Algorithm team
Professor Daisuke Takahashi
- Research on high-performance numerical computation
- High-performance parallel numerical computation software
- High-performance computing using GPUs and MIC (Many Integrated Core) processors
- High-precision computation algorithms and their applications
In order to carry out large-scale scientific computations within a limited amount of time, we study algorithms and programming techniques that draw out as much of a supercomputer’s performance as possible. Writing fast programs demands a deep understanding of both computer architecture and mathematics, but it is a rewarding field, because the effort you put in is reflected directly in the numbers you measure.
Personal page
Associate Professor Hiroto Tadano
- Research on large-scale linear computation algorithms
- Construction of fast, accurate and reliable algorithms for large-scale systems of linear equations
- Development of preconditioning methods for accelerating systems of linear equations
- Development of fast solution methods for large-scale eigenvalue problems in parallel computing environments
We develop numerical algorithms for problems such as systems of linear equations and eigenvalue problems.
Personal page
The computers used by the Algorithm team
Our laboratory works in cooperation with the Center for Computational Sciences, University of Tsukuba, and depending on the research topic students can use Pegasus (theoretical peak performance 6.5 PFLOPS), the supercomputer operated by the University of Tsukuba since December 2022. Miyabi (theoretical peak performance 80.1 PFLOPS), the supercomputer operated by the Joint Center for Advanced High Performance Computing (JCAHPC), is also available. Both systems have many nodes equipped with high-performance CPUs and GPUs and large amounts of memory, and can rapidly perform large-scale computations that would be difficult on an ordinary computer. Students in the Algorithm team make active use of these supercomputers in their research.
FFT (Fast Fourier Transform)
Here we introduce the FFT, one of Professor Takahashi’s research topics.
Members
Daisuke Takahashi Professor
- Numerical computation
- Many-core
- Accelerators
We study algorithms and programming techniques that draw out as much of a supercomputer's performance as possible, so that large-scale simulations can be carried out within a limited amount of time. Writing fast programs requires a deep understanding of both how computers work and mathematics, but since your effort is reflected directly in the performance numbers, it is a rewarding field.
Hiroto Tadano Associate Professor
- Linear equations
- Numerical computation
Our group develops algorithms for numerical linear algebra. Numerical linear algebra may not be a familiar research field to many people, but what we do is use computers to solve things like large-scale systems of linear equations. Some of you may wonder what on earth that is good for, but because large-scale linear systems and the like show up in so many places when simulating various phenomena on a computer, it has become an indispensable foundational technology. Why not join us and study algorithms that are useful in all kinds of fields?
Shota Kawakami D1
Research on methods for computing high-precision FFTs using lower-precision FFTs
Yutaro Yamane M2
Implementation of an FFT using half-precision SIMD arithmetic
Kenta Shimazaki M1
Research on ill-conditioned saddle point linear systems of equations
Shun Konita M1
Ryota Ogino B4
Recent Works
- Performance improvement of the Block GWBiCGSTAB method by variable grouping of recurrence relations齋藤 颯人, 多田野 寛人: “Performance improvement of the Block GWBiCGSTAB method by variable grouping of recurrence relations,” The 1st Meeting of FY2022 of the Study Group on High-Performance Solution Methods and Visualization Techniques for Nonlinear Problems, 2022. (in Japanese)
