Implementing Flexible Computation Rules with Subexpression-level Loop Transformation

Computation Decomposition and Alignment (CDA) is a new loop transformation framework that extends the linear loop transformation framework and the more recently proposed Computation Alignment frameworks by linearly transforming computations at the granularity of subexpressions. It can be applied to achieve a number of optimization objectives, including the removal of data alignment constraints, the elimination of ownership tests, the reduction of cache connicts, and improvements in data access locality. In this paper we show how CDA can be used to eeectively implement exible computation rules with the objective of minimizing communication and, whenever possible, eliminating intrinsics that test whether computations need to be executed or not. We describe CDA, show how it can be used to implement exible computation rules, and present an algorithm for deriving appropriate CDA transformations.