WFMath
1.0.1
|
00001 // MersenneTwister.h 00002 // Mersenne Twister random number generator -- a C++ class MTRand 00003 // Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus 00004 // Richard J. Wagner v1.0 15 May 2003 rjwagner@writeme.com 00005 00006 // The Mersenne Twister is an algorithm for generating random numbers. It 00007 // was designed with consideration of the flaws in various other generators. 00008 // The period, 2^19937-1, and the order of equidistribution, 623 dimensions, 00009 // are far greater. The generator is also fast; it avoids multiplication and 00010 // division, and it benefits from caches and pipelines. For more information 00011 // see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html 00012 00013 // Reference 00014 // M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally 00015 // Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on 00016 // Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30. 00017 00018 // Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, 00019 // Copyright (C) 2000 - 2003, Richard J. Wagner 00020 // All rights reserved. 00021 // 00022 // Redistribution and use in source and binary forms, with or without 00023 // modification, are permitted provided that the following conditions 00024 // are met: 00025 // 00026 // 1. Redistributions of source code must retain the above copyright 00027 // notice, this list of conditions and the following disclaimer. 00028 // 00029 // 2. Redistributions in binary form must reproduce the above copyright 00030 // notice, this list of conditions and the following disclaimer in the 00031 // documentation and/or other materials provided with the distribution. 00032 // 00033 // 3. The names of its contributors may not be used to endorse or promote 00034 // products derived from this software without specific prior written 00035 // permission. 00036 // 00037 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 00038 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 00039 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 00040 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR 00041 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 00042 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 00043 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 00044 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 00045 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 00046 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 00047 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 00048 00049 // The original code included the following notice: 00050 // 00051 // When you use this, send an email to: matumoto@math.keio.ac.jp 00052 // with an appropriate reference to your work. 00053 // 00054 // It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu 00055 // when you write. 00056 00057 // changed the #ifndef for wfmath in case someone uses both the lib 00058 // and the identical header separately 00059 00060 #ifndef MERSENNETWISTER_WFMATH_H 00061 #define MERSENNETWISTER_WFMATH_H 00062 00063 // Not thread safe (unless auto-initialization is avoided and each thread has 00064 // its own MTRand object) 00065 00066 #include <iosfwd> 00067 #include <climits> 00068 #include <cmath> 00069 00070 // namespace safety for inclusion in the lib 00071 00072 namespace WFMath { 00073 00074 class MTRand { 00075 // Data 00076 public: 00077 typedef unsigned long uint32; // unsigned integer type, at least 32 bits 00078 00079 static const uint32 N = 624; // length of state vector 00080 static const uint32 SAVE = N + 1; // length of array for save() 00081 00082 protected: 00083 static const uint32 M = 397; // period parameter 00084 00085 uint32 state[N]; // internal state 00086 uint32 *pNext; // next value to get from state 00087 int left; // number of values left before reload needed 00088 00089 00090 //Methods 00091 public: 00092 MTRand( const uint32& oneSeed ); // initialize with a simple uint32 00093 MTRand( uint32 *const bigSeed, uint32 const seedLength = N ); // or an array 00094 MTRand(); // auto-initialize with /dev/urandom or time() and clock() 00095 00096 // Do NOT use for CRYPTOGRAPHY without securely hashing several returned 00097 // values together, otherwise the generator state can be learned after 00098 // reading 624 consecutive values. 