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1.1 root 1: /*
2: * Copyright (c) 1986 Regents of the University of California.
3: * All rights reserved. The Berkeley software License Agreement
4: * specifies the terms and conditions for redistribution.
5: */
6:
7: #ifndef lint
8: static char sccsid[] = "@(#)rnd.c 1.1 (Berkeley) 12/9/86";
9: #endif not lint
10:
11: /*
12: * code for when the good (berkeley) random number generator is around
13: */
14:
15: rnd(num)
16: {
17: return (random() % num);
18: }
19:
20: srnd(num)
21: {
22: srandom(num);
23: }
24:
25: #ifdef NO_RANDOM
26:
27: #ifndef lint
28: static char sccsid[] = "@(#)random.c 4.2 (Berkeley) 83/01/02";
29: #endif
30:
31: #include <stdio.h>
32:
33: /*
34: * random.c:
35: * An improved random number generation package. In addition to the standard
36: * rand()/srand() like interface, this package also has a special state info
37: * interface. The initstate() routine is called with a seed, an array of
38: * bytes, and a count of how many bytes are being passed in; this array is then
39: * initialized to contain information for random number generation with that
40: * much state information. Good sizes for the amount of state information are
41: * 32, 64, 128, and 256 bytes. The state can be switched by calling the
42: * setstate() routine with the same array as was initiallized with initstate().
43: * By default, the package runs with 128 bytes of state information and
44: * generates far better random numbers than a linear congruential generator.
45: * If the amount of state information is less than 32 bytes, a simple linear
46: * congruential R.N.G. is used.
47: * Internally, the state information is treated as an array of longs; the
48: * zeroeth element of the array is the type of R.N.G. being used (small
49: * integer); the remainder of the array is the state information for the
50: * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
51: * state information, which will allow a degree seven polynomial. (Note: the
52: * zeroeth word of state information also has some other information stored
53: * in it -- see setstate() for details).
54: * The random number generation technique is a linear feedback shift register
55: * approach, employing trinomials (since there are fewer terms to sum up that
56: * way). In this approach, the least significant bit of all the numbers in
57: * the state table will act as a linear feedback shift register, and will have
58: * period 2^deg - 1 (where deg is the degree of the polynomial being used,
59: * assuming that the polynomial is irreducible and primitive). The higher
60: * order bits will have longer periods, since their values are also influenced
61: * by pseudo-random carries out of the lower bits. The total period of the
62: * generator is approximately deg*(2**deg - 1); thus doubling the amount of
63: * state information has a vast influence on the period of the generator.
64: * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
65: * when the period of the shift register is the dominant factor. With deg
66: * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
67: * predicted by this formula.
68: */
69:
70:
71:
72: /*
73: * For each of the currently supported random number generators, we have a
74: * break value on the amount of state information (you need at least this
75: * many bytes of state info to support this random number generator), a degree
76: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
77: * the separation between the two lower order coefficients of the trinomial.
78: */
79:
80: #define TYPE_0 0 /* linear congruential */
81: #define BREAK_0 8
82: #define DEG_0 0
83: #define SEP_0 0
84:
85: #define TYPE_1 1 /* x**7 + x**3 + 1 */
86: #define BREAK_1 32
87: #define DEG_1 7
88: #define SEP_1 3
89:
90: #define TYPE_2 2 /* x**15 + x + 1 */
91: #define BREAK_2 64
92: #define DEG_2 15
93: #define SEP_2 1
94:
95: #define TYPE_3 3 /* x**31 + x**3 + 1 */
96: #define BREAK_3 128
97: #define DEG_3 31
98: #define SEP_3 3
99:
100: #define TYPE_4 4 /* x**63 + x + 1 */
101: #define BREAK_4 256
102: #define DEG_4 63
103: #define SEP_4 1
104:
105:
106: /*
107: * Array versions of the above information to make code run faster -- relies
108: * on fact that TYPE_i == i.
