Progressive Optimization of Batched LU Factorization on GPUs

Ahmad Abdelfattah; Stanimire Tomov; Jack Dongarra

doi:10.1109/HPEC.2019.8916270

Progressive Optimization of Batched LU Factorization on GPUs

Ahmad Abdelfattah, Stanimire Tomov, Jack Dongarra

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

This paper presents a progressive approach for optimizing the batched LU factorization on graphics processing units (GPUs). The paper shows that the reliance on level-3 BLAS routines for performance does not really pay off, and that it is indeed important to pay attention to the memory-bound part of the algorithm, especially when the problem size is very small. In this context, we develop a size-aware multi-level blocking technique that utilizes different granularities for kernel fusion according to the problem size. Our experiments, which are conducted on a Tesla V100 GPU, show that the multi-level blocking technique achieves speedups for single/double precisions that are up to 3.28×/2.69× against the generic LAPACK-style implementation. It is also up to 8.72×/7.2× faster than the cuBLAS library for single and double precisions, respectively. The developed solution is integrated into the open-source MAGMA library.

Original language	English
Title of host publication	2019 IEEE High Performance Extreme Computing Conference, HPEC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728150208
DOIs	https://doi.org/10.1109/HPEC.2019.8916270
State	Published - Sep 2019
Externally published	Yes
Event	2019 IEEE High Performance Extreme Computing Conference, HPEC 2019 - Waltham, United States Duration: Sep 24 2019 → Sep 26 2019

Publication series

Name	2019 IEEE High Performance Extreme Computing Conference, HPEC 2019

Conference

Conference	2019 IEEE High Performance Extreme Computing Conference, HPEC 2019
Country/Territory	United States
City	Waltham
Period	09/24/19 → 09/26/19

Funding

ACKNOWLEDGMENT This work is partially supported by NSF grant No. OAC-1740250 and CSR 1514286, NVIDIA, and by the Exascale Computing Project (17-SC-20-SC). This work is partially supported by NSF grant No. OAC- 1740250 and CSR 1514286, NVIDIA, and by the Exascale Computing Project (17-SC-20-SC).

Keywords

Batch computation
GPU computing
LU factorization

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10.1109/HPEC.2019.8916270

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title = "Progressive Optimization of Batched LU Factorization on GPUs",

abstract = "This paper presents a progressive approach for optimizing the batched LU factorization on graphics processing units (GPUs). The paper shows that the reliance on level-3 BLAS routines for performance does not really pay off, and that it is indeed important to pay attention to the memory-bound part of the algorithm, especially when the problem size is very small. In this context, we develop a size-aware multi-level blocking technique that utilizes different granularities for kernel fusion according to the problem size. Our experiments, which are conducted on a Tesla V100 GPU, show that the multi-level blocking technique achieves speedups for single/double precisions that are up to 3.28×/2.69× against the generic LAPACK-style implementation. It is also up to 8.72×/7.2× faster than the cuBLAS library for single and double precisions, respectively. The developed solution is integrated into the open-source MAGMA library.",

keywords = "Batch computation, GPU computing, LU factorization",

author = "Ahmad Abdelfattah and Stanimire Tomov and Jack Dongarra",

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year = "2019",

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doi = "10.1109/HPEC.2019.8916270",

language = "English",

series = "2019 IEEE High Performance Extreme Computing Conference, HPEC 2019",

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Abdelfattah, A, Tomov, S & Dongarra, J 2019, Progressive Optimization of Batched LU Factorization on GPUs. in 2019 IEEE High Performance Extreme Computing Conference, HPEC 2019., 8916270, 2019 IEEE High Performance Extreme Computing Conference, HPEC 2019, Institute of Electrical and Electronics Engineers Inc., 2019 IEEE High Performance Extreme Computing Conference, HPEC 2019, Waltham, United States, 09/24/19. https://doi.org/10.1109/HPEC.2019.8916270

Progressive Optimization of Batched LU Factorization on GPUs. / Abdelfattah, Ahmad; Tomov, Stanimire; Dongarra, Jack.
2019 IEEE High Performance Extreme Computing Conference, HPEC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8916270 (2019 IEEE High Performance Extreme Computing Conference, HPEC 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Abdelfattah, Ahmad

AU - Tomov, Stanimire

AU - Dongarra, Jack

PY - 2019/9

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N2 - This paper presents a progressive approach for optimizing the batched LU factorization on graphics processing units (GPUs). The paper shows that the reliance on level-3 BLAS routines for performance does not really pay off, and that it is indeed important to pay attention to the memory-bound part of the algorithm, especially when the problem size is very small. In this context, we develop a size-aware multi-level blocking technique that utilizes different granularities for kernel fusion according to the problem size. Our experiments, which are conducted on a Tesla V100 GPU, show that the multi-level blocking technique achieves speedups for single/double precisions that are up to 3.28×/2.69× against the generic LAPACK-style implementation. It is also up to 8.72×/7.2× faster than the cuBLAS library for single and double precisions, respectively. The developed solution is integrated into the open-source MAGMA library.

AB - This paper presents a progressive approach for optimizing the batched LU factorization on graphics processing units (GPUs). The paper shows that the reliance on level-3 BLAS routines for performance does not really pay off, and that it is indeed important to pay attention to the memory-bound part of the algorithm, especially when the problem size is very small. In this context, we develop a size-aware multi-level blocking technique that utilizes different granularities for kernel fusion according to the problem size. Our experiments, which are conducted on a Tesla V100 GPU, show that the multi-level blocking technique achieves speedups for single/double precisions that are up to 3.28×/2.69× against the generic LAPACK-style implementation. It is also up to 8.72×/7.2× faster than the cuBLAS library for single and double precisions, respectively. The developed solution is integrated into the open-source MAGMA library.

KW - Batch computation

KW - GPU computing

KW - LU factorization

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M3 - Conference contribution

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ER -

Progressive Optimization of Batched LU Factorization on GPUs

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Keywords

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