# Complexite de l'evaluation parallele des circuits arithmetiques

Abstract : Algorithms for the parallel evaluation of expressions and arithmetic circuits may be considered as extractors of the intrinsic parallelism contained in sequential programs; far beyond the parallelism that can be read from the dependence graph, this parallelism comes from the meaning of the operators that are employed. The knowledge of their algebraic properties, such as associativity or distributivity, allows the reorganization of the computations without affecting the results. The more the algebraic structure used in the program possesses such properties, the more they can be taken into account to speed up the parallel evaluation of the program. We generalize the algorithms designed for programs over semi-rings in order to propose an algorithm, the complexity of which improves previously known upper bounds for the evaluation of arithmetic circuits over lattices. Simulations of this algorithm highlight its power as an automatic complexity predictor''. Furthermore, the explicit reorganization of the computations by means of these evaluation algorithms, by means of a complete compilation, helps to compare real algorithms for distributed memory machines with theoretical parallel ones. A prototype of the compiler has been developed, based on a simplification/extension of the C language. Then, the use of these techniques in the area of automatic parallelization of nested loops is discussed: they can help the detection of hidden reductions in these nested loops in an easy and efficient way, by providing relevant information on the probability of the existence of reductions. This last point proves that the design of theoretical parallel algorithms is related to the search for effective parallelization.
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Submitted on : Wednesday, February 25, 2004 - 2:33:43 PM
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• HAL Id : tel-00005109, version 1

### Citation

Nathalie Revol. Complexite de l'evaluation parallele des circuits arithmetiques. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1994. Français. ⟨tel-00005109⟩

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