# Rabin fingerprint: k > lg(n*m/e), e is the upper bound on the error probability
# Karp-Rabin fingerprint: <= pi(n(n-m+1))/pi(M)

# 32-bit
M = 2**32-1
k = 31

# 16-bit
# M = 2**16-1
# k = 13

def fpi(a):
    p = Primes()
    a_next = p.next(a)
    i = 0
    jump = 1
    lastdirection = -2
    while(True):
        print(f'{jump:010d}', end='\r')
        # print(f'{i}, {jump}')
        val = p.unrank(i)
        if val == a_next:
            return i # i-1, is the value we search for, but we count from 0, so i is correct
        elif val > a_next:
            if lastdirection == 2:
                # print('mul')
                lastdirection -= 1
                jump *= 2
            else:
                # print('div')
                jump //= 2
            lastdirection += 1
            # print(jump)
            i -= jump
        else:
            if lastdirection == -2:
                # print('mul')
                lastdirection += 1
                jump *= 2
            else:
                # print('div')
                jump //= 2
            lastdirection -= 1
            i += jump

# Rabin fingerprint
# k = lg(n*m/e) <=>
# 2^k = n*m/e <=>
# 2^k/(n*m) = 1/e <=>
# n*m/(2^k) = e

# Karp-Rabin fingerprint
# e = pi(n(n-m+1))/pi(M)

# print(pi(2**32-1))

# e_rabin = n*m/(2^k)

piM = fpi(M)
for m in [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000]:
    for n in [10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000]:
        if m>=n:
            continue
        print(f'(n, m) = ({n}, {m})')
        e_rabin = n*m/(2**k)
        print(f'Rabin: {float(e_rabin):.2e}')
        e_karpr = fpi(n*(n-m+1))/piM
        print(f'KarpR: {float(e_karpr):.2e}')
        print()
        print(f'{e_karpr} >= 1 is {e_karpr >= 1} | {e_rabin} >= 1 is {e_rabin >= 1}')
        if float(e_karpr) >= 1 or float(e_rabin) >= 1:
            break