Unique Sets Oriented Partitioning of Nested Loops with Non-uniform Dependences

Although m a n y methods exist f o r nested loop partitioning, most of t hem perform poorly when parallelizing loops with non-uniform dependences. This paper addresses the issue of parallelizing nested loops with non-uniform dependences. Our approach is based o n convex hull theory, which has adequate information t o handle non-uniform dependences. W e introduce the concept of Complete Dependence Convex Hull, unique head and tail sets and abstract the dependence information into these sets. These sets f o r m the basis of the iteration space partitions. The properties of the unique head and tail sets are derived using Convex Hull theory. Depending o n the relative placement of these unique sets, the partitioning problem i s grouped in to several cases. Several partitioning schemes are also suggested f o r implementing our technique. Preliminary implementation results of our scheme on the Cray 5916 and comparison with other schemes show a dramatic improvement in performance.