Matteo Croci
Stochastic rounding: implementation, error analysis and applications
Croci, Matteo; Fasi, Massimiliano; Higham, Nicholas J.; Mary, Theo; Mikaitis, Mantas
Authors
Dr Massimiliano Fasi massimiliano.fasi@durham.ac.uk
Assistant Professor
Nicholas J. Higham
Theo Mary
Mantas Mikaitis
Abstract
Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to x. This rounding mode was first proposed for use in computer arithmetic in the 1950s and it is currently experiencing a resurgence of interest. If used to compute the inner product of two vectors of length n in floating-point arithmetic, it yields an error bound with constant n−−√u with high probability, where u is the unit round-off. This is not necessarily the case for round to nearest (RN), for which the worst-case error bound has constant nu. A particular attraction of SR is that, unlike RN, it is immune to the phenomenon of stagnation, whereby a sequence of tiny updates to a relatively large quantity is lost. We survey SR by discussing its mathematical properties and probabilistic error analysis, its implementation, and its use in applications, with a focus on machine learning and the numerical solution of differential equations.
Citation
Croci, M., Fasi, M., Higham, N. J., Mary, T., & Mikaitis, M. (2022). Stochastic rounding: implementation, error analysis and applications. Royal Society Open Science, 9(3), Article 211631. https://doi.org/10.1098/rsos.211631
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 4, 2022 |
Online Publication Date | Mar 9, 2022 |
Publication Date | 2022-03 |
Deposit Date | Mar 14, 2022 |
Publicly Available Date | Jun 30, 2022 |
Journal | Royal Society Open Science |
Publisher | The Royal Society |
Peer Reviewed | Peer Reviewed |
Volume | 9 |
Issue | 3 |
Article Number | 211631 |
DOI | https://doi.org/10.1098/rsos.211631 |
Related Public URLs | http://eprints.maths.manchester.ac.uk/2843/ |
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Copyright Statement
© 2022 The Authors.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
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