Pitfalls of computer arithmetic
Discussions today on this list comment on irregularites of computer
arithmetic, and the problems that they pose for software
implementations of interval arithmetic.
While many numerical programmers are aware of troublesome aspects of
the Intel x86 (IA-32) floating-point architecture, now 28+ years old,
I suspect that many more programmers are not. Here is a pointer to a
recent paper that brings together many of these issues; the DOI takes
you directly to a download site for a PDF:
@String{j-TOPLAS = "ACM Transactions on Programming Languages
and Systems"}
@Article{Monniaux:2008:PVF,
author = "David Monniaux",
title = "The pitfalls of verifying floating-point
computations",
journal = j-TOPLAS,
volume = "30",
number = "3",
pages = "12:1--12:41",
month = may,
year = "2008",
CODEN = "ATPSDT",
DOI = "http://doi.acm.org/10.1145/1353445.1353446";,
ISSN = "0164-0925",
bibdate = "Wed Jun 11 19:14:53 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/";,
abstract = "Current critical systems often use a lot of
floating-point computations, and thus the testing or
static analysis of programs containing floating-point
operators has become a priority. However, correctly
defining the semantics of common implementations of
floating-point is tricky, because semantics may change
according to many factors beyond source-code level,
such as choices made by compilers. We here give
concrete examples of problems that can appear and
solutions for implementing in analysis software.",
acknowledgement = ack-nhfb,
articleno = "12",
}
-------------------------------------------------------------------------------
- Nelson H. F. Beebe Tel: +1 801 581 5254 -
- University of Utah FAX: +1 801 581 4148 -
- Department of Mathematics, 110 LCB Internet e-mail: beebe@xxxxxxxxxxxxx -
- 155 S 1400 E RM 233 beebe@xxxxxxx beebe@xxxxxxxxxxxx -
- Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe/ -
-------------------------------------------------------------------------------