Python fails on math

[Ian]

On 22/02/2011 13:20, christian schulze wrote:
> Hey guys,
>
> I just found out, how much Python fails on simple math. I checked a
> simple equation for a friend.
>
> [code]
>>>> from math import e as e
>>>> from math import sqrt as sqrt
>>>> 2*e*sqrt(3) - 2*e == 2*e*(sqrt(3) - 1)
> False
> [/code]
>
> So WTF? The equation is definitive equivalent. (See http://mathbin.net/59158)
>
> PS:
>
> #1:
>>>> 2.0 * e * sqrt(3.0) - 2.0 * e
> 3.9798408154464964
>
> #2:
>>>> 2.0 * e * (sqrt(3.0) -1.0)
> 3.979840815446496
>
> I was wondering what exactly is failing here. The math module? Python,
> or the IEEE specifications?
>
> --
What has failed you is your understanding of what floating point means.  
Both sides of your equation contain e which is an irrational number.

No irrational number and many rational ones cannot be expressed exactly 
in IEEE format. (1/3, 1/7)

All that has happened is that the two sides have come out with very 
slightly different approximations to numbers that they cannot express 
exactly.

Regards

Ian