As scientific computation continues to scale, efficient use of floating-point arithmetic
processors is critical. Lower precision allows streaming architectures to perform more …

We define several abstract semantics for the static analysis of finite precision computations,
that bound not only the ranges of values taken by numerical variables of a program, but also …

We present a new numerical abstract domain for static analysis of the errors introduced by
the approximation by floating-point arithmetic of real numbers computation, by abstract …

Astrée was the first static analyzer able to prove automatically the total absence of runtime
errors of actual industrial programs of hundreds of thousand lines. What makes Astrée such …

This paper deals with the digital electrical flight control system of the Airbus airplanes. This
system is built to very stringent dependability requirements both in terms of safety (the …

We present an analysis to automatically determine if a program represents a continuous
function, or equivalently, if infinitesimal changes to its inputs can only cause infinitesimal …

We present a new method for solving the fixed point equations that appear in the static
analysis of programs by abstract interpretation. We introduce and analyze a policy iteration …

Floating-point arithmetic is essential for many embedded and safety-critical systems, such as
in the avionics industry. Inaccuracies in floating-point calculations can cause subtle changes …

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 …

Floating-point computation is ubiquitous in high-performance scientific computing, but
rounding error can compromise the results of extended calculations, especially at large …