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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: lcrand.c,v 1.4 2000/12/06 20:31:06 mdw Exp $ |
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4 | * |
5 | * Simple linear congruential generator |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
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. |
18 | * |
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. |
23 | * |
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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: lcrand.c,v $ |
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33 | * Revision 1.4 2000/12/06 20:31:06 mdw |
34 | * Simplify uniform range transformation. |
35 | * |
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36 | * Revision 1.3 2000/06/17 11:29:03 mdw |
37 | * Add the flags word to the generic generator. |
38 | * |
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39 | * Revision 1.2 1999/12/13 15:34:01 mdw |
40 | * Add support for seeding from a generic pseudorandom source. |
41 | * |
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42 | * Revision 1.1 1999/12/10 23:15:27 mdw |
43 | * Noncryptographic random number generator. |
44 | * |
45 | */ |
46 | |
47 | /*----- Header files ------------------------------------------------------*/ |
48 | |
49 | #include <stdarg.h> |
50 | #include <stdio.h> |
51 | #include <stdlib.h> |
52 | #include <string.h> |
53 | |
54 | #include <mLib/bits.h> |
55 | #include <mLib/sub.h> |
56 | |
57 | #include "grand.h" |
58 | #include "lcrand.h" |
59 | |
60 | /*----- Magic numbers -----------------------------------------------------*/ |
61 | |
62 | /* --- The generator parameters --- */ |
63 | |
64 | #define P LCRAND_P /* Modulus */ |
65 | #define A LCRAND_A /* Multiplier (primitive mod @p@) */ |
66 | #define C LCRAND_C /* Additive constant */ |
67 | |
68 | /* --- Precomputed values for modular reduction --- */ |
69 | |
70 | #define D 5 /* %$p = 2^{32} - d$% */ |
71 | |
72 | /* --- Other useful bits --- */ |
73 | |
74 | #define P256 4294967040u /* Highest multiple of 256 < %$p$% */ |
75 | |
76 | /*----- Main code ---------------------------------------------------------*/ |
77 | |
78 | /* --- @lcrand@ --- * |
79 | * |
80 | * Arguments: @uint32 x@ = seed value |
81 | * |
82 | * Returns: New state of the generator. |
83 | * |
84 | * Use: Steps the generator. Returns %$ax + c \bmod p$%. |
85 | */ |
86 | |
87 | uint32 lcrand(uint32 x) |
88 | { |
89 | uint32 a[2], xx[2]; |
90 | uint32 yy[2]; |
91 | |
92 | /* --- Unpack things into the arrays --- */ |
93 | |
94 | a[0] = U16(A); a[1] = U16(A >> 16); |
95 | xx[0] = U16(x); xx[1] = U16(x >> 16); |
96 | |
97 | /* --- Multiply everything together --- * |
98 | * |
99 | * This is plain old long multiplication, although it looks a bit strange. |
100 | * I set up the top and bottom partial products directly where they're |
101 | * supposed to be. The cross terms I add together, with the low 16 bits in |
102 | * @q@ and the high 32 bits in @p@. These I then add into the product. |
103 | */ |
104 | |
105 | { |
106 | uint32 p, q; |
107 | |
108 | yy[0] = a[0] * xx[0]; |
109 | yy[1] = a[1] * xx[1]; |
110 | |
111 | p = a[0] * xx[1]; |
112 | q = p + a[1] * xx[0]; |
113 | p = ((q < p) << 16) + (q >> 16); |
114 | q = U16(q) << 16; |
115 | |
116 | q += yy[0]; |
117 | if (q < yy[0]) |
118 | p++; |
119 | else |
120 | p += (q >> 16) >> 16; |
121 | yy[0] = q; |
122 | |
123 | yy[1] += p; |
124 | } |
125 | |
126 | /* --- Now reduce mod p --- * |
127 | * |
128 | * I'm using shifts and adds to do the multiply step here. This needs to |
129 | * be changed if @D@ ever becomes something other than 5. |
130 | */ |
131 | |
132 | #if D != 5 |
133 | # error "Change shift sequence!" |
134 | #endif |
135 | |
136 | { |
137 | uint32 q; |
138 | |
139 | q = yy[1]; |
140 | x = yy[0]; |
141 | |
142 | while (q) { |
143 | uint32 y, z; |
144 | y = q >> 30; |
145 | z = q << 2; |
146 | z += q; |
147 | if (z < q) |
148 | y++; |
149 | else |
150 | y += (q >> 16) >> 16; |
151 | q = y; |
152 | x += z; |
153 | if (x < z || x > P) |
154 | x -= P; |
155 | } |
156 | } |
157 | |
158 | /* --- Now add on the constant --- */ |
159 | |
160 | x += C; |
161 | if (x < C || x >= P) |
162 | x -= P; |
163 | |
164 | /* --- Done --- */ |
165 | |
166 | return (x); |
167 | } |
