+++ /dev/null
-from .cldivrem import cldivrem
-from .clmul import clmul
-from .pack_poly import pack_poly, unpack_poly
-import unittest
-
-
-class GF2Poly:
- """Polynomial with GF(2) coefficients.
-
- `self.coefficients`: a list where `coefficients[-1] != 0`.
- `coefficients[i]` is the coefficient for `x ** i`.
- """
-
- def __init__(self, coefficients=None):
- self.coefficients = []
- if coefficients is not None:
- if not isinstance(coefficients, (tuple, list)):
- coefficients = list(coefficients)
- # reversed to resize self.coefficients once
- for i in reversed(range(len(coefficients))):
- self[i] = coefficients[i]
-
- def __len__(self):
- return len(self.coefficients)
-
- @property
- def degree(self):
- return len(self) - 1
-
- @property
- def lc(self):
- """leading coefficient."""
- return 0 if len(self) == 0 else self.coefficients[-1]
-
- def __getitem__(self, key):
- assert key >= 0
- if key < len(self):
- return self.coefficients[key]
- return 0
-
- def __setitem__(self, key, value):
- assert key >= 0
- assert value == 0 or value == 1
- if key < len(self):
- self.coefficients[key] = value
- while len(self) and self.coefficients[-1] == 0:
- self.coefficients.pop()
- elif value != 0:
- self.coefficients += [0] * (key + 1 - len(self))
- self.coefficients[key] = value
-
- def __repr__(self):
- return f"GF2Poly({self.coefficients})"
-
- def __iadd__(self, rhs):
- for i in range(max(len(self), len(rhs))):
- self[i] ^= rhs[i]
- return self
-
- def __add__(self, rhs):
- return GF2Poly(self).__iadd__(rhs)
-
- def __isub__(self, rhs):
- return self.__iadd__(rhs)
-
- def __sub__(self, rhs):
- return self.__add__(rhs)
-
- def __iter__(self):
- return iter(self.coefficients)
-
- def __mul__(self, rhs):
- retval = GF2Poly()
- # reversed to resize retval.coefficients once
- for i in reversed(range(len(self))):
- if self[i]:
- for j in reversed(range(len(rhs))):
- retval[i + j] ^= rhs[j]
- return retval
-
- def __ilshift__(self, amount):
- """multiplies `self` by the polynomial `x**amount`"""
- if len(self) != 0:
- self.coefficients[:0] = [0] * amount
- return self
-
- def __lshift__(self, amount):
- """returns the polynomial `self * x**amount`"""
- return GF2Poly(self).__ilshift__(amount)
-
- def __irshift__(self, amount):
- """divides `self` by the polynomial `x**amount`, discarding the
- remainder.
- """
- if amount < len(self):
- del self.coefficients[:amount]
- else:
- del self.coefficients[:]
- return self
-
- def __rshift__(self, amount):
- """divides `self` by the polynomial `x**amount`, discarding the
- remainder.
- """
- return GF2Poly(self).__irshift__(amount)
-
- def __divmod__(self, divisor):
- # based on https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Euclidean_division
- assert isinstance(divisor, GF2Poly)
- if len(divisor) == 0:
- raise ZeroDivisionError
- q = GF2Poly()
- r = GF2Poly(self)
- while r.degree >= divisor.degree:
- shift = r.degree - divisor.degree
- q[shift] ^= 1
- r -= divisor << shift
- return q, r
-
- def __floordiv__(self, divisor):
- q, r = divmod(self, divisor)
- return q
-
- def __mod__(self, divisor):
- q, r = divmod(self, divisor)
- return r
-
- def __eq__(self, rhs):
- if isinstance(rhs, GF2Poly):
- return self.coefficients == rhs.coefficients
- return NotImplemented
-
-
-class TestGF2Poly(unittest.TestCase):
- def test_add(self):
- a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
- b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0])
- c = a + b
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
- self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]))
- c = b + a
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
- self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]))
- a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
- b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1])
- c = a + b
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
- c = a - b
- self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
- c = b - a
- self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
-
- def test_shift(self):
- a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
- c = a << 0
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- c = a << 5
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly(
- [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- c = a << 10
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly(
- [0] * 10 + [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- c = a >> 0
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- c = a >> 5
