Recursive Python implementation of Karatsuba multiplication

karatsuba_multiplication.py

#!/usr/bin/env python3


def karatsuba_mul(m: int, n: int) -> int:
    """
    Implementation of recursive Karatsuba multiplication

    >>> karatsuba_mul(56, 12)
    672
    >>> karatsuba_mul(78, 34)
    2652
    >>> karatsuba_mul(56 + 78, 12 + 34)
    6164
    >>> karatsuba_mul(46, 134)
    6164
    >>> karatsuba_mul(5678, 1234)
    7006652
    >>> karatsuba_mul(1234, 5678)
    7006652
    >>> karatsuba_mul(4, 1441)
    5764
    >>> karatsuba_mul(23847, 3498)
    83416806
    """
    if m // 10 == 0 and n // 10 == 0:
        return m * n
    else:
        k = max(map(lambda i: len(str(i)), (m, n))) // 2
        a, b = m // (10**k), m % (10**k)
        c, d = n // (10**k), n % (10**k)

        ac, bd = karatsuba_mul(a, c), karatsuba_mul(b, d)
        bc_plus_ad = karatsuba_mul(a + b, c + d) - ac - bd

        return (ac * (10 ** (2 * k))) + (bc_plus_ad * (10**k)) + bd