# Arbitrary precision real arithmetic: design and algorithms

1 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We describe here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation. A real number is represented as a sequence of finite $B$-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the application of this function to its arguments, according to the sequences representing these arguments. For each algorithm we prove that the resulting sequence is a valid representation of the exact real result. This arithmetic is the first abritrary precision real arithmetic with mathematically proved algorithms.
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https://hal.archives-ouvertes.fr/hal-02545650
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Submitted on : Friday, April 17, 2020 - 11:44:39 AM
Last modification on : Sunday, June 26, 2022 - 9:41:12 AM

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lip6.2003.003.pdf
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• HAL Id : hal-02545650, version 1

### Citation

Valérie Ménissier-Morain. Arbitrary precision real arithmetic: design and algorithms. [Research Report] lip6.2003.003, LIP6. 2003. ⟨hal-02545650⟩

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