/* rng/cmrg.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough

 * 

 * 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 3 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.

 */

#include <config.h>

#include <stdlib.h>

#include <gsl/gsl_rng.h>

/* This is a combined multiple recursive generator. The sequence is,

   z_n = (x_n - y_n) mod m1

   where the two underlying generators x and y are,

   x_n = (a_{1} x_{n-1} + a_{2} x_{n-2} + a_{3} x_{n-3}) mod m1

   y_n = (b_{1} y_{n-1} + b_{2} y_{n-2} + b_{3} y_{n-3}) mod m2

   with coefficients a11 ... a23,

   a_{1} = 0,     a_{2} = 63308, a_{3} = -183326

   b_{1} = 86098, b_{2} = 0,     b_{3} = -539608

   and moduli m1, m2,

   m1 = 2^31 - 1 = 2147483647

   m2 = 2^31 - 2000169 = 2145483479

   We initialize the generator with 

   x_1 = s_1 MOD m1, x_2 = s_2 MOD m1, x_3 = s_3 MOD m1

   y_1 = s_4 MOD m2, y_2 = s_5 MOD m2, y_3 = s_6 MOD m2

   where s_n = (69069 * s_{n-1}) mod 2^32 and s_0 = s is the

   user-supplied seed.

   NOTE: According to the paper the initial values for x_n must lie in

   the range 0 <= x_n <= (m1 - 1) and the initial values for y_n must

   lie in the range 0 <= y_n <= (m2 - 1), with at least one non-zero

   value -- our seeding procedure satisfies these constraints.

   We then use 7 iterations of the generator to "warm up" the internal

   state.

   The theoretical value of z_{10008} is 719452880. The subscript 10008

   means (1) seed the generator with s=1, (2) do the seven warm-up

   iterations that are part of the seeding process, (3) then do 10000

   actual iterations.

   The period of this generator is about 2^205.

   From: P. L'Ecuyer, "Combined Multiple Recursive Random Number

   Generators," Operations Research, 44, 5 (1996), 816--822.

   This is available on the net from L'Ecuyer's home page,

   http://www.iro.umontreal.ca/~lecuyer/myftp/papers/combmrg.ps

   ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/combmrg.ps */

static inline unsigned long int cmrg_get (void *vstate);

static double cmrg_get_double (void *vstate);

static void cmrg_set (void *state, unsigned long int s);

static const long int m1 = 2147483647, m2 = 2145483479;

static const long int a2 = 63308, qa2 = 33921, ra2 = 12979;

static const long int a3 = -183326, qa3 = 11714, ra3 = 2883;

static const long int b1 = 86098, qb1 = 24919, rb1 = 7417;

static const long int b3 = -539608, qb3 = 3976, rb3 = 2071;

typedef struct

  {

    long int x1, x2, x3;        /* first component */

    long int y1, y2, y3;        /* second component */

  }

cmrg_state_t;

static inline unsigned long int

cmrg_get (void *vstate)

{

  cmrg_state_t *state = (cmrg_state_t *) vstate;

  /* Component 1 */

  {

    long int h3 = state->x3 / qa3;

    long int p3 = -a3 * (state->x3 - h3 * qa3) - h3 * ra3;

    long int h2 = state->x2 / qa2;

    long int p2 = a2 * (state->x2 - h2 * qa2) - h2 * ra2;

    if (p3 < 0)

      p3 += m1;

    if (p2 < 0)

      p2 += m1;

    state->x3 = state->x2;

    state->x2 = state->x1;

    state->x1 = p2 - p3;

    if (state->x1 < 0)

      state->x1 += m1;

  }

  /* Component 2 */

  {

    long int h3 = state->y3 / qb3;

    long int p3 = -b3 * (state->y3 - h3 * qb3) - h3 * rb3;

    long int h1 = state->y1 / qb1;

    long int p1 = b1 * (state->y1 - h1 * qb1) - h1 * rb1;

    if (p3 < 0)

      p3 += m2;

    if (p1 < 0)

      p1 += m2;

    state->y3 = state->y2;

    state->y2 = state->y1;

    state->y1 = p1 - p3;

    if (state->y1 < 0)

      state->y1 += m2;

  }

  if (state->x1 < state->y1)

    return (state->x1 - state->y1 + m1);

  else

    return (state->x1 - state->y1);

}

static double 

cmrg_get_double (void *vstate)

{

  return cmrg_get (vstate) / 2147483647.0 ;

}

static void

cmrg_set (void *vstate, unsigned long int s)

{

  /* An entirely adhoc way of seeding! This does **not** come from

     L'Ecuyer et al */

  cmrg_state_t *state = (cmrg_state_t *) vstate;

  if (s == 0)

    s = 1;      /* default seed is 1 */

#define LCG(n) ((69069 * n) & 0xffffffffUL)

  s = LCG (s);

  state->x1 = s % m1;

  s = LCG (s);

  state->x2 = s % m1;

  s = LCG (s);

  state->x3 = s % m1;

  s = LCG (s);

  state->y1 = s % m2;

  s = LCG (s);

  state->y2 = s % m2;

  s = LCG (s);

  state->y3 = s % m2;

  /* "warm it up" */

  cmrg_get (state);

  cmrg_get (state);

  cmrg_get (state);

  cmrg_get (state);

  cmrg_get (state);

  cmrg_get (state);

  cmrg_get (state);

}

static const gsl_rng_type cmrg_type =

{"cmrg",                        /* name */

 2147483646,                    /* RAND_MAX */

 0,                             /* RAND_MIN */

 sizeof (cmrg_state_t),

 &cmrg_set,

 &cmrg_get,

 &cmrg_get_double};

const gsl_rng_type *gsl_rng_cmrg = &cmrg_type;