src/math/MersenneTwister.hpp

// MersenneTwister.h
// Mersenne Twister random number generator -- a C++ class MTRand
// Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
// Richard J. Wagner  v1.0  15 May 2003  rjwagner@writeme.com

// The Mersenne Twister is an algorithm for generating random numbers.  It
// was designed with consideration of the flaws in various other generators.
// The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
// are far greater.  The generator is also fast; it avoids multiplication and
// division, and it benefits from caches and pipelines.  For more information
// see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html

// Reference
// M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
// Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
// Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.

// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
// Copyright (C) 2000 - 2003, Richard J. Wagner
// All rights reserved.                          
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
//   1. Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
//
//   3. The names of its contributors may not be used to endorse or promote 
//      products derived from this software without specific prior written 
//      permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

// The original code included the following notice:
//
//     When you use this, send an email to: matumoto@math.keio.ac.jp
//     with an appropriate reference to your work.
//
// It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu
// when you write.

#ifndef MERSENNETWISTER_H
#define MERSENNETWISTER_H

// Not thread safe (unless auto-initialization is avoided and each thread has
// its own MTRand object)

#include <cassert>
#include <iostream>
#include <limits.h>
#include <stdio.h>
#include <time.h>
#include <math.h>
#include <vector>
namespace oopse {

  class MTRand {
    // Data
  public:
    typedef unsigned long uint32;  // unsigned integer type, at least 32 bits
        
    enum { N = 624 };       // length of state vector
    enum { SAVE = N + 1 };  // length of array for save()

  private:
    enum { M = 397 };  // period parameter
        
    uint32 state[N];   // internal state
    uint32 *pNext;     // next value to get from state
    int left;          // number of values left before reload needed
    int nstrides_;
    int stride_;

    //Methods
  public:
    MTRand( const uint32& oneSeed, int nstrides, int stride);  // initialize with a simple uint32
    MTRand( uint32 *const bigSeed, uint32 const seedLength, int nstrides, int stride);  // or an array
    MTRand(int nstrides, int stride);  // auto-initialize with /dev/urandom or time() and clock()
        
    // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
    // values together, otherwise the generator state can be learned after
    // reading 624 consecutive values.
        
    // Access to 32-bit random numbers
    double rand();                          // real number in [0,1]
    double rand( const double& n );         // real number in [0,n]
    double randExc();                       // real number in [0,1)
    double randExc( const double& n );      // real number in [0,n)
    double randDblExc();                    // real number in (0,1)
    double randDblExc( const double& n );   // real number in (0,n)
    uint32 randInt();                       // integer in [0,2^32-1] (modified for striding)
    uint32 rawRandInt();                    // original randInt
    uint32 randInt( const uint32& n );      // integer in [0,n] for n < 2^32
    double operator()() { return rand(); }  // same as rand()
        
    // Access to 53-bit random numbers (capacity of IEEE double precision)
    double rand53();  // real number in [0,1)
        
    // Access to nonuniform random number distributions
    double randNorm( const double mean = 0.0, const double variance = 0.0 );
        
    // Re-seeding functions with same behavior as initializers
    void seed( const uint32 oneSeed );
    void seed( uint32 *const bigSeed, const uint32 seedLength = N );
    void seed();

    std::vector<uint32>generateSeeds(); 
        
    // Saving and loading generator state
    void save( uint32* saveArray ) const;  // to array of size SAVE
    void load( uint32 *const loadArray );  // from such array
    friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
    friend std::istream& operator>>( std::istream& is, MTRand& mtrand );

  protected:
    void initialize( const uint32 oneSeed );
    void reload();
    uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
    uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
    uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
    uint32 mixBits( const uint32& u, const uint32& v ) const
    { return hiBit(u) | loBits(v); }
    uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
    { return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
    static uint32 hash( time_t t, clock_t c );
  };


  inline MTRand::MTRand( const uint32& oneSeed, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
    assert(stride_ < nstrides_ && stride_ >= 0);
    seed(oneSeed); 
  }

  inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
    assert(stride_ < nstrides_ && stride_ >= 0);
    seed(bigSeed,seedLength); 
  }

  inline MTRand::MTRand(int nstrides, int stride)       : nstrides_(nstrides), stride_(stride){
    assert(stride_ < nstrides_ && stride_ >= 0);
    seed(); 
  }

