HARDWARE REQUIREMENTS FOR NUMERICAL SOFTWARE
WG 2.5 has felt from its beginning that it should establish a platform
for the requests of the numerical community concerning hardware
features (essentially arithmetic) of computing systems.
Some of the basic ideas of the group on this subject are reflected in
the article by W. S. Brown, "A realistic model of floating-point
computation", in Mathematical Software III, ed.
John R. Rice, Academic
Press, New York 1977, pp. 343-360. See also W. S. Brown and S. I.
Feldman, "Environment Parameters and Basic Functions for Floating-
Point Computation", ACM Transactions on Mathematical Software, Vol. 6
(1980), pp. 510-523.
Two other documents have been prepared:
- "Desirable floating-point arithmetic and elementary functions for
numerical computation" by T. E. Hull, SIGNUM Newsletter, Vol. 14
(1979, No. 1), pp. 96-99.
- "Principles and preferences for computer arithmetic" by Ch. Reinsch,
SIGNUM Newsletter, Vol. 14 (1979, No. 1), pp. 12-27.
WG 2.5 has also given advice and support to the IEEE Microprocessor
Standards Committee, which prepared a standard for binary floating-point
arithmetic, see Computer (IEEE), Vol. 14, No. 3, (March 1981), pp.
51-87. Our group organized a panel discussion on this project at IFIP
Congress 80. At the request of the group, IFIP has officially supported
the standard, called IEEE 754. Also a radix-independent standard for
floating-point arithmetic, through an IEEE group chaired by WG 2.5
member Jim Cody, has been adopted, IEEE 854.
1. IEEE 754-1985 Binary Floating-Point Arithmetic (ANSI/IEEE
Standard), IEEE Computer Society Press, Catalog No. SH10116, 1985.
Now officially IEC 60559.
2. IEEE 854-1987 Radix and Format Independent Floating-Point
Arithmetic (ANSI/IEEE Standard), IEEE Computer Society Press, Catalog
No. SH11460, 1987.
The group has also been involved in the revision of IEEE 754, which work
was finalized in 2008 with the IEEE Standard for Floating-Point Arithmetic
(IEEE 754-2008).
It has also inspired the establishment
of a standards activity in interval arithmetic, IEEE P1788.
A working conference
on "Aspects of Computation on Asynchronous Parallel
Processors" was organized by WG 2.5 at Stanford University, California,
22-25 August 1988.
The following items are not the results of any WG 2.5 activities, but are
mentioned here due to the strong relevance to the subject being discussed.
Excellent reviews of floating-point computation and the associated
software problems are:
1. Nicholas J. Higham:
Accuracy and Stability of Numerical
Algorithms, SIAM, Philadelphia, Pennsylvania 1996.
See especially Chapter 25 (Chapter 27 in the second edition) "Software Issues in Floating Point Arithmetic".
Order Form for the Second Edition, 2002.
2. Michael L. Overton: Numerical Computing with IEEE Floating Point Arithmetic,
SIAM, Philadelphia, Pennsylvania 2001.
Order Form.
Last modified: May 29, 2014
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