Towards a Compiler Analysis for Parallel Algorithmic Skeletons

Parallelizing compilers aim to detect data-parallel loops in sequential programs, which – after suitable transformation – can be safely and profitably executed in parallel. However, in the traditional model safe parallelization requires provable absence of dependences. At the same time, several well-known parallel algorithmic skeletons cannot be easily expressed in a data dependence framework due to spurious depedences, which prevent parallel execution. In this paper we argue that commutativity is a more suitable concept supporting formal characterization of parallel algorithmic skeletons. We show that existing commutativity definitions cannot be easily adapted for practical use, and develop a new concept of commutativity based on liveness, which readily integrates with existing compiler analyses. This enables us to develop formal definitions of parallel algorithmic skeletons such as task farms, MapReduce and Divide&Conquer. We show that existing informal characterizations of various parallel algorithmic skeletons are captured by our abstract formalizations. In this way we provide the urgently needed formal characterization of widely used parallel constructs allowing their immediate use in novel parallelizing compilers.