def optimized_poly_rounded_div(self, a: Sequence[IntOrFQ],
b: Sequence[IntOrFQ]) -> Sequence[IntOrFQ]:
dega = deg(a)
degb = deg(b)
temp = [x for x in a]
o = [0 for x in a]
for i in range(dega - degb, -1, -1):
o[i] = int(o[i] + temp[degb + i] *
prime_field_inv(int(b[degb]), self.field_modulus))
for c in range(degb + 1):
temp[c + i] = (temp[c + i] - o[c])
return [x % self.field_modulus for x in o[:deg(o) + 1]]
def inv(self: T_FQP) -> T_FQP:
lm, hm = (
[1] + [0] * self.degree,
[0] * (self.degree + 1),
)
low, high = (
# Ignore mypy yelling about the inner types for the tuples being incompatible
cast(List[IntOrFQ], list(self.coeffs + (0,))),
cast(List[IntOrFQ], list(self.modulus_coeffs + (1,))),
)
while deg(low):
r = cast(List[IntOrFQ], list(poly_rounded_div(high, low)))
r += [0] * (self.degree + 1 - len(r))
nm = [x for x in hm]
new = [x for x in high]
if len(lm) != self.degree + 1:
raise Exception("Length of lm is not {}".format(self.degree + 1))
elif len(hm) != self.degree + 1:
raise Exception("Length of hm is not {}".format(self.degree + 1))
elif len(nm) != self.degree + 1:
raise Exception("Length of nm is not {}".format(self.degree + 1))
elif len(low) != self.degree + 1:
raise Exception("Length of low is not {}".format(self.degree + 1))
elif len(high) != self.degree + 1:
raise Exception("Length of high is not {}".format(self.degree + 1))
elif len(new) != self.degree + 1:
raise Exception("Length of new is not {}".format(self.degree + 1))
for i in range(self.degree + 1):
for j in range(self.degree + 1 - i):
nm[i + j] -= lm[i] * int(r[j])
new[i + j] -= low[i] * int(r[j])
lm, low, hm, high = nm, new, lm, low
return type(self)(lm[:self.degree]) / low[0]
def inv(self: T_FQP) -> T_FQP:
lm, hm = [1] + [0] * self.degree, [0] * (self.degree + 1)
low, high = (
cast(List[IntOrFQ], list(self.coeffs + (0, ))),
cast(List[IntOrFQ], list(self.modulus_coeffs + (1, ))),
)
while deg(low):
r = cast(List[IntOrFQ],
list(self.optimized_poly_rounded_div(high, low)))
r += [0] * (self.degree + 1 - len(r))
nm = [x for x in hm]
new = [x for x in high]
# assert len(lm) == len(hm) == len(low) == len(high) == len(nm) == len(new) == self.degree + 1 # noqa: E501
for i in range(self.degree + 1):
for j in range(self.degree + 1 - i):
nm[i + j] -= lm[i] * int(r[j])
new[i + j] -= low[i] * r[j]
nm = [x % self.field_modulus for x in nm]
new = [int(x) % self.field_modulus for x in new]
lm, low, hm, high = nm, new, lm, low
return type(self)(lm[:self.degree]) / low[0]