Commutativity Analysis: A New Technique for Automatically Parallelizing Serial Programs

This paper introduces a new analysis technique, commutativity analysis, for automatically parallelizing programs written in sequential, imperative programming languages. Commutativity analysis aggregates both data and computation into larger grain units. It then analyzes the computation at this granularity to discover when pieces of the computation commute (i.e. generate the same result regardless of the order in which they execute). If all of the operations required to perform a given computation commute, the compiler can automatically generate parallel code. This approach differs from standard approaches based on data dependence analysis in that it generates parallel programs that may violate the data dependences of the original serial program. Commutativity analysis can therefore automatically parallelize programs that are inherently beyond the reach of any compiler that preserves the data dependences. In this paper we formally define a set of conditions that the compiler can use to automatically detect commuting operations, prove that if operations meet these conditions then their executions commute and show how to exploit the commutativity information to automatically generate parallel code.