Maximizing parallelism and minimizing synchronization with affine partitions

This paper presents an algorithm to find the optimal affine partitions that maximize the degree of parallelism and minimize the degree of synchronization in programs with arbitrary loop nestings and affine data accesses. The problem is formulated without the use of imprecise data dependence abstractions such as data dependence vectors. The algorithm presented subsumes previously proposed loop transformation algorithms that are based on unimodular transformations, loop distribution, fusion, scaling, reindexing, and statement reordering.