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