Optimization of a Class of Multi-Dimensional Integrals on Parallel Machines.
Chi‐Chung Lam, Ponnuswamy Sadayappan, Rephael Wenger · 1997
Multi-dimensional summations involving products of arrays arise in certain kinds of computational physics calculations that model electronic structure. Besides the issue of optimal distribution of the arrays among the processors, there is also scope for reordering of the operations using algebraic properties (commutativity, associativity, distributive law) to significantly reduce the number of operations executed. A framework for optimization of computational cost and communication cost has been developed, that can be used to synthesize efficient code. 1 Introduction This paper addresses the problem of compile-time optimization of a particular form of nested loop computations. The problem was motivated by the structure of some computations found in a computational physics application that models electronic structure. In addition to the issue of mapping of data and computations to optimize performance, there is also potential for optimizing the total number of arithmetic operations by ...