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 [rescinded 22 July 1999]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