Missed optimization in math expression: sin(asin(a)) == a

[zamazan4ik]

Bugzilla Link	35603
Version	trunk
OS	All
Blocks	#34959
CC	@hfinkel,@rotateright

Extended Description

clang(trunk) with '--std=c++17 -O3 -march=native -ffast-math' flags for this code:

#include <cmath>

double test(double a)
{
    return sin(asin(a));
}

generates this assembly:

test(double): # @test(double)
  push rax
  call __asin_finite
  pop rax
  jmp sin # TAILCALL

But sin(asin(a)) == a. So there is no reason to call anything.

[zamazan4ik]

The same issue about cos(acos(x)).

[zamazan4ik]

See a lot of optimizations here: https://github.com/gcc-mirror/gcc/blob/07b69d3f1cd3dd8ebb0af1fbff95914daee477d2/gcc/match.pd

[hfinkel]

Is this right? sin is periodic, so there's some range reduction here. Maybe this is true only if we know the value is between 0 and 2*pi?

[llvmbot]

sin(asin(a)) = a requires: -1 <= a <= 1. Implementing this requires introducing additional cmp instructions, so the question would it actually be better?

[hfinkel]

sin(asin(a)) = a requires: -1 <= a <= 1. Implementing this requires
introducing additional cmp instructions, so the question would it actually
be better?

It could be. asin is likely non-trivial to compute. In any case, -ffast-math implies no NaNs, and asin returns NaN outside of [-1:1], so sin(asin(a)) = a seems like a fine fast-math optimization.

[RKSimon]

mentioned in issue #34959