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/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000 The R Development 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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *  DESCRIPTION
 *
 *  The quantile function of the Poisson 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 qpois(double p, double lambda, int lower_tail, int log_p)
{
    double mu, sigma, gamma, z, y;
#ifdef IEEE_754
    if (ISNAN(p) || ISNAN(lambda))
    return p + lambda;
#endif
    if(!R_FINITE(lambda))
    ML_ERR_return_NAN;
    R_Q_P01_check(p);
    if(lambda < 0) ML_ERR_return_NAN;

    if (p == R_DT_0) return 0;
    if (p == R_DT_1) return ML_POSINF;

    if(lambda == 0) return 0;

    mu = lambda;
    sigma = sqrt(lambda);
    gamma = sigma;

    /* 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 ML_POSINF;
    }
    /* temporary hack --- FIXME --- */
    if (p + 1.01*DBL_EPSILON >= 1.) return ML_POSINF;

    /* y := approx.value (Cornish-Fisher expansion) :  */
    z = qnorm(p, 0., 1., /*lower_tail*/LTRUE, /*log_p*/LFALSE);
    y = floor(mu + sigma * (z + gamma * (z*z - 1) / 6) + 0.5);

    z = ppois(y, lambda, /*lower_tail*/LTRUE, /*log_p*/LFALSE);

    /* fuzz to ensure left continuity; 1 - 1e-7 may lose too much : */
    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 */
    for(;;) {
        if(y == 0 ||
           (z = ppois(y - 1, lambda, /*l._t.*/LTRUE, /*log_p*/LFALSE)) < p)
        return y;
        y = y - 1;
    }
    }
    else {      /* search to the right */
    for(;;) {
        y = y + 1;
        if((z = ppois(y, lambda, /*l._t.*/LTRUE, /*log_p*/LFALSE)) >= p)
        return y;
    }
    }
}