def testFactorizeLargePrimes(self):
random_obj = intalg.MiniIntRandom(42)
for ps in ([1073741827, 1152921504606847009],
[34359738421, 1180591620717411303449],
[7, 1763668414462081],
[100003],
[10000000019],
[1000000000039], # Slow but tolerable.
[10000000019] * 9,
[1000000007] * 10,
[1000000007] + [1000000009] * 2 + [1000000021] * 3):
n = 1
for p in ps:
n *= p
divisors = set() # All divisors based on ps, except for 1.
for i in xrange(1, 1 << len(ps)):
r = 1
for j in xrange(0, len(ps)):
if i & (1 << j):
r *= ps[j]
divisors.add(r)
r = intalg.brent(n, random_obj)
assert r in divisors
r = intalg.pollard(n, random_obj)
assert r in divisors
sps = intalg.finder_slow_factorize(n)
assert sps == ps, (n, sps, ps)
sps = intalg.factorize(n)
assert sps == ps, (n, sps, ps)
def testFactorizeLargePrimes(self):
random_obj = intalg.MiniIntRandom(42)
for ps in (
[1073741827, 1152921504606847009],
[34359738421, 1180591620717411303449],
[7, 1763668414462081],
[100003],
[10000000019],
[1000000000039], # Slow but tolerable.
[10000000019] * 9,
[1000000007] * 10,
[1000000007] + [1000000009] * 2 + [1000000021] * 3):
n = 1
for p in ps:
n *= p
divisors = set() # All divisors based on ps, except for 1.
for i in xrange(1, 1 << len(ps)):
r = 1
for j in xrange(0, len(ps)):
if i & (1 << j):
r *= ps[j]
divisors.add(r)
r = intalg.brent(n, random_obj)
assert r in divisors
r = intalg.pollard(n, random_obj)
assert r in divisors
sps = intalg.finder_slow_factorize(n)
assert sps == ps, (n, sps, ps)
sps = intalg.factorize(n)
assert sps == ps, (n, sps, ps)
def testPollardComposite(self):
random_obj = intalg.MiniIntRandom(42)
for n in intalg.yield_composites():
if n > 100000:
break
b = intalg.pollard(n, random_obj)
assert b > 1
assert b <= n
self.assertEquals(0, n % b, (b, n))
def testPollardComposite(self):
random_obj = intalg.MiniIntRandom(42)
for n in intalg.yield_composites():
if n > 100000:
break
b = intalg.pollard(n, random_obj)
assert b > 1
assert b <= n
self.assertEquals(0, n % b, (b, n))
def testPollardPrime(self):
random_obj = intalg.MiniIntRandom(42)
for n in intalg.primes_upto(100000):
b = intalg.pollard(n, random_obj)
self.assertEquals(b, n)
def testPollardPrime(self):
random_obj = intalg.MiniIntRandom(42)
for n in intalg.primes_upto(100000):
b = intalg.pollard(n, random_obj)
self.assertEquals(b, n)
