It takes as many bits to store the number 0 as the number 1, but the implementation claims it takes no bits at all to store a 0.

>>> (1).bit_length() == (0).bit_length() and True or False
False

It takes one extra bit to store the sign for negative numbers, but this isn't reflected in the implementations.

>>> (-1).bit_length() == 1 + (1).bit_length() and True or False
False

Look at Include/longobject.h and https://docs.python.org/3/library/stdtypes.html?highlight=bit_length#int.bit_length .

>>> (0).bit_length.__doc__
"int.bit_length() -> int\n\nNumber of bits necessary to represent self in binary.\n>>> bin(37)\n'0b100101'\n>>> (37).bit_length()\n6"

The library documentation has clearly been written in disregard of the advertised functionality in the docstrings of the methods.

The documentation is just echoing the flaws of the unit tests.

For the Python 3 variant of this issue, it can be added that the library documentation wrongly states that the method is "New in version 3.1.".

Thank you for your expertise.