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. Neither the name of the University nor the names of its contributors
14 * may be used to endorse or promote products derived from this software
15 * without specific prior written permission.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
18 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
21 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
22 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
23 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
25 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
26 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 * SUCH DAMAGE.
28 */
29
30 /*
31 * Per the statement at http://opensource.org/licenses/bsd-license.php,
32 *
33 * The advertising clause in the license appearing on BSD Unix files was
34 * officially rescinded by the Director of the Office of Technology
35 * Licensing of the University of California on July 22 1999. He states
36 * that clause 3 is "hereby deleted in its entirety."
37 *
38 * I removed the advertising clause in the above copyright.
39 * The above web site points to
40 * ftp://ftp.cs.berkeley.edu/pub/4bsd/README.Impt.License.Change.
41 *
42 * Arnold Robbins
43 * 15 September 2007
44 */
45
46 #if defined(LIBC_SCCS) && !defined(lint)
47 static const char sccsid[] = "@(#)random.c 8.2 (Berkeley) 5/19/95";
48 #endif /* LIBC_SCCS and not lint */
49
50 #ifdef HAVE_CONFIG_H /* gawk addition */
51 #include <config.h>
52 #endif
53
54 #ifdef HAVE_FCNTL_H
55 #include <fcntl.h>
56 #endif
57 #include <stdio.h>
58 #include <stdlib.h>
59 #ifdef HAVE_UNISTD_H
60 #include <unistd.h>
61 #endif
62
63 #include <assert.h>
64
65 #include "random.h" /* gawk addition */
66
67 #ifdef HAVE_SYS_TIME_H /* gawk addition */
68 #include <sys/time.h>
69 #endif
70
71 #if 0
72 #include <sys/cdefs.h>
73 __FBSDID("$FreeBSD: /repoman/r/ncvs/src/lib/libc/stdlib/random.c,v 1.24 2004/01/20 03:02:18 das Exp $");
74
75 #include "namespace.h"
76 #include <sys/time.h> /* for srandomdev() */
77 #include <fcntl.h> /* for srandomdev() */
78 #include <stdint.h>
79 #include <stdio.h>
80 #include <stdlib.h>
81 #include <unistd.h> /* for srandomdev() */
82 #include "un-namespace.h"
83 #endif
84
85 /*
86 * random.c:
87 *
88 * An improved random number generation package. In addition to the standard
89 * rand()/srand() like interface, this package also has a special state info
90 * interface. The initstate() routine is called with a seed, an array of
91 * bytes, and a count of how many bytes are being passed in; this array is
92 * then initialized to contain information for random number generation with
93 * that much state information. Good sizes for the amount of state
94 * information are 32, 64, 128, and 256 bytes. The state can be switched by
95 * calling the setstate() routine with the same array as was initiallized
96 * with initstate(). By default, the package runs with 128 bytes of state
97 * information and generates far better random numbers than a linear
98 * congruential generator. If the amount of state information is less than
99 * 32 bytes, a simple linear congruential R.N.G. is used.
100 *
101 * Internally, the state information is treated as an array of uint32_t's; the
102 * zeroeth element of the array is the type of R.N.G. being used (small
103 * integer); the remainder of the array is the state information for the
104 * R.N.G. Thus, 32 bytes of state information will give 7 ints worth of
105 * state information, which will allow a degree seven polynomial. (Note:
106 * the zeroeth word of state information also has some other information
107 * stored in it -- see setstate() for details).
108 *
109 * The random number generation technique is a linear feedback shift register
110 * approach, employing trinomials (since there are fewer terms to sum up that
111 * way). In this approach, the least significant bit of all the numbers in
112 * the state table will act as a linear feedback shift register, and will
113 * have period 2^deg - 1 (where deg is the degree of the polynomial being
114 * used, assuming that the polynomial is irreducible and primitive). The
115 * higher order bits will have longer periods, since their values are also
116 * influenced by pseudo-random carries out of the lower bits. The total
117 * period of the generator is approximately deg*(2**deg - 1); thus doubling
118 * the amount of state information has a vast influence on the period of the
119 * generator. Note: the deg*(2**deg - 1) is an approximation only good for
120 * large deg, when the period of the shift is the dominant factor.
