How to correctly and standardly compare floats?

Question

Every time I start a new project and when I need to compare some float or double variables I write the code like this one:

if (fabs(prev.min[i] - cur->min         


        

Answer 1

Thanks for your answers, they helped me a lot. I've read these materials:first and second

The answer is to use my own function for relative comparison:

bool areEqualRel(float a, float b, float epsilon) {
    return (fabs(a - b) <= epsilon * std::max(fabs(a), fabs(b)));
}

This is the most suitable solution for my needs. However I've wrote some tests and other comparison methods. I hope this will be useful for somebody. areEqualRel passes these tests, others don't.

#include <iostream>
#include <limits>
#include <algorithm>

using std::cout;
using std::max;

bool areEqualAbs(float a, float b, float epsilon) {
    return (fabs(a - b) <= epsilon);
}

bool areEqual(float a, float b, float epsilon) {
    return (fabs(a - b) <= epsilon * std::max(1.0f, std::max(a, b)));
}

bool areEqualRel(float a, float b, float epsilon) {
    return (fabs(a - b) <= epsilon * std::max(fabs(a), fabs(b)));
}

int main(int argc, char *argv[])
{
    cout << "minimum: " << FLT_MIN      << "\n";
    cout << "maximum: " << FLT_MAX      << "\n";
    cout << "epsilon: " << FLT_EPSILON  << "\n";

    float a = 0.0000001f;
    float b = 0.0000002f;
    if (areEqualRel(a, b, FLT_EPSILON)) {
        cout << "are equal a: " << a << " b: " << b << "\n";
    }
    a = 1000001.f;
    b = 1000002.f;
    if (areEqualRel(a, b, FLT_EPSILON)) {
        cout << "are equal a: " << a << " b: " << b << "\n";
    }
}

Answer 2

The Standard provides an epsilon value. It's in <limits> and you can access the value by std::numeric_limits<float>::epsilon and std::numeric_limits<double>::epsilon. There are other values in there, but I didn't check what exactly is.