Team : PEQUAN
Departure date : 12/31/2015
Supervision : Jean-Claude BAJARD Co-supervision : LAUTER Christoph
Toward a Modern Floating-Point Environment
This work investigates two ways of enlarging the current floating-point environment:
support of several implementation versions for each mathematical function (elementary such as exp or log and special such as erf or Γ);
provide IEEE754 operations that mix the inputs and the output of different radices.
As the number of various implementations for each mathematical function is large, this work is focused on code generation. We support black-box functions, so user-specified parametrized functions. This work contains a novel algorithm for domain splitting and an approach to replace branching on reconstruction by a polynomial. Since the revision of the IEEE754 Standard in 2008 it is possible to mix numbers of different precisions in one operation. However, there is no mechanism that allows users to mix numbers of different radices in one operation. This research starts an examination of mixed-radix arithmetic with the worst cases search for FMA. A novel algorithm to convert a decimal character sequence of arbitrary length to a binary floating-point number is presented. It is independent of currently-set rounding mode and produces correctly-rounded results.
Defence : 12/11/2015 - 14h - Site Jussieu 25-26/105 Jury members : Jean-Claude BAJARD, LIP6, UPMC
Sylvie BOLDO, INRIA Saclay [Rapporteur]
Philippe LANGLOIS, DALI. Université de Perpignan Via Domitia [Rapporteur]
Jean-Marie CHESNEAUX, Polytech'Paris-UPMC
Laurent-Stéphane DIDIER, Université de Toulon
Florent de DINECHIN, INSA Lyon
Christoph LAUTER, LIP6, UPMC
Olga A. Kupriianova, Ch. Lauter : “Metalibm: A Mathematical Functions Code Generator”, 4th International Congress on Mathematical Software (ICMS 2004), vol. 8592, Lecture Notes in Computer Science, Seoul, South Korea, pp. 713-717, (Springer), (ISBN: 978-3-662-44198-5) (2014)