Updated for Python3
This commit is contained in:
Ethan L. Miller
parent
54cbe3c594
commit
0d92601702
70
galois.py
70
galois.py
@ -23,13 +23,19 @@ class GaloisNumber:
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The class supports "normal" syntax for the addition, subtraction, multiplication,
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division, additive inverse (-), and multiplicative inverse (~) operations.
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'''
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def __init__ (self, x, value=0):
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def __init__ (self, x, field=None):
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if isinstance(x, GaloisNumber):
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self.field = x.field
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self.value = x.value
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elif type(field) not in (GaloisFieldLog, GaloisFieldDirect):
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raise ValueError ("Must specify field")
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else:
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self.field = x
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self.assign (value)
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self.field = field
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if type(x) == bytes:
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x = int.from_bytes (x, 'big')
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elif type(x) != int:
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raise ValueError ("Must be an integer or bytes")
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self.assign (x)
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def assign (self, v):
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'''
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@ -37,13 +43,13 @@ class GaloisNumber:
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the field with which the GaloisNumber instance was defined.
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'''
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if v > self.field.size:
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raise GaloisException ("Value {0} is outside field".format (v))
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raise ValueError ("Value {0} is outside field".format (v))
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self.value = v
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def __add__ (self, other):
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if self.field != other.field:
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raise GaloisException ("Field elements from different fields")
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return GaloisNumber (self.field, self.value ^ other.value)
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return GaloisNumber (self.value ^ other.value, self.field)
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def __iadd__ (self, other):
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if self.field != other.field:
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@ -72,11 +78,14 @@ class GaloisNumber:
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raise GaloisException ("Field elements from different fields")
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self.value = self.field.direct_multiply (self.value, other.value)
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def __div__ (self, other):
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def __floordiv__ (self, other):
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if self.field != other.field:
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raise GaloisException ("Field elements from different fields")
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return self.field.divide (self, other)
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def __truediv__ (self, other):
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return self // other
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def __eq__ (self, other):
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if self.field != other.field:
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raise GaloisException ("Field elements from different fields")
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@ -128,33 +137,32 @@ class GaloisFieldLog:
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a = v1.value
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b = v2.value
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if a == 0 or b == 0:
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return GaloisNumber (self, 0)
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return GaloisNumber (self, self.antilog_tbl[(self.log_tbl[a] + self.log_tbl[b]) %
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(self.size - 1)])
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return GaloisNumber (0, self)
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return GaloisNumber (self.antilog_tbl[(self.log_tbl[a] + self.log_tbl[b]) % (self.size - 1)], self)
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def invert (self, v):
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if v.value == 0:
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return GaloisNumber(self, 0)
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return GaloisNumber(0, self)
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elif v.value == 1:
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return GaloisNumber (self, 1)
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return GaloisNumber (1, self)
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else:
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return GaloisNumber (self, self.antilog_tbl[self.size - 1 - self.log_tbl[v.value]])
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return GaloisNumber (self.antilog_tbl[self.size - 1 - self.log_tbl[v.value]], self)
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def divide (self, v1, v2):
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return self.multiply (v1, self.invert(v2))
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def self_test (self):
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mul_identity = GaloisNumber (self, 1)
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v = GaloisNumber (self)
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g_0 = GaloisNumber (self, 0)
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g_1 = GaloisNumber (self, 1)
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mul_identity = GaloisNumber (1, self)
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v = GaloisNumber (0, self)
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g_0 = GaloisNumber (0, self)
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g_1 = GaloisNumber (1, self)
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for i in range (self.size):
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v.assign (i)
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if i == 0: continue
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assert v * ~v == mul_identity, "Multiplicative inverse failed at {}".format (i)
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assert g_0 - v == -v, "Additive inverse failed at {}".format (i)
