On Optimizing a Class of Multi-Dimensional Loops with Reduction for  Parallel Execution

Lam, Clk; Sadayappan, P.; Wenger, Rephael

doi:10.1142/s0129626497000176

Cited by 70 publications

(40 citation statements)

References 13 publications

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“…Whilst algorithms which can speed up tensor network contractions by optimising the bubbling used [3][4][5], as discusssed above, the underlying computational problem is NP-complete [6,7] Even ignoring the specific bubbling used, the complexity of the overall contraction procedure can also be shown to be prohibitive in general. Consider a network made from the binary tensors e and n. The value of e is 1 if and only if all indices are identical, and zero otherwise, whilst n has value 1 if and only if all legs differ and 0 otherwise.…”

Section: Computational Complexitymentioning

confidence: 99%

“…The remaining freedom is that of a unitary 7 on the virtual level, rather than general invertible matrix. This technique is heavily used in tensor network algorithms as a method of increasing numerical stability.…”

Section: Gauge Freedommentioning

confidence: 99%

“…The reduced density matrix on some subset of spins R will therefore be represented as 7 If you include the ability to expand the bond dimension then this grows to an isometric freedom.…”

Section: Mixed States and Many Body Operatorsmentioning

confidence: 99%

See 2 more Smart Citations

Hand-waving and interpretive dance: an introductory course on tensor networks

Bridgeman

Chubb

2017

J. Phys. A: Math. Theor.

321

300

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View the article online for updates and enhancements. AbstractThe curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes.These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states.The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.

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Section: Computational Complexitymentioning

confidence: 99%

Section: Gauge Freedommentioning

confidence: 99%

See 1 more Smart Citation

Hand-waving and interpretive dance: an introductory course on tensor networks

Bridgeman

Chubb

2017

J. Phys. A: Math. Theor.

321

300

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show abstract

“…More recently, extensions to the polyhedral framework have been proposed, allowing it to capture reduction computations [11,17,48]. Such efforts are described in [13], but they are fragile in the presence of non static control flow.…”

Section: Related and Future Workmentioning

confidence: 99%

Automatic Matching of Legacy Code to Heterogeneous APIs

Ginsbach

Remmelg

Steuwer

et al. 2018

Proceedings of the Twenty-Third International Conference on Architectural Support for Programming Languages and Operating Syste

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Heterogeneous accelerators often disappoint. They provide the prospect of great performance, but only deliver it when using vendor specific optimized libraries or domain specific languages. This requires considerable legacy code modifications, hindering the adoption of heterogeneous computing.This paper develops a novel approach to automatically detect opportunities for accelerator exploitation. We focus on calculations that are well supported by established APIs: sparse and dense linear algebra, stencil codes and generalized reductions and histograms. We call them idioms and use a custom constraint-based Idiom Description Language (IDL) to discover them within user code. Detected idioms are then mapped to BLAS libraries, cuSPARSE and clSPARSE and two DSLs: Halide and Lift.We implemented the approach in LLVM and evaluated it on the NAS and Parboil sequential C/C++ benchmarks, where we detect 60 idiom instances. In those cases where idioms are a significant part of the sequential execution time, we generate code that achieves 1.26× to over 20× speedup on integrated and external GPUs.CCS Concepts • Computer systems organization → Heterogeneous (hybrid) systems; • Software and its engineering → Domain specific languages; ACM Reference Format:

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“…More recently, extensions to the polyhedral framework have been proposed, allowing it to capture some reduction computations [8,14,32]. Such efforts are described in [12].…”

Section: Related Workmentioning

confidence: 99%

Discovery and exploitation of general reductions: A constraint based approach

Ginsbach¹,

O’Boyle²

2017

2017 IEEE/ACM International Symposium on Code Generation and Optimization (CGO)

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Discovering and exploiting scalar reductions in programs has been studied for many years. The discovery of more complex reduction operations has, however, received less attention. Such reductions contain compile-time unknown parameters, indirect memory accesses and dynamic control flow, which are challenging for existing approaches.In this paper we develop a new compiler based approach that automatically detects a wide class of reductions. This is based on a constraint formulation of the reduction idiom and has been implemented as an LLVM pass. We use a custom constraint solver to identify program subsets that adhere to the constraint specification. Once discovered, we automatically generate parallel code to exploit the reduction.This approach is robust and was evaluated on C versions of well known benchmark suites: NAS, Parboil and Rodinia. We detected 84 scalar reductions and 6 histograms, outperforming existing approaches. We show that the exploitation of histograms gives significant performance improvement.

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On Optimizing a Class of Multi-Dimensional Loops with Reduction for Parallel Execution

Cited by 70 publications

References 13 publications

Hand-waving and interpretive dance: an introductory course on tensor networks

Hand-waving and interpretive dance: an introductory course on tensor networks

Automatic Matching of Legacy Code to Heterogeneous APIs

Discovery and exploitation of general reductions: A constraint based approach

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