Fast multiprecision evaluation of series of rational numbers

  • Bruno Haible
  • Thomas Papanikolaou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)

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)2M(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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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Bruno Haible
    • 1
  • Thomas Papanikolaou
    • 2
  1. 1.ILOGGentilly Cedex
  2. 2.Laboratoire A2XTalence Cedex

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