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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: lcrand.c,v 1.5 2004/04/08 01:36:15 mdw Exp $ |
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4 | * |
5 | * Simple linear congruential generator |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
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18 | * |
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19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
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23 | * |
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24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <stdarg.h> |
33 | #include <stdio.h> |
34 | #include <stdlib.h> |
35 | #include <string.h> |
36 | |
37 | #include <mLib/bits.h> |
38 | #include <mLib/sub.h> |
39 | |
40 | #include "grand.h" |
41 | #include "lcrand.h" |
42 | |
43 | /*----- Magic numbers -----------------------------------------------------*/ |
44 | |
45 | /* --- The generator parameters --- */ |
46 | |
47 | #define P LCRAND_P /* Modulus */ |
48 | #define A LCRAND_A /* Multiplier (primitive mod @p@) */ |
49 | #define C LCRAND_C /* Additive constant */ |
50 | |
51 | /* --- Precomputed values for modular reduction --- */ |
52 | |
53 | #define D 5 /* %$p = 2^{32} - d$% */ |
54 | |
55 | /* --- Other useful bits --- */ |
56 | |
57 | #define P256 4294967040u /* Highest multiple of 256 < %$p$% */ |
58 | |
59 | /*----- Main code ---------------------------------------------------------*/ |
60 | |
61 | /* --- @lcrand@ --- * |
62 | * |
63 | * Arguments: @uint32 x@ = seed value |
64 | * |
65 | * Returns: New state of the generator. |
66 | * |
67 | * Use: Steps the generator. Returns %$ax + c \bmod p$%. |
68 | */ |
69 | |
70 | uint32 lcrand(uint32 x) |
71 | { |
72 | uint32 a[2], xx[2]; |
73 | uint32 yy[2]; |
74 | |
75 | /* --- Unpack things into the arrays --- */ |
76 | |
77 | a[0] = U16(A); a[1] = U16(A >> 16); |
78 | xx[0] = U16(x); xx[1] = U16(x >> 16); |
79 | |
80 | /* --- Multiply everything together --- * |
81 | * |
82 | * This is plain old long multiplication, although it looks a bit strange. |
83 | * I set up the top and bottom partial products directly where they're |
84 | * supposed to be. The cross terms I add together, with the low 16 bits in |
85 | * @q@ and the high 32 bits in @p@. These I then add into the product. |
86 | */ |
87 | |
88 | { |
89 | uint32 p, q; |
90 | |
91 | yy[0] = a[0] * xx[0]; |
92 | yy[1] = a[1] * xx[1]; |
93 | |
94 | p = a[0] * xx[1]; |
95 | q = p + a[1] * xx[0]; |
96 | p = ((q < p) << 16) + (q >> 16); |
97 | q = U16(q) << 16; |
98 | |
99 | q += yy[0]; |
100 | if (q < yy[0]) |
101 | p++; |
102 | else |
103 | p += (q >> 16) >> 16; |
104 | yy[0] = q; |
105 | |
106 | yy[1] += p; |
107 | } |
108 | |
109 | /* --- Now reduce mod p --- * |
110 | * |
111 | * I'm using shifts and adds to do the multiply step here. This needs to |
112 | * be changed if @D@ ever becomes something other than 5. |
113 | */ |
114 | |
115 | #if D != 5 |
116 | # error "Change shift sequence!" |
117 | #endif |
118 | |
119 | { |
120 | uint32 q; |
121 | |
122 | q = yy[1]; |
123 | x = yy[0]; |
124 | |
125 | while (q) { |
126 | uint32 y, z; |
127 | y = q >> 30; |
128 | z = q << 2; |
129 | z += q; |
130 | if (z < q) |
131 | y++; |
132 | else |
133 | y += (q >> 16) >> 16; |
134 | q = y; |
135 | x += z; |
136 | if (x < z || x > P) |
137 | x -= P; |
138 | } |
139 | } |
140 | |
141 | /* --- Now add on the constant --- */ |
142 | |
143 | x += C; |
144 | if (x < C || x >= P) |
145 | x -= P; |
146 | |
147 | /* --- Done --- */ |
148 | |
149 | return (x); |
150 | } |
151 | |
152 | /* --- @lcrand_range@ --- * |
153 | * |
154 | * Arguments: @uint32 *x@ = pointer to seed value (updated) |
155 | * @uint32 m@ = limit allowable |
156 | * |
157 | * Returns: A uniformly distributed pseudorandom integer in the interval |
158 | * %$[0, m)$%. |
159 | */ |
160 | |
161 | uint32 lcrand_range(uint32 *x, uint32 m) |
162 | { |
163 | uint32 xx = *x; |
164 | uint32 r = P - P % m; |
