Current critical systems often use a lot of floating-point computations, and thus the testing or
static analysis of programs containing floating-point operators has become a priority …

The manipulation of real numbers by computers is approximated by floatingpoint arithmetic,
which uses a finite representation of numbers. This implies that a (small in general) rounding …

Programs using floating-point arithmetic are prone to accuracy problems caused by
rounding and catastrophic cancellation. These phenomena provoke bugs that are …

This paper tackles the important, difficult problem of detecting program inputs that trigger
large floating-point errors in numerical code. It introduces a novel, principled dynamic …

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 …

Given the variety of numerical errors that can occur, floating-point programs are difficult to
write, test and debug. One common practice employed by developers without an advanced …

We introduce FPBench, a standard benchmark format for validation and optimization of
numerical accuracy in floating-point computations. FPBench is a first step toward addressing …

Formal verification of numerical programs is notoriously difficult. On the one hand, there exist
automatic tools specialized in floating-point arithmetic, such as Gappa, but they target very …

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 …

High confidence in floating-point programs requires proving numerical properties of final
and intermediate values. One may need to guarantee that a value stays within some range …