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DEFINITIONS
This source file includes following definitions.
- Scm_MTInitByUI
- Scm_MTInitByArray
- Scm_MTGenrandU32
- Scm_MTGenrandF32
- Scm_MTGenrandF64
- xlog2
- genrand_int_small
- Scm_MTGenrandInt
- mt_allocate
- Scm_Init_mt_random
1 /*
2 * mt-random.c - implements MT19937 random number generation algorithm
3 *
4 * Mersenne Twister algorithm invented by Makoto Matsumoto & Takuji Nishimura.
5 * http://www.math.keio.ac.jp/~matumoto/emt.html
6 * This code is based on mt18837ar.c (2002/1/16). It is released under
7 * BSD license.
8 * I modified the code in the following parts.
9 * - make it modular, esp., all the state information is kept in
10 * the allocated memory for random number generator object.
11 * - changed the names of the functions
12 * - added stuff to make it as a Gauche extension module.
13 * $Id: mt-random.c,v 1.16 2005/09/10 09:39:12 shirok Exp $
14 *
15 * The original copyright notice follows.
16 */
17 /*
18 A C-program for MT19937, with initialization improved 2002/1/26.
19 Coded by Takuji Nishimura and Makoto Matsumoto.
20
21 Before using, initialize the state by using init_genrand(seed)
22 or init_by_array(init_key, key_length).
23
24 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
25 All rights reserved.
26
27 Redistribution and use in source and binary forms, with or without
28 modification, are permitted provided that the following conditions
29 are met:
30
31 1. Redistributions of source code must retain the above copyright
32 notice, this list of conditions and the following disclaimer.
33
34 2. Redistributions in binary form must reproduce the above copyright
35 notice, this list of conditions and the following disclaimer in the
36 documentation and/or other materials provided with the distribution.
37
38 3. The names of its contributors may not be used to endorse or promote
39 products derived from this software without specific prior written
40 permission.
41
42 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
43 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
44 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
45 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
46 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
47 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
48 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
49 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
50 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
51 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
52 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
53
54
55 Any feedback is very welcome.
56 http://www.math.keio.ac.jp/matumoto/emt.html
57 email: matumoto@math.keio.ac.jp
58 */
59
60 #include "mt-random.h"
61 #include <math.h>
62
63 /* Period parameters */
64 #define M 397
65 #define MATRIX_A 0x9908b0dfUL /* constant vector a */
66 #define UPPER_MASK 0x80000000UL /* most significant w-r bits */
67 #define LOWER_MASK 0x7fffffffUL /* least significant r bits */
68
69 /* initializes mt[N] with a seed */
70 void Scm_MTInitByUI(ScmMersenneTwister *mt, unsigned long s)
71 {
72 int mti;
73 mt->mt[0]= s & 0xffffffffUL;
74 for (mti=1; mti<N; mti++) {
75 mt->mt[mti] =
76 (1812433253UL * (mt->mt[mti-1] ^ (mt->mt[mti-1] >> 30)) + mti);
77 /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
