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# D:/VL/BuildSystem/VL_DISTRO/Visualization_Library_SDK/src/vlCore/MersenneTwister.hpp

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    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  v1.1  28 September 2009  wagnerr@umich.edu
    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
    00012 // http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
    00013
    00014 // Reference
    00015 // M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
    00016 // Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
    00017 // Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
    00018
    00019 // Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
    00020 // Copyright (C) 2000 - 2009, Richard J. Wagner
    00021 // All rights reserved.
    00022 //
    00023 // Redistribution and use in source and binary forms, with or without
    00024 // modification, are permitted provided that the following conditions
    00025 // are met:
    00026 //
    00027 //   1. Redistributions of source code must retain the above copyright
    00028 //      notice, this list of conditions and the following disclaimer.
    00029 //
    00030 //   2. Redistributions in binary form must reproduce the above copyright
    00031 //      notice, this list of conditions and the following disclaimer in the
    00032 //      documentation and/or other materials provided with the distribution.
    00033 //
    00034 //   3. The names of its contributors may not be used to endorse or promote
    00035 //      products derived from this software without specific prior written
    00036 //      permission.
    00037 //
    00038 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
    00039 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
    00040 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
    00041 // ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
    00042 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
    00043 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
    00044 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
    00045 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
    00046 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
    00047 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
    00048 // POSSIBILITY OF SUCH DAMAGE.
    00049
    00050 // The original code included the following notice:
    00051 //
    00052 //     When you use this, send an email to: m-mat@math.sci.hiroshima-u.ac.jp
    00053 //     with an appropriate reference to your work.
    00054 //
    00055 // It would be nice to CC: wagnerr@umich.edu and Cokus@math.washington.edu
    00056 // when you write.
    00057
    00058 // Minor modifications made by Michele Bosi:
    00059 // - MTRand renamed MersenneTwister.
    00060 // - MersenneTwister derived from vl::Object.
    00061 // - MersenneTwister included in vl namespace to avoid collisions with other MersenneTwister versions.
    00062 // - prepended VL_ to MERSENNETWISTER_H to avoid collisions with other MersenneTwister headers.
    00063 // - fixed minor warnings.
    00064
    00065 #ifndef VL_MERSENNETWISTER_H
    00066 #define VL_MERSENNETWISTER_H
    00067
    00068 // Not thread safe (unless auto-initialization is avoided and each thread has
    00069 // its own MersenneTwister object)
    00070
    00071 #include <iostream>
    00072 #include <climits>
    00073 #include <cstdio>
    00074 #include <ctime>
    00075 #include <cmath>
    00076 #include <vlCore/Object.hpp>
    00077
    00078 namespace vl
    00079 {
    00080   //-------------------------------------------------------------------------
    00081   class MersenneTwister;
    00082   //-------------------------------------------------------------------------
    00083   VLCORE_EXPORT MersenneTwister* defMersenneTwister();
    00084   VLCORE_EXPORT void setDefMersenneTwister(MersenneTwister*);
    00085   //-------------------------------------------------------------------------
    00086   class MersenneTwister: public Object
    00087   {
    00088   // Data
    00089   public:
    00090       typedef unsigned long uint32;  // unsigned integer type, at least 32 bits
    00091
    00092       enum { N = 624 };       // length of state vector
    00093       enum { SAVE = N + 1 };  // length of array for save()
    00094
    00095   protected:
    00096       enum { M = 397 };  // period parameter
    00097
    00098       uint32 state[N];   // internal state
    00099       uint32 *pNext;     // next value to get from state
    00100       int left;          // number of values left before reload needed
    00101
    00102   // Methods
    00103   public:
    00104       MersenneTwister( const uint32 oneSeed );  // initialize with a simple uint32
    00105       MersenneTwister( uint32 *const bigSeed, uint32 const seedLength = N );  // or array
    00106       MersenneTwister();  // auto-initialize with /dev/urandom or time() and clock()
    00107       MersenneTwister( const MersenneTwister& o );  // copy
    00108
    00109       // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
    00110       // values together, otherwise the generator state can be learned after
    00111       // reading 624 consecutive values.
