[Clang] No-zero result from `a*a - b*b` when a == b

[zhqrbitee]

Hi,
For below codes,

#include <iostream>
#include <cmath>

double test1(double a, double b) {
    return (a*a - b*b) ;
}


int main() {
    std::cout << "---------------------------------" << std::endl;
    std::cout << test1(1.1, 1.1) << std::endl;
    std::cout << "---------------------------------" << std::endl;
    return 0;
}

If a == b, then I would expect the test1 function return me exactly 0.0, as a * a should be exactly equal to b * b. However, it always return me a small value in my MacBook (with M2 chips).
I compared the assembly codes from latest clang and GCC with -O3 in compiler explorer (in arm64): both of them use fused multiply-add instructions, but the GCC one can produce 0.0 as expected, while the clang one produces 8.88178e-18.

The compiler explorer link is: https://godbolt.org/z/93Tej6d66

I know floating-point issues can be subtle, but it seems returning 0.0 in this case makes more sense to me.

[efriedma-quic]

If I modify your test slightly, both clang and gcc produce a non-zero result:

#include <iostream>
#include <cmath>

double test(double a, double b) {
    return (a*a - b*b) ;
}

double (*test1)(double a, double b) = test;
int main() {
    std::cout << "---------------------------------" << std::endl;
    std::cout << test1(1.1, 1.1) << std::endl;
    std::cout << "---------------------------------" << std::endl;
    return 0;
}

This is just how floating-point works: 1.1*1.1 produces a value which is rounded, and if you do a fused multiply-add of 1.1*1.1-(1.1*1.1), the closest float is not zero. If you really don't want contraction, you can use -ffp-contract=off.