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72 lines
1.8 KiB
Python
72 lines
1.8 KiB
Python
from random import randint
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try:
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import sympy.ntheory
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except ImportError:
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sympy = None
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class Factorization:
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@staticmethod
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def find_small_multiplier_lopatin(what):
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"""Finds the small multiplier by using Lopatin's method"""
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g = 0
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for i in range(3):
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q = (randint(0, 127) & 15) + 17
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x = randint(0, 1000000000) + 1
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y = x
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lim = 1 << (i + 18)
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for j in range(1, lim):
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a, b, c = x, x, q
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while b != 0:
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if (b & 1) != 0:
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c += a
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if c >= what:
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c -= what
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a += a
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if a >= what:
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a -= what
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b >>= 1
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x = c
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z = y - x if x < y else x - y
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g = Factorization.gcd(z, what)
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if g != 1:
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break
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if (j & (j - 1)) == 0:
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y = x
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if g > 1:
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break
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p = what // g
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return min(p, g)
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@staticmethod
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def gcd(a, b):
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"""Calculates the greatest common divisor"""
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while a != 0 and b != 0:
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while b & 1 == 0:
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b >>= 1
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while a & 1 == 0:
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a >>= 1
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if a > b:
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a -= b
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else:
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b -= a
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return a if b == 0 else b
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@staticmethod
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def factorize(pq):
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"""Factorizes the given number and returns both
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the divisor and the number divided by the divisor
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"""
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if sympy:
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return tuple(sympy.ntheory.factorint(pq).keys())
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else:
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divisor = Factorization.find_small_multiplier_lopatin(pq)
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return divisor, pq // divisor
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