Algorithms for summation and dot product of floating-point numbers are presented which are
fast in terms of measured computing time. We show that the computed results are as …

Several formalizations of floating-point arithmetic have been designed for the Coq system, a
generic proof assistant. Their different purposes have favored some specific applications …

In this article, we introduce a simple formal semantics for floating-point numbers with errors
which is expressive enough to be formally compared to the other methods. Next, we define …

Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to
approximate real numbers. Due to its limited range and precision, its use can become quite …

This paper proposes, EFTSanitizer, a fast shadow execution framework for detecting and
debugging numerical errors during late stages of testing especially for long-running …

We introduce a concrete semantics for floating-point operations which describes the
propagation of roundoff errors throughout a calculation. This semantics is used to assert the …

We analyze several classical basic building blocks of double-word arithmetic (frequently
called “double-double arithmetic” in the literature): the addition of a double-word number …

We present algorithms for performing the five elementary arithmetic operations (,,×,, and) in
floating point arithmetic with stochastic rounding, and demonstrate the value of these …

This paper presents a study of some basic blocks needed in the design of floating-point
summation algorithms. In particular, in radix-2 floating-point arithmetic, we show that among …

We consider the computation of the Euclidean (or L2) norm of an n-dimensional vector in
floating-point arithmetic. We review the classical solutions used to avoid spurious overflow …