- Construction and performance evaluation of a block-global hybrid iterative method for linear systems with multiple right-hand sides菅沼 夏樹, 多田野 寛人: “Construction and performance evaluation of a block-global hybrid iterative method for linear systems with multiple right-hand sides,” The 2022 Annual Meeting of the Japan Society for Industrial and Applied Mathematics (JSIAM), 2022. (in Japanese)
- Application and performance evaluation of a method using block structures for saddle point problems appearing in image reconstruction problemsShota Ishikawa, Hiroto Tadano, Ayumu Saitoh, Application and performance evaluation of a method using block structures for saddle point problems appearing in image reconstruction problems, JSIAM Letters, 2022, Vol. 14, p. 115-118, published 2022/08/25, Online ISSN 1883-0617, Print ISSN 1883-0609, https://doi.org/10.14495/jsiaml.14.115, https://www.jstage.jst.go.jp/article/jsiaml/14/0/14_115/_article/-char/ja
- Application and performance evaluation of preconditioning using block structures for saddle point linear systems arising in image reconstruction problems石川 翔大, 多田野 寛人, 齋藤 歩: Application and performance evaluation of preconditioning using block structures for saddle point linear systems arising in image reconstruction problems,” The 2021 Annual Meeting of the Japan Society for Industrial and Applied Mathematics (JSIAM), 2021. (in Japanese)
- Acceleration of solving saddle point linear systems arising in three-dimensional model reconstruction problems石川 翔大, 多田野 寛人, 齋藤 歩: “Acceleration of solving saddle point linear systems arising in three-dimensional model reconstruction problems,” The 1st Meeting of FY2020 of the Study Group on Solution Methods and Visualization for Nonlinear Problems, 2020. (in Japanese)
- Performance evaluation of preconditioned iterative methods for saddle point linear systems arising in three-dimensional model reconstruction problems石川 翔大, 多田野 寛人, 齋藤 歩: “Performance evaluation of preconditioned iterative methods for saddle point linear systems arising in three-dimensional model reconstruction problems,” The 17th Joint Conference of Activity Groups of the Japan Society for Industrial and Applied Mathematics (JSIAM), 2021. (in Japanese)
- 倉本 亮世, 多田野 寛人, Improving the accuracy of approximate solutions of block product-type iterative methods for linear systems with multiple right-hand sides, Transactions of the Japan Society for Industrial and Applied Mathematics (JSIAM), 2020, Vol. 30, No. 4, p. 290-319, published 2020/12/25, Online ISSN 2424-0982, https://doi.org/10.11540/jsiamt.30.4_290, https://www.jstage.jst.go.jp/article/jsiamt/30/4/30_290/_article/-char/ja (in Japanese)
- Development of preconditioned iterative methods for saddle point linear systems arising in three-dimensional model reconstruction problems石川 翔大, 多田野 寛人, 齋藤 歩: “Development of preconditioned iterative methods for saddle point linear systems arising in three-dimensional model reconstruction problems,” The 30th Meeting of the JSIAM Activity Group on Algorithms for Matrix / Eigenvalue Problems and their Applications, No. 8, Dec 2020. (in Japanese)
- 長橋 朋也, 高橋 大介: "Construction of a Zero-Aware Pattern Database for sliding puzzles using MPI/OpenMP parallelization,” IPSJ SIG Technical Report, 195th HPC Meeting (HPC195), (in Japanese)
- 川上 昌汰, 高橋 大介: “Implementation and evaluation of an octuple-precision fast Fourier transform on GPUs,” IPSJ SIG Technical Report, 194th HPC Meeting (HPC194), (in Japanese)
- Numerical verification of Legendre's conjecture山口博將, 高橋大介: “Numerical verification of Legendre's conjecture,” Proceedings of the 85th IPSJ National Convention, Vol. 2023, No. 1, Feb. 2023. (in Japanese)
- Takuya Edamatsu and Daisuke Takahashi. 2023. Efficient Large Integer Multiplication with Arm SVE Instructions. In Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region (HPCAsia '23). Association for Computing Machinery, New York, NY, USA, 9–17. https://doi.org/10.1145/3578178.3578193
