Tools for the Design of Reliable and Efficient Functions Evaluation Libraries. (Outils pour la conception de bibliothèques de calcul de fonctions efficaces et fiables)

The design of function evaluation libraries is a complex task that requires a great care and dedication, especially when one wants to satisfy high standards of reliability and performance. In actual practice, it cannot be correctly performed, as a routine operation, without tools that not only help the designer to find his way in a complex and extended solution space but also to guarantee that his solutions are correct and (almost) optimal. As of the present state of the art, one has to think in terms of “toolbox” from which he can smartly mix-and-match the utensils that fit better his goals rather than expect to have at hand a solve-all automatic device. The work presented here is dedicated to the design and implementation of such tools in two realms: ∙ the consolidation of Ziv’s 1 rounding test that is used, in a more or less empirical way, for the implementation of functions approximation; ∙ the development of an implementation of the SLZ-algorithm2 in order to solve the Table Maker Dilemma for the function with quad-precision floating point (IEEE-754 Binary128 format) arguments and images. 1Named after Abraham Ziv. 2Named after Vincent Lefèvre, Damien Stehlé and Paul Zimmermann.