1 /*
2 * Copyright (c) 1983, 1993
3 * The Regents of the University of California. 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 * $FreeBSD: src/lib/libc/stdlib/random.c,v 1.4.2.2 1999/09/05 11:16:45 peter Exp $
34 *
35 */
36
37 #if defined(LIBC_SCCS) && !defined(lint)
38 static char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
39 #endif /* LIBC_SCCS and not lint */
40
41 #include "config.h"
42 #include <sys/types.h>
43 #ifdef HAVE_UNISTD_H
44 # include <unistd.h>
45 #endif
46 #include <stdio.h>
47
48 #include <l_stdlib.h>
49 #include <ntp_random.h>
50 #include <ntp_unixtime.h>
51
52 /*
53 * random.c:
54 *
55 * An improved random number generation package. In addition to the standard
56 * rand()/srand() like interface, this package also has a special state info
57 * interface. The initstate() routine is called with a seed, an array of
58 * bytes, and a count of how many bytes are being passed in; this array is
59 * then initialized to contain information for random number generation with
60 * that much state information. Good sizes for the amount of state
61 * information are 32, 64, 128, and 256 bytes. The state can be switched by
62 * calling the setstate() routine with the same array as was initiallized
63 * with initstate(). By default, the package runs with 128 bytes of state
64 * information and generates far better random numbers than a linear
65 * congruential generator. If the amount of state information is less than
66 * 32 bytes, a simple linear congruential R.N.G. is used.
67 *
68 * Internally, the state information is treated as an array of longs; the
69 * zeroeth element of the array is the type of R.N.G. being used (small
70 * integer); the remainder of the array is the state information for the
71 * R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
72 * state information, which will allow a degree seven polynomial. (Note:
73 * the zeroeth word of state information also has some other information
74 * stored in it -- see setstate() for details).
75 *
76 * The random number generation technique is a linear feedback shift register
77 * approach, employing trinomials (since there are fewer terms to sum up that
78 * way). In this approach, the least significant bit of all the numbers in
79 * the state table will act as a linear feedback shift register, and will
80 * have period 2^deg - 1 (where deg is the degree of the polynomial being
81 * used, assuming that the polynomial is irreducible and primitive). The
82 * higher order bits will have longer periods, since their values are also
83 * influenced by pseudo-random carries out of the lower bits. The total
84 * period of the generator is approximately deg*(2**deg - 1); thus doubling
85 * the amount of state information has a vast influence on the period of the
86 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
87 * large deg, when the period of the shift register is the dominant factor.
88 * With deg equal to seven, the period is actually much longer than the
89 * 7*(2**7 - 1) predicted by this formula.
90 *
91 * Modified 28 December 1994 by Jacob S. Rosenberg.
92 * The following changes have been made:
93 * All references to the type u_int have been changed to unsigned long.
94 * All references to type int have been changed to type long. Other
95 * cleanups have been made as well. A warning for both initstate and
96 * setstate has been inserted to the effect that on Sparc platforms
97 * the 'arg_state' variable must be forced to begin on word boundaries.
98 * This can be easily done by casting a long integer array to char *.
99 * The overall logic has been left STRICTLY alone. This software was
100 * tested on both a VAX and Sun SpacsStation with exactly the same
101 * results. The new version and the original give IDENTICAL results.
102 * The new version is somewhat faster than the original. As the
103 * documentation says: "By default, the package runs with 128 bytes of
104 * state information and generates far better random numbers than a linear
105 * congruential generator. If the amount of state information is less than
106 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
107 * 128 bytes, this new version runs about 19 percent faster and for a 16
108 * byte buffer it is about 5 percent faster.
109 */
110
111 /*
112 * For each of the currently supported random number generators, we have a
113 * break value on the amount of state information (you need at least this
114 * many bytes of state info to support this random number generator), a degree
115 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
116 * the separation between the two lower order coefficients of the trinomial.
