Fast address sequence generation for data-parallel programs using integer lattices

Abstract

In data-parallel languages such as High Performance Fortran and Fortran D, arrays are mapped to processors through a two step process involving alignment followed by distribution. A compiler that generates code for each processor has to compute the sequence of local memory addresses accessed by each processor and the sequence of sends and receives for a given processor to access non-local data. In this paper, we present a novel approach based on integer lattices. The set of elements referenced can be generated by integer linear combinations of basis vectors. Our linear algorithm determines the basis vectors as a function of the mapping. Using the basis vectors, we derive a loop nest that enumerates the addresses, which are points in the lattice generated by the basis vectors. Experimental results show that our approach is better than that of a recent linear time solution to this problem.