### Abstract

Dense-matrix-vector multiplication is one of the well-known important matrix calculations. This calculation is provided a general matrix-vector multiplication (GEMV) function in the basic linear algebra subprograms (BLAS) libraries for several computation hardware. Traditionally, studies focus one large dense-matrix (the length of each side of the dense matrix is long)-vector multiplication. However, some applications require acceleration of numerous small dense-matrix-vector multiplications. This feature is provided by batched BLAS libraries. This calculation is also needed to compute a hierarchical-matrix-vector multiplication. In this study, we implemented numerous small dense-matrix-vector multiplications on a Pascal GPU and evaluated the performance. Thus, we considered the impact of optimization parameters and succeeded in obtaining a better performance than previous works. The maximum differences from our previous work is 28.47% and from batched GEMV of MAGMA BLAS is upto 81.81%. Moreover, we considered the use of two optimization parameters in one GPU kernel; one parameter was applied to some matrices, whereas the second parameter was applied to other matrices. The amount of the improvement was limited (upto 5%), a performance improvement was achieved. Our result will serve as a good reference for users who need to use numerous small dense-matrix-vector multiplications on a GPU and want to optimize a matrix-vector multiplication by hand-Tuning and auto-Tuning.

Original language | English |
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Title of host publication | Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 9-16 |

Number of pages | 8 |

ISBN (Electronic) | 9781728148823 |

DOIs | |

Publication status | Published - Oct 2019 |

Event | 13th IEEE International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019 - Singapore, Singapore Duration: Oct 1 2019 → Oct 4 2019 |

### Publication series

Name | Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019 |
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### Conference

Conference | 13th IEEE International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019 |
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Country | Singapore |

City | Singapore |

Period | 10/1/19 → 10/4/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Hardware and Architecture
- Electrical and Electronic Engineering
- Control and Optimization

### Cite this

*Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019*(pp. 9-16). [8906754] (Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MCSoC.2019.00009

**Optimization of numerous small dense-matrix-vector multiplications in h-matrix arithmetic on gpu.** / Ohshima, Satoshi; Yamazaki, Ichitaro; Ida, Akihiro; Yokota, Rio.

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

*Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019.*, 8906754, Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019, Institute of Electrical and Electronics Engineers Inc., pp. 9-16, 13th IEEE International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019, Singapore, Singapore, 10/1/19. https://doi.org/10.1109/MCSoC.2019.00009

}

TY - GEN

T1 - Optimization of numerous small dense-matrix-vector multiplications in h-matrix arithmetic on gpu

AU - Ohshima, Satoshi

AU - Yamazaki, Ichitaro

AU - Ida, Akihiro

AU - Yokota, Rio

PY - 2019/10

Y1 - 2019/10

N2 - Dense-matrix-vector multiplication is one of the well-known important matrix calculations. This calculation is provided a general matrix-vector multiplication (GEMV) function in the basic linear algebra subprograms (BLAS) libraries for several computation hardware. Traditionally, studies focus one large dense-matrix (the length of each side of the dense matrix is long)-vector multiplication. However, some applications require acceleration of numerous small dense-matrix-vector multiplications. This feature is provided by batched BLAS libraries. This calculation is also needed to compute a hierarchical-matrix-vector multiplication. In this study, we implemented numerous small dense-matrix-vector multiplications on a Pascal GPU and evaluated the performance. Thus, we considered the impact of optimization parameters and succeeded in obtaining a better performance than previous works. The maximum differences from our previous work is 28.47% and from batched GEMV of MAGMA BLAS is upto 81.81%. Moreover, we considered the use of two optimization parameters in one GPU kernel; one parameter was applied to some matrices, whereas the second parameter was applied to other matrices. The amount of the improvement was limited (upto 5%), a performance improvement was achieved. Our result will serve as a good reference for users who need to use numerous small dense-matrix-vector multiplications on a GPU and want to optimize a matrix-vector multiplication by hand-Tuning and auto-Tuning.

AB - Dense-matrix-vector multiplication is one of the well-known important matrix calculations. This calculation is provided a general matrix-vector multiplication (GEMV) function in the basic linear algebra subprograms (BLAS) libraries for several computation hardware. Traditionally, studies focus one large dense-matrix (the length of each side of the dense matrix is long)-vector multiplication. However, some applications require acceleration of numerous small dense-matrix-vector multiplications. This feature is provided by batched BLAS libraries. This calculation is also needed to compute a hierarchical-matrix-vector multiplication. In this study, we implemented numerous small dense-matrix-vector multiplications on a Pascal GPU and evaluated the performance. Thus, we considered the impact of optimization parameters and succeeded in obtaining a better performance than previous works. The maximum differences from our previous work is 28.47% and from batched GEMV of MAGMA BLAS is upto 81.81%. Moreover, we considered the use of two optimization parameters in one GPU kernel; one parameter was applied to some matrices, whereas the second parameter was applied to other matrices. The amount of the improvement was limited (upto 5%), a performance improvement was achieved. Our result will serve as a good reference for users who need to use numerous small dense-matrix-vector multiplications on a GPU and want to optimize a matrix-vector multiplication by hand-Tuning and auto-Tuning.

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U2 - 10.1109/MCSoC.2019.00009

DO - 10.1109/MCSoC.2019.00009

M3 - Conference contribution

AN - SCOPUS:85076162251

T3 - Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019

SP - 9

EP - 16

BT - Proceedings - 2019 IEEE 13th International Symposium on Embedded Multicore/Many-Core Systems-on-Chip, MCSoC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

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