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6599da04 JM |
1 | /* |
2 | * Copyright (c) 1983 Regents of the University of California. | |
3 | * All rights reserved. | |
4 | * | |
f3636679 JM |
5 | * Redistribution and use in source and binary forms, with or without |
6 | * modification, are permitted provided that the following conditions | |
7 | * are met: | |
8 | * 1. Redistributions of source code must retain the above copyright | |
9 | * notice, this list of conditions and the following disclaimer. | |
10 | * 2. Redistributions in binary form must reproduce the above copyright | |
11 | * notice, this list of conditions and the following disclaimer in the | |
12 | * documentation and/or other materials provided with the distribution. | |
13 | * 3. [rescinded 22 July 1999] | |
14 | * 4. Neither the name of the University nor the names of its contributors | |
15 | * may be used to endorse or promote products derived from this software | |
16 | * without specific prior written permission. | |
17 | * | |
18 | * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND | |
19 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
20 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
21 | * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE | |
22 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
23 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
24 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
25 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
26 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
27 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
28 | * SUCH DAMAGE. | |
6599da04 JM |
29 | */ |
30 | ||
31 | /* | |
32 | * This is derived from the Berkeley source: | |
33 | * @(#)random.c 5.5 (Berkeley) 7/6/88 | |
34 | * It was reworked for the GNU C Library by Roland McGrath. | |
35 | */ | |
36 | ||
37 | #include <errno.h> | |
38 | ||
39 | #if 0 | |
40 | ||
41 | #include <ansidecl.h> | |
42 | #include <limits.h> | |
43 | #include <stddef.h> | |
44 | #include <stdlib.h> | |
45 | ||
46 | #else | |
47 | ||
48 | #define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */ | |
49 | #define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/ | |
50 | ||
51 | #ifdef __STDC__ | |
52 | # define PTR void * | |
fb9939b8 MM |
53 | # ifndef NULL |
54 | # define NULL (void *) 0 | |
55 | # endif | |
6599da04 JM |
56 | #else |
57 | # define PTR char * | |
fb9939b8 MM |
58 | # ifndef NULL |
59 | # define NULL (void *) 0 | |
60 | # endif | |
6599da04 JM |
61 | #endif |
62 | ||
63 | #endif | |
64 | ||
65 | long int random (); | |
66 | ||
67 | /* An improved random number generation package. In addition to the standard | |
68 | rand()/srand() like interface, this package also has a special state info | |
69 | interface. The initstate() routine is called with a seed, an array of | |
70 | bytes, and a count of how many bytes are being passed in; this array is | |
71 | then initialized to contain information for random number generation with | |
72 | that much state information. Good sizes for the amount of state | |
73 | information are 32, 64, 128, and 256 bytes. The state can be switched by | |
74 | calling the setstate() function with the same array as was initiallized | |
75 | with initstate(). By default, the package runs with 128 bytes of state | |
76 | information and generates far better random numbers than a linear | |
77 | congruential generator. If the amount of state information is less than | |
78 | 32 bytes, a simple linear congruential R.N.G. is used. Internally, the | |
79 | state information is treated as an array of longs; the zeroeth element of | |
80 | the array is the type of R.N.G. being used (small integer); the remainder | |
81 | of the array is the state information for the R.N.G. Thus, 32 bytes of | |
82 | state information will give 7 longs worth of state information, which will | |
83 | allow a degree seven polynomial. (Note: The zeroeth word of state | |
84 | information also has some other information stored in it; see setstate | |
