Stochastic Rounding: Implementation, Error Analysis, and Applications

International audience ; 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.