00099 00100 // Access to 32-bit random numbers 00101 template<typename FloatT> 00102 FloatT rand(); // real number in [0,1] 00103 float randf(); // real number in [0,1] 00104 float randf( const float& n ); // real number in [0,n] 00105 double rand(); // real number in [0,1] 00106 double rand( const double& n ); // real number in [0,n] 00107 double randExc(); // real number in [0,1) 00108 double randExc( const double& n ); // real number in [0,n) 00109 double randDblExc(); // real number in (0,1) 00110 double randDblExc( const double& n ); // real number in (0,n) 00111 uint32 randInt(); // integer in [0,2^32-1] 00112 uint32 randInt( const uint32& n ); // integer in [0,n] for n < 2^32 00113 double operator()() { return rand(); } // same as rand() 00114 00115 // Access to 53-bit random numbers (capacity of IEEE double precision) 00116 double rand53(); // real number in [0,1) 00117 00118 // Access to nonuniform random number distributions 00119 double randNorm( const double& mean = 0.0, const double& variance = 0.0 ); 00120 00121 // Re-seeding functions with same behavior as initializers 00122 void seed( const uint32 oneSeed ); 00123 void seed( uint32 *const bigSeed, const uint32 seedLength = N ); 00124 void seed(); 00125 00126 // Saving and loading generator state 00127 void save( uint32* saveArray ) const; // to array of size SAVE 00128 void load( uint32 *const loadArray ); // from such array 00129 friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand ); 00130 friend std::istream& operator>>( std::istream& is, MTRand& mtrand ); 00131 00132 static MTRand instance; 00133 00134 protected: 00135 void initialize( const uint32 oneSeed ); 00136 void reload(); 00137 uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; } 00138 uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; } 00139 uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; } 00140 uint32 mixBits( const uint32& u, const uint32& v ) const 00141 { return hiBit(u) | loBits(v); } 00142 uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const 00143 { return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); } 00144 }; 00145 00146 00147 inline MTRand::MTRand( const uint32& oneSeed ) : pNext(0), left(0) 00148 { seed(oneSeed); } 00149 00150 inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength ) : pNext(0), left(0) 00151 { seed(bigSeed,seedLength); } 00152 00153 inline MTRand::MTRand() : pNext(0), left(0) 00154 { seed(); } 00155 00156 template<> 00157 inline float MTRand::rand<float>() 00158 { return float(randInt()) * (1.0f/4294967295.0f); } 00159 00160 template<> 00161 inline double MTRand::rand<double>() 00162 { return double(randInt()) * (1.0/4294967295.0); } 00163 00164 inline float MTRand::randf() 00165 { return float(randInt()) * (1.0f/4294967295.0f); } 00166 00167 inline float MTRand::randf( const float& n ) 00168 { return randf() * n; } 00169 00170 inline double MTRand::rand() 00171 { return double(randInt()) * (1.0/4294967295.0); } 00172 00173 inline double MTRand::rand( const double& n ) 00174 { return rand() * n; } 00175 00176 inline double MTRand::randExc() 00177 { return double(randInt()) * (1.0/4294967296.0); } 00178 00179 inline double MTRand::randExc( const double& n ) 00180 { return randExc() * n; } 00181 00182 inline double MTRand::randDblExc() 00183 { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); } 00184 00185 inline double MTRand::randDblExc( const double& n ) 00186 { return randDblExc() * n; } 00187 00188 inline double MTRand::rand53() 00189 { 00190 uint32 a = randInt() >> 5, b = randInt() >> 6; 00191 return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0); // by Isaku Wada 00192 } 00193 00194 inline double MTRand::randNorm( const double& mean, const double& variance ) 00195 { 00196 // Return a real number from a normal (Gaussian) distribution with given 00197 // mean and variance by Box-Muller method 00198 double r = std::sqrt( -2.0 * std::log( 1.0-randDblExc()) ) * variance; 00199 double phi = 2.0 * 3.14159265358979323846264338328 * randExc(); 00200 return mean + r * std::cos(phi); 00201 } 00202 00203 inline MTRand::uint32 MTRand::randInt() 00204 { 00205 // Pull a 32-bit integer from the generator state 00206 // Every other access function simply transforms the numbers extracted here 00207 00208 if( left == 0 ) reload(); 00209 --left; 00210 00211 register uint32 s1; 00212 s1 = *pNext++; 00213 s1 ^= (s1 >> 11); 00214 s1 ^= (s1 << 7) & 0x9d2c5680UL; 00215 s1 ^= (s1 << 15) & 0xefc60000UL; 00216 return ( s1 ^ (s1 >> 18) ); 00217 } 00218 00219 inline MTRand::uint32 MTRand::randInt( const uint32& n ) 00220 { 00221 // Find which bits are used in n 00222 // Optimized by Magnus Jonsson (magnus@smartelectronix.com) 00223 uint32 used = n; 00224 used |= used >> 1; 00225 used |= used >> 2; 00226 used |= used >> 4; 00227 used |= used >> 8; 00228 used |= used >> 16; 00229 00230 // Draw numbers until one is found in [0,n] 00231 uint32 i; 00232 do 00233 i = randInt() & used; // toss unused bits to shorten search 00234 while( i > n ); 00235 return i; 00236 } 00237 00238 00239 inline void MTRand::seed( const uint32 oneSeed ) 00240 { 00241 // Seed the generator with a simple uint32 00242 initialize(oneSeed); 00243 reload(); 00244 } 00245 00246 00247 inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength ) 00248 { 00249 // Seed the generator with an array of uint32's 00250 // There are 2^19937-1 possible initial states. This function allows 00251 // all of those to be accessed by providing at least 19937 bits (with a 00252 // default seed length of N = 624 uint32's). Any bits above the lower 32 00253 // in each element are discarded. 