168 | |
169 | /* --- @lcrand_range@ --- * |
170 | * |
171 | * Arguments: @uint32 *x@ = pointer to seed value (updated) |
172 | * @uint32 m@ = limit allowable |
173 | * |
174 | * Returns: A uniformly distributed pseudorandom integer in the interval |
175 | * %$[0, m)$%. |
176 | */ |
177 | |
178 | uint32 lcrand_range(uint32 *x, uint32 m) |
179 | { |
180 | uint32 xx = *x; |
181 | uint32 r = P - P % m; |
182 | do xx = lcrand(xx); while (xx >= r); |
183 | *x = xx; |
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184 | return (xx % m); |
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185 | } |
186 | |
187 | /*----- Generic interface -------------------------------------------------*/ |
188 | |
189 | typedef struct gctx { |
190 | grand r; |
191 | uint32 x; |
192 | } gctx; |
193 | |
194 | static void gdestroy(grand *r) |
195 | { |
196 | gctx *g = (gctx *)r; |
197 | DESTROY(g); |
198 | } |
199 | |
200 | static int gmisc(grand *r, unsigned op, ...) |
201 | { |
202 | gctx *g = (gctx *)r; |
203 | va_list ap; |
204 | int rc = 0; |
205 | va_start(ap, op); |
206 | |
207 | switch (op) { |
208 | case GRAND_CHECK: |
209 | switch (va_arg(ap, unsigned)) { |
210 | case GRAND_CHECK: |
211 | case GRAND_SEEDINT: |
212 | case GRAND_SEEDUINT32: |
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213 | case GRAND_SEEDRAND: |
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214 | rc = 1; |
215 | break; |
216 | default: |
217 | rc = 0; |
218 | break; |
219 | } |
220 | break; |
221 | case GRAND_SEEDINT: |
222 | g->x = va_arg(ap, unsigned); |
223 | break; |
224 | case GRAND_SEEDUINT32: |
225 | g->x = va_arg(ap, uint32); |
226 | break; |
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227 | case GRAND_SEEDRAND: { |
228 | grand *rr = va_arg(ap, grand *); |
229 | uint32 x; |
230 | do x = rr->ops->word(rr); while (x >= P || x == LCRAND_FIXEDPT); |
231 | g->x = x; |
232 | } break; |
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233 | default: |
234 | GRAND_BADOP; |
235 | break; |
236 | } |
237 | |
238 | va_end(ap); |
239 | return (rc); |
240 | } |
241 | |
242 | static uint32 graw(grand *r) |
243 | { |
244 | gctx *g = (gctx *)r; |
245 | g->x = lcrand(g->x); |
246 | return (g->x); |
247 | } |
248 | |
249 | static octet gbyte(grand *r) |
250 | { |
251 | gctx *g = (gctx *)r; |
252 | uint32 x = g->x; |
253 | do x = lcrand(x); while (x >= P256); |
254 | g->x = x; |
255 | return (x / (P256 / 256)); |
256 | } |
257 | |
258 | static uint32 grange(grand *r, uint32 l) |
259 | { |
260 | gctx *g = (gctx *)r; |
261 | return (lcrand_range(&g->x, l)); |
262 | } |
263 | |
264 | static const grand_ops gops = { |
265 | "lcrand", |
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266 | LCRAND_P, 0, |
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267 | gmisc, gdestroy, |
268 | graw, gbyte, grand_word, grange, grand_fill |
269 | }; |
270 | |
271 | /* --- @lcrand_create@ --- * |
272 | * |
273 | * Arguments: @uint32 x@ = initial seed |
274 | * |
275 | * Returns: Pointer to a generic generator. |
276 | * |
277 | * Use: Constructs a generic generator interface over a linear |
278 | * congruential generator. |
279 | */ |
280 | |
281 | grand *lcrand_create(uint32 x) |
282 | { |
283 | gctx *g = CREATE(gctx); |
284 | g->r.ops = &gops; |
285 | g->x = x; |
286 | return (&g->r); |
287 | } |
288 | |
289 | /*----- Test rig ----------------------------------------------------------*/ |
290 | |
291 | #ifdef TEST_RIG |
292 | |
293 | #include <mLib/testrig.h> |
294 | |
295 | static int verify(dstr *v) |
296 | { |
297 | uint32 x = *(uint32 *)v[0].buf; |
298 | uint32 y = *(uint32 *)v[1].buf; |
299 | uint32 z = lcrand(x); |
300 | int ok = 1; |
301 | if (y != z) { |
302 | fprintf(stderr, |
303 | "\n*** lcrand failed. lcrand(%lu) = %lu, expected %lu\n", |
304 | (unsigned long)x, (unsigned long)z, (unsigned long)y); |
305 | ok = 0; |
306 | } |
307 | return (ok); |
308 | } |
309 | |
310 | static test_chunk tests[] = { |
311 | { "lcrand", verify, { &type_uint32, &type_uint32, 0 } }, |
312 | { 0, 0, { 0 } } |
313 | }; |
314 | |
315 | int main(int argc, char *argv[]) |
316 | { |
317 | test_run(argc, argv, tests, SRCDIR"/tests/lcrand"); |
318 | return (0); |
319 | } |
320 | |
321 | #endif |
322 | |
323 | /*----- That's all, folks -------------------------------------------------*/ |