A new paper on the "Source of Numerical Differences" makes interesting reading for Cray users. This 30-page document is authored by Dr. C.J. Suchyta, III of Cray Research. A brief excerpt:
- Floating-point numbers are approximations to exact real numbers, and floating-point operations are approximations to exact real arithmetic operations. When approximate operations are applied to approximate values, they must yield approximate results. Therefore, the last few bits of a floating-point result are best thought of as noise that is random and unpredictable. Any program that depends on the exact values of the least significant bits is numerically suspect.
The full paper is available online in PostScript format at ftp://ftp.ucar.edu/docs/cray/numdiff.ps