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# Finding Epsilon 0

In Brief | Find the machine epsilon of a computer, that is, the smallest number E such that 1+E != 1 . (using single precision only) |

Language | C |

# 's

` 1/* By David Isaacson, 2003`

2 * Released into the Public Domain

3 *

4 * epsilon.c

5 * The puropse of this program is to find the machine epsilon of this computer, that is,

6 * the smallest number E such that 1+E != 1 . (using single precision only)

7 */

8

9#include <stdio.h>

10

11int main()

12{

13 float max = 1; //This is the lowest value that we know works.

14 //(By works, I mean that 1+E!=1)

15 float min = 0; //This is the highest value that we know doesn't work.

16 float test = 0; //This is our test varible. Duh.

17

18 do

19 {

20 test=(max+min)/2; //Set test to avg of max & min

21

22 if((1+test)!=1) //If we're too high, set the max to test and try again

23 max=test; //(We're trying to center in on the right value)

24 if((1+test)==1) //If we're too low, set the min to test and try again

25 min=test;

26

27 }while(test!=((max+min)/2)); //If max and min are not changing, they must be so

28 //close that there is no number in between that the

29 //computer can represent.

30 //So, either test=min= the highest value that

31 //doesn't work, or test=max= the lowest

32 //value that does work. Either way we're done.

33

34 printf("The epsilon for your machine is %e.\n",max);

35 //max is the lowest value that works.

36

37 return 0;

38

39}

40

41/* When running this program on my computer (Power Mac G4 533 MHz running Mac OS X 10.2), I

42 * recieved the result:

43 *

44 * The epsilon for your machine is 5.960465e-08.

45 */

Find the machine epsilon of a computer, that is, the smallest number E such that 1+E != 1 . (using single precision only)

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