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);
48 debug = 0; // change this by hand for debug
52 RandomGenerator::~RandomGenerator() {
55 int RandomGenerator::srand(int x) {
57 while (x <= 0) // random seed of zero means
58 x = time(0) % RandomGenerator::rand_max; // randomize with time
61 printf("==== srand(%10d) (%10d) rand_max=%x =====\n",
62 x, x0, RandomGenerator::rand_max);
64 RandomGenerator::srandom(x);
65 return x; // let caller know seed used
68 int RandomGenerator::rand() {
69 int rv; // a posative int
70 while ((rv = RandomGenerator::random()) <= 0) // neg or zero causes probs
73 printf("==== rand(): %10d =====\n", rv);
77 int RandomGenerator::rand(int v) {
78 assert(v >= 0 && v <= RandomGenerator::rand_max); // illegal arg
80 // remove biases, esp. when v is large (e.g. v == (rand_max/4)*3;)
81 int rv, maxV =(RandomGenerator::rand_max / v) * v;
82 assert(maxV <= RandomGenerator::rand_max);
83 while ((rv = RandomGenerator::random()) >= maxV)
85 return rv % v; // mod it down to 0..(maxV-1)
88 int RandomGenerator::rand(int u, int v) {
90 return u + RandomGenerator::rand(v-u);
93 double RandomGenerator::randf(double v) {
96 rv = ((double)RandomGenerator::random())/RandomGenerator::rand_max * v;
97 } while (rv >= v); // rounding might cause rv==v
100 printf("==== rand(): %f =====\n", rv);
104 double RandomGenerator::randf(double u, double v) {
105 return u + RandomGenerator::randf(v-u);
108 //-----------------------------------------------------------------------
110 // Copyright (C) 2002 Michael Ringgaard. All rights reserved.
111 // Copyright (C) 1983, 1993 The Regents of the University of California.
113 // Redistribution and use in source and binary forms, with or without
114 // modification, are permitted provided that the following conditions
117 // 1. Redistributions of source code must retain the above copyright
118 // notice, this list of conditions and the following disclaimer.
119 // 2. Redistributions in binary form must reproduce the above copyright
120 // notice, this list of conditions and the following disclaimer in the
121 // documentation and/or other materials provided with the distribution.
122 // 3. Neither the name of the project nor the names of its contributors
123 // may be used to endorse or promote products derived from this software
124 // without specific prior written permission.
126 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
127 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
128 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
129 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
130 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
131 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
132 // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
133 // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
134 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
135 // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
142 // An improved random number generation package. In addition to the standard
143 // rand()/srand() like interface, this package also has a special state info
144 // interface. The initstate() routine is called with a seed, an array of
145 // bytes, and a count of how many bytes are being passed in; this array is
146 // then initialized to contain information for random number generation with
147 // that much state information. Good sizes for the amount of state
148 // information are 32, 64, 128, and 256 bytes. The state can be switched by
149 // calling the setstate() routine with the same array as was initiallized
150 // with initstate(). By default, the package runs with 128 bytes of state
151 // information and generates far better random numbers than a linear
152 // congruential generator. If the amount of state information is less than
153 // 32 bytes, a simple linear congruential R.N.G. is used.
155 // Internally, the state information is treated as an array of longs; the
156 // zeroeth element of the array is the type of R.N.G. being used (small
157 // integer); the remainder of the array is the state information for the
158 // R.N.G. Thus, 32 bytes of state information will give 7 longs worth of
159 // state information, which will allow a degree seven polynomial. (Note:
160 // the zeroeth word of state information also has some other information
161 // stored in it -- see setstate() for details).
163 // The random number generation technique is a linear feedback shift register
164 // approach, employing trinomials (since there are fewer terms to sum up that
165 // way). In this approach, the least significant bit of all the numbers in
166 // the state table will act as a linear feedback shift register, and will
167 // have period 2^deg - 1 (where deg is the degree of the polynomial being
168 // used, assuming that the polynomial is irreducible and primitive). The
169 // higher order bits will have longer periods, since their values are also
170 // influenced by pseudo-random carries out of the lower bits. The total
171 // period of the generator is approximately deg*(2**deg - 1); thus doubling
172 // the amount of state information has a vast influence on the period of the
173 // generator. Note: the deg*(2**deg - 1) is an approximation only good for
174 // large deg, when the period of the shift is the dominant factor.
175 // With deg equal to seven, the period is actually much longer than the
176 // 7*(2**7 - 1) predicted by this formula.
178 // Modified 28 December 1994 by Jacob S. Rosenberg.
182 // For each of the currently supported random number generators, we have a
183 // break value on the amount of state information (you need at least this
184 // many bytes of state info to support this random number generator), a degree
185 // for the polynomial (actually a trinomial) that the R.N.G. is based on, and
186 // the separation between the two lower order coefficients of the trinomial.
