Why doesn't GCC optimize a*a*a*a*a*a to (a*a*a)*(a*a*a)?

Question

I am doing some numerical optimization on a scientific application. One thing I noticed is that GCC will optimize the call pow(a,2) by compiling it into a

Answer 1

gcc actually can do this optimization, even for floating-point numbers. For example,

double foo(double a) {
  return a*a*a*a*a*a;
}

becomes

foo(double):
    mulsd   %xmm0, %xmm0
    movapd  %xmm0, %xmm1
    mulsd   %xmm0, %xmm1
    mulsd   %xmm1, %xmm0
    ret

with -O -funsafe-math-optimizations. This reordering violates IEEE-754, though, so it requires the flag.

Signed integers, as Peter Cordes pointed out in a comment, can do this optimization without -funsafe-math-optimizations since it holds exactly when there is no overflow and if there is overflow you get undefined behavior. So you get

foo(long):
    movq    %rdi, %rax
    imulq   %rdi, %rax
    imulq   %rdi, %rax
    imulq   %rax, %rax
    ret

with just -O. For unsigned integers, it's even easier since they work mod powers of 2 and so can be reordered freely even in the face of overflow.