Optimization of memory usage requirement for a class of loops implementing multi-dimensional integrals

Abstract

Multi-dimensional integrals of products of several arrays arise in certain scientific computations. In the context of these integral calculations, this paper addresses a memory usage minimization problem. Based on a framework that models the relationship between loop fusion and memory usage, we propose an algorithm for finding a loop fusion configuration that minimizes memory usage.A practical example shows the performance improvement obtained by our algorithm on an electronic structure computation.