find largest power of two less than X number?

Question

I m doing this

def power_two(n, base = -1):
    result = 2 ** base
    if result < n:
        base += 1
        power_two(n, base)
    else:
        if result == n:
            print base
        else:
            print base - 1

what is the pythonic way to find largest power of two less than X number?

EDIT example: power_two(100) return only the power

Answer 1

Use a logarithm, truncate it and then raise it to the power of 2:

def power_two(n):
    return 2**int(math.log(n, 2)))

Update: returning only the power:

def power_two(n):
    return int(math.log(n, 2))

Answer 2

Two ways, first works only in Python 2.7 and maybe 3+:

import random
for number in (random.randint(0,1<<32) for _ in range(16)):
    print "%20i,%4i, %4i" % (number, number.bit_length()-1, len(bin(number))-3)

Answer 3

You could use bit_length():

def power_two(n):
    return n.bit_length() - 1

By definition for n != 0: 2**(n.bit_length()-1) <= abs(n) < 2**n.bit_length()