    00112
    00113       // Access to 32-bit random numbers
    00114       uint32 randInt();                     // integer in [0,2^32-1]
    00115       uint32 randInt( const uint32 n );     // integer in [0,n] for n < 2^32
    00116       double rand();                        // real number in [0,1]
    00117       double rand( const double n );        // real number in [0,n]
    00118       double randExc();                     // real number in [0,1)
    00119       double randExc( const double n );     // real number in [0,n)
    00120       double randDblExc();                  // real number in (0,1)
    00121       double randDblExc( const double n );  // real number in (0,n)
    00122       double operator()();                  // same as rand()
    00123
    00124       // Access to 53-bit random numbers (capacity of IEEE double precision)
    00125       double rand53();  // real number in [0,1)
    00126
    00127       // Access to nonuniform random number distributions
    00128       double randNorm( const double mean = 0.0, const double stddev = 1.0 );
    00129
    00130       // Re-seeding functions with same behavior as initializers
    00131       void seed( const uint32 oneSeed );
    00132       void seed( uint32 *const bigSeed, const uint32 seedLength = N );
    00133       void seed();
    00134
    00135       // Saving and loading generator state
    00136       void save( uint32* saveArray ) const;  // to array of size SAVE
    00137       void load( uint32 *const loadArray );  // from such array
    00138       friend std::ostream& operator<<( std::ostream& os, const MersenneTwister& mtrand );
    00139       friend std::istream& operator>>( std::istream& is, MersenneTwister& mtrand );
    00140       MersenneTwister& operator=( const MersenneTwister& o );
    00141
    00142   protected:
    00143       void initialize( const uint32 oneSeed );
    00144       void reload();
    00145       uint32 hiBit( const uint32 u ) const { return u & 0x80000000UL; }
    00146       uint32 loBit( const uint32 u ) const { return u & 0x00000001UL; }
    00147       uint32 loBits( const uint32 u ) const { return u & 0x7fffffffUL; }
    00148       uint32 mixBits( const uint32 u, const uint32 v ) const
    00149           { return hiBit(u) | loBits(v); }
    00150       uint32 magic( const uint32 u ) const
    00151           { return loBit(u) ? 0x9908b0dfUL : 0x0UL; }
    00152       uint32 twist( const uint32 m, const uint32 s0, const uint32 s1 ) const
    00153           { return m ^ (mixBits(s0,s1)>>1) ^ magic(s1); }
    00154       static uint32 hash( time_t t, clock_t c );
    00155   };
    00156
    00157   // Functions are defined in order of usage to assist inlining
    00158
    00159   inline MersenneTwister::uint32 MersenneTwister::hash( time_t t, clock_t c )
    00160   {
    00161       // Get a uint32 from t and c
    00162       // Better than uint32(x) in case x is floating point in [0,1]
    00163       // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)
    00164
    00165       static uint32 differ = 0;  // guarantee time-based seeds will change
    00166
    00167       uint32 h1 = 0;
    00168       unsigned char *p = (unsigned char *) &t;
    00169       for( size_t i = 0; i < sizeof(t); ++i )
    00170       {
    00171           h1 *= UCHAR_MAX + 2U;
    00172           h1 += p[i];
    00173       }
    00174       uint32 h2 = 0;
    00175       p = (unsigned char *) &c;
    00176       for( size_t j = 0; j < sizeof(c); ++j )
    00177       {
    00178           h2 *= UCHAR_MAX + 2U;
    00179           h2 += p[j];
    00180       }
    00181       return ( h1 + differ++ ) ^ h2;
    00182   }
    00183
    00184   inline void MersenneTwister::initialize( const uint32 seed )
    00185   {
    00186       // Initialize generator state with seed
    00187       // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
    00188       // In previous versions, most significant bits (MSBs) of the seed affect
    00189       // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
    00190       register uint32 *s = state;
    00191       register uint32 *r = state;
    00192       register int i = 1;
