This paper introduces a static analysis technique for computing formally verified round-off
error bounds of floating-point functional expressions. The technique is based on a …

This paper presents an abstract interpretation framework for the round-off error analysis of
floating-point programs. This framework defines a parametric abstract analysis that …

Rigorous estimation of maximum floating-point round-off errors is an important capability
central to many formal verification tools. Unfortunately, available techniques for this task …

Small round-off errors in safety-critical systems can lead to catastrophic consequences. In
this context, determining if the result computed by a floating-point program is accurate …

Elementary function calls are a common feature in numerical programs. While their
implementations in mathematical libraries are highly optimized, function evaluation is …

The development of sound and efficient tools that automatically perform floating-point round-
off error analysis is an active area of research with applications to embedded systems and …

We present a new tool that generates bounds on the values and the round-off errors of
programs using floating point operations. The tool is based on forward error analysis and …

Static value analysis is a classical approach for verifying programs with floating-point
computations. Value analysis mainly relies on abstract interpretation and over-approximates …

In the context of deductive program verification, handling floating-point computations is
challenging. The level of proof success and proof automation highly depends on the way the …

Roundoff errors cannot be avoided when implementing numerical programs with finite
precision. The ability to reason about rounding is especially important if one wants to …