/*

 *  R : A Computer Language for Statistical Data Analysis

 *  Copyright (C) 2006 The R Core Team

 *

 *  This program is free software; you can redistribute it and/or modify

 *  it under the terms of the GNU General Public License as published by

 *  the Free Software Foundation; either version 2 of the License, or

 *  (at your option) any later version.

 *

 *  This program is distributed in the hope that it will be useful,

 *  but WITHOUT ANY WARRANTY; without even the implied warranty of

 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

 *  GNU General Public License for more details.

 *

 *  You should have received a copy of the GNU General Public License

 *  along with this program; if not, a copy is available at

 *  https://www.R-project.org/Licenses/

 */

#include "nmath.h"

#include "dpq.h"

double qnbeta(double p, double a, double b, double ncp,

        int lower_tail, int log_p)

{

    const static double accu = 1e-15;

    const static double Eps = 1e-14; /* must be > accu */

    double ux, lx, nx, pp;

#ifdef IEEE_754

    if (ISNAN(p) || ISNAN(a) || ISNAN(b) || ISNAN(ncp))

  return p + a + b + ncp;

#endif

    if (!R_FINITE(a)) ML_WARN_return_NAN;

    if (ncp < 0. || a <= 0. || b <= 0.) ML_WARN_return_NAN;

    R_Q_P01_boundaries(p, 0, 1);

    p = R_DT_qIv(p);

    /* Invert pnbeta(.) :

     * 1. finding an upper and lower bound */

    if(p > 1 - DBL_EPSILON) return 1.0;

    pp = fmin2(1 - DBL_EPSILON, p * (1 + Eps));

    for(ux = 0.5;

  ux < 1 - DBL_EPSILON && pnbeta(ux, a, b, ncp, TRUE, FALSE) < pp;

  ux = 0.5*(1+ux));

    pp = p * (1 - Eps);

    for(lx = 0.5;

  lx > DBL_MIN && pnbeta(lx, a, b, ncp, TRUE, FALSE) > pp;

  lx *= 0.5);

    /* 2. interval (lx,ux)  halving : */

    do {

  nx = 0.5 * (lx + ux);

  if (pnbeta(nx, a, b, ncp, TRUE, FALSE) > p) ux = nx; else lx = nx;

    }

    while ((ux - lx) / nx > accu);

    return 0.5 * (ux + lx);

}