What should be the epsilon value when performing double value equal comparison

Question

Here is the output for the below program.

value is : 2.7755575615628914E-17 Double.compare with zero : 1 isEqual with zero : true 

My question is, what should be an epsilon value? Is there any robust way to obtain the value, instead of picking a number out from the sky.

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package sandbox;  /**  *  * @author yccheok  */ public class Main {      /**      * @param args the command line arguments      */     public static void main(String[] args) {         double zero = 1.0/5.0 + 1.0/5.0 - 1.0/10.0 - 1.0/10.0 - 1.0/10.0 - 1.0/10.0;         System.out.println("value is : " + zero);         System.out.println("Double.compare with zero : " + Double.compare(zero, 0.0));         System.out.println("isEqual with zero : " + isEqual(zero, 0.0));     }      public static boolean isEqual(double d0, double d1) {         final double epsilon = 0.0000001;         return d0 == d1 ? true : Math.abs(d0 - d1) < epsilon;     } } 

Answer 1

I like (pseudo code, I don't do java)

bool fuzzyEquals(double a, double b) {     return abs(a - b) < eps * max(abs(a), abs(b)); } 

with epsilon being a few times the machine epsilon. Take 10^-12 if you don't know what to use.

This is quite problem dependant however. If the computations giving a and b are prone to roundoff error, or involve many operations, or are themselves within some (known) accuracy, you want to take a bigger epsilon.

Ths point is to use relative precision, not absolute.