3 // A strong random number generator
5 // Copyright (C) 2006 Allen King
6 // Copyright (C) 2002 Michael Ringgaard. All rights reserved.
7 // Copyright (C) 1983, 1993 The Regents of the University of California.
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions
13 // 1. Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 // 2. Redistributions in binary form must reproduce the above copyright
16 // notice, this list of conditions and the following disclaimer in the
17 // documentation and/or other materials provided with the distribution.
18 // 3. Neither the name of the project nor the names of its contributors
19 // may be used to endorse or promote products derived from this software
20 // without specific prior written permission.
22 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
23 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
24 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
25 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
26 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
27 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
28 // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
29 // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
30 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
31 // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
34 // Transliterated into C++ Allen King 060417, from sources on
35 // http://www.jbox.dk/sanos/source/lib/random.c.html
42 #include "random_generator.hpp"
44 RandomGenerator systemRandom; // global random number generator
46 RandomGenerator::RandomGenerator() {
47 assert(sizeof(int) >= 4);
49 debug = 0; // change this by hand for debug
53 RandomGenerator::~RandomGenerator() {
56 int RandomGenerator::srand(int x) {
58 while (x <= 0) // random seed of zero means
59 x = time(0) % RandomGenerator::rand_max; // randomize with time
62 printf("==== srand(%10d) (%10d) rand_max=%x =====\n",
63 x, x0, RandomGenerator::rand_max);
65 RandomGenerator::srandom(x);
66 return x; // let caller know seed used
69 int RandomGenerator::rand() {
70 int rv; // a posative int
71 while ((rv = RandomGenerator::random()) <= 0) // neg or zero causes probs
74 printf("==== rand(): %10d =====\n", rv);
78 int RandomGenerator::rand(int v) {
79 assert(v >= 0 && v <= RandomGenerator::rand_max); // illegal arg
81 // remove biases, esp. when v is large (e.g. v == (rand_max/4)*3;)
82 int rv, maxV =(RandomGenerator::rand_max / v) * v;
83 assert(maxV <= RandomGenerator::rand_max);
84 while ((rv = RandomGenerator::random()) >= maxV)
86 return rv % v; // mod it down to 0..(maxV-1)
89 int RandomGenerator::rand(int u, int v) {
91 return u + RandomGenerator::rand(v-u);
94 double RandomGenerator::randf(double v) {
97 rv = ((double)RandomGenerator::random())/RandomGenerator::rand_max * v;
98 } while (rv >= v); // rounding might cause rv==v
101 printf("==== rand(): %f =====\n", rv);
105 double RandomGenerator::randf(double u, double v) {
106 return u + RandomGenerator::randf(v-u);
109 //-----------------------------------------------------------------------
111 // Copyright (C) 2002 Michael Ringgaard. All rights reserved.
112 // Copyright (C) 1983, 1993 The Regents of the University of California.
114 // Redistribution and use in source and binary forms, with or without
115 // modification, are permitted provided that the following conditions
118 // 1. Redistributions of source code must retain the above copyright
119 // notice, this list of conditions and the following disclaimer.
120 // 2. Redistributions in binary form must reproduce the above copyright
121 // notice, this list of conditions and the following disclaimer in the
122 // documentation and/or other materials provided with the distribution.
123 // 3. Neither the name of the project nor the names of its contributors
124 // may be used to endorse or promote products derived from this software
125 // without specific prior written permission.
127 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
128 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
129 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
130 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
131 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
132 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
133 // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
134 // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
135 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
136 // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
143 // An improved random number generation package. In addition to the standard
144 // rand()/srand() like interface, this package also has a special state info
145 // interface. The initstate() routine is called with a seed, an array of
146 // bytes, and a count of how many bytes are being passed in; this array is
147 // then initialized to contain information for random number generation with
148 // that much state information. Good sizes for the amount of state
149 // information are 32, 64, 128, and 256 bytes. The state can be switched by
150 // calling the setstate() routine with the same array as was initiallized
151 // with initstate(). By default, the package runs with 128 bytes of state
152 // information and generates far better random numbers than a linear
153 // congruential generator. If the amount of state information is less than
154 // 32 bytes, a simple linear congruential R.N.G. is used.
156 // Internally, the state information is treated as an array of longs; the
157 // zeroeth element of the array is the type of R.N.G. being used (small
158 // integer); the remainder of the array is the state information for the
159 // R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
160 // state information, which will allow a degree seven polynomial. (Note:
161 // the zeroeth word of state information also has some other information
162 // stored in it -- see setstate() for details).
164 // The random number generation technique is a linear feedback shift register
165 // approach, employing trinomials (since there are fewer terms to sum up that
166 // way). In this approach, the least significant bit of all the numbers in
167 // the state table will act as a linear feedback shift register, and will
168 // have period 2^deg - 1 (where deg is the degree of the polynomial being
169 // used, assuming that the polynomial is irreducible and primitive). The
170 // higher order bits will have longer periods, since their values are also
171 // influenced by pseudo-random carries out of the lower bits. The total
172 // period of the generator is approximately deg*(2**deg - 1); thus doubling
173 // the amount of state information has a vast influence on the period of the
174 // generator. Note: the deg*(2**deg - 1) is an approximation only good for
175 // large deg, when the period of the shift is the dominant factor.
