White Paper from the Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing

Roman Iakymchuk (1, 2) , Daichi Mukunoki (3) , Artur Podobas (3) , Fabienne Jézéquel (4, 2) , Toshiyuki Imamura (3) , Norihisa Fujita (5) , Jens Huthmann (3) , Shuhei Kudo (3) , Yiyu Tan (3) , Jens Domke (3) , Kai Torben Ohlhus (6) , Takeshi Fukaya (7) , Takeo Hoshi (8) , Yuki Murakami (9) , Maho Nakata , Takeshi Ogita (10) , Kentaro Sano (3) , Taisuke Boku (5)

1 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
3 RIKEN CCS - RIKEN Center for Computational Science [Kobe]
4 UP2 - Université Panthéon-Assas
5 Université de Tsukuba = University of Tsukuba
6 TWCU - Tokyo Woman's Christian University
7 Hokkaido University [Sapporo, Japan]
8 Tottori University
9 UoA - University of Aizu [Japan]
10 Tokyo Woman's Christian University, Department of Mathematics

In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However , precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-precision computing through precision-tuning, which adjusts the optimal precision for each operation and data. Several studies have been already conducted for it so far (e.g. Precimoniuos and Verrou), but the scope of those studies is limited to the precision-tuning alone. Hence, we aim to propose a broader concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. In 2019, we have started the Minimal-Precision Computing project to propose a more broad concept of the minimal-precision computing system with precision-tuning, involving both hardware and software stack. Specifically, our system combines (1) a precision-tuning method based on Discrete Stochastic Arithmetic (DSA), (2) arbitrary-precision arithmetic libraries, (3) fast and accurate numerical libraries, and (4) Field-Programmable Gate Array (FPGA) with High-Level Synthesis (HLS). In this white paper, we aim to provide an overview of various technologies related to minimal-and mixed-precision, to outline the future direction of the project, as well as to discuss current challenges together with our project members and guest speakers at the LSPANC 2020 workshop; https://www.r-ccs.riken.jp/labs/lpnctrt/lspanc2020jan/.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Arithmétique des ordinateurs; Analyse numérique [math.NA]; Logiciel mathématique [cs.MS]

Roman Iakymchuk, Daichi Mukunoki, Artur Podobas, Fabienne Jézéquel, Toshiyuki Imamura, et al.. White Paper from the Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing. 2020. ⟨hal-02536316⟩