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([1, 1, 0, 1, 0, 1]))
- c = a >> 10
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([1]))
- c = a >> 11
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([]))
- c = a >> 100
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(c, GF2Poly([]))
-
- def test_mul(self):
- a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
- b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1])
- c = a * b
- expected = GF2Poly([0, 0, 1, 0, 1, 0, 1, 1, 1, 0,
- 0, 1, 0, 1, 1, 0, 0, 1, 1])
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
- self.assertEqual(c, expected)
-
- def test_divmod(self):
- a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
- b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1])
- q, r = divmod(a, b)
- self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
- self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
- self.assertEqual(q, GF2Poly([1, 1, 1]))
- self.assertEqual(r, GF2Poly([1, 0, 1, 0, 0, 1, 0, 1]))
- q = a // b
- self.assertEqual(q, GF2Poly([1, 1, 1]))
- r = a % b
- self.assertEqual(r, GF2Poly([1, 0, 1, 0, 0, 1, 0, 1]))
-
-
-class TestCL(unittest.TestCase):
- def test_cldivrem(self):
- n_width = 8
- d_width = 4
- width = max(n_width, d_width)
- for nv in range(2 ** n_width):
- n = GF2Poly(unpack_poly(nv))
- for dv in range(1, 2 ** d_width):
- d = GF2Poly(unpack_poly(dv))
- with self.subTest(n=str(n), nv=nv, d=str(d), dv=dv):
- q_expected, r_expected = divmod(n, d)
- self.assertEqual(q_expected * d + r_expected, n)
- q, r = cldivrem(nv, dv, width)
- q_expected = pack_poly(q_expected.coefficients)
- r_expected = pack_poly(r_expected.coefficients)
- self.assertEqual((q, r), (q_expected, r_expected))
-
- def test_clmul(self):
- a_width = 5
- b_width = 5
- for av in range(2 ** a_width):
- a = GF2Poly(unpack_poly(av))
- for bv in range(2 ** b_width):
- b = GF2Poly(unpack_poly(bv))
- with self.subTest(a=str(a), av=av, b=str(b), bv=bv):
- expected = a * b
- product = clmul(av, bv)
- expected = pack_poly(expected.coefficients)
- self.assertEqual(product, expected)
-
-
-if __name__ == "__main__":
- unittest.main()
--- /dev/null
+from .cldivrem import cldivrem
+from .clmul import clmul
+from .pack_poly import pack_poly, unpack_poly
+import unittest
+
+
+class GF2Poly:
+ """Polynomial with GF(2) coefficients.
+
+ `self.coefficients`: a list where `coefficients[-1] != 0`.
+ `coefficients[i]` is the coefficient for `x ** i`.
+ """
+
+ def __init__(self, coefficients=None):
+ self.coefficients = []
+ if coefficients is not None:
+ if not isinstance(coefficients, (tuple, list)):
+ coefficients = list(coefficients)
+ # reversed to resize self.coefficients once
+ for i in reversed(range(len(coefficients))):
+ self[i] = coefficients[i]
+
+ def __len__(self):
+ return len(self.coefficients)
+
+ @property
+ def degree(self):
+ return len(self) - 1
+
+ @property
+ def lc(self):
+ """leading coefficient."""
+ return 0 if len(self) == 0 else self.coefficients[-1]
+
+ def __getitem__(self, key):
+ assert key >= 0
+ if key < len(self):
+ return self.coefficients[key]
+ return 0
+
+ def __setitem__(self, key, value):
+ assert key >= 0
+ assert value == 0 or value == 1
+ if key < len(self):
+ self.coefficients[key] = value
+ while len(self) and self.coefficients[-1] == 0:
+ self.coefficients.pop()
+ elif value != 0:
+ self.coefficients += [0] * (key + 1 - len(self))
+ self.coefficients[key] = value
+
+ def __repr__(self):
+ return f"GF2Poly({self.coefficients})"
+
+ def __iadd__(self, rhs):
+ for i in range(max(len(self), len(rhs))):
+ self[i] ^= rhs[i]
+ return self
+
+ def __add__(self, rhs):
+ return GF2Poly(self).__iadd__(rhs)
+
+ def __isub__(self, rhs):
+ return self.__iadd__(rhs)
+
+ def __sub__(self, rhs):
+ return self.__add__(rhs)
+
+ def __iter__(self):
+ return iter(self.coefficients)
+
+ def __mul__(self, rhs):
+ retval = GF2Poly()
+ # reversed to resize retval.coefficients once
+ for i in reversed(range(len(self))):
+ if self[i]:
+ for j in reversed(range(len(rhs))):
+ retval[i + j] ^= rhs[j]
+ return retval
+
+ def __ilshift__(self, amount):
+ """multiplies `self` by the polynomial `x**amount`"""
+ if len(self) != 0:
+ self.coefficients[:0] = [0] * amount
+ return self
+
+ def __lshift__(self, amount):
+ """returns the polynomial `self * x**amount`"""
+ return GF2Poly(self).__ilshift__(amount)
+
+ def __irshift__(self, amount):
+ """divides `self` by the polynomial `x**amount`, discarding the
+ remainder.
