Fast and correctly rounded logarithms in double-precision
LIP, projet Arénaire, École normale
supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07,
France; email@example.com; firstname.lastname@example.org; Jean-Michel.Muller@ens-lyon.fr
This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best current mathematical libraries, while trying to minimize the proof work. The implementation of the natural logarithm is detailed to illustrate these questions.
Mathematics Subject Classification: 26-04 / 65D15 / 65Y99
Key words: Floating-point / elementary functions / logarithm / correct rounding.
© EDP Sciences, 2007