Partial redundancy elimination in SSA form

Abstract

The SSAPRE algorithm for performing partial redundancy elimination based entirely on SSA form is presented. The algorithm is formulated based on a new conceptual framework, the factored redundancy graph, for analyzing redundancy, and represents the first sparse approach to the classical problem of partial redundancy elimination. At the same time, it provides new perspectives on the problem and on methods for its solution. With the algorithm description, theorems and their proofs are given showing that the algorithm produces the best possible code by the criteria of computational optimality and lifetime optimality of the introduced temporaries. In addition to the base algorithm, a practical implementation of SSAPRE that exhibits additional compile-time efficiencies is described. In closing, measurement statistics are provided that characterize the instances of the partial redundancy problem from a set of benchmark programs and compare optimazation time spent by an implementation of SSAPRE against a classical partial redundancy emlimination implementation. The data lend insight into the nature of partial redundancy elimination and demonstrate the expediency of this new approach.