121 * With deg equal to seven, the period is actually much longer than the
122 * 7*(2**7 - 1) predicted by this formula.
123 *
124 * Modified 28 December 1994 by Jacob S. Rosenberg.
125 * The following changes have been made:
126 * All references to the type u_int have been changed to unsigned long.
127 * All references to type int have been changed to type long. Other
128 * cleanups have been made as well. A warning for both initstate and
129 * setstate has been inserted to the effect that on Sparc platforms
130 * the 'arg_state' variable must be forced to begin on word boundaries.
131 * This can be easily done by casting a long integer array to char *.
132 * The overall logic has been left STRICTLY alone. This software was
133 * tested on both a VAX and Sun SpacsStation with exactly the same
134 * results. The new version and the original give IDENTICAL results.
135 * The new version is somewhat faster than the original. As the
136 * documentation says: "By default, the package runs with 128 bytes of
137 * state information and generates far better random numbers than a linear
138 * congruential generator. If the amount of state information is less than
139 * 32 bytes, a simple linear congruential R.N.G. is used." For a buffer of
140 * 128 bytes, this new version runs about 19 percent faster and for a 16
141 * byte buffer it is about 5 percent faster.
142 *
143 * Modified 06 February 2016 by Nelson H. F. Beebe to interface to a
144 * shuffle buffer, producing a huge period, and removing long-range
145 * correlations of the basic low-level generator. See comments and
146 * literature references in random() at the end of this file.
147 */
148
149 #define SHUFFLE_BITS 9 /* see comments in random() below for this choice */
150 #define SHUFFLE_MAX (1 << SHUFFLE_BITS) /* MUST be power of two */
151 #define SHUFFLE_MASK (SHUFFLE_MAX - 1) /* (k & SHUFFLE_MASK) is in [0, SHUFFLE_MAX - 1] */
152
153 static int shuffle_init = 1;
154 static long shuffle_buffer[SHUFFLE_MAX];
155
156 /*
157 * For each of the currently supported random number generators, we have a
158 * break value on the amount of state information (you need at least this
159 * many bytes of state info to support this random number generator), a degree
160 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and
161 * the separation between the two lower order coefficients of the trinomial.
162 */
163 #define TYPE_0 0 /* linear congruential */
164 #define BREAK_0 8
165 #define DEG_0 0
166 #define SEP_0 0
167
168 #define TYPE_1 1 /* x**7 + x**3 + 1 */
169 #define BREAK_1 32
170 #define DEG_1 7
171 #define SEP_1 3
172
173 #define TYPE_2 2 /* x**15 + x + 1 */
174 #define BREAK_2 64
175 #define DEG_2 15
176 #define SEP_2 1
177
178 #define TYPE_3 3 /* x**31 + x**3 + 1 */
179 #define BREAK_3 128
180 #define DEG_3 31
181 #define SEP_3 3
182
183 #define TYPE_4 4 /* x**63 + x + 1 */
184 #define BREAK_4 256
185 #define DEG_4 63
186 #define SEP_4 1
187
188 /*
189 * Array versions of the above information to make code run faster --
190 * relies on fact that TYPE_i == i.
