Annotation of OpenXM/src/kan96xx/gmp-2.0.2-ssh-2/random.c, Revision 1.1.1.1
1.1 takayama 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, with or without
6: * modification, are permitted provided that the following conditions
7: * are met:
8: * 1. Redistributions of source code must retain the above copyright
9: * notice, this list of conditions and the following disclaimer.
10: * 2. Redistributions in binary form must reproduce the above copyright
11: * notice, this list of conditions and the following disclaimer in the
12: * documentation and/or other materials provided with the distribution.
13: * 3. All advertising materials mentioning features or use of this software
14: * must display the following acknowledgement:
15: * This product includes software developed by the University of
16: * California, Berkeley and its contributors.
17: * 4. Neither the name of the University nor the names of its contributors
18: * may be used to endorse or promote products derived from this software
19: * without specific prior written permission.
20: *
21: * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22: * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24: * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25: * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26: * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27: * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28: * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29: * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30: * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31: * SUCH DAMAGE.
32: */
33:
34: #if defined(LIBC_SCCS) && !defined(lint)
35: static char sccsid[] = "@(#)random.c 5.9 (Berkeley) 2/23/91";
36: #endif /* LIBC_SCCS and not lint */
37:
38: #include <stdio.h>
39: #include <stdlib.h>
40: #include <sys/types.h>
41:
42: /*
43: * random.c:
44: *
45: * An improved random number generation package. In addition to the standard
46: * rand()/srand() like interface, this package also has a special state info
47: * interface. The initstate() routine is called with a seed, an array of
48: * bytes, and a count of how many bytes are being passed in; this array is
49: * then initialized to contain information for random number generation with
50: * that much state information. Good sizes for the amount of state
51: * information are 32, 64, 128, and 256 bytes. The state can be switched by
52: * calling the setstate() routine with the same array as was initiallized
53: * with initstate(). By default, the package runs with 128 bytes of state
54: * information and generates far better random numbers than a linear
55: * congruential generator. If the amount of state information is less than
56: * 32 bytes, a simple linear congruential R.N.G. is used.
57: *
58: * Internally, the state information is treated as an array of longs; the
59: * zeroeth element of the array is the type of R.N.G. being used (small
60: * integer); the remainder of the array is the state information for the
61: * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
62: * state information, which will allow a degree seven polynomial. (Note:
63: * the zeroeth word of state information also has some other information
64: * stored in it -- see setstate() for details).
65: *
66: * The random number generation technique is a linear feedback shift register
67: * approach, employing trinomials (since there are fewer terms to sum up that
68: * way). In this approach, the least significant bit of all the numbers in
69: * the state table will act as a linear feedback shift register, and will
70: * have period 2^deg - 1 (where deg is the degree of the polynomial being
71: * used, assuming that the polynomial is irreducible and primitive). The
72: * higher order bits will have longer periods, since their values are also
73: * influenced by pseudo-random carries out of the lower bits. The total
74: * period of the generator is approximately deg*(2**deg - 1); thus doubling
75: * the amount of state information has a vast influence on the period of the
76: * generator. Note: the deg*(2**deg - 1) is an approximation only good for
77: * large deg, when the period of the shift register is the dominant factor.
78: * With deg equal to seven, the period is actually much longer than the
79: * 7*(2**7 - 1) predicted by this formula.
80: */
81:
82: /*
83: * For each of the currently supported random number generators, we have a
84: * break value on the amount of state information (you need at least this
85: * many bytes of state info to support this random number generator), a degree
86: * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
87: * the separation between the two lower order coefficients of the trinomial.
