Transformations of nested loops with non-convex iteration spaces

Xue, Jingling

doi:10.1016/0167-8191(95)00069-0

Cited by 9 publications

(8 citation statements)

References 9 publications

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“…With such a representation for each statement and a precise characterization of inter or intra-statement dependences and reuses, it is convenient to find optimal loop transformation based on some cost functions using linear algebra and linear programming. The polyhedral model is applicable to a subset of imperative languages like C or JAVA known as static control programs [1]. They have the following properties: (1) loop bounds are affine expressions and loop conditions depend only on outer loop counters and constant parameters; (2) memory access in the loop statements are affine functions; (3) control statements are for loops and if conditionals with affine conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The polyhedral model is applicable to a subset of imperative languages like C or JAVA known as static control programs [1]. They have the following properties: (1) loop bounds are affine expressions and loop conditions depend only on outer loop counters and constant parameters; (2) memory access in the loop statements are affine functions; (3) control statements are for loops and if conditionals with affine conditions. A maximal set of consecutive statements with static control in any program is called a static control part (SCoP).…”

Section: Introductionmentioning

confidence: 99%

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Polyhedral Model Based Data Locality Optimization for Embedded Applications

Xinyu

2010

2010 IEEE/ACM Int'l Conference on Green Computing and Communications &Amp; Int'l Conference on Cyber, Physical and Social Compu

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The need for compilers of embedded systems to find effective ways of optimizing series of loop-nests is urgent. This is especially so for streaming applications such as M-Jpeg, H.264 etc. which are popular in embedded systems. The loop bounds and memory references of these applications are primarily affine functions of the outer loop counters and constant parameters. The polyhedral model provides powerful abstractions to optimize loop nests with such regular accesses. Affine transformations in this model capture a complex sequence of execution-reordering loop transformations. We propose a solution to the data locality optimization problem for the embedded systems by using the polyhedral model. Experiments show that our technique leads to 35% reduction in external memory accesses over best gcc optimization result.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polyhedral Model Based Data Locality Optimization for Embedded Applications

Xinyu

2010

2010 IEEE/ACM Int'l Conference on Green Computing and Communications &Amp; Int'l Conference on Cyber, Physical and Social Compu

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“…A complete description of static control parts was given by Xue [128] and their applicability to compute intensive, scientific or embedded applications have been extensively discussed by Girbal et al and Palkovič [51,89]. Frameworks to highlight SCoPs in general programs and to extract both iteration domains and subscript functions already exist or are in active development in compiler platforms like WRAP-IT/URUK for Open64 [51], Graphite for GCC [90], IBM XL/C compiler, the ROSE Compiler, R-Stream from Reservoir Labs, and in the prototype compilers PoCC and Loopo.…”

Section: Pre-processing For Scopsmentioning

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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“…Transformation frameworks such as the polyhedral framework [17][18][19][20][21][22] enable the specification and exploration of a space of possible compile-time reordering transformations for static control parts [23]. Static control parts (SCoP) require that the loop bounds and array accesses in the loops being transformed be affine functions of the loop iterators and variables that do not change in the loops.…”

Section: Introductionmentioning

confidence: 99%

Set and Relation Manipulation for the Sparse Polyhedral Framework

Strout

Georg

Olschanowsky

2013

Languages and Compilers for Parallel Computing

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Abstract. The Sparse Polyhedral Framework (SPF) extends the Polyhedral Model by using the uninterpreted function call abstraction for the compile-time specification of run-time reordering transformations such as loop and data reordering and sparse tiling approaches that schedule irregular sets of iteration across loops. The Polyhedral Model represents sets of iteration points in imperfectly nested loops with unions of polyhedral and represents loop transformations with affine functions applied to such polyhedra sets. Existing tools such as ISL, Cloog, and Omega manipulate polyhedral sets and affine functions, however the ability to represent the sets and functions where some of the constraints include uninterpreted function calls such as those needed in the SPF is non-existant or severely restricted. This paper presents algorithms for manipulating sets and relations with uninterpreted function symbols to enable the Sparse Polyhedral Framework. The algorithms have been implemented in an open source, C++ library called IEGenLib (The Inspector/Executor Generator Library).

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Transformations of nested loops with non-convex iteration spaces

Cited by 9 publications

References 9 publications

Polyhedral Model Based Data Locality Optimization for Embedded Applications

Polyhedral Model Based Data Locality Optimization for Embedded Applications

Iterative optimization in the polyhedral model

Set and Relation Manipulation for the Sparse Polyhedral Framework

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