Mapping deviation: a technique to adapt or to guard loop transformation intuitions for legality

Parallel architectures are now omnipresent in mainstream electronic devices and exploiting them efficiently is a challenge for all developers. Hence, they need the support of languages, libraries and tools to assist them in the optimization or parallelization task. Compilers can provide a major help by automating this work. However they are very fragile black-boxes. A compiler may take a bad optimization decision because of imprecise heuristics or may turn off an optimization because of imprecise analyses, without providing much control or feedback to the end user. To address this issue, we introduce mapping deviation, a new compiler technique that aims at providing a useful feedback on the semantics of a given program restructuring. Starting from a transformation intuition a user or a compiler wants to apply, our algorithm studies its correctness and can suggest changes or conditions to make it possible rather than being limited to the classical go/no-go answer. This algorithm builds on state-of-the-art polyhedral representation of programs and provides a high flexibility. We present two example applications of this technique: improving semi-automatic optimization tools for programmers and automatically designing runtime tests to check the correctness of a transformation for compilers.