Publication
IEEE TC
Paper

The Parallel Evaluation of Arithmetic Expressions Without Division

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Abstract

As computers become capable of executing more arithmetic operations simultaneously, the question of compiling for such machines becomes more important. In this correspondence we consider arbitrary arithmetic expressions of n distinct variables with operations restricted to addition, subtraction, and multiplication. We first construct a scheme whereby any such expression can be evaluated in at most 3 log<inf>2</inf>n + 0(1) steps if sufficiently many processors are available. We then improve this result and reduce 3 log<inf>2</inf>n to 2.465 log<inf>2</inf>n. Finally, we deduce some results that apply when a fixed number of processors are available. Copyright © 1973 by The Institute of Electrical and Electronics Engineers, Inc.

Date

01 Jan 1973

Publication

IEEE TC

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