This math scares me

[Ken Seehof]

You're not alone, but there is a good explanation for what you see, and it
is not generally considered a bug in python, though some would like to
change python to give more visually correct results.

This is also true of many other programming languages, such as C and C++.
The reason is that the computer stores your number in binary.  Turns out
that 10.55 (or 0.55) does not have an exact representation in binary,
therefore you get a "rounding error".  To give you an idea of what I am
talking about, consider that in decimal, you can't represent 1/3 exactly
(you get 0.33333333...).

Let's take a simpler example:

>>> 0.2
0.20000000000000001

What happened here?  Well 0.2 = 1/5, which works fine in decimal.  When you
convert that to binary, it looks like this:
0.2 (decimal)  =  0.0011001100110011001100110011001100110011001100110011...
(binary).

The reason your desk calculator gets the right result is that it represents
numbers in decimal internally.  If python did the same, it would run
significantly slower than it does because most computers prefer to do math
in binary.  However, switching to decimal floating point is a proposed
change for a future version of python, along with making 1/2 = 0.5 (or some
other equivalent answer (right now, 1 / 2 = 0 (try it) ) ) and other stuff.

Keep in mind that any floating point system will have rounding errors.
Doing math in decimal merely hides the wierd unexpected ones like the one
you found (at the cost of slowing things down).  Some people propose that
python keeps fractional numbers in rational form (i.e. A/B).  This would
completely solve the rounding error problem (for division and
multiplication, that is), but would make python really really really slow.
There are various other compromises but there is unfortunately no good
solution to this dilemma at all.

These numerical issues cause endless debates among python people.  As you
will see, there will probably be a stream of endless innane babble in
response to this message.  I think there's a SIG or a PEP or something
(couldn't find it) where this debate is supposed to be instead of here.

----- Original Message -----
From: "William Park" <parkw at better.net>
To: <costas at springmail.com>
Cc: <python-list at python.org>
Sent: Monday, March 12, 2001 2:03 PM
Subject: Re: This math scares me


> On Mon, Mar 12, 2001 at 09:34:58PM +0000, costas at springmail.com wrote:
> > Ok, I can see maybe division having problems. But why does addition of
> > the two numbers below:
> >
> > 5.01+5.54
> >
> > give me this?
> >
> > 10.550000000000001
>
> It's called 'Round-off error'.
>
> ---William Park, Open Geometry Consulting, Linux/Python, 8 CPUs.
>
> --
> http://mail.python.org/mailman/listinfo/python-list
>