A polyhedral approach to ease the composition of program transformations

Abstract

We wish to extend the effectiveness of loop-restructuring compilers by improving the robustness of loop transformations and easing their composition in long sequences. We propose a formal and practical framework for program transformation. Our framework is well suited for iterative optimization techniques searching not only for the appropriate parameters of a given transformation, but for the program transformations themselves, and especially for compositions of program transformations. This framework is based on a unified polyhedral representation of loops and statements, enabling the application of generalized control and data transformations without reference to a syntactic program representation. The key to our framework is to clearly separate the impact of each program transformation on three independent components: the iteration domain, the iteration schedule and the memory access functions. The composition of generalized transformations builds on normalization rules specific to each component of the representation. Our techniques have been implemented on top of Open64/ORC. © Springer-Verlag 2004.