Microsoft KB Archive/184234

= Incorrect rounding results occur when you use some functions in Visual C++ =

Article ID: 184234

Article Last Modified on 1/9/2006

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APPLIES TO


 * Microsoft Visual C++ 2.0 Professional Edition
 * Microsoft Visual C++ 2.1
 * Microsoft Visual C++ 2.2
 * Microsoft Visual C++ 4.0 Standard Edition
 * Microsoft Visual C++ 4.1 Subscription
 * Microsoft Visual C++ 4.2 Enterprise Edition
 * Microsoft Visual C++ 5.0 Enterprise Edition
 * Microsoft Visual C++ 6.0 Enterprise Edition
 * Microsoft Visual C++ 4.2 Professional Edition
 * Microsoft Visual C++ 5.0 Professional Edition
 * Microsoft Visual C++ 6.0 Professional Edition
 * Microsoft Visual C++ 6.0 Standard Edition
 * Microsoft Visual C++ 2005 Express Edition
 * Microsoft Visual C++ .NET 2003 Standard Edition
 * Microsoft Visual C++ .NET 2002 Standard Edition

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This article was previously published under Q184234



SYMPTOMS
You might get incorrect rounding results when you use the following functions:
 * _fcvt
 * printf
 * fprintf
 * sprintf
 * vprintf
 * vfprintf
 * vsprintf



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, Visual C++ 2005 (32-bit compiler), and Visual C++ .NET (32-bit compiler) and Visual C++ 1.52 (16-bit compiler).

Sample Code

 * 1) include 
 * 2) include 

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.

