Alan Gauld wrote:
"Steven D'Aprano" <st...@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:
[st...@sylar ~]$ python3 -m timeit -s "import math" "math.sqrt(1234567)"
1000000 loops, best of 3: 0.486 usec per loop
[st...@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:
[st...@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
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