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/* 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., 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;
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