cmrg.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* rng/cmrg.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 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., 675 Mass Ave, Cambridge, MA 02139, 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;