Automatic partitioning of parallel loops with parallelepiped-shaped tiles

In this paper, an efficient algorithm to implement loop partitioning is introduced and evaluated. We start from results of Agarwal et al. (1995) whose aim is to minimize the number of accessed data throughout the computation of a tile; this number is called the cumulative footprint of the tile. We improve these results along several directions. First, we derive a new formulation of the cumulative footprint, allowing for an analytical solution of the optimization problem stated by Agarwal et al.. Second, we deal with arbitrary parallelepiped-shaped tiles, as opposed to rectangular tiles. We design an efficient heuristic to determine the optimal tile shape in this general setting and we show its usefulness using both examples of Agarwal et al. and a large collection of randomly generated data.