Improving tiling, reducing compilation time, and extending the scope of polyhedral compilation
Mohamed Riyadh Baghdadi · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
Multi-core processors are now in widespread use in almost all areas of computing: desktops, laptops and accelerators such as GPGPUs (General Purpose Graphics Processing Units). To harness the power of multi-core processors and complex memory hierarchies, the need for powerful compiler optimizations and especially loop nest transformations is now in high demand. The polyhedral optimization framework is showing promising results in addressing such a problem. It's an algebraic program representation and a set of analyses, transformations and code generation algorithms that enable a compiler to reason about advanced loop nest transformations addressing most of the parallelism and locality-enhancing challenges.In this thesis we address some of the limitations of the polyhedral framework. We address three problems and propose practical solutions to these three problems.The first problem is related to the ability to apply tiling on code that has false dependences (loop nest tiling is an optimization that changes the order of execution of statements in a loop nest in order to enhance data locality; false dependences are induced by the reuse of a single memory location to store multiple values during the life of the program). To preserve the validity of loop nest transformations and parallelization, data-dependences need to be analyzed. Memory dependences come in two varieties: true dependences (a.k.a. flow dependences) and false dependences (a.k.a. output and anti dependences). While true dependences must be satisfied in order to preserve the correct order of computations. False dependences reduce the degrees of freedom for loop transformations. In particular, loop tiling is severely limited in the presence of these dependences. While array expansion, a transformation that transforms scalars into arrays and arrays into higher dimensional arrays, removes all false dependences, the overhead of this transformation on memory and the detrimental impact on register-level reuse can be catastrophic. We propose and evaluate a compilation technique to safely ignore a large number of false dependences in order to enable loop nest tiling in the polyhedral model. It is based on the precise characterization of interferences between live range intervals, and it does not incur any scalar or array expansion.The second problem is related to the long compilation time that one may experience when using polyhedral tools to optimize a program. Particularly, the long execution time of the Pluto affine scheduling algorithm. The Pluto affine scheduling algorithm is the algorithm that is responsible for changing the schedule (order of execution) of statements in order to optimize the code (maximize parallelism and data locality). Reducing the execution time of this affine scheduling algorithm enhances the overall compilation time. We introduce and evaluate a technique called offline statement clustering. It is a practical technique designed to reduce the execution time of the Pluto affine scheduling algorithm without much loss in optimization opportunities. Using this technique, the statements of the program are clustered into macro-statements, the Pluto affine scheduling algorithm is then used to schedule the macro-statements instead of scheduling the original statements of the program. Since the number of macro-statements is less than the number of statements in the original program, scheduling the macro-statements is in general faster than scheduling the original statements of the program. We present the statement clustering algorithm, we show how offline statement clustering integrates transparently with the work-flow of a state-of-the-art polyhedral compiler and present two heuristics for choosing how statements should be clustered together. We show experimentally that statement clustering can reduce the scheduling time by a factor of 8x (in median) without a significant loss in optimization opportunities...