Depending on instruction set, significant speedups are observed for the vectorized path:
log1p wall time is reduced 60-93% (2.5x - 15x speedup)
expm1 wall time is reduced 0-85% (1x - 7x speedup)
The scalar path is slower by 20-30% due to the extra branch needed to handle +infinity correctly.
Full benchmarks measured on Intel(R) Xeon(R) Gold 6154 here: https://bitbucket.org/snippets/rmlarsen/MXBkpM
This makes both the small and huge argument cases faster because:
- for small inputs this removes the last pselect
- for large inputs only the reduction part follows a scalar path,
the rest use the same SIMD path as the small-argument case.
- no FMA: 1ULP up to 3pi, 2ULP up to sin(25966) and cos(18838), fallback to std::sin/cos for larger inputs
- FMA: 1ULP up to sin(117435.992) and cos(71476.0625), fallback to std::sin/cos for larger inputs
It is based on the SSE version which is much more accurate, though very slightly slower.
This changeset also includes the following required changes:
- add packet-float to packet-int type traits
- add packet float<->int reinterpret casts
- add faster pselect for AVX based on blendv
