4 * Copyright (c) 1997 Ben Harrison, and others
6 * This software may be copied and distributed for educational, research,
7 * and not for profit purposes provided that this copyright and statement
8 * are included in all such copies. Other copyrights may also apply.
12 /* Purpose: a simple random number generator -BEN- */
24 * Angband 2.7.9 introduced a new (optimized) random number generator,
25 * based loosely on the old "random.c" from Berkeley but with some major
26 * optimizations and algorithm changes. See below for more details.
28 * Code by myself (benh@phial.com) and Randy (randy@stat.tamu.edu).
30 * This code provides (1) a "decent" RNG, based on the "BSD-degree-63-RNG"
31 * used in Angband 2.7.8, but rather optimized, and (2) a "simple" RNG,
32 * based on the simple "LCRNG" currently used in Angband, but "corrected"
33 * to give slightly better values. Both of these are available in two
34 * flavors, first, the simple "mod" flavor, which is fast, but slightly
35 * biased at high values, and second, the simple "div" flavor, which is
36 * less fast (and potentially non-terminating) but which is not biased
37 * and is much less subject to low-bit-non-randomness problems.
39 * You can select your favorite flavor by proper definition of the
40 * "randint0()" macro in the "defines.h" file.
42 * Note that, in Angband 2.8.0, the "state" table will be saved in the
43 * savefile, so a special "initialization" phase will be necessary.
45 * Note the use of the "simple" RNG, first you activate it via
46 * "Rand_quick = TRUE" and "Rand_value = seed" and then it is used
47 * automatically used instead of the "complex" RNG, and when you are
48 * done, you de-activate it via "Rand_quick = FALSE" or choose a new
49 * seed via "Rand_value = seed".
52 * RNG algorithm was fully rewritten. Upper comment is OLD.
62 * Current "state" table for the RNG
63 * Only index 0 to 3 are used
65 u32b Rand_state[RAND_DEG] = {
77 static u64b u64b_xor(u64b a, u64b b)
81 result.dw[0] = a.dw[0] ^ b.dw[0];
82 result.dw[1] = a.dw[1] ^ b.dw[1];
87 static u64b u64b_shiftl(u64b x, int k)
92 result.dw[1] = (x.dw[1] << k) | (x.dw[0] >> (32 - k));
93 result.dw[0] = (x.dw[0] << k);
96 result.dw[1] = (x.dw[0] << (k - 32));
103 static u64b u64b_rotl(u64b x, int k)
108 result.dw[0] = (x.dw[0] << k) | (x.dw[1] >> (32 - k));
109 result.dw[1] = (x.dw[1] << k) | (x.dw[0] >> (32 - k));
112 result.dw[0] = (x.dw[0] >> (64 - k)) | (x.dw[1] << (k - 32));
113 result.dw[1] = (x.dw[1] >> (64 - k)) | (x.dw[0] << (k - 32));
119 static u64b u64b_add(u64b a, u64b b)
123 result.dw[0] = a.dw[0] + b.dw[0];
124 result.dw[1] = a.dw[1] + b.dw[1];
126 if (result.dw[0] < a.dw[0])
133 * Initialize Xorshift Algorithm state
135 static void Rand_Xorshift_seed(u32b seed, u32b* state)
139 /* Initialize Xorshift Algorithm RNG */
140 for (i = 1; i <= 4; ++ i) {
141 seed = 1812433253UL * (seed ^ (seed >> 30)) + i;
150 static u32b Rand_Xorshift(u32b* state)
152 u32b t = state[0] ^ (state[0] << 11);
158 state[3] = (state[3] ^ (state[3] >> 19)) ^ (t ^ (t >> 8));
165 * Xoroshiro128+ Algorithm
167 static u32b Rand_Xoroshiro128plus(u32b* state)
169 const u64b s0 = *((u64b*)state);
170 u64b s1 = *((u64b*)state + 1);
171 const u64b result = u64b_add(s0, s1);
