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Stochastic Rounding: Implementation, Error Analysis, and Applications

Abstract : Stochastic rounding randomly maps a real number to one of the two nearest values in a finite precision number system. First proposed for use in computer arithmetic in the 1950s, it is attracting renewed interest. If used in floating-point arithmetic in the computation of the inner product of two vectors of length n, it yields an error bounded by √nu with high probability, where u is the unit roundoff, which is not necessarily the case for round to nearest. A particular attraction of stochastic rounding is that, unlike round to nearest, it is immune to the phenomenon of stagnation, whereby a sequence of tiny updates to a relatively large quantity are lost. We survey stochastic rounding, covering its mathematical properties and probabilistic error analysis, its implementation, and its use in applications, including deep learning and the numerical solution of differential equations.
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Preprints, Working Papers, ...
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Submitted on : Thursday, October 14, 2021 - 2:18:57 PM
Last modification on : Tuesday, January 4, 2022 - 5:51:18 AM
Long-term archiving on: : Saturday, January 15, 2022 - 6:58:38 PM


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  • HAL Id : hal-03378080, version 1


Matteo Croci, Massimiliano Fasi, Nicholas Higham, Théo Mary, Mantas Mikaitis. Stochastic Rounding: Implementation, Error Analysis, and Applications. 2021. ⟨hal-03378080⟩



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