1 /*
2 * Copyright (c) 1983, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * %sccs.include.redist.c%
6 */
7
8 #if defined(LIBC_SCCS) && !defined(lint)
9 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 05/19/95";
10 #endif /* LIBC_SCCS and not lint */
11
12 #include <stdio.h>
13 #include <stdlib.h>
14
15 /*
16 * random.c:
17 *
18 * An improved random number generation package. In addition to the standard
19 * rand()/srand() like interface, this package also has a special state info
20 * interface. The initstate() routine is called with a seed, an array of
21 * bytes, and a count of how many bytes are being passed in; this array is
22 * then initialized to contain information for random number generation with
23 * that much state information. Good sizes for the amount of state
24 * information are 32, 64, 128, and 256 bytes. The state can be switched by
25 * calling the setstate() routine with the same array as was initiallized
26 * with initstate(). By default, the package runs with 128 bytes of state
27 * information and generates far better random numbers than a linear
28 * congruential generator. If the amount of state information is less than
29 * 32 bytes, a simple linear congruential R.N.G. is used.
30 *
31 * Internally, the state information is treated as an array of longs; the
32 * zeroeth element of the array is the type of R.N.G. being used (small
33 * integer); the remainder of the array is the state information for the
34 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
35 * state information, which will allow a degree seven polynomial. (Note:
36 * the zeroeth word of state information also has some other information
37 * stored in it -- see setstate() for details).
38 *
39 * The random number generation technique is a linear feedback shift register
40 * approach, employing trinomials (since there are fewer terms to sum up that
41 * way). In this approach, the least significant bit of all the numbers in
42 * the state table will act as a linear feedback shift register, and will
43 * have period 2^deg - 1 (where deg is the degree of the polynomial being
44 * used, assuming that the polynomial is irreducible and primitive). The
45 * higher order bits will have longer periods, since their values are also
46 * influenced by pseudo-random carries out of the lower bits. The total
47 * period of the generator is approximately deg*(2**deg - 1); thus doubling
48 * the amount of state information has a vast influence on the period of the
49 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
50 * large deg, when the period of the shift register is the dominant factor.
51 * With deg equal to seven, the period is actually much longer than the
52 * 7*(2**7 - 1) predicted by this formula.
53 *
54 * Modified 28 December 1994 by Jacob S. Rosenberg.
55 * The following changes have been made:
56 * All references to the type u_int have been changed to unsigned long.
57 * All references to type int have been changed to type long. Other
58 * cleanups have been made as well. A warning for both initstate and
59 * setstate has been inserted to the effect that on Sparc platforms
60 * the 'arg_state' variable must be forced to begin on word boundaries.
61 * This can be easily done by casting a long integer array to char *.
62 * The overall logic has been left STRICTLY alone. This software was
63 * tested on both a VAX and Sun SpacsStation with exactly the same
64 * results. The new version and the original give IDENTICAL results.
65 * The new version is somewhat faster than the original. As the
66 * documentation says: "By default, the package runs with 128 bytes of
67 * state information and generates far better random numbers than a linear
68 * congruential generator. If the amount of state information is less than
69 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
70 * 128 bytes, this new version runs about 19 percent faster and for a 16
71 * byte buffer it is about 5 percent faster.
72 */
73
74 /*
75 * For each of the currently supported random number generators, we have a
76 * break value on the amount of state information (you need at least this
77 * many bytes of state info to support this random number generator), a degree
78 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
79 * the separation between the two lower order coefficients of the trinomial.
80 */
81 #define TYPE_0 0 /* linear congruential */
82 #define BREAK_0 8
83 #define DEG_0 0
84 #define SEP_0 0
85
86 #define TYPE_1 1 /* x**7 + x**3 + 1 */
87 #define BREAK_1 32
88 #define DEG_1 7
89 #define SEP_1 3
90
91 #define TYPE_2 2 /* x**15 + x + 1 */
92 #define BREAK_2 64
93 #define DEG_2 15
94 #define SEP_2 1
95
96 #define TYPE_3 3 /* x**31 + x**3 + 1 */
97 #define BREAK_3 128
98 #define DEG_3 31
99 #define SEP_3 3
100
101 #define TYPE_4 4 /* x**63 + x + 1 */
102 #define BREAK_4 256
103 #define DEG_4 63
104 #define SEP_4 1
105
106 /*
107 * Array versions of the above information to make code run faster --
108 * relies on fact that TYPE_i == i.
