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 …

Programs with floating-point computations are often derived from mathematical models or
designed with the semantics of the real numbers in mind. However, for a given input, the …

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 …

Floating-point computations are quickly finding their way in the design of safety-and mission-
critical systems, despite the fact that designing floating-point algorithms is significantly more …

Testing integer software with symbolic execution is wellestablished but floating-point
remains a specialty feature. Modern symbolic floating-point tactics include concretization …

In floating-point programs, guard instability occurs when the control flow of a conditional
statement diverges from its ideal execution under real arithmetic. This phenomenon is …

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 …

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 …

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 …

Tools that automatically prove the absence or detect the presence of large floating-point
roundoff errors or the special values NaN and Infinity greatly help developers to reason …