----- Original Message -----
From: "Devon McCormick" <[EMAIL PROTECTED]>
To: "Programming forum" <[email protected]>
Sent: Thursday, February 07, 2008 6:26 PM
Subject: Re: [Jprogramming] Algorithm to represent floating
pointnumbersasfractions
Interestingly, the English entry for this (continued fractions) on
Wikipedia
(http://en.wikipedia.org/wiki/Continued_fractions) mentions "The
denominator
is usually a power of two on modern computers, and a power of ten on
electronic calculators, so a variant of Euclid's GCD algorithm can be used
to give exact results." (referring to
http://en.wikipedia.org/wiki/Euclidean_algorithm)
This ties in with Roger's use of GCD in his solution. The explicit
algorithm these pages give for computing continued
fractions looks potentially expensive as it relies on repeated inversion.
I
would think Roger's J version would be simpler to code in C if you have a
GCD routine already.
Playing around with continued fractions, I noticed a few interesting
things.
First of all, I defined
contfrac=: 13 : '(+`%)/1,44$y'"1 NB. Arbitrary 44 as this seems to
give
about 16 digits precision
but it displays as
([: (+`%`:3) 1 , 44 $ ])"1
Why is my "/" replaced by "`:3"? It seems to work as expected.
Anyway, trying this for a few sets of values revealed that very simple
inputs give interesting results:
contfrac 1 1
1.618034 NB. Phi (the golden ratio)
contfrac 1 2
1.4142136 NB. %:2
contfrac 2 2
1.7320508 NB. %:3
Yes, I have programmed long ago a GCD routine for C. It uses Euclid's
algorithm, but it is limited to integer values.
Anyway, from the point of view of efficiency, take into consideration that a
GCD routine needs also repeated division or modulus operations.
Best regards.
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