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Research on Rational Number Arithmetic Library in Many-Core Massively Parallel Cluster

Research Project

Project/Area Number 16K00168
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field High performance computing
Research InstitutionUniversity of Tsukuba

Principal Investigator

TAKAHASHI Daisuke  筑波大学, 計算科学研究センター, 教授 (00292714)

Research Collaborator SAMUKAWA HIKARU  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords有理数算術演算 / 多倍長整数演算 / モジュラー算術演算 / SIMD化 / 有理数計算 / 並列化 / 有理数演算 / 並列処理 / 多倍長精度演算 / メニーコアプロセッサ / 高速フーリエ変換
Outline of Final Research Achievements

We performed vectorization using SIMD instructions in the hierarchy of multiple-precision integer arithmetic. Specifically, we evaluated the performance by speeding up unsigned 64-bit integer division for multiple dividend and divisor using SIMD instructions. Using this method, we proposed a fast calculation method of BBP type formula that calculates a specific digit of mathematical constants. In addition, vectorization with Intel AVX-512 instruction is performed by using reduced-radix representation in multiple-precision integer multiplication. We implemented modular arithmetic to speed up rational arithmetic in a rational arithmetic programming environment.

Academic Significance and Societal Importance of the Research Achievements

多倍長演算ライブラリとしてGNU Multi-Precision Library(GMP)が知られているが、SIMD命令はほとんど用いられていない。本研究課題では多倍長乗算および複数の被除数と除数に対する符号なし64ビット整数除算をSIMD命令を用いて高速化することができた。多倍長演算は現在公開鍵暗号などで広く用いられており、本研究課題で提案した手法はこれらの高速化に貢献できると期待できる。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (7 results)

All 2019 2018 2017 2016

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (5 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] On the computation and verification of π using BBP-type formulas2019

    • Author(s)
      Daisuke Takahashi
    • Journal Title

      The Ramanujan Journal

      Volume: 印刷中 Issue: 1 Pages: 177-186

    • DOI

      10.1007/s11139-018-0104-x

    • NAID

      120007168375

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computation of the 100 quadrillionth hexadecimal digit of π on a cluster of Intel Xeon Phi processors2018

    • Author(s)
      Daisuke Takahashi
    • Journal Title

      Parallel Computing

      Volume: 75 Pages: 1-10

    • DOI

      10.1016/j.parco.2018.02.002

    • NAID

      120007133897

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Intel AVX-512命令を用いた複数の整数除算の高速化2018

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Acceleration of Large Integer Multiplication with Intel AVX-512 Instructions2018

    • Author(s)
      Takuya Edamatsu and Daisuke Takahashi
    • Organizer
      20th IEEE International Conference on High Performance Computing and Communications (HPCC-2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 有理数計算プログラミング環境での有理数BLASの並列化について2017

    • Author(s)
      寒川光
    • Organizer
      情報処理学会第158回 ハイパフォーマンスコンピューティング研究会
    • Place of Presentation
      大月ホテル和風館(静岡県熱海市)
    • Year and Date
      2017-03-08
    • Related Report
      2016 Research-status Report
  • [Presentation] 数学定数の特定の桁を計算するBBP型公式の高速計算法2017

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Research-status Report
  • [Presentation] SIMD命令を用いた整数除算の高速化2016

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2020-03-30  

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