EPITA CSI 2006 and UPS Master 2 ( March -

Emerging micro-processors introduce unprecedented parallel computing capabilities and deeper memory hierarchies, increasing the importance of loop transformations in optimizing compilers. Because compiler heuristics rely on simplistic performance models, and because they are bound to a limited set of transformations sequences, they only uncover a fraction of the peak performance on typical benchmarks. Iterative optimization is a maturing framework addressing these limitations, but so far, it was not successfully applied complex loop transformation sequences because of the combinatorics of the optimization search space. We focus on the class of loop transformation which can be expressed as one-dimensional affine schedules. We define a systematic exploration method to enumerate the space of all legal, distinct transformations in this class This method is based on an upstream characterization, as opposed to state-of-the-art downstream filtering approaches. Our results demonstrate orders of magnitude improvements in the size of the search space and in the convergence speed of a dedicated iterative optimization heuristic. Feedback-directed and iterative optimizations have become essential defenses in the fight of optimizing compilers fight to stay competitive with hand-optimized code: they freshen the static information flow with dynamic properties, adapting to complex architecture behaviors, and compensating for the inaccurate single-shot of model-based heuristics. Whether a single application (for client-side iterative optimization) or a reference benchmark suite (for in-house compiler tuning) are considered, the two main trends are: • tuning or specializing an individual heuristic, adapting the profitability or decision model of a given transformation; • tuning or specializing the selection and parameterization of existing (black-box) compiler phases. This study takes a more offensive position in this fight. To avoid diminishing returns in tuning individual phases or combinations of those, we collapse multiple optimization phases into a single, unconventional, iterative search algorithm. By construction, the search space we explore encompasses all legal program transformations in a particular class. Technically, we consider the whole class of loop nest transformations that can be modeled as one-dimensional schedules, a significant leap in model and search space complexity compared to state-of-the-art applications of iterative optimization. We make the following contributions: • we statically construct the optimization space of all, arbitrarily complex, arbitrarily long sequences of loop transformations that can be expressed as one-dimensional affine schedules (using a polyhedral abstraction); • this search space is built free of illegal and redundant transformation sequences, avoiding them altogether at the very source of the exploration; • we demonstrate multiple orders of magnitude reduction in the size of the search space, compared to filtering-based approaches on loop transformation sequences or state-of-theart affine schedule enumeration techniques; • these smaller search spaces are amenable to fast-converging, mathematically founded operation research algorithms, allowing to compute the exact size of the space and to traverse it exhaustively;