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Polynomial.py
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Polynomial.py
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#!/usr/bin/python
from numpy import roll
from numpy.polynomial import polynomial
import copy
class Field:
def __init__(self, degree = 0, generator = None):
if generator is not None:
self._degree = generator.degree()
self._generator = generator
else:
self._degree = degree
self._generator = self._createGenerator(degree)
self._maxAlphaPow = pow(2, self._degree) - 1
self._alphaPowerMap = self._getPowerMap()
def getAlpha(self, degree):
if degree < 0:
degree = self._maxAlphaPow - degree
poly = Polynomial(0b1) * degree
result = poly % self._generator
result.trimPoly()
return result
def getAlphaPower(self, poly):
return self._alphaPowerMap.get(poly, None)
def getGenerator(self):
return self._generator
def multiplyAlpha(self, a1, a2):
if a1 is None or a2 is None:
return None
return (a1 + a2) % self._maxAlphaPow
def powerAlpha(self, a1, a2):
return (a1 * a2) % self._maxAlphaPow
def addAlpha(self, a1, a2):
if a1 is None and a2 is None:
return None
elif a1 is None:
return a2
elif a2 is None:
return a1
a1Poly = self.getAlpha(a1)
a2Poly = self.getAlpha(a2)
resultPoly = a1Poly + a2Poly
return self.getAlphaPower(resultPoly)
def divideAlpha(self, a1, a2):
return (a1 - a2) % self._maxAlphaPow
def getReversedPower(self, power):
return self._maxAlphaPow - power
# W razie potrzeby wiekszych: http://theory.cs.uvic.ca/gen/poly.html
def _createGenerator(self, fieldDegree):
minimalPolys = [0b11, 0b111, 0b1011, 0b10011, 0b100101, 0b1000011,
0211, 0435, 0b1000000011, 0b10000001001]
try:
return Polynomial(minimalPolys[fieldDegree-1])
except IndexError:
raise ValueError('There is no minimal polynomial in table for field degree = ' + str(fieldDegree))
def _getPowerMap(self):
result = {}
for i in range(self._maxAlphaPow):
alphaPoly = self.getAlpha(i)
if result.get(alphaPoly, None) is not None:
raise RuntimeError("Incorrect primitive polynomial given")
result[alphaPoly] = i
return result
class Polynomial:
def __init__(self, number = 0, poly = None):
if poly is not None:
self._poly = poly
else:
self._poly = self._getPolynomial(number)
def degree(self):
try:
return (len(self._poly) - 1) - self._poly[::-1].index(1)
except ValueError:
return 0
def hammingWeight(self):
weight = 0
for bit in self._poly:
if bit > 0:
weight += 1
return weight
def copy(self):
return Polynomial(poly=list(self._poly))
def _getMaxDegree(self, alphaPower, maxAlphaPower):
if alphaPower * self.degree() > maxAlphaPower:
return maxAlphaPower
else:
return alphaPower * self.degree()
def _sumAlpha(self, poly, m, field):
result = Polynomial(0)
for i in range(len(poly)):
if poly[i] == 1:
result += field.getAlpha(i)
return field.getAlphaPower(result)
def getAlphaMap(self):
result = {}
self.trimPoly()
for i in range(len(self._poly)):
if self._poly[i] == 1:
result[i] = 0
return result
@staticmethod
def addUsingAlphaMap(map1, map2, field):
result = copy.deepcopy(map1)
for key, value in map2.iteritems():
value2 = result.get(key, None)
result[key] = field.addAlpha(value, value2)
return result
@staticmethod
def multiplyUsingAlphaMap(map1, map2, field):
result = {}
for key1, value1 in map1.iteritems():
for key2, value2 in map2.iteritems():
multiplyIndex = key1 + key2
partMul = field.multiplyAlpha(value1, value2)
result[multiplyIndex] = field.addAlpha(result.get(multiplyIndex, None), partMul)
return result
@staticmethod
def divideUsingAlphaMap(divisor, division, field):
remainder = copy.deepcopy(divisor)
Polynomial._normalizeAlphaMap(remainder)
div = copy.deepcopy(division)
Polynomial._normalizeAlphaMap(div)
