4 hundred quadrillonth?

[Gary Herron]

R. David Murray wrote:
> 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
>   

Which won't change the fact that 0.8 and lots of other favorite floats 
are still not representable exactly, but it will hide this fact from 
most newbies.  One of the nicer results of this will be that these 
(almost) weekly questions and discussions will be come a thing of the 
past. 

With a sigh of relief,
Gary Herron