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33 * $FreeBSD: src/contrib/ntp/libntp/random.c,v 1.1.1.1.2.1 2001/12/21 17:39:09 roberto Exp $
34 * $DragonFly: src/contrib/ntp/libntp/Attic/random.c,v 1.2 2003/06/17 04:24:04 dillon Exp $
38 #if defined(LIBC_SCCS) && !defined(lint)
39 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
40 #endif /* LIBC_SCCS and not lint */
43 #ifdef HAVE_SYS_TYPES_H
44 # include <sys/types.h>
51 #include <ntp_types.h>
56 * An improved random number generation package. In addition to the standard
57 * rand()/srand() like interface, this package also has a special state info
58 * interface. The initstate() routine is called with a seed, an array of
59 * bytes, and a count of how many bytes are being passed in; this array is
60 * then initialized to contain information for random number generation with
61 * that much state information. Good sizes for the amount of state
62 * information are 32, 64, 128, and 256 bytes. The state can be switched by
63 * calling the setstate() routine with the same array as was initiallized
64 * with initstate(). By default, the package runs with 128 bytes of state
65 * information and generates far better random numbers than a linear
66 * congruential generator. If the amount of state information is less than
67 * 32 bytes, a simple linear congruential R.N.G. is used.
69 * Internally, the state information is treated as an array of longs; the
70 * zeroeth element of the array is the type of R.N.G. being used (small
71 * integer); the remainder of the array is the state information for the
72 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
73 * state information, which will allow a degree seven polynomial. (Note:
74 * the zeroeth word of state information also has some other information
75 * stored in it -- see setstate() for details).
77 * The random number generation technique is a linear feedback shift register
78 * approach, employing trinomials (since there are fewer terms to sum up that
79 * way). In this approach, the least significant bit of all the numbers in
80 * the state table will act as a linear feedback shift register, and will
81 * have period 2^deg - 1 (where deg is the degree of the polynomial being
82 * used, assuming that the polynomial is irreducible and primitive). The
83 * higher order bits will have longer periods, since their values are also
84 * influenced by pseudo-random carries out of the lower bits. The total
85 * period of the generator is approximately deg*(2**deg - 1); thus doubling
86 * the amount of state information has a vast influence on the period of the
87 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
88 * large deg, when the period of the shift register is the dominant factor.
89 * With deg equal to seven, the period is actually much longer than the
90 * 7*(2**7 - 1) predicted by this formula.
92 * Modified 28 December 1994 by Jacob S. Rosenberg.
93 * The following changes have been made:
94 * All references to the type u_int have been changed to unsigned long.
95 * All references to type int have been changed to type long. Other
96 * cleanups have been made as well. A warning for both initstate and
97 * setstate has been inserted to the effect that on Sparc platforms
98 * the 'arg_state' variable must be forced to begin on word boundaries.
99 * This can be easily done by casting a long integer array to char *.
100 * The overall logic has been left STRICTLY alone. This software was
101 * tested on both a VAX and Sun SpacsStation with exactly the same
102 * results. The new version and the original give IDENTICAL results.
103 * The new version is somewhat faster than the original. As the
104 * documentation says: "By default, the package runs with 128 bytes of
105 * state information and generates far better random numbers than a linear
106 * congruential generator. If the amount of state information is less than
107 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
108 * 128 bytes, this new version runs about 19 percent faster and for a 16
109 * byte buffer it is about 5 percent faster.
113 * For each of the currently supported random number generators, we have a
114 * break value on the amount of state information (you need at least this
115 * many bytes of state info to support this random number generator), a degree
116 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
117 * the separation between the two lower order coefficients of the trinomial.
119 #define TYPE_0 0 /* linear congruential */
124 #define TYPE_1 1 /* x**7 + x**3 + 1 */
129 #define TYPE_2 2 /* x**15 + x + 1 */
134 #define TYPE_3 3 /* x**31 + x**3 + 1 */
139 #define TYPE_4 4 /* x**63 + x + 1 */
145 * Array versions of the above information to make code run faster --
146 * relies on fact that TYPE_i == i.
