A theory of compaction-based parallelization

We present a simple and uniform transformational system for extracting parallelism from programs. The transformations are studied as a formal system. We define a measure of program improvement, and show that the transformations improve programs with respect to the measure. We show that it is possible to compute limits of infinite sequences of the transformations; this allows our system to implement software pipelining, and leads to a general solution to the problem of software pipelining in the presence of tests. Using the primitive transformations and the limit-taking transformation, it is possible to express the classical parallelization techniques for vector, multiprocessor, and VLIW machines. Thus, our transformational system can be viewed as a formal foundation for the area of parallelization. We present implementations of two techniques, doacross and a simple form of vectorization. © 1990.