191 */
192 #define MAX_TYPES 5 /* max number of types above */
193
194 #ifdef USE_WEAK_SEEDING
195 #define NSHUFF 0
196 #else /* !USE_WEAK_SEEDING */
197 #define NSHUFF 50 /* to drop some "seed -> 1st value" linearity */
198 #endif /* !USE_WEAK_SEEDING */
199
200 static const int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
201 static const int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
202
203 /*
204 * Initially, everything is set up as if from:
205 *
206 * initstate(1, randtbl, 128);
207 *
208 * Note that this initialization takes advantage of the fact that srandom()
209 * advances the front and rear pointers 10*rand_deg times, and hence the
210 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth
211 * element of the state information, which contains info about the current
212 * position of the rear pointer is just
213 *
214 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
215 */
216
217 static uint32_t randtbl[DEG_3 + 1] = {
218 TYPE_3,
219 #ifdef USE_WEAK_SEEDING
220 /* Historic implementation compatibility */
221 /* The random sequences do not vary much with the seed */
222 0x9a319039, 0x32d9c024, 0x9b663182, 0x5da1f342, 0xde3b81e0, 0xdf0a6fb5,
223 0xf103bc02, 0x48f340fb, 0x7449e56b, 0xbeb1dbb0, 0xab5c5918, 0x946554fd,
224 0x8c2e680f, 0xeb3d799f, 0xb11ee0b7, 0x2d436b86, 0xda672e2a, 0x1588ca88,
225 0xe369735d, 0x904f35f7, 0xd7158fd6, 0x6fa6f051, 0x616e6b96, 0xac94efdc,
226 0x36413f93, 0xc622c298, 0xf5a42ab8, 0x8a88d77b, 0xf5ad9d0e, 0x8999220b,
227 0x27fb47b9,
228 #else /* !USE_WEAK_SEEDING */
229 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
230 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
231 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
232 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
233 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
234 0xf3bec5da
235 #endif /* !USE_WEAK_SEEDING */
236 };
237
238 /*
239 * fptr and rptr are two pointers into the state info, a front and a rear
240 * pointer. These two pointers are always rand_sep places aparts, as they
241 * cycle cyclically through the state information. (Yes, this does mean we
242 * could get away with just one pointer, but the code for random() is more
243 * efficient this way). The pointers are left positioned as they would be
244 * from the call
245 *
246 * initstate(1, randtbl, 128);
247 *
248 * (The position of the rear pointer, rptr, is really 0 (as explained above
249 * in the initialization of randtbl) because the state table pointer is set
250 * to point to randtbl[1] (as explained below).
251 */
252 static uint32_t *fptr = &randtbl[SEP_3 + 1];
253 static uint32_t *rptr = &randtbl[1];
254
255 /*
256 * The following things are the pointer to the state information table, the
257 * type of the current generator, the degree of the current polynomial being
258 * used, and the separation between the two pointers. Note that for efficiency
259 * of random(), we remember the first location of the state information, not
260 * the zeroeth. Hence it is valid to access state[-1], which is used to
261 * store the type of the R.N.G. Also, we remember the last location, since
262 * this is more efficient than indexing every time to find the address of
263 * the last element to see if the front and rear pointers have wrapped.
264 */
265 static uint32_t *state = &randtbl[1];
266 static int rand_type = TYPE_3;
267 static int rand_deg = DEG_3;
268 static int rand_sep = SEP_3;
269 static uint32_t *end_ptr = &randtbl[DEG_3 + 1];
270
271 static inline uint32_t good_rand(int32_t);
272
273 static inline uint32_t good_rand (int32_t x)
274 {
275 #ifdef USE_WEAK_SEEDING
276 /*
277 * Historic implementation compatibility.
278 * The random sequences do not vary much with the seed,
279 * even with overflowing.
280 */
281 return (1103515245 * x + 12345);
282 #else /* !USE_WEAK_SEEDING */
283 /*
284 * Compute x = (7^5 * x) mod (2^31 - 1)
285 * wihout overflowing 31 bits:
286 * (2^31 - 1) = 127773 * (7^5) + 2836
287 * From "Random number generators: good ones are hard to find",
288 * Park and Miller, Communications of the ACM, vol. 31, no. 10,
289 * October 1988, p. 1195.
