A heuristic for improving the regularity of accesses by global loop transformations in the polyhedral model

Our approach for global loop transformations aimed at optimizing data transfer and storage is based on an extended polytope model. The transformations are performed in two steps: a placement step that maps the individual polytopes to a common iteration space and an ordering step defining an order in the common iteration space. Recently, Danckaert has proposed to split the placement step itself into a first substep dealing with the linear part of the mappings and focusing on the regularity of accesses and a second substep dealing with the translation part and focusing on the locality. In this context, he developed a criterion for optimizing the regularity of the dependencies between read and write operations together with a search procedure. This paper shows that this optimization criterion is in fact an approximation of the dimension of the dependency distance vector polytope. We further present some improvements on the existing search procedure together with two new search procedures.