85 | for details). The random number generation technique is a linear feedback | |
86 | shift register approach, employing trinomials (since there are fewer terms | |
87 | to sum up that way). In this approach, the least significant bit of all | |
88 | the numbers in the state table will act as a linear feedback shift register, | |
89 | and will have period 2^deg - 1 (where deg is the degree of the polynomial | |
90 | being used, assuming that the polynomial is irreducible and primitive). | |
91 | The higher order bits will have longer periods, since their values are | |
92 | also influenced by pseudo-random carries out of the lower bits. The | |
93 | total period of the generator is approximately deg*(2**deg - 1); thus | |
94 | doubling the amount of state information has a vast influence on the | |
95 | period of the generator. Note: The deg*(2**deg - 1) is an approximation | |
96 | only good for large deg, when the period of the shift register is the | |
97 | dominant factor. With deg equal to seven, the period is actually much | |
98 | longer than the 7*(2**7 - 1) predicted by this formula. */ | |
99 | ||
100 | ||
101 | ||
102 | /* For each of the currently supported random number generators, we have a | |
103 | break value on the amount of state information (you need at least thi | |
104 | bytes of state info to support this random number generator), a degree for | |
105 | the polynomial (actually a trinomial) that the R.N.G. is based on, and | |
106 | separation between the two lower order coefficients of the trinomial. */ | |
107 | ||
108 | /* Linear congruential. */ | |
109 | #define TYPE_0 0 | |
110 | #define BREAK_0 8 | |
111 | #define DEG_0 0 | |
112 | #define SEP_0 0 | |
113 | ||
114 | /* x**7 + x**3 + 1. */ | |
115 | #define TYPE_1 1 | |
116 | #define BREAK_1 32 | |
117 | #define DEG_1 7 | |
118 | #define SEP_1 3 | |
119 | ||
120 | /* x**15 + x + 1. */ | |
121 | #define TYPE_2 2 | |
122 | #define BREAK_2 64 | |
123 | #define DEG_2 15 | |
124 | #define SEP_2 1 | |
125 | ||
126 | /* x**31 + x**3 + 1. */ | |
127 | #define TYPE_3 3 | |
128 | #define BREAK_3 128 | |
129 | #define DEG_3 31 | |
130 | #define SEP_3 3 | |
131 | ||
132 | /* x**63 + x + 1. */ | |
133 | #define TYPE_4 4 | |
134 | #define BREAK_4 256 | |
135 | #define DEG_4 63 | |
136 | #define SEP_4 1 | |
137 | ||
138 | ||
139 | /* Array versions of the above information to make code run faster. | |
140 | Relies on fact that TYPE_i == i. */ | |
141 | ||
142 | #define MAX_TYPES 5 /* Max number of types above. */ | |
143 | ||
144 | static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; | |
145 | static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; | |
146 | ||
147 | ||
148 | ||
149 | /* Initially, everything is set up as if from: | |
150 | initstate(1, randtbl, 128); | |
151 | Note that this initialization takes advantage of the fact that srandom | |
152 | advances the front and rear pointers 10*rand_deg times, and hence the | |
153 | rear pointer which starts at 0 will also end up at zero; thus the zeroeth | |
154 | element of the state information, which contains info about the current | |
155 | position of the rear pointer is just | |
156 | (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */ | |
157 | ||
158 | static long int randtbl[DEG_3 + 1] = | |
159 | { TYPE_3, | |
160 | 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, | |
161 | 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb, | |
162 | 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd, | |
163 | 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, | |
164 | 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7, | |
165 | 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc, | |
166 | 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, | |
167 | 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 | |
168 | }; | |
169 | ||
170 | /* FPTR and RPTR are two pointers into the state info, a front and a rear | |
171 | pointer. These two pointers are always rand_sep places aparts, as they | |
172 | cycle through the state information. (Yes, this does mean we could get | |
