PRB: Inaccurate Representation of Large Double Values (59407)


The information in this article applies to:

  • Microsoft C for MS-DOS
  • Microsoft C for OS/2
  • Microsoft Visual C++ for Windows, 16-bit edition 1.0
  • Microsoft Visual C++ for Windows, 16-bit edition 1.5
  • Microsoft Visual C++, 32-bit Editions 1.0
  • Microsoft Visual C++, 32-bit Editions 2.0
  • Microsoft Visual C++, 32-bit Editions 4.0
  • Microsoft Visual C++, 32-bit Editions 5.0
  • Microsoft Visual C++, 32-bit Editions 6.0
This article was previously published under Q59407

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);
   }
}
The above sample code produces the following output: 
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
Modification Type:MinorLast Reviewed:7/5/2005
Keywords:kbCompiler kbprb KB59407
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