A new memory-saving technique to map system of affine recurrence equations (SARE) onto distributed memory systems

Abstract

In this work we present a procedure for automatic parallel code generation in the case of algorithms described through Set of Affine Recurrence Equations (SARE); starting from the original SARE description in an N-dimensional iteration space, the algorithm is converted into a parallel code for an m-dimensional distributed memory parallel machine (m<N). The used projection technique is based on the polytope model. Some affine transformations are introduced to project the polytope from the original iteration space onto another polytope, preserving the SARE semantic, in the processor-time (t,p) space. Along with polytope transformation, we give a methodology to generate the code within processors and a technique to avoid the memory wasting typical of SARE implementations. Finally a cost function, used to guide the heuristic search for the polytope transformation and derived from the actual implementation of the method on an MPP SIMD machine, is introduced.