Beyond IEEE754 Floating-Point Arithmetic
This works starts with shedding some light on the 2008 version of the IEEE754 Standard for Floating-Point Arithmetic and its realization in the Floating-Point environment offered by current systems. Analyzing the parts of the Standard that are still missing, such as support for heterogeneous operations, it proposes algorithmic solutions to these open issues. The work then extends these considerations to possible future extensions to the Standard. These extensions come in manifold aspects: classical enhancements such as extended precision or higher level operations such as faithfully rounded Euclidian Norms as well as operations that allow the binary and decimal floating-point formats to be mixed.
It then tries to pass from the level of manually written numerical codes to code generation of numerical codes. These meta-arithmetic approaches are studied at the example of mathematical functions such as log, sin, cos or even special functions, defined by differential equations. Code generation is shown to be an effective way of providing a modern floating-point environment.
Finally, this work looks into reliable floating-point algorithms, providing a priori error guarantees on their output. These algorithms are utilized as a convenience for the generation of fixed-point codes for the implementation of Linear Time Invariant Filters.
Defence : 05/22/2019
Jury members :
Sylvie Boldo, Directrice de Recherche INRIA [Rapporteur]
Milos Ercegovac, Distinguished Professor à l'UCLA [Rapporteur]
Philippe Langlois, Professeur à l'Université de Perpignan [Rapporteur]
Jean-Guillaume Dumas, Professeur à l'Université de Grenoble, Examinateur
Stef Graillat, Professeur à Sorbonne Université, Examinateur
Siegfried Rump, Professeur à l'Université de Hamburg