This article presents a multiple-precision binary floating-point library, written in the ISO C
language, and based on the GNU MP library. Its particularity is to extend to arbitrary …

In this note I describe a computational study of the successive maxima of the relative sum-of-
divisors function ρ (n):= σ (n)/n. These maxima occur at superabundant and colossally …

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 …

In this article, we describe a new library for computing guaranteed bounds of the solutions of
Initial Value Problems (IVP). Given an initial value problem and an end point, our library …

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 …

Finite precision computations can severely affect the accuracy of computed solutions. We
present a static analysis, and a prototype implementing this analysis for C codes, for …

Stone Duality (ASD) is a direct axiomatisation of general topology, in contrast to the
traditional and all other contemporary approaches, which rely on a prior notion of discrete …

In this paper we will discuss various aspects of computable/constructive analysis, namely
semantics, proofs and computations. We will present some of the problems and solutions of …

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 …

The hadronic photon structure function F 2 γ has been measured in the Q 2 range from 4 to
30 GeV 2/c 4 and down to x values of order 0.001, using data taken with the DELPHI …