def test_mod_inv(self):
for i in range(TESTS):
a = randint(1, 10000000)
b = randint(1, 10000000)
g = nt.gcd(a, b)
# ensure a, b are relatively prime
a, b = a / g, b / g
ainv = nt.modinv(a, b)
self.assertEqual((a * ainv) % b, 1)
def pollard_rho(n):
def f(x):
ret = pow(x, 2, n) + 1
return 0 if ret == n else ret
x = 2
y = 1
cnt = 10000
while x != y: # and cnt > 0:
cnt -= 1
x = f(x)
y = f(y)
g = nt.gcd(n, abs(x - y))
#print('x = {}, y = {}, g = {}'.format(x, y, g))
if 1 < g and g < n:
#print('iteration: {}'.format(10000-cnt))
return g
x = f(x)
#print('iteration: {}'.format(10000-cnt))
if cnt == 0:
return 'max iteration exceeded'
return 'not found, maybe prime'
def test_gcd(self):
self.assertEqual(nt.gcd(15, 6), 3)
def test_gcd_rand(self):
for i in range(TESTS):
a = randint(1, 10000000)
b = randint(1, 10000000)
g = nt.gcd(a, b)
self.assertEqual(nt.gcd(a / g, b / g), 1)
def test_gcd_one(self):
for i in range(TESTS):
a = randint(1, 10000000)
self.assertEqual(nt.gcd(a, 1), 1)
def test_gcd_rev(self):
for i in range(TESTS):
a = randint(1, 10000000)
b = randint(1, 10000000)
self.assertEqual(nt.gcd(a, b), nt.gcd(b, a))