The Power Test for Data Dependence

This paper introduces a data dependence decision algorithm, called the Power Test; the Power Test is a combination of Banerjee's Generalized GCD dependence algorithm and the Fourier-Motzkin method t o eliminate variables in a system of inequalities. In addition t o having certain advantages over previous dependence algorithms (such as increased precision, the ability t o handle multiple subscripts simultaneously, the ability t o handle complex multiple loop limits, and others), it can also easily generate dependence direction vector information. This paper briefly reviews previous work in data dependence decision algorithms, and describes the Power Test. Several examples which motivated the development of this test are examined, including those which demonstrate additional power of the Power Test. Vectorizing and parallelizing compilers are common in the supercomputer and mini-supercomputer commercial market; these compilers inspect the patterns of d a t a usage in programs , especially array usage in loops, often representing these patterns a s a d a t a dependence graph. With this information, compilers can often automatically detect parallelism in loops, or report t o the user specific reasons why a particular loop cannot be executed in parallel. Additional performance improvement can be attained by using certain program transformations t o take advantage of architectural features, such as improving memory locality t o take advantage of cache memories. In order t o determine what restructuring transformations are legal, d a t a dependence tests are devised t o detect those programs or loops whose semantics will be violated by the transformation. In order t o allow the most freedom in applying restructuring transformations, a compiler needs a precise d a t a dependence test. Much of the theory behind d a t a dependence testing for array references in loops can be reduced t o solving simultaneous diophantine equations. The d a t a dependence problem for array references can be stated as: Given a set of nested loops surrounding two statements (not necessarily distinct) where each statement contains a reference t o a n array: L1: f o r I1 = el t o ul do