From chemistry-request -8 at 8- ccl.net Tue Jun 25 19:47:50 1991
Date: Tue, 25 Jun 91 17:56:58 CDT
From: twhitley*- at -*ncsa.uiuc.edu (Timothy A. Whitley)
To: chemistry ^at^ ccl.net
Subject: Epsilon
Status: R

  Eric Stahlberg's code does one too many divide; the results of his code
are too small by a factor of two.  The test is for a "just noticeable
difference" from 1.0, not a "too small to be noticed difference."

  I believe that it should go like this:

      PROGRAM MACHPR
      REAL*4 R4,TOL4,ZERO4
      REAL*8 R8,TOL8,ZERO8
*MDC*IF IBM CRAY
      REAL*16 R16,TOL16,ZERO16
*MDC*ENDIF
C
      ZERO4=0.0
      ZERO8=0.0
      R4=1.0
      TOL4=R4
  100 IF ((R4+TOL4).EQ.R4) GOTO 200
      PRINT *,TOL4
      TOL4=TOL4/2.0
      GOTO 100
 200  tol4 = tol4 * 2.0
      PRINT *,'MACHINE PRECISION R4 IS GT :', TOL4
      R8=1.0
      TOL8=R8
  300 IF ((R8+TOL8).EQ.R8) GOTO 400
      PRINT *,TOL8
      TOL8=TOL8/2.0
      GOTO 300
 400  tol8 = tol8 * 2.0
      PRINT *,'MACHINE PRECISION R8 IS GT :', TOL8
*MDC*IF IBM CRAY
      R16=1.0
      TOL16=R16
  500 IF ((R16+TOL16).EQ.R16) GOTO 600
      PRINT *,TOL16
      TOL16=TOL16/2.0
      GOTO 500
 600  tol16 = tol16 * 2.0
      PRINT *,'MACHINE PRECISION R16 IS GT :', TOL16
*MDC*ENDIF
      STOP
      END


C code from one of the earlier pseudo-code examples looks like:

main()
{
   float eps = 0.00001;
   float y = 1.0;
   float x;

Again:
   x = y + eps;      /* find rough value of eps */
   if (x > y)
     {
      eps = 0.5*eps;
      goto Again;
     }

   eps = 2.0*eps;

Again1:
   x = y + eps;       /* find value of eps within 1% */
   if (x > y)
     {
      eps = 0.99*eps;
      goto Again1;
     }

   eps = eps/0.99;

   printf("%e",eps);
}


  Under Cray UNICOS, there is also a /usr/include/float.h file which
specifies the epsilon limits.

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   Tim Whitley            ((  Internet...twhitley _-at-_)ncsa.uiuc.edu
   Cray Research, Inc.     )) Phone......(217) 244-4863
   4139 Beckman Institute ((  FAX........(217) 244-2909
   405 N. Mathews Avenue   )) "The views presented herein are not those
   Urbana, IL 61801       ((   of Cray Research, but are solely my own."
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