176 // With deg equal to seven, the period is actually much longer than the
177 // 7*(2**7 - 1) predicted by this formula.
179 // Modified 28 December 1994 by Jacob S. Rosenberg.
183 // For each of the currently supported random number generators, we have a
184 // break value on the amount of state information (you need at least this
185 // many bytes of state info to support this random number generator), a degree
186 // for the polynomial (actually a trinomial) that the R.N.G. is based on, and
187 // the separation between the two lower order coefficients of the trinomial.
189 void RandomGenerator::initialize() {
191 #define NSHUFF 100 // To drop part of seed -> 1st value correlation
193 //static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
194 //static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
209 // Initially, everything is set up as if from:
211 // initstate(1, randtbl, 128);
213 // Note that this initialization takes advantage of the fact that srandom()
214 // advances the front and rear pointers 10*rand_deg times, and hence the
215 // rear pointer which starts at 0 will also end up at zero; thus the zeroeth
216 // element of the state information, which contains info about the current
217 // position of the rear pointer is just
219 // MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
221 randtbl[ 0] = TYPE_3;
222 randtbl[ 1] = 0x991539b1;
223 randtbl[ 2] = 0x16a5bce3;
224 randtbl[ 3] = 0x6774a4cd;
225 randtbl[ 4] = 0x3e01511e;
226 randtbl[ 5] = 0x4e508aaa;
227 randtbl[ 6] = 0x61048c05;
228 randtbl[ 7] = 0xf5500617;
229 randtbl[ 8] = 0x846b7115;
230 randtbl[ 9] = 0x6a19892c;
231 randtbl[10] = 0x896a97af;
232 randtbl[11] = 0xdb48f936;
233 randtbl[12] = 0x14898454;
234 randtbl[13] = 0x37ffd106;
235 randtbl[14] = 0xb58bff9c;
236 randtbl[15] = 0x59e17104;
237 randtbl[16] = 0xcf918a49;
238 randtbl[17] = 0x09378c83;
239 randtbl[18] = 0x52c7a471;
240 randtbl[19] = 0x8d293ea9;
241 randtbl[20] = 0x1f4fc301;
242 randtbl[21] = 0xc3db71be;
243 randtbl[22] = 0x39b44e1c;
244 randtbl[23] = 0xf8a44ef9;
245 randtbl[24] = 0x4c8b80b1;
246 randtbl[25] = 0x19edc328;
247 randtbl[26] = 0x87bf4bdd;
248 randtbl[27] = 0xc9b240e5;
249 randtbl[28] = 0xe9ee4b1b;
250 randtbl[29] = 0x4382aee7;
251 randtbl[30] = 0x535b6b41;
252 randtbl[31] = 0xf3bec5da;
254 // static long randtbl[DEG_3 + 1] =
257 // 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
258 // 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
259 // 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
260 // 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
261 // 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
267 // fptr and rptr are two pointers into the state info, a front and a rear
268 // pointer. These two pointers are always rand_sep places aparts, as they
269 // cycle cyclically through the state information. (Yes, this does mean we
270 // could get away with just one pointer, but the code for random() is more
271 // efficient this way). The pointers are left positioned as they would be
274 // initstate(1, randtbl, 128);
276 // (The position of the rear pointer, rptr, is really 0 (as explained above
277 // in the initialization of randtbl) because the state table pointer is set
278 // to point to randtbl[1] (as explained below).
281 fptr = &randtbl[SEP_3 + 1];
285 // The following things are the pointer to the state information table, the
286 // type of the current generator, the degree of the current polynomial being
287 // used, and the separation between the two pointers. Note that for efficiency
288 // of random(), we remember the first location of the state information, not
289 // the zeroeth. Hence it is valid to access state[-1], which is used to
290 // store the type of the R.N.G. Also, we remember the last location, since
291 // this is more efficient than indexing every time to find the address of
292 // the last element to see if the front and rear pointers have wrapped.
299 end_ptr = &randtbl[DEG_3 + 1];
304 // Compute x = (7^5 * x) mod (2^31 - 1)
305 // wihout overflowing 31 bits:
306 // (2^31 - 1) = 127773 * (7^5) + 2836
307 // From "Random number generators: good ones are hard to find",
308 // Park and Miller, Communications of the ACM, vol. 31, no. 10,
309 // October 1988, p. 1195.
312 __inline static long good_rand(long x)
316 // Can't be initialized with 0, so use another value.
317 if (x == 0) x = 123459876;
320 x = 16807 * lo - 2836 * hi;
321 if (x < 0) x += 0x7fffffff;
328 // Initialize the random number generator based on the given seed. If the
329 // type is the trivial no-state-information type, just remember the seed.
