How to determine if two doubles are nearly equal

Question

I'm trying to find some Java code to determine if two doubles are nearly equal. I did a lot of Googling and found bits and pieces that I've put together here. Where it starts to escape me is the use of a "relative epsilon". This approach seems like what I'm looking for. I don't want to have to specify the epsilon directly but want to use an epsilon based on the magnitudes of the two arguments. Here is the code I put together, I need a sanity check on it. (P.S. I know just enough math to be dangerous.)

public class MathUtils
{
    // http://stackoverflow.com/questions/3728246/what-should-be-the-
    // epsilon-value-when-performing-double-value-equal-comparison
    // ULP = Unit in Last Place
    public static double relativeEpsilon( double a, double b )
    {
        return Math.max( Math.ulp( a ), Math.ulp( b ) );
    }

    public static boolean nearlyEqual( double a, double b )
    {
        return nearlyEqual( a, b, relativeEpsilon( a, b ) );
    }

    // http://floating-point-gui.de/errors/comparison/
    public static boolean nearlyEqual( double a, double b, double epsilon )
    {
        final double absA = Math.abs( a );
        final double absB = Math.abs( b );
        final double diff = Math.abs( a - b );

        if( a == b )
        {
            // shortcut, handles infinities
            return true;
        }
        else if( a == 0 || b == 0 || absA + absB < Double.MIN_NORMAL )
        {
            // a or b is zero or both are extremely close to it
            // relative error is less meaningful here
            // NOT SURE HOW RELATIVE EPSILON WORKS IN THIS CASE
            return diff < ( epsilon * Double.MIN_NORMAL );
        }
        else
        {
            // use relative error
            return diff / Math.min( ( absA + absB ), Double.MAX_VALUE ) < epsilon;
        }
    }
}

Answer 1

I would use a library for this, the one I normally use is DoubleMath fro Googles Guava library. https://google.github.io/guava/releases/19.0/api/docs/com/google/common/math/DoubleMath.html

if (DoubleMath.fuzzyEquals(a, b, epsilon)) { // a and b are equal within the tolerance given } there is also a fuzzyCompare.