Testing for numerical computations

Author

Karpovsky, Mark

Author_Institution

State University of New York at Binghamton, Computer Science Department, School of Advanced Technology, Binghamton, USA

Volume

127

Issue

2

fYear

1980

fDate

3/1/1980 12:00:00 AM

Firstpage

69

Lastpage

76

Abstract

We consider the problem of error detection in programs or specialised devices computing real functions f(x), where the argument x is represented in binary form. For error detection we use the linear check inequalities |¿¿¿¿¿¿T f(x ¿¿ ¿¿) ¿¿ C| ¿¿ ¿¿, where ¿¿ ¿¿ 0 is some given small constant, ¿¿denotes componentwise addition mod 2 of binary vectors, T is some set of binary vectors and C is a constant. A method for the construction of a minimal check set T and constant C for the given f(x) and ¿¿ is proposed. This method is based on the techniques of Walsh transforms and least-absolute-error polynomial approximation. Several important examples of optimal checks for programs computing exponential, logarithmic and trigonometric functions will be given.

Keywords

program testing; Walsh transforms; check inequalities; error detection; exponential functions; logarithmic functions; minimal check set; numerical computations; polynomial approximation; program testing; programs; real functions; trigonometric functions;

fLanguage

English

Journal_Title

Computers and Digital Techniques, IEE Proceedings E

Publisher

iet

ISSN

0143-7062

Type

jour

DOI

10.1049/ip-e.1980.0013

Filename

4647553