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/* rng/mrg.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <stdlib.h>
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#include <gsl/gsl_rng.h>
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/* This is a fifth-order multiple recursive generator. The sequence is,
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x_n = (a_1 x_{n-1} + a_5 x_{n-5}) mod m
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with a_1 = 107374182, a_2 = a_3 = a_4 = 0, a_5 = 104480 and m = 2^31-1.
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We initialize the generator with x_n = s_n MOD m for n = 1..5,
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where s_n = (69069 * s_{n-1}) mod 2^32, and s_0 = s is the
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user-supplied seed.
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NOTE: According to the paper the seeds must lie in the range [0,
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2^31 - 2] with at least one non-zero value -- our seeding procedure
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satisfies these constraints.
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We then use 6 iterations of the generator to "warm up" the internal
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state.
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With this initialization procedure the theoretical value of
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z_{10006} is 2064828650 for s = 1. The subscript 10006 means (1)
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seed the generator with s = 1, (2) do the 6 warm-up iterations
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that are part of the seeding process, (3) then do 10000 actual
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iterations.
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The period of this generator is about 2^155.
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From: P. L'Ecuyer, F. Blouin, and R. Coutre, "A search for good
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multiple recursive random number generators", ACM Transactions on
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Modeling and Computer Simulation 3, 87-98 (1993). */
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static inline unsigned long int mrg_get (void *vstate);
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static double mrg_get_double (void *vstate);
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static void mrg_set (void *state, unsigned long int s);
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static const long int m = 2147483647;
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static const long int a1 = 107374182, q1 = 20, r1 = 7;
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static const long int a5 = 104480, q5 = 20554, r5 = 1727;
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typedef struct
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{
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long int x1, x2, x3, x4, x5;
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}
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mrg_state_t;
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static inline unsigned long int
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mrg_get (void *vstate)
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{
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mrg_state_t *state = (mrg_state_t *) vstate;
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long int p1, h1, p5, h5;
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h5 = state->x5 / q5;
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p5 = a5 * (state->x5 - h5 * q5) - h5 * r5;
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if (p5 > 0)
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p5 -= m;
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h1 = state->x1 / q1;
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p1 = a1 * (state->x1 - h1 * q1) - h1 * r1;
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if (p1 < 0)
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p1 += m;
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state->x5 = state->x4;
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state->x4 = state->x3;
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state->x3 = state->x2;
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state->x2 = state->x1;
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state->x1 = p1 + p5;
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if (state->x1 < 0)
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state->x1 += m;
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return state->x1;
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}
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static double
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mrg_get_double (void *vstate)
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{
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return mrg_get (vstate) / 2147483647.0 ;
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}
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static void
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mrg_set (void *vstate, unsigned long int s)
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{
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/* An entirely adhoc way of seeding! This does **not** come from
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L'Ecuyer et al */
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mrg_state_t *state = (mrg_state_t *) vstate;
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if (s == 0)
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s = 1; /* default seed is 1 */
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#define LCG(n) ((69069 * n) & 0xffffffffUL)
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s = LCG (s);
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state->x1 = s % m;
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s = LCG (s);
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state->x2 = s % m;
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s = LCG (s);
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state->x3 = s % m;
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s = LCG (s);
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state->x4 = s % m;
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s = LCG (s);
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state->x5 = s % m;
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/* "warm it up" with at least 5 calls to go through
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all the x values */
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mrg_get (state);
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mrg_get (state);
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mrg_get (state);
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mrg_get (state);
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mrg_get (state);
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mrg_get (state);
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return;
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}
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static const gsl_rng_type mrg_type =
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{"mrg", /* name */
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2147483646, /* RAND_MAX */
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0, /* RAND_MIN */
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sizeof (mrg_state_t),
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&mrg_set,
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&mrg_get,
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&mrg_get_double};
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const gsl_rng_type *gsl_rng_mrg = &mrg_type;
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