88: */
89: #define TYPE_0 0 /* linear congruential */
90: #define BREAK_0 8
91: #define DEG_0 0
92: #define SEP_0 0
93:
94: #define TYPE_1 1 /* x**7 + x**3 + 1 */
95: #define BREAK_1 32
96: #define DEG_1 7
97: #define SEP_1 3
98:
99: #define TYPE_2 2 /* x**15 + x + 1 */
100: #define BREAK_2 64
101: #define DEG_2 15
102: #define SEP_2 1
103:
104: #define TYPE_3 3 /* x**31 + x**3 + 1 */
105: #define BREAK_3 128
106: #define DEG_3 31
107: #define SEP_3 3
108:
109: #define TYPE_4 4 /* x**63 + x + 1 */
110: #define BREAK_4 256
111: #define DEG_4 63
112: #define SEP_4 1
113:
114: /*
115: * Array versions of the above information to make code run faster --
116: * relies on fact that TYPE_i == i.
117: */
118: #define MAX_TYPES 5 /* max number of types above */
119:
120: static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
121: static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
122:
123: /*
124: * Initially, everything is set up as if from:
125: *
126: * initstate(1, &randtbl, 128);
127: *
128: * Note that this initialization takes advantage of the fact that srandom()
129: * advances the front and rear pointers 10*rand_deg times, and hence the
130: * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
131: * element of the state information, which contains info about the current
132: * position of the rear pointer is just
133: *
134: * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
135: */
136:
137: static long randtbl[DEG_3 + 1] = {
138: TYPE_3,
139: 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
140: 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
141: 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
142: 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
143: 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
144: 0x27fb47b9,
145: };
146:
147: /*
148: * fptr and rptr are two pointers into the state info, a front and a rear
149: * pointer. These two pointers are always rand_sep places aparts, as they
150: * cycle cyclically through the state information. (Yes, this does mean we
151: * could get away with just one pointer, but the code for random() is more
152: * efficient this way). The pointers are left positioned as they would be
153: * from the call
154: *
155: * initstate(1, randtbl, 128);
156: *
157: * (The position of the rear pointer, rptr, is really 0 (as explained above
158: * in the initialization of randtbl) because the state table pointer is set
159: * to point to randtbl[1] (as explained below).
160: */
161: static long *fptr = &randtbl[SEP_3 + 1];
162: static long *rptr = &randtbl[1];
163:
164: /*
165: * The following things are the pointer to the state information table, the
166: * type of the current generator, the degree of the current polynomial being
167: * used, and the separation between the two pointers. Note that for efficiency
168: * of random(), we remember the first location of the state information, not
169: * the zeroeth. Hence it is valid to access state[-1], which is used to
170: * store the type of the R.N.G. Also, we remember the last location, since
171: * this is more efficient than indexing every time to find the address of
172: * the last element to see if the front and rear pointers have wrapped.
173: */
174: static long *state = &randtbl[1];
175: static int rand_type = TYPE_3;
176: static int rand_deg = DEG_3;
177: static int rand_sep = SEP_3;
178: static long *end_ptr = &randtbl[DEG_3 + 1];
179:
180: long random();
181:
182: /*
183: * srandom:
184: *
185: * Initialize the random number generator based on the given seed. If the
186: * type is the trivial no-state-information type, just remember the seed.
187: * Otherwise, initializes state[] based on the given "seed" via a linear
188: * congruential generator. Then, the pointers are set to known locations
189: * that are exactly rand_sep places apart. Lastly, it cycles the state
190: * information a given number of times to get rid of any initial dependencies
191: * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
192: * for default usage relies on values produced by this routine.
193: */
194: void
195: srandom(x)
196: unsigned int x;
197: {
198: register int i, j;
199:
200: if (rand_type == TYPE_0)
201: state[0] = x;
202: else {
203: j = 1;
204: state[0] = x;
205: for (i = 1; i < rand_deg; i++)
206: state[i] = 1103515245 * state[i - 1] + 12345;
207: fptr = &state[rand_sep];
208: rptr = &state[0];
209: for (i = 0; i < 10 * rand_deg; i++)
210: (void)random();
211: }
212: }
213:
214: /*
215: * initstate:
216: *
217: * Initialize the state information in the given array of n bytes for future
218: * random number generation. Based on the number of bytes we are given, and
219: * the break values for the different R.N.G.'s, we choose the best (largest)
220: * one we can and set things up for it. srandom() is then called to
221: * initialize the state information.
