From: Florian Gross <flgr@...>
Date: 2004-12-01T04:07:46+09:00
Subject: Re: [OFF] Python 2.4 released

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Austin Ziegler wrote:

> I think that BigDecimal handles this just fine. Note as well that
> with the Rational class (require 'rational'), you get support for
> real rational numbers. If you add 'mathn', you get full support
> including with division, etc.
> 
>   require 'rational'
>   Rational.reduce(22, 7)    # => Rational(22, 7)
> 
>   require 'mathn'
>   "%0.9f" % [ 22 / 7 ]      # => "3.142857143"
>   (22 / 7).class            # => Rational
> 
> BigDecimal works with Numerics, BigIntegers, and Floats, I think.

It's impressive how much you can do with Standard Ruby. Add some glue 
(see attachment) to it and you can do things like this one and get exact 
results:

(1 .. 100).inject(0) { |state, item| state + 1 / item }.to_s(50)
# => "5.18737751763962026080511767565825315790897212670845"

Where 50 is the number of floating point digits. Increase it and you get 
more and more detail. It's wonderful how simple things can be with Ruby.

It all kind of makes me wonder if Rationals could be added with a 
different notation to Ruby -- maybe 0.5R + 0.4R. You would always need 
to specify the precision on output, but I think that is okay.


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require 'mathn'
require 'bigdecimal'
require 'bigdecimal/util'

class Rational
  alias :old_to_s :to_s

  def to_s(precision = nil)
    if precision then
      if precision == 0 then
        self.to_d(1).to_s("F").to_i.to_s
      else
        self.to_d(precision + 1).to_s("F")
      end
    else
      old_to_s
    end
  end
end

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