On 11/21/2014 03:15 AM, Stephen Tucker wrote:
On Thu, Nov 20, 2014 at 6:00 PM, Serhiy Storchaka <storch...@gmail.com>
wrote:
On 01.11.14 03:29, Steven D'Aprano wrote:
There is an algorithm for calculating the integer square root of any
positive integer using only integer operations:
Here is my optimized implementation inspired by Christian's ideas.
....
def isqrt(n):
if n < 0:
raise ValueError
if n == 0:
return 0
if n <= C1:
return int(math.sqrt(n))
if n <= C2:
x = int(math.sqrt(n))
else:
b = (n.bit_length() - C3) // 2
x = int(math.sqrt(n >> (2 * b))) << b
y = (x + n // x) // 2
if y == x:
return x
while True:
x = y
y = (x + n // x) // 2
if y >= x:
return x
> Serhiy,
>
> This looks very good indeed. As a matter of interest, is there any
> particular reason you have used 2*b instead of b+b? Might b+b be faster
> than b*2?
>
> Also, in various lines, you use //2. Would >>1 be quicker? On reflection,
> perhaps you have had to use //2 because >>1 cannot be used in those
> situations.
>
> Stephen Tucker.
>
(Please don't top-post here. I moved your remarks after the code you're
referencing, so that others may see it in the preferred order)
It's been probably two decades since I've been in a programming
situation where that kind of difference mattered. In Python in
particular, the actual arithmetic or bit shifting is probably only one
part in a hundred, and in modern processors all these operations tend to
be very close in timing.
You're welcome to use the timeit module to try to measure it. But I
doubt it makes a difference of more than one part in a thousand. And in
some situations I can imagine b+b to be slower than 2*b. (For example,
if b were global)
--
DaveA
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