On the optimality of Feautrier's scheduling algorithm

Vivien, Frédéric

doi:10.1002/cpe.780

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…In this sense, it has also some similarities with the seminal work of Karp, Miller, and Winograd on systems of uniform recurrence equations [25]. Our algorithm to generate ranking functions is inspired by the algorithm of Feautrier [19] and its completeness [32] for scheduling affine loops. Counting techniques using Ehrhart polynomials are also standard for optimizing loops [11].…”

Section: Related Workmentioning

confidence: 96%

Static Analysis

Cousot

Martel²

2010

Lecture Notes in Computer Science

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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Related Workmentioning

confidence: 96%

Static Analysis

Cousot

Martel²

2010

Lecture Notes in Computer Science

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“…Thus Feautrier's algorithm cannot be optimal with respect to the dependence abstraction it was designed for. However, among all affine functions, it can find one with the "right" parallelism extraction, in other words, the algorithm is optimal with respect to the class of functions it considers [36].…”

Section: Going Beyond Thanks To the Affine Form Of Farkas Lemmamentioning

confidence: 98%

Understanding loops: The influence of the decomposition of Karp, Miller, and Winograd

Darte

2010

Eighth ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMOCODE 2010)

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Loops are a fundamental control structure in programming languages. Being able to analyze, to transform, to optimize loops is a key feature for compilers to handle repetitive schemes with a complexity proportional to the program size and not to the number of operations it describes. This is true for the generation of optimized software as well as for the generation of hardware, for both sequential and parallel execution. The goal of this talk is to recall one of the most important theory to understand loops -the decomposition of Karp, Miller, and Winograd (1967) for systems of uniform recurrence equations -and its connections with two different developments on loops: the theory of transformation and parallelization of (nested) DO loops and the theory of ranking functions for proving the termination of (imperative) programs with WHILE loops. Other connections, which will not be covered, include reachability problems in vector addition systems and Petri nets.

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“…Darte-Vivien's scheduling As the framework of Feautrier which we build from is the most powerful among the class of algorithms that find affine schedules [56], the LP formulation in Darte-Vivien's scheduling [22] can directly be approximated by our method.…”

Section: Applications To Other Loop Transformation Problemsmentioning

confidence: 99%

Sub-polyhedral scheduling using (unit-)two-variable-per-inequality polyhedra

Upadrasta

Cohen

2013

Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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International audiencePolyhedral compilation has been successful in the design and implementation of complex loop nest optimizers and parallelizing compilers. The algorithmic complexity and scalability limitations remain one important weakness. We address it using sub-polyhedral under-aproximations of the systems of constraints resulting from affine scheduling problems. We propose a sub-polyhedral scheduling technique using (Unit-)Two-Variable-Per-Inequality or (U)TVPI Polyhedra. This technique relies on simple polynomial time algorithms to under-approximate a general polyhedron into (U)TVPI polyhedra. We modify the state-of-the-art PLuTo compiler using our scheduling technique, and show that for a majority of the Polybench (2.0) kernels, the above under-approximations yield polyhedra that are non-empty. Solving the under-approximated system leads to asymptotic gains in complexity, and shows practically significant improvements when compared to a traditional LP solver. We also verify that code generated by our sub-polyhedral parallelization prototype matches the performance of PLuTo-optimized code when the under-approximation preserves feasibility

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On the optimality of Feautrier's scheduling algorithm

Cited by 6 publications

References 11 publications

Static Analysis

Static Analysis

Understanding loops: The influence of the decomposition of Karp, Miller, and Winograd

Sub-polyhedral scheduling using (unit-)two-variable-per-inequality polyhedra

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