On Design and Implementation of a Generic Number Type for Real Algebraic Number Computations Based on Expression Dags

We report on the design and implementation of a number type called Real_algebraic. This number type allows us to compute the sign of arithmetic expressions involving the operations . The sign computation is always correct and, in this sense, not subject to rounding errors. We focus on modularity and...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics in computer science 2010-12, Vol.4 (4), p.539-556
Hauptverfasser: Mörig, Marc, Rössling, Ivo, Schirra, Stefan
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We report on the design and implementation of a number type called Real_algebraic. This number type allows us to compute the sign of arithmetic expressions involving the operations . The sign computation is always correct and, in this sense, not subject to rounding errors. We focus on modularity and use generic programming techniques to make key parts of the implementation exchangeable. Thus, our design allows for easily performing experiments with different implementations or thereby tailoring the number type for specific tasks. For many problems in computational geometry, instantiations of our number type Real_algebraic are a user-friendly alternative for implementing the exact geometric computation paradigm in order to abandon numerical robustness problems.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-011-0086-1