PRB: Inaccurate Representation of Large Double Values

• The Microsoft C/C++ Compiler (CL.EXE) included with: - 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, versions 1.0, 1.5 - Microsoft Visual C++, 32-bit Edition, versions 1.0, 2.0, 4.0, 5.0

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