Python can't divide??!?!

[Dan Williams]

Ummmm...

This is weird. Sorry if it's known about (how can it NOT be, I wonder?) but
I haven't seen any reference to it anywhere.

I'm running the latest Python (2.3.3) on Windows XP Pro, i386 architecture.

Fire up python or whatever.

Do this: Result:

3 / 5 0 Fair enough, int / int = int
3 / 5.0 0.5999999999999 9998 eh?
3.0 / 3 0.5999999999999 9998 ummmm...
3.0 / 5.0 0.5999999999999 9998 how did I guess...

That's just an example. Python cannot divide. Period. If you try 1.0 / 3 you
get 0.3333333333333 3331, and from this, the above example, and a few tests,
I speculate that *something* is subtracting 2 from the last digit *after*
the division is done.

Wacky.

Now, is this just me, or can someone else duplicate it? I've tried it on two
computers here, but they're both Win XP. I'm about to test it on Linux but I
figured I'd write this first.

Dan

[Stephen Boulet]

Re: Python can't divide??!?!

Works fine here:
[color=blue][color=green][color=darkred]
>>> a = 3/5
>>> b = 3/5.0
>>> c = 3.0/3
>>> d = 3.0/5.0
>>>
>>> print "%f %f %f %f" % (a,b,c,d)[/color][/color][/color]
0.000000 0.600000 1.000000 0.600000

but
[color=blue][color=green][color=darkred]
>>> print "%.17f %.17f %.17f %.17f" % (a,b,c,d)[/color][/color][/color]
0.0000000000000 0000 0.5999999999999 9998 1.0000000000000 0000
0.5999999999999 9998

;)

Stephen


Dan Williams wrote:
[color=blue]
> Ummmm...
>
> This is weird. Sorry if it's known about (how can it NOT be, I wonder?) but
> I haven't seen any reference to it anywhere.
>
> I'm running the latest Python (2.3.3) on Windows XP Pro, i386 architecture.
>
> Fire up python or whatever.
>
> Do this: Result:
>
> 3 / 5 0 Fair enough, int / int = int
> 3 / 5.0 0.5999999999999 9998 eh?
> 3.0 / 3 0.5999999999999 9998 ummmm...
> 3.0 / 5.0 0.5999999999999 9998 how did I guess...
>
> That's just an example. Python cannot divide. Period. If you try 1.0 / 3 you
> get 0.3333333333333 3331, and from this, the above example, and a few tests,
> I speculate that *something* is subtracting 2 from the last digit *after*
> the division is done.
>
> Wacky.
>
> Now, is this just me, or can someone else duplicate it? I've tried it on two
> computers here, but they're both Win XP. I'm about to test it on Linux but I
> figured I'd write this first.
>
> Dan
>
>
>[/color]

[Dan Bishop]

Re: Python can't divide??!?!

"Dan Williams" <dan@ithium.net > wrote in message news:<mailman.1 252.1076003166. 12720.python-list@python.org >...[color=blue]
> Ummmm...
>
> This is weird. Sorry if it's known about (how can it NOT be, I wonder?) but
> I haven't seen any reference to it anywhere.[/color]

Then you haven't been looking hard enough.
[color=blue]
> I'm running the latest Python (2.3.3) on Windows XP Pro, i386 architecture.
>
> Fire up python or whatever.
>
> Do this: Result:
>
> 3 / 5 0 Fair enough, int / int = int[/color]

This is for bug-compatibility with old versions of Python. It is
strongly recommended that all new Python scripts use "from __future__
import division".
[color=blue]
> 3 / 5.0 0.5999999999999 9998 eh?
> 3.0 / 3 0.5999999999999 9998 ummmm...
> 3.0 / 5.0 0.5999999999999 9998 how did I guess...[/color]

It makes perfect sense when you remember that computers do math in
binary. In binary, 3/5 is equal to 0.1 0011 0011 0011 0011 0011
0011..., which is rounded to (C99 notation) 0x1.33333333333 333333p-1.
The exact decimal equivalent of this is
0.5999999999999 999777955395074 968691915273666 3818359375. In the
default 17 significant digits format, this rounds to
0.5999999999999 9998.
[color=blue]
> That's just an example. Python cannot divide. Period.[/color]

It's off by only 37 parts per quintillion.
[color=blue]
> If you try 1.0 / 3 you get 0.3333333333333 3331,[/color]

More precisely, you get 0x1.55555555555 55p-2, or
0.3333333333333 333148296162562 473909929394721 98486328125.
[color=blue]
> and from this, the above example, and a few tests,
> I speculate that *something* is subtracting 2 from the last digit *after*
> the division is done.[/color]

*Nothing* is subtracting from the last digit because your floating
part hardware has no concept of decimal digits, only bits.
[color=blue]
> Now, is this just me, or can someone else duplicate it?[/color]

Everyone in the world who has binary floating part hardware can
duplicate it, whether they're using Python or not.

[Erik Max Francis]

Re: Python can't divide??!?!

Dan Williams wrote:
[color=blue]
> Fire up python or whatever.
>
> Do this: Result:
>
> 3 / 5 0 Fair enough, int / int = int
> 3 / 5.0 0.5999999999999 9998 eh?
> 3.0 / 3 0.5999999999999 9998 ummmm...
> 3.0 / 5.0 0.5999999999999 9998 how did I guess...
>
> That's just an example. Python cannot divide. Period.[/color]

Neither can C, C++, Java, Perl, or any of the other countless
programming languages which use floating point.

