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- */
20 * Angband 2.7.9 introduced a new (optimized) random number generator,
21 * based loosely on the old "random.c" from Berkeley but with some major
22 * optimizations and algorithm changes. See below for more details.
24 * Code by myself (benh@phial.com) and Randy (randy@stat.tamu.edu).
26 * This code provides (1) a "decent" RNG, based on the "BSD-degree-63-RNG"
27 * used in Angband 2.7.8, but rather optimized, and (2) a "simple" RNG,
28 * based on the simple "LCRNG" currently used in Angband, but "corrected"
29 * to give slightly better values. Both of these are available in two
30 * flavors, first, the simple "mod" flavor, which is fast, but slightly
31 * biased at high values, and second, the simple "div" flavor, which is
32 * less fast (and potentially non-terminating) but which is not biased
33 * and is much less subject to low-bit-non-randomness problems.
35 * You can select your favorite flavor by proper definition of the
36 * "randint0()" macro in the "defines.h" file.
38 * Note that, in Angband 2.8.0, the "state" table will be saved in the
39 * savefile, so a special "initialization" phase will be necessary.
41 * Note the use of the "simple" RNG, first you activate it via
42 * "Rand_quick = TRUE" and "Rand_value = seed" and then it is used
43 * automatically used instead of the "complex" RNG, and when you are
44 * done, you de-activate it via "Rand_quick = FALSE" or choose a new
45 * seed via "Rand_value = seed".
48 * RNG algorithm was fully rewritten. Upper comment is OLD.
58 * Current "state" table for the RNG
59 * Only index 0 to 3 are used
61 u32b Rand_state[RAND_DEG] = {
70 * Initialize Xorshift Algorithm state
72 static void Rand_Xorshift_init(u32b seed, u32b* state)
76 /* Initialize Xorshift Algorithm RNG */
77 for (i = 1; i <= 4; ++ i) {
78 seed = 1812433253UL * (seed ^ (seed >> 30)) + i;
86 static u32b Rand_Xorshift(u32b* state)
88 u32b t = state[0] ^ (state[0] << 11);
94 state[3] = (state[3] ^ (state[3] >> 19)) ^ (t ^ (t >> 8));
99 static const u32b Rand_Xorshift_max = 0xFFFFFFFF;
102 * Initialize the RNG using a new seed
104 void Rand_state_init(u32b seed)
106 Rand_Xorshift_init(seed, Rand_state);
110 * Backup the RNG state
112 void Rand_state_backup(u32b* backup_state)
116 for (i = 0; i < 4; ++ i) {
117 backup_state[i] = Rand_state[i];
122 * Restore the RNG state
124 void Rand_state_restore(u32b* backup_state)
128 for (i = 0; i < 4; ++ i) {
129 Rand_state[i] = backup_state[i];
135 * Extract a "random" number from 0 to m-1, via "division"
137 static s32b Rand_div_impl(s32b m, u32b* state)
143 /* Hack -- simple case */
144 if (m <= 1) return (0);
146 scaling = Rand_Xorshift_max / m;
150 ret = Rand_Xorshift(state);
151 } while (ret >= past);
153 return ret / scaling;
156 s32b Rand_div(s32b m)
158 return Rand_div_impl(m, Rand_state);
165 * The number of entries in the "randnor_table"
167 #define RANDNOR_NUM 256
170 * The standard deviation of the "randnor_table"
172 #define RANDNOR_STD 64
175 * The normal distribution table for the "randnor()" function (below)
177 static s16b randnor_table[RANDNOR_NUM] =
179 206, 613, 1022, 1430, 1838, 2245, 2652, 3058,
180 3463, 3867, 4271, 4673, 5075, 5475, 5874, 6271,
181 6667, 7061, 7454, 7845, 8234, 8621, 9006, 9389,
182 9770, 10148, 10524, 10898, 11269, 11638, 12004, 12367,
183 12727, 13085, 13440, 13792, 14140, 14486, 14828, 15168,
184 15504, 15836, 16166, 16492, 16814, 17133, 17449, 17761,
185 18069, 18374, 18675, 18972, 19266, 19556, 19842, 20124,
186 20403, 20678, 20949, 21216, 21479, 21738, 21994, 22245,
188 22493, 22737, 22977, 23213, 23446, 23674, 23899, 24120,
189 24336, 24550, 24759, 24965, 25166, 25365, 25559, 25750,
190 25937, 26120, 26300, 26476, 26649, 26818, 26983, 27146,
191 27304, 27460, 27612, 27760, 27906, 28048, 28187, 28323,
