Abstract
This paper addresses the compile-time optimization of a class of nested-loop computations that arise in some computational physics applications. The computations involve summations over products of array terms in order to compute multi-dimensional surface and volume integrals. Reordering additions and multiplications and applying the distributive law can significantly reduce the number of operations required in evaluating these summations. In a multiprocessor environment, proper distribution of the arrays among processors will reduce the inter-processor communication time. We present a formal description of the operation minimization problem, a proof of its NP-completeness, and a pruning strategy for finding the optimal solution in small cases. We also give an algorithm for determining the optimal distribution of the arrays among processors in a multiprocessor environment.
Supported in part by NSF grant DMR-9520319.
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© 1997 Springer-Verlag Berlin Heidelberg
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Lam, CC., Sadayappan, P., Wenger, R. (1997). Optimal reordering and mapping of a class of nested-loops for parallel execution. In: Sehr, D., Banerjee, U., Gelernter, D., Nicolau, A., Padua, D. (eds) Languages and Compilers for Parallel Computing. LCPC 1996. Lecture Notes in Computer Science, vol 1239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017261
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DOI: https://doi.org/10.1007/BFb0017261
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