Multi-dimensional Incremental Loop Fusion for Data Locality

A#ne loop transformations have often been used for program optimization. Usually their focus lies on single loop nests. A few recent approaches also handle global programs with multiple loop nests but they are not really scalable towards realistic applications with dozens of nests. To reduce complexity, we split a#ne transformations into a linear transformation step and a translation step. This translation step can be used to perform general multidimensional loop fusion. We show that loop fusion can be performed incrementally and provide a greedy algorithm, which we illustrate on a simple example. Finally, we present a heuristic for data locality and provide some experimental results