ndtri

Inverse of Normal distribution function.

SYNOPSIS:

double x, y, ndtri();
x = ndtri(y);

DESCRIPTION:

Returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.
For small arguments 0 < y < exp(-2), the program computes z = sqrt(-2.0 * log(y)); then the approximation is x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
There are two rational functions P/Q, one for 0 < y < exp(-32) and the other for y up to exp(-2).
For larger arguments, w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).

ACCURACY:

                      Relative error:
arithmetic   domain        # trials      peak         rms
    DEC      0.125, 1         5500       9.5e-17     2.1e-17
    DEC      6e-39, 0.135     3500       5.7e-17     1.3e-17
    IEEE     0.125, 1        20000       7.2e-16     1.3e-16
    IEEE     3e-308, 0.135   50000       4.6e-16     9.8e-17

ERROR MESSAGES:

message     condition    value returned
domain       x <= 0        -MAXNUM
domain       x >= 1         MAXNUM