Confidence Intervals for Stochastic Arithmetic

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