Monte Carlo Arithmetic D . Random rounding can be used to produce roundoff errors that are truly random and uncorrelated, and that have zero expected bias.
Randomization has both theoretical and practical benefits.
It has the effect of transforming any floating-point computation into a Monte Carlo computation, and roundoff analysis into statistical analysis. Unlike much previous work in this area, MCA makes no assumptions about the resulting roundoff error distributions, such as that they are normal. By running a program multiple times, one directly measures the sensitivity of particular outputs to random perturbations of particular inputs. MCA thus gives a way to implement roundoff analysis, using random variables for roundoff errors, so that the roundoff distributions can be studied explicitly. It encourages an empirical approach to evaluating numerical quality, and gives a way to exploit the Monte Carlo method in numerical computation.