1,897 research outputs found
White Paper from Workshop on Large-scale Parallel Numerical Computing Technology (LSPANC 2020): HPC and Computer Arithmetic toward Minimal-Precision Computing
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/
Numerical validation in quadruple precision using stochastic arithmetic
International audienceDiscrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs. DSA is implemented in the CADNA library that can analyze the numerical quality of single and double precision programs. In this article, we show how the CADNA library has been improved to enable the estimation of rounding errors in programs using quadruple precision floating-point variables, i.e. having 113-bit mantissa length. Although an implementation of DSA called SAM exists for arbitrary precision programs, a significant performance improvement has been obtained with CADNA compared to SAM for the numerical validation of programs with 113-bit mantissa length variables. This new version of CADNA has been sucessfully used for the control of accuracy in quadruple precision applications, such as a chaotic sequence and the computation of multiple roots of polynomials. We also describe a new version of the PROMISE tool, based on CADNA, that aimed at reducing in numerical programs the number of double precision variable declarations in favor of single precision ones, taking into account a requested accuracy of the results. The new version of PROMISE can now provide type declarations mixing single, double and quadruple precision
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