  inline double MTRand::rand()
  { return double(randInt()) * (1.0/4294967295.0); }

  inline double MTRand::rand( const double& n )
  { return rand() * n; }

  inline double MTRand::randExc()
  { return double(randInt()) * (1.0/4294967296.0); }

  inline double MTRand::randExc( const double& n )
  { return randExc() * n; }

  inline double MTRand::randDblExc()
  { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }

  inline double MTRand::randDblExc( const double& n )
  { return randDblExc() * n; }

  inline double MTRand::rand53()
  {
    uint32 a = randInt() >> 5, b = randInt() >> 6;
    return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
  }

  inline double MTRand::randNorm( const double mean, const double variance )
  {
    // Return a real number from a normal (Gaussian) distribution with given
    // mean and variance by Box-Muller method
    double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
    double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
    return mean + r * cos(phi);
  }

  /**
   * This function is modified from the original to allow for random
   * streams on parallel jobs.  It now takes numbers from by striding
   * through the random stream and picking up only one of the random
   * numbers per nstrides_.  The number it picks is the stride_'th
   * number in the stride sequence.  
   */
  inline MTRand::uint32 MTRand::randInt() {
 
    std::vector<uint32> ranNums(nstrides_);
  
    for (int i = 0; i < nstrides_; ++i) {
      ranNums[i] = rawRandInt();
    }
  
    return ranNums[stride_];
  }

  /** 
   * This is the original randInt function which implements the mersenne
   * twister.
   */
  inline MTRand::uint32 MTRand::rawRandInt()
  {
    // Pull a 32-bit integer from the generator state
    // Every other access function simply transforms the numbers extracted here
        
    if( left == 0 ) reload();
    --left;
                
    register uint32 s1;
    s1 = *pNext++;
    s1 ^= (s1 >> 11);
    s1 ^= (s1 <<  7) & 0x9d2c5680UL;
    s1 ^= (s1 << 15) & 0xefc60000UL;
    return ( s1 ^ (s1 >> 18) );
  }

  inline MTRand::uint32 MTRand::randInt( const uint32& n )
  {
    // Find which bits are used in n
    // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
    uint32 used = n;
    used |= used >> 1;
    used |= used >> 2;
    used |= used >> 4;
    used |= used >> 8;
    used |= used >> 16;
        
    // Draw numbers until one is found in [0,n]
    uint32 i;
    do
      i = randInt() & used;  // toss unused bits to shorten search
    while( i > n );
    return i;
  }


  inline void MTRand::seed( const uint32 oneSeed )
  {
    // Seed the generator with a simple uint32
    initialize(oneSeed);
    reload();
  }


  inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
  {
    // Seed the generator with an array of uint32's
    // There are 2^19937-1 possible initial states.  This function allows
    // all of those to be accessed by providing at least 19937 bits (with a
    // default seed length of N = 624 uint32's).  Any bits above the lower 32
    // in each element are discarded.
    // Just call seed() if you want to get array from /dev/urandom
    initialize(19650218UL);
    register int i = 1;
    register uint32 j = 0;
    register int k = ( N > seedLength ? N : seedLength );
    for( ; k; --k )
      {
        state[i] =
          state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
        state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
        state[i] &= 0xffffffffUL;
        ++i;  ++j;
        if( i >= N ) { state[0] = state[N-1];  i = 1; }
        if( j >= seedLength ) j = 0;
      }
    for( k = N - 1; k; --k )
      {
        state[i] =
          state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
        state[i] -= i;
        state[i] &= 0xffffffffUL;
        ++i;
        if( i >= N ) { state[0] = state[N-1];  i = 1; }
      }
    state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
    reload();
  }


  inline void MTRand::seed()
  {
    std::vector<uint32> seeds;

    seeds = generateSeeds();

    if (seeds.size() == 1) {
      seed( seeds[0] );
    } else {
      seed( &seeds[0], seeds.size() );
    }
  }


  inline std::vector<MTRand::uint32> MTRand::generateSeeds() {
    // Seed the generator with an array from /dev/urandom if available
    // Otherwise use a hash of time() and clock() values

    std::vector<uint32> bigSeed; 

    // First try getting an array from /dev/urandom
    FILE* urandom = fopen( "/dev/urandom", "rb" );
    if( urandom )
      {
        bigSeed.resize(N);
        register uint32 *s = &bigSeed[0];
        register int i = N;
        register bool success = true;
        while( success && i-- )
          success = fread( s++, sizeof(uint32), 1, urandom );
        fclose(urandom);
        if( success ) { return bigSeed; }
      }
  
