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pzqd: PEZY-SC2 Acceleration of Double-Double Precision Arithmetic Library for High-Precision BLAS

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Computational and Experimental Simulations in Engineering (ICCES 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 75))

Abstract

We implemented pzqd, a high precision arithmetic library for the PEZY-SC2 that is based on Hida et al.’s QD library. PEZY-SC2 is an MIMD (multiple instruction stream, multiple data stream) -type many-core processor. We optimized matrix-matrix multiplication (Rgemm) in double-double precision (DD) on the PEZY-SC2. Porting the CPU code to PEZY-SC2 code is relatively easy because PEZY-SC2 is a MIMD-type processor; it runs all the threads independently. As a proof of concept, we ported pzqd with minimal modifications to the original QD library; pzqd can treat a DD type variable in a unified way on the host CPU and the PEZY-SC2. The performance of our implementation of Rgemm in DD (DD-Rgemm) on the PEZY-SC2 attained 75% of the peak performance of DD, which is 20 times faster than an Intel Xeon E5-2618L v3, even including the communication time between the host CPU and the PEZY-SC2. The most important technique for optimizing the DD-Rgemm on the PEZY-SC2 is to make use of the high-speed scratch-pad memory (local memory) installed in each core. We stored the \(2\times 2\) DD block matrices and other temporary variables in local memory by reducing the number of threads to increase the local memory size per thread as they occupy local memory even for this block size.

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Acknowledgements

We used the Shoubu System B installed at RIKEN in collaboration with RIKEN, PEZY Computing, and ExaScaler Inc. A subsidy supporting this research for advanced use of high-performance general-purpose computers was provided by the Ministry of Education, Culture, Sports, Science, and Technology. A Grant-in-Aid for Scientific Research (B) (KAKENHI: 18H03206) also supported this research.

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Authors and Affiliations

  1. PEZY Computing, 5F Chiyoda Ogawamachi Crosta, 1-11, Tokyo, 101-0052, Japan

    Toshiaki Hishinuma

  2. RIKEN, Wako, Saitama, 351-0198, Japan

    Maho Nakata

Authors
  1. Toshiaki Hishinuma
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  2. Maho Nakata
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Correspondence to Toshiaki Hishinuma .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Tokyo University of Science, Noda, Chiba, Japan

    Hiroshi Okada

  2. Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA

    Satya N. Atluri

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Hishinuma, T., Nakata, M. (2020). pzqd: PEZY-SC2 Acceleration of Double-Double Precision Arithmetic Library for High-Precision BLAS. In: Okada, H., Atluri, S. (eds) Computational and Experimental Simulations in Engineering. ICCES 2019. Mechanisms and Machine Science, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-030-27053-7_61

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  • DOI: https://doi.org/10.1007/978-3-030-27053-7_61

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  • Online ISBN: 978-3-030-27053-7

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