Should we compare floating point numbers for equality against a *relative* error?

Question

So far I\'ve seen many posts dealing with equality of floating point numbers. The standard answer to a question like \"how should we decide if x and y are equal?\" is

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Answer 1

Using relative error is at least not as bad as using absolute errors, but it has subtle problems for values near zero due to rounding issues. A far from perfect, but somewhat robust algorithm combines absolute and relative error approaches:

boolean approxEqual(float a, float b, float absEps, float relEps) {
    // Absolute error check needed when comparing numbers near zero.
    float diff = abs(a - b);
    if (diff <= absEps) {
        return true;
    }

    // Symmetric relative error check without division.
    return (diff <= relEps * max(abs(a), abs(b)));
}

I adapted this code from Bruce Dawson's excellent article Comparing Floating Point Numbers, 2012 Edition, a required read for anyone doing floating-point comparisons -- an amazingly complex topic with many pitfalls.