On loop transformations of nested loops with affine dependencies Original Research Article

Automatic transformation of a sequential program into a parallel form has a large practical impact. In particular, the parallelization of loop nests with uniform dependencies is well understood. The most common parallelization methods used are loop-level transformations based on unimodular transformations, and the most useful unimodular transformations are inner and outer loop parallelization which are built on linear schedules. In this paper, we consider a larger class of loop nests: loop nests with affine dependencies. For affine loop nests, we provide a generalization of both, inner and outer loop parallelization. For this, the dependencies of the extremal points of the index space need to be considered. We sketch an implementation of our parallelization techniques, and outline a method for the synthesis of array processors from affine loop nests.