def gcd(A, B):
A, B = int(A), int(B)
steps = Steps()
while B != A and B != 0:
temp = B
steps.add_mod()
B = A % B
A = temp
return A, steps
def fermats_diff_of_squares_prewrapper(N):
steps = Steps()
factors = []
steps.add_mod()
while N % 2 == 0:
factors.append(2)
N = N / 2
steps.add_mod()
unfactored = [N]
return factors, steps, unfactored
def harts_one_line(N, L=-1):
steps = Steps()
if L == -1:
L = N
for i in xrange(1, L):
steps.add_sqrt(N * i)
s = int(math.ceil(math.sqrt(N * i)))
steps.add_mod()
m = (s * s) % N
isq, isq_steps = is_square(m)
steps.append(isq_steps)
if (isq):
break
steps.add_sqrt(m)
t = math.sqrt(m)
f1, gcd_steps = gcd(s - t, N)
f2 = N / f1
steps.append(gcd_steps)
return f1, f2, steps
def pollards_pminus1(N, B=None, steps=None):
if steps == None:
steps = Steps()
if B == None:
steps.add_cuberoot(N)
B = math.pow(N, 1.0 / 3.0)
primes_list = get_primes()
a, i = 2, 0
a_set = set([])
while True:
pi = primes_list[i]
if pi > B:
break
steps.add_log(B)
steps.add_log(pi)
e = int(math.floor(math.log(B) / math.log(pi)))
steps.add_exp(pi, e)
f = pi**e
steps.add_exp(a, f)
steps.add_mod()
a_hold = powering.power_mod(a, f, N) #(a**f) % N
if a_hold == 0:
break
a = a_hold
a_set.add(a)
i += 1
for a in a_set:
g, g_steps = gcd(a - 1, N)
steps.append(g_steps)
if 1 < g and g < N:
return g, N / g, steps
return None, None, steps
def trial_division(N, when_to_stop=None):
primes_list = get_primes()
m, pi, p = N, 0, 2
steps = Steps()
factors = []
if when_to_stop == None:
when_to_stop = math.sqrt(N)
steps.add_sqrt(N)
while (p <= when_to_stop):
steps.add_mod()
if m % p == 0:
m = m / p
factors.append(p)
else:
pi += 1
p = primes_list[pi]
num_unfactored = 0
if m != 1:
factors.append(m)
if m not in primes_list:
num_unfactored = 1
return factors, steps, num_unfactored