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Research on algorithm of fast Fourier transform in exascale system

Research Project

Project/Area Number 19K11989
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60090:High performance computing-related
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)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsエクサスケールシステム / 高速フーリエ変換 / 数論変換 / メニーコアプロセッサ / SIMD化 / 並列化 / GPU / 最適化
Outline of Research at the Start

高速フーリエ変換(fast Fourier transform、以下FFT)は、科学技術計算において今日広く用いられているアルゴリズムである。今後の技術動向から2021~2022年度にはエクサフロップスを超える性能を持つ次世代のスーパーコンピュータが出現すると予想されている。本研究では、エクサスケールシステムにおけるFFTアルゴリズムを実現すると共に、メニーコアプロセッサやGPUを搭載した超並列クラスタにおいて性能評価を行うことにより、エクサスケールシステムに適したアルゴリズム及び最適化手法を見出すことを目的とする。

Outline of Final Research Achievements

We implemented the Fast Fourier Transform (FFT) algorithm, which effectively uses SIMD instructions on a single many-core processor. We also implemented and evaluated a parallel three-dimensional FFT with overlapping computations and communication using two-dimensional decomposition on a massively parallel cluster of many cores. Furthermore, we parallelized and evaluated the performance of the Number-Theoretic Transform, which generalizes the Discrete Fourier Transform over complex numbers to a ring and a finite field.

Academic Significance and Societal Importance of the Research Achievements

エクサスケールシステムにおけるFFTアルゴリズムを実現するとともに、メニーコアプロセッサやGPUを搭載した超並列クラスタにおいて性能評価を行うことにより、エクサスケールシステムに適したアルゴリズム及び最適化手法を見出すことができた。
今後エクサスケール計算環境でFFTを用いた科学技術計算が行われる際に、計算時間を短縮することができるものと期待される。

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (11 results)

All 2024 2022 2021 2020 2019

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (8 results) (of which Int'l Joint Research: 4 results)

  • [Journal Article] An Implementation of Parallel Number-Theoretic Transform Using Intel AVX-512 Instructions2022

    • Author(s)
      Daisuke Takahashi
    • Journal Title

      Proc. 24th International Workshop on Computer Algebra in Scientific Computing (CASC 2022), Lecture Notes in Computer Science

      Volume: 13366 Pages: 318-332

    • DOI

      10.1007/978-3-031-14788-3_18

    • ISBN
      9783031147876, 9783031147883
    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fast Multiple Montgomery Multiplications Using Intel AVX-512IFMA Instructions2020

    • Author(s)
      Daisuke Takahashi
    • Journal Title

      Proc. 20th International Conference on Computational Science and Its Applications (ICCSA 2020), Part V, Lecture Notes in Computer Science

      Volume: 12253 Pages: 655-663

    • DOI

      10.1007/978-3-030-58814-4_52

    • ISBN
      9783030588137, 9783030588144
    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Implementation of Parallel 3-D Real FFT with 2-D Decomposition on Intel Xeon Phi Clusters2020

    • Author(s)
      Daisuke Takahashi
    • Journal Title

      Proc. 13th International Conference on Parallel Processing and Applied Mathematics (PPAM 2019), Part I, Lecture Notes in Computer Science

      Volume: 12043 Pages: 151-161

    • DOI

      10.1007/978-3-030-43229-4_14

    • ISBN
      9783030432287, 9783030432294
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] Implementation of Parallel Number-Theoretic Transform on GPU Clusters2024

    • Author(s)
      Daisuke Takahashi
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing (PP24)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Intel AVX-512IFMA命令を用いた並列数論変換の実現と評価2022

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2022 Research-status Report
  • [Presentation] Parallel Implementation of FFT in a Finite Field2022

    • Author(s)
      Daisuke Takahashi
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing (PP22)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 二次元分割を用いた並列三次元FFTにおける計算と通信のオーバーラップの自動チューニング2021

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Research-status Report
  • [Presentation] Automatic Tuning of Computation-Communication Overlap for Parallel 3-D FFT with 2-D Decomposition2021

    • Author(s)
      Daisuke Takahashi
    • Organizer
      SIAM Conference on Computational Science and Engineering (CSE21)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Intel AVX-512IFMA命令を用いた複数のMontgomery乗算の高速化2020

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2020年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Implementation of Parallel 3-D Real FFT with 2-D Decomposition on Intel Xeon Phi Clusters2020

    • Author(s)
      Daisuke Takahashi
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing (PP20)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Xeon Phiクラスタにおける二次元分割を用いた並列三次元実数FFTの実現と評価2019

    • Author(s)
      高橋大介
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2025-01-30  

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