Geometric Pattern Prediction and Scheduling of Uniform Dependence Loops

One of the primary tasks in the area of boundary value problems, including uniform dependence loops, is predicting the execution propagation, as well as finding an optimal time schedule. The index space of a uniform dependence loop, due to the existence of dependence vectors, is split into subspaces of points that can be executed at a certain time instance. The geometric representation of these sets form certain polygonal shapes called patterns, with special attributes and characteristics. In this work, we present a new geometric methodology for predicting the execution propagation of the pattern boundaries. A simple low-cost scheduling algorithm is based on the presented (pattern) analysis.