From: Mark Hubbart <discordantus@...>
Date: 2005-05-06T06:27:31+09:00
Subject: Re: Float to Rational

On 5/5/05, Christoph <chr_mail@gmx.net> wrote:
> Zane Dodson schrieb:
> 
> >Knuth has a discussion of this in `Seminumerical Algorithms, The Art
> >of Computer Programming, vol. 2.'
> >
> >In the third edition, it is in sec. 4.5.3 (pp. 356ff).  See also
> >exercise 4.5.3.2
> >
> >
> Florian's solution is of course nothing but continued fraction
> - without the (relative) error term he could be into a long wait
> calling  #to_r  unless he is very lucky ..

Thanks to those who mentioned the "continued fractions" method. Here's
a new implementation:

----
require 'mathn'

class Numeric
  def inverse
    1/self
  end
end

class Float
  
  def to_r
    n = 1
    n *= 2 until (self*n) % 1 == 0
    (self*n).to_i/n
  end
  
  def round_to_r
    return self.to_i if self % 1 == 0
    n = self
    ops = []
    count = 0
    until ((n%1).round - n%1).abs < 1e-8 || count > 20 ||
          n.abs == 1.0/0.0 || n == 0.0/0.0
      int, dec = n.divmod 1
      ops.concat [[:+, int.to_i], [:inverse]]
      n = 1/dec
      count += 1
    end
    n = n.round
    ops.reverse.inject(n.round){|n, op| n.send(*op)}
  end
end
----

Use Float#to_r for an exact representation of the float value, or
Float#round_to_r for an extremely close representation of it.

cheers,
Mark