[Python-Dev] Re: PEP239 (Rational Numbers) Reference Implementation and new issues

[M.-A. Lemburg]

[discussion on the syntax to create rationals]

Are you sure that you really want a special syntax for this
rather than just a simply constructor like rat(2,3) ?

Just think of how difficult it would be to explain how the
following would work (assuming that you use @ as the magical
operator):

	1 @ 2.3
	1.5 @ 1.3
	1j+3.4 @ 2

Note that intution isn't going to help here because you are
missing a precision indicator. mxNumber has a constructor called
FareyRational() which converts floats to rationals:

    FareyRational(value, maxden)
	 Returns a Rational-object reflecting the given value
	 and using maxden as maximum denominator

Here's the algorithm:

/* Farey Function

    This is a GNU MP implementation of the following function which
    Scott David Daniels posted to the Python Cookbook;
    http://www.activestate.com/ASPN/Python/Cookbook/Recipe/52317 :

     def farey(v, lim):
	'''Named after James Farey, an English surveyor.
	No error checking on args -- lim = max denominator,
	results are (numerator, denominator), (1,0) is infinity
	'''
	if v < 0:
	  n,d = farey(-v, lim)
	  return -n,d
	z = lim-lim   # get 0 of right type for denominator
	lower, upper = (z,z+1), (z+1,z)
	while 1:
	  mediant = (lower[0] + upper[0]), (lower[1]+upper[1])
	  if v * mediant[1] > mediant[0]:
	      if lim < mediant[1]: return upper
	      lower = mediant
	  elif v * mediant[1] == mediant[0]:
	      if lim >= mediant[1]: return mediant
	      if lower[1] < upper[1]: return lower
	      return upper
	  else:
	      if lim < mediant[1]: return lower
	      upper = mediant

    A nice proof of the algorithm can be found at "Cut the Knot":
    http://www.cut-the-knot.com/blue/Farey.html

*/

-- 
Marc-Andre Lemburg
CEO eGenix.com Software GmbH
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