The full text of this article:

A multi-dimensional Interval Reduction test
by Jia-Hwa Wu, Chih-Ping Chu
International Journal of High Performance Computing and Networking (IJHPCN), Vol. 4, No. 5/6, 2006
Abstract: Two-dimensional arrays occur quite frequently in real programmes. In general, for multi-dimensional 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 Interval Reduction (IR) test. The multi-dimensional IR test can be applied towards testing whether there are integer solutions for multi-dimensional arrays under constant limits, increasing the testing precision and exploiting the degree of loop parallelisation and vectorisation. Experiments with benchmarks showing the effects of the multi-dimensional IR test are also presented.

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