117 */
118 #define TYPE_0 0 /* linear congruential */
119 #define BREAK_0 8
120 #define DEG_0 0
121 #define SEP_0 0
122
123 #define TYPE_1 1 /* x**7 + x**3 + 1 */
124 #define BREAK_1 32
125 #define DEG_1 7
126 #define SEP_1 3
127
128 #define TYPE_2 2 /* x**15 + x + 1 */
129 #define BREAK_2 64
130 #define DEG_2 15
131 #define SEP_2 1
132
133 #define TYPE_3 3 /* x**31 + x**3 + 1 */
134 #define BREAK_3 128
135 #define DEG_3 31
136 #define SEP_3 3
137
138 #define TYPE_4 4 /* x**63 + x + 1 */
139 #define BREAK_4 256
140 #define DEG_4 63
141 #define SEP_4 1
142
143 #define MAX_TYPES 5 /* max number of types above */
144
145 /*
146 * Initially, everything is set up as if from:
147 *
148 * initstate(1, randtbl, 128);
149 *
150 * Note that this initialization takes advantage of the fact that srandom()
151 * advances the front and rear pointers 10*rand_deg times, and hence the
152 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
153 * element of the state information, which contains info about the current
154 * position of the rear pointer is just
155 *
156 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
157 */
158
159 static unsigned long randtbl[DEG_3 + 1] = {
160 TYPE_3,
161 #ifdef USE_WEAK_SEEDING
162 /* Historic implementation compatibility */
163 /* The random sequences do not vary much with the seed */
164 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
165 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
166 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
167 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
168 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
169 0x27fb47b9,
170 #else /* !USE_WEAK_SEEDING */
171 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
172 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
173 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
174 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
175 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
176 0xf3bec5da
177 #endif /* !USE_WEAK_SEEDING */
178 };
179
180 /*
181 * fptr and rptr are two pointers into the state info, a front and a rear
182 * pointer. These two pointers are always rand_sep places aparts, as they
183 * cycle cyclically through the state information. (Yes, this does mean we
184 * could get away with just one pointer, but the code for random() is more
185 * efficient this way). The pointers are left positioned as they would be
186 * from the call
187 *
188 * initstate(1, randtbl, 128);
189 *
190 * (The position of the rear pointer, rptr, is really 0 (as explained above
191 * in the initialization of randtbl) because the state table pointer is set
192 * to point to randtbl[1] (as explained below).
193 */
194 static unsigned long *fptr = &randtbl[SEP_3 + 1];
195 static unsigned long *rptr = &randtbl[1];
196
197 /*
198 * The following things are the pointer to the state information table, the
199 * type of the current generator, the degree of the current polynomial being
200 * used, and the separation between the two pointers. Note that for efficiency
201 * of random(), we remember the first location of the state information, not
202 * the zeroeth. Hence it is valid to access state[-1], which is used to
203 * store the type of the R.N.G. Also, we remember the last location, since
204 * this is more efficient than indexing every time to find the address of
205 * the last element to see if the front and rear pointers have wrapped.
206 */
207 static unsigned long *state = &randtbl[1];
208 static long rand_type = TYPE_3;
209 static long rand_deg = DEG_3;
210 static long rand_sep = SEP_3;
211 static unsigned long *end_ptr = &randtbl[DEG_3 + 1];
212
213 static inline long good_rand (long);
214
215 static inline long
good_rand(register long x)216 good_rand (
217 register long x
218 )
219 {
220 #ifdef USE_WEAK_SEEDING
221 /*
222 * Historic implementation compatibility.
223 * The random sequences do not vary much with the seed,
224 * even with overflowing.
225 */
226 return (1103515245 * x + 12345);
227 #else /* !USE_WEAK_SEEDING */
228 /*
229 * Compute x = (7^5 * x) mod (2^31 - 1)
230 * wihout overflowing 31 bits:
231 * (2^31 - 1) = 127773 * (7^5) + 2836
232 * From "Random number generators: good ones are hard to find",
233 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
234 * October 1988, p. 1195.
235 */
236 register long hi, lo;
237
238 hi = x / 127773;
239 lo = x % 127773;
240 x = 16807 * lo - 2836 * hi;
241 if (x <= 0)
242 x += 0x7fffffff;
243 return (x);
244 #endif /* !USE_WEAK_SEEDING */
245 }
246
247 /*
248 * srandom:
249 *
250 * Initialize the random number generator based on the given seed. If the
251 * type is the trivial no-state-information type, just remember the seed.
252 * Otherwise, initializes state[] based on the given "seed" via a linear
253 * congruential generator. Then, the pointers are set to known locations
254 * that are exactly rand_sep places apart. Lastly, it cycles the state
255 * information a given number of times to get rid of any initial dependencies
256 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
257 * for default usage relies on values produced by this routine.
