Compute the 75th percentile of the standard normal distribution with ndtri algorithm

ndtri_75th_percentile.py

# Approximate the median of the standard half-normal distribution by
# computing the 75th percentile of the standard normal distribution using
# the algorithm from the original implementation of scipy.special.ndtri
#
# Based on the code from https://stackoverflow.com/questions/41338539#41338979
# which was based on the original implementation in ndtri.c

s2pi = 2.50662827463100050242E0

P0 = [
    -5.99633501014107895267E1,
    9.80010754185999661536E1,
    -5.66762857469070293439E1,
    1.39312609387279679503E1,
    -1.23916583867381258016E0,
]

Q0 = [
    1,
    1.95448858338141759834E0,
    4.67627912898881538453E0,
    8.63602421390890590575E1,
    -2.25462687854119370527E2,
    2.00260212380060660359E2,
    -8.20372256168333339912E1,
    1.59056225126211695515E1,
    -1.18331621121330003142E0,
]

def polevl(x, coef):
    accum = 0
    for c in coef:
        accum = x * accum + c
    return accum

y0 = 0.75
y = y0
y = y - 0.5
y2 = y * y
x = y + y * (y2 * polevl(y2, P0) / polevl(y2, Q0))
x = x * s2pi
print(x)