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/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000, 2002 The R Development Core Team
 *  Copyright (C) 2003--2004 The R Foundation
 *
 *  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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *  DESCRIPTION
 *
 *  The quantile function of the binomial distribution.
 *
 *  METHOD
 *
 *  Uses the Cornish-Fisher Expansion to include a skewness
 *  correction to a normal approximation.  This gives an
 *  initial value which never seems to be off by more than
 *  1 or 2.  A search is then conducted of values close to
 *  this initial start point.
 */
#include "nmath.h"
#include "dpq.h"


double qbinom(double p, double n, double pr, int lower_tail, int log_p)
{
    double q, mu, sigma, gamma, z, y;

#ifdef IEEE_754
    if (ISNAN(p) || ISNAN(n) || ISNAN(pr))
    return p + n + pr;
#endif
    if(!R_FINITE(p) || !R_FINITE(n) || !R_FINITE(pr))
    ML_ERR_return_NAN;
    R_Q_P01_check(p);

    if(n != floor(n + 0.5)) ML_ERR_return_NAN;
    if (pr < 0 || pr > 1 || n < 0)
    ML_ERR_return_NAN;

    if (pr == 0. || n == 0) return 0.;
    if (p == R_DT_0) return 0.;
    if (p == R_DT_1) return n;

    q = 1 - pr;
    if(q == 0.) return n; /* covers the full range of the distribution */
    mu = n * pr;
    sigma = sqrt(n * pr * q);
    gamma = (q - pr) / sigma;

#ifdef DEBUG_qbinom
    REprintf("qbinom(p=%7g, n=%g, pr=%7g, l.t.=%d, log=%d): sigm=%g, gam=%g\n",
         p,n,pr, lower_tail, log_p, sigma, gamma);
#endif
    /* Note : "same" code in qpois.c, qbinom.c, qnbinom.c --
     * FIXME: This is far from optimal [cancellation for p ~= 1, etc]: */
    if(!lower_tail || log_p) {
    p = R_DT_qIv(p); /* need check again (cancellation!): */
    if (p == 0.) return 0.;
    if (p == 1.) return n;
    }
    /* temporary hack --- FIXME --- */
    if (p + 1.01*DBL_EPSILON >= 1.) return n;

    /* y := approx.value (Cornish-Fisher expansion) :  */
    z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
    y = floor(mu + sigma * (z + gamma * (z*z - 1) / 6) + 0.5);
    if(y > n) /* way off */ y = n;

#ifdef DEBUG_qbinom
    REprintf("  new (p,1-p)=(%7g,%7g), z=qnorm(..)=%7g, y=%5g\n", p, 1-p, z, y);
#endif
    z = pbinom(y, n, pr, /*lower_tail*/TRUE, /*log_p*/FALSE);

    /* fuzz to ensure left continuity: */
    p *= 1 - 64*DBL_EPSILON;

/*-- Fixme, here y can be way off --
  should use interval search instead of primitive stepping down or up */

#ifdef maybe_future
    if((lower_tail && z >= p) || (!lower_tail && z <= p)) {
#else
    if(z >= p) {
#endif
            /* search to the left */
#ifdef DEBUG_qbinom
    REprintf("\tnew z=%7g >= p = %7g  --> search to left (y--) ..\n", z,p);
#endif
    for(;;) {
        if(y == 0 ||
           (z = pbinom(y - 1, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p)
        return y;
        y = y - 1;
    }
    }
    else {      /* search to the right */
#ifdef DEBUG_qbinom
    REprintf("\tnew z=%7g < p = %7g  --> search to right (y++) ..\n", z,p);
#endif
    for(;;) {
        y = y + 1;
        if(y == n ||
           (z = pbinom(y, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) >= p)
        return y;
    }
    }
}