Multiplication and Power Modulo operations for large numbers in Python

modulo_operations.py

cal_add_mod_dict = {}
cal_sub_mod_dict = {}
cal_mul_mod_dict = {}
cal_pow_mod_dict = {}

def cal_add_mod(a, b, n):
    """Calculates (a+b) mod n"""
    t = (a,b,n)
    if t not in cal_add_mod_dict:
        cal_add_mod_dict[t] = (a % n + b % n) % n
        
    return cal_add_mod_dict[t]

def cal_sub_mod(a, b, n):
    """Calculates (a-b) mod n"""
    t = (a,b,n)
    if t not in cal_sub_mod_dict:
        cal_sub_mod_dict[t] = (a % n - b % n) % n
        
    return cal_sub_mod_dict[t]

def cal_mul_mod(a, b, n):
    """Calculates (a * b) mod n"""
    t = (a,b,n)
    if t not in cal_mul_mod_dict:
        if a > n:
            a = a%n
        if b > n:
            b = b%n
        c = (a * b) // n
        r = (a * b - c * n) % n
        r = r + m if r < 0 else r
        cal_mul_mod_dict[t] = r

    return cal_mul_mod_dict[t]

def cal_pow_mod(a, k, n):
    """Calculates (a to power k) mod n"""
    t = (a,k,n)
    if t not in cal_pow_mod_dict:
        r = 0 if n == 1 else 1
        while k > 0:
            if k & 1:
                r = cal_mul_mod(r, a, n)
            k = k >> 1;
            a = cal_mul_mod(a, a, n);
        cal_pow_mod_dict[t] = r

    return cal_pow_mod_dict[t]