This is a mix of an issue and a feature request. I have noticed that calling .bit_length() is significantly slower in PyPy than any other basic operation on an integer. For example, this benchmark

#z = 0
z = 2**62
def main():
    y = 0
    for x in range(z, z + 10**9):
        y += x.bit_length()
    print(y)

main()

takes 16 s to run locally when z=2**62, and 9 s when z=0. That is about 30 times slower than any other basic operation such as y += x % 10 or y += min(x, 15).

By implementing my own bit length function, I can make it run in about 0.9 s for z=2**62

table = [0] * 2**16
for i in range(1, len(table)):
    table[i] = 1 + table[i//2]

def bitlength(x):
    count = 0
    if x >= 2**32:
        x >>= 32
        count += 32
    if x >= 2**16:
        x >>= 16
        count += 16
    return count + table[x]

z = 2**62
def main():
    y = 0
    for x in range(z, z + 10**9):
        y += bitlength(x)
    print(y)

main()

Would it be possible to speed up the built in bit_length()? If I understand PyPy's source code correctly, it uses a very naive and slow algorithm to compute the bit length

https://github.com/python/cpython/blob/b13a5df52fc854d1097e8b5419cb8802dc4059e0/Include/internal/pycore_bitutils.h#L143-L180

Edit: While on the topic. Seems that bit_count is suffering from the same exact issue.