single-rnd.c
1 //! @file single-rnd.c
2 //! @author J. Marcel van der Veer
3
4 //! @section Copyright
5 //!
6 //! This file is part of Algol68G - an Algol 68 compiler-interpreter.
7 //! Copyright 2001-2024 J. Marcel van der Veer [algol68g@xs4all.nl].
8
9 //! @section License
10 //!
11 //! This program is free software; you can redistribute it and/or modify it
12 //! under the terms of the GNU General Public License as published by the
13 //! Free Software Foundation; either version 3 of the License, or
14 //! (at your option) any later version.
15 //!
16 //! This program is distributed in the hope that it will be useful, but
17 //! WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18 //! or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
19 //! more details. You should have received a copy of the GNU General Public
20 //! License along with this program. If not, see [http://www.gnu.org/licenses/].
21
22 //! @section Synopsis
23 //!
24 //! REAL pseudo-random number generator.
25
26 #include "a68g.h"
27
28 // Next part is a "stand-alone" version of GNU Scientific Library (GSL)
29 // random number generator "taus113", based on GSL file "rng/taus113.c".
30 //
31 // Copyright (C) 2002 Atakan Gurkan
32 // Based on the file taus.c which has the notice
33 // Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
34 //
35 // This program is free software; you can redistribute it and/or modify
36 // it under the terms of the GNU General Public License as published by
37 // the Free Software Foundation; either version 3 of the License, or (at
38 // your option) any later version.
39 //
40 // This program is distributed in the hope that it will be useful, but
41 // WITHOUT ANY WARRANTY; without even the implied warranty of
42 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
43 // General Public License for more details.
44 //
45 // You should have received a copy of the GNU General Public License
46 // along with this program; if not, write to the Free Software
47 // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
48 // This is a maximally equidistributed combined, collision free
49 // Tausworthe generator, with a period ~2^{113}. The sequence is,
50 // x_n = (z1_n ^ z2_n ^ z3_n ^ z4_n)
51 // b = (((z1_n << 6) ^ z1_n) >> 13)
52 // z1_{n+1} = (((z1_n & 4294967294) << 18) ^ b)
53 // b = (((z2_n << 2) ^ z2_n) >> 27)
54 // z2_{n+1} = (((z2_n & 4294967288) << 2) ^ b)
55 // b = (((z3_n << 13) ^ z3_n) >> 21)
56 // z3_{n+1} = (((z3_n & 4294967280) << 7) ^ b)
57 // b = (((z4_n << 3) ^ z4_n) >> 12)
58 // z4_{n+1} = (((z4_n & 4294967168) << 13) ^ b)
59 // computed modulo 2^32. In the formulas above '^' means exclusive-or
60 // (C-notation), not exponentiation.
61 // The algorithm is for 32-bit integers, hence a bitmask is used to clear
62 // all but least significant 32 bits, after left shifts, to make the code
63 // work on architectures where integers are 64-bit.
64 // The generator is initialized with
65 // z{i+1} = (69069 * zi) MOD 2^32 where z0 is the seed provided
66 // During initialization a check is done to make sure that the initial seeds
67 // have a required number of their most significant bits set.
68 // After this, the state is passed through the RNG 10 times to ensure the
69 // state satisfies a recurrence relation.
70 // References:
71 // P. L'Ecuyer, "Tables of Maximally-Equidistributed Combined LFSR Generators",
72 // Mathematics of Computation, 68, 225 (1999), 261--269.
73 // http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
74 // P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe Generators",
75 // Mathematics of Computation, 65, 213 (1996), 203--213.
76 // http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
77 // the online version of the latter contains corrections to the print version.
