| /* 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)] ] |
| */ |