The polyhedral model provides powerful abstractions to optimize loop nests with regular accesses. Affine transformations in this model capture a complex sequence of execution-reordering loop transformations that can improve performance by parallelization as well as locality enhancement. Although a significant body of research has addressed affine scheduling and partitioning, the problem of automaticallyfinding good affine transforms forcommunication-optimized coarsegrained parallelization together with locality optimization for the general case of arbitrarily-nested loop sequences remains a challenging problem.#R##N##R##N#We propose an automatic transformation framework to optimize arbitrarilynested loop sequences with affine dependences for parallelism and locality simultaneously. The approach finds good tiling hyperplanes by embedding a powerful and versatile cost function into an Integer Linear Programming formulation. These tiling hyperplanes are used for communication-minimized coarse-grained parallelization as well as for locality optimization. The approach enables the minimization of inter-tile communication volume in the processor space, and minimization of reuse distances for local execution at each node. Programs requiring one-dimensional versusmulti-dimensional time schedules (with scheduling-based approaches) are all handled with the same algorithm. Synchronization-free parallelism, permutable loops or pipelined parallelismat various levels can be detected. Preliminary studies of the framework show promising results.
['Uday Bondhugula', 'Muthu Manikandan Baskaran', 'Sriram Krishnamoorthy', 'J. Ramanujam', 'Atanas Rountev', 'P. Sadayappan']
Automatic transformations for communication-minimized parallelization and locality optimization in the polyhedral model