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Composite Arithmetic: Proposal for a New Standard

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Holmes, WN (1997) Composite Arithmetic: Proposal for a New Standard. Computer, 30 (3). pp. 65-73. ISSN 0018-9162

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Abstract

Frustrated by the limitations of integer arithmetic, scientists and engineers developed a floating-point number representation. The subsequent adoption of a binary floating-point standard greatly enhanced scientific computing. But floating-point is too specialized for spreadsheets and inadequate for computer graphics. It also complicates programming. Finally, it does not even yield exact results: One very popular calculator gives the answer -0.000000001 to the calculation ((1 \divide 3) x 3)-1! These circumstances, coupled with developments in circuit technology and computation, have encouraged and made possible a more general arithmetic. In this article I propose what I call composite arithmetic, which combines aspects of traditional integer and floating-point arithmetics with less familiar aspects of rational and logarithmic arithmetics. Composite arithmetic complements the binary floating-point standard and satisfies more diverse computational needs. Successful development of a composite arithmetic standard would be most timely, given the burgeoning ability to manufacture complex processors and the interest in extended forms of arithmetic being shown in the research literature. It would also be highly beneficial in support of better electronic calculator arithmetic and standard operation of generic software packages such as those including spreadsheet capabilities.

Item Type: Article
Keywords: arithmetic, computer arithmetic, standard, integer arithmetic, rational arithmetic, floating point arithmetic, symmetric level indexed arithmetic, number representation
Journal or Publication Title: Computer
Page Range: pp. 65-73
ISSN: 0018-9162
Identification Number - DOI: 10.1109/2.573666
Additional Information: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. Copyright 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Date Deposited: 26 Sep 2007
Last Modified: 18 Nov 2014 03:22
URI: http://eprints.utas.edu.au/id/eprint/2003
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