On the Arithmetic Intensity of Distributed-Memory Dense Matrix Multiplication Involving a Symmetric Input Matrix (SYMM) - Algorithmes Parallèles et Optimisation Access content directly
Conference Papers Year : 2023

On the Arithmetic Intensity of Distributed-Memory Dense Matrix Multiplication Involving a Symmetric Input Matrix (SYMM)

Abstract

Dense matrix multiplication involving a symmetric input matrix (SYMM) is implemented in reference distributed-memory codes with the same data distribution as its general analogue (GEMM). We show that, when the symmetric matrix is dominant, such a 2D block-cyclic (2D BC) scheme leads to a lower arithmetic intensity (AI) of SYMM than that of GEMM by a factor of 2. We propose alternative data distributions preserving the memory benefit of SYMM of storing only half of the matrix while achieving up to the same AI as GEMM. We also show that, in the case we can afford the same memory footprint as GEMM, SYMM can achieve a higher AI. We propose a task-based design of SYMM independent of the data distribution. This design allows for scalable A-stationary SYMM with which all discussed data distributions, may they be very irregular, can be easily assessed. We have integrated the resulting code in a reduction dimension algorithm involving a randomized singular value decomposition dominated by SYMM. An experimental study shows a compelling impact on performance.
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hal-04093162 , version 1 (09-05-2023)

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  • HAL Id : hal-04093162 , version 1

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Emmanuel Agullo, Alfredo Buttari, Olivier Coulaud, Lionel Eyraud-Dubois, Mathieu Faverge, et al.. On the Arithmetic Intensity of Distributed-Memory Dense Matrix Multiplication Involving a Symmetric Input Matrix (SYMM). IPDPS 2023 - 37th International Parallel and Distributed Processing Symposium, IEEE, May 2023, St. Petersburg, FL, United States. pp.357-367. ⟨hal-04093162⟩
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