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1.1 root 1: #ifndef lint
2: static char sccsid[] = "@(#)random.c 4.2 (Berkeley) 83/01/02";
3: #endif
4:
5: #include <stdio.h>
6:
7: /*
8: * random.c:
9: * An improved random number generation package. In addition to the standard
10: * rand()/srand() like interface, this package also has a special state info
11: * interface. The initstate() routine is called with a seed, an array of
12: * bytes, and a count of how many bytes are being passed in; this array is then
13: * initialized to contain information for random number generation with that
14: * much state information. Good sizes for the amount of state information are
15: * 32, 64, 128, and 256 bytes. The state can be switched by calling the
16: * setstate() routine with the same array as was initiallized with initstate().
17: * By default, the package runs with 128 bytes of state information and
18: * generates far better random numbers than a linear congruential generator.
19: * If the amount of state information is less than 32 bytes, a simple linear
20: * congruential R.N.G. is used.
21: * Internally, the state information is treated as an array of longs; the
22: * zeroeth element of the array is the type of R.N.G. being used (small
23: * integer); the remainder of the array is the state information for the
24: * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
25: * state information, which will allow a degree seven polynomial. (Note: the
26: * zeroeth word of state information also has some other information stored
27: * in it -- see setstate() for details).
28: * The random number generation technique is a linear feedback shift register
29: * approach, employing trinomials (since there are fewer terms to sum up that
30: * way). In this approach, the least significant bit of all the numbers in
31: * the state table will act as a linear feedback shift register, and will have
32: * period 2^deg - 1 (where deg is the degree of the polynomial being used,
33: * assuming that the polynomial is irreducible and primitive). The higher
34: * order bits will have longer periods, since their values are also influenced
35: * by pseudo-random carries out of the lower bits. The total period of the
36: * generator is approximately deg*(2**deg - 1); thus doubling the amount of
37: * state information has a vast influence on the period of the generator.
38: * Note: the deg*(2**deg - 1) is an approximation only good for large deg,
39: * when the period of the shift register is the dominant factor. With deg
40: * equal to seven, the period is actually much longer than the 7*(2**7 - 1)
41: * predicted by this formula.
42: */
43:
44:
45:
46: /*
47: * For each of the currently supported random number generators, we have a
48: * break value on the amount of state information (you need at least this
49: * many bytes of state info to support this random number generator), a degree
50: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
51: * the separation between the two lower order coefficients of the trinomial.
52: */
53:
54: #define TYPE_0 0 /* linear congruential */
55: #define BREAK_0 8
56: #define DEG_0 0
57: #define SEP_0 0
58:
59: #define TYPE_1 1 /* x**7 + x**3 + 1 */
60: #define BREAK_1 32
61: #define DEG_1 7
62: #define SEP_1 3
63:
64: #define TYPE_2 2 /* x**15 + x + 1 */
65: #define BREAK_2 64
66: #define DEG_2 15
67: #define SEP_2 1
68:
69: #define TYPE_3 3 /* x**31 + x**3 + 1 */
70: #define BREAK_3 128
71: #define DEG_3 31
72: #define SEP_3 3
73:
74: #define TYPE_4 4 /* x**63 + x + 1 */
75: #define BREAK_4 256
76: #define DEG_4 63
77: #define SEP_4 1
78:
79:
80: /*
81: * Array versions of the above information to make code run faster -- relies
82: * on fact that TYPE_i == i.
83: */
84:
85: #define MAX_TYPES 5 /* max number of types above */
86:
87: static int degrees[ MAX_TYPES ] = { DEG_0, DEG_1, DEG_2,
88: DEG_3, DEG_4 };
89:
90: static int seps[ MAX_TYPES ] = { SEP_0, SEP_1, SEP_2,
91: SEP_3, SEP_4 };
92:
93:
94:
95: /*
96: * Initially, everything is set up as if from :
97: * initstate( 1, &randtbl, 128 );
98: * Note that this initialization takes advantage of the fact that srandom()
99: * advances the front and rear pointers 10*rand_deg times, and hence the
100: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
101: * element of the state information, which contains info about the current
102: * position of the rear pointer is just
103: * MAX_TYPES*(rptr - state) + TYPE_3 == TYPE_3.
