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Fast multiprecision evaluation of series of rational numbers

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Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O((log N)2 M(N)), where M(N) is the time needed to multiply two N-bit numbers. Applications include fast algorithms for elementary functions, π, hypergeometric functions at rational points, ζ(3), Euler's, Catalan's and Apéry's constant. The algorithms are suitable for parallel computation.

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Author information

Authors and Affiliations

  1. ILOG, 9 rue de Verdun, F - 94253, Gentilly Cedex

    Bruno Haible

  2. Laboratoire A2X, 351 cours de la Libération, F - 33 405, Talence Cedex

    Thomas Papanikolaou

Authors
  1. Bruno Haible
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  2. Thomas Papanikolaou
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Haible, B., Papanikolaou, T. (1998). Fast multiprecision evaluation of series of rational numbers. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054873

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  • DOI: https://doi.org/10.1007/BFb0054873

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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