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

ID: Q184234

The information in this article applies to:

Microsoft Visual C++, 32-bit Editions, versions 2.0, 2.1, 2.2, 4.0, 4.1, 4.2, 5.0, 6.0

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 (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
Version : winnt:2.0,2.1,2.2,4.0,4.1,4.2,5.0,6.0
Platform : winnt
Issue type : kbprb