1 /*
2 * Copyright (c) 1983 Regents of the University of California.
3 * All rights reserved.
4 *
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 [rescinded 22 July 1999]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.
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 /*
38
39 @deftypefn Supplement {long int} random (void)
40 @deftypefnx Supplement void srandom (unsigned int @var{seed})
41 @deftypefnx Supplement void* initstate (unsigned int @var{seed}, void *@var{arg_state}, unsigned long @var{n})
42 @deftypefnx Supplement void* setstate (void *@var{arg_state})
43
44 Random number functions. @code{random} returns a random number in the
45 range 0 to @code{LONG_MAX}. @code{srandom} initializes the random
46 number generator to some starting point determined by @var{seed}
47 (else, the values returned by @code{random} are always the same for each
48 run of the program). @code{initstate} and @code{setstate} allow fine-grained
49 control over the state of the random number generator.
50
51 @end deftypefn
52
53 */
54
55 #include <errno.h>
56
57 #if 0
58
59 #include <ansidecl.h>
60 #include <limits.h>
61 #include <stddef.h>
62 #include <stdlib.h>
63
64 #else
65
66 #define ULONG_MAX ((unsigned long)(~0L)) /* 0xFFFFFFFF for 32-bits */
67 #define LONG_MAX ((long)(ULONG_MAX >> 1)) /* 0x7FFFFFFF for 32-bits*/
68
69 #ifdef __STDC__
70 # define PTR void *
71 # ifndef NULL
72 # define NULL (void *) 0
73 # endif
74 #else
75 # define PTR char *
76 # ifndef NULL
77 # define NULL (void *) 0
78 # endif
79 #endif
80
81 #endif
82
83 long int random (void);
84
85 /* An improved random number generation package. In addition to the standard
86 rand()/srand() like interface, this package also has a special state info
87 interface. The initstate() routine is called with a seed, an array of
88 bytes, and a count of how many bytes are being passed in; this array is
89 then initialized to contain information for random number generation with
90 that much state information. Good sizes for the amount of state
91 information are 32, 64, 128, and 256 bytes. The state can be switched by
92 calling the setstate() function with the same array as was initiallized
93 with initstate(). By default, the package runs with 128 bytes of state
94 information and generates far better random numbers than a linear
95 congruential generator. If the amount of state information is less than
96 32 bytes, a simple linear congruential R.N.G. is used. Internally, the
97 state information is treated as an array of longs; the zeroeth element of
98 the array is the type of R.N.G. being used (small integer); the remainder
99 of the array is the state information for the R.N.G. Thus, 32 bytes of
100 state information will give 7 longs worth of state information, which will
101 allow a degree seven polynomial. (Note: The zeroeth word of state
102 information also has some other information stored in it; see setstate
103 for details). The random number generation technique is a linear feedback
104 shift register approach, employing trinomials (since there are fewer terms
105 to sum up that way). In this approach, the least significant bit of all
106 the numbers in the state table will act as a linear feedback shift register,
107 and will have period 2^deg - 1 (where deg is the degree of the polynomial
108 being used, assuming that the polynomial is irreducible and primitive).
109 The higher order bits will have longer periods, since their values are
110 also influenced by pseudo-random carries out of the lower bits. The
111 total period of the generator is approximately deg*(2**deg - 1); thus
112 doubling the amount of state information has a vast influence on the
113 period of the generator. Note: The deg*(2**deg - 1) is an approximation
114 only good for large deg, when the period of the shift register is the
115 dominant factor. With deg equal to seven, the period is actually much
116 longer than the 7*(2**7 - 1) predicted by this formula. */
117
118
119
120 /* For each of the currently supported random number generators, we have a
121 break value on the amount of state information (you need at least thi
122 bytes of state info to support this random number generator), a degree for
123 the polynomial (actually a trinomial) that the R.N.G. is based on, and
124 separation between the two lower order coefficients of the trinomial. */
125
126 /* Linear congruential. */
127 #define TYPE_0 0
128 #define BREAK_0 8
129 #define DEG_0 0
130 #define SEP_0 0
131
132 /* x**7 + x**3 + 1. */
133 #define TYPE_1 1
134 #define BREAK_1 32
135 #define DEG_1 7
136 #define SEP_1 3
137
138 /* x**15 + x + 1. */
139 #define TYPE_2 2
140 #define BREAK_2 64
141 #define DEG_2 15
142 #define SEP_2 1
143
144 /* x**31 + x**3 + 1. */
145 #define TYPE_3 3
146 #define BREAK_3 128
147 #define DEG_3 31
148 #define SEP_3 3
149
150 /* x**63 + x + 1. */
151 #define TYPE_4 4
152 #define BREAK_4 256
153 #define DEG_4 63
154 #define SEP_4 1
155
156
157 /* Array versions of the above information to make code run faster.
