Deriving dense linear algebra libraries

Bientinesi, Paolo; Gunnels, John A.; Myers, Margaret; Quintana–Ort́ı, Enrique S.; Rhodes, Timothy; Geijn, Robert A.; Zee, Field G.

doi:10.1007/s00165-011-0221-4

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…where A, B and C are matrices and α and β are scalars. This kernel is considered the main building block in dense linear algebra because many other operations can be expressed in terms of several GEMM invocations [7]. GEMM belongs to Level 3 of the BLAS specification [8].…”

Section: General Matrix-matrix Multiplicationmentioning

confidence: 99%

Energy-efficient algebra kernels in FPGA for High Performance Computing

Favaro¹,

Dufrechou

Ezzatti

et al. 2021

JCS&T

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The dissemination of multi-core architectures and the later irruption of massively parallel devices, led to a revolution in High-Performance Computing (HPC) platforms in the last decades. As a result, Field-Programmable Gate Arrays (FPGAs) are re-emerging as a versatile and more energy-efficient alternative to other platforms. Traditional FPGA design implies using low-level Hardware Description Languages (HDL) such as VHDL or Verilog, which follow an entirely different programming model than standard software languages, and their use requires specialized knowledge of the underlying hardware. In the last years, manufacturers started to make big efforts to provide High-Level Synthesis (HLS) tools, in order to allow a grater adoption of FPGAs in the HPC community.Our work studies the use of multi-core hardware and different FPGAs to address Numerical Linear Algebra (NLA) kernels such as the general matrix multiplication GEMM and the sparse matrix-vector multiplication SpMV. Specifically, we compare the behavior of fine-tuned kernels in a multi-core CPU processor and HLS implementations on FPGAs. We perform the experimental evaluation of our implementations on a low-end and a cutting-edge FPGA platform, in terms of runtime and energy consumption, and compare the results against the Intel MKL library in CPU.

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Section: General Matrix-matrix Multiplicationmentioning

confidence: 99%

Energy-efficient algebra kernels in FPGA for High Performance Computing

Favaro¹,

Dufrechou

Ezzatti

et al. 2021

JCS&T

View full text Add to dashboard Cite

show abstract

“…Since this early work, we have derived hundreds of algorithms which are incorporated in a high-performance linear algebra software library, libflame [38,39]. A discussion of this work targeting the Formal Methods community can be found in a Formal Aspects of Computing paper [2], which uses the solution of a triangular Sylvester equation as an example.…”

Section: Impact On Algorithms For Matrix Operationsmentioning

confidence: 99%

A Simple Methodology for Computing Families of Algorithms

Parikh,

Myers,

Vuduc

et al. 2018

Preprint

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Discovering "good" algorithms for an operation is often considered an art best left to experts. What if there is a simple methodology, an algorithm, for systematically deriving a family of algorithms as well as their cost analyses, so that the best algorithm can be chosen? We discuss such an approach for deriving loop-based algorithms. The example used to illustrate this methodology, evaluation of a polynomial, is itself simple yet the best algorithm that results is surprising to a non-expert: Horner's rule. We finish by discussing recent advances that make this approach highly practical for the domain of high-performance linear algebra software libraries.

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“…A Formal Linear Algebra Method Environment (FLAME) focuses on issues related to programming of linear algebra programs. The focus of the FLAME project is to automatically generate efficient linear algebra codes for the underlying platform [17] [18]. Under the umbrella of FLAME project, BLAS-like Library Instantiation Software (BLIS) focuses on rapid scheduling of BLAS-like kernels on multicore architectures.…”

Section: Software Packages For Multicore Platformsmentioning

confidence: 99%

Accelerating BLAS on Custom Architecture through Algorithm-Architecture Co-design

Merchant,

Vatwani,

Chattopadhyay

et al. 2016

Preprint

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Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15 to 57% of the theoretical peak performance at 65W to 240W respectively for compute bound operations like Double/Single Precision General Matrix Multiplication (XGEMM). For bandwidth bound operations like Single/Double precision Matrix-vector Multiplication (XGEMV) the performance is merely 5 to 7% of the theoretical peak performance in multicores and GPGPUs respectively. Achieving performance in BLAS requires moving away from conventional wisdom and evolving towards customized accelerator tailored for BLAS through algorithm-architecture co-design. In this paper, we present acceleration of Level-1 (vector operations), Level-2 (matrix-vector operations), and Level-3 (matrix-matrix operations) BLAS through algorithm architecture co-design on a Coarse-grained Reconfigurable Architecture (CGRA). We choose REDEFINE CGRA as a platform for our experiments since REDEFINE can be adapted to support domain of interest through tailor-made Custom Function Units (CFUs). For efficient sequential realization of BLAS, we present design of a Processing Element (PE) and perform micro-architectural enhancements in the PE to achieve up-to 74% of the theoretical peak performance of PE in DGEMM, 40% in DGEMV and 20% in double precision inner product (DDOT). We attach this PE to REDEFINE CGRA as a CFU and show the scalability of our solution. Finally, we show performance improvement of 3-140x in PE over commercially available Intel micro-architectures, ClearSpeed CSX700, FPGA, and Nvidia GPGPUs.

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Deriving dense linear algebra libraries

Cited by 8 publications

References 21 publications

Energy-efficient algebra kernels in FPGA for High Performance Computing

Energy-efficient algebra kernels in FPGA for High Performance Computing

A Simple Methodology for Computing Families of Algorithms

Accelerating BLAS on Custom Architecture through Algorithm-Architecture Co-design

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