Machine epsilon is the smallest number when it is added to 1 your computer assumes it 1 briefely. It depends the physical features of your computer. After this definition let us create the pseudocode of a program that computes your machines' epsilons.




epsilon=1
DO
IF(1+epsilon<=1) EXIT
epsilon=epsilon/2
END DO
epsilon=epsilon*2

The code above is the pseudocode of a machine epsilon algorythm. I guess you know about pseudocode :) If you do not know do not be sorry since it is nothing :P It is a description of an algorythm that is language independent.YOu just write on what you think to do. That is it!

Now let me give you the Java code of that algorythm and the output of it.

import javax.swing.JOptionPane;

public class epsilon{
public static void main(String args[]){
double epsilon = 1.0;
for(int i=1; i<100000; i++){

if(epsilon+1.0<=1.0){
break;
}
else{
epsilon=epsilon/2.0;
}
}
epsilon=2*epsilon;
JOptionPane.showMessageDialog(null,"The epsilon of the machine is:"+epsilon);
}
}

Since i have explained each line of a java code example i think you can understand the steps and pseudocode helps you in this issue as well.

So my output is in the figure below. But do not be confused if you have not got the same output since it depends the physical features of your PC!



I will keep giving some java examples as well. Using Java in mathematic will suprise you or mathematics will suprise you ;)