258 */
259 void
ntp_srandom(unsigned long x)260 ntp_srandom(
261 unsigned long x
262 )
263 {
264 long i;
265
266 if (rand_type == TYPE_0) {
267 state[0] = x;
268 } else {
269 state[0] = x;
270 for (i = 1; i < rand_deg; i++)
271 state[i] = good_rand(state[i - 1]);
272 fptr = &state[rand_sep];
273 rptr = &state[0];
274 for (i = 0; i < 10 * rand_deg; i++)
275 x = ntp_random();
276 }
277
278 /* seed the likely faster (and poorer) rand() as well */
279 srand((u_int)x);
280 }
281
282 /*
283 * srandomdev:
284 *
285 * Many programs choose the seed value in a totally predictable manner.
286 * This often causes problems. We seed the generator using the much more
287 * secure urandom(4) interface. Note that this particular seeding
288 * procedure can generate states which are impossible to reproduce by
289 * calling srandom() with any value, since the succeeding terms in the
290 * state buffer are no longer derived from the LC algorithm applied to
291 * a fixed seed.
292 */
293 #ifdef NEED_SRANDOMDEV
294 void
ntp_srandomdev(void)295 ntp_srandomdev( void )
296 {
297 struct timeval tv;
298 unsigned long junk; /* Purposely used uninitialized */
299
300 GETTIMEOFDAY(&tv, NULL);
301 ntp_srandom(getpid() ^ tv.tv_sec ^ tv.tv_usec ^ junk);
302 return;
303 }
304 #endif
305
306
307 /*
308 * ntp_initstate() and ntp_setstate() are unused in our codebase and
309 * trigger warnings due to casting to a more-strictly-aligned pointer
310 * on alignment-sensitive platforms. #ifdef them away to save noise,
311 * build time, and binary space, but retain the code in case we find a
312 * use.
313 */
314 #ifdef COMPILE_UNUSED_FUNCTIONS
315 /*
316 * Array versions of the above information to make code run faster --
317 * relies on fact that TYPE_i == i.
318 */
319 #define MAX_TYPES 5 /* max number of types above */
320
321 static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
322 static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
323
324 /*
325 * initstate:
326 *
327 * Initialize the state information in the given array of n bytes for future
328 * random number generation. Based on the number of bytes we are given, and
329 * the break values for the different R.N.G.'s, we choose the best (largest)
330 * one we can and set things up for it. srandom() is then called to
331 * initialize the state information.
332 *
333 * Note that on return from srandom(), we set state[-1] to be the type
334 * multiplexed with the current value of the rear pointer; this is so
335 * successive calls to initstate() won't lose this information and will be
336 * able to restart with setstate().
337 *
338 * Note: the first thing we do is save the current state, if any, just like
339 * setstate() so that it doesn't matter when initstate is called.
340 *
341 * Returns a pointer to the old state.
342 *
343 * Note: The Sparc platform requires that arg_state begin on a long
344 * word boundary; otherwise a bus error will occur. Even so, lint will
345 * complain about mis-alignment, but you should disregard these messages.
346 */
347 char *
ntp_initstate(unsigned long seed,char * arg_state,long n)348 ntp_initstate(
349 unsigned long seed, /* seed for R.N.G. */
350 char *arg_state, /* pointer to state array */
351 long n /* # bytes of state info */
352 )
353 {
354 register char *ostate = (char *)(&state[-1]);
355 register long *long_arg_state = (long *) arg_state;
356
357 if (rand_type == TYPE_0)
358 state[-1] = rand_type;
359 else
360 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
361 if (n < BREAK_0) {
362 (void)fprintf(stderr,
363 "random: not enough state (%ld bytes); ignored.\n", n);
364 return(0);
365 }
366 if (n < BREAK_1) {
367 rand_type = TYPE_0;
368 rand_deg = DEG_0;
369 rand_sep = SEP_0;
370 } else if (n < BREAK_2) {
371 rand_type = TYPE_1;
372 rand_deg = DEG_1;
373 rand_sep = SEP_1;
374 } else if (n < BREAK_3) {
375 rand_type = TYPE_2;
376 rand_deg = DEG_2;
377 rand_sep = SEP_2;
378 } else if (n < BREAK_4) {
379 rand_type = TYPE_3;
380 rand_deg = DEG_3;
381 rand_sep = SEP_3;
382 } else {
383 rand_type = TYPE_4;
384 rand_deg = DEG_4;
385 rand_sep = SEP_4;
386 }
387 state = (unsigned long *) (long_arg_state + 1); /* first location */
388 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
389 ntp_srandom(seed);
390 if (rand_type == TYPE_0)
391 long_arg_state[0] = rand_type;
392 else
393 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
394 return(ostate);
395 }
396
397 /*
398 * setstate:
399 *
400 * Restore the state from the given state array.
