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1.1 root 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 are permitted
6: * provided that: (1) source distributions retain this entire copyright
7: * notice and comment, and (2) distributions including binaries display
8: * the following acknowledgement: ``This product includes software
9: * developed by the University of California, Berkeley and its contributors''
10: * in the documentation or other materials provided with the distribution
11: * and in all advertising materials mentioning features or use of this
12: * software. Neither the name of the University nor the names of its
13: * contributors may be used to endorse or promote products derived
14: * from this software without specific prior written permission.
15: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
16: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
17: * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
18: */
19:
20: #if defined(LIBC_SCCS) && !defined(lint)
21: static char sccsid[] = "@(#)random.c 5.7 (Berkeley) 6/1/90";
22: #endif /* LIBC_SCCS and not lint */
23:
24: #include <stdio.h>
25:
26: /*
27: * random.c:
28: * An improved random number generation package. In addition to the standard
29: * rand()/srand() like interface, this package also has a special state info
30: * interface. The initstate() routine is called with a seed, an array of
31: * bytes, and a count of how many bytes are being passed in; this array is then
32: * initialized to contain information for random number generation with that
33: * much state information. Good sizes for the amount of state information are
34: * 32, 64, 128, and 256 bytes. The state can be switched by calling the
35: * setstate() routine with the same array as was initiallized with initstate().
36: * By default, the package runs with 128 bytes of state information and
37: * generates far better random numbers than a linear congruential generator.
38: * If the amount of state information is less than 32 bytes, a simple linear
39: * congruential R.N.G. is used.
40: * Internally, the state information is treated as an array of longs; the
41: * zeroeth element of the array is the type of R.N.G. being used (small
42: * integer); the remainder of the array is the state information for the
43: * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
44: * state information, which will allow a degree seven polynomial. (Note: the
45: * zeroeth word of state information also has some other information stored
46: * in it -- see setstate() for details).
47: * The random number generation technique is a linear feedback shift register
48: * approach, employing trinomials (since there are fewer terms to sum up that
49: * way). In this approach, the least significant bit of all the numbers in
50: * the state table will act as a linear feedback shift register, and will have
51: * period 2^deg - 1 (where deg is the degree of the polynomial being used,
52: * assuming that the polynomial is irreducible and primitive). The higher
53: * order bits will have longer periods, since their values are also influenced
54: * by pseudo-random carries out of the lower bits. The total period of the
55: * generator is approximately deg*(2**deg - 1); thus doubling the amount of
56: * state information has a vast influence on the period of the generator.
57: * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
58: * when the period of the shift register is the dominant factor. With deg
59: * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
60: * predicted by this formula.
61: */
62:
63:
64:
65: /*
66: * For each of the currently supported random number generators, we have a
67: * break value on the amount of state information (you need at least this
68: * many bytes of state info to support this random number generator), a degree
69: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
70: * the separation between the two lower order coefficients of the trinomial.
71: */
72:
73: #define TYPE_0 0 /* linear congruential */
74: #define BREAK_0 8
75: #define DEG_0 0
76: #define SEP_0 0
77:
78: #define TYPE_1 1 /* x**7 + x**3 + 1 */
79: #define BREAK_1 32
80: #define DEG_1 7
81: #define SEP_1 3
82:
83: #define TYPE_2 2 /* x**15 + x + 1 */
84: #define BREAK_2 64
85: #define DEG_2 15
86: #define SEP_2 1
87:
88: #define TYPE_3 3 /* x**31 + x**3 + 1 */
89: #define BREAK_3 128
90: #define DEG_3 31
91: #define SEP_3 3
92:
93: #define TYPE_4 4 /* x**63 + x + 1 */
94: #define BREAK_4 256
95: #define DEG_4 63
96: #define SEP_4 1
97:
98:
99: /*
100: * Array versions of the above information to make code run faster -- relies
101: * on fact that TYPE_i == i.
102: */
103:
104: #define MAX_TYPES 5 /* max number of types above */
105:
106: static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
107: DEG_3, DEG_4 };
108:
109: static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
110: SEP_3, SEP_4 };
111:
112:
113:
114: /*
115: * Initially, everything is set up as if from :
116: * initstate( 1, &randtbl, 128 );
117: * Note that this initialization takes advantage of the fact that srandom()
118: * advances the front and rear pointers 10*rand_deg times, and hence the
119: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
120: * element of the state information, which contains info about the current
121: * position of the rear pointer is just
122: * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
123: */
124:
125: static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
126: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
127: 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
128: 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
129: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
130: 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
131: 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
132: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
133: 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
134:
135: /*
136: * fptr and rptr are two pointers into the state info, a front and a rear
137: * pointer. These two pointers are always rand_sep places aparts, as they cycle
138: * cyclically through the state information. (Yes, this does mean we could get
139: * away with just one pointer, but the code for random() is more efficient this
140: * way). The pointers are left positioned as they would be from the call
141: * initstate( 1, randtbl, 128 )
142: * (The position of the rear pointer, rptr, is really 0 (as explained above
143: * in the initialization of randtbl) because the state table pointer is set
144: * to point to randtbl[1] (as explained below).
145: */
146:
147: static long *fptr = &randtbl[ SEP_3 + 1 ];
148: static long *rptr = &randtbl[ 1 ];
149:
150:
151:
152: /*
153: * The following things are the pointer to the state information table,
154: * the type of the current generator, the degree of the current polynomial
155: * being used, and the separation between the two pointers.
156: * Note that for efficiency of random(), we remember the first location of
157: * the state information, not the zeroeth. Hence it is valid to access
158: * state[-1], which is used to store the type of the R.N.G.
