def __init__(self, base):
self.size = len(base)
for i in range(self.size):
if base[i] == 0:
raise ValueError("rns_base is invalid")
# The base must be coprime
for j in base[:i]:
if gcd(base[i], j) != 1:
raise ValueError("rns_base is invalid")
self.base = base
self.base_prod = None
self.punctured_prod_list = [0] * self.size
self.inv_punctured_prod_mod_base_list = [0] * self.size
if self.size > 1:
# Compute punctured product
for i in range(self.size):
self.punctured_prod_list[i] = multiply_many_except(self.base, self.size, i)
# Compute the full product
self.base_prod = self.punctured_prod_list[0] * self.base[0]
# Compute inverses of punctured products mod primes
for i in range(self.size):
self.inv_punctured_prod_mod_base_list[i] = (
self.punctured_prod_list[i] % self.base[i]
)
self.inv_punctured_prod_mod_base_list[i] = invert_mod(
self.inv_punctured_prod_mod_base_list[i], self.base[i]
)
else:
self.base_prod = self.base[0]
self.punctured_prod_list[0] = 1
self.inv_punctured_prod_mod_base_list[0] = 1
def test_multiply_many_except(operand, count, exp, result):
assert multiply_many_except(operand, count, exp) == result
