Development of accurate and reproducible matrix computation library for massively parallel environments

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K20286
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60100:Computational science-related
• Research Institution: Institute of Physical and Chemical Research
• Principal Investigator: Mukunoki Daichi 国立研究開発法人理化学研究所, 計算科学研究センター, 研究員 (90742289)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: 高精度 / 再現性 / 行列計算 / 疎行列反復法

Outline of Final Research Achievements

In this study, we developed the Basic Linear Algebra Subprograms (BLAS) for massively parallel architectures, which is accurate and can ensure reproducibility of computation results among different environments. Focusing mainly on the Ozaki scheme, we have developed a high-performance implementation of accurate and reproducible BLAS routines, and demonstrated its application to sparse iterative solvers on CPUs and GPUs. As further applications, we proposed an implementation of a single/double precision matrix multiplications using low-precision arithmetic units (Tensor Cores) and a binary128 matrix multiplication using single/double precision matrix multiplications.

Free Research Field

高性能計算

Academic Significance and Societal Importance of the Research Achievements

CPUおよびGPUにおいて高精度かつ計算結果の再現が可能なBLASルーチンを実現し，疎行列ソルバーへの応用を示した．既存手法と比べて性能および実装が容易であり，応用数理分野での応用も期待できる．またAI向け低精度演算器を単精度・倍精度の行列計算に応用可能であることを示した．今後のハードウェアデザインへのインパクトも期待できる．