Non-integer arithmetic is prone to numerical errors due to the finite representation of
numbers. These errors propagate, possibly non-linearly, throughout the variables of a …

We consider the problem of estimating the numerical accuracy of programs with operations
in fixed-point arithmetic and variables of arbitrary, mixed precision, and possibly non …

Side-channel attacks, which are capable of breaking secrecy via side-channel information,
pose a growing threat to the implementation of cryptographic algorithms. Masking is an …

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 …

We present a new process for the verification of numerical programs with tight functional
specifications that feature exact arithmetic including selected transcendental functions. The …

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 …

Motivated by the practical need for verifying embedded control programs involving linear,
polynomial, and transcendental arithmetics, we demonstrate in this paper a CEGAR …

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 …

Efficient tools for error analysis of programs with floating-point computations are available.
Most of them provide an over-approximation of the floating-point errors. The point is that …

Test instability in a floating-point program occurs when the control flow of the program
diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by …