104: */
105:
106: static long randtbl[ DEG_3 + 1 ] = { TYPE_3,
107: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342,
108: 0xde3b81e0, 0xdf0a6fb5, 0xf103bc02, 0x48f340fb,
109: 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
110: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86,
111: 0xda672e2a, 0x1588ca88, 0xe369735d, 0x904f35f7,
112: 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
113: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b,
114: 0xf5ad9d0e, 0x8999220b, 0x27fb47b9 };
115:
116: /*
117: * fptr and rptr are two pointers into the state info, a front and a rear
118: * pointer. These two pointers are always rand_sep places aparts, as they cycle
119: * cyclically through the state information. (Yes, this does mean we could get
120: * away with just one pointer, but the code for random() is more efficient this
121: * way). The pointers are left positioned as they would be from the call
122: * initstate( 1, randtbl, 128 )
123: * (The position of the rear pointer, rptr, is really 0 (as explained above
124: * in the initialization of randtbl) because the state table pointer is set
125: * to point to randtbl[1] (as explained below).
126: */
127:
128: static long *fptr = &randtbl[ SEP_3 + 1 ];
129: static long *rptr = &randtbl[ 1 ];
130:
131:
132:
133: /*
134: * The following things are the pointer to the state information table,
135: * the type of the current generator, the degree of the current polynomial
136: * being used, and the separation between the two pointers.
137: * Note that for efficiency of random(), we remember the first location of
138: * the state information, not the zeroeth. Hence it is valid to access
139: * state[-1], which is used to store the type of the R.N.G.
140: * Also, we remember the last location, since this is more efficient than
141: * indexing every time to find the address of the last element to see if
142: * the front and rear pointers have wrapped.
143: */
144:
145: static long *state = &randtbl[ -1 ];
146:
147: static int rand_type = TYPE_3;
148: static int rand_deg = DEG_3;
149: static int rand_sep = SEP_3;
150:
151: static long *end_ptr = &randtbl[ DEG_3 + 1 ];
152:
153:
154:
155: /*
156: * srandom:
157: * Initialize the random number generator based on the given seed. If the
158: * type is the trivial no-state-information type, just remember the seed.
159: * Otherwise, initializes state[] based on the given "seed" via a linear
160: * congruential generator. Then, the pointers are set to known locations
161: * that are exactly rand_sep places apart. Lastly, it cycles the state
162: * information a given number of times to get rid of any initial dependencies
163: * introduced by the L.C.R.N.G.
164: * Note that the initialization of randtbl[] for default usage relies on
165: * values produced by this routine.
166: */
167:
168: srandom( x )
169:
170: unsigned x;
171: {
172: register int i, j;
173:
174: if( rand_type == TYPE_0 ) {
175: state[ 0 ] = x;
176: }
177: else {
178: j = 1;
179: state[ 0 ] = x;
180: for( i = 1; i < rand_deg; i++ ) {
181: state[i] = 1103515245*state[i - 1] + 12345;
182: }
183: fptr = &state[ rand_sep ];
184: rptr = &state[ 0 ];
185: for( i = 0; i < 10*rand_deg; i++ ) random();
186: }
187: }
188:
189:
190:
191: /*
192: * initstate:
193: * Initialize the state information in the given array of n bytes for
194: * future random number generation. Based on the number of bytes we
195: * are given, and the break values for the different R.N.G.'s, we choose
196: * the best (largest) one we can and set things up for it. srandom() is
197: * then called to initialize the state information.
198: * Note that on return from srandom(), we set state[-1] to be the type
199: * multiplexed with the current value of the rear pointer; this is so
200: * successive calls to initstate() won't lose this information and will
201: * be able to restart with setstate().
202: * Note: the first thing we do is save the current state, if any, just like
203: * setstate() so that it doesn't matter when initstate is called.
204: * Returns a pointer to the old state.