173 s1 = u64b_xor(s0, s1);
174 *((u64b*)state) = u64b_xor(u64b_xor(u64b_rotl(s0, 55), s1), u64b_shiftl(s1, 14));
175 *((u64b*)state + 1) = u64b_rotl(s1, 36);
180 static const u32b Rand_Xorshift_max = 0xFFFFFFFF;
183 * Initialize the RNG using a new seed
185 void Rand_state_set(u32b seed)
187 Rand_Xorshift_seed(seed, Rand_state);
190 void Rand_state_init(void)
194 FILE *fp = fopen(RNG_DEVICE, "r");
197 fread(Rand_state, sizeof(Rand_state[0]), 4, fp);
198 } while ((Rand_state[0] | Rand_state[1] | Rand_state[2] | Rand_state[3]) == 0);
202 #elif defined(WINDOWS)
204 HCRYPTPROV hProvider;
206 CryptAcquireContext(&hProvider, NULL, NULL, PROV_RSA_FULL, 0);
209 CryptGenRandom(hProvider, sizeof(Rand_state[0]) * 4, (BYTE*)Rand_state);
210 } while ((Rand_state[0] | Rand_state[1] | Rand_state[2] | Rand_state[3]) == 0);
212 CryptReleaseContext(hProvider, 0);
217 u32b seed = (time(NULL));
219 /* Mutate the seed on Unix machines */
220 seed = ((seed >> 3) * (getpid() << 1));
223 Rand_state_set(seed);
229 * Backup the RNG state
231 void Rand_state_backup(u32b* backup_state)
235 for (i = 0; i < 4; ++ i) {
236 backup_state[i] = Rand_state[i];
241 * Restore the RNG state
243 void Rand_state_restore(u32b* backup_state)
247 for (i = 0; i < 4; ++ i) {
248 Rand_state[i] = backup_state[i];
254 * Extract a "random" number from 0 to m-1, via "division"
256 static s32b Rand_div_impl(s32b m, u32b* state)
262 /* Hack -- simple case */
263 if (m <= 1) return (0);
265 scaling = Rand_Xorshift_max / m;
269 ret = Rand_Xoroshiro128plus(state);
270 } while (ret >= past);
272 return ret / scaling;
275 s32b Rand_div(s32b m)
277 return Rand_div_impl(m, Rand_state);
284 * The number of entries in the "randnor_table"
286 #define RANDNOR_NUM 256
289 * The standard deviation of the "randnor_table"
291 #define RANDNOR_STD 64
294 * The normal distribution table for the "randnor()" function (below)
296 static s16b randnor_table[RANDNOR_NUM] =
298 206, 613, 1022, 1430, 1838, 2245, 2652, 3058,
299 3463, 3867, 4271, 4673, 5075, 5475, 5874, 6271,
300 6667, 7061, 7454, 7845, 8234, 8621, 9006, 9389,
301 9770, 10148, 10524, 10898, 11269, 11638, 12004, 12367,
302 12727, 13085, 13440, 13792, 14140, 14486, 14828, 15168,
303 15504, 15836, 16166, 16492, 16814, 17133, 17449, 17761,
304 18069, 18374, 18675, 18972, 19266, 19556, 19842, 20124,
305 20403, 20678, 20949, 21216, 21479, 21738, 21994, 22245,
307 22493, 22737, 22977, 23213, 23446, 23674, 23899, 24120,
308 24336, 24550, 24759, 24965, 25166, 25365, 25559, 25750,
309 25937, 26120, 26300, 26476, 26649, 26818, 26983, 27146,
310 27304, 27460, 27612, 27760, 27906, 28048, 28187, 28323,
311 28455, 28585, 28711, 28835, 28955, 29073, 29188, 29299,
312 29409, 29515, 29619, 29720, 29818, 29914, 30007, 30098,
313 30186, 30272, 30356, 30437, 30516, 30593, 30668, 30740,
314 30810, 30879, 30945, 31010, 31072, 31133, 31192, 31249,
316 31304, 31358, 31410, 31460, 31509, 31556, 31601, 31646,
317 31688, 31730, 31770, 31808, 31846, 31882, 31917, 31950,
318 31983, 32014, 32044, 32074, 32102, 32129, 32155, 32180,
319 32205, 32228, 32251, 32273, 32294, 32314, 32333, 32352,
320 32370, 32387, 32404, 32420, 32435, 32450, 32464, 32477,
321 32490, 32503, 32515, 32526, 32537, 32548, 32558, 32568,
