  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/.
