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 "math/random_generator.hpp"
44 RandomGenerator systemRandom; // global random number generator
46 RandomGenerator::RandomGenerator() :
57 assert(sizeof(int) >= 4);
59 debug = 0; // change this by hand for debug
63 RandomGenerator::~RandomGenerator() {
66 int RandomGenerator::srand(int x) {
68 while (x <= 0) // random seed of zero means
69 x = time(0) % RandomGenerator::rand_max; // randomize with time
72 printf("==== srand(%10d) (%10d) rand_max=%x =====\n",
73 x, x0, RandomGenerator::rand_max);
75 RandomGenerator::srandom(x);
76 return x; // let caller know seed used
79 int RandomGenerator::rand() {
80 int rv; // a positive int
81 while ((rv = RandomGenerator::random()) <= 0) // neg or zero causes probs
84 printf("==== rand(): %10d =====\n", rv);
88 int RandomGenerator::rand(int v) {
89 assert(v >= 0 && v <= RandomGenerator::rand_max); // illegal arg
91 // remove biases, esp. when v is large (e.g. v == (rand_max/4)*3;)
92 int rv, maxV =(RandomGenerator::rand_max / v) * v;
93 assert(maxV <= RandomGenerator::rand_max);
94 while ((rv = RandomGenerator::random()) >= maxV)
96 return rv % v; // mod it down to 0..(maxV-1)
99 int RandomGenerator::rand(int u, int v) {
101 return u + RandomGenerator::rand(v-u);
104 double RandomGenerator::randf(double v) {
107 rv = ((double)RandomGenerator::random())/RandomGenerator::rand_max * v;
108 } while (rv >= v); // rounding might cause rv==v
111 printf("==== rand(): %f =====\n", rv);
115 double RandomGenerator::randf(double u, double v) {
116 return u + RandomGenerator::randf(v-u);
119 //-----------------------------------------------------------------------
121 // Copyright (C) 2002 Michael Ringgaard. All rights reserved.
122 // Copyright (C) 1983, 1993 The Regents of the University of California.
124 // Redistribution and use in source and binary forms, with or without
125 // modification, are permitted provided that the following conditions
128 // 1. Redistributions of source code must retain the above copyright
129 // notice, this list of conditions and the following disclaimer.
130 // 2. Redistributions in binary form must reproduce the above copyright
131 // notice, this list of conditions and the following disclaimer in the
132 // documentation and/or other materials provided with the distribution.
133 // 3. Neither the name of the project nor the names of its contributors
134 // may be used to endorse or promote products derived from this software
135 // without specific prior written permission.
137 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
138 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
139 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
140 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
141 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
142 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
143 // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
144 // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
145 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
146 // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
153 // An improved random number generation package. In addition to the standard
154 // rand()/srand() like interface, this package also has a special state info
155 // interface. The initstate() routine is called with a seed, an array of
156 // bytes, and a count of how many bytes are being passed in; this array is
157 // then initialized to contain information for random number generation with
158 // that much state information. Good sizes for the amount of state
159 // information are 32, 64, 128, and 256 bytes. The state can be switched by
160 // calling the setstate() routine with the same array as was initialized
161 // with initstate(). By default, the package runs with 128 bytes of state
162 // information and generates far better random numbers than a linear
163 // congruential generator. If the amount of state information is less than
164 // 32 bytes, a simple linear congruential R.N.G. is used.
166 // Internally, the state information is treated as an array of longs; the
167 // zeroeth element of the array is the type of R.N.G. being used (small
168 // integer); the remainder of the array is the state information for the
169 // R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
170 // state information, which will allow a degree seven polynomial. (Note:
171 // the zeroeth word of state information also has some other information
172 // stored in it -- see setstate() for details).
174 // The random number generation technique is a linear feedback shift register
175 // approach, employing trinomials (since there are fewer terms to sum up that
176 // way). In this approach, the least significant bit of all the numbers in
177 // the state table will act as a linear feedback shift register, and will
178 // have period 2^deg - 1 (where deg is the degree of the polynomial being
179 // used, assuming that the polynomial is irreducible and primitive). The
180 // higher order bits will have longer periods, since their values are also
181 // influenced by pseudo-random carries out of the lower bits. The total
182 // period of the generator is approximately deg*(2**deg - 1); thus doubling
183 // the amount of state information has a vast influence on the period of the
184 // generator. Note: the deg*(2**deg - 1) is an approximation only good for
185 // large deg, when the period of the shift is the dominant factor.
186 // With deg equal to seven, the period is actually much longer than the
187 // 7*(2**7 - 1) predicted by this formula.
189 // Modified 28 December 1994 by Jacob S. Rosenberg.
