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Stochastic Rounding

Unlike the previous approaches, which either round to the nearest number, or strictly up and down to obtain bounds, the stochastic approach rounds numbers at each stage randomly. The final result is obtained by performing the desired computation several times using this stochastic rounding technique, and then using probability theory to estimate the true result.

Clearly this approach does not guarantee the accuracy of the result in the way that interval analysis might, but in general it will give a better result than ordinary floating point arithmetic. The stochastic rounding technique also gives probabilistic information about the reliability of the calculation.

Martin Escardo