Precise math.log(x, 2) in Python

Question

In python, I need to get the rounded down logarithm of positive integers for base 2, including big numbers.

However, since floating point math is used, I might get bad results, for example:

>>> import math
>>> int(math.log(281474976710655, 2))
48

However:

>>> 2 ** 48
281474976710656

So the correct result, rounded down, should be 47.

How can I get the correct value?

Answer 1

In Python 3, integers have a .bit_length method, so you should use that to get your rounded down base 2 logarithm.

Here's a short demo:

m = 2 ** 1000
for n in (281474976710655, m-1, m, m+1):
    a = n.bit_length() - 1
    b = 2 ** a
    print(a, b <= n < 2 * b)

output

47 True
999 True
1000 True
1000 True