4 hundred quadrillonth?

[R. David Murray]

Gary Herron <gherron at islandtraining.com> wrote:
> MRAB wrote:
> > Grant Edwards wrote:
> >> On 2009-05-21, Christian Heimes <lists at cheimes.de> wrote:
> >>> seanm.py at gmail.com schrieb:
> >>>> The explaination in my introductory Python book is not very
> >>>> satisfying, and I am hoping someone can explain the following to me:
> >>>>
> >>>>>>> 4 / 5.0
> >>>> 0.80000000000000004
> >>>>
> >>>> 4 / 5.0 is 0.8. No more, no less. So what's up with that 4 at the end.
> >>>> It bothers me.
> >>> Welcome to IEEE 754 floating point land! :)
> >>
> >> Floating point is sort of like quantum physics: the closer you
> >> look, the messier it gets.
> 
> +1 as QOTW
> 
> And just to add one bit of clarity:  This problem has nothing to do with 
> the OP's division of 4 by 5.0, but rather that the value of 0.8 itself 
> cannot be represented exactly in IEEE 754.  Just try
> 
>  >>> print repr(0.8)  # No division needed
> '0.80000000000000004'

Python 3.1b1+ (py3k:72432, May  7 2009, 13:51:24) 
[GCC 4.1.2 (Gentoo 4.1.2)] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> 4 / 5.0
0.8
>>> print(repr(0.8))
0.8

In py3k Eric Smith and Mark Dickinson have implemented Gay's floating
point algorithm for Python so that the shortest repr that will round
trip correctly is what is used as the floating point repr....

--David