Newton's method based array subscripts dependence test framework

Auto-parallelization compilization is an essential way to obtain high efficient parallel code for High Performance Computers (HPCs) and Chip Multi-Processors (CMPs). For the parallelizing compilers, a fundamental step is array dependence analysis used for identifying the parallelizable code. Whereas, the existing dependence analysis approaches are only capable of recognizing few types of dependences, e.g. linear array subscript expressions or nonlinear monotonic subscript expressions, single or coupled subscripts, etc. The widely existing pseudo-dependence will prevent further optimization. In order to eliminate the pseudo-dependence as much as possible, many test algorithms should be integrated into compilers, which makes the compilers complex and redundant. In this paper, we propose a Newton's method based array subscript dependence test framework, and demonstrate our method by an practical example. Compared with the existing approaches, our framework supports both single and coupled subscripts, and has few constraints on the expressions of subscripts.