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    $\begingroup$ In your Godbolt compiler explorer link, your function has if(n==0) return 0; (not return 1 like in your question). x^0 = 1, so that's a bug. Not that it matters for the rest of the question, though; the iterative asm checks for that special case first. But strangely, the iterative implementation introduces a multiply of 1 * x that wasn't present in the source, even if we make a float version. gcc.godbolt.org/z/eqwine (and gcc only succeeds with -ffast-math.) $\endgroup$ Commented Mar 16, 2019 at 10:01
  • $\begingroup$ @PeterCordes Good catch. The return 0 has been fixed. The multiplication by 1 is interesting. I'm not sure what to make of it. $\endgroup$ Commented Mar 16, 2019 at 18:06
  • $\begingroup$ I think it's a side-effect of the way GCC transforms when turning it into a loop. Clearly gcc has some missed optimizations here, e.g. missing it for float without -ffast-math, even though it's the same value being multiplied every time. (Except for the 1.0f` which might be the sticking point?) $\endgroup$ Commented Mar 16, 2019 at 18:11