401 *
402 * Note: it is important that we also remember the locations of the pointers
403 * in the current state information, and restore the locations of the pointers
404 * from the old state information. This is done by multiplexing the pointer
405 * location into the zeroeth word of the state information.
406 *
407 * Note that due to the order in which things are done, it is OK to call
408 * setstate() with the same state as the current state.
409 *
410 * Returns a pointer to the old state information.
411 *
412 * Note: The Sparc platform requires that arg_state begin on a long
413 * word boundary; otherwise a bus error will occur. Even so, lint will
414 * complain about mis-alignment, but you should disregard these messages.
415 */
416 char *
ntp_setstate(char * arg_state)417 ntp_setstate(
418 char *arg_state /* pointer to state array */
419 )
420 {
421 register unsigned long *new_state = (unsigned long *) arg_state;
422 register long type = new_state[0] % MAX_TYPES;
423 register long rear = new_state[0] / MAX_TYPES;
424 char *ostate = (char *)(&state[-1]);
425
426 if (rand_type == TYPE_0)
427 state[-1] = rand_type;
428 else
429 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
430 switch(type) {
431 case TYPE_0:
432 case TYPE_1:
433 case TYPE_2:
434 case TYPE_3:
435 case TYPE_4:
436 rand_type = type;
437 rand_deg = degrees[type];
438 rand_sep = seps[type];
439 break;
440 default:
441 (void)fprintf(stderr,
442 "random: state info corrupted; not changed.\n");
443 }
444 state = (new_state + 1);
445 if (rand_type != TYPE_0) {
446 rptr = &state[rear];
447 fptr = &state[(rear + rand_sep) % rand_deg];
448 }
449 end_ptr = &state[rand_deg]; /* set end_ptr too */
450 return(ostate);
451 }
452 #endif /* COMPILE_UNUSED_FUNCTIONS */
453
454
455 /*
456 * random:
457 *
458 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
459 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
460 * the same in all the other cases due to all the global variables that have
461 * been set up. The basic operation is to add the number at the rear pointer
462 * into the one at the front pointer. Then both pointers are advanced to
463 * the next location cyclically in the table. The value returned is the sum
464 * generated, reduced to 31 bits by throwing away the "least random" low bit.
465 *
466 * Note: the code takes advantage of the fact that both the front and
467 * rear pointers can't wrap on the same call by not testing the rear
468 * pointer if the front one has wrapped.
469 *
470 * Returns a 31-bit random number.
471 */
472 long
ntp_random(void)473 ntp_random( void )
474 {
475 register long i;
476 register unsigned long *f, *r;
477
478 if (rand_type == TYPE_0) {
479 i = state[0];
480 state[0] = i = (good_rand(i)) & 0x7fffffff;
481 } else {
482 /*
483 * Use local variables rather than static variables for speed.
484 */
485 f = fptr; r = rptr;
486 *f += *r;
487 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
488 if (++f >= end_ptr) {
489 f = state;
490 ++r;
491 }
492 else if (++r >= end_ptr) {
493 r = state;
494 }
495
496 fptr = f; rptr = r;
497 }
498 return(i);
499 }
500
501 /*
502 * ntp_uurandom()
503 *
504 * Generate a Uniform-distributed Unity based random number. Replaces a
505 * few locations where the transformation was made in an ad-hoc style
506 * (and in one instance, wrong...)
507 *
508 * returns a number in [0.0 .. 1.0], both ends inclusive
509 */
510 double
ntp_uurandom(void)511 ntp_uurandom( void )
512 {
513 return (double)ntp_random() / 0x7FFFFFFFu;
514 }
515