Optimal Code Motion in the Presence of Large Expressions

Oliver R uthing Department of Computer Science University of Dortmund D-44221 Dortmund, Germany [email protected] Abstract Common algorithms for partial redundancy elimination that are sensitive to register pressure are designed from a single-expression point of view. For each computation under investigation unnecessary code motion is avoided as far as possible. Unfortunately, such a view is only adequate when dealing with a at universe of expressions. In a more realistic setting where both composite expressions and their subexpressions are subjected to code motion trade-o s among the lifetimes of symbolic registers have to be taken into account. In this paper we present a polynomial time algorithm for the elimination of partially redundant computations that uniformly minimizes the total number of lifetime ranges at each program point. This is achieved by a re nement of our algorithm for lazy code motion [12] that incorporates optimal register tradeo s being computed by means of maximum bipartite graph matchings. 1 Motivation Partial redundancy elimination (PRE) is a technique that avoids unnecessary recomputations of values at run-time. Originating with the pioneering work of Morel and Renvoise [16] a number of improvements have been proposed [5, 6, 7, 9, 18], among which the avoidance of unnecessary code motion had a predominating role. The reason for this lies in the fact that algorithms for PRE use temporaries (symbolic registers) in order to keep the values of prior evaluations along Copyright 1998 IEEE. Published in the Proceedings of ICCL'98, May 1998 Chicago, Illinois. 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. Contact: Manager, Copyrights and Permissions / IEEE Service Center / 445 Hoes Lane / P.O. Box 1331 / Piscataway, NJ 08855-1331, USA. Telephone: + Intl. 908-5623966. some program paths. Therefore, unnecessarily large lifetimes of temporaries contribute to register pressure. Lazy code motion (LCM) [12, 13] was the rst algorithm that succeeded in reducing the lifetime ranges of temporaries to a minimum while avoiding partial redundancies as far as possible. Unfortunately, LCM su ers from the same drawback as all other known algorithms for PRE. It is designed from a single-expression point of view, and can only be extended to sets of expressions with a at structure, i. e. to sets of expressions that do not contain composite expressions and their subexpressions at once. This is a serious limitation, as a reasonable code motion algorithm should be capable of moving both large expressions and their subexpressions at once. The phenomenon is illustrated by means of the example of Figure 1.