290 */
291 int32_t hi, lo;
292
293 /* Can't be initialized with 0, so use another value. */
294 if (x == 0)
295 x = 123459876;
296 hi = x / 127773;
297 lo = x % 127773;
298 x = 16807 * lo - 2836 * hi;
299 if (x < 0)
300 x += 0x7fffffff;
301 return (x);
302 #endif /* !USE_WEAK_SEEDING */
303 }
304
305 /*
306 * srandom:
307 *
308 * Initialize the random number generator based on the given seed. If the
309 * type is the trivial no-state-information type, just remember the seed.
310 * Otherwise, initializes state[] based on the given "seed" via a linear
311 * congruential generator. Then, the pointers are set to known locations
312 * that are exactly rand_sep places apart. Lastly, it cycles the state
313 * information a given number of times to get rid of any initial dependencies
314 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
315 * for default usage relies on values produced by this routine.
316 */
317 void
318 srandom(unsigned long x)
319 {
320 int i, lim;
321
322 shuffle_init = 1;
323
324 state[0] = (uint32_t)x;
325 if (rand_type == TYPE_0)
326 lim = NSHUFF;
327 else {
328 for (i = 1; i < rand_deg; i++)
329 state[i] = good_rand(state[i - 1]);
330 fptr = &state[rand_sep];
331 rptr = &state[0];
332 lim = 10 * rand_deg;
333 }
334 for (i = 0; i < lim; i++)
335 (void)random();
336 }
337
338 #if 0 /* gawk doesn't use this */
339 /*
340 * srandomdev:
341 *
342 * Many programs choose the seed value in a totally predictable manner.
343 * This often causes problems. We seed the generator using the much more
344 * secure random(4) interface. Note that this particular seeding
345 * procedure can generate states which are impossible to reproduce by
346 * calling srandom() with any value, since the succeeding terms in the
347 * state buffer are no longer derived from the LC algorithm applied to
348 * a fixed seed.
349 */
350 void
351 srandomdev()
352 {
353 int fd, done;
354 size_t len;
355
356 if (rand_type == TYPE_0)
357 len = sizeof state[0];
358 else
359 len = rand_deg * sizeof state[0];
360
361 done = 0;
362 fd = open("/dev/random", O_RDONLY, 0);
363 if (fd >= 0) {
364 if (read(fd, (void *) state, len) == (ssize_t) len)
365 done = 1;
366 close(fd);
367 }
368
369 if (!done) {
370 struct timeval tv;
371 unsigned long junk;
372
373 gettimeofday(&tv, NULL);
374 srandom((getpid() << 16) ^ tv.tv_sec ^ tv.tv_usec ^ junk);
375 return;
376 }
377
378 if (rand_type != TYPE_0) {
379 fptr = &state[rand_sep];
380 rptr = &state[0];
381 }
382 }
383 #endif
384
385 /*
386 * initstate:
387 *
388 * Initialize the state information in the given array of n bytes for future
389 * random number generation. Based on the number of bytes we are given, and
390 * the break values for the different R.N.G.'s, we choose the best (largest)
391 * one we can and set things up for it. srandom() is then called to
392 * initialize the state information.
393 *
394 * Note that on return from srandom(), we set state[-1] to be the type
395 * multiplexed with the current value of the rear pointer; this is so
396 * successive calls to initstate() won't lose this information and will be
397 * able to restart with setstate().
398 *
399 * Note: the first thing we do is save the current state, if any, just like
400 * setstate() so that it doesn't matter when initstate is called.
401 *
402 * Returns a pointer to the old state.
403 *
404 * Note: The Sparc platform requires that arg_state begin on an int
405 * word boundary; otherwise a bus error will occur. Even so, lint will
406 * complain about mis-alignment, but you should disregard these messages.
