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
40 #include "random_generator.hpp"
41 #include "scripting/squirrel_util.hpp"
43 RandomGenerator systemRandom; // global random number generator
45 RandomGenerator::RandomGenerator() {
46 assert(sizeof(int) >= 4);
51 RandomGenerator::~RandomGenerator() {
54 int RandomGenerator::srand(int x) {
55 while (x == 0) // random seed of zero means
56 x = time(0); // randomize with time
57 assert(x < RAND_MAX); // only allow posative 31-bit seeds
58 assert(sizeof(int) >= 4);
60 return x; // let caller know seed used
63 int RandomGenerator::rand() { return random(); }
65 int RandomGenerator::rand(int v) {
66 assert(v != 0 && v <= RAND_MAX); // illegal arg: 0 or too big
67 return RandomGenerator::random() % v;
70 int RandomGenerator::rand(int u, int v) {
72 return u + RandomGenerator::rand(v-u);
75 double RandomGenerator::randf(double v) {
77 while ((rv = (double)RandomGenerator::random() / RAND_MAX * v) >= v)
82 double RandomGenerator::randf(double u, double v) {
83 return u + RandomGenerator::randf(v-u);
86 //-----------------------------------------------------------------------
88 // Copyright (C) 2002 Michael Ringgaard. All rights reserved.
89 // Copyright (C) 1983, 1993 The Regents of the University of California.
91 // Redistribution and use in source and binary forms, with or without
92 // modification, are permitted provided that the following conditions
95 // 1. Redistributions of source code must retain the above copyright
96 // notice, this list of conditions and the following disclaimer.
97 // 2. Redistributions in binary form must reproduce the above copyright
98 // notice, this list of conditions and the following disclaimer in the
99 // documentation and/or other materials provided with the distribution.
100 // 3. Neither the name of the project nor the names of its contributors
101 // may be used to endorse or promote products derived from this software
102 // without specific prior written permission.
104 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
105 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
106 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
107 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
108 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
109 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
110 // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
111 // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
112 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
113 // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
120 // An improved random number generation package. In addition to the standard
121 // rand()/srand() like interface, this package also has a special state info
122 // interface. The initstate() routine is called with a seed, an array of
123 // bytes, and a count of how many bytes are being passed in; this array is
124 // then initialized to contain information for random number generation with
125 // that much state information. Good sizes for the amount of state
126 // information are 32, 64, 128, and 256 bytes. The state can be switched by
127 // calling the setstate() routine with the same array as was initiallized
128 // with initstate(). By default, the package runs with 128 bytes of state
129 // information and generates far better random numbers than a linear
130 // congruential generator. If the amount of state information is less than
131 // 32 bytes, a simple linear congruential R.N.G. is used.
133 // Internally, the state information is treated as an array of longs; the
134 // zeroeth element of the array is the type of R.N.G. being used (small
135 // integer); the remainder of the array is the state information for the
136 // R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
137 // state information, which will allow a degree seven polynomial. (Note:
138 // the zeroeth word of state information also has some other information
139 // stored in it -- see setstate() for details).
141 // The random number generation technique is a linear feedback shift register
142 // approach, employing trinomials (since there are fewer terms to sum up that
143 // way). In this approach, the least significant bit of all the numbers in
144 // the state table will act as a linear feedback shift register, and will
145 // have period 2^deg - 1 (where deg is the degree of the polynomial being
146 // used, assuming that the polynomial is irreducible and primitive). The
147 // higher order bits will have longer periods, since their values are also
148 // influenced by pseudo-random carries out of the lower bits. The total
149 // period of the generator is approximately deg*(2**deg - 1); thus doubling
150 // the amount of state information has a vast influence on the period of the
151 // generator. Note: the deg*(2**deg - 1) is an approximation only good for
152 // large deg, when the period of the shift is the dominant factor.
153 // With deg equal to seven, the period is actually much longer than the
154 // 7*(2**7 - 1) predicted by this formula.
156 // Modified 28 December 1994 by Jacob S. Rosenberg.
160 // For each of the currently supported random number generators, we have a
161 // break value on the amount of state information (you need at least this
162 // many bytes of state info to support this random number generator), a degree
163 // for the polynomial (actually a trinomial) that the R.N.G. is based on, and
164 // the separation between the two lower order coefficients of the trinomial.