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assert v * g_1 == v, "Multiplicative identity failed at {}".format (i)
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vb = GaloisNumber (self)
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vb = GaloisNumber (0, self)
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for a in range (1, self.multiply_test_size):
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v.assign (random.randint (1, self.size - 1))
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vb.assign (random.randint (1, self.size - 1))
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@ -184,7 +192,7 @@ class GaloisFieldDirect:
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self.bits = bits
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self.size = (1 << bits)
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self.prim = self.poly_defaults[bits] if not primitive_polynomial else primitive_polynomial
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self.value_format = repr_prefix + '{:0>' + str(bits / 4) + 'x}'
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self.value_format = repr_prefix + '{:0>' + str(bits // 4) + 'x}'
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self.alpha = alpha
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def __eq__ (self, other):
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@ -194,7 +202,7 @@ class GaloisFieldDirect:
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return self.value_format.format (v)
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def multiply (self, v1, v2):
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return GaloisNumber (self, self.direct_multiply (v1.value, v2.value))
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return GaloisNumber (self.direct_multiply (v1.value, v2.value), self)
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def direct_multiply (self, a, b):
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# Multiplication is commutative, and it's faster if we use the smaller value as the
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@ -223,24 +231,24 @@ class GaloisFieldDirect:
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to field width in bits.
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'''
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if v.value == 0:
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return GaloisNumber(self, 0)
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return GaloisNumber(0, self)
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elif v.value == 1:
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return GaloisNumber (self, 1)
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return GaloisNumber (1, self)
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inv = 1
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sq = v.value
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for i in range (1, self.bits):
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sq = self.direct_multiply (sq, sq)
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inv = self.direct_multiply (inv, sq)
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return GaloisNumber (self, inv)
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return GaloisNumber (inv, self)
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def divide (self, v1, v2):
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return self.multiply (v1, self.invert(v2))
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def self_test (self):
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mul_identity = GaloisNumber (self, 1)
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v = GaloisNumber (self)
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g_0 = GaloisNumber (self, 0)
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g_1 = GaloisNumber (self, 1)
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mul_identity = GaloisNumber (1, self)
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v = GaloisNumber (0, self)
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g_0 = GaloisNumber (0, self)
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g_1 = GaloisNumber (1, self)
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small_field = self.size < self.max_test_size
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n_tests = (self.size - 1) if small_field else self.max_test_size
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for i in range (0, n_tests):
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@ -248,7 +256,7 @@ class GaloisFieldDirect:
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assert v * ~v == mul_identity, "Multiplicative inverse failed at {}".format (i)
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assert g_0 - v == -v, "Additive inverse failed at {}".format (i)
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assert v * g_1 == v, "Multiplicative identity failed at {}".format (i)
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vb = GaloisNumber (self)
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vb = GaloisNumber (0, self)
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for a in range (1, self.max_test_size):
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v.assign (random.randint (1, self.size - 1))
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vb.assign (random.randint (1, self.size - 1))
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@ -261,16 +269,16 @@ if __name__ == '__main__':
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print ('\nTesting direct fields...........')
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for width in GaloisFieldDirect.field_widths:
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field = GaloisFieldDirect (width)
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g0 = GaloisNumber (field, 2)
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g1 = GaloisNumber (field, 7)
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g0 = GaloisNumber (2, field)
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g1 = GaloisNumber (7, field)
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print ('{0} + {1} = {2}'.format (g0, g1, g0 + g1))
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if field.self_test ():
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print ("{0} bit field (direct) passed!".format (width))
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print ('\nTesting log fields...........')
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for width in GaloisFieldLog.field_widths:
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field = GaloisFieldLog (width)
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g0 = GaloisNumber (field, 2)
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g1 = GaloisNumber (field, 7)
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g0 = GaloisNumber (2, field)
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g1 = GaloisNumber (7, field)
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print ('{0} + {1} = {2}'.format (g0, g1, g0 + g1))
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if field.self_test ():
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print ("{0} bit field (log) passed!".format (width))
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