407 */
408 char *
409 initstate(
410 unsigned long seed, /* seed for R.N.G. */
411 char *arg_state, /* pointer to state array */
412 long n) /* # bytes of state info */
413 {
414 char *ostate = (char *)(&state[-1]);
415 uint32_t *int_arg_state = (uint32_t *)arg_state;
416
417 if (rand_type == TYPE_0)
418 state[-1] = rand_type;
419 else
420 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
421 if (n < BREAK_0) {
422 (void)fprintf(stderr,
423 "random: not enough state (%ld bytes); ignored.\n", n);
424 return(0);
425 }
426 if (n < BREAK_1) {
427 rand_type = TYPE_0;
428 rand_deg = DEG_0;
429 rand_sep = SEP_0;
430 } else if (n < BREAK_2) {
431 rand_type = TYPE_1;
432 rand_deg = DEG_1;
433 rand_sep = SEP_1;
434 } else if (n < BREAK_3) {
435 rand_type = TYPE_2;
436 rand_deg = DEG_2;
437 rand_sep = SEP_2;
438 } else if (n < BREAK_4) {
439 rand_type = TYPE_3;
440 rand_deg = DEG_3;
441 rand_sep = SEP_3;
442 } else {
443 rand_type = TYPE_4;
444 rand_deg = DEG_4;
445 rand_sep = SEP_4;
446 }
447 state = int_arg_state + 1; /* first location */
448 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */
449 srandom(seed);
450 if (rand_type == TYPE_0)
451 int_arg_state[0] = rand_type;
452 else
453 int_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
454 return(ostate);
455 }
456
457 /*
458 * setstate:
459 *
460 * Restore the state from the given state array.
461 *
462 * Note: it is important that we also remember the locations of the pointers
463 * in the current state information, and restore the locations of the pointers
464 * from the old state information. This is done by multiplexing the pointer
465 * location into the zeroeth word of the state information.
466 *
467 * Note that due to the order in which things are done, it is OK to call
468 * setstate() with the same state as the current state.
469 *
470 * Returns a pointer to the old state information.
471 *
472 * Note: The Sparc platform requires that arg_state begin on an int
473 * word boundary; otherwise a bus error will occur. Even so, lint will
474 * complain about mis-alignment, but you should disregard these messages.
475 */
476 char *
477 setstate(char *arg_state) /* pointer to state array */
478 {
479 uint32_t *new_state = (uint32_t *)arg_state;
480 uint32_t type = new_state[0] % MAX_TYPES;
481 uint32_t rear = new_state[0] / MAX_TYPES;
482 char *ostate = (char *)(&state[-1]);
483
484 if (rand_type == TYPE_0)
485 state[-1] = rand_type;
486 else
487 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
488 switch(type) {
489 case TYPE_0:
490 case TYPE_1:
491 case TYPE_2:
492 case TYPE_3:
493 case TYPE_4:
494 rand_type = type;
495 rand_deg = degrees[type];
496 rand_sep = seps[type];
497 break;
498 default:
499 (void)fprintf(stderr,
500 "random: state info corrupted; not changed.\n");
501 }
502 state = new_state + 1;
503 if (rand_type != TYPE_0) {
504 rptr = &state[rear];
505 fptr = &state[(rear + rand_sep) % rand_deg];
506 }
507 end_ptr = &state[rand_deg]; /* set end_ptr too */
508 return(ostate);
509 }
510
511 /*
512 * random:
513 *
514 * If we are using the trivial TYPE_0 R.N.G., just do the old linear
515 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is
516 * the same in all the other cases due to all the global variables that have
517 * been set up. The basic operation is to add the number at the rear pointer
518 * into the one at the front pointer. Then both pointers are advanced to
519 * the next location cyclically in the table. The value returned is the sum
520 * generated, reduced to 31 bits by throwing away the "least random" low bit.
521 *
522 * Note: the code takes advantage of the fact that both the front and
523 * rear pointers can't wrap on the same call by not testing the rear
524 * pointer if the front one has wrapped.
525 *
526 * Returns a 31-bit random number.
527 */
528 static long
529 random_old()
530 {
531 uint32_t i;
532 uint32_t *f, *r;
533
534 if (rand_type == TYPE_0) {
535 i = state[0];
536 state[0] = i = (good_rand(i)) & 0x7fffffff;
537 } else {
538 /*
539 * Use local variables rather than static variables for speed.
