2 A C-program for MT19937, with initialization improved 2002/1/26.
3 Coded by Takuji Nishimura and Makoto Matsumoto.
5 Before using, initialize the state by using init_genrand(seed)
6 or init_by_array(init_key, key_length).
8 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
11 Modified 2007 by Steven G. Johnson for use with NLopt (to avoid
12 namespace pollution, use uint32_t instead of unsigned long,
13 and add the urand function). Modified 2009 to add normal-distributed
16 Redistribution and use in source and binary forms, with or without
17 modification, are permitted provided that the following conditions
20 1. Redistributions of source code must retain the above copyright
21 notice, this list of conditions and the following disclaimer.
23 2. Redistributions in binary form must reproduce the above copyright
24 notice, this list of conditions and the following disclaimer in the
25 documentation and/or other materials provided with the distribution.
27 3. The names of its contributors may not be used to endorse or promote
28 products derived from this software without specific prior written
31 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
32 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
33 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
34 FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
35 COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
36 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
37 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
38 SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
39 HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
40 STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
41 ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
42 OF THE POSSIBILITY OF SUCH DAMAGE.
45 Any feedback is very welcome.
46 http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
47 email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
50 #include "nlopt-util.h"
52 #if defined(HAVE_STDINT_H)
57 # if SIZEOF_UNSIGNED_LONG == 4
58 typedef unsigned long uint32_t;
59 # elif SIZEOF_UNSIGNED_INT == 4
60 typedef unsigned int uint32_t;
62 # error No 32-bit unsigned integer type
66 /* Period parameters */
69 #define MATRIX_A 0x9908b0dfUL /* constant vector a */
70 #define UPPER_MASK 0x80000000UL /* most significant w-r bits */
71 #define LOWER_MASK 0x7fffffffUL /* least significant r bits */
73 /* SGJ 2010: make RNG thread-safe by declaring the RNG state as thread-local
74 storage, at least for GCC, MSVC, and Intel C++ */
76 static THREADLOCAL uint32_t mt[N]; /* the array for the state vector */
77 static THREADLOCAL int mti=N+1; /* mti==N+1 means mt[N] is not initialized */
79 /* initializes mt[N] with a seed */
80 void nlopt_init_genrand(unsigned long s)
82 mt[0]= s & 0xffffffffUL;
83 for (mti=1; mti<N; mti++) {
85 (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
86 /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
87 /* In the previous versions, MSBs of the seed affect */
88 /* only MSBs of the array mt[]. */
89 /* 2002/01/09 modified by Makoto Matsumoto */
90 mt[mti] &= 0xffffffffUL;
91 /* for >32 bit machines */
95 /* generates a random number on [0,0xffffffff]-interval */
96 static uint32_t nlopt_genrand_int32(void)
99 static uint32_t mag01[2]={0x0UL, MATRIX_A};
100 /* mag01[x] = x * MATRIX_A for x=0,1 */
102 if (mti >= N) { /* generate N words at one time */
105 if (mti == N+1) /* if init_genrand() has not been called, */
106 nlopt_init_genrand(5489UL); /* a default initial seed is used */
108 for (kk=0;kk<N-M;kk++) {
109 y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
110 mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
113 y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
114 mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
116 y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
117 mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];
126 y ^= (y << 7) & 0x9d2c5680UL;
127 y ^= (y << 15) & 0xefc60000UL;
133 #if 0 /* not used in NLopt */
135 /* initialize by an array with array-length */
136 /* init_key is the array for initializing keys */
137 /* key_length is its length */
138 /* slight change for C++, 2004/2/26 */
139 static void nlopt_init_by_array(uint32_t init_key[], int key_length)
142 nlopt_init_genrand(19650218UL);
144 k = (N>key_length ? N : key_length);
146 mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
147 + init_key[j] + j; /* non linear */
148 mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
150 if (i>=N) { mt[0] = mt[N-1]; i=1; }
151 if (j>=key_length) j=0;
153 for (k=N-1; k; k--) {
154 mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
155 - i; /* non linear */
156 mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
158 if (i>=N) { mt[0] = mt[N-1]; i=1; }
161 mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */
164 /* generates a random number on [0,0x7fffffff]-interval */
165 static long nlopt_genrand_int31(void)
167 return (long)(nlopt_genrand_int32()>>1);
170 /* generates a random number on [0,1]-real-interval */
171 static double nlopt_genrand_real1(void)
173 return nlopt_genrand_int32()*(1.0/4294967295.0);
174 /* divided by 2^32-1 */
177 /* generates a random number on [0,1)-real-interval */
178 static double nlopt_genrand_real2(void)
180 return nlopt_genrand_int32()*(1.0/4294967296.0);
181 /* divided by 2^32 */
184 /* generates a random number on (0,1)-real-interval */
185 static double nlopt_genrand_real3(void)
187 return (((double)nlopt_genrand_int32()) + 0.5)*(1.0/4294967296.0);
188 /* divided by 2^32 */
193 /* generates a random number on [0,1) with 53-bit resolution*/
194 static double nlopt_genrand_res53(void)
196 uint32_t a=nlopt_genrand_int32()>>5, b=nlopt_genrand_int32()>>6;
197 return(a*67108864.0+b)*(1.0/9007199254740992.0);
199 /* These real versions are due to Isaku Wada, 2002/01/09 added */
201 /* generate uniform random number in [a,b) with 53-bit resolution,
203 double nlopt_urand(double a, double b)
205 return(a + (b - a) * nlopt_genrand_res53());
208 /* generate a uniform random number in [0,n), added by SGJ */
209 int nlopt_iurand(int n)
211 return(nlopt_genrand_int32() % n);
214 /* normal-distributed random numbers with the given mean and std. deviation,
216 double nlopt_nrand(double mean, double stddev)
218 // Box-Muller algorithm to generate Gaussian from uniform
219 // see Knuth vol II algorithm P, sec. 3.4.1
222 v1 = nlopt_urand(-1, 1);
223 v2 = nlopt_urand(-1, 1);
230 return mean + v1 * sqrt(-2 * log(s) / s) * stddev;
239 uint32_t init[4]={0x123, 0x234, 0x345, 0x456}, length=4;
240 init_by_array(init, length);
241 printf("1000 outputs of nlopt_genrand_int32()\n");
242 for (i=0; i<1000; i++) {
243 printf("%10lu ", nlopt_genrand_int32());
244 if (i%5==4) printf("\n");
246 printf("\n1000 outputs of genrand_real2()\n");
247 for (i=0; i<1000; i++) {
248 printf("%10.8f ", genrand_real2());
249 if (i%5==4) printf("\n");