Message-passing code generation for non-rectangular tiling transformations

Tiling is a well known loop transformation used to reduce communication overhead in distributed memory machines. Although a lot of theoretical research has been done concerning the selection of proper tile shapes that reduce processor idle times, there is no complete approach to automatically parallelize non-rectangularly tiled iteration spaces and consequently there are no actual experimental results to verify previous theoretical work on the effect of the tile shape on the overall completion time of a tiled algorithm. This paper presents a complete end-to-end framework to generate automatic message-passing code for tiled iteration spaces. It considers general parallelepiped tiling transformations and convex iteration spaces. We aim to address all problems concerning data parallel code generation efficiently by transforming the initial non-rectangular tile to a rectangular one. In this way, data distribution and the respective communication pattern become simple and straightforward. We have implemented our parallelizing techniques in a tool which automatically generates MPI code and run several benchmarks on a cluster of PCs. Our experimental results show the merit of general parallelepiped tiling transformations, and verify previous theoretical work on scheduling-optimal, non-rectangular tile shapes. 2006 Elsevier B.V. All rights reserved.