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

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.