540 */
541 f = fptr; r = rptr;
542 *f += *r;
543 i = (*f >> 1) & 0x7fffffff; /* chucking least random bit */
544 if (++f >= end_ptr) {
545 f = state;
546 ++r;
547 }
548 else if (++r >= end_ptr) {
549 r = state;
550 }
551
552 fptr = f; rptr = r;
553 }
554 return((long)i);
555 }
556
557 long
558 random()
559 {
560 /*
561 * This function is a wrapper to the original random(), now renamed
562 * random_old(), to interpose a shuffle buffer to dramatically extend
563 * the generator period at nearly zero additional execution cost,
564 * and an additional storage cost set by the size of the
565 * shuffle buffer (default: 512 longs, or 2K or 4K bytes).
566 * The algorithm was first described in
567 *
568 * Carter Bays and S. D. Durham
569 * Improving a Poor Random Number Generator
570 * ACM Transactions on Mathematical Software (TOMS) 2(1) 59--64 (March 1976)
571 * http://dx.doi.org/10.1145/355666.355670
572 *
573 * and later revisited in
574 *
575 * Carter Bays
576 * C364. Improving a random number generator: a comparison between two shuffling methods
577 * Journal of Statistical Computation and Simulation 36(1) 57--59 (May 1990)
578 * http://dx.doi.org/10.1080/00949659008811264
579 *
580 * The second paper is critically important because it
581 * emphasizes how an apparently trivial change to the final
582 * element selection can destroy the period-lengthening
583 * feature of the original shuffle algorithm.
584 *
585 * Here is a table of the increase in period size for a
586 * shuffle generator using 32-bit and 64-bit unsigned integer
587 * linear congruential generators, which are known to have
588 * significant correlations, and are thus inadvisable for
589 * serious work with random numbers:
590 *
591 * hocd128> for (n = 32; n < 4096; n *= 2) \
592 * printf("%7d\t%12.3.4e\t%12.3.4e\n",
593 * n, \
594 * sqrt(PI * gamma(n + 1)/(2**32 - 1)) / (2**32 - 1), \\
595 * sqrt(PI * gamma(n + 1)/(2**64 - 1)) / (2**64 - 1))
596 *
597 * 32 3.230e+03 1.148e-11
598 * 64 2.243e+30 7.969e+15
599 * 128 3.910e+93 1.389e+79
600 * 256 1.844e+239 6.552e+224
601 * 512 1.174e+569 4.172e+554
602 * 1024 4.635e+1305 1.647e+1291
603 * 2048 8.144e+2932 2.893e+2918
604 *
605 * A generator giving one result per nanosecond would produce
606 * about 3.16e16 random numbers per year, so even for
607 * massively parallel operations with, say, one million CPU
608 * cores, it could not produce more than 10**23 values per
609 * year. The main benefit of an enormous period is that it
610 * makes long-range correlations vanishingly unlikely, even
611 * when starting seeds are similar (e.g., seeds of 0, 1, 2,
612 * ...), and therefore makes possible families of generators
613 * (needed in parallel computations) where the probability of
614 * sequence overlap between family members is essentially
615 * zero.
616 */
617
618 int k;
619 long r;
620 static long s = 0xcafefeedL;
621
622 if (shuffle_init) { /* first time, or seed changed by srand() */
623 for (k = 0; k < SHUFFLE_MAX; k++)
624 shuffle_buffer[k] = random_old();
625
626 s = random_old();
627 shuffle_init = 0;
628 }
629
630 r = random_old();
631 k = s & SHUFFLE_MASK; /* random index into shuffle_buffer[] */
632
633 assert(0L <= k && k < SHUFFLE_MAX);
634
635 s = shuffle_buffer[k];
636 shuffle_buffer[k] = r;
637
638 return (s);
639 }