[Comparing floats Knuth]

compareFloats.cpp

#include <cmath>
// return true if the difference between a and b is less than absEpsilon (a very small number, e.g. 1e-12), or within relEpsilon percent of the larger of a and b
bool approximatelyEqualAbsRel(double a, double b, double absEpsilon, double relEpsilon)
{
    // Check if the numbers are really close -- needed when comparing numbers near zero.
    double diff = fabs(a - b);
    if (diff <= absEpsilon)
        return true;
 
    // Otherwise fall back to Knuth's algorithm
    return diff <= ( (fabs(a) < fabs(b) ? fabs(b) : fabs(a)) * relEpsilon);
}

@tdm-development, you are very welcome! Good luck!