173 | away with just one pointer, but the code for random is more efficient | |
174 | this way). The pointers are left positioned as they would be from the call: | |
175 | initstate(1, randtbl, 128); | |
176 | (The position of the rear pointer, rptr, is really 0 (as explained above | |
177 | in the initialization of randtbl) because the state table pointer is set | |
178 | to point to randtbl[1] (as explained below).) */ | |
179 | ||
180 | static long int *fptr = &randtbl[SEP_3 + 1]; | |
181 | static long int *rptr = &randtbl[1]; | |
182 | ||
183 | ||
184 | ||
185 | /* The following things are the pointer to the state information table, | |
186 | the type of the current generator, the degree of the current polynomial | |
187 | being used, and the separation between the two pointers. | |
188 | Note that for efficiency of random, we remember the first location of | |
189 | the state information, not the zeroeth. Hence it is valid to access | |
190 | state[-1], which is used to store the type of the R.N.G. | |
191 | Also, we remember the last location, since this is more efficient than | |
192 | indexing every time to find the address of the last element to see if | |
193 | the front and rear pointers have wrapped. */ | |
194 | ||
195 | static long int *state = &randtbl[1]; | |
196 | ||
197 | static int rand_type = TYPE_3; | |
198 | static int rand_deg = DEG_3; | |
199 | static int rand_sep = SEP_3; | |
200 | ||
2f59c8eb | 201 | static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])]; |
6599da04 JM |
202 | \f |
203 | /* Initialize the random number generator based on the given seed. If the | |
204 | type is the trivial no-state-information type, just remember the seed. | |
205 | Otherwise, initializes state[] based on the given "seed" via a linear | |
206 | congruential generator. Then, the pointers are set to known locations | |
207 | that are exactly rand_sep places apart. Lastly, it cycles the state | |
208 | information a given number of times to get rid of any initial dependencies | |
209 | introduced by the L.C.R.N.G. Note that the initialization of randtbl[] | |
210 | for default usage relies on values produced by this routine. */ | |
211 | void | |
212 | srandom (x) | |
213 | unsigned int x; | |
214 | { | |
215 | state[0] = x; | |
216 | if (rand_type != TYPE_0) | |
217 | { | |
218 | register long int i; | |
219 | for (i = 1; i < rand_deg; ++i) | |
220 | state[i] = (1103515145 * state[i - 1]) + 12345; | |
221 | fptr = &state[rand_sep]; | |
222 | rptr = &state[0]; | |
223 | for (i = 0; i < 10 * rand_deg; ++i) | |
224 | random(); | |
225 | } | |
226 | } | |
227 | \f | |
228 | /* Initialize the state information in the given array of N bytes for | |
229 | future random number generation. Based on the number of bytes we | |
230 | are given, and the break values for the different R.N.G.'s, we choose | |
231 | the best (largest) one we can and set things up for it. srandom is | |
232 | then called to initialize the state information. Note that on return | |
233 | from srandom, we set state[-1] to be the type multiplexed with the current | |
234 | value of the rear pointer; this is so successive calls to initstate won't | |
235 | lose this information and will be able to restart with setstate. | |
236 | Note: The first thing we do is save the current state, if any, just like | |
237 | setstate so that it doesn't matter when initstate is called. | |
238 | Returns a pointer to the old state. */ | |
239 | PTR | |
240 | initstate (seed, arg_state, n) | |
241 | unsigned int seed; | |
242 | PTR arg_state; | |
243 | unsigned long n; | |
244 | { | |
245 | PTR ostate = (PTR) &state[-1]; | |
246 | ||
247 | if (rand_type == TYPE_0) | |
248 | state[-1] = rand_type; | |
249 | else | |
250 | state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; | |
251 | if (n < BREAK_1) | |
252 | { | |
253 | if (n < BREAK_0) | |
254 | { | |
255 | errno = EINVAL; | |
256 | return NULL; | |
257 | } | |
258 | rand_type = TYPE_0; | |
259 | rand_deg = DEG_0; | |
260 | rand_sep = SEP_0; | |
261 | } | |
262 | else if (n < BREAK_2) | |
263 | { | |
264 | rand_type = TYPE_1; | |