193 // For each of the currently supported random number generators, we have a
194 // break value on the amount of state information (you need at least this
195 // many bytes of state info to support this random number generator), a degree
196 // for the polynomial (actually a trinomial) that the R.N.G. is based on, and
197 // the separation between the two lower order coefficients of the trinomial.
199 void RandomGenerator::initialize() {
201 #define NSHUFF 100 // To drop part of seed -> 1st value correlation
203 //static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
204 //static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
219 // Initially, everything is set up as if from:
221 // initstate(1, randtbl, 128);
223 // Note that this initialization takes advantage of the fact that srandom()
224 // advances the front and rear pointers 10*rand_deg times, and hence the
225 // rear pointer which starts at 0 will also end up at zero; thus the zeroeth
226 // element of the state information, which contains info about the current
227 // position of the rear pointer is just
229 // MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
231 randtbl[ 0] = TYPE_3;
232 randtbl[ 1] = 0x991539b1;
233 randtbl[ 2] = 0x16a5bce3;
234 randtbl[ 3] = 0x6774a4cd;
235 randtbl[ 4] = 0x3e01511e;
236 randtbl[ 5] = 0x4e508aaa;
237 randtbl[ 6] = 0x61048c05;
238 randtbl[ 7] = 0xf5500617;
239 randtbl[ 8] = 0x846b7115;
240 randtbl[ 9] = 0x6a19892c;
241 randtbl[10] = 0x896a97af;
242 randtbl[11] = 0xdb48f936;
243 randtbl[12] = 0x14898454;
244 randtbl[13] = 0x37ffd106;
245 randtbl[14] = 0xb58bff9c;
246 randtbl[15] = 0x59e17104;
247 randtbl[16] = 0xcf918a49;
248 randtbl[17] = 0x09378c83;
249 randtbl[18] = 0x52c7a471;
250 randtbl[19] = 0x8d293ea9;
251 randtbl[20] = 0x1f4fc301;
252 randtbl[21] = 0xc3db71be;
253 randtbl[22] = 0x39b44e1c;
254 randtbl[23] = 0xf8a44ef9;
255 randtbl[24] = 0x4c8b80b1;
256 randtbl[25] = 0x19edc328;
257 randtbl[26] = 0x87bf4bdd;
258 randtbl[27] = 0xc9b240e5;
259 randtbl[28] = 0xe9ee4b1b;
260 randtbl[29] = 0x4382aee7;
261 randtbl[30] = 0x535b6b41;
262 randtbl[31] = 0xf3bec5da;
264 // static long randtbl[DEG_3 + 1] =
267 // 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
268 // 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
269 // 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
270 // 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
271 // 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
276 // fptr and rptr are two pointers into the state info, a front and a rear
277 // pointer. These two pointers are always rand_sep places aparts, as they
278 // cycle cyclically through the state information. (Yes, this does mean we
279 // could get away with just one pointer, but the code for random() is more
280 // efficient this way). The pointers are left positioned as they would be
283 // initstate(1, randtbl, 128);
285 // (The position of the rear pointer, rptr, is really 0 (as explained above
286 // in the initialization of randtbl) because the state table pointer is set
287 // to point to randtbl[1] (as explained below).
290 fptr = &randtbl[SEP_3 + 1];
294 // The following things are the pointer to the state information table, the
295 // type of the current generator, the degree of the current polynomial being
296 // used, and the separation between the two pointers. Note that for efficiency
297 // of random(), we remember the first location of the state information, not
298 // the zeroeth. Hence it is valid to access state[-1], which is used to
299 // store the type of the R.N.G. Also, we remember the last location, since
300 // this is more efficient than indexing every time to find the address of
301 // the last element to see if the front and rear pointers have wrapped.
308 end_ptr = &randtbl[DEG_3 + 1];
313 // Compute x = (7^5 * x) mod (2^31 - 1)
314 // without overflowing 31 bits:
315 // (2^31 - 1) = 127773 * (7^5) + 2836
316 // From "Random number generators: good ones are hard to find",
317 // Park and Miller, Communications of the ACM, vol. 31, no. 10,
318 // October 1988, p. 1195.
321 __inline static long good_rand(long x)
325 // Can't be initialized with 0, so use another value.
326 if (x == 0) x = 123459876;
329 x = 16807 * lo - 2836 * hi;
330 if (x < 0) x += 0x7fffffff;
337 // Initialize the random number generator based on the given seed. If the
338 // type is the trivial no-state-information type, just remember the seed.
339 // Otherwise, initializes state[] based on the given "seed" via a linear
340 // congruential generator. Then, the pointers are set to known locations
341 // that are exactly rand_sep places apart. Lastly, it cycles the state
342 // information a given number of times to get rid of any initial dependencies
343 // introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
344 // for default usage relies on values produced by this routine.