188 void RandomGenerator::initialize() {
190 #define NSHUFF 100 // To drop part of seed -> 1st value correlation
192 //static long degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 };
193 //static long seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 };
208 // Initially, everything is set up as if from:
210 // initstate(1, randtbl, 128);
212 // Note that this initialization takes advantage of the fact that srandom()
213 // advances the front and rear pointers 10*rand_deg times, and hence the
214 // rear pointer which starts at 0 will also end up at zero; thus the zeroeth
215 // element of the state information, which contains info about the current
216 // position of the rear pointer is just
218 // MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3.
220 randtbl[ 0] = TYPE_3;
221 randtbl[ 1] = 0x991539b1;
222 randtbl[ 2] = 0x16a5bce3;
223 randtbl[ 3] = 0x6774a4cd;
224 randtbl[ 4] = 0x3e01511e;
225 randtbl[ 5] = 0x4e508aaa;
226 randtbl[ 6] = 0x61048c05;
227 randtbl[ 7] = 0xf5500617;
228 randtbl[ 8] = 0x846b7115;
229 randtbl[ 9] = 0x6a19892c;
230 randtbl[10] = 0x896a97af;
231 randtbl[11] = 0xdb48f936;
232 randtbl[12] = 0x14898454;
233 randtbl[13] = 0x37ffd106;
234 randtbl[14] = 0xb58bff9c;
235 randtbl[15] = 0x59e17104;
236 randtbl[16] = 0xcf918a49;
237 randtbl[17] = 0x09378c83;
238 randtbl[18] = 0x52c7a471;
239 randtbl[19] = 0x8d293ea9;
240 randtbl[20] = 0x1f4fc301;
241 randtbl[21] = 0xc3db71be;
242 randtbl[22] = 0x39b44e1c;
243 randtbl[23] = 0xf8a44ef9;
244 randtbl[24] = 0x4c8b80b1;
245 randtbl[25] = 0x19edc328;
246 randtbl[26] = 0x87bf4bdd;
247 randtbl[27] = 0xc9b240e5;
248 randtbl[28] = 0xe9ee4b1b;
249 randtbl[29] = 0x4382aee7;
250 randtbl[30] = 0x535b6b41;
251 randtbl[31] = 0xf3bec5da;
253 // static long randtbl[DEG_3 + 1] =
256 // 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05,
257 // 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454,
258 // 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471,
259 // 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1,
260 // 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41,
266 // fptr and rptr are two pointers into the state info, a front and a rear
267 // pointer. These two pointers are always rand_sep places aparts, as they
268 // cycle cyclically through the state information. (Yes, this does mean we
269 // could get away with just one pointer, but the code for random() is more
270 // efficient this way). The pointers are left positioned as they would be
273 // initstate(1, randtbl, 128);
275 // (The position of the rear pointer, rptr, is really 0 (as explained above
276 // in the initialization of randtbl) because the state table pointer is set
277 // to point to randtbl[1] (as explained below).
280 fptr = &randtbl[SEP_3 + 1];
284 // The following things are the pointer to the state information table, the
285 // type of the current generator, the degree of the current polynomial being
286 // used, and the separation between the two pointers. Note that for efficiency
287 // of random(), we remember the first location of the state information, not
288 // the zeroeth. Hence it is valid to access state[-1], which is used to
289 // store the type of the R.N.G. Also, we remember the last location, since
290 // this is more efficient than indexing every time to find the address of
291 // the last element to see if the front and rear pointers have wrapped.
298 end_ptr = &randtbl[DEG_3 + 1];
303 // Compute x = (7^5 * x) mod (2^31 - 1)
304 // wihout overflowing 31 bits:
305 // (2^31 - 1) = 127773 * (7^5) + 2836
306 // From "Random number generators: good ones are hard to find",
307 // Park and Miller, Communications of the ACM, vol. 31, no. 10,
308 // October 1988, p. 1195.
311 __inline static long good_rand(long x)
315 // Can't be initialized with 0, so use another value.
316 if (x == 0) x = 123459876;
319 x = 16807 * lo - 2836 * hi;
320 if (x < 0) x += 0x7fffffff;
327 // Initialize the random number generator based on the given seed. If the
328 // type is the trivial no-state-information type, just remember the seed.
329 // Otherwise, initializes state[] based on the given "seed" via a linear
330 // congruential generator. Then, the pointers are set to known locations
331 // that are exactly rand_sep places apart. Lastly, it cycles the state
332 // information a given number of times to get rid of any initial dependencies
333 // introduced by the L.C.R.N.G. Note that the initialization of randtbl[]
334 // for default usage relies on values produced by this routine.
