#include "xlisp.h"
#include "xlstat.h"

#define TWOVRPI 0.636619772367581343
#define HALF_PI 1.5707963268
#define EPSILON .000001

/* CACM Algorithm 395, by G. W. Hill */

VOID studentbase P3C(double *, x, double *, df, double *, cdf)
{
  double t, y, b, a, z, j, n;

  n = *df;
  z = 1.0;
  t = (*x) * (*x);
  y = t / n;
  b = 1.0 + y;
 
  if (n > floor(n) || (n >= 20 && t < n) || (n > 20)) {
    if (n < 2.0 && n != 1.0) {
      /* beta integral aproximation for small df */
      double  da = 0.5, db = 0.5 * n, dx, dp;
      int ia = 0, ib = floor(db);
  
      dx = db / (db + da * t);
      betabase(&dx, &db, &da, &ib, &ia, &dp);
      *cdf = (*x >= 0) ? 1.0 - .5 * dp : .5 * dp;
    }
    else {
      /* asymptotic series for large or non-integer df */
      if(y > EPSILON) y = log(b);
      a = n - 0.5;
      b = 48.0 * a * a;
      y = a * y;
      y = (((((-0.4 * y - 3.3) * y - 24.0) * y - 85.5)
            / (0.8 * y * y + 100.0 + b) + y + 3.0) / b + 1.0) * sqrt(y);

      y = -1.0 * y;
      normbase(&y, cdf);
      if (*x > 0.0) *cdf = 1.0 - *cdf;
    }
  }
  else {
    /* nested summation of cosine series */
    if (n < 20 && t < 4.0) {
      a = y = sqrt(y);
      if(n == 1.0) a = 0.0;
    }
    else {
      a = sqrt(b);
      y = a * n;
      for(j = 2; fabs(a - z) > EPSILON; j += 2.0) {
        z = a;
        y = (y * (j - 1)) / (b * j);
        a = a + y / (n + j);
      }
      n += 2.0;
      z = y = 0.0;
      a = -a;
    }
    for(n = n - 2.0; n > 1.0; n -= 2.0) a = ((n - 1.0) / (b * n)) * a + y;
    a = (fabs(n) < EPSILON) ? a/sqrt(b) : TWOVRPI * (atan(y) + a / b);
    *cdf = z - a;
    if(*x > 0.0) *cdf = 1.0 - 0.5 * *cdf;
    else *cdf = 0.5 * *cdf;
  }
}

/* CACM Algorithm 396, by G. W. Hill */

double ppstudent P3C(double, pp, double, n, int *, ifault)
{
  double sq, p, a, b, c, d, x, y;

  /* convert to double upper tailed probability */
  p = (pp < 0.5) ? 2.0 * pp : 2.0 * (1.0 - pp);

  if (n <= 3.0) {
    if (n == 1) sq = tan(HALF_PI * (1.0 - p));
    else if (n == 2.0) sq = sqrt(2.0 / (p * (2.0 - p)) - 2.0);
    else {
      sq = ppbeta(p, 0.5 * n, 0.5, ifault);
      if (sq != 0.0) sq = sqrt((n / sq) - n);
    }
  }
  else {
    a = 1.0 / (n - 0.5);
    b = 48.0 / (a * a);
    c = ((20700.0 * a / b - 98.0) * a - 16) * a + 96.36;
    d = ((94.5 / (b + c) - 3.0) / b + 1.0) * sqrt(a * HALF_PI) * n;
    x = d * p;
    y = pow(x, 2.0 / n);
    if (y > 0.05 + a) {
      /* asymptotic inverse expansion about normal */
      x = ppnd(0.5 * p, ifault);
      y = x * x;
      if (n < 5) c = c + 0.3 * (n - 4.5) * (x + 0.6);
      c = (((0.05 * d * x - 5.0) * x - 7.0) * x - 2.0) * x + b + c;
      y = (((((0.4 * y + 6.3) * y + 36.0) * y + 94.5) / c - y - 3.0) / b
           + 1.0) * x;
      y = a * y * y;
      y = (y > .002) ? exp(y) - 1.0 : 0.5 * y * y + y;
    }
    else {
      y = ((1.0 / (((n + 6.0) / (n * y) - 0.089 * d - 0.822)
                   * (n + 2.0) * 3.0) + 0.5 / (n + 4.0)) * y - 1.0)
        * (n + 1.0) / (n + 2.0) + 1.0 / y;
    }
    sq = sqrt(n * y);
  }

  /* decode based on tail */
  if (pp < 0.5) sq = -sq;
  return(sq);
}