109: */
110:
111: #define MAX_TYPES 5 /* max number of types above */
112:
113: static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
114: DEG_3, DEG_4 };
115:
116: static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
117: SEP_3, SEP_4 };
118:
119:
120:
121: /*
122: * Initially, everything is set up as if from :
123: * initstate( 1, &randtbl, 128 );
124: * Note that this initialization takes advantage of the fact that srandom()
125: * advances the front and rear pointers 10*rand_deg times, and hence the
126: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
127: * element of the state information, which contains info about the current
128: * position of the rear pointer is just
129: * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
130: */
131:
132: static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
133: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
134: 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
135: 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
136: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
137: 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
138: 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
139: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
140: 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
141:
142: /*
143: * fptr and rptr are two pointers into the state info, a front and a rear
144: * pointer. These two pointers are always rand_sep places aparts, as they cycle
145: * cyclically through the state information. (Yes, this does mean we could get
146: * away with just one pointer, but the code for random() is more efficient this
147: * way). The pointers are left positioned as they would be from the call
148: * initstate( 1, randtbl, 128 )
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:
154: static long *fptr = &randtbl[ SEP_3 + 1 ];
155: static long *rptr = &randtbl[ 1 ];
156:
157:
158:
159: /*
160: * The following things are the pointer to the state information table,
161: * the type of the current generator, the degree of the current polynomial
162: * being used, and the separation between the two pointers.
163: * Note that for efficiency of random(), we remember the first location of
164: * the state information, not the zeroeth. Hence it is valid to access
165: * state[-1], which is used to store the type of the R.N.G.
166: * Also, we remember the last location, since this is more efficient than
167: * indexing every time to find the address of the last element to see if
168: * the front and rear pointers have wrapped.
169: */
170:
171: static long *state = &randtbl[ 1 ];
172:
173: static int rand_type = TYPE_3;
174: static int rand_deg = DEG_3;
175: static int rand_sep = SEP_3;
176:
177: static long *end_ptr = &randtbl[ DEG_3 + 1 ];
178:
179:
180:
181: /*
182: * srandom:
183: * Initialize the random number generator based on the given seed. If the
184: * type is the trivial no-state-information type, just remember the seed.
185: * Otherwise, initializes state[] based on the given "seed" via a linear
186: * congruential generator. Then, the pointers are set to known locations
187: * that are exactly rand_sep places apart. Lastly, it cycles the state
188: * information a given number of times to get rid of any initial dependencies
189: * introduced by the L.C.R.N.G.
190: * Note that the initialization of randtbl[] for default usage relies on
191: * values produced by this routine.
192: */
193:
194: srandom( x )
195:
196: unsigned x;
197: {
198: register int i, j;
199:
200: if( rand_type == TYPE_0 ) {
201: state[ 0 ] = x;
202: }
203: else {
204: j = 1;
205: state[ 0 ] = x;
206: for( i = 1; i < rand_deg; i++ ) {
207: state[i] = 1103515245*state[i - 1] + 12345;
208: }
209: fptr = &state[ rand_sep ];
210: rptr = &state[ 0 ];
211: for( i = 0; i < 10*rand_deg; i++ ) random();
212: }
213: }
214:
215:
216:
217: /*
218: * initstate:
219: * Initialize the state information in the given array of n bytes for
220: * future random number generation. Based on the number of bytes we
221: * are given, and the break values for the different R.N.G.'s, we choose
222: * the best (largest) one we can and set things up for it. srandom() is
223: * then called to initialize the state information.
224: * Note that on return from srandom(), we set state[-1] to be the type
225: * multiplexed with the current value of the rear pointer; this is so
226: * successive calls to initstate() won't lose this information and will
227: * be able to restart with setstate().
228: * Note: the first thing we do is save the current state, if any, just like
229: * setstate() so that it doesn't matter when initstate is called.
230: * Returns a pointer to the old state.
