Does Python optimize low-power functions?

[Neil Cerutti]

On 2013-12-06, John Ladasky <john_ladasky at sbcglobal.net> wrote:
> The following two functions return the same result:
>
>     x**2
>     x*x
>
> But they may be computed in different ways.  The first choice
> can accommodate non-integer powers and so it would logically
> proceed by taking a logarithm, multiplying by the power (in
> this case, 2), and then taking the anti-logarithm.  But for a
> trivial value for the power like 2, this is clearly a wasteful
> choice.  Just multiply x by itself, and skip the expensive log
> and anti-log steps.
> 
> My question is, what do Python interpreters do with power
> operators where the power is a small constant, like 2?  Do they
> know to take the shortcut?

It uses a couple of fast algorithms for computing powers. Here's
the excerpt with the comments identifying the algorithms used.
>From longobject.c:

2873 if (Py_SIZE(b) <= FIVEARY_CUTOFF) {
2874         /* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
2875         /* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf    */
...
2886 else {
2887         /* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */

The only outright optimization of the style I think your
describing that I can see is it quickly returns zero when modulus
is one.

I'm not a skilled or experienced CPython source reader, though.

-- 
Neil Cerutti