On 08/04/2018 07:22 AM, Giuliano Augusto Faulin Belinassi wrote: > Closes bug #86829 > > Description: Adds substitution rules for both sin(atan(x)) and > cos(atan(x)). These formulas are replaced by x / sqrt(x*x + 1) and 1 / > sqrt(x*x + 1) respectively, providing up to 10x speedup. This identity > can be proved mathematically. > > Changelog: > > 2018-08-03 Giuliano Belinassi <giuliano.belina...@usp.br> > > * match.pd: add simplification rules to sin(atan(x)) and cos(atan(x)). > > Bootstrap and Testing: > There were no unexpected failures in a proper testing in GCC 8.1.0 > under a x86_64 running Ubuntu 18.04. I understand these are mathematical identities. But floating point arthmetic in a compiler isn't nearly that clean :-) We have to worry about overflows, underflows, rounding, and the simple fact that many floating point numbers can't be exactly represented.
Just as an example, compare the results for x = 0x1.fffffffffffffp1023 I think sin(atan (x)) is well defined in that case. But the x*x isn't because it overflows. So I think this has to be somewhere under the -ffast-math umbrella. And the testing requirements for that are painful -- you have to verify it doesn't break the spec benchmark. I know Richi acked in the PR, but that might have been premature. jeff
