Communication-free data alignment for arrays with exponential references in parallelizing compilers for scalable parallel systems

Abstract

In loops, some arrays are referenced with induction variables. To parallelize such kind of loops, those induction variables should be substituted. Thus, those array references that were substituted are formulated as nonlinear expressions. The goal of data alignment is to intelligently map the computations and data onto a set of virtual processors which are organized as a Cartesian grid (or a template in HPF terms), and to provide data locality for parallelizing compilers so that data access communication costs can be minimized. Most data alignment methods are mainly devised to align the referenced arrays using linear subscripts or quadratic subscripts with n loop index variables, and the methods are well developed. Seldom work, however, is researched on the nonlinear expressions of index variables. This paper proposes a new communication-free data alignment technique to align the referenced arrays using exponential subscripts with n loop index variables or other complex nonlinear expressions. The experimental results using SPEC95FP Benchmarks point out that the techniques proposed in the paper can improve the execution time of the subroutines in these benchmarks.