Violated dependence analysis

The polyhedral model is a powerful framework to reason about high level loop transformations. Yet the lack of scalable algorithms and tools has deterred actors from both academia and industry to put this model to practical use. Indeed, for fundamental complexity reasons, its applicability has long been limited to simple kernels. Recent developments broke some generally accepted ideas about these limitations. In particular, new algorithms made it possible to compute the target code for full SPEC benchmarks while this code generation step was expected not to be scalable.Instancewise array dependence analysis computes a finite, intensional representation of the (statically unbounded) set of all dynamic dependences. This problem has always been considered non-scalable and/or an overkill with respect to less expressive and faster dependence tests. On the contrary, this article presents experimental evidence of its applicability to full SPEC CPU2000 benchmarks. To make this possible, we revisit the characterization of data dependences, considering relations between time dimensions of the transformed space. Beyond algorithmic benefits, this naturally leads to a novel way of reasoning about violated dependences across arbitrary transformation sequences. Reasoning about violated dependences relieves the compiler designer from the cumbersome task of implementing specific legality checks for each single transformation. It also allows, in the case of invalid transformations, to precisely determine the violated dependences that need to be corrected. Identifying these violations can in turn enable automatic correction schemes to fix an illegal transformation sequence with minimal changes.