The efficient computation of ownership sets in HPF

Ownership sets are fundamental to the partitioning of program computations across processors by the owner-computes rule. These sets arise due to the mapping of arrays onto processors. In this paper, we focus on how ownership sets can be efficiently determined in the context of the HPF language and show how the structure of these sets can be symbolically characterized in the presence of arbitrary array alignment and array distribution directives. Our starting point is a system of equalities and inequalities due to Ancourt et al. (1995) that captures the array mapping problem in HPF. We arrive at a refined system that enables us to efficiently solve for the ownership set using the Fourier-Motzkin Elimination technique and that requires the course vector as the only auxiliary vector. The formulation makes it possible to enumerate the elements of the ownership set exactly once, a feature that is very beneficial when such sets are applied to handle DO loops qualified by HPF´s INDEPENDENT directive. We develop important and general properties pertaining to HPF alignments and distributions and show how they can be used to eliminate redundant communication due to array replication. Polynomial-time schemes that determine whether the ownership set of a particular processor, with respect to some array, is the empty set or whether the ownership set of every processor, with respect to some array, is the empty set, are presented. We show how distribution directives with unspecified processor meshes can be efficiently handled at compile time. We also show how to avoid the generation of communication code when pairs of array references are ultimately mapped onto the same processors. Experimental data demonstrating the improved code performance that the latter optimization enables is presented and discussed