From: Axel Etzold <AEtzold@...>
Date: 2007-07-17T22:02:13+09:00
Subject: Re: Force calculation result to BigDecimal

Dear Robert,

> Indeed!  I'd rather not use Float at all in this project as it's 
> financial math and float quirks will cause me problems.  I'd be prepared 
> to take the performance hit and just turn off Float if I could...

you could use a "continued fractions" approximation

http://mathworld.wolfram.com/ContinuedFraction.html

to your Float number and then work with fractions without
any further loss in accuracy. Continued fractions are in a sense the
best possible approximations to irrational numbers 
(and of course to rational numbers, the latter being 
fractions themselves).

Once you have a fraction (use the code below to get it
from a continued fraction), you can calculate with it in Ruby
using Rational:

require "rational"
a=Rational(1,2)
b=Rational(3,4)
p a+b  # => Rational (5,4) , as 5/4 == 1/2+3/4
p (a+b).to_f  # => 1.25 

Below is some code to give you the continued fraction representation
(4) in the webpage cited above.

From the continued fraction representation, you can obtain the
partial quotients mentioned in (11) of the cited webpage  by the method cont_fract_to_fract below.


Best regards,

Axel 


----------------
class Float
	def cont_fract_appr(*prec)
		a=[self.floor]
		t=[self-self.floor]
		res=[]
		if prec==[]
			prec=10**-8
		else
			prec=prec[0]
		end
		k=1
		rem=t[-1]
		while rem.abs>prec
			r_new=1/t[-1]
			if (r_new+prec).floor>r_new.floor
				r_new=r_new+prec
			end
			a[k]=r_new.floor
			t[k]=r_new-r_new.floor
			k=k+1
			p,q=(a.cont_fract_to_fract)
			rem=(self-p[-1].to_f/q[-1].to_f).abs
		end
		return a
	end
end

class Array
       def cont_fract_to_fract
               # produce the partial fractions (see eq. 11 of webpage)
		p=[0,1]
		q=[1,0]
		for n in 2..self.length+1
			p<<self[n-2]*p[-1]+p[-2]
			q<<self[n-2]*q[-1]+q[-2]
		end
		return p,q
	end
end
# usage example:


f=Math::PI
r=f.cont_fract_appr
p 'the continued fraction approximation (to precision 10**-8 is)'
p r

-- 
Psssst! Schon vom neuen GMX MultiMessenger geh�rt?
Der kanns mit allen: http://www.gmx.net/de/go/multimessenger