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Arbitrary precision real arithmetic: design and proved algorithms

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 real arithmetic with mathematically proved algorithms.
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Submitted on : Tuesday, May 5, 2015 - 11:34:17 AM
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Valérie Ménissier-Morain. Arbitrary precision real arithmetic: design and proved algorithms. Journal of Logic and Algebraic Programming, Elsevier, 2005, 64 (1), pp.13-39. ⟨10.1016/j.jlap.2004.07.003⟩. ⟨hal-01148736⟩



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