Parallelism for Nested Loops with Non-uniform and Flow Dependences

Abstract

Abstract. Many methods are proposed in order to parallelize loops with nonuniform dependence, but most of such approaches perform poorly due to irregular and complex dependence constraints. This paper proposes an efficient method of tiling and transforming nested loops with non-uniform and flow dependences for maximizing parallelism. Our approach is based on the Convex Hull theory that has adequate information to handle non-uniform dependences, and also based on minimum dependence distance tiling, the unique set oriented partitioning, and three region partitioning methods. We will first show how to find the incrementing minimum dependence distance. Next, we will propose how to tile the iteration space efficiently according to the incrementing minimum dependence distance. Finally, we will show how to achieve more parallelism by loop interchanging and how to transform it into parallel loops.Comparison with some other methods shows more parallelism than other existing methods.