158 Relies on fact that TYPE_i == i. */
159
160 #define MAX_TYPES 5 /* Max number of types above. */
161
162 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
163 static int seps[MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
164
165
166
167 /* Initially, everything is set up as if from:
168 initstate(1, randtbl, 128);
169 Note that this initialization takes advantage of the fact that srandom
170 advances the front and rear pointers 10*rand_deg times, and hence the
171 rear pointer which starts at 0 will also end up at zero; thus the zeroeth
172 element of the state information, which contains info about the current
173 position of the rear pointer is just
174 (MAX_TYPES * (rptr - state)) + TYPE_3 == TYPE_3. */
175
176 static long int randtbl[DEG_3 + 1] =
177 { TYPE_3,
178 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
179 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
180 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
181 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
182 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
183 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
184 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
185 0xf5ad9d0e, 0x8999220b, 0x27fb47b9
186 };
187
188 /* FPTR and RPTR are two pointers into the state info, a front and a rear
189 pointer. These two pointers are always rand_sep places aparts, as they
190 cycle through the state information. (Yes, this does mean we could get
191 away with just one pointer, but the code for random is more efficient
192 this way). The pointers are left positioned as they would be from the call:
193 initstate(1, randtbl, 128);
194 (The position of the rear pointer, rptr, is really 0 (as explained above
195 in the initialization of randtbl) because the state table pointer is set
196 to point to randtbl[1] (as explained below).) */
197
198 static long int *fptr = &randtbl[SEP_3 + 1];
199 static long int *rptr = &randtbl[1];
200
201
202
203 /* The following things are the pointer to the state information table,
204 the type of the current generator, the degree of the current polynomial
205 being used, and the separation between the two pointers.
206 Note that for efficiency of random, we remember the first location of
207 the state information, not the zeroeth. Hence it is valid to access
208 state[-1], which is used to store the type of the R.N.G.
209 Also, we remember the last location, since this is more efficient than
210 indexing every time to find the address of the last element to see if
211 the front and rear pointers have wrapped. */
212
213 static long int *state = &randtbl[1];
214
215 static int rand_type = TYPE_3;
216 static int rand_deg = DEG_3;
217 static int rand_sep = SEP_3;
218
219 static long int *end_ptr = &randtbl[sizeof(randtbl) / sizeof(randtbl[0])];
220
221 /* Initialize the random number generator based on the given seed. If the
222 type is the trivial no-state-information type, just remember the seed.
223 Otherwise, initializes state[] based on the given "seed" via a linear
224 congruential generator. Then, the pointers are set to known locations
225 that are exactly rand_sep places apart. Lastly, it cycles the state
226 information a given number of times to get rid of any initial dependencies
227 introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
228 for default usage relies on values produced by this routine. */
229 void
srandom(unsigned int x)230 srandom (unsigned int x)
231 {
232 state[0] = x;
233 if (rand_type != TYPE_0)
234 {
235 register long int i;
236 for (i = 1; i < rand_deg; ++i)
237 state[i] = (1103515145 * state[i - 1]) + 12345;
238 fptr = &state[rand_sep];
239 rptr = &state[0];
240 for (i = 0; i < 10 * rand_deg; ++i)
241 random();
242 }
243 }
244
245 /* Initialize the state information in the given array of N bytes for
246 future random number generation. Based on the number of bytes we
247 are given, and the break values for the different R.N.G.'s, we choose
248 the best (largest) one we can and set things up for it. srandom is
249 then called to initialize the state information. Note that on return
250 from srandom, we set state[-1] to be the type multiplexed with the current
251 value of the rear pointer; this is so successive calls to initstate won't
252 lose this information and will be able to restart with setstate.
253 Note: The first thing we do is save the current state, if any, just like
254 setstate so that it doesn't matter when initstate is called.
