Deriving parallel computations from functional specifications: A seismic example on a hypercube

Abstract

Three algorithms developed for a seismic model illustrate that, when the target hardware has many processing elements, functional programs can exhibit better performance than programs developed with conventional techniques. This stands in contrast to the widely held belief that functional programs necessarily pay in poor performance for their advantages in conciseness and likelihood of correctness. Two of the algorithms evolved from an analysis of the seismic model with the goal of finding parts of the computation that could proceed in parallel. The first algorithm has a low communication to computation ratio. The second and third algorithms have higher ratios trading communication time for computation time. The third algorithm was derived from a presentation of the input/output relationship of the model expressed as a composition of mathematical functions. This algorithm exhibited substantially better performance than either of the others. The algorithm achieves its good performance by setting up a producer-consumer pipeline between simultaneously operating portions of the computation. This pipeline balances computation and interprocessor communication more effectively than the other two algorithms.