    00193       *s++ = seed & 0xffffffffUL;
    00194       for( ; i < N; ++i )
    00195       {
    00196           *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
    00197           r++;
    00198       }
    00199   }
    00200
    00201   inline void MersenneTwister::reload()
    00202   {
    00203       // Generate N new values in state
    00204       // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
    00205       static const int MmN = int(M) - int(N);  // in case enums are unsigned
    00206       register uint32 *p = state;
    00207       register int i;
    00208       for( i = N - M; i--; ++p )
    00209           *p = twist( p[M], p[0], p[1] );
    00210       for( i = M; --i; ++p )
    00211           *p = twist( p[MmN], p[0], p[1] );
    00212       *p = twist( p[MmN], p[0], state[0] );
    00213
    00214       left = N, pNext = state;
    00215   }
    00216
    00217   inline void MersenneTwister::seed( const uint32 oneSeed )
    00218   {
    00219       // Seed the generator with a simple uint32
    00220       initialize(oneSeed);
    00221       reload();
    00222   }
    00223
    00224   inline void MersenneTwister::seed( uint32 *const bigSeed, const uint32 seedLength )
    00225   {
    00226       // Seed the generator with an array of uint32's
    00227       // There are 2^19937-1 possible initial states.  This function allows
    00228       // all of those to be accessed by providing at least 19937 bits (with a
    00229       // default seed length of N = 624 uint32's).  Any bits above the lower 32
    00230       // in each element are discarded.
    00231       // Just call seed() if you want to get array from /dev/urandom
    00232       initialize(19650218UL);
    00233       register int i = 1;
    00234       register uint32 j = 0;
    00235       register int k = ( N > seedLength ? (int)N : (int)seedLength );
    00236       for( ; k; --k )
    00237       {
    00238           state[i] =
    00239           state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
    00240           state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
    00241           state[i] &= 0xffffffffUL;
    00242           ++i;  ++j;
    00243           if( i >= N ) { state[0] = state[N-1];  i = 1; }
    00244           if( j >= seedLength ) j = 0;
    00245       }
    00246       for( k = N - 1; k; --k )
    00247       {
    00248           state[i] =
    00249           state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
    00250           state[i] -= i;
    00251           state[i] &= 0xffffffffUL;
    00252           ++i;
    00253           if( i >= N ) { state[0] = state[N-1];  i = 1; }
    00254       }
    00255       state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
    00256       reload();
    00257   }
    00258
    00259   inline void MersenneTwister::seed()
    00260   {
    00261       // Seed the generator with an array from /dev/urandom if available
    00262       // Otherwise use a hash of time() and clock() values
    00263
    00264       // First try getting an array from /dev/urandom
    00265       FILE* urandom = fopen( "/dev/urandom", "rb" );
    00266       if( urandom )
    00267       {
    00268           uint32 bigSeed[N];
    00269           register uint32 *s = bigSeed;
    00270           register int i = N;
    00271           register bool success = true;
    00272           while( success && i-- )
    00273               success = fread( s++, sizeof(uint32), 1, urandom ) != 0;
    00274           fclose(urandom);
    00275           if( success ) { seed( bigSeed, N );  return; }
    00276       }
    00277
    00278       // Was not successful, so use time() and clock() instead
    00279       seed( hash( time(NULL), clock() ) );
    00280   }
    00281
    00282   inline MersenneTwister::MersenneTwister( const uint32 oneSeed )
    00283       { seed(oneSeed); }
    00284
    00285   inline MersenneTwister::MersenneTwister( uint32 *const bigSeed, const uint32 seedLength )
    00286       { seed(bigSeed,seedLength); }
    00287
    00288   inline MersenneTwister::MersenneTwister()
    00289       { seed(); }
    00290
