Description of why floating point numbers may lose precision in Visual C++ (145889)

SUMMARY

Floating point decimal values generally do not have an exact binary representation. This is a side effect of how the CPU represents floating point data. For this reason, you may experience some loss of precision, and some floating point operations may produce unexpected results.

This behavior is the end result of one of the following:

The binary representation of the decimal number may not be exact. -or-
There is a type mismatch between the numbers used (for example, mixing float and double).

To resolve the behavior, you can either ensure that the value is greater or less than what you need, or you can get and use a Binary Coded Decimal (BCD) library that will maintain the precision.

MORE INFORMATION

Microsoft uses the Institute of Electrical and Electronics Engineers, Inc. (IEEE) floating point format for floating point number representation. For information about the actual binary representation of floating point values in a CPU and how precision and accuracy are affected in a floating point calculation, please see the following articles in the Microsoft Knowledge Base:

36068 INFO: IEEE Floating-Point Representation and MS Languages

125056 INFO: Precision and Accuracy in Floating-Point Calculations

Sample Code

   /* Compile options needed: none
      Value of c is printed with a decimal point precision of 10 and
      6 (printf rounded value by default) to show the difference
   */ 

   #include <stdio.h>
   #define EPSILON 0.0001   // Define your own tolerance.
   #define FLOAT_EQ(x,v) (((v - EPSILON) < x) && (x <( v + EPSILON)))

   void main()
   {
    float a,b,c
    a=1.345f;
    b=1.123f;
    c=a+b;

   //if (FLOAT_EQ(c, 2.468))        // Remove comment for correct result.

    if (c == 2.468)                 //Comment this line for correct result.
     printf("They are equal\n");
    else
     printf("They are not equal!!The value of c is %13.10f,or %f",c,c);
   }

The Output Result

They are not equal. The value of c is 2.4679999352 or 2.468000.

For EPSILON, you may use the constants FLT_EPSILON defined for float as 1.192092896e-07F or DBL_EPSILON defined for double as 2.2204460492503131 e-016. You need to include float.h for these constants. These constants are defined as the smallest positive number x, such that x+1.0 is not equal to 1.0. Because this is a very small number it is advisable that you employ user-defined tolerance for calculations involving very large numbers.