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LIP6 2003/003

  • Reports
    Arithmétique réelle en précision arbitraire: conception et algorithmes
  • V. Ménissier-Morain
  • 67 pages - 05/23/2003- document en - http://www.lip6.fr/lip6/reports/2003/lip6.2003.003.pdf - 632 Ko
  • Contact : Valerie.Menissier-Morain (at) nulllip6.fr
  • Ancien Thème : CALFOR
  • We describe here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation.
    A real number is represented as a sequence of finite $B$-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the application of this function to its arguments, according to the sequences representing these arguments. For each algorithm we prove that the resulting sequence is a valid representation of the exact real result.
    This arithmetic is the first abritrary precision real arithmetic with mathematically proved algorithms.
  • Keywords : Arithmetic, Arbitrary precision, Computable real numbers, Proved arithmetic
  • Publisher : David.Massot (at) nulllip6.fr
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