From: Mark Hubbart <discord@...>
Date: 2004-05-14T00:52:43+09:00
Subject: Re: Major Addition Bug?


On May 12, 2004, at 11:58 PM, Jeff Mitchell wrote:

> Just a nitpick: this should be
>
> class Float
>    def ==(other)
>       abs(self - other) < 0.000000000001
>    end
> end

yeah, yeah... :) I realized when I read someone else's version of it 
that I had forgotten to take the absolute value. :/

Also, I hadn't thought of something else. Since it's a floating point 
number, you can't have a fixed epsilon for all comparisons. Very large 
numbers would always fail unless exactly equal, and very small numbers 
would always pass, even if very different.
So, epsilon should be generated from one of the floats you are 
comparing. That way, if you are comparing floats that are off in the 
1e200 or 1e-200 range, you will still get things right. Comparing 
(num1-num2).abs to num1*1e-8 will check that they are equal within 8 
significant digits.

   class Float
     def approx_eql?(other, epsilon=1e-8)
       epsilon *= self # fit epsilon to the number
       (self - other).abs < epsilon
     end
   end

This could be extended to allow either an epsilon, or an integer number 
of digits to check.

cheers,
--Mark