74 lines
1.8 KiB
Python
74 lines
1.8 KiB
Python
# Rabin fingerprint: k > lg(n*m/e), e is the upper bound on the error probability
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# Karp-Rabin fingerprint: <= pi(n(n-m+1))/pi(M)
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# 32-bit
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M = 2**32-1
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k = 31
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# 16-bit
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# M = 2**16-1
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# k = 13
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def fpi(a):
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p = Primes()
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a_next = p.next(a)
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i = 0
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jump = 1
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lastdirection = -2
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while(True):
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print(f'{jump:010d}', end='\r')
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# print(f'{i}, {jump}')
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val = p.unrank(i)
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if val == a_next:
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return i # i-1, is the value we search for, but we count from 0, so i is correct
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elif val > a_next:
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if lastdirection == 2:
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# print('mul')
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lastdirection -= 1
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jump *= 2
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else:
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# print('div')
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jump //= 2
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lastdirection += 1
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# print(jump)
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i -= jump
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else:
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if lastdirection == -2:
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# print('mul')
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lastdirection += 1
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jump *= 2
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else:
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# print('div')
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jump //= 2
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lastdirection -= 1
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i += jump
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# Rabin fingerprint
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# k = lg(n*m/e) <=>
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# 2^k = n*m/e <=>
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# 2^k/(n*m) = 1/e <=>
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# n*m/(2^k) = e
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# Karp-Rabin fingerprint
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# e = pi(n(n-m+1))/pi(M)
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# print(pi(2**32-1))
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# e_rabin = n*m/(2^k)
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piM = fpi(M)
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for m in [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000]:
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for n in [10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000]:
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if m>=n:
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continue
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print(f'(n, m) = ({n}, {m})')
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e_rabin = n*m/(2**k)
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print(f'Rabin: {float(e_rabin):.2e}')
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e_karpr = fpi(n*(n-m+1))/piM
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print(f'KarpR: {float(e_karpr):.2e}')
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print()
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print(f'{e_karpr} >= 1 is {e_karpr >= 1} | {e_rabin} >= 1 is {e_rabin >= 1}')
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if float(e_karpr) >= 1 or float(e_rabin) >= 1:
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break
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