from random import randint

F = GF(2)
PR = PolynomialRing(F, 'x')
k = 31
P = PR.irreducible_element(k)
m = 100

# Test the calculation for moving the left edge of the sliding window
for _ in range(1):
    q = tuple(randint(0, 1) for _ in range(m))
    for i in range(1, m+1):
        for j in range(i+1, m+1):
            assert (PR(q[:i]) % P) == (PR(q) % P) - (PR(f'x^{i}')*PR(q[i:]) % P)

# Moving the right side of the window is as described in the Rabin Fingerprint article

# Next step (TODO)
# pattern     = (1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1)
# period      = (1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0)
# m           = len(pattern)
# s_period    = tuple(list(period)+[0]*(m-len(period)))
# pattern_1   = (1)
# period_1    = (1)
# s_period_1  = tuple(list(period_1)+[0]*(m-len(period_1)))
# pattern_2   = (1,0)
# period_2    = (1,0)
# s_period_2  = tuple(list(period_2)+[0]*(m-len(period_2)))
# pattern_4   = (1,0,1,1)
# period_4    = (1,0,1)
# s_period_4  = tuple(list(period_4)+[0]*(m-len(period_4)))
# pattern_8   = (1,0,1,1,1,1,0,1)
# period_8    = (1,0,1,1,1)
# s_period_8  = tuple(list(period_8)+[0]*(m-len(period_8)))
# pattern_16  = (1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1)
# period_16   = (1,0,1,1,1,1,0,1,1,0,1,0)
# s_period_16 = tuple(list(period_16)+[0]*(m-len(period_16)))

# for i in range(len(pattern)-len(pattern_4)-len(period_4)):
#     assert PR(pattern[i+len(period_4):i+len(pattern_4)+len(period_4)]) == PR(pattern[i:i+len(pattern_4)] + pattern[i+len(pattern_4):i+len(pattern_4)+len(period_4)]) - PR(s_period_4)
    # assert PR(pattern[i+len(period_4):i+len(pattern_4)+len(period_4)]) == pattern[i-len(period_4):i+len(pattern_4)-len(period_4)]+pattern[i+len(pattern_4)-len(period_4):i+len(pattern_4)-len(period_4)] - PR(s_period_4)

# Does the bits of a prime number correspond to the coefficients of an irreducible polynomial?
k = 31
reducible = 0
irreducible = 0
for p in Primes()[200000000:200010000]:#[100000:100000]:
# for p in range(2147483648,2147483648+10000):
    poly = PR(tuple(bin(p)[2:][::-1]))
    # print(f'{poly.degree()}')
    if poly.degree() > k:
        break
    if poly.degree() != k:
        continue
    irr = poly.is_irreducible()
    # print(f'The polynomial {poly}, corresponding to the prime {p}, being an irreducible polynomial is {irr}.')
    if irr:
        irreducible += 1
    else:
        reducible += 1

print(f'{irreducible}/{reducible+irreducible} of the primes correspond to irreducible polynomials. That is {float(irreducible/(reducible+irreducible))*100}%')

progress = 0
the_same = 0
different = 0
for p in Primes()[200000000:200010000]:
    progress += 1
    print(f'\r{progress}/10000', end='')
    p_poly = PR(tuple(bin(p)[2:][::-1]))
    if not p_poly.is_irreducible():
        continue
    # i = p + randint(1,2**29)
    i = p + randint(1,p-1)
    # print(f'{i}, {p}, {2*p}, {i%p}')
    i_poly = PR(tuple(bin(i)[2:][::-1]))
    i_mod_p = i % p
    i_mod_p_poly = PR(tuple(bin(i_mod_p)[2:][::-1]))
    # print(f'i_poly: {i_poly}')
    # print(f'p_poly: {p_poly}')
    # print(f'i_mod_p_poly: {i_mod_p_poly}')
    if i_mod_p_poly == i_poly % p_poly:
        the_same += 1
    else:
        different += 1
    # if not i_mod_p_poly == i_poly - (p_poly - PR(f'x^{p_poly.degree()}')):
    # if not i_mod_p_poly == i_poly % p_poly:
    #     print()
    #     print('ERROR')
    #     print(i_mod_p_poly)
    #     # print(i_poly - (p_poly - PR(f'x^{p_poly.degree()}')))
    #     print(i_poly % p_poly)
    #     break
    # assert i_mod_p_poly == i_poly - (p_poly - PR(f'x^{p_poly.degree()}'))

print()
print(f'{the_same}/{the_same+different} are the same as if we did polynomial calculations. This is {float(the_same/(the_same+different))*100}%')