Abstract | ||
---|---|---|
In this paper we reinvestigate a well-known expression first published in [7], which is often used to illustrate catastrophic
cancellation as well as the fact that identical output in different precisions does not imply reliability. The purpose of
revisiting this expression is twofold. First, we show in Section 2 that the effect of the cancellation is very different on
different IEEE 754 compliant platforms, and we unravel the underlying (hardware) reasons which are unknown to many numerical
analysts. Besides illustrating cancellation, this expression also counters the common misbelief among many numerical analysts
that a same program will deliver identical results on all IEEE conforming systems. Second, in Section 3 we use, illustrate
and comment upon the cross-platform didactical tool Arithmetic Explorer developed at the University of Antwerp, by means of
which we performed the bit level analysis of the expression evaluation under investigation on the different machines. We believe
that this tool, which is freely available from the authors, can be of use to all of us teaching a first numerical analysis
course. |
Year | DOI | Venue |
---|---|---|
2001 | 10.1007/s006070170028 | Computing |
Keywords | DocType | Volume |
AMS Subject Classifications: 65-04,65G10,65Y99.,Key Words: Computer arithmetic,IEEE floating-point,catastrophic cancellation. | Journal | 66 |
Issue | ISSN | Citations |
3 | 1436-5057 | 6 |
PageRank | References | Authors |
1.61 | 0 | 4 |
Name | Order | Citations | PageRank |
---|---|---|---|
Annie Cuyt | 1 | 161 | 41.48 |
Brigitte M. Verdonk | 2 | 87 | 27.05 |
Stefan Becuwe | 3 | 14 | 4.28 |
Peter Kuterna | 4 | 6 | 1.61 |