Floating point math issues

The pitfalls of floating-point mathematics

One important thing to remember when writing computer programs is that floating-point mathematics is not exact but is an approximation. In most programming languages, floating-point real numbers are composed of groups of 4 or 8 bytes. This means that floating-point numbers are not infinitely precise, but have a maximum precision. As a consequence, floating-point math operations (especially multiplication and division) can often lead to different results than anticipated.

Here are some excellent references about floating-point math:

• //The Perils of Floating Point// by Bruce M. Bush
• Fun with Floating Point Arithmetic

Safe floating-point division

From http://groups.google.com/group/comp.lang.fortran/browse_thread/thread/8b367f44c419fa1d/

Thank you to all that offered their suggestions for a "safe division" routine to prevent overflow. For those that are curious about the solution to the problem, I found useful to adopt a subroutine along the lines suggested by William Long:

    if(exponent(a) - exponent (b) >= maxexponent(a) .OR. b==0)Then 
     q=altv 
    else 
     q=a/b 
    endif 

The = in the >= is to take into account the case when the fractional part of a is 1.111... and that of b is 1.

It works very well.

Thank you again,

Julio.

We have implemented the above algorithm into GEOS-Chem. See routine SAFE_DIV in error_mod.f:

      FUNCTION SAFE_DIV( N, D, ALTV ) RESULT( Q )
!
!******************************************************************************
!  Subroutine SAFE_DIV performs "safe division", that is to prevent overflow,
!  underflow, NaN, or infinity errors.  An alternate value is returned if the 
!  division cannot be performed. (bmy, 2/26/08)
!
!  For more information, see the discussion on: http://groups.google.com/group/comp.lang.fortran/browse_thread/thread/8b367f44c419fa1d/
!
!  Arguments as Input:
!  ============================================================================
!  (1 ) N    : Numerator for the division 
!  (2 ) D    : Divisor for the division
!  (3 ) ALTV : Alternate value to be returned if the division can't be done
!
!  NOTES: 
!******************************************************************************
!
      ! Arguments
      REAL*8, INTENT(IN) :: N, D, ALTV
     
      ! Function value
      REAL*8             :: Q

      !==================================================================
      ! SAFE_DIV begins here! 
      !==================================================================
      IF ( EXPONENT(N) - EXPONENT(D) >= MAXEXPONENT(N) .or. D==0 ) THEN
         Q = ALTV
      ELSE
         Q = N / D
      ENDIF

      ! Return to calling program
      END FUNCTION SAFE_DIV