192 28455, 28585, 28711, 28835, 28955, 29073, 29188, 29299,
193 29409, 29515, 29619, 29720, 29818, 29914, 30007, 30098,
194 30186, 30272, 30356, 30437, 30516, 30593, 30668, 30740,
195 30810, 30879, 30945, 31010, 31072, 31133, 31192, 31249,
197 31304, 31358, 31410, 31460, 31509, 31556, 31601, 31646,
198 31688, 31730, 31770, 31808, 31846, 31882, 31917, 31950,
199 31983, 32014, 32044, 32074, 32102, 32129, 32155, 32180,
200 32205, 32228, 32251, 32273, 32294, 32314, 32333, 32352,
201 32370, 32387, 32404, 32420, 32435, 32450, 32464, 32477,
202 32490, 32503, 32515, 32526, 32537, 32548, 32558, 32568,
203 32577, 32586, 32595, 32603, 32611, 32618, 32625, 32632,
204 32639, 32645, 32651, 32657, 32662, 32667, 32672, 32677,
206 32682, 32686, 32690, 32694, 32698, 32702, 32705, 32708,
207 32711, 32714, 32717, 32720, 32722, 32725, 32727, 32729,
208 32731, 32733, 32735, 32737, 32739, 32740, 32742, 32743,
209 32745, 32746, 32747, 32748, 32749, 32750, 32751, 32752,
210 32753, 32754, 32755, 32756, 32757, 32757, 32758, 32758,
211 32759, 32760, 32760, 32761, 32761, 32761, 32762, 32762,
212 32763, 32763, 32763, 32764, 32764, 32764, 32764, 32765,
213 32765, 32765, 32765, 32766, 32766, 32766, 32766, 32767,
219 * Generate a random integer number of NORMAL distribution
221 * The table above is used to generate a pseudo-normal distribution,
222 * in a manner which is much faster than calling a transcendental
223 * function to calculate a true normal distribution.
225 * Basically, entry 64*N in the table above represents the number of
226 * times out of 32767 that a random variable with normal distribution
227 * will fall within N standard deviations of the mean. That is, about
228 * 68 percent of the time for N=1 and 95 percent of the time for N=2.
230 * The table above contains a "faked" final entry which allows us to
231 * pretend that all values in a normal distribution are strictly less
232 * than four standard deviations away from the mean. This results in
233 * "conservative" distribution of approximately 1/32768 values.
235 * Note that the binary search takes up to 16 quick iterations.
237 s16b randnor(int mean, int stand)
243 s16b high = RANDNOR_NUM;
246 if (stand < 1) return (mean);
248 /* Roll for probability */
249 tmp = (s16b)randint0(32768);
254 int mid = (low + high) >> 1;
256 /* Move right if forced */
257 if (randnor_table[mid] < tmp)
262 /* Move left otherwise */
269 /* Convert the index into an offset */
270 offset = (long)stand * (long)low / RANDNOR_STD;
272 /* One half should be negative */
273 if (randint0(100) < 50) return (mean - offset);
275 /* One half should be positive */
276 return (mean + offset);
282 * Generates damage for "2d6" style dice rolls
284 s16b damroll(int num, int sides)
287 for (i = 0; i < num; i++) sum += randint1(sides);
293 * Same as above, but always maximal
295 s16b maxroll(int num, int sides)
297 return (num * sides);
302 * Given a numerator and a denominator, supply a properly rounded result,
303 * using the RNG to smooth out remainders. -LM-
305 s32b div_round(s32b n, s32b d)
309 /* Refuse to divide by zero */
316 if ((ABS(n) % ABS(d)) > randint0(ABS(d)))
318 /* Increase the absolute value */
319 if (n * d > 0L) tmp += 1L;
331 * Extract a "random" number from 0 to m-1, using the RNG.
333 * This function should be used when generating random numbers in
334 * "external" program parts like the main-*.c files. It preserves
335 * the current RNG state to prevent influences on game-play.
337 * Could also use rand() from <stdlib.h> directly. XXX XXX XXX
339 u32b Rand_external(u32b m)
341 static bool initialized = FALSE;
342 static u32b Rand_state_external[4];
346 /* Initialize with new seed */
347 u32b seed = time(NULL);
348 Rand_Xorshift_init(seed, Rand_state_external);
352 return Rand_div_impl(m, Rand_state_external);