222: *
223: * Note that on return from srandom(), we set state[-1] to be the type
224: * multiplexed with the current value of the rear pointer; this is so
225: * successive calls to initstate() won't lose this information and will be
226: * able to restart with setstate().
227: *
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: *
231: * Returns a pointer to the old state.
232: */
233: char *
234: initstate(seed, arg_state, n)
235: unsigned int seed; /* seed for R.N.G. */
236: char *arg_state; /* pointer to state array */
237: int n; /* # bytes of state info */
238: {
239: register char *ostate = (char *)(&state[-1]);
240:
241: if (rand_type == TYPE_0)
242: state[-1] = rand_type;
243: else
244: state[-1] = MAX_TYPES * (rptr - state) + rand_type;
245: if (n < BREAK_0) {
246: (void)fprintf(stderr,
247: "random: not enough state (%d bytes); ignored.\n", n);
248: return(0);
249: }
250: if (n < BREAK_1) {
251: rand_type = TYPE_0;
252: rand_deg = DEG_0;
253: rand_sep = SEP_0;
254: } else if (n < BREAK_2) {
255: rand_type = TYPE_1;
256: rand_deg = DEG_1;
257: rand_sep = SEP_1;
258: } else if (n < BREAK_3) {
259: rand_type = TYPE_2;
260: rand_deg = DEG_2;
261: rand_sep = SEP_2;
262: } else if (n < BREAK_4) {
263: rand_type = TYPE_3;
264: rand_deg = DEG_3;
265: rand_sep = SEP_3;
266: } else {
267: rand_type = TYPE_4;
268: rand_deg = DEG_4;
269: rand_sep = SEP_4;
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)
275: state[-1] = rand_type;
276: else
277: state[-1] = MAX_TYPES*(rptr - state) + rand_type;
278: return(ostate);
279: }
280:
281: /*
282: * setstate:
283: *
284: * Restore the state from the given state array.
285: *
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: *
291: * Note that due to the order in which things are done, it is OK to call
292: * setstate() with the same state as the current state.
293: *
294: * Returns a pointer to the old state information.
295: */
296: char *
297: setstate(arg_state)
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)
306: state[-1] = rand_type;
307: else
308: state[-1] = MAX_TYPES * (rptr - state) + rand_type;
309: switch(type) {
310: case TYPE_0:
311: case TYPE_1:
312: case TYPE_2:
313: case TYPE_3:
314: case TYPE_4:
315: rand_type = type;
316: rand_deg = degrees[type];
317: rand_sep = seps[type];
318: break;
319: default:
320: (void)fprintf(stderr,
321: "random: state info corrupted; not changed.\n");
322: }
323: state = &new_state[1];
324: if (rand_type != TYPE_0) {
325: rptr = &state[rear];
326: fptr = &state[(rear + rand_sep) % rand_deg];
327: }
328: end_ptr = &state[rand_deg]; /* set end_ptr too */
329: return(ostate);
330: }
331:
332: /*
333: * random:
334: *
335: * If we are using the trivial TYPE_0 R.N.G., just do the old linear
336: * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
337: * the same in all the other cases due to all the global variables that have
338: * been set up. The basic operation is to add the number at the rear pointer
339: * into the one at the front pointer. Then both pointers are advanced to
340: * the next location cyclically in the table. The value returned is the sum
341: * generated, reduced to 31 bits by throwing away the "least random" low bit.
342: *
343: * Note: the code takes advantage of the fact that both the front and
344: * rear pointers can't wrap on the same call by not testing the rear
345: * pointer if the front one has wrapped.
346: *
347: * Returns a 31-bit random number.
348: */
349: long
350: random()
351: {
352: long i;
353:
354: if (rand_type == TYPE_0)
355: i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff;
356: else {
357: *fptr += *rptr;
358: i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */
359: if (++fptr >= end_ptr) {
360: fptr = state;
361: ++rptr;
362: } else if (++rptr >= end_ptr)
363: rptr = state;
364: }
365: return(i);
366: }
367:
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