Energy efficiency and performance frontiers for sparse computations on GPU supercomputers

Anzt, Hartwig; Tomov, Stanimire; Dongarra, Jack

doi:10.1145/2712386.2712387

Cited by 10 publications

(8 citation statements)

References 34 publications

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“…Röhrig-Zöllner et al [19] discuss performance optimization techniques for the block Jacobi-Davidson method to compute a few eigenpairs of large-scale sparse matrices, and report reduced time-to-solution using block methods over single vector counterparts for quantum mechanics problems and PDEs. Finally, Anzt et al [20] describe an SpMM implementation based on the SELLC matrix format, and show that performance improvements in the SpMM kernel can translate into performance improvements in a block eigensolver running on GPUs.…”

Section: Introductionmentioning

confidence: 99%

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

Aktulga

Afibuzzaman

Williams

et al. 2017

IEEE Trans. Parallel Distrib. Syst.

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Abstract-As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. We consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We present techniques to significantly improve the SpMM and the transpose operation SpMM T by using the compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.

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Section: Introductionmentioning

confidence: 99%

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

Aktulga

Afibuzzaman

Williams

et al. 2017

IEEE Trans. Parallel Distrib. Syst.

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“…They showed that in terms of GFLOPS/W, the SpMV kernel was better in the Intel Sandy Bridge than in the NVIDIA GPU, but they only considered the CSR format and presented the results with using only one type of sparse matrices (R-MAT). In [3], the authors unveiled some energy efficiency and performance frontiers for sparse computations on GPU-based supercomputers. LOBPCG (Locally Optimal Block Preconditioned Conjugate Gradient) was chosen as a benchmark as it combines between sparse and dense linear algebra operations including the SpMV kernel.…”

Section: Related Workmentioning

confidence: 99%

BestSF

Benatia

Wang

et al. 2018

ACM Trans. Archit. Code Optim.

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The Sparse Matrix-Vector Multiplication (SpMV) kernel dominates the computing cost in numerous scientific applications. Many implementations based on different sparse formats were proposed to improve this kernel on the recent GPU architectures. However, it has been widely observed that there is no "best-for-all" sparse format for the SpMV kernel on GPU. Indeed, serious performance degradation of an order of magnitude can be observed without a careful selection of the sparse format to use. To address this problem, we propose in this article BestSF (Best Sparse Format), a new learning-based sparse meta-format that automatically selects the most appropriate sparse format for a given input matrix. To do so, BestSF relies on a cost-sensitive classification system trained using Weighted Support Vector Machines (WSVMs) to predict the best sparse format for each input sparse matrix. Our experimental results on two different NVIDIA GPU architectures using a large number of real-world sparse matrices show that BestSF achieved a noticeable overall performance improvement over using a single sparse format. While BestSF is trained to select the best sparse format in terms of performance (GFLOPS), our further experimental investigations revealed that using BestSF also led, in most of the test cases, to the best energy efficiency (MFLOPS/W). To prove its practical effectiveness, we also evaluate the performance and energy efficiency improvement achieved when using BestSF as a building block in a GPU-based Preconditioned Conjugate Gradient (PCG) iterative solver.

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“…As the CG and its preconditioned variant arise as a combination of matrixvector and vector-operations, the optimization for coalescent memory reads boils down to the sparse matrix vector product. There exists extensive work on optimizing storage format and sparse matrix vector performance for GPUs, and in this work we focus on using the CSR, ELL, and SELLP formats, known to provide good performance [4]. To reduce the memory traffic, it is necessary to use algorithm-specific kernels that apply kernel-fusion to the basic linear algebra operations whenever possible [1].…”

Section: Sparse Linear Algebra On Gpusmentioning

confidence: 99%

Accelerating the Conjugate Gradient Algorithm with GPUs in CFD Simulations

Anzt

Baboulin

Dongarra

et al. 2017

High Performance Computing for Computational Science – VECPAR 2016

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This paper illustrates how GPU computing can be used to accelerate computational fluid dynamics (CFD) simulations. For sparse linear systems arising from finite volume discretization, we evaluate and optimize the performance of Conjugate Gradient (CG) routines designed for manycore accelerators and compare against an industrial CPU-based implementation. We also investigate how the recent advances in preconditioning, such as iterative Incomplete Cholesky (IC, as symmetric case of ILU) preconditioning, match the requirements for solving real world problems.

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Energy efficiency and performance frontiers for sparse computations on GPU supercomputers

Cited by 10 publications

References 34 publications

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

BestSF

Accelerating the Conjugate Gradient Algorithm with GPUs in CFD Simulations

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