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 …

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 …

Reasoning about floating-point is difficult and becomes only more so if there is an interplay
between floating-point and bit-level operations. Even though real-world floating-point …

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 …

Numerical code uses floating-point arithmetic and necessarily suffers from roundoff and
truncation errors. Error analysis is the process to quantify such uncertainty in the solution to …

Floating-point arithmetic is a very efficient solution to perform computations in the real field.
However, it induces rounding errors making results computed in floating-point differ from …

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

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 …

Floating-point arithmetic plays a central role in science, engineering, and finance by
enabling developers to approximate real arithmetic. To address numerical issues in large …