Stochastic Rounding: Implementation, Error Analysis, and Applications - Archive ouverte HAL Access content directly
Journal Articles Royal Society Open Science Year : 2022

Stochastic Rounding: Implementation, Error Analysis, and Applications

Massimiliano Fasi
  • Function : Author
  • PersonId : 1247865
  • IdHAL : mfasi
Théo Mary
Mantas Mikaitis
  • Function : Author
  • PersonId : 1113436


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.
Fichier principal
Vignette du fichier
surveySR.pdf (506.16 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03378080 , version 1 (14-10-2021)


  • HAL Id : hal-03378080 , version 1


Matteo Croci, Massimiliano Fasi, Nicholas J Higham, Théo Mary, Mantas Mikaitis. Stochastic Rounding: Implementation, Error Analysis, and Applications. Royal Society Open Science, In press. ⟨hal-03378080⟩
135 View
327 Download


Gmail Facebook X LinkedIn More