    // Was not successful, so use time() and clock() instead

    bigSeed.push_back(hash( time(NULL), clock()));
    return bigSeed;
  }


  inline void MTRand::initialize( const uint32 seed )
  {
    // Initialize generator state with seed
    // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
    // In previous versions, most significant bits (MSBs) of the seed affect
    // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
    register uint32 *s = state;
    register uint32 *r = state;
    register int i = 1;
    *s++ = seed & 0xffffffffUL;
    for( ; i < N; ++i )
      {
        *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
        r++;
      }
  }


  inline void MTRand::reload()
  {
    // Generate N new values in state
    // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
    register uint32 *p = state;
    register int i;
    for( i = N - M; i--; ++p )
      *p = twist( p[M], p[0], p[1] );
    for( i = M; --i; ++p )
      *p = twist( p[M-N], p[0], p[1] );
    *p = twist( p[M-N], p[0], state[0] );

    left = N, pNext = state;
  }


  inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
  {
    // Get a uint32 from t and c
    // Better than uint32(x) in case x is floating point in [0,1]
    // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)

    static uint32 differ = 0;  // guarantee time-based seeds will change

    uint32 h1 = 0;
    unsigned char *p = (unsigned char *) &t;
    for( size_t i = 0; i < sizeof(t); ++i )
      {
        h1 *= UCHAR_MAX + 2U;
        h1 += p[i];
      }
    uint32 h2 = 0;
    p = (unsigned char *) &c;
    for( size_t j = 0; j < sizeof(c); ++j )
      {
        h2 *= UCHAR_MAX + 2U;
        h2 += p[j];
      }
    return ( h1 + differ++ ) ^ h2;
  }


  inline void MTRand::save( uint32* saveArray ) const
  {
    register uint32 *sa = saveArray;
    register const uint32 *s = state;
    register int i = N;
    for( ; i--; *sa++ = *s++ ) {}
    *sa = left;
  }


  inline void MTRand::load( uint32 *const loadArray )
  {
    register uint32 *s = state;
    register uint32 *la = loadArray;
    register int i = N;
    for( ; i--; *s++ = *la++ ) {}
    left = *la;
    pNext = &state[N-left];
  }


  inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
  {
    register const MTRand::uint32 *s = mtrand.state;
    register int i = mtrand.N;
    for( ; i--; os << *s++ << "\t" ) {}
    return os << mtrand.left;
  }


  inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
  {
    register MTRand::uint32 *s = mtrand.state;
    register int i = mtrand.N;
    for( ; i--; is >> *s++ ) {}
    is >> mtrand.left;
    mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
    return is;
  }

