# [Numpy-discussion] Re: indexing problem

Gary Ruben gruben at bigpond.net.au
Mon Feb 13 20:50:02 CST 2006

```Hi David,
So, I think what you had done would be OK provided you removed the
x**0.5 case to avoid the problem Tim raised and checked that the
exponent is an integer, not just a scalar.
Does anyone see a problem with this approach.
Gary R.

David M. Cooke wrote:
> Gary Ruben <gruben at bigpond.net.au> writes:
>
>> Tim Hochberg wrote:
>> <snip>
>>> However, I'm not convinced this is a good idea for numpy. This would
>>> introduce a discontinuity in a**b that could cause problems in some
>>> cases. If, for instance, one were running an iterative solver of
>>> some sort (something I've been known to do), and b was a free
>>> variable, it could get stuck at b = 2 since things would go
>>> nonmonotonic there.
>> I don't quite understand the problem here. Tim says Python special
>> cases integer powers but then talks about the problem when b is a
>> floating type. I think special casing x**2 and maybe even x**3 when
>> the power is an integer is still a good idea.
>
> Well, what I had done with Numeric did special case x**0, x**1,
> x**(-1), x**0.5, x**2, x**3, x**4, and x**5, and only when the
> exponent was a scalar (so x**y where y was an array wouldn't be). I
> think this is very useful, as I don't want to microoptimize my code to
> x*x instead of x**2. The reason for just scalar exponents was so
> choosing how to do the power was lifted out of the inner loop. With
> that, x**2 was as fast as x*x.
>

```