def primefac(n, trial_limit=1000, rho_rounds=42000, verbose=False,
methods=(_primefac.pollardRho_brent, _primefac.pollard_pm1, _primefac.williams_pp1, _primefac.ecm, _primefac.mpqs,
_primefac.fermat, _primefac.factordb), timeout=60):
from _primefac import isprime, isqrt, primegen
from six.moves import xrange, reduce
from random import randrange
import six
timeout = timeout - 1
if n < 2:
return
if isprime(n):
yield n
return
factors, nroot = [], isqrt(n)
# Note that we remove factors of 2 whether the user wants to or not.
for p in primegen():
if n % p == 0:
while n % p == 0:
yield p
n //= p
nroot = isqrt(n)
if isprime(n):
yield n
return
if p > nroot:
if n != 1:
yield n
return
if p >= trial_limit:
break
if isprime(n):
yield n
return
if rho_rounds == "inf":
factors = [n]
while len(factors) != 0:
n = min(factors)
factors.remove(n)
f = _primefac.pollardRho_brent(n)
if isprime(f):
yield f
else:
factors.append(f)
n //= f
if isprime(n):
yield n
else:
factors.append(n)
return
factors, difficult = [n], []
while len(factors) != 0:
rhocount = 0
n = factors.pop()
try:
g = n
while g == n:
x, c, g = randrange(1, n), randrange(1, n), 1
y = x
while g == 1:
if rhocount >= rho_rounds:
raise Exception
rhocount += 1
x = (x**2 + c) % n
y = (y**2 + c) % n
y = (y**2 + c) % n
g = gcd(x-y, n)
# We now have a nontrivial factor g of n. If we took too long to get here, we're actually at the except statement.
if isprime(g):
yield g
else:
factors.append(g)
n //= g
if isprime(n):
yield n
else:
factors.append(n)
except Exception:
difficult.append(n) # Factoring n took too long. We'll have multifactor chug on it.
factors = difficult
while len(factors) != 0:
n = min(factors)
factors.remove(n)
f = multifactor(n, methods=methods, verbose=verbose, timeout=timeout)
if isprime(f):
yield f
else:
factors.append(f)
n //= f
if isprime(n):
yield n
else:
factors.append(n)
def primefac(n,
trial_limit=1000,
rho_rounds=42000,
verbose=False,
methods=factoring_methods.values()):
from random import randrange
if n < 2:
return
if _primefac.isprime(n):
yield n
return
factors, nroot = [], _primefac.isqrt(n)
# Note that we remove factors of 2 whether the user wants to or not.
for p in _primefac.primegen():
if n % p == 0:
while n % p == 0:
yield p
n //= p
nroot = _primefac.isqrt(n)
if _primefac.isprime(n):
yield n
return
if p > nroot:
if n != 1:
yield n
return
if p >= trial_limit:
break
if _primefac.isprime(n):
yield n
return
if rho_rounds == "inf":
factors = [n]
while len(factors) != 0:
n = min(factors)
factors.remove(n)
f = _primefac.pollardRho_brent(n)
if _primefac.isprime(f):
yield f
else:
factors.append(f)
n //= f
if _primefac.isprime(n):
yield n
else:
factors.append(n)
return
factors, difficult = [n], []
while len(factors) != 0:
rhocount = 0
n = factors.pop()
try:
g = n
while g == n:
x, c, g = randrange(1, n), randrange(1, n), 1
y = x
while g == 1:
if rhocount >= rho_rounds:
raise Exception
rhocount += 1
x = (x**2 + c) % n
y = (y**2 + c) % n
y = (y**2 + c) % n
g = _primefac.gcd(x - y, n)
# We now have a nontrivial factor g of n. If we took too long to
# get here, we're actually at the except statement.
if _primefac.isprime(g):
yield g
else:
factors.append(g)
n //= g
if _primefac.isprime(n):
yield n
else:
factors.append(n)
except Exception:
# Factoring n took too long. We'll have multifactor chug on it.
difficult.append(n)
factors = difficult
while len(factors) != 0:
n = min(factors)
factors.remove(n)
f = multifactor(n, methods=methods, verbose=verbose)
if _primefac.isprime(f):
yield f
else:
factors.append(f)
n //= f
if _primefac.isprime(n):
yield n
else:
factors.append(n)