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Re: Unexpected results comparing float to Fraction

References <51f68d9c$0$30000$c3e8da3$5496439d@news.astraweb.com> <51F693B4.9000201@mrabarnett.plus.com> <kt6g36$d6s$1@ger.gmane.org>
Date 2013-07-29 14:35 -0600
Subject Re: Unexpected results comparing float to Fraction
From Ian Kelly <ian.g.kelly@gmail.com>
Newsgroups comp.lang.python
Message-ID <mailman.5267.1375130131.3114.python-list@python.org> (permalink)

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On Jul 29, 2013 1:37 PM, "Serhiy Storchaka" <storchaka@gmail.com> wrote:
>
> 29.07.13 19:09, MRAB написав(ла):
>
>> I'm surprised that Fraction(1/3) != Fraction(1, 3); after all, floats
>> are approximate anyway, and the float value 1/3 is more likely to be
>> Fraction(1, 3) than Fraction(6004799503160661, 18014398509481984).
>
>
> >>> def approximate_fraction(f):
>     prev_numer, numer = 0, 1
>     prev_denom, denom = 1, 0
>     r = f
>     while True:
>         i = math.floor(r)
>         prev_numer, numer = numer, i * numer + prev_numer
>         prev_denom, denom = denom, i * denom + prev_denom
>         if i == r or numer / denom == f:
>             break
>         r = 1 / (r - i)
>
>     return Fraction(numer, denom)
>
> >>> approximate_fraction(1/3)
> Fraction(1, 3)
> >>> approximate_fraction(1e-17)
> Fraction(1, 100000000000000000)
> >>> approximate_fraction(math.pi)
> Fraction(245850922, 78256779)
>
> I guess the Fraction constructor is more faster than this function.

You might be able to speed it up a bit with numpy and the observation that
the update is a matrix multiplication. But I don't think that you can get
away from it being an iterative algorithm.

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Thread

Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-07-29 15:43 +0000
  Re: Unexpected results comparing float to Fraction Ian Kelly <ian.g.kelly@gmail.com> - 2013-07-29 09:50 -0600
  Re: Unexpected results comparing float to Fraction MRAB <python@mrabarnett.plus.com> - 2013-07-29 17:09 +0100
  Re: Unexpected results comparing float to Fraction Chris Angelico <rosuav@gmail.com> - 2013-07-29 17:20 +0100
    Re: Unexpected results comparing float to Fraction Rotwang <sg552@hotmail.co.uk> - 2013-07-29 19:20 +0100
    Re: Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-07-29 19:32 +0000
  Re: Unexpected results comparing float to Fraction MRAB <python@mrabarnett.plus.com> - 2013-07-29 17:48 +0100
    Re: Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-07-29 17:27 +0000
  Re: Unexpected results comparing float to Fraction Ian Kelly <ian.g.kelly@gmail.com> - 2013-07-29 10:40 -0600
    Re: Unexpected results comparing float to Fraction Rotwang <sg552@hotmail.co.uk> - 2013-07-29 19:16 +0100
      Re: Unexpected results comparing float to Fraction Ian Kelly <ian.g.kelly@gmail.com> - 2013-07-29 13:33 -0600
  Re: Unexpected results comparing float to Fraction MRAB <python@mrabarnett.plus.com> - 2013-07-29 18:04 +0100
    Re: Unexpected results comparing float to Fraction Grant Edwards <invalid@invalid.invalid> - 2013-07-29 18:46 +0000
    Re: Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-07-29 20:19 +0000
  Re: Unexpected results comparing float to Fraction Terry Reedy <tjreedy@udel.edu> - 2013-07-29 13:08 -0400
    Re: Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-07-29 17:29 +0000
      Re: Unexpected results comparing float to Fraction Terry Reedy <tjreedy@udel.edu> - 2013-07-29 16:48 -0400
  Re: Unexpected results comparing float to Fraction Chris Angelico <rosuav@gmail.com> - 2013-07-29 18:14 +0100
  Re: Unexpected results comparing float to Fraction Ian Kelly <ian.g.kelly@gmail.com> - 2013-07-29 11:35 -0600
  Re: Unexpected results comparing float to Fraction Serhiy Storchaka <storchaka@gmail.com> - 2013-07-29 22:34 +0300
  Re: Unexpected results comparing float to Fraction Ian Kelly <ian.g.kelly@gmail.com> - 2013-07-29 14:35 -0600
  Unexpected results comparing float to Fraction Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2013-07-30 14:32 +0100
  Re: Unexpected results comparing float to Fraction Tony the Tiger <tony@tiger.invalid> - 2013-07-31 15:23 -0500
    Re: Unexpected results comparing float to Fraction Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-08-01 06:20 +0000
      Re: Unexpected results comparing float to Fraction Chris Angelico <rosuav@gmail.com> - 2013-08-01 07:32 +0100
      Re: Unexpected results comparing float to Fraction Oscar Benjamin <oscar.j.benjamin@gmail.com> - 2013-08-01 10:44 +0100
      Re: Unexpected results comparing float to Fraction Chris Angelico <rosuav@gmail.com> - 2013-08-01 10:48 +0100

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