From: "John W. Kennedy" <jwkenne@...>
Date: 2005-11-28T08:17:29+09:00
Subject: Re: floating point subtraction question

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".

If, on the other hand, you are working with money, don't use fractions. 
Calculate in cents (or centimes, or new pence, or whatever), and only 
divide by 100 (or whatever) at the last moment, when you're printing 
your results.

(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.)

-- 
John W. Kennedy
"But now is a new thing which is very old--
that the rich make themselves richer and not poorer,
which is the true Gospel, for the poor's sake."
   -- Charles Williams.  "Judgement at Chelmsford"