Synthesizing efficient out-of-core programs for block recursive algorithms using block-cyclic data distributions

In this paper, we present a framework for synthesizing I/O efficient out-of-core programs for block recursive algorithms, such as the fast Fourier transform (FFT) and block matrix transposition algorithms. Our framework uses an algebraic representation which is based on tensor products and other mat...

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Veröffentlicht in:IEEE transactions on parallel and distributed systems Jg. 10; H. 3; S. 297 - 315
Hauptverfasser: Zhiyong Li, Reif, J.H., Gupta, S.K.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.03.1999
Schlagworte:
Algorithms
Application software
Blocking
Communication networks
Computer applications
Concurrent computing
Costs
Dynamic programming
Fast Fourier transforms
Fourier transforms
Mathematical analysis
Mathematical models
Network synthesis
Programmable logic arrays
Recursive
Tensile stress
Tensors
ISSN:1045-9219, 1558-2183
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Zusammenfassung:In this paper, we present a framework for synthesizing I/O efficient out-of-core programs for block recursive algorithms, such as the fast Fourier transform (FFT) and block matrix transposition algorithms. Our framework uses an algebraic representation which is based on tensor products and other matrix operations. The programs are optimized for the striped Vitter and Shriver's two-level memory model in which data can be distributed using various cyclic(B) distributions in contrast to the normally used physical track distribution cyclic(B/sub d/), where B/sub d/ is the physical disk block size. We first introduce tensor bases to capture the semantics of block-cyclic data distributions of out-of-core data and also data access patterns to out-of-core data. We then present program generation techniques for tensor products and matrix transposition. We accurately represent the number of parallel I/O operations required for the synthesized programs for tensor products and matrix transposition as a function of tensor bases and data distributions. We introduce an algorithm to determine the data distribution which optimizes the performance of the synthesized programs. Further, we formalize the procedure of synthesizing efficient out-of-core programs for tensor product formulas with various block-cyclic distributions as a dynamic programming problem. We demonstrate the effectiveness of our approach through several examples. We show that the choice of an appropriate data distribution can reduce the number of passes to access out-of-core data by as large as eight times for a tensor product and the dynamic programming approach can largely reduce the number of passes to access out-of-core data for the overall tensor product formulas.
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ISSN:1045-9219
1558-2183
DOI:10.1109/71.755830