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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