148 #define MAX_TYPES 5 /* max number of types above */
150 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
151 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
154 * Initially, everything is set up as if from:
156 * initstate(1, randtbl, 128);
158 * Note that this initialization takes advantage of the fact that srandom()
159 * advances the front and rear pointers 10*rand_deg times, and hence the
160 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
161 * element of the state information, which contains info about the current
162 * position of the rear pointer is just
164 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
167 static long randtbl[DEG_3 + 1] = {
169 #ifdef USE_WEAK_SEEDING
170 /* Historic implementation compatibility */
171 /* The random sequences do not vary much with the seed */
172 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
173 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
174 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
175 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
176 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
178 #else /* !USE_WEAK_SEEDING */
179 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
180 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
181 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
182 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
183 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
185 #endif /* !USE_WEAK_SEEDING */
189 * fptr and rptr are two pointers into the state info, a front and a rear
190 * pointer. These two pointers are always rand_sep places aparts, as they
191 * cycle cyclically through the state information. (Yes, this does mean we
192 * could get away with just one pointer, but the code for random() is more
193 * efficient this way). The pointers are left positioned as they would be
196 * initstate(1, randtbl, 128);
198 * (The position of the rear pointer, rptr, is really 0 (as explained above
199 * in the initialization of randtbl) because the state table pointer is set
200 * to point to randtbl[1] (as explained below).
202 static long *fptr = &randtbl[SEP_3 + 1];
203 static long *rptr = &randtbl[1];
206 * The following things are the pointer to the state information table, the
207 * type of the current generator, the degree of the current polynomial being
208 * used, and the separation between the two pointers. Note that for efficiency
209 * of random(), we remember the first location of the state information, not
210 * the zeroeth. Hence it is valid to access state[-1], which is used to
211 * store the type of the R.N.G. Also, we remember the last location, since
212 * this is more efficient than indexing every time to find the address of
213 * the last element to see if the front and rear pointers have wrapped.
215 static long *state = &randtbl[1];
216 static long rand_type = TYPE_3;
217 static long rand_deg = DEG_3;
218 static long rand_sep = SEP_3;
219 static long *end_ptr = &randtbl[DEG_3 + 1];
221 static inline long good_rand P((long));
222 long random P((void));
229 #ifdef USE_WEAK_SEEDING
231 * Historic implementation compatibility.
232 * The random sequences do not vary much with the seed,
233 * even with overflowing.
235 return (1103515245 * x + 12345);
236 #else /* !USE_WEAK_SEEDING */
238 * Compute x = (7^5 * x) mod (2^31 - 1)
239 * wihout overflowing 31 bits:
240 * (2^31 - 1) = 127773 * (7^5) + 2836
241 * From "Random number generators: good ones are hard to find",
242 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
243 * October 1988, p. 1195.
245 register long hi, lo;
249 x = 16807 * lo - 2836 * hi;
253 #endif /* !USE_WEAK_SEEDING */
259 * Initialize the random number generator based on the given seed. If the
260 * type is the trivial no-state-information type, just remember the seed.
261 * Otherwise, initializes state[] based on the given "seed" via a linear
262 * congruential generator. Then, the pointers are set to known locations
263 * that are exactly rand_sep places apart. Lastly, it cycles the state
264 * information a given number of times to get rid of any initial dependencies
265 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
266 * for default usage relies on values produced by this routine.
275 if (rand_type == TYPE_0)
279 for (i = 1; i < rand_deg; i++)
280 state[i] = good_rand(state[i - 1]);
281 fptr = &state[rand_sep];
283 for (i = 0; i < 10 * rand_deg; i++)
291 * Many programs choose the seed value in a totally predictable manner.
