/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-2002 the R Development Core Team
 *
 *  Merge in to MAGRO:
 *  Copyright (C) 2010 Wataru Uda 
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 *  SYNOPSIS
 *
 *    #include <nmath.h>
 *    double exp_rand(NMATH_STATE *state);
 *
 *  DESCRIPTION
 *
 *    Random variates from the standard exponential distribution.
 *
 *  REFERENCE
 *
 *    Ahrens, J.H. and Dieter, U. (1972).
 *    Computer methods for sampling from the exponential and
 *    normal distributions.
 *    Comm. ACM, 15, 873-882.
 */

#include "nmath.h"

/* q[k-1] = sum(log(2)^k / k!)  k=1,..,n, */
/* The highest n (here 8) is determined by q[n-1] = 1.0 */
/* within standard precision */
const double q[] = 
{
    0.6931471805599453,
    0.9333736875190459,
    0.9888777961838675,
    0.9984959252914960,
    0.9998292811061389,
    0.9999833164100727,
    0.9999985691438767,
    0.9999998906925558,
    0.9999999924734159,
    0.9999999995283275,
    0.9999999999728814,
    0.9999999999985598,
    0.9999999999999289,
    0.9999999999999968,
    0.9999999999999999,
    1.0000000000000000
};

double exp_rand(NMATH_STATE *state)
{
    double a, u, ustar, umin;
    int i;

    a = 0.0;
    /* precaution if u = 0 is ever returned */
    u = unif_rand(state);
    while (u <= 0.0 || u >= 1.0) u = unif_rand(state);
    for (; ; )
    {
        u += u;
        if (u > 1.0)
            break;
        a += q[0];
    }
    u -= 1.0;

    if (u <= q[0])
        return a + u;

    i = 0;
    ustar = unif_rand(state);
    umin = ustar;
    do
    {
        ustar = unif_rand(state);
        if (ustar < umin)
            umin = ustar;
        i++;
    } while (u > q[i]);
    return a + umin * q[0];
}