166 void RandomGenerator::initialize() {
168 #define NSHUFF 100 // To drop part of seed -> 1st value correlation
170 //static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
171 //static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
186 // Initially, everything is set up as if from:
188 // initstate(1, randtbl, 128);
190 // Note that this initialization takes advantage of the fact that srandom()
191 // advances the front and rear pointers 10*rand_deg times, and hence the
192 // rear pointer which starts at 0 will also end up at zero; thus the zeroeth
193 // element of the state information, which contains info about the current
194 // position of the rear pointer is just
196 // MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
198 randtbl[ 0] = TYPE_3;
199 randtbl[ 1] = 0x991539b1;
200 randtbl[ 2] = 0x16a5bce3;
201 randtbl[ 3] = 0x6774a4cd;
202 randtbl[ 4] = 0x3e01511e;
203 randtbl[ 5] = 0x4e508aaa;
204 randtbl[ 6] = 0x61048c05;
205 randtbl[ 7] = 0xf5500617;
206 randtbl[ 8] = 0x846b7115;
207 randtbl[ 9] = 0x6a19892c;
208 randtbl[10] = 0x896a97af;
209 randtbl[11] = 0xdb48f936;
210 randtbl[12] = 0x14898454;
211 randtbl[13] = 0x37ffd106;
212 randtbl[14] = 0xb58bff9c;
213 randtbl[15] = 0x59e17104;
214 randtbl[16] = 0xcf918a49;
215 randtbl[17] = 0x09378c83;
216 randtbl[18] = 0x52c7a471;
217 randtbl[19] = 0x8d293ea9;
218 randtbl[20] = 0x1f4fc301;
219 randtbl[21] = 0xc3db71be;
220 randtbl[22] = 0x39b44e1c;
221 randtbl[23] = 0xf8a44ef9;
222 randtbl[24] = 0x4c8b80b1;
223 randtbl[25] = 0x19edc328;
224 randtbl[26] = 0x87bf4bdd;
225 randtbl[27] = 0xc9b240e5;
226 randtbl[28] = 0xe9ee4b1b;
227 randtbl[29] = 0x4382aee7;
228 randtbl[30] = 0x535b6b41;
229 randtbl[31] = 0xf3bec5da;
231 // static long randtbl[DEG_3 + 1] =
234 // 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
235 // 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
236 // 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
237 // 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
238 // 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
244 // fptr and rptr are two pointers into the state info, a front and a rear
245 // pointer. These two pointers are always rand_sep places aparts, as they
246 // cycle cyclically through the state information. (Yes, this does mean we
247 // could get away with just one pointer, but the code for random() is more
248 // efficient this way). The pointers are left positioned as they would be
251 // initstate(1, randtbl, 128);
253 // (The position of the rear pointer, rptr, is really 0 (as explained above
254 // in the initialization of randtbl) because the state table pointer is set
255 // to point to randtbl[1] (as explained below).
258 fptr = &randtbl[SEP_3 + 1];
262 // The following things are the pointer to the state information table, the
263 // type of the current generator, the degree of the current polynomial being
264 // used, and the separation between the two pointers. Note that for efficiency
265 // of random(), we remember the first location of the state information, not
266 // the zeroeth. Hence it is valid to access state[-1], which is used to
267 // store the type of the R.N.G. Also, we remember the last location, since
268 // this is more efficient than indexing every time to find the address of
269 // the last element to see if the front and rear pointers have wrapped.
276 end_ptr = &randtbl[DEG_3 + 1];
281 // Compute x = (7^5 * x) mod (2^31 - 1)
282 // wihout overflowing 31 bits:
283 // (2^31 - 1) = 127773 * (7^5) + 2836
284 // From "Random number generators: good ones are hard to find",
285 // Park and Miller, Communications of the ACM, vol. 31, no. 10,
286 // October 1988, p. 1195.
289 __inline static long good_rand(long x)
293 // Can't be initialized with 0, so use another value.
294 if (x == 0) x = 123459876;
297 x = 16807 * lo - 2836 * hi;
298 if (x < 0) x += 0x7fffffff;
305 // Initialize the random number generator based on the given seed. If the
306 // type is the trivial no-state-information type, just remember the seed.
307 // Otherwise, initializes state[] based on the given "seed" via a linear
308 // congruential generator. Then, the pointers are set to known locations
309 // that are exactly rand_sep places apart. Lastly, it cycles the state
310 // information a given number of times to get rid of any initial dependencies
311 // introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
312 // for default usage relies on values produced by this routine.