00254 // Just call seed() if you want to get array from /dev/urandom 00255 initialize(19650218UL); 00256 register unsigned i = 1; 00257 register uint32 j = 0; 00258 register unsigned k = ( N > seedLength ? N : seedLength ); 00259 for( ; k; --k ) 00260 { 00261 state[i] = 00262 state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL ); 00263 state[i] += ( bigSeed[j] & 0xffffffffUL ) + j; 00264 state[i] &= 0xffffffffUL; 00265 ++i; ++j; 00266 if( i >= N ) { state[0] = state[N-1]; i = 1; } 00267 if( j >= seedLength ) j = 0; 00268 } 00269 for( k = N - 1; k; --k ) 00270 { 00271 state[i] = 00272 state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL ); 00273 state[i] -= i; 00274 state[i] &= 0xffffffffUL; 00275 ++i; 00276 if( i >= N ) { state[0] = state[N-1]; i = 1; } 00277 } 00278 state[0] = 0x80000000UL; // MSB is 1, assuring non-zero initial array 00279 reload(); 00280 } 00281 00282 00283 inline void MTRand::initialize( const uint32 seed ) 00284 { 00285 // Initialize generator state with seed 00286 // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier. 00287 // In previous versions, most significant bits (MSBs) of the seed affect 00288 // only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto. 00289 register uint32 *s = state; 00290 register uint32 *r = state; 00291 register unsigned i = 1; 00292 *s++ = seed & 0xffffffffUL; 00293 for( ; i < N; ++i ) 00294 { 00295 *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL; 00296 r++; 00297 } 00298 } 00299 00300 00301 inline void MTRand::reload() 00302 { 00303 // Generate N new values in state 00304 // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com) 00305 register uint32 *p = state; 00306 register int i; 00307 for( i = N - M; i--; ++p ) 00308 *p = twist( p[M], p[0], p[1] ); 00309 for( i = M; --i; ++p ) 00310 *p = twist( p[M-N], p[0], p[1] ); 00311 *p = twist( p[M-N], p[0], state[0] ); 00312 00313 left = N, pNext = state; 00314 } 00315 00316 00317 00318 inline void MTRand::save( uint32* saveArray ) const 00319 { 00320 register uint32 *sa = saveArray; 00321 register const uint32 *s = state; 00322 register int i = N; 00323 for( ; i--; *sa++ = *s++ ) {} 00324 *sa = left; 00325 } 00326 00327 00328 inline void MTRand::load( uint32 *const loadArray ) 00329 { 00330 register uint32 *s = state; 00331 register uint32 *la = loadArray; 00332 register int i = N; 00333 for( ; i--; *s++ = *la++ ) {} 00334 left = *la; 00335 pNext = &state[N-left]; 00336 } 00337 00338 00339 } // namespace 00340 00341 #endif // MERSENNETWISTER_H 00342 00343 // Change log: 00344 // 00345 // v0.1 - First release on 15 May 2000 00346 // - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus 00347 // - Translated from C to C++ 00348 // - Made completely ANSI compliant 00349 // - Designed convenient interface for initialization, seeding, and 00350 // obtaining numbers in default or user-defined ranges 00351 // - Added automatic seeding from /dev/urandom or time() and clock() 00352 // - Provided functions for saving and loading generator state 00353 // 00354 // v0.2 - Fixed bug which reloaded generator one step too late 00355 // 00356 // v0.3 - Switched to clearer, faster reload() code from Matthew Bellew 00357 // 00358 // v0.4 - Removed trailing newline in saved generator format to be consistent 00359 // with output format of built-in types 00360 // 00361 // v0.5 - Improved portability by replacing static const int's with enum's and 00362 // clarifying return values in seed(); suggested by Eric Heimburg 00363 // - Removed MAXINT constant; use 0xffffffffUL instead 00364 // 00365 // v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits 00366 // - Changed integer [0,n] generator to give better uniformity 00367 // 00368 // v0.7 - Fixed operator precedence ambiguity in reload() 00369 // - Added access for real numbers in (0,1) and (0,n) 00370 // 00371 // v0.8 - Included time.h header to properly support time_t and clock_t 00372 // 00373 // v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto 00374 // - Allowed for seeding with arrays of any length 00375 // - Added access for real numbers in [0,1) with 53-bit resolution 00376 // - Added access for real numbers from normal (Gaussian) distributions 00377 // - Increased overall speed by optimizing twist() 00378 // - Doubled speed of integer [0,n] generation 00379 // - Fixed out-of-range number generation on 64-bit machines 00380 // - Improved portability by substituting literal constants for long enum's 00381 // - Changed license from GNU LGPL to BSD