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