LEXICOGRAPHIC BINARY REPRESENTATION OF THE RATIONALS

Discussion in 'NZ Computing' started by don.lotto@paradise.net.nz, Feb 15, 2005.

  1. Guest

    ------
    i am looking for my article

    beeblet newsletter of bbc/acorn computer user group
    october OCT 1987--------
    which may predate this research

    donald s mcdonald-----
    continued fractions a code for hashing your PIN (Numbers.)

    10-millionth rational in mcdonald scheme. sci.math
    don.lotto nz
    15.2.05

    -----------------------------------------­-----
    forward------------
    89-CSE-16.
    ($1.75)


    LCF: A LEXICOGRAPHIC BINARY REPRESENTATION OF THE RATIONALS
    Peter Kornerup David W. Matula*
    Odense University Southern Methodist University
    April 1989


    ~~~~~A new binary representation of the rationals derived from
    their
    continued fraction expansions is described and analysed. The
    concepts
    "adjacency", "mediant" and "convergent" (best rational
    approximation) from
    the literature on Farey fractions and continued fractions are
    suitably
    extended to provide a foundation for this new binary representation
    system.
    Worst case representation-induced precision loss for any real
    number by a
    fixed length representable number of the system is shown to be at most
    19% of
    bit word length, with no precision loss whatsoever induced
    in the
    representation of any reasonably sized rational number. The
    representation
    is proposed as host for a computer arithmetic synergistically
    supporting
    exact rational and approximate real computation.


    *~This research was partially supported by the National Science
    Foundation
    ~~under grant DCR-8315289.
    ------------------------------------------------------------­-----------------

    89-CSE-17.
    ($1.00)
     
    , Feb 15, 2005
    #1
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