import random

PRIME = 2**130-5

def modulo_theory_simple(loops: int):
    prime = 97

    for _ in range(loops):
        value_a = random.randint(1,97)
        value_b = random.randint(1,97)

        value_a_high = value_a // 10
        value_a_low = value_a % 10  # Ignore this modulo, in base 2 it is a mask

        prod_high = value_a_high * value_b
        prod_low = value_a_low * value_b

        mod_high = (prod_high*10) % prime
        mod_low = prod_low % prime

        mod_sum = (mod_high + mod_low) % prime

        mod_conventional = (value_a * value_b) % prime

        if mod_sum != mod_conventional:
            print(f"{value_a}")
            print(f"{value_b}")
            print(f"{mod_sum=}")
            print(f"{mod_conventional=}")

def modulo_theory_full(loops: int):
    for _ in range(loops):
        value_a = random.randint(1,PRIME)
        value_b = random.randint(1,2**128)

        a_partials = [(value_a >> 26*i) & (2**26-1) for i in range(5)]

        prods = [a_partial * value_b for a_partial in a_partials]

        mods = [friendly_modulo(prod, 26*i) for i, prod in enumerate(prods)]


        mod_sum = friendly_modulo(sum(mods), 0)

        mod_conventional = (value_a * value_b) % PRIME

        if mod_sum != mod_conventional:
            print(f"{value_a}")
            print(f"{value_b}")
            print(f"{mod_sum=}")
            print(f"{mod_conventional=}")

def friendly_modulo(val: int, shift_amount: int) -> int:
    high_part = val >> (130-shift_amount)
    low_part = (val << shift_amount) & (2**130-1)

    high_part *= 5

    val = high_part + low_part

    high_part = val >> 130
    low_part = val & (2**130-1)

    high_part *= 5

    val = high_part + low_part

    if val >= PRIME:
        val -= PRIME

    return val

if __name__ == "__main__":
    #modulo_theory_simple(10000000)
    modulo_theory_full(100000)