MELQUIOND , Guillaume

We propose the addition of new functions to the C++0x standard library that provide floating-point operations (+, -, *, /, sqrt and fma) as well as conversion functions with directed rounding. This set of functions is necessary to provide efficient support for interval arithmetic and related computations, and they directly map to IEEE-754...

Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study...

Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study...

The verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of traditional tools. In fact, the inherent difficulty of computing such bounds often...

We present the design of the Boost interval arithmetic library, a C++ library designed to efficiently handle mathematical intervals in a generic way. Interval computations are an essential tool for reliable computing. Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-and-bound...

We propose a design for multi-valued logic, for integration into the C++ standard. The main motivation for this class comes from interval arithmetic, where it can be conveniently used as return type of comparison operators. It also has many other potential applications.

We report on the design of the Boost interval arithmetic library, a C++ library designed to efficiently handle mathematical intervals in a generic way. The design of the library is unique in that it uses policies to specify the variable behaviors: rounding, checking, comparisons. As a result, with the proper policies, our interval library is...

Interval arithmetic is a basic tool for certified mathematical computations, it is presented in many references. We describe here the formal proposal to include interval arithmetic in the C++ standard library.

Double rounding is a phenomenon that may occur when different floating- point precisions are available on the same system. Although double rounding is, in general, innocuous, it may change the behavior of some useful small floating-point algorithms. We analyze the potential influence of double rounding on the Fast2Sum and 2Sum algorithms, on...