Effective Implementation of Matrix–Vector Multiplication on Intel's AVX multicore Processor

Hassan, Somaia Awad; Mahmoud, Mountasser M.M.; Hemeida, Ashraf Mohamed; Saber, Mahmoud A.

doi:10.1016/j.cl.2017.06.003

Cited by 8 publications

(19 citation statements)

References 18 publications

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“…Our 2D-tiling method for parallel matrix-matrix multiplication utilizing AVX512 intrinsics is more complex than conventional multiplication or matrix-vector multiplication [14,15]. Figure 1(g) shows our proposed algorithm.…”

Section: D-tiling For Parallel Matrix-matrix Multiplication Utilizing...mentioning

confidence: 99%

An Improvement of the Matrix-Matrix Multiplication Speed using 2D-Tiling and AVX512 Intrinsics for Multi-Core Architectures

Oo¹,

Chaikan²

2021

ASEAN Sci Tech Rept

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Matrix-matrix multiplication is a time-consuming operation in scientific and engineering applications. When the matrix size is large, it will take a lot of computation time, resulting in slow software which is unacceptable in real-time applications. In this paper, 2D-tiling, loop unrolling, data padding, OpenMP directives, and AVX512 intrinsics are utilized to increase the speed of matrix-matrix multiplication on multi-core architectures. Our algorithm, tested on a Core i9-7900X machine, is more than two times faster than the operations offered by the OpenBLAS and Eigen libraries for single and double precision floating-point matrices. We also propose an equation for parameter tuning which allows our algorithm to be adapted to process any size of matrix on CPUs with different cache organizations.

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Section: D-tiling For Parallel Matrix-matrix Multiplication Utilizing...mentioning

confidence: 99%

An Improvement of the Matrix-Matrix Multiplication Speed using 2D-Tiling and AVX512 Intrinsics for Multi-Core Architectures

Oo¹,

Chaikan²

2021

ASEAN Sci Tech Rept

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“…It is widely employed in many scientific disciplines, such as machine learning, 1 data mining, 2 quantum chemistry, 3 mathematical physics, 4 and high-performance computing. 5,6 Implementations of MVM are prescribed by the Basic Linear Algebra Subprograms (BLAS), which is a specification of low-level routines that support portable high performance. 7,8 BLAS became a building block for the creation of the BLAS++ API, which is introduced by the Software for Linear Algebra Targeting Exascale (SLATE) project.…”

Section: Introductionmentioning

confidence: 99%

“…7,8 BLAS became a building block for the creation of the BLAS++ API, which is introduced by the Software for Linear Algebra Targeting Exascale (SLATE) project. 9 Approaches of two main types can be applied to optimize MVM on modern processors: 5 those based on manual-tuning and auto-tuning. Manually optimizing MVM for a new architecture requires expert knowledge and time.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, we propose an analytical approach, which takes O(1) time and can be used to analytically obtain effective * single-threaded and multi-threaded implementations of MVM without access to the target architecture. In particular, to apply analytical modeling, we introduce a modification of the latest implementations of MVM, 5,6 which can be produced using common loop transformations (e.g., scalar replacement, 21 tiling, 22 interchange, 22 vectorization, 23 and parallelization 24 ). Since such transformations can be performed during compilation, the modification can be generated automatically by a compiler.…”

Section: Introductionmentioning

confidence: 99%

“…20 We identify the empirical near-optimal parameter values for described implementations of MVM, which should otherwise be found using either manual-tuning or auto-tuning. 5,6 Our contributions are summarized as follows:…”

Section: Introductionmentioning

confidence: 99%

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The efficiency of matrix–vector multiplication is of considerable importance. No current approaches can optimize this sufficiently well under severe time constraints. All major existing methods are based on either manual‐tuning or auto‐tuning and can therefore be time‐consuming. We introduce an alternative model‐driven approach, which is used to map the implementation of matrix–vector multiplication to a target architecture and analytically obtain its parameters. The approach yields the performance that is competitive with optimized Basic Linear Algebra Subprograms (BLAS)‐like dense linear algebra libraries without the need for manual‐tuning or auto‐tuning. Our method provides competitive performance across hardware architectures and can be utilized to obtain single‐threaded and multi‐threaded implementations on multicore processors. We expect that this approach allows the community to progress from valuable engineering solutions to techniques with a broader application.

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Effective Implementation of Matrix–Vector Multiplication on Intel's AVX multicore Processor

Cited by 8 publications

References 18 publications

An Improvement of the Matrix-Matrix Multiplication Speed using 2D-Tiling and AVX512 Intrinsics for Multi-Core Architectures

An Improvement of the Matrix-Matrix Multiplication Speed using 2D-Tiling and AVX512 Intrinsics for Multi-Core Architectures

Analytical modeling of matrix–vector multiplication on multicore processors

High performance and energy efficient sobel edge detection

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