#include "internal.h"

static inline double
erfinv(double x)
{
    /* useful constants */
    static double
      a0 = 1.1975323115670912564578e0, a1 = 4.7072688112383978012285e1,
      a2 = 6.9706266534389598238465e2, a3 = 4.8548868893843886794648e3,
      a4 = 1.6235862515167575384252e4, a5 = 2.3782041382114385731252e4,
      a6 = 1.1819493347062294404278e4, a7 = 8.8709406962545514830200e2,

      b0 = 1.0000000000000000000e0, b1 = 4.2313330701600911252e1,
      b2 = 6.8718700749205790830e2, b3 = 5.3941960214247511077e3,
      b4 = 2.1213794301586595867e4, b5 = 3.9307895800092710610e4,
      b6 = 2.8729085735721942674e4, b7 = 5.2264952788528545610e3,

      c0 = 1.42343711074968357734e0,  c1 = 4.63033784615654529590e0,
      c2 = 5.76949722146069140550e0,  c3 = 3.64784832476320460504e0,
      c4 = 1.27045825245236838258e0,  c5 = 2.41780725177450611770e-1,
      c6 = 2.27238449892691845833e-2, c7 = 7.74545014278341407640e-4,

      d0 = 1.4142135623730950488016887e0,  d1 = 2.9036514445419946173133295e0,
      d2 = 2.3707661626024532365971225e0,  d3 = 9.7547832001787427186894837e-1,
      d4 = 2.0945065210512749128288442e-1, d5 = 2.1494160384252876777097297e-2,
      d6 = 7.7441459065157709165577218e-4, d7 = 1.4859850019840355905497876e-9,

      e0 = 6.65790464350110377720e0,  e1 = 5.46378491116411436990e0,
      e2 = 1.78482653991729133580e0,  e3 = 2.96560571828504891230e-1,
      e4 = 2.65321895265761230930e-2, e5 = 1.24266094738807843860e-3,
      e6 = 2.71155556874348757815e-5, e7 = 2.01033439929228813265e-7,

      f0 = 1.414213562373095048801689e0,  f1 = 8.482908416595164588112026e-1,
      f2 = 1.936480946950659106176712e-1, f3 = 2.103693768272068968719679e-2,
      f4 = 1.112800997078859844711555e-3, f5 = 2.611088405080593625138020e-5,
      f6 = 2.010321207683943062279931e-7, f7 = 2.891024605872965461538222e-15,

      Ln2 = 0.693147180559945309417232121458176568075500134360255254120680009;

    int s;
    double r, z1, z2;

    if(x < 0) {
        s = -1;
        x = -x;
    } else {
        s = +1;
    }

    if(x <= 0.85) {
        r = 0.180625 - 0.25*x*x;
        z1 = ((((((a7*r+a6)*r+a5)*r+a4)*r+a3)*r+a2)*r+a1)*r + a0;
        z2 = ((((((b7*r+b6)*r+b5)*r+b4)*r+b3)*r+b2)*r+b1)*r + b0;
        return s*(x*z1) / z2;
    }
    r = sqrt(Ln2 - log(1.0-x));
    if(r <= 5.0) {
        r -= 1.6;
        z1 = ((((((c7*r+c6)*r+c5)*r+c4)*r+c3)*r+c2)*r+c1)*r + c0;
        z2 = ((((((d7*r+d6)*r+d5)*r+d4)*r+d3)*r+d2)*r+d1)*r + d0;
    } else {
        r -= 5.0;
        z1 = ((((((e7*r+e6)*r+e5)*r+e4)*r+e3)*r+e2)*r+e1)*r + e0;
        z2 = ((((((f7*r+f6)*r+f5)*r+f4)*r+f3)*r+f2)*r+f1)*r + f0;
    }

    return s*z1/z2;
}

double
rng·normal(void)
{
    double f;
    f = rng·random();

    return sqrt(2)*erfinv(2*f-1);
}