322 32577, 32586, 32595, 32603, 32611, 32618, 32625, 32632,
323 32639, 32645, 32651, 32657, 32662, 32667, 32672, 32677,
325 32682, 32686, 32690, 32694, 32698, 32702, 32705, 32708,
326 32711, 32714, 32717, 32720, 32722, 32725, 32727, 32729,
327 32731, 32733, 32735, 32737, 32739, 32740, 32742, 32743,
328 32745, 32746, 32747, 32748, 32749, 32750, 32751, 32752,
329 32753, 32754, 32755, 32756, 32757, 32757, 32758, 32758,
330 32759, 32760, 32760, 32761, 32761, 32761, 32762, 32762,
331 32763, 32763, 32763, 32764, 32764, 32764, 32764, 32765,
332 32765, 32765, 32765, 32766, 32766, 32766, 32766, 32767,
338 * Generate a random integer number of NORMAL distribution
340 * The table above is used to generate a pseudo-normal distribution,
341 * in a manner which is much faster than calling a transcendental
342 * function to calculate a true normal distribution.
344 * Basically, entry 64*N in the table above represents the number of
345 * times out of 32767 that a random variable with normal distribution
346 * will fall within N standard deviations of the mean. That is, about
347 * 68 percent of the time for N=1 and 95 percent of the time for N=2.
349 * The table above contains a "faked" final entry which allows us to
350 * pretend that all values in a normal distribution are strictly less
351 * than four standard deviations away from the mean. This results in
352 * "conservative" distribution of approximately 1/32768 values.
354 * Note that the binary search takes up to 16 quick iterations.
356 s16b randnor(int mean, int stand)
362 s16b high = RANDNOR_NUM;
365 if (stand < 1) return (s16b)(mean);
367 /* Roll for probability */
368 tmp = (s16b)randint0(32768);
373 int mid = (low + high) >> 1;
375 /* Move right if forced */
376 if (randnor_table[mid] < tmp)
381 /* Move left otherwise */
388 /* Convert the index into an offset */
389 offset = (long)stand * (long)low / RANDNOR_STD;
391 /* One half should be negative */
392 if (randint0(100) < 50) return (mean - offset);
394 /* One half should be positive */
395 return (mean + offset);
401 * Generates damage for "2d6" style dice rolls
403 s16b damroll(int num, int sides)
406 for (i = 0; i < num; i++) sum += randint1(sides);
412 * Same as above, but always maximal
414 s16b maxroll(int num, int sides)
416 return (num * sides);
421 * Given a numerator and a denominator, supply a properly rounded result,
422 * using the RNG to smooth out remainders. -LM-
424 s32b div_round(s32b n, s32b d)
428 /* Refuse to divide by zero */
435 if ((ABS(n) % ABS(d)) > randint0(ABS(d)))
437 /* Increase the absolute value */
438 if (n * d > 0L) tmp += 1L;
450 * Extract a "random" number from 0 to m-1, using the RNG.
452 * This function should be used when generating random numbers in
453 * "external" program parts like the main-*.c files. It preserves
454 * the current RNG state to prevent influences on game-play.
456 * Could also use rand() from <stdlib.h> directly. XXX XXX XXX
458 s32b Rand_external(s32b m)
460 static bool initialized = FALSE;
461 static u32b Rand_state_external[4];
465 /* Initialize with new seed */
466 u32b seed = (u32b)time(NULL);
467 Rand_Xorshift_seed(seed, Rand_state_external);
471 return Rand_div_impl(m, Rand_state_external);