Open AccessJournal Article
Exact real arithmetic systems: Results of competition
TLDR
A competition between systems for doing exact real number computations was held in September 2000 and the results obtained are presented and a short evaluation of the different approaches used.Abstract:
A competition between systems for doing exact real number computations was held in September 2000. We present the results obtained and give a short evaluation of the different approaches used.read more
Citations
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Journal Article
A survey of Exact arithmetic implementations
Paul Gowland,David Lester +1 more
TL;DR: A survey of practical systems for exact arithmetic can be found in this article, where the authors describe some of the methods used in their implementation, and suggest reasons for the performance differences displayed by the competing systems at this years CCA Exact Arithmetic Competition.
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Arbitrary precision real arithmetic: design and algorithms
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The constructive reals as a Java library
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Effective continued fractions
TL;DR: This work forms the basis of a proof that there is an effective representation of the computable reals as continued fractions and demonstrates that the basic arithmetic operations are computable using this representation.
References
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Book ChapterDOI
The iRRAM: Exact Arithmetic in C++
TL;DR: The iRRAM as mentioned in this paper is a very efficient C++ package for error-free real arithmetic based on the concept of Real-RAM, which can be used for arithmetic over trigonometric functions and linear algebra even with sparse matrices.
Journal ArticleDOI
A New Representation for Exact Real Numbers
Abbas Edalat,Peter John Potts +1 more
TL;DR: It is shown that there is a canonical choice of four sign matrices which are generated by rotation of S1 by π/4, and the ordinary signed digit representation of real numbers in a given base induces a canonicalchoice of digit matrices.
Journal Article
A survey of Exact arithmetic implementations
Paul Gowland,David Lester +1 more
TL;DR: A survey of practical systems for exact arithmetic can be found in this article, where the authors describe some of the methods used in their implementation, and suggest reasons for the performance differences displayed by the competing systems at this years CCA Exact Arithmetic Competition.
Book
Computability and complexity in analysis : 4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000 : selected papers
TL;DR: Computability and complexity in analysis of real numbers are discussed in this paper, where the authors present a survey of real number implementations over p-Adic Fields and define a generic root operation for exact real arithmetic.