    00291   inline MersenneTwister::MersenneTwister( const MersenneTwister& o ): Object(o)
    00292   {
    00293       register const uint32 *t = o.state;
    00294       register uint32 *s = state;
    00295       register int i = N;
    00296       for( ; i--; *s++ = *t++ ) {}
    00297       left = o.left;
    00298       pNext = &state[N-left];
    00299   }
    00300
    00301   inline MersenneTwister::uint32 MersenneTwister::randInt()
    00302   {
    00303       // Pull a 32-bit integer from the generator state
    00304       // Every other access function simply transforms the numbers extracted here
    00305
    00306       if( left == 0 ) reload();
    00307       --left;
    00308
    00309       register uint32 s1;
    00310       s1 = *pNext++;
    00311       s1 ^= (s1 >> 11);
    00312       s1 ^= (s1 <<  7) & 0x9d2c5680UL;
    00313       s1 ^= (s1 << 15) & 0xefc60000UL;
    00314       return ( s1 ^ (s1 >> 18) );
    00315   }
    00316
    00317   inline MersenneTwister::uint32 MersenneTwister::randInt( const uint32 n )
    00318   {
    00319       // Find which bits are used in n
    00320       // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
    00321       uint32 used = n;
    00322       used |= used >> 1;
    00323       used |= used >> 2;
    00324       used |= used >> 4;
    00325       used |= used >> 8;
    00326       used |= used >> 16;
    00327
    00328       // Draw numbers until one is found in [0,n]
    00329       uint32 i;
    00330       do
    00331           i = randInt() & used;  // toss unused bits to shorten search
    00332       while( i > n );
    00333       return i;
    00334   }
    00335
    00336   inline double MersenneTwister::rand()
    00337       { return double(randInt()) * (1.0/4294967295.0); }
    00338
    00339   inline double MersenneTwister::rand( const double n )
    00340       { return rand() * n; }
    00341
    00342   inline double MersenneTwister::randExc()
    00343       { return double(randInt()) * (1.0/4294967296.0); }
    00344
    00345   inline double MersenneTwister::randExc( const double n )
    00346       { return randExc() * n; }
    00347
    00348   inline double MersenneTwister::randDblExc()
    00349       { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
    00350
    00351   inline double MersenneTwister::randDblExc( const double n )
    00352       { return randDblExc() * n; }
    00353
    00354   inline double MersenneTwister::rand53()
    00355   {
    00356       uint32 a = randInt() >> 5, b = randInt() >> 6;
    00357       return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
    00358   }
    00359
    00360   inline double MersenneTwister::randNorm( const double mean, const double stddev )
    00361   {
    00362       // Return a real number from a normal (Gaussian) distribution with given
    00363       // mean and standard deviation by polar form of Box-Muller transformation
    00364       double x, y, r;
    00365       do
    00366       {
    00367           x = 2.0 * rand() - 1.0;
    00368           y = 2.0 * rand() - 1.0;
    00369           r = x * x + y * y;
    00370       }
    00371       while ( r >= 1.0 || r == 0.0 );
    00372       double s = sqrt( -2.0 * log(r) / r );
    00373       return mean + x * s * stddev;
    00374   }
    00375
    00376   inline double MersenneTwister::operator()()
    00377   {
    00378       return rand();
    00379   }
    00380
    00381   inline void MersenneTwister::save( uint32* saveArray ) const
    00382   {
    00383       register const uint32 *s = state;
    00384       register uint32 *sa = saveArray;
    00385       register int i = N;
    00386       for( ; i--; *sa++ = *s++ ) {}
    00387       *sa = left;
    00388   }
    00389
    00390   inline void MersenneTwister::load( uint32 *const loadArray )
    00391   {
    00392       register uint32 *s = state;
    00393       register uint32 *la = loadArray;
    00394       register int i = N;
    00395       for( ; i--; *s++ = *la++ ) {}
    00396       left = *la;
    00397       pNext = &state[N-left];
    00398   }
    00399
    00400   inline std::ostream& operator<<( std::ostream& os, const MersenneTwister& mtrand )
