Q59407: PRB: Inaccurate Representation of Large Double Values

Article: Q59407
Product(s): Microsoft C Compiler
Version(s): 1.0,1.5,2.0,4.0,5.0,6.0
Operating System(s): 
Keyword(s): kbCompiler kbVC100 kbVC150 kbVC200 kbVC400 kbVC500 kbVC600
Last Modified: 29-NOV-2001

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The information in this article applies to:

- Microsoft C for MS-DOS 
- Microsoft C for OS/2 
- Microsoft C/C++ for MS-DOS 
- 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 
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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

Additional query words: 8.00 8.00c 9.00

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Keywords          : kbCompiler kbVC100 kbVC150 kbVC200 kbVC400 kbVC500 kbVC600 
Technology        : kbVCsearch kbVC400 kbAudDeveloper kbZNotKeyword8 kbvc150 kbvc100 kbCCompSearch kbZNotKeyword3 kbVC500 kbVC600 kbVC200 kbVC32bitSearch kbVC16bitSearch kbVC500Search
Version           : :1.0,1.5,2.0,4.0,5.0,6.0
Issue type        : kbprb

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