|
0
|
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 [rescinded 22 July 1999]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
|
|
|
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
|
|
|
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
|
|
|
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
|
|
|
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 }
|
