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Motivations for an arbitrary precision interval arithmetic and the MPFI library

Nathalie Revol 1 Fabrice Rouillier 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate results, interval computations require small input intervals; this explains why bisection is so often employed in interval algorithms. The MPFI library has been built in order to fulfill this need: indeed, no existing library met the required specifications. The main features of this library are briefly given and a comparison with a fixed-preci- sion interval arithmetic, on a specific problem, is presented: it shows that the overhead due to the multiple precision is completely admissible. Eventually, some applications based on MPFI are given: robotics, isolation of polynomial real roots (by an algorithm combining symbolic and numerical computations) and approximation of real roots with arbitrary accuracy.
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Submitted on : Tuesday, May 23, 2006 - 7:46:05 PM
Last modification on : Saturday, September 11, 2021 - 3:17:51 AM


  • HAL Id : inria-00072090, version 1



Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the MPFI library. [Research Report] RR-4498, LIP RR-2002-27, INRIA, LIP. 2002. ⟨inria-00072090⟩



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