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...

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Vydané v:Mathematics in computer science Ročník 4; číslo 4; s. 539 - 556
Hlavní autori: Mörig, Marc, Rössling, Ivo, Schirra, Stefan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel SP Birkhäuser Verlag Basel 01.12.2010
Predmet:
Computer Science
Mathematics
Mathematics and Statistics
Primary 68W30
Exact geometric computation
Algorithm engineering
Secondary 65D99
Symbolic numeric computation
ISSN:1661-8270, 1661-8289
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Popis
Shrnutí: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