Methods for linear and nonlinear array data dependence analysis with the chains of recurrences algebra

The presence of data dependences between statements in a loop iteration space imposes strict constraints on statement order and loop restructuring when preserving program semantics. A compiler determines the safe partial ordering of statements that enhance performance by explicitly disproving the presence of dependences. As a result, the false positive rate of a dependence analysis technique is a crucial factor in the effectiveness of a restructuring compiler's ability to optimize the execution of performance-critical code fragments. This dissertation investigates reducing the false positive rate by improving the accuracy of analysis methods for dependence problems and increasing the total number of problems analyzed. Fundamental to these improvements is the rephrasing of the dependence problem in terms of Chains of Recurrences (CR), a formalism that has been shown to be conducive to efficient loop induction variable analysis. An infrastructure utilizing CR-analysis methods and enhanced dependence testing techniques is developed and tested. Experimental results indicate capabilities of dependence analysis methods can be improved without a reduction in efficiency. This results in a reduction in the false positive rate and an increase in the number of optimized and parallelized code fragments.