}
#endif  // MERSENNETWISTER_H

// Change log:
//
// v0.1 - First release on 15 May 2000
//      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
//      - Translated from C to C++
//      - Made completely ANSI compliant
//      - Designed convenient interface for initialization, seeding, and
//        obtaining numbers in default or user-defined ranges
//      - Added automatic seeding from /dev/urandom or time() and clock()
//      - Provided functions for saving and loading generator state
//
// v0.2 - Fixed bug which reloaded generator one step too late
//
// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
//
// v0.4 - Removed trailing newline in saved generator format to be consistent
//        with output format of built-in types
//
// v0.5 - Improved portability by replacing static const int's with enum's and
//        clarifying return values in seed(); suggested by Eric Heimburg
//      - Removed MAXINT constant; use 0xffffffffUL instead
//
// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
//      - Changed integer [0,n] generator to give better uniformity
//
// v0.7 - Fixed operator precedence ambiguity in reload()
//      - Added access for real numbers in (0,1) and (0,n)
//
// v0.8 - Included time.h header to properly support time_t and clock_t
//
// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
//      - Allowed for seeding with arrays of any length
//      - Added access for real numbers in [0,1) with 53-bit resolution
//      - Added access for real numbers from normal (Gaussian) distributions
//      - Increased overall speed by optimizing twist()
//      - Doubled speed of integer [0,n] generation
//      - Fixed out-of-range number generation on 64-bit machines
//      - Improved portability by substituting literal constants for long enum's
//      - Changed license from GNU LGPL to BSD
Revision:	895
Committed:	Mon Mar 13 22:42:40 2006 UTC (19 years, 7 months ago) by tim
File size:	16328 byte(s)
Log Message:	LangevinDynamics in progress
#	User	Rev	Content
1	tim	380	// MersenneTwister.h
2			// Mersenne Twister random number generator -- a C++ class MTRand
3			// Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
4			// Richard J. Wagner v1.0 15 May 2003 rjwagner@writeme.com
5
6			// The Mersenne Twister is an algorithm for generating random numbers. It
7			// was designed with consideration of the flaws in various other generators.
8			// The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
9			// are far greater. The generator is also fast; it avoids multiplication and
10			// division, and it benefits from caches and pipelines. For more information
11			// see the inventors' web page at http://www.math.keio.ac.jp/~matumoto/emt.html
12
13			// Reference
14			// M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
15			// Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
16			// Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
17
18			// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
19			// Copyright (C) 2000 - 2003, Richard J. Wagner
20			// All rights reserved.
21			//
22			// Redistribution and use in source and binary forms, with or without
23			// modification, are permitted provided that the following conditions
24			// are met:
25			//
26			// 1. Redistributions of source code must retain the above copyright
27			// notice, this list of conditions and the following disclaimer.
28			//
29			// 2. Redistributions in binary form must reproduce the above copyright
30			// notice, this list of conditions and the following disclaimer in the
31			// documentation and/or other materials provided with the distribution.
32			//
33			// 3. The names of its contributors may not be used to endorse or promote
34			// products derived from this software without specific prior written
35			// permission.
36			//
37			// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
38			// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
39			// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
40			// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
41			// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
42			// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
43			// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
44			// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
45			// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
46			// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
47			// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
48
49			// The original code included the following notice:
50			//
51			// When you use this, send an email to: matumoto@math.keio.ac.jp
52			// with an appropriate reference to your work.
53			//
54			// It would be nice to CC: rjwagner@writeme.com and Cokus@math.washington.edu
55			// when you write.
56
57			#ifndef MERSENNETWISTER_H
58			#define MERSENNETWISTER_H
59
60			// Not thread safe (unless auto-initialization is avoided and each thread has
61			// its own MTRand object)
62
63			#include <cassert>