314 void RandomGenerator::srandom(unsigned long x)
319 if (rand_type == TYPE_0)
323 for (i = 1; i < rand_deg; i++) state[i] = good_rand(state[i - 1]);
324 fptr = &state[rand_sep];
330 for (i = 0; i < lim; i++) random();
333 #ifdef NOT_FOR_SUPERTUX // use in supertux doesn't require these methods,
334 // which are not portable to as many platforms as
335 // SDL. The cost is that the variability of the
336 // initial seed is reduced to only 32 bits of
337 // randomness, seemingly enough. PAK 060420
341 // Many programs choose the seed value in a totally predictable manner.
342 // This often causes problems. We seed the generator using the much more
343 // secure random() interface. Note that this particular seeding
344 // procedure can generate states which are impossible to reproduce by
345 // calling srandom() with any value, since the succeeding terms in the
346 // state buffer are no longer derived from the LC algorithm applied to
349 void RandomGenerator::srandomdev()
354 if (rand_type == TYPE_0)
355 len = sizeof state[0];
357 len = rand_deg * sizeof state[0];
360 fd = open("/dev/urandom", O_RDONLY);
363 if (read(fd, state, len) == len) done = 1;
371 gettimeofday(&tv, NULL);
372 srandom(tv.tv_sec ^ tv.tv_usec);
376 if (rand_type != TYPE_0)
378 fptr = &state[rand_sep];
387 // Initialize the state information in the given array of n bytes for future
388 // random number generation. Based on the number of bytes we are given, and
389 // the break values for the different R.N.G.'s, we choose the best (largest)
390 // one we can and set things up for it. srandom() is then called to
391 // initialize the state information.
393 // Note that on return from srandom(), we set state[-1] to be the type
394 // multiplexed with the current value of the rear pointer; this is so
395 // successive calls to initstate() won't lose this information and will be
396 // able to restart with setstate().
398 // Note: the first thing we do is save the current state, if any, just like
399 // setstate() so that it doesn't matter when initstate is called.
401 // Returns a pointer to the old state.
404 char * RandomGenerator::initstate(unsigned long seed, char *arg_state, long n)
406 char *ostate = (char *) (&state[-1]);
407 long *long_arg_state = (long *) arg_state;
409 if (rand_type == TYPE_0)
410 state[-1] = rand_type;
412 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
414 if (n < BREAK_0) return NULL;
422 else if (n < BREAK_2)
428 else if (n < BREAK_3)
434 else if (n < BREAK_4)
447 state = (long *) (long_arg_state + 1); // First location
448 end_ptr = &state[rand_deg]; // Must set end_ptr before srandom
451 if (rand_type == TYPE_0)
452 long_arg_state[0] = rand_type;
454 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
463 // Restore the state from the given state array.
465 // Note: it is important that we also remember the locations of the pointers
466 // in the current state information, and restore the locations of the pointers
467 // from the old state information. This is done by multiplexing the pointer
468 // location into the zeroeth word of the state information.
470 // Note that due to the order in which things are done, it is OK to call
471 // setstate() with the same state as the current state.
473 // Returns a pointer to the old state information.
476 char * RandomGenerator::setstate(char *arg_state)
478 long *new_state = (long *) arg_state;
479 long type = new_state[0] % MAX_TYPES;
480 long rear = new_state[0] / MAX_TYPES;
481 char *ostate = (char *) (&state[-1]);
483 if (rand_type == TYPE_0)
484 state[-1] = rand_type;
486 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
496 rand_deg = degrees[type];
497 rand_sep = seps[type];
501 state = (long *) (new_state + 1);
502 if (rand_type != TYPE_0)
505 fptr = &state[(rear + rand_sep) % rand_deg];
507 end_ptr = &state[rand_deg]; // Set end_ptr too
512 #endif //NOT_FOR_SUPERTUX
516 // If we are using the trivial TYPE_0 R.N.G., just do the old linear
517 // congruential bit. Otherwise, we do our fancy trinomial stuff, which is
518 // the same in all the other cases due to all the global variables that have
519 // been set up. The basic operation is to add the number at the rear pointer
520 // into the one at the front pointer. Then both pointers are advanced to
521 // the next location cyclically in the table. The value returned is the sum
522 // generated, reduced to 31 bits by throwing away the "least random" low bit.
524 // Note: the code takes advantage of the fact that both the front and
525 // rear pointers can't wrap on the same call by not testing the rear
526 // pointer if the front one has wrapped.
528 // Returns a 31-bit random number.
531 long RandomGenerator::random()
536 throw std::runtime_error("uninitialized RandomGenerator object");
539 if (rand_type == TYPE_0)
542 state[0] = i = (good_rand(i)) & 0x7fffffff;
548 i = (*f >> 1) & 0x7fffffff; // Chucking least random bit
554 else if (++r >= end_ptr)