98 lines
3.6 KiB
Python
98 lines
3.6 KiB
Python
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from random import randint
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F = GF(2)
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PR = PolynomialRing(F, 'x')
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k = 31
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P = PR.irreducible_element(k)
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m = 100
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# Test the calculation for moving the left edge of the sliding window
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for _ in range(1):
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q = tuple(randint(0, 1) for _ in range(m))
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for i in range(1, m+1):
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for j in range(i+1, m+1):
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assert (PR(q[:i]) % P) == (PR(q) % P) - (PR(f'x^{i}')*PR(q[i:]) % P)
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# Moving the right side of the window is as described in the Rabin Fingerprint article
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# Next step (TODO)
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# 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)
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# 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)
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# m = len(pattern)
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# s_period = tuple(list(period)+[0]*(m-len(period)))
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# pattern_1 = (1)
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# period_1 = (1)
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# s_period_1 = tuple(list(period_1)+[0]*(m-len(period_1)))
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# pattern_2 = (1,0)
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# period_2 = (1,0)
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# s_period_2 = tuple(list(period_2)+[0]*(m-len(period_2)))
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# pattern_4 = (1,0,1,1)
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# period_4 = (1,0,1)
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# s_period_4 = tuple(list(period_4)+[0]*(m-len(period_4)))
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# pattern_8 = (1,0,1,1,1,1,0,1)
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# period_8 = (1,0,1,1,1)
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# s_period_8 = tuple(list(period_8)+[0]*(m-len(period_8)))
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# pattern_16 = (1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,1)
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# period_16 = (1,0,1,1,1,1,0,1,1,0,1,0)
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# s_period_16 = tuple(list(period_16)+[0]*(m-len(period_16)))
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# for i in range(len(pattern)-len(pattern_4)-len(period_4)):
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# 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)
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# 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)
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# Does the bits of a prime number correspond to the coefficients of an irreducible polynomial?
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k = 31
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reducible = 0
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irreducible = 0
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for p in Primes()[200000000:200010000]:#[100000:100000]:
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# for p in range(2147483648,2147483648+10000):
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poly = PR(tuple(bin(p)[2:][::-1]))
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# print(f'{poly.degree()}')
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if poly.degree() > k:
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break
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if poly.degree() != k:
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continue
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irr = poly.is_irreducible()
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# print(f'The polynomial {poly}, corresponding to the prime {p}, being an irreducible polynomial is {irr}.')
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if irr:
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irreducible += 1
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else:
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reducible += 1
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print(f'{irreducible}/{reducible+irreducible} of the primes correspond to irreducible polynomials. That is {float(irreducible/(reducible+irreducible))*100}%')
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progress = 0
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the_same = 0
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different = 0
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for p in Primes()[200000000:200010000]:
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progress += 1
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print(f'\r{progress}/10000', end='')
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p_poly = PR(tuple(bin(p)[2:][::-1]))
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if not p_poly.is_irreducible():
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continue
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# i = p + randint(1,2**29)
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i = p + randint(1,p-1)
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# print(f'{i}, {p}, {2*p}, {i%p}')
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i_poly = PR(tuple(bin(i)[2:][::-1]))
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i_mod_p = i % p
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i_mod_p_poly = PR(tuple(bin(i_mod_p)[2:][::-1]))
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# print(f'i_poly: {i_poly}')
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# print(f'p_poly: {p_poly}')
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# print(f'i_mod_p_poly: {i_mod_p_poly}')
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if i_mod_p_poly == i_poly % p_poly:
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the_same += 1
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else:
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different += 1
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# if not i_mod_p_poly == i_poly - (p_poly - PR(f'x^{p_poly.degree()}')):
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# if not i_mod_p_poly == i_poly % p_poly:
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# print()
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# print('ERROR')
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# print(i_mod_p_poly)
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# # print(i_poly - (p_poly - PR(f'x^{p_poly.degree()}')))
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# print(i_poly % p_poly)
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# break
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# assert i_mod_p_poly == i_poly - (p_poly - PR(f'x^{p_poly.degree()}'))
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print()
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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}%')
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