Compile-Time Partitioning of Three-Dimensional Iteration Spaces

This paper presents a strategy for compile-time partitioning of generalised threedimensional iteration spaces; it can be applied to loop nests comprising two inner nested loops both of which have bounds linearly dependent on the index of the outermost parallel loop. The strategy is analysed using symbolic analysis techniques for enumerating loop iterations which can provide estimates for the load imbalance, and experimentally evaluated on a virtual shared memory parallel computer. 1 Introduction Loop partitioning refers to this stage of the parallelisation process which deals with the formation of groups of loop iterations that can be executed in parallel; using a scheduling scheme, these groups are assigned to processors. Partitioning and scheduling constitute a fundamental problem to be solved on parallel computers [13]; this is generally termed as mapping. When mapping loop nests, it is essential to minimise overheads, such as load imbalance, communication, etc., thus increasing ..