109 */
110 #define MAX_TYPES 5 /* max number of types above */
111
112 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
113 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
114
115 /*
116 * Initially, everything is set up as if from:
117 *
118 * initstate(1, &randtbl, 128);
119 *
120 * Note that this initialization takes advantage of the fact that srandom()
121 * advances the front and rear pointers 10*rand_deg times, and hence the
122 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
123 * element of the state information, which contains info about the current
124 * position of the rear pointer is just
125 *
126 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
127 */
128
129 static long randtbl[DEG_3 + 1] = {
130 TYPE_3,
131 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
132 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
133 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
134 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
135 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
136 0x27fb47b9,
137 };
138
139 /*
140 * fptr and rptr are two pointers into the state info, a front and a rear
141 * pointer. These two pointers are always rand_sep places aparts, as they
142 * cycle cyclically through the state information. (Yes, this does mean we
143 * could get away with just one pointer, but the code for random() is more
144 * efficient this way). The pointers are left positioned as they would be
145 * from the call
146 *
147 * initstate(1, randtbl, 128);
148 *
149 * (The position of the rear pointer, rptr, is really 0 (as explained above
150 * in the initialization of randtbl) because the state table pointer is set
151 * to point to randtbl[1] (as explained below).
152 */
153 static long *fptr = &randtbl[SEP_3 + 1];
154 static long *rptr = &randtbl[1];
155
156 /*
157 * The following things are the pointer to the state information table, the
158 * type of the current generator, the degree of the current polynomial being
159 * used, and the separation between the two pointers. Note that for efficiency
160 * of random(), we remember the first location of the state information, not
161 * the zeroeth. Hence it is valid to access state[-1], which is used to
162 * store the type of the R.N.G. Also, we remember the last location, since
163 * this is more efficient than indexing every time to find the address of
164 * the last element to see if the front and rear pointers have wrapped.
165 */
166 static long *state = &randtbl[1];
167 static long rand_type = TYPE_3;
168 static long rand_deg = DEG_3;
169 static long rand_sep = SEP_3;
170 static long *end_ptr = &randtbl[DEG_3 + 1];
171
172 /*
173 * srandom:
174 *
175 * Initialize the random number generator based on the given seed. If the
176 * type is the trivial no-state-information type, just remember the seed.
177 * Otherwise, initializes state[] based on the given "seed" via a linear
178 * congruential generator. Then, the pointers are set to known locations
179 * that are exactly rand_sep places apart. Lastly, it cycles the state
180 * information a given number of times to get rid of any initial dependencies
181 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
182 * for default usage relies on values produced by this routine.
183 */
184 void
srandom(x)185 srandom(x)
186 unsigned long x;
187 {
188 register long i;
189
190 if (rand_type == TYPE_0)
191 state[0] = x;
192 else {
193 state[0] = x;
194 for (i = 1; i < rand_deg; i++)
195 state[i] = 1103515245 * state[i - 1] + 12345;
196 fptr = &state[rand_sep];
197 rptr = &state[0];
198 for (i = 0; i < 10 * rand_deg; i++)
199 (void)random();
200 }
201 }
202
203 /*
204 * initstate:
205 *
206 * Initialize the state information in the given array of n bytes for future
207 * random number generation. Based on the number of bytes we are given, and
208 * the break values for the different R.N.G.'s, we choose the best (largest)
209 * one we can and set things up for it. srandom() is then called to
210 * initialize the state information.
211 *
212 * Note that on return from srandom(), we set state[-1] to be the type
213 * multiplexed with the current value of the rear pointer; this is so
214 * successive calls to initstate() won't lose this information and will be
215 * able to restart with setstate().
216 *
217 * Note: the first thing we do is save the current state, if any, just like
218 * setstate() so that it doesn't matter when initstate is called.
219 *
220 * Returns a pointer to the old state.
221 *
222 * Note: The Sparc platform requires that arg_state begin on a long
223 * word boundary; otherwise a bus error will occur. Even so, lint will
224 * complain about mis-alignment, but you should disregard these messages.
