Question

The machine epsilon is canonically defined as the smallest number which added to one, gives a result different from one.

There is a Double.Epsilon but the name is very misleading: it is the smallest (denormalized) Double value representable, and thus useless for any kind of numeric programming.

I’d like to get the true epsilon for the Double type, so that not to have to hardcode tolerances into my program. How do I do this ?

Answer 1

It’s(on my machine):

   1.11022302462516E-16

You can easily calculate it:

        double machEps = 1.0d;

        do {
           machEps /= 2.0d;
        }
        while ((double)(1.0 + machEps) != 1.0);

        Console.WriteLine( "Calculated machine epsilon: " + machEps );

Edited:

I calcualted 2 times epsilon, now it should be correct.