Numerical algorithms lie at the heart of many safety-critical aerospace systems. The
complexity and hybrid nature of these systems often requires the use of interactive theorem …

Numerical programs may require a high level of guarantee. This can be achieved by
applying formal methods, such as machine-checked proofs. But these tools handle …

Round-off errors arising from the difference between real numbers and their floating-point
representation cause the control flow of conditional floating-point statements to deviate from …

In this article, we introduce a simple formal semantics for floating-point numbers with errors
which is expressive enough to be formally compared to the other methods. Next, we define …

Ordinary differential equations (ODEs) are used to model the evolution of the state of a
system over time. They are ubiquitous in the physical sciences and are often used in …

We present a case study of a formal verification of a numerical program that computes the
discretization of a simple partial differential equation. Bounding the rounding error was tricky …

We provide concrete evidence that floating-point computations in C programs can be
verified in a homogeneous verification setting based on Coq only, by evaluating the …

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 …

Formal verification of complex algorithms is challenging. Verifying their implementations in
reasonable time is infeasible using current verification tools and usually involves intricate …

On recent architectures, a numerical program may give different answers depending on the
execution hardware and the compilation. Our goal is to formally prove properties about …