Motivations for an arbitrary precision interval arithmetic and the mpfi library

Nathalie Revol 1 Fabrice Rouillier 2, 3
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
3 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : MPFI is a library implementing interval arithmetic with arbitrary accuracy. It can be freely downloaded (including source code and documentation). It is written in C and is based on the MPFR library for arbitrary precision floating-point arithmetic, which is in turn built upon the GMP library. MPFR has been chosen because it provides outward rounding, even for the elementary functions, which is mandatory to implement interval arithmetic. An important issue in interval computation is "computing in the large", {\it i.e.} getting tight enclosures for the range of a function over a large interval. However, this issue has no well established answer, and one common way to circumvent the problem consists in bisecting the input interval again and again, until the evaluation of the function upon each sub-part is tight enough. For some problems, such as roots approximations or optimization of a "very flat" function, splitting beyond the limits of usual (single or double) floating-point capacities reveals necessary in order to reach the required accuracy on the function evaluation.
Document type :
Conference papers
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https://hal.inria.fr/inria-00100985
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Submitted on : Tuesday, September 26, 2006 - 2:53:19 PM
Last modification on : Thursday, March 21, 2019 - 1:20:53 PM

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  • HAL Id : inria-00100985, version 1

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Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the mpfi library. SIAM Workshop on Validated Computing 2002, 2002, Toronto, Canada. pp.155-161. ⟨inria-00100985⟩

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