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A precise dependence analysis for multi-dimensional arrays under specific dependence direction

JOURNAL OF SYSTEMS AND SOFTWARE 2002年第2期63卷 99-112页

作者： Chang, WL Chu, CP Wu, JH So Taiwan Univ Technol Dept Informat Management Tainan 701 Taiwan Natl Cheng Kung Univ Dept Comp Sci & Informat Engn Tainan 701 Taiwan

In process of automatic parallelizing/vectorizing constant-bound loops with multi-dimensional arrays under specific dependence direction, the Lambda test is claimed to be an efficient and precise data dependence analysis method that can check whether there exist generally inexact 'real-valued' solutions to the derived dependence equations. In this paper, we propose a precise data dependence analysis method - the multi-dimensional direction vector I test. The multi-dimensional direction vector I test can be applied towards testing whether there exist generally accurate 'integer-valued' solutions to the dependence equations derived from multi-dimensional arrays under specific dependence direction in constant-bound loops. Experiments with benchmark showed that the accuracy rate and the improvement rate for the proposed method are approximately 33.3% and 21.6%, respectively. (C) 2001 Elsevier Science Inc. All rights reserved.

关键词： parallelizing/vectorizing compilers data dependence analysis loop parallelization supercomputing

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The generalized Direction Vector I test

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PARALLEL COMPUTING 2001年第8期27卷 1117-1144页

作者： Chang, WL Chu, CP Natl Cheng Kung Univ Dept Comp Sci & Informat Engn Tainan 701 Taiwan

The Direction Vector I (DVI) test [IEEE Transaction on Parallel and Distributed Systems 4 (11) (1993) 1280] is an efficient and precise data dependence method to determine whether integer solutions exist for one-dimensional arrays with constant bounds under any given direction vectors. In this paper, we generalize the (DVI) test. The generalized Direction Vector I (GDVI) test can be applied towards determining whether integer solutions exist for one-dimensional arrays with both constant and variable limits under any given direction vectors, improving the precision and applicability of the DVI test. Experiments with benchmark showed that among 12152 pairs of tested one-dimensional arrays consisting of the same pair of array references with different direction vectors. 2124 had their data dependence analysis amended by the CDVI test. That is. the GDVI test increases the success rate of the DVI test by approximately 17.5%. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： parallelizing/vectorizing compilers data dependence analysis parallel computing

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A multi-dimensional version of the I test

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PARALLEL COMPUTING 2001年第13期27卷 1783-1799页

作者： Chang, WL Chu, CP Wu, JH Natl Cheng Kung Univ Dept Comp Sci & Informat Engn Tainan 701 Taiwan Kung Shan Inst Technol Dept Informat Management Tainan 701 Taiwan

Two-dimensional arrays with linear subscripts occur quite frequently in real programs. In general, for multi-dimensional linear arrays under constant bounds the Lambda test is an efficient data dependence method to check whether there exist real solutions. In this paper, we propose a multi-dimensional version of the I test, the multi-dimensional I test. that can be applied to testing whether there are integer solutions for multi-dimensional linear arrays under constant limits. Experiments with benchmark showing the effects of the multi-dimensional I test on testing precision and testing efficiency are also presented. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： parallelizing/vectorizing compilers data dependence analysis loop parallelization loop vectorization

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