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(slib.info)Rationalize

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Rationalize
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  `(require 'rationalize)'

  The procedure "rationalize" is interesting because most programming
languages do not provide anything analogous to it.  Thanks to Alan
Bawden for contributing this algorithm.

 - Function: rationalize x y
     Computes the correct result for exact arguments (provided the
     implementation supports exact rational numbers of unlimited
     precision); and produces a reasonable answer for inexact arguments
     when inexact arithmetic is implemented using floating-point.

  `Rationalize' has limited use in implementations lacking exact
(non-integer) rational numbers.  The following procedures return a list
of the numerator and denominator.

 - Function: find-ratio x y
     `find-ratio' returns the list of the _simplest_ numerator and
     denominator whose quotient differs from X by no more than Y.

     (find-ratio 3/97 .0001)             => (3 97)
     (find-ratio 3/97 .001)              => (1 32)

 - Function: find-ratio-between x y
     `find-ratio-between' returns the list of the _simplest_ numerator
     and denominator between X and Y.

     (find-ratio-between 2/7 3/5)        => (1 2)
     (find-ratio-between -3/5 -2/7)      => (-1 2)