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LEXICOGRAPHIC BINARY REPRESENTATION OF THE RATIONALS

 
 
don.lotto@paradise.net.nz
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      02-15-2005
------
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)

 
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