Find the Single Precision Value for Machine Epsilon

This is a part of the student software manual project for Math 5610: Computational Linear Algebra and Solution of Systems of Equations.

Routine Name: smaceps

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c smaceps.f90

and can be added to a program using

$ gfortran program.f90 smaceps.o

Description/Purpose: This routine will compute the single precision value for the machine epsilon. This is a routine for analyzing the behavior of any computer. This usually will need to be run one time for each computer.

Input: There are no inputs needed.

Output:

mach_eps : REAL - single precision machine epsilon value

i : INTEGER - the number of binary digits that represent machine epsilon

Usage/Example:

This routine has no inputs and can be implemented in a program as follows

CALL smaceps(mach_eps, i)
WRITE(*,*) mach_eps, i

The outputs from the above code:

   5.96046448E-08          24

The number of decimal digits that can be represented is roughly eight (E-8 on the end of the first value) and the number of binary digits that represent machine epsilon are 24.

Implementation/Code: The code for smaceps can be seen below.

SUBROUTINE smaceps(mach_eps, i)
	IMPLICIT NONE
	
	REAL, INTENT(OUT) :: mach_eps
	INTEGER, INTENT(OUT) :: i
	REAL :: one, approx
	
	! Initialize variables. These are set an arbitrary number that we are
	! going to use to determine the machine precision of the computer.
	one = 1.0
	mach_eps = 1.0
	approx = one + mach_eps
	
	! Do loop to calculate machine precision. Divides the arbitrary
	! number chosen above by 2 at each iteration until the computer
	! cannot tell the difference between `approx` and `one`.
	DO i=1, 1000
		mach_eps = mach_eps / 2.
		approx = one + mach_eps
		
		! If the computer cannot tell the difference between `approx`
		! and `one`, the subroutine exits with `i` (the number of
		! iterations), and `mach_eps` (machine precision).
		IF(ABS(approx - one) == 0.0) RETURN
		
	END DO

END SUBROUTINE