A realistic model for error estimates in the evaluation of elementary functions

Author

Frankowski, Krzysztof S.

Author_Institution

Comput. Sci. Dept., Univ. of Minnesota, Minneapolis, MN, USA

fYear

1978

fDate

25-27 Oct. 1978

Firstpage

70

Lastpage

74

Abstract

Floating point error analysis, as described by J. H. Wilkinson (1963) has two known drawbacks: it is too pessimistic and too cumbersome for everyday use. This paper describes a realistic model for error analysis, gives examples of simple formulae frequently used in the calculation of elementary functions, and analyses the error generated in single precision computations with these formulae, using the proposed model for error analysis. The paper also presents error bounds for various polynomial evaluations, as predicted by the model. Model verification is done using double precision arithmetic.

Keywords

error analysis; floating point arithmetic; formal verification; polynomials; double precision arithmetic; elementary function evaluation; error estimation; floating point error analysis; model verification; polynomial evaluations; realistic model; single precision computations; Algorithm design and analysis; Computational modeling; Error analysis; Mathematical model; Measurement uncertainty; Polynomials; Floating point error; computer arithmetic; evaluation of elementary functions; polynomial evaluation;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic (ARITH), 1978 IEEE 4th Symposium on

Conference_Location

Santa Monica, CA

Type

conf

DOI

10.1109/ARITH.1978.6155776

Filename

6155776