64			#include <iostream>
65			#include <limits.h>
66			#include <stdio.h>
67			#include <time.h>
68			#include <math.h>
69	tim	384	#include <vector>
70			namespace oopse {
71	tim	380
72	gezelter	507	class MTRand {
73			// Data
74			public:
75			typedef unsigned long uint32; // unsigned integer type, at least 32 bits
76	tim	380
77	gezelter	507	enum { N = 624 }; // length of state vector
78			enum { SAVE = N + 1 }; // length of array for save()
79	tim	380
80	gezelter	507	private:
81			enum { M = 397 }; // period parameter
82	tim	380
83	gezelter	507	uint32 state[N]; // internal state
84			uint32 *pNext; // next value to get from state
85			int left; // number of values left before reload needed
86			int nstrides_;
87			int stride_;
88	tim	380
89	gezelter	507	//Methods
90			public:
91			MTRand( const uint32& oneSeed, int nstrides, int stride); // initialize with a simple uint32
92			MTRand( uint32 *const bigSeed, uint32 const seedLength, int nstrides, int stride); // or an array
93			MTRand(int nstrides, int stride); // auto-initialize with /dev/urandom or time() and clock()
94	tim	380
95	gezelter	507	// Do NOT use for CRYPTOGRAPHY without securely hashing several returned
96			// values together, otherwise the generator state can be learned after
97			// reading 624 consecutive values.
98	tim	380
99	gezelter	507	// Access to 32-bit random numbers
100			double rand(); // real number in [0,1]
101			double rand( const double& n ); // real number in [0,n]
102			double randExc(); // real number in [0,1)
103			double randExc( const double& n ); // real number in [0,n)
104			double randDblExc(); // real number in (0,1)
105			double randDblExc( const double& n ); // real number in (0,n)
106			uint32 randInt(); // integer in [0,2^32-1] (modified for striding)
107			uint32 rawRandInt(); // original randInt
108			uint32 randInt( const uint32& n ); // integer in [0,n] for n < 2^32
109			double operator()() { return rand(); } // same as rand()
110	tim	380
111	gezelter	507	// Access to 53-bit random numbers (capacity of IEEE double precision)
112			double rand53(); // real number in [0,1)
113	tim	380
114	gezelter	507	// Access to nonuniform random number distributions
115	tim	895	double randNorm( const double mean = 0.0, const double variance = 0.0 );
116	tim	380
117	gezelter	507	// Re-seeding functions with same behavior as initializers
118			void seed( const uint32 oneSeed );
119			void seed( uint32 *const bigSeed, const uint32 seedLength = N );
120			void seed();
121	tim	384
122	gezelter	507	std::vector<uint32>generateSeeds();
123	tim	384
124	gezelter	507	// Saving and loading generator state
125			void save( uint32* saveArray ) const; // to array of size SAVE
126			void load( uint32 *const loadArray ); // from such array
127			friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
128			friend std::istream& operator>>( std::istream& is, MTRand& mtrand );
129	tim	380
130	gezelter	507	protected:
131			void initialize( const uint32 oneSeed );
132			void reload();
133			uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
134			uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
135			uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
136			uint32 mixBits( const uint32& u, const uint32& v ) const
137			{ return hiBit(u) \| loBits(v); }
138			uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
139			{ return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
140			static uint32 hash( time_t t, clock_t c );
141			};
142	tim	380
143
144	gezelter	507	inline MTRand::MTRand( const uint32& oneSeed, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
145	tim	380	assert(stride_ < nstrides_ && stride_ >= 0);
146			seed(oneSeed);
147	gezelter	507	}
148	tim	380
149	gezelter	507	inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
150	tim	380	assert(stride_ < nstrides_ && stride_ >= 0);
151			seed(bigSeed,seedLength);
152	gezelter	507	}
153	tim	380
154	gezelter	507	inline MTRand::MTRand(int nstrides, int stride) : nstrides_(nstrides), stride_(stride){
155	tim	380	assert(stride_ < nstrides_ && stride_ >= 0);
156			seed();
157	gezelter	507	}
158	tim	380
159	gezelter	507	inline double MTRand::rand()
160			{ return double(randInt()) * (1.0/4294967295.0); }
161	tim	380
162	gezelter	507	inline double MTRand::rand( const double& n )
163			{ return rand() * n; }
164	tim	380
165	gezelter	507	inline double MTRand::randExc()
166			{ return double(randInt()) * (1.0/4294967296.0); }
167	tim	380
168	gezelter	507	inline double MTRand::randExc( const double& n )
169			{ return randExc() * n; }
170	tim	380
171	gezelter	507	inline double MTRand::randDblExc()
172			{ return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
173	tim	380
174	gezelter	507	inline double MTRand::randDblExc( const double& n )
175			{ return randDblExc() * n; }
176	tim	380
177	gezelter	507	inline double MTRand::rand53()
178			{
179			uint32 a = randInt() >> 5, b = randInt() >> 6;
180			return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0); // by Isaku Wada
