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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 the above copyright notice and this paragraph are
7: * duplicated in all such forms and that any documentation,
8: * advertising materials, and other materials related to such
9: * distribution and use acknowledge that the software was developed
10: * by the University of California, Berkeley. The name of the
11: * University may not be used to endorse or promote products derived
12: * from this software without specific prior written permission.
13: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
14: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
15: * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
16: */
17:
18: #if defined(LIBC_SCCS) && !defined(lint)
19: static char sccsid[] = "@(#)random.c 5.5 (Berkeley) 7/6/88";
20: #endif /* LIBC_SCCS and not lint */
21:
22: #include <stdio.h>
23:
24: /*
25: * random.c:
26: * An improved random number generation package. In addition to the standard
27: * rand()/srand() like interface, this package also has a special state info
28: * interface. The initstate() routine is called with a seed, an array of
29: * bytes, and a count of how many bytes are being passed in; this array is then
30: * initialized to contain information for random number generation with that
31: * much state information. Good sizes for the amount of state information are
32: * 32, 64, 128, and 256 bytes. The state can be switched by calling the
33: * setstate() routine with the same array as was initiallized with initstate().
34: * By default, the package runs with 128 bytes of state information and
35: * generates far better random numbers than a linear congruential generator.
36: * If the amount of state information is less than 32 bytes, a simple linear
37: * congruential R.N.G. is used.
38: * Internally, the state information is treated as an array of longs; the
39: * zeroeth element of the array is the type of R.N.G. being used (small
40: * integer); the remainder of the array is the state information for the
41: * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
42: * state information, which will allow a degree seven polynomial. (Note: the
43: * zeroeth word of state information also has some other information stored
44: * in it -- see setstate() for details).
45: * The random number generation technique is a linear feedback shift register
46: * approach, employing trinomials (since there are fewer terms to sum up that
47: * way). In this approach, the least significant bit of all the numbers in
48: * the state table will act as a linear feedback shift register, and will have
49: * period 2^deg - 1 (where deg is the degree of the polynomial being used,
50: * assuming that the polynomial is irreducible and primitive). The higher
51: * order bits will have longer periods, since their values are also influenced
52: * by pseudo-random carries out of the lower bits. The total period of the
53: * generator is approximately deg*(2**deg - 1); thus doubling the amount of
54: * state information has a vast influence on the period of the generator.
55: * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
56: * when the period of the shift register is the dominant factor. With deg
57: * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
58: * predicted by this formula.
59: */
60:
61:
62:
63: /*
64: * For each of the currently supported random number generators, we have a
65: * break value on the amount of state information (you need at least this
66: * many bytes of state info to support this random number generator), a degree
67: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
68: * the separation between the two lower order coefficients of the trinomial.
69: */
70:
71: #define TYPE_0 0 /* linear congruential */
72: #define BREAK_0 8
73: #define DEG_0 0
74: #define SEP_0 0
75:
76: #define TYPE_1 1 /* x**7 + x**3 + 1 */
77: #define BREAK_1 32
78: #define DEG_1 7
79: #define SEP_1 3
80:
81: #define TYPE_2 2 /* x**15 + x + 1 */
82: #define BREAK_2 64
83: #define DEG_2 15
84: #define SEP_2 1
85:
86: #define TYPE_3 3 /* x**31 + x**3 + 1 */
87: #define BREAK_3 128
88: #define DEG_3 31
89: #define SEP_3 3
90:
91: #define TYPE_4 4 /* x**63 + x + 1 */
92: #define BREAK_4 256
93: #define DEG_4 63
94: #define SEP_4 1
95:
96:
97: /*
98: * Array versions of the above information to make code run faster -- relies
99: * on fact that TYPE_i == i.
