def test_small_negative(self):
self.assertEqual(factorize(-1), {-1: 1})
self.assertEqual(factorize(-2), {-1: 1, 2: 1})
self.assertEqual(factorize(-3), {-1: 1, 3: 1})
self.assertEqual(factorize(-4), {-1: 1, 2: 2})
self.assertEqual(factorize(-5), {-1: 1, 5: 1})
self.assertEqual(factorize(-6), {-1: 1, 2: 1, 3: 1})
self.assertEqual(factorize(-7), {-1: 1, 7: 1})
self.assertEqual(factorize(-8), {-1: 1, 2: 3})
self.assertEqual(factorize(-9), {-1: 1, 3: 2})
self.assertEqual(factorize(-10), {-1: 1, 2: 1, 5: 1})
def test_small_negative():
assertEqual(factorize(-1), {-1: 1})
assertEqual(factorize(-2), {-1: 1, 2: 1})
assertEqual(factorize(-3), {-1: 1, 3: 1})
assertEqual(factorize(-4), {-1: 1, 2: 2})
assertEqual(factorize(-5), {-1: 1, 5: 1})
assertEqual(factorize(-6), {-1: 1, 2: 1, 3: 1})
assertEqual(factorize(-7), {-1: 1, 7: 1})
assertEqual(factorize(-8), {-1: 1, 2: 3})
assertEqual(factorize(-9), {-1: 1, 3: 2})
assertEqual(factorize(-10), {-1: 1, 2: 1, 5: 1})
def test_small():
assert factorize(1) == {1: 1}
assert factorize(2) == {2: 1}
assert factorize(3) == {3: 1}
assert factorize(4) == {2: 2}
assert factorize(5) == {5: 1}
assert factorize(6) == {2: 1, 3: 1}
assert factorize(7) == {7: 1}
assert factorize(8) == {2: 3}
assert factorize(9) == {3: 2}
assert factorize(10) == {2: 1, 5: 1}
def test_small(self):
self.assertEqual(factorize(1), {1: 1})
self.assertEqual(factorize(2), {2: 1})
self.assertEqual(factorize(3), {3: 1})
self.assertEqual(factorize(4), {2: 2})
self.assertEqual(factorize(5), {5: 1})
self.assertEqual(factorize(6), {2: 1, 3: 1})
self.assertEqual(factorize(7), {7: 1})
self.assertEqual(factorize(8), {2: 3})
self.assertEqual(factorize(9), {3: 2})
self.assertEqual(factorize(10), {2: 1, 5: 1})
def test_small_negative():
assert factorize(-1) == {-1: 1}
assert factorize(-2) == {-1: 1, 2: 1}
assert factorize(-3) == {-1: 1, 3: 1}
assert factorize(-4) == {-1: 1, 2: 2}
assert factorize(-5) == {-1: 1, 5: 1}
assert factorize(-6) == {-1: 1, 2: 1, 3: 1}
assert factorize(-7) == {-1: 1, 7: 1}
assert factorize(-8) == {-1: 1, 2: 3}
assert factorize(-9) == {-1: 1, 3: 2}
assert factorize(-10) == {-1: 1, 2: 1, 5: 1}
def test_small():
assertEqual(factorize(1), {1: 1})
assertEqual(factorize(2), {2: 1})
assertEqual(factorize(3), {3: 1})
assertEqual(factorize(4), {2: 2})
assertEqual(factorize(5), {5: 1})
assertEqual(factorize(6), {2: 1, 3: 1})
assertEqual(factorize(7), {7: 1})
assertEqual(factorize(8), {2: 3})
assertEqual(factorize(9), {3: 2})
assertEqual(factorize(10), {2: 1, 5: 1})
def test_sqrt_composite_all(self):
print "\nTesting all residues by small composite modules"
for n in [
10,
30,
50,
99,
100,
655,
1025,
1337,
7 ** 3 * 3,
2 ** 6 * 13,
2 ** 4 * 3 ** 3 * 5,
3 * 3 * 5 * 7,
1024,
]:
f = factorize(n)
print " Testing %s = %s" % (n, f)
for x in xrange(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
self.check_valid_sqrt_composite(None, a, f)
self.check_jacobi(a, n, is_sqrt)
self.assertTrue(has_sqrtmod(a, f))
self.check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_all():
print("\nTesting all residues by small composite modules")
ns = [
10,
30,
50,
99,
100,
655,
1025,
1337,
7**3 * 3,
2**6 * 13,
2**4 * 3**3 * 5,
3 * 3 * 5 * 7,
1024,
]
for n in ns:
f = factorize(n)
print(" Testing %s = %s" % (n, f))
for x in range(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
check_valid_sqrt_composite(None, a, f)
check_jacobi(a, n, is_sqrt)
assert has_sqrtmod(a, f)
check_valid_sqrt_composite(x, a, f)
def test_errors():
with pytest.raises(TypeError):
factorize("1")
with pytest.raises(TypeError):
factorize(10.3)
with pytest.raises(TypeError):
factorize(complex(10, 3))