205: */
206:
207: char *
208: initstate( seed, arg_state, n )
209:
210: unsigned seed; /* seed for R. N. G. */
211: char *arg_state; /* pointer to state array */
212: int n; /* # bytes of state info */
213: {
214: register char *ostate = (char *)( &state[ -1 ] );
215:
216: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
217: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
218: if( n < BREAK_1 ) {
219: if( n < BREAK_0 ) {
220: fprintf( stderr, "initstate: not enough state (%d bytes) with which to do jack; ignored.\n" );
221: return;
222: }
223: rand_type = TYPE_0;
224: rand_deg = DEG_0;
225: rand_sep = SEP_0;
226: }
227: else {
228: if( n < BREAK_2 ) {
229: rand_type = TYPE_1;
230: rand_deg = DEG_1;
231: rand_sep = SEP_1;
232: }
233: else {
234: if( n < BREAK_3 ) {
235: rand_type = TYPE_2;
236: rand_deg = DEG_2;
237: rand_sep = SEP_2;
238: }
239: else {
240: if( n < BREAK_4 ) {
241: rand_type = TYPE_3;
242: rand_deg = DEG_3;
243: rand_sep = SEP_3;
244: }
245: else {
246: rand_type = TYPE_4;
247: rand_deg = DEG_4;
248: rand_sep = SEP_4;
249: }
250: }
251: }
252: }
253: state = &( ( (long *)arg_state )[1] ); /* first location */
254: end_ptr = &state[ rand_deg ]; /* must set end_ptr before srandom */
255: srandom( seed );
256: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
257: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
258: return( ostate );
259: }
260:
261:
262:
263: /*
264: * setstate:
265: * Restore the state from the given state array.
266: * Note: it is important that we also remember the locations of the pointers
267: * in the current state information, and restore the locations of the pointers
268: * from the old state information. This is done by multiplexing the pointer
269: * location into the zeroeth word of the state information.
270: * Note that due to the order in which things are done, it is OK to call
271: * setstate() with the same state as the current state.
272: * Returns a pointer to the old state information.
273: */
274:
275: char *
276: setstate( arg_state )
277:
278: char *arg_state;
279: {
280: register long *new_state = (long *)arg_state;
281: register int type = new_state[0]%MAX_TYPES;
282: register int rear = new_state[0]/MAX_TYPES;
283: char *ostate = (char *)( &state[ -1 ] );
284:
285: if( rand_type == TYPE_0 ) state[ -1 ] = rand_type;
286: else state[ -1 ] = MAX_TYPES*(rptr - state) + rand_type;
287: switch( type ) {
288: case TYPE_0:
289: case TYPE_1:
290: case TYPE_2:
291: case TYPE_3:
292: case TYPE_4:
293: rand_type = type;
294: rand_deg = degrees[ type ];
295: rand_sep = seps[ type ];
296: break;
297:
298: default:
299: fprintf( stderr, "setstate: state info has been munged; not changed.\n" );
300: }
301: state = &new_state[ 1 ];
302: if( rand_type != TYPE_0 ) {
303: rptr = &state[ rear ];
304: fptr = &state[ (rear + rand_sep)%rand_deg ];
305: }
306: end_ptr = &state[ rand_deg ]; /* set end_ptr too */
307: return( ostate );
308: }
309:
310:
311:
312: /*
313: * random:
314: * If we are using the trivial TYPE_0 R.N.G., just do the old linear
315: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is the
316: * same in all ther other cases due to all the global variables that have been
317: * set up. The basic operation is to add the number at the rear pointer into
318: * the one at the front pointer. Then both pointers are advanced to the next
319: * location cyclically in the table. The value returned is the sum generated,
320: * reduced to 31 bits by throwing away the "least random" low bit.
321: * Note: the code takes advantage of the fact that both the front and
322: * rear pointers can't wrap on the same call by not testing the rear
323: * pointer if the front one has wrapped.
324: * Returns a 31-bit random number.
325: */
326:
327: long
328: random()
329: {
330: long i;
331:
332: if( rand_type == TYPE_0 ) {
333: i = state[0] = ( state[0]*1103515245 + 12345 )&0x7fffffff;
334: }
335: else {
336: *fptr += *rptr;
337: i = (*fptr >> 1)&0x7fffffff; /* chucking least random bit */
338: if( ++fptr >= end_ptr ) {
339: fptr = state;
340: ++rptr;
341: }
342: else {
343: if( ++rptr >= end_ptr ) rptr = state;
344: }
345: }
346: return( i );
347: }
348:
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