From: William James <w_a_x_man@...>
Date: 2005-11-28T08:42:29+09:00
Subject: Re: floating point subtraction question


John W. Kennedy wrote:
> Nicholas Rahn wrote:
> > Hi,
> >
> > I'm a bit confused with some simple floating point arithmetic:
> >
> > % ruby -e 'puts "#{(1.2 - 1.0) == 0.2}"'
> > false
> >
> > % ruby -e 'puts "#{(1.5 - 1.0) == 0.5}"'
> > true
> >
> > I'm sure there's a perfectly logical reason for this, but i think i've
> > been staring at it for too long to see what it is.
> >
> > Can anyone shed some light on this?
> >
> > Thanks for your help,
> > Nick
> >
> > ps:
> > % ruby -v
> > ruby 1.8.3 (2005-06-23) [i486-linux]
>
> This has nothing to do with Ruby, itself, but is a basic characteristic
> of nearly all languages and nearly all computers.
>
> Remember how you can't make 1/3 a decimal fraction, because it's
> 0.3333333333333 -- carried out to infinity, so that if you add 1/3 + 1/3
> + 1/3, you get 0.9999999 -- carried out to infinity, instead of 1.0?
> Well, computers (almost always) use binary fractions, and you can't make
> 1/10 a binary fraction, because it comes out as 0.000110011001100110011
> -- carried out to infinity, and so you get the same kind of problem.
>
> If you are doing science or engineering, it doesn't matter, because
> things in the real world don't come out as neat decimal fractions,
> anyway. But you do want to avoid checking for equality. Instead of
>
>     x==y
>
> look for
>
>     abs(x-y)<epsilon
>
> where epsilon is some really small number that serves for your purposes
> as "practically equal".
>

> (IBM mainframes have hardware to handle decimal fractions directly, and
> a very few languages -- COBOL, RPG, PL/I, and Ada '95 come to mind --
> have the extra features to make use of it. Some other languages, Java,
> for example, include libraries to help you do the "calculate in cents"
> trick. Ruby, however, does not at present include either facility.)

BASIC on the 8-bit Atari used binary-coded decimal.