On the Automatic Parallelization of Subscripted Subscript Patterns Using Array Property Analysis

Parallelizing loops with subscripted subscript patterns at compile-time has long been a challenge for automatic parallelizers. In the class of irregular applications that we have analyzed, the presence of subscripted subscript patterns was one of the primary reasons why a significant number of loops could not be automatically parallelized. Loops with such patterns can be parallelized, if the subscript array or the expression in which the subscript array appears possess certain properties, such as monotonicity. The information required to prove the existence of these properties is often present in the application code itself. This suggests that their automatic detection may be feasible. In this paper, we present an algebra for representing and reasoning about subscript array properties, and we discuss a compile-time algorithm, based on symbolic range aggregation, that can prove monotonicity and parallelize key loops. We show that this algorithm can produce significant performance gains, not only in the parallelized loops, but also in the overall applications.