255 Returns a pointer to the old state. */
256 PTR
initstate(unsigned int seed,PTR arg_state,unsigned long n)257 initstate (unsigned int seed, PTR arg_state, unsigned long n)
258 {
259 PTR ostate = (PTR) &state[-1];
260
261 if (rand_type == TYPE_0)
262 state[-1] = rand_type;
263 else
264 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
265 if (n < BREAK_1)
266 {
267 if (n < BREAK_0)
268 {
269 errno = EINVAL;
270 return NULL;
271 }
272 rand_type = TYPE_0;
273 rand_deg = DEG_0;
274 rand_sep = SEP_0;
275 }
276 else if (n < BREAK_2)
277 {
278 rand_type = TYPE_1;
279 rand_deg = DEG_1;
280 rand_sep = SEP_1;
281 }
282 else if (n < BREAK_3)
283 {
284 rand_type = TYPE_2;
285 rand_deg = DEG_2;
286 rand_sep = SEP_2;
287 }
288 else if (n < BREAK_4)
289 {
290 rand_type = TYPE_3;
291 rand_deg = DEG_3;
292 rand_sep = SEP_3;
293 }
294 else
295 {
296 rand_type = TYPE_4;
297 rand_deg = DEG_4;
298 rand_sep = SEP_4;
299 }
300
301 state = &((long int *) arg_state)[1]; /* First location. */
302 /* Must set END_PTR before srandom. */
303 end_ptr = &state[rand_deg];
304 srandom(seed);
305 if (rand_type == TYPE_0)
306 state[-1] = rand_type;
307 else
308 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
309
310 return ostate;
311 }
312
313 /* Restore the state from the given state array.
314 Note: It is important that we also remember the locations of the pointers
315 in the current state information, and restore the locations of the pointers
316 from the old state information. This is done by multiplexing the pointer
317 location into the zeroeth word of the state information. Note that due
318 to the order in which things are done, it is OK to call setstate with the
319 same state as the current state
320 Returns a pointer to the old state information. */
321
322 PTR
setstate(PTR arg_state)323 setstate (PTR arg_state)
324 {
325 register long int *new_state = (long int *) arg_state;
326 register int type = new_state[0] % MAX_TYPES;
327 register int rear = new_state[0] / MAX_TYPES;
328 PTR ostate = (PTR) &state[-1];
329
330 if (rand_type == TYPE_0)
331 state[-1] = rand_type;
332 else
333 state[-1] = (MAX_TYPES * (rptr - state)) + rand_type;
334
335 switch (type)
336 {
337 case TYPE_0:
338 case TYPE_1:
339 case TYPE_2:
340 case TYPE_3:
341 case TYPE_4:
342 rand_type = type;
343 rand_deg = degrees[type];
344 rand_sep = seps[type];
345 break;
346 default:
347 /* State info munged. */
348 errno = EINVAL;
349 return NULL;
350 }
351
352 state = &new_state[1];
353 if (rand_type != TYPE_0)
354 {
355 rptr = &state[rear];
356 fptr = &state[(rear + rand_sep) % rand_deg];
357 }
358 /* Set end_ptr too. */
359 end_ptr = &state[rand_deg];
360
361 return ostate;
362 }
363
364 /* If we are using the trivial TYPE_0 R.N.G., just do the old linear
365 congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
366 same in all ther other cases due to all the global variables that have been
367 set up. The basic operation is to add the number at the rear pointer into
368 the one at the front pointer. Then both pointers are advanced to the next
369 location cyclically in the table. The value returned is the sum generated,
370 reduced to 31 bits by throwing away the "least random" low bit.
371 Note: The code takes advantage of the fact that both the front and
372 rear pointers can't wrap on the same call by not testing the rear
373 pointer if the front one has wrapped. Returns a 31-bit random number. */
374
375 long int
random(void)376 random (void)
377 {
378 if (rand_type == TYPE_0)
379 {
380 state[0] = ((state[0] * 1103515245) + 12345) & LONG_MAX;
381 return state[0];
382 }
383 else
384 {
385 long int i;
386 *fptr += *rptr;
387 /* Chucking least random bit. */
388 i = (*fptr >> 1) & LONG_MAX;
389 ++fptr;
390 if (fptr >= end_ptr)
391 {
392 fptr = state;
393 ++rptr;
394 }
395 else
396 {
397 ++rptr;
398 if (rptr >= end_ptr)
399 rptr = state;
400 }
401 return i;
402 }
403 }
404