picomath

import math

def rational_approximation(t):

    # Abramowitz and Stegun formula 26.2.23.
    # The absolute value of the error should be less than 4.5 e-4.
    c = [2.515517, 0.802853, 0.010328]
    d = [1.432788, 0.189269, 0.001308]
    numerator = (c[2]*t + c[1])*t + c[0]
    denominator = ((d[2]*t + d[1])*t + d[0])*t + 1.0
    return t - numerator / denominator


def normal_CDF_inverse(p):

    assert p > 0.0 and p < 1

    # See article above for explanation of this section.
    if p < 0.5:
        # F^-1(p) = - G^-1(p)
        return -rational_approximation( math.sqrt(-2.0*math.log(p)) )
    else:
        # F^-1(p) = G^-1(1-p)
        return rational_approximation( math.sqrt(-2.0*math.log(1.0-p)) )