Formal Derivation of Divide-and-Conquer Programs: A Case Study in the Multidimensional FFT's (1997)
| Venue: | Formal Methods for Parallel Programming: Theory and Applications. Workshop at IPPS'97 |
| Citations: | 4 - 3 self |
BibTeX
@INPROCEEDINGS{Gorlatch97formalderivation,
author = {Sergei Gorlatch and Holger Bischof},
title = {Formal Derivation of Divide-and-Conquer Programs: A Case Study in the Multidimensional FFT's},
booktitle = {Formal Methods for Parallel Programming: Theory and Applications. Workshop at IPPS'97},
year = {1997},
pages = {80--94}
}
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Abstract
This paper reports a case study in the development of parallel programs in the Bird-Meertens formalism (BMF), starting from divide-and-conquer algorithm specifications. The contribution of the paper is two-fold: (1) we classify divide-and-conquer algorithms and formally derive a parameterized family of parallel implementations for an important subclass of divide-and-conquer, called DH (distributable homomorphisms); (2) we systematically adjust the mathematical specification of the Fast Fourier Transform (FFT) to the DH format and thereby obtain a generic SPMD program, well suited for implementation under MPI. The target program includes the efficient FFT solutions used in practice the binary-exchange and the 2D- and 3D-transpose implementations as its special cases.
