Using elementary linear algebra to solve data alignment for arrays with linear or quadratic references

Abstract

Data alignment that facilitates data locality so that the data access communication costs can be minimized, helps distributed memory parallel machines improve their throughput. Most data alignment methods are devised mainly to align the arrays referenced using linear subscripts or quadratic subscripts with few (one or two) loop index variables. In this paper, we propose two communication-free alignment techniques to align the arrays referenced using linear subscripts or quadratic subscripts with multiple loop index variables. The experimental results from our techniques on Vector Loop and TRFD of the Perfect Benchmarks reveal that our techniques can improve the execution times of the subroutines in these benchmarks.