Oops, forgot one part of the doc definition in the proposed additional
tests:

for x in range(-65000, 65000):
    k = x.numbits()
    assert k == len(bin(x).lstrip('-0b'))
    if x > 0:
        assert 2 ** (k-1) <= x < 2**k
        assert k == 1 + math.floor(math.log(x) / math.log(2))
    elif x == 0:
        assert k == 0
    else:
        assert k == (-x).numbits()