159: * Also, we remember the last location, since this is more efficient than
160: * indexing every time to find the address of the last element to see if
161: * the front and rear pointers have wrapped.
162: */
163:
164: static long *state = &randtbl[ 1 ];
165:
166: static int rand_type = TYPE_3;
167: static int rand_deg = DEG_3;
168: static int rand_sep = SEP_3;
169:
170: static long *end_ptr = &randtbl[ DEG_3 + 1 ];
171:
172:
173:
174: /*
175: * srandom:
176: * Initialize the random number generator based on the given seed. If the
177: * type is the trivial no-state-information type, just remember the seed.
178: * Otherwise, initializes state[] based on the given "seed" via a linear
179: * congruential generator. Then, the pointers are set to known locations
180: * that are exactly rand_sep places apart. Lastly, it cycles the state
181: * information a given number of times to get rid of any initial dependencies
182: * introduced by the L.C.R.N.G.
183: * Note that the initialization of randtbl[] for default usage relies on
184: * values produced by this routine.
185: */
186:
187: srandom( x )
188:
189: unsigned x;
190: {
191: register int i, j;
192: long random();
193:
194: if( rand_type == TYPE_0 ) {
195: state[ 0 ] = x;
196: }
197: else {
198: j = 1;
199: state[ 0 ] = x;
200: for( i = 1; i < rand_deg; i++ ) {
201: state[i] = 1103515245*state[i - 1] + 12345;
202: }
203: fptr = &state[ rand_sep ];
204: rptr = &state[ 0 ];
205: for( i = 0; i < 10*rand_deg; i++ ) random();
206: }
207: }
208:
209:
210:
211: /*
212: * initstate:
213: * Initialize the state information in the given array of n bytes for
214: * future random number generation. Based on the number of bytes we
215: * are given, and the break values for the different R.N.G.'s, we choose
216: * the best (largest) one we can and set things up for it. srandom() is
217: * then called to initialize the state information.
218: * Note that on return from srandom(), we set state[-1] to be the type
219: * multiplexed with the current value of the rear pointer; this is so
220: * successive calls to initstate() won't lose this information and will
221: * be able to restart with setstate().
222: * Note: the first thing we do is save the current state, if any, just like
223: * setstate() so that it doesn't matter when initstate is called.
224: * Returns a pointer to the old state.
225: */
226:
227: char *
228: initstate( seed, arg_state, n )
229:
230: unsigned seed; /* seed for R. N. G. */
231: char *arg_state; /* pointer to state array */
232: int n; /* # bytes of state info */
233: {
234: register char *ostate = (char *)( &state[ -1 ] );
235:
236: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
237: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
238: if( n < BREAK_1 ) {
239: if( n < BREAK_0 ) {
240: fprintf( stderr, "initstate: not enough state (%d bytes); ignored.\n", n );
241: return 0;
242: }
243: rand_type = TYPE_0;
244: rand_deg = DEG_0;
245: rand_sep = SEP_0;
246: }
247: else {
248: if( n < BREAK_2 ) {
249: rand_type = TYPE_1;
250: rand_deg = DEG_1;
251: rand_sep = SEP_1;
252: }
253: else {
254: if( n < BREAK_3 ) {
255: rand_type = TYPE_2;
256: rand_deg = DEG_2;
257: rand_sep = SEP_2;
258: }
259: else {
260: if( n < BREAK_4 ) {
261: rand_type = TYPE_3;
262: rand_deg = DEG_3;
263: rand_sep = SEP_3;
264: }
265: else {
266: rand_type = TYPE_4;
267: rand_deg = DEG_4;
268: rand_sep = SEP_4;
269: }
270: }
271: }
272: }
273: state = &( ( (long *)arg_state )[1] ); /* first location */
274: end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
275: srandom( seed );
276: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
277: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
278: return( ostate );
279: }
280:
281:
282:
283: /*
284: * setstate:
285: * Restore the state from the given state array.
286: * Note: it is important that we also remember the locations of the pointers
287: * in the current state information, and restore the locations of the pointers
288: * from the old state information. This is done by multiplexing the pointer
289: * location into the zeroeth word of the state information.
290: * Note that due to the order in which things are done, it is OK to call
291: * setstate() with the same state as the current state.
292: * Returns a pointer to the old state information.
293: */
294:
295: char *
296: setstate( arg_state )
297:
298: char *arg_state;
299: {
300: register long *new_state = (long *)arg_state;
301: register int type = new_state[0]%MAX_TYPES;
302: register int rear = new_state[0]/MAX_TYPES;
303: char *ostate = (char *)( &state[ -1 ] );
304:
305: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
306: else 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:
318: default:
319: fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
320: }
321: state = &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:
332: /*
333: * random:
334: * If we are using the trivial TYPE_0 R.N.G., just do the old linear
335: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
336: * same in all ther other cases due to all the global variables that have been
337: * set up. The basic operation is to add the number at the rear pointer into
338: * the one at the front pointer. Then both pointers are advanced to the next
339: * location cyclically in the table. The value returned is the sum generated,
340: * reduced to 31 bits by throwing away the "least random" low bit.
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: * Returns a 31-bit random number.
345: */
346:
347: long
348: random()
349: {
350: long i;
351:
352: if( rand_type == TYPE_0 ) {
353: i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
354: }
355: else {
356: *fptr += *rptr;
357: i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
358: if( ++fptr >= end_ptr ) {
359: fptr = state;
360: ++rptr;
361: }
362: else {
363: if( ++rptr >= end_ptr ) rptr = state;
364: }
365: }
366: return( i );
367: }
368:
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