How safe is a set of floats?

[Dave Borne]

On 4 May 2007 07:21:49 -0700, Thomas Nelson <thn at mail.utexas.edu> wrote:
> I want to generate all the fractions between 1 and limit (with
> limit>1) in an orderly fashion, without duplicates.

Might I suggest the Stern-Brocot tree
(http://en.wikipedia.org/wiki/Stern-Brocot_tree)
It will eliminate the need for sets as the algorithm gurantees: "Every
positive rational number can be found in this tree exactly once and in
lowest terms". The order will be different than your algorithm,
though.

#An overly simplified fraction class for this example:
class Fraction:
  def __init__ (self, num, den):
    self.num = num
    self.den = den
  def __repr__ (self):
      return '%(num)d/%(den)d' % self.__dict__

def all_ratios(limit):
    seq = [Fraction(1,1), Fraction(limit,1)]
    while True:
        newseq = seq[:1]
        pairs = [seq[x:x+2] for x in range(len(seq)-1)]
        for pair in pairs:
            #find the mediant value between each pair in the series
            newval = Fraction(pair[0].num+pair[1].num, pair[0].den+pair[1].den)
            yield newval
            newseq.append(newval)
            newseq.append(pair[1])
        seq = newseq


-Dave