You should never assume the compiler is allowed to reorder floating-point computations like it does with integers. Integer math is exact, within its domain. Floating-point math is not. The IEEE-754 standard knows this, and the compiler knows this.
replyAh, fair point, it has been a while since I've needed fast inexact math.
replyThough... they are allowed to cache common subexpressions, and my point about dependency chains is quite relevant on modern hardware. So x*x, x*x*x, etc may each be computed once. And since arithmetic operators are left-to-right associative, the rather ugly code, as written, is fast and not as wasteful as it appears.
> And since arithmetic operators are left-to-right associative, the rather ugly code, as written, is fast and not as wasteful as it appears.
replyThis is incorrect, for exactly the reason you are citing: A * x * x * x * x = (((A * x) * x) * x) * x), which means that (x * x) is nowhere to be seen in the expression and cannot be factored out. Now, if you wrote x * x * x * x * A instead, _then_ the compiler could have done partial CSE against the term with B, although still not as much as you'd like.
The compiler is often not allowed to rearrange such operations due to a change in intermediate results. So one would have to activate something like fastmath for this code, but that’s probably not desired for all code, so one has to introduce a small library, and so on. Debug builds may be using different compilation flags, and suddenly performance can become terrible while debugging. Performance can also tank because a new compiler version optimizes differently, etc. So in general I don’t think this advice is true.
replyProbably for ints unconditionally. For floats in Sesse__'s example without `-ffast-math`, I count 10 muls, 2 muladds, 1 add. With `-ffast-math`, 1 mul, 3 muladds. <https://godbolt.org/z/dPrbfjzEx>
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