225 */
226 char *
initstate(seed,arg_state,n)227 initstate(seed, arg_state, n)
228 unsigned long seed; /* seed for R.N.G. */
229 char *arg_state; /* pointer to state array */
230 long n; /* # bytes of state info */
231 {
232 register char *ostate = (char *)(&state[-1]);
233 register long *long_arg_state = (long *) arg_state;
234
235 if (rand_type == TYPE_0)
236 state[-1] = rand_type;
237 else
238 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
239 if (n < BREAK_0) {
240 (void)fprintf(stderr,
241 "random: not enough state (%ld bytes); ignored.\n", n);
242 return(0);
243 }
244 if (n < BREAK_1) {
245 rand_type = TYPE_0;
246 rand_deg = DEG_0;
247 rand_sep = SEP_0;
248 } else if (n < BREAK_2) {
249 rand_type = TYPE_1;
250 rand_deg = DEG_1;
251 rand_sep = SEP_1;
252 } else if (n < BREAK_3) {
253 rand_type = TYPE_2;
254 rand_deg = DEG_2;
255 rand_sep = SEP_2;
256 } else if (n < BREAK_4) {
257 rand_type = TYPE_3;
258 rand_deg = DEG_3;
259 rand_sep = SEP_3;
260 } else {
261 rand_type = TYPE_4;
262 rand_deg = DEG_4;
263 rand_sep = SEP_4;
264 }
265 state = (long *) (long_arg_state + 1); /* first location */
266 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
267 srandom(seed);
268 if (rand_type == TYPE_0)
269 long_arg_state[0] = rand_type;
270 else
271 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
272 return(ostate);
273 }
274
275 /*
276 * setstate:
277 *
278 * Restore the state from the given state array.
279 *
280 * Note: it is important that we also remember the locations of the pointers
281 * in the current state information, and restore the locations of the pointers
282 * from the old state information. This is done by multiplexing the pointer
283 * location into the zeroeth word of the state information.
284 *
285 * Note that due to the order in which things are done, it is OK to call
286 * setstate() with the same state as the current state.
287 *
288 * Returns a pointer to the old state information.
289 *
290 * Note: The Sparc platform requires that arg_state begin on a long
291 * word boundary; otherwise a bus error will occur. Even so, lint will
292 * complain about mis-alignment, but you should disregard these messages.
293 */
294 char *
setstate(arg_state)295 setstate(arg_state)
296 char *arg_state; /* pointer to state array */
297 {
298 register long *new_state = (long *) arg_state;
299 register long type = new_state[0] % MAX_TYPES;
300 register long rear = new_state[0] / MAX_TYPES;
301 char *ostate = (char *)(&state[-1]);
302
303 if (rand_type == TYPE_0)
304 state[-1] = rand_type;
305 else
306 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
307 switch(type) {
308 case TYPE_0:
309 case TYPE_1:
310 case TYPE_2:
311 case TYPE_3:
312 case TYPE_4:
313 rand_type = type;
314 rand_deg = degrees[type];
315 rand_sep = seps[type];
316 break;
317 default:
318 (void)fprintf(stderr,
319 "random: state info corrupted; not changed.\n");
320 }
321 state = (long *) (new_state + 1);
322 if (rand_type != TYPE_0) {
323 rptr = &state[rear];
324 fptr = &state[(rear + rand_sep) % rand_deg];
325 }
326 end_ptr = &state[rand_deg]; /* set end_ptr too */
327 return(ostate);
328 }
329
330 /*
331 * random:
332 *
333 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
334 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
335 * the same in all the other cases due to all the global variables that have
336 * been set up. The basic operation is to add the number at the rear pointer
337 * into the one at the front pointer. Then both pointers are advanced to
338 * the next location cyclically in the table. The value returned is the sum
339 * generated, reduced to 31 bits by throwing away the "least random" low bit.
340 *
341 * Note: the code takes advantage of the fact that both the front and
342 * rear pointers can't wrap on the same call by not testing the rear
343 * pointer if the front one has wrapped.
344 *
345 * Returns a 31-bit random number.
346 */
347 long
random()348 random()
349 {
350 register long i;
351 register long *f, *r;
352
353 if (rand_type == TYPE_0) {
354 i = state[0];
355 state[0] = i = (i * 1103515245 + 12345) & 0x7fffffff;
356 } else {
357 /*
358 * Use local variables rather than static variables for speed.
359 */
360 f = fptr; r = rptr;
361 *f += *r;
362 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
363 if (++f >= end_ptr) {
364 f = state;
365 ++r;
366 }
367 else if (++r >= end_ptr) {
368 r = state;
369 }
370
371 fptr = f; rptr = r;
372 }
373 return(i);
374 }
375