MersenneTwister.h

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         enum { N = 624 };       // length of state vector
00080         enum { SAVE = N + 1 };  // length of array for save()
00081 
00082 protected:
00083         enum { 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         double rand();                          // real number in [0,1]
00102         double rand( const double& n );         // real number in [0,n]
00103         double randExc();                       // real number in [0,1)
00104         double randExc( const double& n );      // real number in [0,n)
00105         double randDblExc();                    // real number in (0,1)
00106         double randDblExc( const double& n );   // real number in (0,n)
00107         uint32 randInt();                       // integer in [0,2^32-1]
00108         uint32 randInt( const uint32& n );      // integer in [0,n] for n < 2^32
00109         double operator()() { return rand(); }  // same as rand()
00110         
00111         // Access to 53-bit random numbers (capacity of IEEE double precision)
00112         double rand53();  // real number in [0,1)
00113         
00114         // Access to nonuniform random number distributions
00115         double randNorm( const double& mean = 0.0, const double& variance = 0.0 );
00116         
00117         // Re-seeding functions with same behavior as initializers
00118         void seed( const uint32 oneSeed );
00119         void seed( uint32 *const bigSeed, const uint32 seedLength = N );
00120         void seed();
00121         
00122         // Saving and loading generator state
00123         void save( uint32* saveArray ) const;  // to array of size SAVE
00124         void load( uint32 *const loadArray );  // from such array
00125         friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
00126         friend std::istream& operator>>( std::istream& is, MTRand& mtrand );
00127 
00128         static MTRand instance;
00129 
00130 protected:
00131         void initialize( const uint32 oneSeed );
00132         void reload();
00133         uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
00134         uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
00135         uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
00136         uint32 mixBits( const uint32& u, const uint32& v ) const
00137                 { return hiBit(u) | loBits(v); }
00138         uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
00139                 { return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
00140 };
00141 
00142 
00143 inline MTRand::MTRand( const uint32& oneSeed )
00144         { seed(oneSeed); }
00145 
00146 inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
00147         { seed(bigSeed,seedLength); }
00148 
00149 inline MTRand::MTRand()
00150         { seed(); }
00151 
00152 inline double MTRand::rand()
00153         { return double(randInt()) * (1.0/4294967295.0); }
00154 
00155 inline double MTRand::rand( const double& n )
00156         { return rand() * n; }
00157 
00158 inline double MTRand::randExc()
00159         { return double(randInt()) * (1.0/4294967296.0); }
00160 
00161 inline double MTRand::randExc( const double& n )
00162         { return randExc() * n; }
00163 
00164 inline double MTRand::randDblExc()
00165         { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
00166 
00167 inline double MTRand::randDblExc( const double& n )
00168         { return randDblExc() * n; }
00169 
00170 inline double MTRand::rand53()
00171 {
00172         uint32 a = randInt() >> 5, b = randInt() >> 6;
00173         return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
00174 }
00175 
00176 inline double MTRand::randNorm( const double& mean, const double& variance )
00177 {
00178         // Return a real number from a normal (Gaussian) distribution with given
00179         // mean and variance by Box-Muller method
00180         double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
00181         double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
00182         return mean + r * cos(phi);
00183 }
00184 
00185 inline MTRand::uint32 MTRand::randInt()
00186 {
00187         // Pull a 32-bit integer from the generator state
00188         // Every other access function simply transforms the numbers extracted here
00189         
00190         if( left == 0 ) reload();
00191         --left;
00192                 
00193         register uint32 s1;
00194         s1 = *pNext++;
00195         s1 ^= (s1 >> 11);
00196         s1 ^= (s1 <<  7) & 0x9d2c5680UL;
00197         s1 ^= (s1 << 15) & 0xefc60000UL;
00198         return ( s1 ^ (s1 >> 18) );
00199 }
00200 
00201 inline MTRand::uint32 MTRand::randInt( const uint32& n )
00202 {
00203         // Find which bits are used in n
00204         // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
00205         uint32 used = n;
00206         used |= used >> 1;
00207         used |= used >> 2;
00208         used |= used >> 4;
00209         used |= used >> 8;
00210         used |= used >> 16;
00211         
00212         // Draw numbers until one is found in [0,n]
00213         uint32 i;
00214         do
00215                 i = randInt() & used;  // toss unused bits to shorten search
00216         while( i > n );
00217         return i;
00218 }
00219 
00220 
00221 inline void MTRand::seed( const uint32 oneSeed )
00222 {
00223         // Seed the generator with a simple uint32
00224         initialize(oneSeed);
00225         reload();
00226 }
00227 
00228 
00229 inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
00230 {
00231         // Seed the generator with an array of uint32's
00232         // There are 2^19937-1 possible initial states.  This function allows
00233         // all of those to be accessed by providing at least 19937 bits (with a
00234         // default seed length of N = 624 uint32's).  Any bits above the lower 32
00235         // in each element are discarded.
