Polyhedral-Model Guided Loop-Nest Auto-Vectorization

Optimizing compilers apply numerous interdependent optimizations, leading to the notoriously difficult phase-ordering problem - that of deciding which transformations to apply and in which order. Fortunately, new infrastructures such as the polyhedral compilation framework host a variety of transformations, facilitating the efficient exploration and configuration of multiple transformation sequences. Many powerful optimizations, however, remain external to the polyhedral framework, including vectorization. The low-level, target-specific aspects of vectorization for fine-grain SIMD has so far excluded it from being part of the polyhedral framework. In this paper we examine the interactions between loop transformations of the polyhedral framework and subsequent vectorization. We model the performance impact of the different loop transformations and vectorization strategies, and then show how this cost model can be integrated seamlessly into the polyhedral representation. This predictive modelling facilitates efficient exploration and educated decision making to best apply various polyhedral loop transformations while considering the subsequent effects of different vectorization schemes. Our work demonstrates the feasibility and benefit of tuning the polyhedral model in the context of vectorization. Experimental results confirm that our model has accurate predictions, providing speedups of over 2.0times on average over traditional innermost-loop vectorization on PowerPC970 and Cell-SPU SIMD platforms.