bit twiddling extras

As a follow up to this
I commented on what I thought would be a better solution. Richard Jones pointed us at how pyglet solved how to find the net power of two and how to check if a number is a power of two using some nifty bit twiddling.

Will McGugan then timed
both his and pyglets code, but didn't implement my suggestion (I didn't give code).

I have added an implementation of my suggestion and timed all three sets.
The timing shows that although my implementation of is_power_of_2 is fastest by a smidgen; My implementation of next_power_of_2 by iterative comparison of a list is half way between Wills and pyglets implementation, with pyglet the winner.

I have not got timings with psyco.


The code

setup_1 = """
from math import log, ceil
 
def is_power_of_2(n):
    return log(n, 2) % 1.0 == 0.0
 
def next_power_of_2(n):
    return (2 ** ceil(log(n, 2)))
"""

setup_2 = """
def next_power_of_2(v):
    v -= 1
    v |= v >> 1
    v |= v >> 2
    v |= v >> 4
    v |= v >> 8
    v |= v >> 16
    return v + 1
 
def is_power_of_2(v):
    return (v & (v - 1)) == 0
"""

setup_3 = """
list_of_powers = [x**2 for x in range(32)]
set_of_powers = set(list_of_powers)

def next_power_of_2(v):
    for x in list_of_powers:
        if x >= v: return x

def is_power_of_2(n):
    return n in set_of_powers

"""


from timeit import Timer

t1 = Timer("is_power_of_2(128)", setup_1)
t2 = Timer("is_power_of_2(128)", setup_2)
t3 = Timer("next_power_of_2(125)", setup_1)
t4 = Timer("next_power_of_2(125)", setup_2)
t5 = Timer("is_power_of_2(128)", setup_3)
t6 = Timer("next_power_of_2(125)", setup_3)

print "float math is_power_of_2:", t1.timeit()
print "bit-twiddling is_power_of_2:", t2.timeit()
print "set-lookup is_power_of_2:", t5.timeit()
print
print "float math next power of 2:", t3.timeit()
print "bit-twiddling next power of 2:", t4.timeit()
print "list-comparison next power of 2:", t6.timeit()

The Timings

float math is_power_of_2: 2.33588961726
bit-twiddling is_power_of_2: 0.573784377623
set-lookup is_power_of_2: 0.54499859619

float math next power of 2: 3.06279429369
bit-twiddling next power of 2: 2.08060354039
list-comparison next power of 2: 2.58548279181