181			}
182	tim	380
183	tim	895	inline double MTRand::randNorm( const double mean, const double variance )
184	gezelter	507	{
185			// Return a real number from a normal (Gaussian) distribution with given
186			// mean and variance by Box-Muller method
187			double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
188			double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
189			return mean + r * cos(phi);
190			}
191	tim	380
192	gezelter	507	/**
193			* This function is modified from the original to allow for random
194			* streams on parallel jobs. It now takes numbers from by striding
195			* through the random stream and picking up only one of the random
196			* numbers per nstrides_. The number it picks is the stride_'th
197			* number in the stride sequence.
198			*/
199			inline MTRand::uint32 MTRand::randInt() {
200	gezelter	382
201	gezelter	507	std::vector<uint32> ranNums(nstrides_);
202	gezelter	382
203	gezelter	507	for (int i = 0; i < nstrides_; ++i) {
204			ranNums[i] = rawRandInt();
205			}
206
207			return ranNums[stride_];
208	gezelter	382	}
209
210	gezelter	507	/**
211			* This is the original randInt function which implements the mersenne
212			* twister.
213			*/
214			inline MTRand::uint32 MTRand::rawRandInt()
215			{
216			// Pull a 32-bit integer from the generator state
217			// Every other access function simply transforms the numbers extracted here
218	gezelter	382
219	gezelter	507	if( left == 0 ) reload();
220			--left;
221	gezelter	382
222	gezelter	507	register uint32 s1;
223			s1 = *pNext++;
224			s1 ^= (s1 >> 11);
225			s1 ^= (s1 << 7) & 0x9d2c5680UL;
226			s1 ^= (s1 << 15) & 0xefc60000UL;
227			return ( s1 ^ (s1 >> 18) );
228			}
229	tim	380
230	gezelter	507	inline MTRand::uint32 MTRand::randInt( const uint32& n )
231			{
232			// Find which bits are used in n
233			// Optimized by Magnus Jonsson (magnus@smartelectronix.com)
234			uint32 used = n;
235			used \|= used >> 1;
236			used \|= used >> 2;
237			used \|= used >> 4;
238			used \|= used >> 8;
239			used \|= used >> 16;
240	tim	380
241	gezelter	507	// Draw numbers until one is found in [0,n]
242			uint32 i;
243			do
244			i = randInt() & used; // toss unused bits to shorten search
245			while( i > n );
246			return i;
247			}
248	tim	380
249
250	gezelter	507	inline void MTRand::seed( const uint32 oneSeed )
251			{
252			// Seed the generator with a simple uint32
253			initialize(oneSeed);
254			reload();
255			}
256	tim	380
257
258	gezelter	507	inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
259			{
260			// Seed the generator with an array of uint32's
261			// There are 2^19937-1 possible initial states. This function allows
262			// all of those to be accessed by providing at least 19937 bits (with a
263			// default seed length of N = 624 uint32's). Any bits above the lower 32
264			// in each element are discarded.
265			// Just call seed() if you want to get array from /dev/urandom
266			initialize(19650218UL);
267			register int i = 1;
268			register uint32 j = 0;
269			register int k = ( N > seedLength ? N : seedLength );
270			for( ; k; --k )
271			{
272			state[i] =
273			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
274			state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
275			state[i] &= 0xffffffffUL;
276			++i; ++j;
277			if( i >= N ) { state[0] = state[N-1]; i = 1; }
278			if( j >= seedLength ) j = 0;
279			}
280			for( k = N - 1; k; --k )
281			{
282			state[i] =
283			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
284			state[i] -= i;
285			state[i] &= 0xffffffffUL;
286			++i;
287			if( i >= N ) { state[0] = state[N-1]; i = 1; }
288			}
289			state[0] = 0x80000000UL; // MSB is 1, assuring non-zero initial array
290			reload();
291			}
292	tim	380
293
294	gezelter	507	inline void MTRand::seed()
295			{
296			std::vector<uint32> seeds;
297	gezelter	382
298	gezelter	507	seeds = generateSeeds();
299	gezelter	382
300	gezelter	507	if (seeds.size() == 1) {
301			seed( seeds[0] );
302			} else {
303			seed( &seeds[0], seeds.size() );
304			}
305	gezelter	382	}
306	tim	380
307
308	gezelter	507	inline std::vector<MTRand::uint32> MTRand::generateSeeds() {
309			// Seed the generator with an array from /dev/urandom if available
310			// Otherwise use a hash of time() and clock() values
311	gezelter	382
312	gezelter	507	std::vector<uint32> bigSeed;
313	gezelter	382
314	gezelter	507	// First try getting an array from /dev/urandom
315			FILE* urandom = fopen( "/dev/urandom", "rb" );
316			if( urandom )
317			{
318			bigSeed.resize(N);
319			register uint32 *s = &bigSeed[0];
320			register int i = N;
321			register bool success = true;
322			while( success && i-- )
323			success = fread( s++, sizeof(uint32), 1, urandom );
324			fclose(urandom);
325			if( success ) { return bigSeed; }
326			}
327	gezelter	382
328	gezelter	507	// Was not successful, so use time() and clock() instead
329	gezelter	382
330	gezelter	507	bigSeed.push_back(hash( time(NULL), clock()));
331			return bigSeed;
332			}
