Generalized Unimodular Loop Transformations for Distributed Memory Multiprocessors

In this paper, we present a generalized unimodular loop transformation as a simple, systematic and elegant method for partitioning the iteration spaces of nested loops for execution on distributed memory multiprocessors. We present a methodology for deriving the transformations that internalize multiple dependences in a multidimen-sional iteration space without resulting in a deadlocking situation. We then derive the general expression for the bounds of the transformed loops in terms of the bounds of the original space and the transformation matrix elements.