The mapping of linear recurrence equations on regular arrays

Quinton, Patrice; Dongen, Vincent Van

doi:10.1007/bf02477176

Cited by 175 publications

(53 citation statements)

References 20 publications

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“…Affine schedules have been extensively used to design systolic arrays [97] and in automatic parallelization programs [41,35,54], then have seen many other applications.…”

Section: One-dimensional Schedulesmentioning

confidence: 99%

Iterative optimization in the polyhedral model

et al. 2008

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High-level loop optimizations are necessary to achieve good performance over a wide variety of processors. Their performance impact can be significant because they involve in-depth program transformations that aim to sustain a balanced workload over the computational, storage, and communication resources of the target architecture. Therefore, it is mandatory that the compiler accurately models the target architecture as well as the effects of complex code restructuring. However, because optimizing compilers (1) use simplistic performance models that abstract away many of the complexities of modern architectures, (2) rely on inaccurate dependence analysis, and (3) lack frameworks to express complex interactions of transformation sequences, they typically uncover only a fraction of the peak performance available on many applications. We propose a complete iterative framework to address these issues. We rely on the polyhedral model to construct and traverse a large and expressive search space. This space encompasses only legal, distinct versions resulting from the restructuring of any static control loop nest. We first propose a feedback-driven iterative heuristic tailored to the search space properties of the polyhedral model. Though, it quickly converges to good solutions for small kernels, larger benchmarks containing higher dimensional spaces are more challenging and our heuristic misses opportunities for significant performance improvement. Thus, we introduce the use of a genetic algorithm with specialized operators that leverage the polyhedral representation of program dependences. We provide experimental evidence that the genetic algorithm effectively traverses huge optimization spaces, achieving good performance improvements on large loop nests.

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“…Affine schedules have been extensively used to design systolic arrays [97] and in automatic parallelization programs [41,35,54], then have seen many other applications.…”

Section: One-dimensional Schedulesmentioning

confidence: 99%

Iterative optimization in the polyhedral model

et al. 2008

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show abstract

“…Our algorithms for generating the various single-sequential level schedules are based on Quinton's algorithm for generating SSL-U schedules [13,29,30]. To make the paper selfcontained, we first review Quinton's algorithm.…”

Section: Algorithms For Generating Single-sequential Level Schedulesmentioning

confidence: 99%

“…Quinton's approach addresses the analysis and mapping of linear recurrence equations [13, 29,30]. We formulate Quinton's algorithm in the context of loop transformations.…”

Section: Previous Work: Uniform Scheduling Algorithmmentioning

confidence: 99%

“…Much work in the area of mapping recurrence equations to systolic architectures [11,12,15,17,19,24,26,25,27,28,29,30], in contrast, focuses on developing algorithms for loop skewing.…”

Section: Introductionmentioning

confidence: 99%

“…The problem is that there are many such pairs that need to be considered, and they can be infinitely many when the loop bounds are unknown at compile time. We need to rely on a technique called polyhedra decomposition [13,30,32] to manage the complexity of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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