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 …

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 …

Recent renewed interest in optimizing and analyzing floating-point programs has lead to a
diverse array of new tools for numerical programs. These tools are often complementary …

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 …

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 …

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 …

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 …

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

On recent architectures, a numerical program may give different answers depending on the
execution hardware and the compilation. Our goal is to formally prove properties about …

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 …