From: gwtmp01@...
Date: 2005-11-28T08:06:42+09:00
Subject: Re: floating point subtraction question


On Nov 27, 2005, at 5:41 PM, Nicholas Rahn wrote:
> 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.

The short answer is that decimal floating point literals can not
accurately represent the binary floating point values so you get
all sorts of rounding errors.  Take a look at
http://babbage.cs.qc.edu/courses/cs341/IEEE-754.html

In general it is a mistake to use == to compare floating point values  
because
of this mismatch.  An alternate approach is to ask if the difference
between two values is less than some small delta:

instead of	a == b
use		abs(a - b) < delta
for some suitable (small, near zero) value of delta

For all the gory details read "What Every Computer Scientist Should  
Know About Floating-Point"
http://docs.sun.com/source/806-3568/ncg_goldberg.html