292 * This often causes problems. We seed the generator using the much more
293 * secure urandom(4) interface. Note that this particular seeding
294 * procedure can generate states which are impossible to reproduce by
295 * calling srandom() with any value, since the succeeding terms in the
296 * state buffer are no longer derived from the LC algorithm applied to
303 unsigned long junk; /* Purposely used uninitialized */
305 gettimeofday(&tv, NULL);
306 srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
313 * Initialize the state information in the given array of n bytes for future
314 * random number generation. Based on the number of bytes we are given, and
315 * the break values for the different R.N.G.'s, we choose the best (largest)
316 * one we can and set things up for it. srandom() is then called to
317 * initialize the state information.
319 * Note that on return from srandom(), we set state[-1] to be the type
320 * multiplexed with the current value of the rear pointer; this is so
321 * successive calls to initstate() won't lose this information and will be
322 * able to restart with setstate().
324 * Note: the first thing we do is save the current state, if any, just like
325 * setstate() so that it doesn't matter when initstate is called.
327 * Returns a pointer to the old state.
329 * Note: The Sparc platform requires that arg_state begin on a long
330 * word boundary; otherwise a bus error will occur. Even so, lint will
331 * complain about mis-alignment, but you should disregard these messages.
335 unsigned long seed, /* seed for R.N.G. */
336 char *arg_state, /* pointer to state array */
337 long n /* # bytes of state info */
340 register char *ostate = (char *)(&state[-1]);
341 register long *long_arg_state = (long *) arg_state;
343 if (rand_type == TYPE_0)
344 state[-1] = rand_type;
346 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
348 (void)fprintf(stderr,
349 "random: not enough state (%ld bytes); ignored.\n", n);
356 } else if (n < BREAK_2) {
360 } else if (n < BREAK_3) {
364 } else if (n < BREAK_4) {
373 state = (long *) (long_arg_state + 1); /* first location */
374 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
376 if (rand_type == TYPE_0)
377 long_arg_state[0] = rand_type;
379 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
386 * Restore the state from the given state array.
388 * Note: it is important that we also remember the locations of the pointers
389 * in the current state information, and restore the locations of the pointers
390 * from the old state information. This is done by multiplexing the pointer
391 * location into the zeroeth word of the state information.
393 * Note that due to the order in which things are done, it is OK to call
394 * setstate() with the same state as the current state.
396 * Returns a pointer to the old state information.
398 * Note: The Sparc platform requires that arg_state begin on a long
399 * word boundary; otherwise a bus error will occur. Even so, lint will
400 * complain about mis-alignment, but you should disregard these messages.
404 char *arg_state /* pointer to state array */
407 register long *new_state = (long *) arg_state;
408 register long type = new_state[0] % MAX_TYPES;
409 register long rear = new_state[0] / MAX_TYPES;
410 char *ostate = (char *)(&state[-1]);
412 if (rand_type == TYPE_0)
413 state[-1] = rand_type;
415 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
423 rand_deg = degrees[type];
424 rand_sep = seps[type];
427 (void)fprintf(stderr,
428 "random: state info corrupted; not changed.\n");
430 state = (long *) (new_state + 1);
431 if (rand_type != TYPE_0) {
433 fptr = &state[(rear + rand_sep) % rand_deg];
435 end_ptr = &state[rand_deg]; /* set end_ptr too */
442 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
443 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
444 * the same in all the other cases due to all the global variables that have
445 * been set up. The basic operation is to add the number at the rear pointer
446 * into the one at the front pointer. Then both pointers are advanced to
447 * the next location cyclically in the table. The value returned is the sum
448 * generated, reduced to 31 bits by throwing away the "least random" low bit.
450 * Note: the code takes advantage of the fact that both the front and
451 * rear pointers can't wrap on the same call by not testing the rear
452 * pointer if the front one has wrapped.
454 * Returns a 31-bit random number.
460 register long *f, *r;
462 if (rand_type == TYPE_0) {
464 state[0] = i = (good_rand(i)) & 0x7fffffff;
467 * Use local variables rather than static variables for speed.
471 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
472 if (++f >= end_ptr) {
476 else if (++r >= end_ptr) {