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. Saouter, Yannick: New results for witnesses of Robin’s criterion (2022)
  2. Rohou, Simon; Jaulin, Luc: Exact bounded-error continuous-time linear state estimator (2021)
  3. Bouzidi, Yacine; Rouillier, Fabrice: Symbolic methods for solving algebraic systems of equations and applications for testing the structural stability (2020)
  4. Galatolo, Stefano; Monge, Maurizio; Nisoli, Isaia: Existence of noise induced order, a computer aided proof (2020)
  5. Bouzidi, Yacine; Quadrat, Alban; Rouillier, Fabrice: Certified non-conservative tests for the structural stability of discrete multidimensional systems (2019)
  6. Gómez-Serrano, Javier: Computer-assisted proofs in PDE: a survey (2019)
  7. Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong: A rigorous computational approach to linear response (2018)
  8. Cable, Jacob; Süß, Hendrik: On the classification of Kähler-Ricci solitons on Gorenstein del Pezzo surfaces (2018)
  9. Caluza Machado, Fabrício; de Oliveira Filho, Fernando Mário: Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry (2018)
  10. Figueras, Jordi-Lluís; Haro, Alex; Luque, Alejandro: On the sharpness of the Rüssmann estimates (2018)
  11. Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge: Handbook of floating-point arithmetic (2018)
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  13. Dostert, Maria; Guzmán, Cristóbal; de Oliveira Filho, Fernando Mário; Vallentin, Frank: New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry (2017)
  14. Figueras, J.-Ll.; Haro, A.; Luque, A.: Rigorous computer-assisted application of KAM theory: a modern approach (2017)
  15. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  16. Beliakov, Gleb; Matiyasevich, Yuri: A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic (2016)
  17. Platt, D. J.; Trudgian, T. S.: On the first sign change of (\theta(x) -x) (2016)
  18. Rusu, David; Santoprete, Manuele: Bifurcations of central configurations in the four-body problem with some equal masses (2016)
  19. Platt, David J.: Computing (\pi(x)) analytically (2015)
  20. Platt, D. J.; Trudgian, T. S.: Linnik’s approximation to Goldbach’s conjecture, and other problems (2015)

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