+ """
+ if amount < len(self):
+ del self.coefficients[:amount]
+ else:
+ del self.coefficients[:]
+ return self
+
+ def __rshift__(self, amount):
+ """divides `self` by the polynomial `x**amount`, discarding the
+ remainder.
+ """
+ return GF2Poly(self).__irshift__(amount)
+
+ def __divmod__(self, divisor):
+ # based on https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Euclidean_division
+ assert isinstance(divisor, GF2Poly)
+ if len(divisor) == 0:
+ raise ZeroDivisionError
+ q = GF2Poly()
+ r = GF2Poly(self)
+ while r.degree >= divisor.degree:
+ shift = r.degree - divisor.degree
+ q[shift] ^= 1
+ r -= divisor << shift
+ return q, r
+
+ def __floordiv__(self, divisor):
+ q, r = divmod(self, divisor)
+ return q
+
+ def __mod__(self, divisor):
+ q, r = divmod(self, divisor)
+ return r
+
+ def __eq__(self, rhs):
+ if isinstance(rhs, GF2Poly):
+ return self.coefficients == rhs.coefficients
+ return NotImplemented
+
+
+class TestGF2Poly(unittest.TestCase):
+ def test_add(self):
+ a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
+ b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0])
+ c = a + b
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
+ self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]))
+ c = b + a
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
+ self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]))
+ a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
+ b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1])
+ c = a + b
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
+ c = a - b
+ self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
+ c = b - a
+ self.assertEqual(c, GF2Poly([1, 0, 1, 1, 1, 0, 0, 1]))
+
+ def test_shift(self):
+ a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
+ c = a << 0
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ c = a << 5
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly(
+ [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ c = a << 10
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly(
+ [0] * 10 + [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ c = a >> 0
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ c = a >> 5
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([1, 1, 0, 1, 0, 1]))
+ c = a >> 10
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([1]))
+ c = a >> 11
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([]))
+ c = a >> 100
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(c, GF2Poly([]))
+
+ def test_mul(self):
+ a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
+ b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1])
+ c = a * b
+ expected = GF2Poly([0, 0, 1, 0, 1, 0, 1, 1, 1, 0,
+ 0, 1, 0, 1, 1, 0, 0, 1, 1])
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
+ self.assertEqual(c, expected)
+
+ def test_divmod(self):
+ a = GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1])
+ b = GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1])
+ q, r = divmod(a, b)
+ self.assertEqual(a, GF2Poly([1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]))
+ self.assertEqual(b, GF2Poly([0, 0, 1, 0, 1, 1, 1, 1, 1]))
+ self.assertEqual(q, GF2Poly([1, 1, 1]))
+ self.assertEqual(r, GF2Poly([1, 0, 1, 0, 0, 1, 0, 1]))
+ q = a // b
+ self.assertEqual(q, GF2Poly([1, 1, 1]))
+ r = a % b
+ self.assertEqual(r, GF2Poly([1, 0, 1, 0, 0, 1, 0, 1]))
+
+
+class TestCL(unittest.TestCase):
+ def test_cldivrem(self):
+ n_width = 8
+ d_width = 4
+ width = max(n_width, d_width)
+ for nv in range(2 ** n_width):
+ n = GF2Poly(unpack_poly(nv))
+ for dv in range(1, 2 ** d_width):
+ d = GF2Poly(unpack_poly(dv))
+ with self.subTest(n=str(n), nv=nv, d=str(d), dv=dv):
+ q_expected, r_expected = divmod(n, d)
+ self.assertEqual(q_expected * d + r_expected, n)
+ q, r = cldivrem(nv, dv, width)
+ q_expected = pack_poly(q_expected.coefficients)
+ r_expected = pack_poly(r_expected.coefficients)
+ self.assertEqual((q, r), (q_expected, r_expected))
+
+ def test_clmul(self):
+ a_width = 5
+ b_width = 5
+ for av in range(2 ** a_width):
+ a = GF2Poly(unpack_poly(av))
+ for bv in range(2 ** b_width):
+ b = GF2Poly(unpack_poly(bv))
+ with self.subTest(a=str(a), av=av, b=str(b), bv=bv):
+ expected = a * b
+ product = clmul(av, bv)
+ expected = pack_poly(expected.coefficients)
+ self.assertEqual(product, expected)
+
+
+if __name__ == "__main__":
+ unittest.main()
projects / nmutil.git / commitdiff