Re: greatest float smaller than 1.0?


#1

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