Section: New Results

Hybrid Data Dependence Analysis for Loop Transformations

Participants : Diogo Nunes Sampaio, Alain Ketterlin, Fabrice Rastello, Fernando Pereira, Alexandros Labrineas, Péricles Alves, Fabian Gruber.

Loop optimizations such as tiling, vectorization, or parallel task extraction are extremely important to achieve high performance. All such transformations rely on accurate memory dependence information to assess their validity. There are many practical situations, though, where dependence analysis fails to provide precise enough information. In this common scenario, the compiler will conservatively choose not to do any transformation. This happens in particular with low-level IRs (which are more and more common to address performance portability), but also in legacy code with pointers (e.g. C), linearized arrays, etc.

This work addresses the important problem of may-dependence disambiguation through the angle of a combination of static and dynamic analyses (sometimes called a hybrid analysis), similarly to what is already implemented in mainstream compilers, such as GCC, for auto-vectorization. This technique consists of adding a run-time test to disambiguate may-dependencies which static dependence analysis was not able to rule out. We propose two contributions to address this important problem.

The first approach proposes hybrid may-alias disambiguation. It combines two approaches: one that statically computes a symbolic expression of the interval of memory values a pointer may point to and uses dynamic overlap tests on these intervals to prove non-aliasing for each pair of pointers; another that hooks the memory allocator to find the base-pointer of a pointer and thus determine dynamically if a pointer pair belongs to two different allocations (and is thus disjoint) or not. We have applied these ideas on Polly-LLVM, a loop optimizer built on top of the LLVM compilation infrastructure. Our experiments indicate that our method is precise, effective and useful: we can disambiguate every pair of pointer in the loop intensive Polybench benchmark suite. The result of this precision is code quality: the binaries that we generate are 10% faster than those that Polly-LLVM produces without our optimization, at the -O3 optimization level of LLVM.

The second technique extends the non-overlapping intervals approach to may-dependence disambiguation. For this purpose, a powerful quantifier elimination scheme on multivariate-polynomials over integers has been developed. The quality of the presented scheme is important to make this approach realistic. In particular it must be precise (the integer aspect makes this problem very challenging), so that the test succeeds in practical cases, and must lead to negligible overhead. We evaluate preciseness and overhead on a set of 30+ benchmarks using complex loop transformations including loop fusion, skewing, and tiling.

This work is the fruit of the collaboration with UFMG  9.4 , Kalray  8.1   8.2 , STMicroelectronics   8.2 , and with EPI CAMUS in the context of IPL Multicore  9.2 . The first contribution has been presented at ACM OOPSLA'15 [19] . The second has been submitted to PLDI'16.