00236         // Just call seed() if you want to get array from /dev/urandom
00237         initialize(19650218UL);
00238         register int i = 1;
00239         register uint32 j = 0;
00240         register int k = ( N > seedLength ? N : seedLength );
00241         for( ; k; --k )
00242         {
00243                 state[i] =
00244                         state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
00245                 state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
00246                 state[i] &= 0xffffffffUL;
00247                 ++i;  ++j;
00248                 if( i >= N ) { state[0] = state[N-1];  i = 1; }
00249                 if( j >= seedLength ) j = 0;
00250         }
00251         for( k = N - 1; k; --k )
00252         {
00253                 state[i] =
00254                         state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
00255                 state[i] -= i;
00256                 state[i] &= 0xffffffffUL;
00257                 ++i;
00258                 if( i >= N ) { state[0] = state[N-1];  i = 1; }
00259         }
00260         state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
00261         reload();
00262 }
00263 
00264 
00265 inline void MTRand::initialize( const uint32 seed )
00266 {
00267         // Initialize generator state with seed
00268         // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
00269         // In previous versions, most significant bits (MSBs) of the seed affect
00270         // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
00271         register uint32 *s = state;
00272         register uint32 *r = state;
00273         register int i = 1;
00274         *s++ = seed & 0xffffffffUL;
00275         for( ; i < N; ++i )
00276         {
00277                 *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
00278                 r++;
00279         }
00280 }
00281 
00282 
00283 inline void MTRand::reload()
00284 {
00285         // Generate N new values in state
00286         // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
00287         register uint32 *p = state;
00288         register int i;
00289         for( i = N - M; i--; ++p )
00290                 *p = twist( p[M], p[0], p[1] );
00291         for( i = M; --i; ++p )
00292                 *p = twist( p[M-N], p[0], p[1] );
00293         *p = twist( p[M-N], p[0], state[0] );
00294 
00295         left = N, pNext = state;
00296 }
00297 
00298 
00299 
00300 inline void MTRand::save( uint32* saveArray ) const
00301 {
00302         register uint32 *sa = saveArray;
00303         register const uint32 *s = state;
00304         register int i = N;
00305         for( ; i--; *sa++ = *s++ ) {}
00306         *sa = left;
00307 }
00308 
00309 
00310 inline void MTRand::load( uint32 *const loadArray )
00311 {
00312         register uint32 *s = state;
00313         register uint32 *la = loadArray;
00314         register int i = N;
00315         for( ; i--; *s++ = *la++ ) {}
00316         left = *la;
00317         pNext = &state[N-left];
00318 }
00319 
00320 
00321 } // namespace
00322 
00323 #endif  // MERSENNETWISTER_H
00324 
00325 // Change log:
00326 //
00327 // v0.1 - First release on 15 May 2000
00328 //      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
00329 //      - Translated from C to C++
00330 //      - Made completely ANSI compliant
00331 //      - Designed convenient interface for initialization, seeding, and
00332 //        obtaining numbers in default or user-defined ranges
00333 //      - Added automatic seeding from /dev/urandom or time() and clock()
00334 //      - Provided functions for saving and loading generator state
00335 //
00336 // v0.2 - Fixed bug which reloaded generator one step too late
00337 //
00338 // v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
00339 //
00340 // v0.4 - Removed trailing newline in saved generator format to be consistent
00341 //        with output format of built-in types
00342 //
00343 // v0.5 - Improved portability by replacing static const int's with enum's and
00344 //        clarifying return values in seed(); suggested by Eric Heimburg
00345 //      - Removed MAXINT constant; use 0xffffffffUL instead
00346 //
00347 // v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
00348 //      - Changed integer [0,n] generator to give better uniformity
00349 //
00350 // v0.7 - Fixed operator precedence ambiguity in reload()
00351 //      - Added access for real numbers in (0,1) and (0,n)
00352 //
00353 // v0.8 - Included time.h header to properly support time_t and clock_t
00354 //
00355 // v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
00356 //      - Allowed for seeding with arrays of any length
00357 //      - Added access for real numbers in [0,1) with 53-bit resolution
00358 //      - Added access for real numbers from normal (Gaussian) distributions
00359 //      - Increased overall speed by optimizing twist()
00360 //      - Doubled speed of integer [0,n] generation
00361 //      - Fixed out-of-range number generation on 64-bit machines
00362 //      - Improved portability by substituting literal constants for long enum's
00363 //      - Changed license from GNU LGPL to BSD

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