Some Causes of Differences in Floating-Point Results

MS-DOS                 | WINDOWS

The information in this article applies to:

• The Microsoft C/C++ Compiler (CL.EXE) included with:

      - Microsoft C for MS-DOS, versions 6.0, 6.0a, and 6.0ax
      - Microsoft C/C++ for MS-DOS, version 7.0
      - Microsoft Visual C++ for Windows, versions 1.0 and 1.5
  

SUMMARY

This article discusses some reasons why programs might produce different floating-point results when compiled with different compiler options.

The program below produces different results when complied using

   cl -AM -FPi prog.c

   cl -AM -FPa prog.c

MORE INFORMATION

Also, the second number printed in the /FPi case is smaller than DBL_MIN, as defined in FLOAT.H. This situation is also correct because DBL_MIN is the smallest possible NORMALIZED value. (Normalized means that the high- order bit of the mantissa is a one.)

"Denormals" (numbers where there are zeros in some of the high-order bits of the mantissa), however, can represent numbers "x" in the ranges + DBL_MIN > x > 0 and 0 > x > -DBL_MIN. Although this is an unusual situation, it is not an error. A denormal is less precise than a normalized number; however, a denormal is still more precise than 0 (zero) (which is the next best representation). By allowing use of denormal numbers, we make our floating-point result slightly more accurate. The alternate math library (/FPa) represents denormal numbers as 0 (zero).

Another possible cause of differences in floating-point results is the inclusion or omission of the /Op option. When /Op is omitted, the compiler may skip storing intermediate results as 64-bit objects in memory, leaving them instead in the 80-bit registers of the 80x87 (or emulator package). This increases the speed and accuracy of the calculation. However, this can decrease the consistency of the calculations because other intermediate results may have been stored in 64-bit objects in memory anyway. Including /Op forces all intermediate results to be stored in memory, giving more consistent results. This option is often handy in programs involving complicated floating-point calculations.

The program and its output follow:

Sample Code

#include <stdio.h>    // START OF PROG.C
#include <float.h>

void main(void)

    double  a,b,c,prod1,prod2;

    _fpreset();
    a=9.5788979e-283;
    b=8.050847e-1;
    c=9.5588526e-28;

    prod1=a*b;
    printf("\n product1 = %1.15le \n",prod1);
    prod2=c*prod1;
    printf("\n product2 = %1.15le \n",prod2);

Results

 // RESULTS OBTAINED USING CL -AM -FPi  PROG.C

 product1 = 7.711824142152130e-283

 product2 = 7.371619025195353e-310 // This value is less than DBL_MIN

 // RESULTS OBTAINED USING CL -AM -FPa PROG.C

 product1 = 7.711824142152130e-283

 product2 = 0.000000000000000e+000