--
__ Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && &tSftDotIotE
\__/ I thought I might never see another Saturday night.
-- Robert S. MacNamara

[Kurt B. Kaiser]

Re: Python can't divide??!?!

"Dan Williams" <dan@ithium.net > writes:
[color=blue]
> Fire up python or whatever.
>
> Do this: Result:
>
> 3 / 5 0 Fair enough, int / int = int
> 3 / 5.0 0.5999999999999 9998 eh?
> 3.0 / 3 0.5999999999999 9998 ummmm...
> 3.0 / 5.0 0.5999999999999 9998 how did I guess...
>[/color]
[color=blue][color=green][color=darkred]
>>> print 3.0 / 5[/color][/color][/color]
0.6[color=blue][color=green][color=darkred]
>>> print (3.0 / 5)[/color][/color][/color]
0.6[color=blue][color=green][color=darkred]
>>> print (3.0 / 5, 3.0 / 5)[/color][/color][/color]
(0.599999999999 99998, 0.5999999999999 9998)[color=blue][color=green][color=darkred]
>>>[/color][/color][/color]

[...]
[color=blue]
> Wacky.[/color]

:-)

--
KBK

[Josiah Carlson]

Re: Python can't divide??!?!

>>Wacky.

Not wacky, there is a difference between str() and repr():
[color=blue][color=green][color=darkred]
>>> str(3.0/5)[/color][/color][/color]
'0.6'[color=blue][color=green][color=darkred]
>>> repr(3.0/5)[/color][/color][/color]
'0.599999999999 99998'


- Josiah

[Ben Finney]

Re: Python can't divide??!?!

On Thu, 5 Feb 2004 17:44:55 -0000, Dan Williams wrote:[color=blue]
> Python cannot divide. Period.[/color]

Your binary computer can't accurately represent decimal fractions.
Python doesn't try to hide this from you.

<http://www.python.org/doc/tut/node15.html>

--
\ "A celibate clergy is an especially good idea, because it tends |
`\ to suppress any hereditary propensity toward fanaticism." -- |
_o__) Carl Sagan |
Ben Finney <http://bignose.squidly .org/>

[John Hunter]

Re: Python can't divide??!?!

>>>>> "Kurt" == Kurt B Kaiser <kbk@shore.ne t> writes:


This prints a float[color=blue][color=green][color=darkred]
>>> print (3.0 / 5)[/color][/color][/color]
0.6

This prints a tuple of floats[color=blue][color=green][color=darkred]
>>> print (3.0 / 5, 3.0 / 5)[/color][/color][/color]
(0.599999999999 99998, 0.5999999999999 9998)

This prints a (length 1) tuple of floats[color=blue][color=green][color=darkred]
>>> print (3.0 / 5, )[/color][/color][/color]
(0.599999999999 99998,)

The thing that may be tripping you up is that (val) is simply the
value, and (val,) is a tuple containing the value as the first
element. As for printing a value versus a tuple of values, that's the
__repr__ versus __str__ distinction previous posters have referred to.

JDH

[Kurt B. Kaiser]

Re: Python can't divide??!?!

John Hunter <jdhunter@ace.b sd.uchicago.edu > writes:
[color=blue]
> The thing that may be tripping you up is that (val) is simply the
> value, and (val,) is a tuple containing the value as the first
> element. As for printing a value versus a tuple of values, that's the
> __repr__ versus __str__ distinction previous posters have referred to.[/color]

:-)

Tim enlightened me on this issue some years ago, when I suggested a
"solution" using sys.displayhook ;

http://www.google.com/groups?q=g:thl2117804141d&dq=&hl=en&lr=&ie=UTF-8&oe=UTF-8&selm=mailman.991854611.2080.python-list%40python.org

Just try explaining this stuff to a 9 year old learning Python! It
tends to break the expository flow....

--
KBK

"Don't sit there with your face all screwed up. Swallow!
Cod liver oil is good for you"

[Axle]

Re: Python can't divide??!?!

Yes, python can divide... use the / operator

Kurt B. Kaiser wrote:
[color=blue]
> John Hunter <jdhunter@ace.b sd.uchicago.edu > writes:
>
>[color=green]
>>The thing that may be tripping you up is that (val) is simply the
>>value, and (val,) is a tuple containing the value as the first
>>element. As for printing a value versus a tuple of values, that's the
>>__repr__ versus __str__ distinction previous posters have referred to.[/color]
>
>
> :-)
>
> Tim enlightened me on this issue some years ago, when I suggested a
> "solution" using sys.displayhook ;
>
> http://www.google.com/groups?q=g:thl...t%40python.org
>
> Just try explaining this stuff to a 9 year old learning Python! It
> tends to break the expository flow....
>[/color]

[Josiah Carlson]

Re: Python can't divide??!?!

Axle wrote:[color=blue]
> Yes, python can divide... use the / operator[/color]

He was referring to the inaccuracy of binary vs. decimal
representations . Most Computer Science students don't learn about it
until sophomore year of college in their computer architectures class.


3.0 / 5.0 -> .6 in decimal.

When we're dealing with floating point arithmetic in Python (or any
other language that uses IEEE 754 double-precision floating point
representations ), 3.0 / 5.0 is internally represented as:
001111111110001 100110011001100 110011001100110 011001100110011 0011

If we then convert that back into decimal, we get .59999999999999 998.

Binary representation thanks to:

http://babbage.cs.qc.edu/courses/cs341/IEEE-754.html

- Josiah