265 | rand_deg = DEG_1; | |
266 | rand_sep = SEP_1; | |
267 | } | |
268 | else if (n < BREAK_3) | |
269 | { | |
270 | rand_type = TYPE_2; | |
271 | rand_deg = DEG_2; | |
272 | rand_sep = SEP_2; | |
273 | } | |
274 | else if (n < BREAK_4) | |
275 | { | |
276 | rand_type = TYPE_3; | |
277 | rand_deg = DEG_3; | |
278 | rand_sep = SEP_3; | |
279 | } | |
280 | else | |
281 | { | |
282 | rand_type = TYPE_4; | |
283 | rand_deg = DEG_4; | |
284 | rand_sep = SEP_4; | |
285 | } | |
286 | ||
287 | state = &((long int *) arg_state)[1]; /* First location. */ | |
288 | /* Must set END_PTR before srandom. */ | |
289 | end_ptr = &state[rand_deg]; | |
290 | srandom(seed); | |
291 | if (rand_type == TYPE_0) | |
292 | state[-1] = rand_type; | |
293 | else | |
294 | state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; | |
295 | ||
296 | return ostate; | |
297 | } | |
298 | \f | |
299 | /* Restore the state from the given state array. | |
300 | Note: It is important that we also remember the locations of the pointers | |
301 | in the current state information, and restore the locations of the pointers | |
302 | from the old state information. This is done by multiplexing the pointer | |
303 | location into the zeroeth word of the state information. Note that due | |
304 | to the order in which things are done, it is OK to call setstate with the | |
305 | same state as the current state | |
306 | Returns a pointer to the old state information. */ | |
307 | ||
308 | PTR | |
309 | setstate (arg_state) | |
310 | PTR arg_state; | |
311 | { | |
312 | register long int *new_state = (long int *) arg_state; | |
313 | register int type = new_state[0] % MAX_TYPES; | |
314 | register int rear = new_state[0] / MAX_TYPES; | |
315 | PTR ostate = (PTR) &state[-1]; | |
316 | ||
317 | if (rand_type == TYPE_0) | |
318 | state[-1] = rand_type; | |
319 | else | |
320 | state[-1] = (MAX_TYPES * (rptr - state)) + rand_type; | |
321 | ||
322 | switch (type) | |
323 | { | |
324 | case TYPE_0: | |
325 | case TYPE_1: | |
326 | case TYPE_2: | |
327 | case TYPE_3: | |
328 | case TYPE_4: | |
329 | rand_type = type; | |
330 | rand_deg = degrees[type]; | |
331 | rand_sep = seps[type]; | |
332 | break; | |
333 | default: | |
334 | /* State info munged. */ | |
335 | errno = EINVAL; | |
336 | return NULL; | |
337 | } | |
338 | ||
339 | state = &new_state[1]; | |
340 | if (rand_type != TYPE_0) | |
341 | { | |
342 | rptr = &state[rear]; | |
343 | fptr = &state[(rear + rand_sep) % rand_deg]; | |
344 | } | |
345 | /* Set end_ptr too. */ | |
346 | end_ptr = &state[rand_deg]; | |
347 | ||
348 | return ostate; | |
349 | } | |
350 | \f | |
351 | /* If we are using the trivial TYPE_0 R.N.G., just do the old linear | |
352 | congruential bit. Otherwise, we do our fancy trinomial stuff, which is the | |
353 | same in all ther other cases due to all the global variables that have been | |
354 | set up. The basic operation is to add the number at the rear pointer into | |
355 | the one at the front pointer. Then both pointers are advanced to the next | |
356 | location cyclically in the table. The value returned is the sum generated, | |
357 | reduced to 31 bits by throwing away the "least random" low bit. | |
358 | Note: The code takes advantage of the fact that both the front and | |
359 | rear pointers can't wrap on the same call by not testing the rear | |
360 | pointer if the front one has wrapped. Returns a 31-bit random number. */ | |
361 | ||
362 | long int | |
363 | random () | |
364 | { | |
365 | if (rand_type == TYPE_0) | |
366 | { | |
367 | state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX; | |
368 | return state[0]; | |
369 | } | |
370 | else | |
371 | { | |
372 | long int i; | |
373 | *fptr += *rptr; | |
374 | /* Chucking least random bit. */ | |
375 | i = (*fptr >> 1) & LONG_MAX; | |
376 | ++fptr; | |
377 | if (fptr >= end_ptr) | |
378 | { | |
379 | fptr = state; | |
380 | ++rptr; | |
381 | } | |
382 | else | |
383 | { | |
384 | ++rptr; | |
385 | if (rptr >= end_ptr) | |
386 | rptr = state; | |
387 | } | |
388 | return i; | |
389 | } | |
390 | } |