336 void RandomGenerator::srandom(unsigned long x)
341 if (rand_type == TYPE_0)
345 for (i = 1; i < rand_deg; i++) state[i] = good_rand(state[i - 1]);
346 fptr = &state[rand_sep];
352 for (i = 0; i < lim; i++) random();
355 #ifdef NOT_FOR_SUPERTUX // use in supertux doesn't require these methods,
356 // which are not portable to as many platforms as
357 // SDL. The cost is that the variability of the
358 // initial seed is reduced to only 32 bits of
359 // randomness, seemingly enough. PAK 060420
363 // Many programs choose the seed value in a totally predictable manner.
364 // This often causes problems. We seed the generator using the much more
365 // secure random() interface. Note that this particular seeding
366 // procedure can generate states which are impossible to reproduce by
367 // calling srandom() with any value, since the succeeding terms in the
368 // state buffer are no longer derived from the LC algorithm applied to
371 void RandomGenerator::srandomdev()
376 if (rand_type == TYPE_0)
377 len = sizeof state[0];
379 len = rand_deg * sizeof state[0];
382 fd = open("/dev/urandom", O_RDONLY);
385 if (read(fd, state, len) == len) done = 1;
393 gettimeofday(&tv, NULL);
394 srandom(tv.tv_sec ^ tv.tv_usec);
398 if (rand_type != TYPE_0)
400 fptr = &state[rand_sep];
409 // Initialize the state information in the given array of n bytes for future
410 // random number generation. Based on the number of bytes we are given, and
411 // the break values for the different R.N.G.'s, we choose the best (largest)
412 // one we can and set things up for it. srandom() is then called to
413 // initialize the state information.
415 // Note that on return from srandom(), we set state[-1] to be the type
416 // multiplexed with the current value of the rear pointer; this is so
417 // successive calls to initstate() won't lose this information and will be
418 // able to restart with setstate().
420 // Note: the first thing we do is save the current state, if any, just like
421 // setstate() so that it doesn't matter when initstate is called.
423 // Returns a pointer to the old state.
426 char * RandomGenerator::initstate(unsigned long seed, char *arg_state, long n)
428 char *ostate = (char *) (&state[-1]);
429 long *long_arg_state = (long *) arg_state;
431 if (rand_type == TYPE_0)
432 state[-1] = rand_type;
434 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
436 if (n < BREAK_0) return NULL;
444 else if (n < BREAK_2)
450 else if (n < BREAK_3)
456 else if (n < BREAK_4)
469 state = (long *) (long_arg_state + 1); // First location
470 end_ptr = &state[rand_deg]; // Must set end_ptr before srandom
473 if (rand_type == TYPE_0)
474 long_arg_state[0] = rand_type;
476 long_arg_state[0] = MAX_TYPES * (rptr - state) + rand_type;
485 // Restore the state from the given state array.
487 // Note: it is important that we also remember the locations of the pointers
488 // in the current state information, and restore the locations of the pointers
489 // from the old state information. This is done by multiplexing the pointer
490 // location into the zeroeth word of the state information.
492 // Note that due to the order in which things are done, it is OK to call
493 // setstate() with the same state as the current state.
495 // Returns a pointer to the old state information.
498 char * RandomGenerator::setstate(char *arg_state)
500 long *new_state = (long *) arg_state;
501 long type = new_state[0] % MAX_TYPES;
502 long rear = new_state[0] / MAX_TYPES;
503 char *ostate = (char *) (&state[-1]);
505 if (rand_type == TYPE_0)
506 state[-1] = rand_type;
508 state[-1] = MAX_TYPES * (rptr - state) + rand_type;
518 rand_deg = degrees[type];
519 rand_sep = seps[type];
523 state = (long *) (new_state + 1);
524 if (rand_type != TYPE_0)
527 fptr = &state[(rear + rand_sep) % rand_deg];
529 end_ptr = &state[rand_deg]; // Set end_ptr too
534 #endif //NOT_FOR_SUPERTUX
538 // If we are using the trivial TYPE_0 R.N.G., just do the old linear
539 // congruential bit. Otherwise, we do our fancy trinomial stuff, which is
540 // the same in all the other cases due to all the global variables that have
541 // been set up. The basic operation is to add the number at the rear pointer
542 // into the one at the front pointer. Then both pointers are advanced to
543 // the next location cyclically in the table. The value returned is the sum
544 // generated, reduced to 31 bits by throwing away the "least random" low bit.
546 // Note: the code takes advantage of the fact that both the front and
547 // rear pointers can't wrap on the same call by not testing the rear
548 // pointer if the front one has wrapped.
550 // Returns a 31-bit random number.
553 long RandomGenerator::random()
558 throw std::runtime_error("uninitialized RandomGenerator object");
561 if (rand_type == TYPE_0)
564 state[0] = i = (good_rand(i)) & 0x7fffffff;
570 i = (*f >> 1) & 0x7fffffff; // Chucking least random bit
576 else if (++r >= end_ptr)