Compile-time Parallelization of Subscripted Subscript Patterns

An increasing number of scientific applications are making use of irregular data access patterns. An important class of such patterns involve subscripted subscripts, wherein an array value appears in the index expression of another array. Even though the information required to parallelize loops with such patterns is available in the class of programs that we analyze, present compiler techniques fall short of analyzing that information. In this paper we present a study of subscripted subscripts, the properties that define the subscript arrays, and an algorithm based on symbolic range aggregation, that will help prove the presence of some of the properties of the subscript array in the program. We show that, in an important class of programs, the algorithm can boost the performance from essentially sequential execution to close to fully parallel.