PRB: Inaccurate Representation of Large Double Values

• The Microsoft C/C++ Compiler (CL.EXE)
  • Microsoft C for MS-DOS, versions 6.0, 6.0a, 6.0ax
  • Microsoft C for OS/2, versions 6.0, 6.0a
  • Microsoft C/C++ for MS-DOS, version 7.0
  • Microsoft Visual C++ for Windows, 16-bit edition, versions 1.0, 1.5
  • Microsoft Visual C++, 32-bit Editions, versions 1.0, 2.0, 4.0, 5.0, 6.0

SYMPTOMS

In Microsoft C, subtracting double values greater than or equal to 1.0E+025 may return inaccurate results.

CAUSE

This is expected behavior and is due to the imprecise nature of floating-point math. Anytime floating-point math uses large numbers, there will be rounding/truncation errors and errors introduced due to imprecise representation of a result in binary format.

MORE INFORMATION

Because double values are only 15-digit precise, simple subtraction of two large numbers can give unexpected results. The following sample code demonstrates this behavior.

Double values less than 1.0E+25 may not experience the same problem.

Sample Code

#include <stdio.h>

double a = 1E+28, tmp = 9E+28;

void main (void)
{

   printf ("a = %le    tmp = %le\n", a, tmp);

   while (tmp >= 1E+25) {
      tmp -= a;
      printf ("a = %le    tmp = %le\n", a, tmp);
   }
} 

a = 1.000000e+028    tmp = 9.000000e+028
a = 1.000000e+028    tmp = 8.000000e+028
a = 1.000000e+028    tmp = 7.000000e+028
a = 1.000000e+028    tmp = 6.000000e+028
a = 1.000000e+028    tmp = 5.000000e+028
a = 1.000000e+028    tmp = 4.000000e+028
a = 1.000000e+028    tmp = 3.000000e+028
a = 1.000000e+028    tmp = 2.000000e+028
a = 1.000000e+028    tmp = 1.000000e+028
a = 1.000000e+028    tmp = 1.319414e+013 

Additional query words: 8.00 8.00c 9.00

Keywords : kbCompiler kbVC100 kbVC150 kbVC200 kbVC400 kbVC500 kbVC600
Version : 6.0 6.0a 6.0ax 7.0 1.0 1.5 2.0 4
Platform :
Issue type : kbprb