231: */
232:
233: char *
234: initstate( seed, arg_state, n )
235:
236: unsigned seed; /* seed for R. N. G. */
237: char *arg_state; /* pointer to state array */
238: int n; /* # bytes of state info */
239: {
240: register char *ostate = (char *)( &state[ -1 ] );
241:
242: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
243: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
244: if( n < BREAK_1 ) {
245: if( n < BREAK_0 ) {
246: fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n" );
247: return;
248: }
249: rand_type = TYPE_0;
250: rand_deg = DEG_0;
251: rand_sep = SEP_0;
252: }
253: else {
254: if( n < BREAK_2 ) {
255: rand_type = TYPE_1;
256: rand_deg = DEG_1;
257: rand_sep = SEP_1;
258: }
259: else {
260: if( n < BREAK_3 ) {
261: rand_type = TYPE_2;
262: rand_deg = DEG_2;
263: rand_sep = SEP_2;
264: }
265: else {
266: if( n < BREAK_4 ) {
267: rand_type = TYPE_3;
268: rand_deg = DEG_3;
269: rand_sep = SEP_3;
270: }
271: else {
272: rand_type = TYPE_4;
273: rand_deg = DEG_4;
274: rand_sep = SEP_4;
275: }
276: }
277: }
278: }
279: state = &( ( (long *)arg_state )[1] ); /* first location */
280: end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
281: srandom( seed );
282: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
283: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
284: return( ostate );
285: }
286:
287:
288:
289: /*
290: * setstate:
291: * Restore the state from the given state array.
292: * Note: it is important that we also remember the locations of the pointers
293: * in the current state information, and restore the locations of the pointers
294: * from the old state information. This is done by multiplexing the pointer
295: * location into the zeroeth word of the state information.
296: * Note that due to the order in which things are done, it is OK to call
297: * setstate() with the same state as the current state.
298: * Returns a pointer to the old state information.
299: */
300:
301: char *
302: setstate( arg_state )
303:
304: char *arg_state;
305: {
306: register long *new_state = (long *)arg_state;
307: register int type = new_state[0]%MAX_TYPES;
308: register int rear = new_state[0]/MAX_TYPES;
309: char *ostate = (char *)( &state[ -1 ] );
310:
311: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
312: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
313: switch( type ) {
314: case TYPE_0:
315: case TYPE_1:
316: case TYPE_2:
317: case TYPE_3:
318: case TYPE_4:
319: rand_type = type;
320: rand_deg = degrees[ type ];
321: rand_sep = seps[ type ];
322: break;
323:
324: default:
325: fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
326: }
327: state = &new_state[ 1 ];
328: if( rand_type != TYPE_0 ) {
329: rptr = &state[ rear ];
330: fptr = &state[ (rear + rand_sep)%rand_deg ];
331: }
332: end_ptr = &state[ rand_deg ]; /* set end_ptr too */
333: return( ostate );
334: }
335:
336:
337:
338: /*
339: * random:
340: * If we are using the trivial TYPE_0 R.N.G., just do the old linear
341: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
342: * same in all ther other cases due to all the global variables that have been
343: * set up. The basic operation is to add the number at the rear pointer into
344: * the one at the front pointer. Then both pointers are advanced to the next
345: * location cyclically in the table. The value returned is the sum generated,
346: * reduced to 31 bits by throwing away the "least random" low bit.
347: * Note: the code takes advantage of the fact that both the front and
348: * rear pointers can't wrap on the same call by not testing the rear
349: * pointer if the front one has wrapped.
350: * Returns a 31-bit random number.
351: */
352:
353: long
354: random()
355: {
356: long i;
357:
358: if( rand_type == TYPE_0 ) {
359: i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
360: }
361: else {
362: *fptr += *rptr;
363: i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
364: if( ++fptr >= end_ptr ) {
365: fptr = state;
366: ++rptr;
367: }
368: else {
369: if( ++rptr >= end_ptr ) rptr = state;
370: }
371: }
372: return( i );
373: }
374:
375: #endif NO_RANDOM
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