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. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  2. Beliakov, Gleb; Matiyasevich, Yuri: A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic (2016)
  3. Platt, D.J.; Trudgian, T.S.: On the first sign change of $\theta(x) -x$ (2016)
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  7. De Maesschalck, Peter; Popović, Nikola: Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations (2012)
  8. Krämer, Walter: Multiple/arbitrary precision interval computations in C-XSC (2012)
  9. Spandl, Christoph: Computational complexity of iterated maps on the interval (2012)
  10. Graillat, Stef; Jézéquel, Fabienne; Wang, Shiyue; Zhu, Yuxiang: Stochastic arithmetic in multiprecision (2011)
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  12. Krämer, Walter: Verification methods and symbolic computations (2010)
  13. Revol, Nathalie: Standardized interval arithmetic and interval arithmetic used in libraries (2010)
  14. Rouillier, Fabrice: On solving systems of bivariate polynomials (2010)
  15. Lasserre, Jean Bernard; Laurent, Monique; Rostalski, Philipp: Semidefinite characterization and computation of zero-dimensional real radical ideals (2008)
  16. Chabert, Gilles; Jaulin, Luc: Computing the pessimism of inclusion functions (2007)
  17. Gu, Nong; Lazard, Daniel; Rouillier, Fabrice; Xiang, Yong: Using computer algebra to certify the global convergence of a numerical optimization process (2007)
  18. Kuliamin, V.V.: Standardization and testing of implementations of mathematical functions in floating point numbers (2007)
  19. Kreinovich, Vladik; Rump, Siegfried: Towards optimal use of multi-precision arithmetic: a remark (2006)
  20. van der Hoeven, Joris: Effective real numbers in Mmxlib (2006)

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