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 testFactorizeSmall(self):
for n in xrange(1, 100025):
a = list(intalg.yield_slow_factorize(n))
b = intalg.finder_slow_factorize(n)
c = intalg.factorize(n, divisor_finder=intalg.brent)
d = intalg.factorize(n, divisor_finder=intalg.pollard)
assert a == b == c == d, (n, a, b, c, d)
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 testFactorizeSmall(self):
for n in xrange(1, 100025):
a = list(intalg.yield_slow_factorize(n))
b = intalg.finder_slow_factorize(n)
c = intalg.factorize(n, divisor_finder=intalg.brent)
d = intalg.factorize(n, divisor_finder=intalg.pollard)
assert a == b == c == d, (n, a, b, c, d)
def testFactorizeMedium(self):
n = intalg.next_prime(intalg._SMALL_PRIME_LIMIT) ** 2 - 10
limit = n + 20025
while n < limit: # xrange can't take a long (n).
a = list(intalg.yield_slow_factorize(n))
b = intalg.finder_slow_factorize(n)
c = intalg.factorize(n)
c = intalg.factorize(n, divisor_finder=intalg.brent)
d = intalg.factorize(n, divisor_finder=intalg.pollard)
assert a == b == c == d, (n, a, b, c, d)
n += 1
def testFactorizeMedium(self):
n = intalg.next_prime(intalg._SMALL_PRIME_LIMIT)**2 - 10
limit = n + 20025
while n < limit: # xrange can't take a long (n).
a = list(intalg.yield_slow_factorize(n))
b = intalg.finder_slow_factorize(n)
c = intalg.factorize(n)
c = intalg.factorize(n, divisor_finder=intalg.brent)
d = intalg.factorize(n, divisor_finder=intalg.pollard)
assert a == b == c == d, (n, a, b, c, d)
n += 1