78 /* In the previous versions, MSBs of the seed affect */
79 /* only MSBs of the array mt[]. */
80 /* 2002/01/09 modified by Makoto Matsumoto */
81 mt->mt[mti] &= 0xffffffffUL;
82 /* for >32 bit machines */
83 }
84 mt->mti = mti;
85 }
86
87 /* initialize by an array with array-length */
88 /* init_key is the array for initializing keys */
89 /* key_length is its length */
90 void Scm_MTInitByArray(ScmMersenneTwister *mt,
91 ScmInt32 init_key[],
92 unsigned long key_length)
93 {
94 int i, j, k;
95 Scm_MTInitByUI(mt, 19650218UL);
96 i=1; j=0;
97 k = (N>key_length ? N : key_length);
98 for (; k; k--) {
99 mt->mt[i] = (mt->mt[i] ^ ((mt->mt[i-1] ^ (mt->mt[i-1] >> 30)) * 1664525UL))
100 + init_key[j] + j; /* non linear */
101 mt->mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
102 i++; j++;
103 if (i>=N) { mt->mt[0] = mt->mt[N-1]; i=1; }
104 if (j>=key_length) j=0;
105 }
106 for (k=N-1; k; k--) {
107 mt->mt[i] = (mt->mt[i] ^ ((mt->mt[i-1] ^ (mt->mt[i-1] >> 30)) * 1566083941UL))
108 - i; /* non linear */
109 mt->mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
110 i++;
111 if (i>=N) { mt->mt[0] = mt->mt[N-1]; i=1; }
112 }
113
114 mt->mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */
115 }
116
117 /* generates a random number on [0,0xffffffff]-interval */
118 inline unsigned long Scm_MTGenrandU32(ScmMersenneTwister *mt)
119 {
120 unsigned long y;
121 int mti = mt->mti;
122 static unsigned long mag01[2]={0x0UL, MATRIX_A};
123 /* mag01[x] = x * MATRIX_A for x=0,1 */
124
125 if (mti >= N) { /* generate N words at one time */
126 int kk;
127
128 if (mti == N+1) /* if Scm_MTInitByUI() has not been called, */
129 Scm_MTInitByUI(mt, 5489UL); /* a default initial seed is used */
130
131 for (kk=0;kk<N-M;kk++) {
132 y = (mt->mt[kk]&UPPER_MASK)|(mt->mt[kk+1]&LOWER_MASK);
133 mt->mt[kk] = mt->mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
134 }
135 for (;kk<N-1;kk++) {
136 y = (mt->mt[kk]&UPPER_MASK)|(mt->mt[kk+1]&LOWER_MASK);
137 mt->mt[kk] = mt->mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
138 }
139 y = (mt->mt[N-1]&UPPER_MASK)|(mt->mt[0]&LOWER_MASK);
140 mt->mt[N-1] = mt->mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];
141
142 mti = 0;
143 }
144
145 y = mt->mt[mti++];
146
147 /* Tempering */
148 y ^= (y >> 11);
149 y ^= (y << 7) & 0x9d2c5680UL;
150 y ^= (y << 15) & 0xefc60000UL;
151 y ^= (y >> 18);
152
153 mt->mti = mti;
154 return y;
155 }
156
157 /* generates a random number on (0,1) or [0,1) -real-interval */
158 float Scm_MTGenrandF32(ScmMersenneTwister *mt, int exclude0)
159 {
160 float r;
161 do {
162 r = (float)(Scm_MTGenrandU32(mt)*(1.0/4294967296.0));
163 /* divided by 2^32 */
164 } while (exclude0 && r == 0.0); /*if we get 0.0, try another one. */;
165 return r;
166 }
167
168 /* generates a random number on (0,1) or [0,1) with 53-bit resolution*/
169 double Scm_MTGenrandF64(ScmMersenneTwister *mt, int exclude0)
170 {
171 double r;
172 unsigned long a, b;
173 do {
174 a = Scm_MTGenrandU32(mt)>>5;
175 b = Scm_MTGenrandU32(mt)>>6;
176 r = (a*67108864.0+b)*(1.0/9007199254740992.0);
177 } while (exclude0 && r == 0.0); /*if we get 0.0, try another one. */;
178 return r;
179 }
180
181 /*
182 * Generic integer routine for [0, n-1], 0 < n <= 2^32
183 */
184
185 /* if integer N is 2^e, returns e; otherwise, returns -1. */
