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# Rewritten code from /r2/r2/lib/db/_sorts.pyx
from math import sqrt

def _confidence(ups, downs):
    n = ups + downs

    if n == 0:
        return 0

    z = 1.281551565545
    p = float(ups) / n

    left = p + 1/(2*n)*z*z
    right = z*sqrt(p*(1-p)/n + z*z/(4*n*n))
    under = 1+1/n*z*z

    return (left - right) / under

def confidence(ups, downs):
    if ups + downs == 0:
        return 0
    else:
        return _confidence(ups, downs)