- T. Edamatsu and D. Takahashi, "Fast Multiple-Precision Integer Division Using Intel AVX-512," in IEEE Transactions on Emerging Topics in Computing, vol. 11, no. 1, pp. 224-236, 1 Jan.-March 2023, doi: 10.1109/TETC.2022.3196147. keywords: {Instruction sets;Arithmetic;Registers;Approximation algorithms;Costs;Computer architecture;Time measurement;AVX-512;divide-and-conquer;integer division;multi-precision arithmetic;SIMD},
- Sugizaki, Y., Takahashi, D. A Fast Algorithm for Computing the Number of Magic Series. Ann. Comb. 26, 511–532 (2022). https://doi.org/10.1007/s00026-022-00584-5
- Harayama, T., Kudo, S., Mukunoki, D., Imamura, T., Takahashi, D. (2021). A Rapid Euclidean Norm Calculation Algorithm that Reduces Overflow and Underflow. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_7
- A highly accurate and fast method for computing the 2-norm while avoiding overflow and underflow原山 赳幸, 工藤 周平, 椋木 大地, 今村 俊幸, 高橋 大介: “A highly accurate and fast method for computing the 2-norm while avoiding overflow and underflow,” IPSJ SIG Technical Report, 177th HPC Meeting, Vol. 2020-HPC-177, No. 8, Dec 2020. (in Japanese)
- Yukimasa Sugizaki and Daisuke Takahashi. 2020. Fast Computation of the Exact Number of Magic Series with an Improved Montgomery Multiplication Algorithm. In Algorithms and Architectures for Parallel Processing: 20th International Conference, ICA3PP 2020, New York City, NY, USA, October 2–4, 2020, Proceedings, Part II. Springer-Verlag, Berlin, Heidelberg, 365–382. https://doi.org/10.1007/978-3-030-60239-0_25
- Acceleration of modular multiplication using floating-point arithmetic on NVIDIA Volta GPUs杉崎 行優, 高橋 大介: “Acceleration of modular multiplication using floating-point arithmetic on NVIDIA Volta GPUs,” The 2020 Annual Meeting of the Japan Society for Industrial and Applied Mathematics (JSIAM), pp. 419-420, Sep. 2020. (in Japanese)
- Takuya Edamatsu and Daisuke Takahashi. 2019. Accelerating Large Integer Multiplication Using Intel AVX-512IFMA. In Algorithms and Architectures for Parallel Processing: 19th International Conference, ICA3PP 2019, Melbourne, VIC, Australia, December 9–11, 2019, Proceedings, Part I. Springer-Verlag, Berlin, Heidelberg, 60–74. https://doi.org/10.1007/978-3-030-38991-8_5
- Acceleration of multiple-precision integer multiplication using AVX-512IFMA枝松 拓弥, 高橋 大介: “Acceleration of multiple-precision integer multiplication using AVX-512IFMA,” The 2019 Annual Meeting of the Japan Society for Industrial and Applied Mathematics (JSIAM), pp. 400-401, Aug. 2019. (in Japanese)
- T. Edamatsu and D. Takahashi, "Acceleration of Large Integer Multiplication with Intel AVX-512 Instructions," 2018 IEEE 20th International Conference on High Performance Computing and Communications; IEEE 16th International Conference on Smart City; IEEE 4th International Conference on Data Science and Systems (HPCC/SmartCity/DSS), Exeter, UK, 2018, pp. 211-218, doi: 10.1109/HPCC/SmartCity/DSS.2018.00059.
- 佐藤 駿一, 高橋 大介: “Implementation and performance evaluation of sparse matrix-vector multiplication in the SELL format on GPUs,” IPSJ SIG Technical Report, 164th HPC Meeting (HPC164), Vol. 2018-HPC-164, No. 3, Apr. 2018. (in Japanese)
- Implementation of definition files for the Xevolver framework to automate optimization techniques五味 歩武, 高橋 大介: “Implementation of definition files for the Xevolver framework to automate optimization techniques”, IPSJ SIG Technical Report, 155th SIGHPC Meeting (HPC155), Vol. 2016-HPC-155, No. 7, Aug. 2016. (in Japanese)
- A verified fast Fourier transform using rectangular arithmetic based on midpoint-radius interval arithmetic篠塚 敬介, 高橋 大介: “A verified fast Fourier transform using rectangular arithmetic based on midpoint-radius interval arithmetic”, IPSJ SIG Technical Report, 154th SIGHPC Meeting (HPC154), Vol. 2016-HPC-154, No. 9, Apr. 2016. (in Japanese)