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- /* 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 "gsl__config.h"
- #include <stdlib.h>
- #include "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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