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Q184234: PRB: printf() and _fcvt() Might Produce Incorrect Rounding

Article: Q184234
Product(s): Microsoft C Compiler
Version(s): 2.0,2.1,2.2,4.0,4.1,4.2,5.0,6.0
Operating System(s): 
Keyword(s): kbcode kbCompiler kbVC200 kbVC210 kbVC220 kbVC400 kbVC410 kbVC420 kbVC500 kbVC600
Last Modified: 13-JUN-2002

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The information in this article applies to:

- Microsoft Visual C++, versions 2.0, 2.1, 2.2, 4.0, 4.1 
- Microsoft Visual C++, 32-bit Enterprise Edition, versions 4.2, 5.0, 6.0 
- Microsoft Visual C++, 32-bit Professional Edition, versions 4.2, 5.0, 6.0 
- Microsoft Visual C++, 32-bit Learning Edition, version 6.0 
- Microsoft Visual C++.NET (2002) 
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SYMPTOMS
========

You might get incorrect rounding results when you use the printf() and _fcvt()
functions.

CAUSE
=====

In the 16-bit compiler, the floating-point representation for a double data type
is in 80 bits. The 32-bit compiler uses the Institute of Electrical and
Electronics Engineers, Inc. (IEEE) floating-point specification of 64 bits.
Because you cannot always get an exact representation of decimal floating-point
numbers in binary form, the reduction in the number of bits affects the rounding
result for some numbers.

RESOLUTION
==========

The following code demonstrates this behavior. The results are shown for both
Visual C++ 5.0, Visual C++ 6.0, and Visual C++ .NET (32-bit compiler) and Visual
C++ 1.52 (16-bit compiler).

Sample Code
-----------

  #include <stdio.h>
  #include <stdlib.h>

  void main( void )

  {
  double Value;
     int    Decimal;
     int    Sign;

  Value = 6.6975;
  (void) printf( "1)  %.7f  -->  %.3f  -->  %s\n", Value, Value,
  _fcvt( Value, 3, &Decimal, &Sign ) );
  Value = 6.06975;
  (void) printf( "2)  %.7f  -->  %.4f  -->  %s\n", Value, Value,
  _fcvt( Value, 4, &Decimal, &Sign ) );
  Value = 6.006975;
  (void) printf( "3)  %.7f  -->  %.5f  -->  %s\n", Value, Value,
  _fcvt( Value, 5, &Decimal, &Sign ) );
  Value = 1.2345;
  (void) printf( "4)  %.7f  -->  %.3f  -->  %s\n", Value, Value,
  _fcvt( Value, 3, &Decimal, &Sign ) );
  Value = 1.02345;
  (void) printf( "5)  %.7f  -->  %.4f  -->  %s\n", Value, Value,
  _fcvt( Value, 4, &Decimal, &Sign ) );
  Value = 1.002345;
  (void) printf( "6)  %.7f  -->  %.5f  -->  %s\n", Value, Value,
  _fcvt( Value, 5, &Decimal, &Sign ) );
  }

VC++ 1.52c (16-bit compiler) results:

  1)    6.6975000  -->  6.698  -->  6698
  2)    6.0697500  -->  6.0698  -->  60698
  3)    6.0069750  -->  6.00698  -->  600698
  4)    1.2345000  -->  1.235  -->  1235
  5)    1.0234500  -->  1.0235  -->  10235
  6)    1.0023450  -->  1.00235  -->  100235

VC++ 5.0 (32-bit compiler) results:

  1)    6.6975000  -->  6.697  -->  6697
  2)    6.0697500  -->  6.0698  -->  60698
  3)    6.0069750  -->  6.00697  -->  600697
  4)    1.2345000  -->  1.234  -->  1234
  5)    1.0234500  -->  1.0235  -->  10235
  6)    1.0023450  -->  1.00235  -->  100235

With Visual C++ 5.0, test cases 2, 5, and 6 are correct, while 1, 3, and 4 do not
round as expected.

To work around this behavior, add a very small number to the variable used. In
the example above, add 1e-10 to Value. Modify each assignment, as shown in the
following example:

  Value = 6.06975+1e-10;

STATUS
======

This behavior is by design.

MORE INFORMATION
================

By adding the small number, you offset the rounding error that is caused by
inexact representation of some decimal floating-point numbers in binary. You can
make this number even smaller, such as equal to or greater than 1e- 15.

REFERENCES
==========

For more information on using floating-point numbers, please see the following
article in the Microsoft Knowledge Base:

  Q145889 INFO: Why Floating Point Numbers May Lose Precision

Additional query words:

======================================================================
Keywords          : kbcode kbCompiler kbVC200 kbVC210 kbVC220 kbVC400 kbVC410 kbVC420 kbVC500 kbVC600 
Technology        : kbVCsearch kbVC400 kbAudDeveloper kbVC220 kbVC410 kbVC420 kbVC500 kbVC600 kbVC200 kbVC210 kbVC32bitSearch kbVCNET kbVC500Search
Version           : :2.0,2.1,2.2,4.0,4.1,4.2,5.0,6.0
Issue type        : kbprb

=============================================================================

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