# [Tutor] List comprehension question

Steven D'Aprano steve at pearwood.info
Mon Nov 8 22:41:34 CET 2010

```Alan Gauld wrote:
>
> "Steven D'Aprano" <steve at pearwood.info> wrote
>
>> I'm going to be pedantic here... but to quote the Middleman,
>> specificity is the soul of all good communication.
>
> Be pedantic! :-)
> I really liked the explanation although I already sort of knew most of it.
> But there were a few nuggets in there I'd missed, like range() being
> a type all of its own.

Thank you :)

> But one, slightly off-topic, question:
>
>> def proper_divisors(n):
>>     return sum(x for x in range(1, int(math.sqrt(n))) if n%x == 0)
>>
>
> Why use math.sqrt() instead of just using the ** operator?
>
>     return sum(x for x in range(1, int(n**0.5)) if n%x == 0)
>
> I'd have expected ** to be significantly faster than calling the
> function, and given this is a performance tweak...?

Mostly personal taste, but I would expect math.sqrt() to be more
accurate than a generic exponentiation operator, although in this case
the difference shouldn't matter. If your value for n is so large that
you need to care about the floating point rounding errors in n**0.5,
you're probably using the wrong tool.

As for the speed, sqrt() only gets called once, so the difference
shouldn't matter. But for what it's worth:

[steve at sylar ~]\$ python3 -m timeit -s "import math" "math.sqrt(1234567)"
1000000 loops, best of 3: 0.486 usec per loop
[steve at sylar ~]\$ python3 -m timeit "1234567**0.5"
1000000 loops, best of 3: 0.265 usec per loop

So on my machine, the overhead of calling a function is about 0.2
micro-seconds. Compare that to:

[steve at sylar ~]\$ python3 -m timeit -s "n=1234567" "sum(x for x in
range(1, int(n**0.5)) if n%x == 0)"
1000 loops, best of 3: 515 usec per loop

So changing from math.sqrt(n) to n**0.5 increases the overall speed by
approximately 0.04%. Truly a micro-optimization :)

(I'm deliberately not including the time to import math here. I assume
that the function proper_divisors() will be in a module with other maths
related functions, and therefore you need to import it regardless.)

--
Steven

```