Previously, `sinf` used range reduction `mod pi`, but this cannot be used to implement `cosf` since the minimax algorithm for `cosf` does not converge due to critical points at `pi/2`.  In order to be able to share the same range reduction functions for both `sinf` and `cosf`, we change the range reduction to `mod pi/16` for the following reasons:
- The table size is sufficiently small: 32 entries for `sin(k * pi/16)` with `k = 0..31`.  It could be reduced to 16 entries if we treat the final sign separately, with an extra multiplication at the end.
- The polynomials' degrees are reduced to 7/8 from 15, with extra computations to combine `sin` and `cos` with trig sum equality.
- The number of exceptional cases reduced to 2 (with FMA) and 3 (without FMA).
- The latency is reduced while maintaining similar throughput as before.

Reviewed By: zimmermann6

Differential Revision: https://reviews.llvm.org/D130629
parent 77ccf63e
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