100: */
101:
102: #define MAX_TYPES 5 /* max number of types above */
103:
104: static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
105: DEG_3, DEG_4 };
106:
107: static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
108: SEP_3, SEP_4 };
109:
110:
111:
112: /*
113: * Initially, everything is set up as if from :
114: * initstate( 1, &randtbl, 128 );
115: * Note that this initialization takes advantage of the fact that srandom()
116: * advances the front and rear pointers 10*rand_deg times, and hence the
117: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
118: * element of the state information, which contains info about the current
119: * position of the rear pointer is just
120: * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
121: */
122:
123: static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
124: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
125: 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
126: 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
127: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
128: 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
129: 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
130: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
131: 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
132:
133: /*
134: * fptr and rptr are two pointers into the state info, a front and a rear
135: * pointer. These two pointers are always rand_sep places aparts, as they cycle
136: * cyclically through the state information. (Yes, this does mean we could get
137: * away with just one pointer, but the code for random() is more efficient this
138: * way). The pointers are left positioned as they would be from the call
139: * initstate( 1, randtbl, 128 )
140: * (The position of the rear pointer, rptr, is really 0 (as explained above
141: * in the initialization of randtbl) because the state table pointer is set
142: * to point to randtbl[1] (as explained below).
143: */
144:
145: static long *fptr = &randtbl[ SEP_3 + 1 ];
146: static long *rptr = &randtbl[ 1 ];
147:
148:
149:
150: /*
151: * The following things are the pointer to the state information table,
152: * the type of the current generator, the degree of the current polynomial
153: * being used, and the separation between the two pointers.
154: * Note that for efficiency of random(), we remember the first location of
155: * the state information, not the zeroeth. Hence it is valid to access
156: * state[-1], which is used to store the type of the R.N.G.
157: * Also, we remember the last location, since this is more efficient than
158: * indexing every time to find the address of the last element to see if
159: * the front and rear pointers have wrapped.
160: */
161:
162: static long *state = &randtbl[ 1 ];
163:
164: static int rand_type = TYPE_3;
165: static int rand_deg = DEG_3;
166: static int rand_sep = SEP_3;
167:
168: static long *end_ptr = &randtbl[ DEG_3 + 1 ];
169:
170:
171:
172: /*
173: * srandom:
174: * Initialize the random number generator based on the given seed. If the
175: * type is the trivial no-state-information type, just remember the seed.
176: * Otherwise, initializes state[] based on the given "seed" via a linear
177: * congruential generator. Then, the pointers are set to known locations
178: * that are exactly rand_sep places apart. Lastly, it cycles the state
179: * information a given number of times to get rid of any initial dependencies
180: * introduced by the L.C.R.N.G.
181: * Note that the initialization of randtbl[] for default usage relies on
182: * values produced by this routine.
183: */
184:
185: srandom( x )
186:
187: unsigned x;
188: {
189: register int i, j;
190: long random();
191:
192: if( rand_type == TYPE_0 ) {
193: state[ 0 ] = x;
194: }
195: else {
196: j = 1;
197: state[ 0 ] = x;
198: for( i = 1; i < rand_deg; i++ ) {
199: state[i] = 1103515245*state[i - 1] + 12345;
200: }
201: fptr = &state[ rand_sep ];
202: rptr = &state[ 0 ];
203: for( i = 0; i < 10*rand_deg; i++ ) random();
204: }
205: }
206:
207:
208:
209: /*
210: * initstate:
211: * Initialize the state information in the given array of n bytes for
212: * future random number generation. Based on the number of bytes we
213: * are given, and the break values for the different R.N.G.'s, we choose
214: * the best (largest) one we can and set things up for it. srandom() is
215: * then called to initialize the state information.
216: * Note that on return from srandom(), we set state[-1] to be the type
217: * multiplexed with the current value of the rear pointer; this is so
218: * successive calls to initstate() won't lose this information and will
219: * be able to restart with setstate().
220: * Note: the first thing we do is save the current state, if any, just like
221: * setstate() so that it doesn't matter when initstate is called.
222: * Returns a pointer to the old state.
