A loop transformation theory and an algorithm to maximize parallelism

Wolf, Michael E.; Lam, Monica S.

doi:10.1109/71.97902

Cited by 523 publications

(257 citation statements)

References 10 publications

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“…This algorithm generalizes both the Allen-Kennedy algorithm [1] and the Wolf-Lam algorithm [12]. It works on an over-approximation of dependences by polyhedra.…”

Section: The Underlying Schedulermentioning

confidence: 99%

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Scheduling the Computations of a Loop Nest with Respect to a Given Mapping

Darte

Diderich²,

Gengler³

et al. 2000

Euro-Par 2000 Parallel Processing

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Abstract. When parallelizing loop nests for distributed memory parallel computers, we have to specify when the different computations are carried out (computation scheduling), where they are carried out (computation mapping), and where the data are stored (data mapping). We show that even the "best" scheduling and mapping functions can lead to a sequential execution when combined, if they are independently chosen. We characterize when combined scheduling and mapping functions actually lead to a parallel execution. We present an algorithm which computes a scheduling compatible with a given computation mapping, if such a schedule exists.

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“…This algorithm generalizes both the Allen-Kennedy algorithm [1] and the Wolf-Lam algorithm [12]. It works on an over-approximation of dependences by polyhedra.…”

Section: The Underlying Schedulermentioning

confidence: 99%

“…The main algorithms, using exact representations of data dependences, are those of Feautrier [8], and Lim and Lam [10]. Allen and Kennedy [1], Wolf and Lam [12], and Darte and Vivien [5] introduced parallelism detection and scheduling algorithms that use a conservative approximation of the data dependences.…”

Section: Introductionmentioning

confidence: 99%

Scheduling the Computations of a Loop Nest with Respect to a Given Mapping

Darte

Diderich²,

Gengler³

et al. 2000

Euro-Par 2000 Parallel Processing

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show abstract

“…Currently, the dominant transformation framework for affine transformations is the polyhedral framework [72,23,54,31,13,8,48,6]. There are two reasons these techniques cannot be applied when there are indirect memory references.…”

Section: Introductionmentioning

confidence: 99%

An approach for code generation in the Sparse Polyhedral Framework

et al. 2016

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Applications that manipulate sparse data structures contain memory reference patterns that are unknown at compile time due to indirect accesses such as A [B[i]]. To exploit parallelism and improve locality in such applications, prior work has developed a number of run-time reordering transformations (RTRTs). This paper presents the Sparse Polyhedral Framework (SPF) for specifying RTRTs and compositions thereof and algorithms for automatically generating efficient inspector and executor code to implement such transformations. Experimental results indicate that the performance of automatically generated inspectors and executors competes with the performance of hand-written ones in some cases.

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“…These, however, only address fixed sets of techniques. The techniques include peephole optimization [McK65], pre-defined script-based optimization [Bra84], theory-based ordering [Wol91], generic probabilistic techniques [Pot94,Cha95], bottleneck identification and elimination approaches, and approaches using enabling and disabling transformations, [Whi90,Pot92,Hua93].…”

Section: Related Workmentioning

confidence: 99%

A methodology for guided behavioral-level optimization

Guerra¹,

Potkonjak²,

Rabaey³

Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175)

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-Optimization at the early stages of design are crucial. However, due to an overwhelming number of design and optimization options, design exploration is often conducted in a qualitative, ad-hoc manner. This paper presents a methodology and interactive environment for guiding the exploration process. A prototype targeting behavioral-level optimization for datapath-intensive ASIC implementations has been developed. The key to the approach is encapsulated knowledge about the various optimizations and a set of techniques to automatically extract the "essence" of a design description. At each stage in the exploration process, the system suggests and ranks potential optimizations, both in terms of immediate and longer-term impact. It also provides evaluations of the design and of the likely affects each optimization will have on metrics like power and performance. In the new approach, the designer is responsible for making the actual optimization selections. However, using the provided guidance, designers can make decisions in a more informed manner, and therefore can explore the design solution space more effectively. The effectiveness of the approach is demonstrated on a number of designs. IntroductionTraditionally, concentration has been placed in the development of point tools and methodologies which address a single task within the optimization process. For example, in behavioral-level optimization, in addition to the approaches proposed for partitioning, template matching, and clock selection, there exist more than a hundred transformations [Bac94,Par95]. Some optimizations are restricted to optimization of a specific class of computation (e.g. only linear computations). Some focus on power optimization while others target area or throughput. Furthermore, some concentrate on reduction of just a specific sub-metric; for example, different power optimization techniques have been developed for reducing capacitance, for reducing activity, and for enabling voltage scaling.Effective global optimization, or optimization of a global objective function on current-day complex and heterogeneous applications, clearly requires the coordinated application of a collection of techniques. While many of the problems being addressed by the individual techniques are in themselves computationally intractable, an added layer of complexity clearly exists in deriving an entire optimization trajectory. This added complexity is due to the strong interdependency that exists between techniques. Exploring different trajectories is crucial, as a large variability in attainable improvements exists. Exploring all possible sequences of actions inevitably results in combinatorial explosion, however, and thus is not a feasible option. Furthermore, static scripts are not sufficient since their effectiveness is strongly dependent on the particular design. This paper proposes a methodology for enabling systematic and effective global optimization. The approach involves interactively and quantitatively guiding the designer's exploration pro...

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A loop transformation theory and an algorithm to maximize parallelism

Cited by 523 publications

References 10 publications

Scheduling the Computations of a Loop Nest with Respect to a Given Mapping

Scheduling the Computations of a Loop Nest with Respect to a Given Mapping

An approach for code generation in the Sparse Polyhedral Framework

A methodology for guided behavioral-level optimization

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