Port of cephes ``ndtri.c``: inverse normal distribution function.

    See https://github.com/jeremybarnes/cephes/blob/master/cprob/ndtri.c

def _ndtri(y):
    """
    Port of cephes ``ndtri.c``: inverse normal distribution function.

    See https://github.com/jeremybarnes/cephes/blob/master/cprob/ndtri.c
    """
    # approximation for 0 <= abs(z - 0.5) <= 3/8
    P0 = [
        -5.99633501014107895267E1,
        9.80010754185999661536E1,
        -5.66762857469070293439E1,
        1.39312609387279679503E1,
        -1.23916583867381258016E0,
    ]

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

    # Approximation for interval z = sqrt(-2 log y ) between 2 and 8
    # i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
    P1 = [
        4.05544892305962419923E0,
        3.15251094599893866154E1,
        5.71628192246421288162E1,
        4.40805073893200834700E1,
        1.46849561928858024014E1,
        2.18663306850790267539E0,
        -1.40256079171354495875E-1,
        -3.50424626827848203418E-2,
        -8.57456785154685413611E-4,
    ]

    Q1 = [
        1.57799883256466749731E1,
        4.53907635128879210584E1,
        4.13172038254672030440E1,
        1.50425385692907503408E1,
        2.50464946208309415979E0,
        -1.42182922854787788574E-1,
        -3.80806407691578277194E-2,
        -9.33259480895457427372E-4,
    ]

    # Approximation for interval z = sqrt(-2 log y ) between 8 and 64
    # i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
    P2 = [
        3.23774891776946035970E0,
        6.91522889068984211695E0,
        3.93881025292474443415E0,
        1.33303460815807542389E0,
        2.01485389549179081538E-1,
        1.23716634817820021358E-2,
        3.01581553508235416007E-4,
        2.65806974686737550832E-6,
        6.23974539184983293730E-9,
    ]

    Q2 = [
        6.02427039364742014255E0,
        3.67983563856160859403E0,
        1.37702099489081330271E0,
        2.16236993594496635890E-1,
        1.34204006088543189037E-2,
        3.28014464682127739104E-4,
        2.89247864745380683936E-6,
        6.79019408009981274425E-9,
    ]

    sign_flag = 1

    if y > (1 - EXP_NEG2):
        y = 1 - y
        sign_flag = 0

    # Shortcut case where we don't need high precision
    # between -0.135 and 0.135
    if y > EXP_NEG2:
        y -= 0.5
        y2 = y ** 2
        x = y + y * (y2 * _polevl(y2, P0, 4) / _p1evl(y2, Q0, 8))
        x = x * ROOT_2PI
        return x

    x = math.sqrt(-2.0 * math.log(y))
    x0 = x - math.log(x) / x

    z = 1.0 / x
    if x < 8.0:                 # y > exp(-32) = 1.2664165549e-14
        x1 = z * _polevl(z, P1, 8) / _p1evl(z, Q1, 8)
    else:
        x1 = z * _polevl(z, P2, 8) / _p1evl(z, Q2, 8)

    x = x0 - x1
    if sign_flag != 0:
        x = -x

    return x