    00401   {
    00402       register const MersenneTwister::uint32 *s = mtrand.state;
    00403       register int i = mtrand.N;
    00404       for( ; i--; os << *s++ << "\t" ) {}
    00405       return os << mtrand.left;
    00406   }
    00407
    00408   inline std::istream& operator>>( std::istream& is, MersenneTwister& mtrand )
    00409   {
    00410       register MersenneTwister::uint32 *s = mtrand.state;
    00411       register int i = mtrand.N;
    00412       for( ; i--; is >> *s++ ) {}
    00413       is >> mtrand.left;
    00414       mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
    00415       return is;
    00416   }
    00417
    00418   inline MersenneTwister& MersenneTwister::operator=( const MersenneTwister& o )
    00419   {
    00420       if( this == &o ) return (*this);
    00421       register const uint32 *t = o.state;
    00422       register uint32 *s = state;
    00423       register int i = N;
    00424       for( ; i--; *s++ = *t++ ) {}
    00425       left = o.left;
    00426       pNext = &state[N-left];
    00427       return (*this);
    00428   }
    00429
    00430 }
    00431
    00432 #endif  // MERSENNETWISTER_H
    00433
    00434 // Change log:
    00435 //
    00436 // v0.1 - First release on 15 May 2000
    00437 //      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
    00438 //      - Translated from C to C++
    00439 //      - Made completely ANSI compliant
    00440 //      - Designed convenient interface for initialization, seeding, and
    00441 //        obtaining numbers in default or user-defined ranges
    00442 //      - Added automatic seeding from /dev/urandom or time() and clock()
    00443 //      - Provided functions for saving and loading generator state
    00444 //
    00445 // v0.2 - Fixed bug which reloaded generator one step too late
    00446 //
    00447 // v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
    00448 //
    00449 // v0.4 - Removed trailing newline in saved generator format to be consistent
    00450 //        with output format of built-in types
    00451 //
    00452 // v0.5 - Improved portability by replacing static const int's with enum's and
    00453 //        clarifying return values in seed(); suggested by Eric Heimburg
    00454 //      - Removed MAXINT constant; use 0xffffffffUL instead
    00455 //
    00456 // v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
    00457 //      - Changed integer [0,n] generator to give better uniformity
    00458 //
    00459 // v0.7 - Fixed operator precedence ambiguity in reload()
    00460 //      - Added access for real numbers in (0,1) and (0,n)
    00461 //
    00462 // v0.8 - Included time.h header to properly support time_t and clock_t
    00463 //
    00464 // v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
    00465 //      - Allowed for seeding with arrays of any length
    00466 //      - Added access for real numbers in [0,1) with 53-bit resolution
    00467 //      - Added access for real numbers from normal (Gaussian) distributions
    00468 //      - Increased overall speed by optimizing twist()
    00469 //      - Doubled speed of integer [0,n] generation
    00470 //      - Fixed out-of-range number generation on 64-bit machines
    00471 //      - Improved portability by substituting literal constants for long enum's
    00472 //      - Changed license from GNU LGPL to BSD
    00473 //
    00474 // v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"
    00475 //      - Changed randNorm algorithm from basic to polar form for efficiency
    00476 //      - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms
    00477 //      - Cleaned declarations and definitions to please Intel compiler
    00478 //      - Revised twist() operator to work on ones'-complement machines
    00479 //      - Fixed reload() function to work when N and M are unsigned
    00480 //      - Added copy constructor and copy operator from Salvador Espana

Visualization Library v2011.09.1162 Reference Documentation
Copyright 2005-2011 Michele Bosi. All rights reserved.
Updated on Thu Jan 26 2012 00:43:29.
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