Statement-level independent partitioning of uniform recurrences

This papers presents an approach to statement-level independent partitioning of uniform recurrences, i.e., loops with constant dependence distance vectors. Uniform recurrences may be partitioned into independent subsets—of the set of all statement instances— that require no communication or synchronization on a multiprocessor. Therefore, independent partitioning is highly efficient and desirable. This paper presents a method to partition uniform recurrences using statement-level affine schedules, and an algorithm for code generation. We consider a statement instance as a basic unit that can be allocated to a processor, in contrast to existing methods that use an iteration instance. Using this approach, we not only find maximal independent partitions for problems with a single statement inside a perfectly nested loop, but also solve the partitioning problem for multiple statements in a single or multiple nested loops. The method uses schedules derived using linear programming, which is very fast in practice.