Simplify the range reduction steps by choosing the reduction constants
carefully so that the reduced arguments v = r*m_x - 1 and v^2 are exact in double
precision, even without FMA instructions, and -2^-8 <= v < 2^-7. This allows the
polynomial evaluations to be parallelized more efficiently.
Reviewed By: santoshn, zimmermann6
Differential Revision: https://reviews.llvm.org/D147755
Simplify the range reduction steps by choosing the reduction constants
carefully so that the reduced arguments v = r*m_x - 1 and v^2 are exact in double
precision, even without FMA instructions, and -2^-8 <= v < 2^-7. This allows the
polynomial evaluations to be parallelized more efficiently.
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D147676
1) `double log2_eval(double)` function added with better than float precision is added.
2) Some refactoring done to put all auxiliary functions and corresponding data
to one place to reuse the code.
3) Added tests for new functions.
4) Performance and precision tests of the function shows, that it more precise than exiting log2,
(no exceptional cases), but timing is ~5% higer that on current one.
Differential Revision: https://reviews.llvm.org/D132809
New exp2 function algorithm:
1) Improved performance: 8.176 vs 15.270 by core-math perf tool.
2) Improved accuracy. Only two special values left.
3) Lookup table size reduced twice.
Differential Revision: https://reviews.llvm.org/D129005
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
Implement expm1f function that is correctly rounded for all rounding modes. This is based on expf implementation.
From exhaustive testings, using expf implementation, and subtract 1.0 before rounding the final result to single precision
gives correctly rounded results for all |x| > 2^-4 with 1 exception. When |x| < 2^-25, we use x + x^2 (implemented with a
single fma). And for 2^-25 <= |x| <= 2^-4, we use a single degree-8 minimax polynomial generated by Sollya.
Reviewed By: sivachandra, zimmermann6
Differential Revision: https://reviews.llvm.org/D121574
