commit 8eab7b6886662a0b370eab5af96e8a26fa19f6df
author Rasmus Munk Larsen <rmlarsen@google.com> Tue Dec 28 15:00:19 2021 +0000
committer David Tellenbach <david.tellenbach@me.com> Tue Dec 28 15:00:19 2021 +0000
tree c118de03b8e9df57df094d4749ad32c7b0118599
parent 6e95c0cd9acd44dfad2f404e53b7b59083a35207

Improve exp<float>(): Don't flush denormal results +4% speedup.

1. Speed up exp(x) by reducing the polynomial approximant from degree 7 to
degree 6. With exactly representable coefficients computed by the Sollya tool,
this still gives a maximum relative error of 1 ulp, i.e. faithfully rounded, for
arguments where exp(x) is a normalized float. This change results in a speedup
of about 4% for AVX2.


2. Extend the range where exp(x) returns a non-zero result to from ~[-88;88] to
~[-104;88] i.e. return denormalized values for large negative arguments instead
of zero. Compared to exp<double>(x) the denormalized results gradually decrease
in accuracy down to 0.033 relative error for arguments around x = -104 where
exp(x) is ~std::numeric<float>::denorm_min(). This is expected and acceptable.