The Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library)

We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to a constant factor that depends on the implementation) can be obtain.Comment: Conference website at http://cca-net.de/rnc6

Worst Cases for Correct Rounding of the Elementary Functions in Double Precision

We give here the results of a four-year search for the worst cases for correct rounding of the major elementary functions in double precision. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow to easily test libraries that are claimed to provide correctly rounded functions.Nous donnons dans ce rapport les résultats de quatre ans de recherche des pires cas pour l’arrondi correct des principales fonctions élémentaires en double précision. Ces résultats permettent de construire des programmes raisonnablement rapides calculant ces fonctions avec arrondi correct – au moins dans un domaine donné – pour chacun des quatre modes d’arrondi spécifiés par la norme IEEE-754. Ils permettent également de tester des bibliothèques censées fournir l’arrondi correct de ces fonction

Combining rule- and SMT-based reasoning for verifying floating-point Java programs in KeY

Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for floating-point reasoning. This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and ‘Not a Number’ (NaN). In this article, we present the first floating-point support in a deductive verification tool for the Java programming language. Our support in the KeY verifier handles floating-point arithmetics, transcendental functions, and potentially rounding-type casts. We achieve this with a combination of delegation to external SMT solvers on the one hand, and KeY-internal, rule-based reasoning on the other hand, exploiting the complementary strengths of both worlds. We evaluate this integration on new benchmarks and show that this approach is powerful enough to prove the absence of floating-point special values—often a prerequisite for correct programs—as well as functional properties, for realistic benchmarks

Creating a Repository of Economic Models for Education and Research Purposes

The Financial University under the Government of the Russian Federation has expressed interest in developing an educational tool to help students and researchers access economic models. To reach this goal, we conducted extensive research on a variety of models, administered a survey to see potential interest in an economic repository and its components, coded results into a repository, and developed a Wiki to foster educational applications of a repository. As a result, we compiled a version of a repository which could serve as a framework for future development of educational and research applications

New Results on the Distance Between a Segment and Z². Application to the Exact Rounding

This paper presents extensions to Lefèvre's algorithm that computes a lower bound on the distance between a segment and a regular grid Z². This algorithm and, in particular, the extensions are useful in the search for worst cases for the exact rounding of unary elementary functions or base-conversion functions. The proof that is presented here is simpler and less technical than the original proof. This paper also gives benchmark results with various optimization parameters, explanations of these results, and an application to base conversion