Multi-dimensional incremental loop fusion for data locality

Affine 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 affine 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.