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+/* rng/mrg.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 fifth-order multiple recursive generator. The sequence is,
+
+ x_n = (a_1 x_{n-1} + a_5 x_{n-5}) mod m
+
+ with a_1 = 107374182, a_2 = a_3 = a_4 = 0, a_5 = 104480 and m = 2^31-1.
+
+ We initialize the generator with x_n = s_n MOD m for n = 1..5,
+ 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 seeds must lie in the range [0,
+ 2^31 - 2] with at least one non-zero value -- our seeding procedure
+ satisfies these constraints.
+
+ We then use 6 iterations of the generator to "warm up" the internal
+ state.
+
+ With this initialization procedure the theoretical value of
+ z_{10006} is 2064828650 for s = 1. The subscript 10006 means (1)
+ seed the generator with s = 1, (2) do the 6 warm-up iterations
+ that are part of the seeding process, (3) then do 10000 actual
+ iterations.
+
+ The period of this generator is about 2^155.
+
+ From: P. L'Ecuyer, F. Blouin, and R. Coutre, "A search for good
+ multiple recursive random number generators", ACM Transactions on
+ Modeling and Computer Simulation 3, 87-98 (1993). */
+
+static inline unsigned long int mrg_get (void *vstate);
+static double mrg_get_double (void *vstate);
+static void mrg_set (void *state, unsigned long int s);
+
+static const long int m = 2147483647;
+static const long int a1 = 107374182, q1 = 20, r1 = 7;
+static const long int a5 = 104480, q5 = 20554, r5 = 1727;
+
+typedef struct
+ {
+ long int x1, x2, x3, x4, x5;
+ }
+mrg_state_t;
+
+static inline unsigned long int
+mrg_get (void *vstate)
+{
+ mrg_state_t *state = (mrg_state_t *) vstate;
+
+ long int p1, h1, p5, h5;
+
+ h5 = state->x5 / q5;
+ p5 = a5 * (state->x5 - h5 * q5) - h5 * r5;
+ if (p5 > 0)
+ p5 -= m;
+
+ h1 = state->x1 / q1;
+ p1 = a1 * (state->x1 - h1 * q1) - h1 * r1;
+ if (p1 < 0)
+ p1 += m;
+
+ state->x5 = state->x4;
+ state->x4 = state->x3;
+ state->x3 = state->x2;
+ state->x2 = state->x1;
+
+ state->x1 = p1 + p5;
+
+ if (state->x1 < 0)
+ state->x1 += m;
+
+ return state->x1;
+}
+
+static double
+mrg_get_double (void *vstate)
+{
+ return mrg_get (vstate) / 2147483647.0 ;
+}
+
+
+static void
+mrg_set (void *vstate, unsigned long int s)
+{
+ /* An entirely adhoc way of seeding! This does **not** come from
+ L'Ecuyer et al */
+
+ mrg_state_t *state = (mrg_state_t *) vstate;
+
+ if (s == 0)
+ s = 1; /* default seed is 1 */
+
+#define LCG(n) ((69069 * n) & 0xffffffffUL)
+ s = LCG (s);
+ state->x1 = s % m;
+ s = LCG (s);
+ state->x2 = s % m;
+ s = LCG (s);
+ state->x3 = s % m;
+ s = LCG (s);
+ state->x4 = s % m;
+ s = LCG (s);
+ state->x5 = s % m;
+
+ /* "warm it up" with at least 5 calls to go through
+ all the x values */
+
+ mrg_get (state);
+ mrg_get (state);
+ mrg_get (state);
+ mrg_get (state);
+ mrg_get (state);
+ mrg_get (state);
+
+ return;
+}
+
+static const gsl_rng_type mrg_type =
+{"mrg", /* name */
+ 2147483646, /* RAND_MAX */
+ 0, /* RAND_MIN */
+ sizeof (mrg_state_t),
+ &mrg_set,
+ &mrg_get,
+ &mrg_get_double};
+
+const gsl_rng_type *gsl_rng_mrg = &mrg_type;