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/* rng/taus113.c
* Copyright (C) 2002 Atakan Gurkan
* Based on the file taus.c which has the notice
* 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.
*/
/* This is a maximally equidistributed combined, collision free
Tausworthe generator, with a period ~2^{113}. The sequence is,
x_n = (z1_n ^ z2_n ^ z3_n ^ z4_n)
b = (((z1_n << 6) ^ z1_n) >> 13)
z1_{n+1} = (((z1_n & 4294967294) << 18) ^ b)
b = (((z2_n << 2) ^ z2_n) >> 27)
z2_{n+1} = (((z2_n & 4294967288) << 2) ^ b)
b = (((z3_n << 13) ^ z3_n) >> 21)
z3_{n+1} = (((z3_n & 4294967280) << 7) ^ b)
b = (((z4_n << 3) ^ z4_n) >> 12)
z4_{n+1} = (((z4_n & 4294967168) << 13) ^ b)
computed modulo 2^32. In the formulas above '^' means exclusive-or
(C-notation), not exponentiation.
The algorithm is for 32-bit integers, hence a bitmask is used to clear
all but least significant 32 bits, after left shifts, to make the code
work on architectures where integers are 64-bit.
The generator is initialized with
zi = (69069 * z{i+1}) MOD 2^32 where z0 is the seed provided
During initialization a check is done to make sure that the initial seeds
have a required number of their most significant bits set.
After this, the state is passed through the RNG 10 times to ensure the
state satisfies a recurrence relation.
References:
P. L'Ecuyer, "Tables of Maximally-Equidistributed Combined LFSR Generators",
Mathematics of Computation, 68, 225 (1999), 261--269.
http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe Generators",
Mathematics of Computation, 65, 213 (1996), 203--213.
http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
the online version of the latter contains corrections to the print version.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_rng.h>
#define LCG(n) ((69069UL * n) & 0xffffffffUL)
#define MASK 0xffffffffUL
static inline unsigned long int taus113_get (void *vstate);
static double taus113_get_double (void *vstate);
static void taus113_set (void *state, unsigned long int s);
typedef struct
{
unsigned long int z1, z2, z3, z4;
}
taus113_state_t;
static inline unsigned long
taus113_get (void *vstate)
{
taus113_state_t *state = (taus113_state_t *) vstate;
unsigned long b1, b2, b3, b4;
b1 = ((((state->z1 << 6UL) & MASK) ^ state->z1) >> 13UL);
state->z1 = ((((state->z1 & 4294967294UL) << 18UL) & MASK) ^ b1);
b2 = ((((state->z2 << 2UL) & MASK) ^ state->z2) >> 27UL);
state->z2 = ((((state->z2 & 4294967288UL) << 2UL) & MASK) ^ b2);
b3 = ((((state->z3 << 13UL) & MASK) ^ state->z3) >> 21UL);
state->z3 = ((((state->z3 & 4294967280UL) << 7UL) & MASK) ^ b3);
b4 = ((((state->z4 << 3UL) & MASK) ^ state->z4) >> 12UL);
state->z4 = ((((state->z4 & 4294967168UL) << 13UL) & MASK) ^ b4);
return (state->z1 ^ state->z2 ^ state->z3 ^ state->z4);
}
static double
taus113_get_double (void *vstate)
{
return taus113_get (vstate) / 4294967296.0;
}
static void
taus113_set (void *vstate, unsigned long int s)
{
taus113_state_t *state = (taus113_state_t *) vstate;
if (!s)
s = 1UL; /* default seed is 1 */
state->z1 = LCG (s);
if (state->z1 < 2UL)
state->z1 += 2UL;
state->z2 = LCG (state->z1);
if (state->z2 < 8UL)
state->z2 += 8UL;
state->z3 = LCG (state->z2);
if (state->z3 < 16UL)
state->z3 += 16UL;
state->z4 = LCG (state->z3);
if (state->z4 < 128UL)
state->z4 += 128UL;
/* Calling RNG ten times to satify recurrence condition */
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
taus113_get (state);
return;
}
static const gsl_rng_type taus113_type = {
"taus113", /* name */
0xffffffffUL, /* RAND_MAX */
0, /* RAND_MIN */
sizeof (taus113_state_t),
&taus113_set,
&taus113_get,
&taus113_get_double
};
const gsl_rng_type *gsl_rng_taus113 = &taus113_type;
/* Rules for analytic calculations using GNU Emacs Calc:
(used to find the values for the test program)
[ LCG(n) := n * 69069 mod (2^32) ]
[ b1(x) := rsh(xor(lsh(x, 6), x), 13),
q1(x) := xor(lsh(and(x, 4294967294), 18), b1(x)),
b2(x) := rsh(xor(lsh(x, 2), x), 27),
q2(x) := xor(lsh(and(x, 4294967288), 2), b2(x)),
b3(x) := rsh(xor(lsh(x, 13), x), 21),
q3(x) := xor(lsh(and(x, 4294967280), 7), b3(x)),
b4(x) := rsh(xor(lsh(x, 3), x), 12),
q4(x) := xor(lsh(and(x, 4294967168), 13), b4(x))
]
[ S([z1,z2,z3,z4]) := [q1(z1), q2(z2), q3(z3), q4(z4)] ]
*/
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