Expression optimization using unary complement operators

Abstract

For purposes of code optimization there are two basic philosophies of expression analysis: one approach would attempt to do a relatively complete analysis, detecting all redundancies which are logically possible. The other approach would aim at those things which are easily detected and/or highly likely to occur. This paper gives a set of algorithms which derive from the latter philosophy but which are based on general properties rather than specific facts about a particular language or machine. The first section of the paper gives details of a notation used for describing code and defining algorithms. The most significant feature of this notation is that it allows operands to be complemented by any number of “complement operators”. This is done because most of the algorithms make frequent use of the properties of such operators. The second section describes a canonical form for expressions and a series of algorithms based on this form and the properties of complement operators. There are various facets of compiler structure which might bear on the exact usage of these algorithms. Although such considerations are not part of the scope of this paper, occasional comments are made about the relationship of an algorithm to other parts of a compiler. The third section contains a discussion of how these algorithms would fit within an overall optimizer structure.