result = {}
divisionDegree = Polynomial.getMapMaxKey(div)
while remainder and Polynomial.getMapMaxKey(remainder) - divisionDegree >= 0:
remainderDegree = Polynomial.getMapMaxKey(remainder)
currentDegree = remainderDegree - divisionDegree
result[currentDegree] = field.divideAlpha(remainder[remainderDegree],
div[divisionDegree])
for i in range(divisionDegree + 1):
part = field.multiplyAlpha(result[currentDegree], div.get(i, None))
remainder[i + currentDegree] = field.addAlpha(
remainder.get(i + currentDegree, None), part)
Polynomial._normalizeAlphaMap(remainder)
return result, remainder
@staticmethod
def _normalizeAlphaMap(alphaMap):
while len(alphaMap) and alphaMap[Polynomial.getMapMaxKey(alphaMap)] is None:
del alphaMap[Polynomial.getMapMaxKey(alphaMap)]
@staticmethod
def getMapMaxKey(m):
return max(m.keys(), key = int)
@staticmethod
def getValueUsingAlphaMap(polyAlpha, power, field):
result = None
for key, value in polyAlpha.iteritems():
temp = field.powerAlpha(key, power)
temp = field.multiplyAlpha(value, temp)
result = field.addAlpha(result, temp)
return result
def _normalizePoly(self, poly, expectedSize):
norm = [abs(int(i)) % 2 for i in poly]
sizeDiff = expectedSize - len(norm)
if sizeDiff > 0:
norm += [0]*sizeDiff
return norm
def trimPoly(self):
while len(self._poly) and self._poly[-1] == 0:
self._poly.pop()
def _getPolynomial(self, number):
reversedDigit = []
for digit in reversed(self._translateToBinaryList(number)):
reversedDigit.append(digit)
return reversedDigit
def _getNumberFromPoly(self):
number = 0
power = 0
for digit in self._poly:
number += 2 ** power * int(digit)
power += 1
return number
def _translateToBinaryList(self, number):
return [int(d) for d in str(bin(number))[2:]]
def __len__(self):
return len(self._poly)
def __getitem__(self, key):
return self._poly[key]
def __setitem__(self, key, value):
self._poly[key] = value
def __str__(self):
return ' '.join(list(str(bin(self._getNumberFromPoly()))[2:]))
def __repr__(self):
return self._poly.__repr__()
def __int__(self):
return self._getNumberFromPoly()
def __hex__(self):
return hex(self._getNumberFromPoly())
def __oct__(self):
return oct(self._getNumberFromPoly())
def __index__(self):
return self._getNumberFromPoly()
def __mod__(self, other):
result = polynomial.polydiv(self._poly, other._poly)[1]
result = self._normalizePoly(result, len(self._poly))
return Polynomial(poly=result)
def __mul__(self, other):
if isinstance(other, Polynomial):
result = polynomial.polymul(self._poly, other._poly)
else:
result = [0] * other + self._poly
return Polynomial(poly=result)
def __imul__(self, other):
return self.__mul__(other)
def __div__(self, other):
if isinstance(other, Polynomial):
result = polynomial.polydiv(self._poly, other._poly)[0]
else:
result = self._poly[other:]
result = self._normalizePoly(result, len(self._poly))
return Polynomial(poly=result)
def __idiv__(self, other):
return self.__div__(other)
def __add__(self, other):
result = polynomial.polyadd(self._poly, other._poly)
result = self._normalizePoly(result, len(self._poly))
return Polynomial(poly=result)
def __iadd__(self, other):
return self.__add__(other)
def __lshift__(self, other):
result = list(roll(self._poly, other))
return Polynomial(poly=result)
# and this function too
def __rshift__(self, other):
result = list(roll(self._poly, -other))
return Polynomial(poly=result)
def __eq__(self, other):
return self._getNumberFromPoly() == other._getNumberFromPoly()
def __hash__(self):
return self._getNumberFromPoly()
if __name__ == '__main__':
a = Polynomial(0b1000)
b = Polynomial(0b0011)
c = Polynomial(0)
print a
print b
print a*8
print a+b
print a/2
print a%b
print a*b