78
79 #define LCG(n) ((69069UL * n) & 0xffffffffUL)
80 #define MASK 0xffffffffUL
81
82 unt taus113_get (void *vstate);
83 REAL_T taus113_get_double (void *vstate);
84 void taus113_set (void *state, unt long int s);
85
86 typedef struct
87 {
88 unt long int z1, z2, z3, z4;
89 }
90 taus113_state_t;
91
92 static taus113_state_t rng_state;
93
94 unt taus113_get (void *vstate)
95 {
96 taus113_state_t *state = (taus113_state_t *) vstate;
97 unt long b1 = ((((state->z1 << 6UL) & MASK) ^ state->z1) >> 13UL);
98 state->z1 = ((((state->z1 & 4294967294UL) << 18UL) & MASK) ^ b1);
99 unt long b2 = ((((state->z2 << 2UL) & MASK) ^ state->z2) >> 27UL);
100 state->z2 = ((((state->z2 & 4294967288UL) << 2UL) & MASK) ^ b2);
101 unt long b3 = ((((state->z3 << 13UL) & MASK) ^ state->z3) >> 21UL);
102 state->z3 = ((((state->z3 & 4294967280UL) << 7UL) & MASK) ^ b3);
103 unt long b4 = ((((state->z4 << 3UL) & MASK) ^ state->z4) >> 12UL);
104 state->z4 = ((((state->z4 & 4294967168UL) << 13UL) & MASK) ^ b4);
105 return (state->z1 ^ state->z2 ^ state->z3 ^ state->z4);
106 }
107
108 REAL_T taus113_get_double (void *vstate)
109 {
110 return taus113_get (vstate) / 4294967296.0;
111 }
112
113 void taus113_set (void *vstate, unt long int s)
114 {
115 taus113_state_t *state = (taus113_state_t *) vstate;
116 if (!s) {
117 s = 1UL; // default seed is 1
118 }
119 state->z1 = LCG (s);
120 if (state->z1 < 2UL) {
121 state->z1 += 2UL;
122 }
123 state->z2 = LCG (state->z1);
124 if (state->z2 < 8UL) {
125 state->z2 += 8UL;
126 }
127 state->z3 = LCG (state->z2);
128 if (state->z3 < 16UL) {
129 state->z3 += 16UL;
130 }
131 state->z4 = LCG (state->z3);
132 if (state->z4 < 128UL) {
133 state->z4 += 128UL;
134 }
135 // Calling RNG ten times to satify recurrence condition
136 taus113_get (state);
137 taus113_get (state);
138 taus113_get (state);
139 taus113_get (state);
140 taus113_get (state);
141 taus113_get (state);
142 taus113_get (state);
143 taus113_get (state);
144 taus113_get (state);
145 taus113_get (state);
146 return;
147 }
148
149 // Initialise rng.
150
151 void init_rng (unt u)
152 {
153 taus113_set (&rng_state, u);
154 }
155
156 // A68G rng in R mathlib style.
157
158 REAL_T a68_unif_rand (void)
159 {
160 // In [0, 1>
161 return taus113_get_double (&rng_state);
162 }
163
164 REAL_T a68_gauss_rand (void)
165 {
166 // Marsaglia polar method instead of Box-Muller transform.
167 REAL_T s;
168 do {
169 REAL_T v1 = 2 * a68_unif_rand () - 1;
170 REAL_T v2 = 2 * a68_unif_rand () - 1;
171 s = v1 * v1 + v2 * v2;
172 } while (s >= 1 || s == 0); // A fraction (1-pi/4) is rejected.
173 return sqrt (-2 * log (s) / s);
174 }
175
176 static char *state_file = ".Random.seed";
177
178 void GetRNGstate (void)
179 {
180 INT_T fd = open (state_file, A68_READ_ACCESS);
181 if (fd != -1) {
182 ASSERT (read (fd, &rng_state, sizeof (taus113_state_t)) != -1);
183 close (fd);
184 }
185 }
186
187 void PutRNGstate (void)
188 {
189 INT_T fd = open (state_file, A68_WRITE_ACCESS, A68_PROTECTION);
190 if (fd != -1) {
191 ASSERT (write (fd, &rng_state, sizeof (taus113_state_t)) != -1);
192 close (fd);
193 }
194 }
