A Unified Framework for Schedule and Storage Optimization

Abstract

We present a unified mathematical framework for analyzing the tradeoffs between parallelism and storage allocation within a parallelizing compiler. Using this framework, we show how to find the best storage mapping for a given schedule, the best schedule for a given storage mapping, and the best storage mapping that is valid for all legal schedules. Our techniques combines affine scheduling techniques with occupancy vector analysis, and incorporates general affine dependencies across statements and loop nests. We formulate the constraints imposed by the data dependencies and the storage mapping as a set of linear inequalities, and apply numerical programming techniques to efficiently solve for the best occupancy vector. We consider out method to be a first step towards automating a procedure that finds the optimal tradeoff between parallelism and storage space.