Function Evaluation in Unnormalized Arithmetic

Author:

Ashenhurst R. L.1

Affiliation:

1. The University of Chicago, Institute for Computer Research, Chicago, Illinois

Abstract

The evaluation of a function of one argument is a standard computational task. When an unnormalized number representation is used, it is appropriate that function evaluation to subject to certain “adjustment” criteria, defined independently of the computing method. In this paper some such criteria are developed, and their application described. In particular, consideration is given to questions of the extent to which general principles apply (i.e. for large classes of functions of a single argument) and the manner in which particular properties of the functions involved (e.g. the functions evaluated by standard library subroutines) may be invoked. The analysis, although framed in terms of unnormalized arithmetic, gives insight into the general nature of significance propagation through function evaluation, and provides a means for analyzing calculations carried out in the usual normalized arithmetic, particularly in the case where an “index of significance” is employed.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. THE PAPERS;Mathematical Software;1971

2. A Proposed Numerical Accuracy Control System;Interactive Systems for Experimental Applied Mathematics;1968

3. A Theory of Condition;SIAM Journal on Numerical Analysis;1966-06

4. Error Estimation in Computer Calculation;The American Mathematical Monthly;1965-02

5. Error Estimation in Computer Calculation;The American Mathematical Monthly;1965-02

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