Karatsuba Algorithm for Integer Multiplication - Not 100%

karatsuba_integer_multiplier.py

def karatsuba_integer_multiplier(int1: str, int2: str) -> int:
    """
    Assumptions: 
        - int1 and int2 initially handled as strings
        - int1 and int2 have the same size
        - int1 and int2 have even digit numbers
    """
    n = len(int1)
    print(n)
    if n == 2 or n == 3:
        return int(int1) * int(int2)
    
    m = n // 2
    a,b,c,d = int1[:m], int1[m:], int2[:m], int2[m:]
    print(a,b,c,d, m)
    
    ac = karatsuba_integer_multiplier(a,c)
    bd = karatsuba_integer_multiplier(b,d) 
    a_b = str(int(a)+int(b))
    c_d = str(int(c)+int(d))
    ab_cd = karatsuba_integer_multiplier(a_b,c_d) - ac - bd # FIXME a+b not defined

    return 10**n * ac + 10**(n//2) * ab_cd + bd
    
int1 = "5678"
int2 = "1234"

print(karatsuba_integer_multiplier(int1, int2))

int1 = "3141592653589793238462643383279502884197169399375105820974944592"
int2 = "2718281828459045235360287471352662497757247093699959574966967627"

print(str(karatsuba_integer_multiplier(int1, int2)))