From: Nuralanur@...
Date: 2006-05-18T07:11:16+09:00
Subject: Re: greatest float smaller than 1.0?

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If you look into some numerics book , like the one by Stoer and  Burlisch,
they introduce a convention of an epsilon as the smallest positive  number
that a computer can store.
This is of course machine/implementation dependent. I have tried to  find
whether there is a common Ruby definition - but I didn't find  anything,
maybe because Ruby introduces BigFloats along the way automatically.
In any case, this epsilon will be a power of 2.
On my machine, Float::EPSILON is 2**(-52). 
 
(Just type in
 
Float::EPSILON 
 
at irb).
 
Your computer can only represent integer multiples of that number as
floats, so there are all sorts of rounding errors  in  arithmetic - see Stoer 
and Burlisch
or _http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.html_ 
(http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.html)  .
 
Best regards,
 
Axel 

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