e vs exp()?

[Fernando Pérez]

Buckshot wrote:

> Can anyone here explain why I'm getting different results from
> e**2 and exp(2)?  Which is more accurate?
> 
> Python 2.2 (#1, Mar 27 2002, 14:56:58)
> [GCC 2.95.3 20010315 (release)] on sunos5
> Type "help", "copyright", "credits" or "license" for more information.
>>>> from math import *
>>>> e**2
> 7.3890560989306522
>>>> exp(2)
> 7.3890560989306504

As someone already told you, exp(2) gives a more accurate answer. The reason 
is, I think, the following: e**2 simply squares e, and this amplifies the 
error in the value for e (which is stored at finite precision, as a C double 
inside). OTOH, exp(2) computes e**2 to a given accuracy, so it will not be 
propagating the finite-precision error inherent in the 'e' value. As long as 
the exp() function is correctly implemented in the system's math library, it 
should be more accurate than hand-calculations done with 'e'. In most cases 
the difference shouldn't matter, but if you are doing something very 
sensitive to numerical roundoff or require delicately balancing 
cancellations, you may need to pay attention to this.

Cheers,

f.