186 static inline int xlog2(unsigned long n)
187 {
188 #if SIZEOF_LONG == 4
189 # define START_BIT 16
190 # define MAX_BIT 31
191 #else /* assume sizeof(long) == 8 */
192 # define START_BIT 32
193 # define MAX_BIT 63
194 #endif
195 int e = START_BIT;
196 unsigned long m = (1UL<<START_BIT);
197
198 if (n < m) {
199 do {
200 m >>= 1;
201 e--;
202 if (n == m) return e;
203 } while (e >= 0 && n < m);
204 } else if (n > m) {
205 do {
206 m <<= 1;
207 e++;
208 if (n == m) return e;
209 } while (e < MAX_BIT && n > m);
210 } else { /* n == m */
211 return e;
212 }
213 return -1;
214 #undef START_BIT
215 #undef MAX_BIT
216 }
217
218
219 /* generates a random number on [0,n-1], n < 2^32. */
220 static ScmObj genrand_int_small(ScmMersenneTwister *mt, unsigned long n)
221 {
222 int e;
223 unsigned long r;
224 if ((e = xlog2(n)) == 0) {
225 return SCM_MAKE_INT(0);
226 } else if (e > 0) {
227 /* optimize for 2^e case */
228 r = Scm_MTGenrandU32(mt);
229 if (e == 32) return Scm_MakeIntegerFromUI(r);
230 else return Scm_MakeIntegerFromUI(r >> (32-e));
231 } else {
232 double q = floor((double)0xffffffff / (double)n);
233 double qn = q * n;
234 do {
235 r = Scm_MTGenrandU32(mt);
236 } while (r >= qn);
237 return Scm_MakeIntegerFromUI((unsigned long)(r/q));
238 }
239 }
240
241 ScmObj Scm_MTGenrandInt(ScmMersenneTwister *mt, ScmObj n)
242 {
243 if (SCM_INTP(n)) {
244 long m = SCM_INT_VALUE(n);
245 if (m <= 0) goto err;
246 return genrand_int_small(mt, m);
247 }
248 #if SIZEOF_LONG == 4
249 if (SCM_BIGNUMP(n)) {
250 if (SCM_BIGNUM_SIGN(n) <= 0) goto err;
251 if (SCM_BIGNUM_SIZE(n) == 1) {
252 return genrand_int_small(mt, SCM_BIGNUM(n)->values[0]);
253 }
254 if (SCM_BIGNUM_SIZE(n) == 2
255 && SCM_BIGNUM(n)->values[0] == 0
256 && SCM_BIGNUM(n)->values[1] == 1) {
257 return Scm_MakeIntegerFromUI(Scm_MTGenrandU32(mt));
258 }
259 }
260 #endif
261 err:
262 Scm_Error("bad type of argument for n: positive integer up to 2^32 is required, but got %S", n);
263 return SCM_UNDEFINED; /*dummy*/
264 }
265
266 /*
267 * Gauche specific stuff
268 */
269 static ScmObj key_seed;
270 static ScmObj mt_allocate(ScmClass *klass, ScmObj initargs);
271 SCM_DEFINE_BUILTIN_CLASS(Scm_MersenneTwisterClass,
272 NULL, NULL, NULL, mt_allocate,
273 NULL);
274
275 static ScmObj mt_allocate(ScmClass *klass, ScmObj initargs)
276 {
277 ScmObj seed = Scm_GetKeyword(key_seed, initargs, SCM_FALSE);
278 ScmMersenneTwister *mt;
279
280 if (!SCM_FALSEP(seed) && !SCM_EXACTP(seed) && !SCM_U32VECTORP(seed)) {
281 Scm_Error("seed needs to be an exact integer or a u32vector, but got: %S", seed);
282 }
283
284 mt = SCM_NEW(ScmMersenneTwister);
285 SCM_SET_CLASS(mt, &Scm_MersenneTwisterClass);
286 mt->mti = N+1;
287 if (SCM_EXACTP(seed)) {
288 Scm_MTInitByUI(mt, Scm_GetUInteger(seed));
289 } else if (SCM_U32VECTORP(seed)) {
290 Scm_MTInitByArray(mt, (ScmInt32*)SCM_U32VECTOR_ELEMENTS(seed),
291 SCM_U32VECTOR_SIZE(seed));
292 }
293 return SCM_OBJ(mt);
294 }
295
296 extern void Scm_Init_mt_lib(ScmModule*);
297
298 void Scm_Init_mt_random(void)
299 {
300 ScmModule *mod = SCM_FIND_MODULE("math.mt-random", SCM_FIND_MODULE_CREATE);
301 SCM_INIT_EXTENSION(mtrandom);
302 Scm_InitStaticClass(&Scm_MersenneTwisterClass, "<mersenne-twister>",
303 mod, NULL, 0);
304 key_seed = SCM_MAKE_KEYWORD("seed");
305 Scm_Init_mt_lib(mod);
306 }
307