with pytest.raises(TypeError):
factorize((2, 3))
def test_samples():
test_lists = [
set([(3, 1), (5, 5), (19, 2), (1993, 1), (37, 1), (2, 4)]),
set([(2, 100), (3, 50), (5, 20), (7, 15), (11, 10), (13, 5)]),
set([(1993, 5)]),
set([(2, 4000)]),
]
for primes_list in test_lists:
while primes_list:
n = reduce(lambda a, b: a * (b[0] ** b[1]), primes_list, 1)
primes_list_test = set(sorted(factorize(n).items()))
assertEqual(primes_list, primes_list_test)
primes_list.pop()
def test_samples(self):
test_lists = [
set([(3, 1), (5, 5), (19, 2), (1993, 1), (37, 1), (2, 4)]),
set([(2, 100), (3, 50), (5, 20), (7, 15), (11, 10), (13, 5)]),
set([(1993, 5)]),
set([(2, 4000)]),
]
for primes_list in test_lists:
while primes_list:
n = reduce(lambda a, b: a * (b[0]**b[1]), primes_list, 1)
primes_list_test = set(sorted(factorize(n).items()))
self.assertEqual(primes_list, primes_list_test)
primes_list.pop()
def test_sqrt_composite_rand():
print("\nTesting all residues by random composite modules")
for size, ntries in [(2, 2), (3, 3), (5, 10), (7, 20), (10, 20)]:
for i in xrange(ntries):
n = randint_bits(size)
f = factorize(n)
print(" Testing %s-bit number: %s..." % (size, str(n)[:32]))
for x in xrange(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
check_valid_sqrt_composite(None, a, f)
check_jacobi(a, n, is_sqrt)
assertTrue(has_sqrtmod(a, f))
check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_rand(self):
print "\nTesting all residues by random composite modules"
for size, ntries in [(2, 2), (3, 3), (5, 10), (7, 20), (10, 20)]:
for i in xrange(ntries):
n = randint_bits(size)
f = factorize(n)
print " Testing %s-bit number: %s..." % (size, str(n)[:32])
for x in xrange(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
self.check_valid_sqrt_composite(None, a, f)
self.check_jacobi(a, n, is_sqrt)
self.assertTrue(has_sqrtmod(a, f))
self.check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_rand_rand(self):
print("\nTesting random residues by random composite modules")
for size, ntries in [(10, 20), (20, 20), (24, 20), (30, 20)]:
for i in xrange(ntries):
n = randint_bits(size)
f = factorize(n)
print(" Testing %s-bit number: %s..." % (size, str(n)[:32]))
for j in xrange(30):
x = random.randint(0, n - 1)
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
self.check_valid_sqrt_composite(None, a, f)
self.check_jacobi(a, n, is_sqrt)
self.assertTrue(has_sqrtmod(a, f))
self.check_valid_sqrt_composite(x, a, f)
def test_sqrt_composite_all(self):
print "\nTesting all residues by small composite modules"
for n in [
10, 30, 50, 99, 100, 655, 1025, 1337, 7**3 * 3, 2**6 * 13,
2**4 * 3**3 * 5, 3 * 3 * 5 * 7, 1024
]:
f = factorize(n)
print " Testing %s = %s" % (n, f)
for x in xrange(n):
a = pow(x, 2, n)
is_sqrt = has_sqrtmod(a, f)
if is_sqrt:
self.check_valid_sqrt_composite(None, a, f)
self.check_jacobi(a, n, is_sqrt)
self.assertTrue(has_sqrtmod(a, f))
self.check_valid_sqrt_composite(x, a, f)
def test_factorial_mod():
print("\nTesting factorial mod prime powers")
for p, max_e in [(2, 8), (3, 4), (5, 3), (7, 3), (11, 2)]:
print(" prime %s pow up to %s" % (repr(p), repr(max_e)))
for i in range(250):
n = random.randint(1, 3000)
e = random.randint(1, max_e)
my = factorial_mod(n, {p: e})
real = factorial(n) % (p**e)
assert my == real
print("\nTesting factorial mod small composites")
for i in range(150):
n = random.randint(1, 8000)
x = random.randint(0, n * 2)
my = factorial_mod(x, factorize(n))
real = factorial(x) % n
assert my == real
def test_zero():
assert factorize(0) == {0: 1}
def test_zero(self):
self.assertEqual(factorize(0), {0: 1})
def test_zero():
assertEqual(factorize(0), {0: 1})
