Floating Point Arithmetic Notes

For MCS 471 Numerical Analysis

References:

• Prof. Floyd B. Hanson, Basic Floating Point Representation, MSCS, University of Illinois at Chicago, Fall 2002.

• Prof. William Kahan, Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic, EECS, University of California at Berkeley, May 1996. See this postscript paper for more authoritative information by clicking the URL. (not easy).

• Prof. Douglas N. Arnold, Some Disasters Attributable to Bad Numerical Computing, IMA, University of Minnesota; including those due to rounding errors, overflow errors and finite element stress estimation errors.

• Ingo Giese, General Risks and Bugs Literature (WWW 1-3) Page

• Prof. Thomas Huckle, Collection of Software Bugs, Institut fur Informatik, TU Muenchen; including those bug related disasters, risk links, and Bill Gates' interview where he dismisses Windows bugs as having little influence on the marketing of Windows.

• David Golberg, Computer Arithmetic, an Appendix in Computer Architecture: A Quantitative Approach by John Hennessy and David Patterson, Morgan Kaufmann Publ., San Mateo, CA, 1990, pp. A-1ff.

• Prof. G. W. (Pete) Stewart, Afternotes on Numerical Analysis, SIAM, Philadelphia, 1996, pp. 45ff.

• Caution: These references give varying precision numbers, depending on whether the binary unit normalizing digit is counted in the total or not.