330 // Otherwise, initializes state[] based on the given "seed" via a linear
331 // congruential generator. Then, the pointers are set to known locations
332 // that are exactly rand_sep places apart. Lastly, it cycles the state
333 // information a given number of times to get rid of any initial dependencies
334 // introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
335 // for default usage relies on values produced by this routine.
337 void RandomGenerator::srandom(unsigned long x)
342 if (rand_type == TYPE_0)
346 for (i = 1; i < rand_deg; i++) state[i] = good_rand(state[i - 1]);
347 fptr = &state[rand_sep];
353 for (i = 0; i < lim; i++) random();
356 #ifdef NOT_FOR_SUPERTUX // use in supertux doesn't require these methods,
357 // which are not portable to as many platforms as
358 // SDL. The cost is that the variability of the
359 // initial seed is reduced to only 32 bits of
360 // randomness, seemingly enough. PAK 060420
364 // Many programs choose the seed value in a totally predictable manner.
365 // This often causes problems. We seed the generator using the much more
366 // secure random() interface. Note that this particular seeding
367 // procedure can generate states which are impossible to reproduce by
368 // calling srandom() with any value, since the succeeding terms in the
369 // state buffer are no longer derived from the LC algorithm applied to
372 void RandomGenerator::srandomdev()
377 if (rand_type == TYPE_0)
378 len = sizeof state[0];
380 len = rand_deg * sizeof state[0];
383 fd = open("/dev/urandom", O_RDONLY);
386 if (read(fd, state, len) == len) done = 1;
394 gettimeofday(&tv, NULL);
395 srandom(tv.tv_sec ^ tv.tv_usec);
399 if (rand_type != TYPE_0)
401 fptr = &state[rand_sep];
410 // Initialize the state information in the given array of n bytes for future
411 // random number generation. Based on the number of bytes we are given, and
412 // the break values for the different R.N.G.'s, we choose the best (largest)
413 // one we can and set things up for it. srandom() is then called to
414 // initialize the state information.
416 // Note that on return from srandom(), we set state[-1] to be the type
417 // multiplexed with the current value of the rear pointer; this is so
418 // successive calls to initstate() won't lose this information and will be
419 // able to restart with setstate().
421 // Note: the first thing we do is save the current state, if any, just like
422 // setstate() so that it doesn't matter when initstate is called.
424 // Returns a pointer to the old state.
427 char * RandomGenerator::initstate(unsigned long seed, char *arg_state, long n)
429 char *ostate = (char *) (&state[-1]);
430 long *long_arg_state = (long *) arg_state;
432 if (rand_type == TYPE_0)
433 state[-1] = rand_type;
435 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
437 if (n < BREAK_0) return NULL;
445 else if (n < BREAK_2)
451 else if (n < BREAK_3)
457 else if (n < BREAK_4)
470 state = (long *) (long_arg_state + 1); // First location
471 end_ptr = &state[rand_deg]; // Must set end_ptr before srandom
474 if (rand_type == TYPE_0)
475 long_arg_state[0] = rand_type;
477 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
486 // Restore the state from the given state array.
488 // Note: it is important that we also remember the locations of the pointers
489 // in the current state information, and restore the locations of the pointers
490 // from the old state information. This is done by multiplexing the pointer
491 // location into the zeroeth word of the state information.
493 // Note that due to the order in which things are done, it is OK to call
494 // setstate() with the same state as the current state.
496 // Returns a pointer to the old state information.
499 char * RandomGenerator::setstate(char *arg_state)
501 long *new_state = (long *) arg_state;
502 long type = new_state[0] % MAX_TYPES;
503 long rear = new_state[0] / MAX_TYPES;
504 char *ostate = (char *) (&state[-1]);
506 if (rand_type == TYPE_0)
507 state[-1] = rand_type;
509 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
519 rand_deg = degrees[type];
520 rand_sep = seps[type];
524 state = (long *) (new_state + 1);
525 if (rand_type != TYPE_0)
528 fptr = &state[(rear + rand_sep) % rand_deg];
530 end_ptr = &state[rand_deg]; // Set end_ptr too
535 #endif //NOT_FOR_SUPERTUX
539 // If we are using the trivial TYPE_0 R.N.G., just do the old linear
540 // congruential bit. Otherwise, we do our fancy trinomial stuff, which is
541 // the same in all the other cases due to all the global variables that have
542 // been set up. The basic operation is to add the number at the rear pointer
543 // into the one at the front pointer. Then both pointers are advanced to
544 // the next location cyclically in the table. The value returned is the sum
545 // generated, reduced to 31 bits by throwing away the "least random" low bit.
547 // Note: the code takes advantage of the fact that both the front and
548 // rear pointers can't wrap on the same call by not testing the rear
549 // pointer if the front one has wrapped.
551 // Returns a 31-bit random number.
554 long RandomGenerator::random()
559 throw std::runtime_error("uninitialized RandomGenerator object");
562 if (rand_type == TYPE_0)
565 state[0] = i = (good_rand(i)) & 0x7fffffff;
571 i = (*f >> 1) & 0x7fffffff; // Chucking least random bit
577 else if (++r >= end_ptr)