EFFICIENT MAPPING REDUCTIONS USING ISO-PLANES ON THE POLYTOPE MODEL

Abstract

This paper presents a new technique for mapping algorithms onto regular (systolic) arrays. The technique integrates the associativity and commutativity of computations into space-time transformations on the polytope model and involves three categories of transformations: ( 1) iso-planes - forming iso-planes of computations for algorithm representation in contrast to the conventional technique using the data dependence graph; ( 2) increase in dimensionality -mapping a low dimensional algorithm representation into a higher dimensional version with a higher degree of parallelism; and (3) pipestructures - generating and choosing a particular partial order of computations on iso-planes for moving data around the regular array. Three operations for generating pipestructures are introduced: permutation, rotation and reversal. The method presented here increases the available degree of parallelism and thus improves the time complexity of systolic computations. Examples for developing 2-D arrays for 1-D convolution are presented.