Integrating Data Distribution and Loop Transformations

This paper presents a technique for nding good distributions of arrays and suitable loop restructuring transformations so that communication is minimized in the execution of nested loops on message passing machines. For each possible distribution (by one or more dimensions), we derive the best unimodular loop transformation that results in block transfers of data. Unlike other work which focus on either data layout or on program transformations, this paper combines both array distributions and loop transformations resulting in good performance. The techniques described here are suitable for dense linear algebra codes.