333	gezelter	382
334
335	gezelter	507	inline void MTRand::initialize( const uint32 seed )
336			{
337			// Initialize generator state with seed
338			// See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
339			// In previous versions, most significant bits (MSBs) of the seed affect
340			// only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto.
341			register uint32 *s = state;
342			register uint32 *r = state;
343			register int i = 1;
344			*s++ = seed & 0xffffffffUL;
345			for( ; i < N; ++i )
346			{
347			s++ = ( 1812433253UL ( r ^ (r >> 30) ) + i ) & 0xffffffffUL;
348			r++;
349			}
350			}
351	tim	380
352
353	gezelter	507	inline void MTRand::reload()
354			{
355			// Generate N new values in state
356			// Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
357			register uint32 *p = state;
358			register int i;
359			for( i = N - M; i--; ++p )
360			*p = twist( p[M], p[0], p[1] );
361			for( i = M; --i; ++p )
362			*p = twist( p[M-N], p[0], p[1] );
363			*p = twist( p[M-N], p[0], state[0] );
364	tim	380
365	gezelter	507	left = N, pNext = state;
366			}
367	tim	380
368
369	gezelter	507	inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
370			{
371			// Get a uint32 from t and c
372			// Better than uint32(x) in case x is floating point in [0,1]
373			// Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)
374	tim	380
375	gezelter	507	static uint32 differ = 0; // guarantee time-based seeds will change
376	tim	380
377	gezelter	507	uint32 h1 = 0;
378			unsigned char p = (unsigned char ) &t;
379			for( size_t i = 0; i < sizeof(t); ++i )
380			{
381			h1 *= UCHAR_MAX + 2U;
382			h1 += p[i];
383			}
384			uint32 h2 = 0;
385			p = (unsigned char *) &c;
386			for( size_t j = 0; j < sizeof(c); ++j )
387			{
388			h2 *= UCHAR_MAX + 2U;
389			h2 += p[j];
390			}
391			return ( h1 + differ++ ) ^ h2;
392			}
393	tim	380
394
395	gezelter	507	inline void MTRand::save( uint32* saveArray ) const
396			{
397			register uint32 *sa = saveArray;
398			register const uint32 *s = state;
399			register int i = N;
400			for( ; i--; sa++ = s++ ) {}
401			*sa = left;
402			}
403	tim	380
404
405	gezelter	507	inline void MTRand::load( uint32 *const loadArray )
406			{
407			register uint32 *s = state;
408			register uint32 *la = loadArray;
409			register int i = N;
410			for( ; i--; s++ = la++ ) {}
411			left = *la;
412			pNext = &state[N-left];
413			}
414	tim	380
415
416	gezelter	507	inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
417			{
418			register const MTRand::uint32 *s = mtrand.state;
419			register int i = mtrand.N;
420			for( ; i--; os << *s++ << "\t" ) {}
421			return os << mtrand.left;
422			}
423	tim	380
424
425	gezelter	507	inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
426			{
427			register MTRand::uint32 *s = mtrand.state;
428			register int i = mtrand.N;
429			for( ; i--; is >> *s++ ) {}
430			is >> mtrand.left;
431			mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
432			return is;
433			}
434	tim	380
435	tim	384	}
436	tim	380	#endif // MERSENNETWISTER_H
437
438			// Change log:
439			//
440			// v0.1 - First release on 15 May 2000
441			// - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
442			// - Translated from C to C++
443			// - Made completely ANSI compliant
444			// - Designed convenient interface for initialization, seeding, and
445			// obtaining numbers in default or user-defined ranges
446			// - Added automatic seeding from /dev/urandom or time() and clock()
447			// - Provided functions for saving and loading generator state
448			//
449			// v0.2 - Fixed bug which reloaded generator one step too late
450			//
451			// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
452			//
453			// v0.4 - Removed trailing newline in saved generator format to be consistent
454			// with output format of built-in types
455			//
456			// v0.5 - Improved portability by replacing static const int's with enum's and
457			// clarifying return values in seed(); suggested by Eric Heimburg
458			// - Removed MAXINT constant; use 0xffffffffUL instead
459			//
460			// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
461			// - Changed integer [0,n] generator to give better uniformity
462			//
463			// v0.7 - Fixed operator precedence ambiguity in reload()
464			// - Added access for real numbers in (0,1) and (0,n)
465			//
466			// v0.8 - Included time.h header to properly support time_t and clock_t
467			//
468			// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
469			// - Allowed for seeding with arrays of any length
470			// - Added access for real numbers in [0,1) with 53-bit resolution
471			// - Added access for real numbers from normal (Gaussian) distributions
472			// - Increased overall speed by optimizing twist()
473			// - Doubled speed of integer [0,n] generation
474			// - Fixed out-of-range number generation on 64-bit machines
475			// - Improved portability by substituting literal constants for long enum's
476			// - Changed license from GNU LGPL to BSD