Title: Confidence Intervals for Stochastic Arithmetic,
Abstract: Quantifying errors and losses due to the use of Floating-Point (FP)
calculations in industrial scientific computing codes is an important part of
the Verification, Validation and Uncertainty Quantification (VVUQ) process.
Stochastic Arithmetic is one way to model and estimate FP losses of accuracy,
which scales well to large, industrial codes. It exists in different flavors,
such as CESTAC or MCA, implemented in various tools such as CADNA, Verificarlo
or Verrou. These methodologies and tools are based on the idea that FP losses
of accuracy can be modeled via randomness. Therefore, they share the same need
to perform a statistical analysis of programs results in order to estimate the
significance of the results. In this paper, we propose a framework to perform a
solid statistical analysis of Stochastic Arithmetic. This framework unifies all
existing definitions of the number of significant digits (CESTAC and MCA), and
also proposes a new quantity of interest: the number of digits contributing to
the accuracy of the results. Sound confidence intervals are provided for all
estimators, both in the case of normally distributed results, and in the
general case. The use of this framework is demonstrated by two case studies of
large, industrial codes: Europlexus and code\_aster.