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import secrets
from functools import wraps
from public import public
from .context import Action
@public
def gcd(a, b):
"""Euclid's greatest common denominator algorithm."""
if abs(a) < abs(b):
return gcd(b, a)
while abs(b) > 0:
q, r = divmod(a, b)
a, b = b, r
return a
@public
def extgcd(a, b):
"""Extended Euclid's greatest common denominator algorithm."""
if abs(b) > abs(a):
(x, y, d) = extgcd(b, a)
return y, x, d
if abs(b) == 0:
return 1, 0, a
x1, x2, y1, y2 = 0, 1, 1, 0
while abs(b) > 0:
q, r = divmod(a, b)
x = x2 - q * x1
y = y2 - q * y1
a, b, x2, x1, y2, y1 = b, r, x1, x, y1, y
return x2, y2, a
def check(func):
@wraps(func)
def method(self, other):
if type(self) is not type(other):
other = self.__class__(other, self.n)
else:
if self.n != other.n:
raise ValueError
return func(self, other)
return method
@public
class RandomModAction(Action):
"""A random sampling from Z_n."""
order: int
def __init__(self, order: int):
super().__init__()
self.order = order
def __repr__(self):
return f"{self.__class__.__name__}({self.order:x})"
@public
class Mod(object):
"""An element x of ℤₙ."""
def __init__(self, x: int, n: int):
self.x: int = x % n
self.n: int = n
@check
def __add__(self, other):
return Mod((self.x + other.x) % self.n, self.n)
@check
def __radd__(self, other):
return self + other
@check
def __sub__(self, other):
return Mod((self.x - other.x) % self.n, self.n)
@check
def __rsub__(self, other):
return -self + other
def __neg__(self):
return Mod(self.n - self.x, self.n)
def inverse(self):
x, y, d = extgcd(self.x, self.n)
return Mod(x, self.n)
def __invert__(self):
return self.inverse()
@check
def __mul__(self, other):
return Mod((self.x * other.x) % self.n, self.n)
@check
def __rmul__(self, other):
return self * other
@check
def __truediv__(self, other):
return self * ~other
@check
def __rtruediv__(self, other):
return ~self * other
@check
def __floordiv__(self, other):
return self * ~other
@check
def __rfloordiv__(self, other):
return ~self * other
@check
def __div__(self, other):
return self.__floordiv__(other)
@check
def __rdiv__(self, other):
return self.__rfloordiv__(other)
@check
def __divmod__(self, divisor):
q, r = divmod(self.x, divisor.x)
return Mod(q, self.n), Mod(r, self.n)
def __bytes__(self):
return self.x.to_bytes((self.n.bit_length() + 7) // 8, byteorder="big")
@staticmethod
def random(n: int):
with RandomModAction(n):
return Mod(secrets.randbelow(n), n)
def __int__(self):
return self.x
def __eq__(self, other):
if type(other) is int:
return self.x == (other % self.n)
if type(other) is not Mod:
return False
return self.x == other.x and self.n == other.n
def __ne__(self, other):
return not self == other
def __repr__(self):
return str(self.x)
def __pow__(self, n):
if type(n) is not int:
raise TypeError
q = self
r = self if n & 1 else Mod(1, self.n)
i = 2
while i <= n:
q = (q * q)
if n & i == i:
r = (q * r)
i = i << 1
return r
@public
class Undefined(Mod):
def __init__(self):
object.__init__(self)
def __add__(self, other):
raise NotImplementedError
def __radd__(self, other):
raise NotImplementedError
def __sub__(self, other):
raise NotImplementedError
def __rsub__(self, other):
raise NotImplementedError
def __neg__(self):
raise NotImplementedError
def __invert__(self):
raise NotImplementedError
def __mul__(self, other):
raise NotImplementedError
def __rmul__(self, other):
raise NotImplementedError
def __truediv__(self, other):
raise NotImplementedError
def __rtruediv__(self, other):
raise NotImplementedError
def __floordiv__(self, other):
raise NotImplementedError
def __rfloordiv__(self, other):
raise NotImplementedError
def __div__(self, other):
raise NotImplementedError
def __rdiv__(self, other):
raise NotImplementedError
def __divmod__(self, divisor):
raise NotImplementedError
def __bytes__(self):
raise NotImplementedError
def __int__(self):
raise NotImplementedError
def __eq__(self, other):
return False
def __ne__(self, other):
return False
def __repr__(self):
return "Undefined"
def __pow__(self, n):
raise NotImplementedError
|
