Motivations for an arbitrary precision interval arithmetic and the MPFI library. 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-precision interval arithmetic, on a specific problem, is presented. It shows that the overhead due to the multiple precision is completely acceptable. 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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  1. Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong: A rigorous computational approach to linear response (2018)
  2. Cable, Jacob; Süß, Hendrik: On the classification of Kähler-Ricci solitons on Gorenstein del Pezzo surfaces (2018)
  3. Caluza Machado, Fabrício; de Oliveira Filho, Fernando Mário: Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry (2018)
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  16. Spandl, Christoph: Computational complexity of iterated maps on the interval (2012)
  17. Graillat, Stef; Jézéquel, Fabienne; Wang, Shiyue; Zhu, Yuxiang: Stochastic arithmetic in multiprecision (2011)
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  20. Revol, Nathalie: Standardized interval arithmetic and interval arithmetic used in libraries (2010)

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