165 | do xx = lcrand(xx); while (xx >= r); |
166 | *x = xx; |
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167 | return (xx % m); |
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168 | } |
169 | |
170 | /*----- Generic interface -------------------------------------------------*/ |
171 | |
172 | typedef struct gctx { |
173 | grand r; |
174 | uint32 x; |
175 | } gctx; |
176 | |
177 | static void gdestroy(grand *r) |
178 | { |
179 | gctx *g = (gctx *)r; |
180 | DESTROY(g); |
181 | } |
182 | |
183 | static int gmisc(grand *r, unsigned op, ...) |
184 | { |
185 | gctx *g = (gctx *)r; |
186 | va_list ap; |
187 | int rc = 0; |
188 | va_start(ap, op); |
189 | |
190 | switch (op) { |
191 | case GRAND_CHECK: |
192 | switch (va_arg(ap, unsigned)) { |
193 | case GRAND_CHECK: |
194 | case GRAND_SEEDINT: |
195 | case GRAND_SEEDUINT32: |
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196 | case GRAND_SEEDRAND: |
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197 | rc = 1; |
198 | break; |
199 | default: |
200 | rc = 0; |
201 | break; |
202 | } |
203 | break; |
204 | case GRAND_SEEDINT: |
205 | g->x = va_arg(ap, unsigned); |
206 | break; |
207 | case GRAND_SEEDUINT32: |
208 | g->x = va_arg(ap, uint32); |
209 | break; |
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210 | case GRAND_SEEDRAND: { |
211 | grand *rr = va_arg(ap, grand *); |
212 | uint32 x; |
213 | do x = rr->ops->word(rr); while (x >= P || x == LCRAND_FIXEDPT); |
214 | g->x = x; |
215 | } break; |
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216 | default: |
217 | GRAND_BADOP; |
218 | break; |
219 | } |
220 | |
221 | va_end(ap); |
222 | return (rc); |
223 | } |
224 | |
225 | static uint32 graw(grand *r) |
226 | { |
227 | gctx *g = (gctx *)r; |
228 | g->x = lcrand(g->x); |
229 | return (g->x); |
230 | } |
231 | |
232 | static octet gbyte(grand *r) |
233 | { |
234 | gctx *g = (gctx *)r; |
235 | uint32 x = g->x; |
236 | do x = lcrand(x); while (x >= P256); |
237 | g->x = x; |
238 | return (x / (P256 / 256)); |
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239 | } |
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240 | |
241 | static uint32 grange(grand *r, uint32 l) |
242 | { |
243 | gctx *g = (gctx *)r; |
244 | return (lcrand_range(&g->x, l)); |
245 | } |
246 | |
247 | static const grand_ops gops = { |
248 | "lcrand", |
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249 | LCRAND_P, 0, |
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250 | gmisc, gdestroy, |
251 | graw, gbyte, grand_word, grange, grand_fill |
252 | }; |
253 | |
254 | /* --- @lcrand_create@ --- * |
255 | * |
256 | * Arguments: @uint32 x@ = initial seed |
257 | * |
258 | * Returns: Pointer to a generic generator. |
259 | * |
260 | * Use: Constructs a generic generator interface over a linear |
261 | * congruential generator. |
262 | */ |
263 | |
264 | grand *lcrand_create(uint32 x) |
265 | { |
266 | gctx *g = CREATE(gctx); |
267 | g->r.ops = &gops; |
268 | g->x = x; |
269 | return (&g->r); |
270 | } |
271 | |
272 | /*----- Test rig ----------------------------------------------------------*/ |
273 | |
274 | #ifdef TEST_RIG |
275 | |
276 | #include <mLib/testrig.h> |
277 | |
278 | static int verify(dstr *v) |
279 | { |
280 | uint32 x = *(uint32 *)v[0].buf; |
281 | uint32 y = *(uint32 *)v[1].buf; |
282 | uint32 z = lcrand(x); |
283 | int ok = 1; |
284 | if (y != z) { |
285 | fprintf(stderr, |
286 | "\n*** lcrand failed. lcrand(%lu) = %lu, expected %lu\n", |
287 | (unsigned long)x, (unsigned long)z, (unsigned long)y); |
288 | ok = 0; |
289 | } |
290 | return (ok); |
291 | } |
292 | |
293 | static test_chunk tests[] = { |
294 | { "lcrand", verify, { &type_uint32, &type_uint32, 0 } }, |
295 | { 0, 0, { 0 } } |
296 | }; |
297 | |
298 | int main(int argc, char *argv[]) |
299 | { |
300 | test_run(argc, argv, tests, SRCDIR"/tests/lcrand"); |
301 | return (0); |
302 | } |
303 | |
304 | #endif |
305 | |
306 | /*----- That's all, folks -------------------------------------------------*/ |