346 void RandomGenerator::srandom(unsigned long x)
351 if (rand_type == TYPE_0)
355 for (i = 1; i < rand_deg; i++) state[i] = good_rand(state[i - 1]);
356 fptr = &state[rand_sep];
362 for (i = 0; i < lim; i++) random();
365 #ifdef NOT_FOR_SUPERTUX // use in supertux doesn't require these methods,
366 // which are not portable to as many platforms as
367 // SDL. The cost is that the variability of the
368 // initial seed is reduced to only 32 bits of
369 // randomness, seemingly enough. PAK 060420
373 // Many programs choose the seed value in a totally predictable manner.
374 // This often causes problems. We seed the generator using the much more
375 // secure random() interface. Note that this particular seeding
376 // procedure can generate states which are impossible to reproduce by
377 // calling srandom() with any value, since the succeeding terms in the
378 // state buffer are no longer derived from the LC algorithm applied to
381 void RandomGenerator::srandomdev()
386 if (rand_type == TYPE_0)
387 len = sizeof state[0];
389 len = rand_deg * sizeof state[0];
392 fd = open("/dev/urandom", O_RDONLY);
395 if (read(fd, state, len) == len) done = 1;
403 gettimeofday(&tv, NULL);
404 srandom(tv.tv_sec ^ tv.tv_usec);
408 if (rand_type != TYPE_0)
410 fptr = &state[rand_sep];
419 // Initialize the state information in the given array of n bytes for future
420 // random number generation. Based on the number of bytes we are given, and
421 // the break values for the different R.N.G.'s, we choose the best (largest)
422 // one we can and set things up for it. srandom() is then called to
423 // initialize the state information.
425 // Note that on return from srandom(), we set state[-1] to be the type
426 // multiplexed with the current value of the rear pointer; this is so
427 // successive calls to initstate() won't lose this information and will be
428 // able to restart with setstate().
430 // Note: the first thing we do is save the current state, if any, just like
431 // setstate() so that it doesn't matter when initstate is called.
433 // Returns a pointer to the old state.
436 char * RandomGenerator::initstate(unsigned long seed, char *arg_state, long n)
438 char *ostate = (char *) (&state[-1]);
439 long *long_arg_state = (long *) arg_state;
441 if (rand_type == TYPE_0)
442 state[-1] = rand_type;
444 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
446 if (n < BREAK_0) return NULL;
454 else if (n < BREAK_2)
460 else if (n < BREAK_3)
466 else if (n < BREAK_4)
479 state = (long *) (long_arg_state + 1); // First location
480 end_ptr = &state[rand_deg]; // Must set end_ptr before srandom
483 if (rand_type == TYPE_0)
484 long_arg_state[0] = rand_type;
486 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
495 // Restore the state from the given state array.
497 // Note: it is important that we also remember the locations of the pointers
498 // in the current state information, and restore the locations of the pointers
499 // from the old state information. This is done by multiplexing the pointer
500 // location into the zeroeth word of the state information.
502 // Note that due to the order in which things are done, it is OK to call
503 // setstate() with the same state as the current state.
505 // Returns a pointer to the old state information.
508 char * RandomGenerator::setstate(char *arg_state)
510 long *new_state = (long *) arg_state;
511 long type = new_state[0] % MAX_TYPES;
512 long rear = new_state[0] / MAX_TYPES;
513 char *ostate = (char *) (&state[-1]);
515 if (rand_type == TYPE_0)
516 state[-1] = rand_type;
518 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
528 rand_deg = degrees[type];
529 rand_sep = seps[type];
533 state = (long *) (new_state + 1);
534 if (rand_type != TYPE_0)
537 fptr = &state[(rear + rand_sep) % rand_deg];
539 end_ptr = &state[rand_deg]; // Set end_ptr too
544 #endif //NOT_FOR_SUPERTUX
548 // If we are using the trivial TYPE_0 R.N.G., just do the old linear
549 // congruential bit. Otherwise, we do our fancy trinomial stuff, which is
550 // the same in all the other cases due to all the global variables that have
551 // been set up. The basic operation is to add the number at the rear pointer
552 // into the one at the front pointer. Then both pointers are advanced to
553 // the next location cyclically in the table. The value returned is the sum
554 // generated, reduced to 31 bits by throwing away the "least random" low bit.
556 // Note: the code takes advantage of the fact that both the front and
557 // rear pointers can't wrap on the same call by not testing the rear
558 // pointer if the front one has wrapped.
560 // Returns a 31-bit random number.
563 long RandomGenerator::random()
568 throw std::runtime_error("uninitialized RandomGenerator object");
571 if (rand_type == TYPE_0)
574 state[0] = i = (good_rand(i)) & 0x7fffffff;
580 i = (*f >> 1) & 0x7fffffff; // Chucking least random bit
586 else if (++r >= end_ptr)