This is a template file for building an entry in the student software manual project. You should use the formatting below to define an entry in your software manual.
Routine Name: smaceps
Author: Joe Koebbe
Language: Fortran. The code can be compiled using the GNU Fortran compiler (gfortran).
For example,
gfortran smaceps.f
will produce an executable ./a.exe than can be executed. If you want a different name, the following will work a bit better
gfortran -o smaceps smaceps.f
Description/Purpose: This routine will compute the single precision value for the machine epsilon or the number of digits in the representation of real numbers in single precision. 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 in this case. Even though there are arguments supplied, the real purpose is to return values in those variables.
Output: This routine returns a single precision value for the number of decimal digits that can be represented on the computer being queried.
Usage/Example:
The routine has two arguments needed to return the values of the precision in terms of the smallest number that can be represented. Since the code is written in terms of a Fortran subroutine, the values of the machine machine epsilon and the power of two that gives the machine epsilon. Due to implicit Fortran typing, the first argument is a single precision value and the second is an integer.
call smaceps(sval, ipow)
print *, ipow, sval
Output from the lines above:
24 5.96046448E-08
The first value (24) is the number of binary digits that define the machine epsilon and the second is related to the decimal version of the same value. The number of decimal digits that can be represented is roughly eight (E-08 on the end of the second value).
Implementation/Code: The following is the code for smaceps()
subroutine smaceps(seps, ipow)
c
c set up storage for the algorithm
c --------------------------------
c
real seps, one, appone
c
c initialize variables to compute the machine value near 1.0
c ----------------------------------------------------------
c
one = 1.0
seps = 1.0
appone = one + seps
c
c loop, dividing by 2 each time to determine when the difference between one and
c the approximation is zero in single precision
c ---------------------------------------------
c
ipow = 0
do 1 i=1,1000
ipow = ipow + 1
c
c update the perturbation and compute the approximation to one
c ------------------------------------------------------------
c
seps = seps / 2
appone = one + seps
c
c do the comparison and if small enough, break out of the loop and return
c control to the calling code
c ---------------------------
c
if(abs(appone-one) .eq. 0.0) return
c
1 continue
c
c if the code gets to this point, there is a bit of trouble
c ---------------------------------------------------------
c
print *,"The loop limit has been exceeded"
c
c done
c ----
c
return
end
Last Modified: September/2017