New Loop Transformation Techniques for Massive Parallelism

摘要

This paper presents new loop transformation techniques that can extract moreparallelism from a class of programs than existing techniques. A formal mathematical framework which unifies the existing loop transformation techniques is given. We classify schedules of a loop transformation into three classes: uniform, subdomain-variant, and statement-variant. New algorithms for generating these schedules are given. Viewing from the degree of parallelism to be gained by loop transformation, the schedules can also be classified as single-sequential level, multiple-sequential level, and mixed schedule. We described iterative and recursive algorithms to obtain multiple-sequential level and mixed schedules respectively based on the algorithms for single-sequential level schedules.