Communication-Free Data Alignment for Arrays with Exponential References Using Elementary Linear Algebra

For array references with induction variables, after induction variable substitution for those induction variables is performed, those array references substituted are transformed as nonlinear expressions. The goal of data alignment is to intelligently map computations and data onto a set of virtual processors organized as a Cartesian grid with multi-dimensions (or a template in HPF term), and to provide data locality in a program so that the data access communication costs can be minimized. Most data alignment methods are mainly devised to align the arrays referenced using linear subscripts or quadratic subscripts with n loop index variables [Chang, 2004]. In this paper, we propose a new communication-free data alignment technique to align the arrays referenced using exponential subscripts with n loop index variables or other complex nonlinear expressions. The experimental results from our techniques on SPEC95FP Benchmarks point out that the techniques can be applied to improve the execution time of the subroutines in those benchmarks.