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 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
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 testDivisorSum(self):
expected = [
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20,
42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38,
60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120,
72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144,
72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108,
132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]
self.assertEquals([intalg.divisor_sum(i) for i in xrange(1, 101)],
expected)
self.assertEquals([intalg.divisor_sum(intalg.factorize(i))
for i in xrange(1, 101)],
expected)
def testDivisorSum(self):
expected = [
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39,
20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48,
91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72,
98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144,
68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186,
121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144,
120, 252, 98, 171, 156, 217
]
self.assertEquals([intalg.divisor_sum(i) for i in xrange(1, 101)],
expected)
self.assertEquals(
[intalg.divisor_sum(intalg.factorize(i)) for i in xrange(1, 101)],
expected)
def testYieldFactorizeUpto(self):
self.assertEquals(sorted(list(intalg.yield_factorize_upto(100))),
[(i, intalg.factorize(i)) for i in xrange(1, 101)])
def testYieldFactorizeUpto(self):
self.assertEquals(sorted(list(intalg.yield_factorize_upto(100))),
[(i, intalg.factorize(i)) for i in xrange(1, 101)])
