A Transformation--Based Approach for the Design of Parallel/Distributed Scientific Software: the FFT

TL;DR

This paper presents a transformation-based methodology for designing efficient parallel and distributed scientific software, demonstrated on the FFT, resulting in competitive or superior performance compared to standard libraries.

Contribution

It introduces a systematic algebraic transformation approach for designing parallel FFT algorithms with implementation templates in MPI and OpenMP.

Findings

Code often matches or exceeds standard library performance.

The methodology handles a wider range of problem sizes.

Generated code is competitive in efficiency.

Abstract

We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the FFT, starting from a high--level algebraic algorithm description. Abstract multiprocessor plans are developed and refined to specify which computations are to be done by each processor. Templates are then created that specify the locations of computations and data on the processors, as well as data flow among processors. Templates are developed in both the MPI and OpenMP programming styles. Preliminary experiments comparing code constructed using our methodology with code from several standard scientific libraries show that our code is often competitive and sometimes performs better. Interestingly, our code handled a larger range of problem sizes on one target architecture.