We present a new tool that generates bounds on the values and the round-off errors of
programs using floating point operations. The tool is based on forward error analysis and …

Gappa is a tool designed to formally verify the correctness of numerical software and
hardware. It uses interval arithmetic and forward error analysis to bound mathematical …

Roundoff errors cannot be avoided when implementing numerical programs with finite
precision. The ability to reason about rounding is especially important if one wants to …

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 …

The most well-known feature of floating-point arithmetic is the limited precision, which
creates round-off errors and inaccuracies. Another important issue is the limited range …

The development of sound and efficient tools that automatically perform floating-point round-
off error analysis is an active area of research with applications to embedded systems and …

Small round-off errors in safety-critical systems can lead to catastrophic consequences. In
this context, determining if the result computed by a floating-point program is accurate …

This thesis develops tight upper and lower bounds on the relative error in various schemes
for performing floating-point arithmetic, proposes axioms for characterizing the significant …

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 …

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 …