Section: New Results

Simplification and Run-time Resolution of Data Dependence Constraints for Loop Transformations

Participants : Diogo Nunes Sampaio, Alain Ketterlin [Inria CAMUS] , Louis-Noël Pouchet [CSU, USA] , Fabrice Rastello.

Loop optimizations such as tiling, thread-level parallelization or vectorization are essential transformations to improve performance. It is needed to compute dependence information at compile-time to assess their validity, but in many real situations, static dependence analysis fails to provide precise enough information. Part of the reason for this failure comes from the need to handle polynomial constraints in the dependence computation problem: such polynomial constraints can arise from linearized array accesses, typical in compilers IR such as LLVM-IR. In this scenario, the compiler will often be unable to apply aggressive transformations due to lack of conclusive static dependence analysis. This work tackles the problem of eliminating quantifiers in systems of inequalities using polynomial constraints. In particular, we design a quantifier elimination scheme on integer multivariate-polynomials, which can aid application of off-the-shelf polyhedral transformations on a larger class of programs, that holds polynomial memory access and affine loop bounds. We make a significant leap in accuracy compared to prior approaches, enabling to implement a hybrid optimizing compilation scheme. In this scheme, a test is evaluated at run-time to determine the legality of the program transformation chosen by the compiler, falling back to executing the original code if the test fails. This test integrates all may-dependences, involving polynomial inequalities, and is simplified by quantifier elimination at compile-time using our techniques. The preciseness of the presented scheme and the low run-time overhead of the test are key to make this approach realistic. We experimentally validate our technique on 25 benchmarks using complex loop transformations, achieving negligible overhead. Preciseness is assessed by the observed success of generated test in practical cases. We compare our variable elimination technique to other existing tools and demonstrate we achieve better precision when dealing with polynomial memory accesses.

This work is the fruit of the collaboration 8.4 with OSU.