223: */
224:
225: char *
226: initstate( seed, arg_state, n )
227:
228: unsigned seed; /* seed for R. N. G. */
229: char *arg_state; /* pointer to state array */
230: int n; /* # bytes of state info */
231: {
232: register char *ostate = (char *)( &state[ -1 ] );
233:
234: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
235: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
236: if( n < BREAK_1 ) {
237: if( n < BREAK_0 ) {
238: fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n", n );
239: return;
240: }
241: rand_type = TYPE_0;
242: rand_deg = DEG_0;
243: rand_sep = SEP_0;
244: }
245: else {
246: if( n < BREAK_2 ) {
247: rand_type = TYPE_1;
248: rand_deg = DEG_1;
249: rand_sep = SEP_1;
250: }
251: else {
252: if( n < BREAK_3 ) {
253: rand_type = TYPE_2;
254: rand_deg = DEG_2;
255: rand_sep = SEP_2;
256: }
257: else {
258: if( n < BREAK_4 ) {
259: rand_type = TYPE_3;
260: rand_deg = DEG_3;
261: rand_sep = SEP_3;
262: }
263: else {
264: rand_type = TYPE_4;
265: rand_deg = DEG_4;
266: rand_sep = SEP_4;
267: }
268: }
269: }
270: }
271: state = &( ( (long *)arg_state )[1] ); /* first location */
272: end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
273: srandom( seed );
274: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
275: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
276: return( ostate );
277: }
278:
279:
280:
281: /*
282: * setstate:
283: * Restore the state from the given state array.
284: * Note: it is important that we also remember the locations of the pointers
285: * in the current state information, and restore the locations of the pointers
286: * from the old state information. This is done by multiplexing the pointer
287: * location into the zeroeth word of the state information.
288: * Note that due to the order in which things are done, it is OK to call
289: * setstate() with the same state as the current state.
290: * Returns a pointer to the old state information.
291: */
292:
293: char *
294: setstate( arg_state )
295:
296: char *arg_state;
297: {
298: register long *new_state = (long *)arg_state;
299: register int type = new_state[0]%MAX_TYPES;
300: register int rear = new_state[0]/MAX_TYPES;
301: char *ostate = (char *)( &state[ -1 ] );
302:
303: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
304: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
305: switch( type ) {
306: case TYPE_0:
307: case TYPE_1:
308: case TYPE_2:
309: case TYPE_3:
310: case TYPE_4:
311: rand_type = type;
312: rand_deg = degrees[ type ];
313: rand_sep = seps[ type ];
314: break;
315:
316: default:
317: fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
318: }
319: state = &new_state[ 1 ];
320: if( rand_type != TYPE_0 ) {
321: rptr = &state[ rear ];
322: fptr = &state[ (rear + rand_sep)%rand_deg ];
323: }
324: end_ptr = &state[ rand_deg ]; /* set end_ptr too */
325: return( ostate );
326: }
327:
328:
329:
330: /*
331: * random:
332: * If we are using the trivial TYPE_0 R.N.G., just do the old linear
333: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
334: * same in all ther other cases due to all the global variables that have been
335: * set up. The basic operation is to add the number at the rear pointer into
336: * the one at the front pointer. Then both pointers are advanced to the next
337: * location cyclically in the table. The value returned is the sum generated,
338: * reduced to 31 bits by throwing away the "least random" low bit.
339: * Note: the code takes advantage of the fact that both the front and
340: * rear pointers can't wrap on the same call by not testing the rear
341: * pointer if the front one has wrapped.
342: * Returns a 31-bit random number.
343: */
344:
345: long
346: random()
347: {
348: long i;
349:
350: if( rand_type == TYPE_0 ) {
351: i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
352: }
353: else {
354: *fptr += *rptr;
355: i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
356: if( ++fptr >= end_ptr ) {
357: fptr = state;
358: ++rptr;
359: }
360: else {
361: if( ++rptr >= end_ptr ) rptr = state;
362: }
363: }
364: return( i );
365: }
366:
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