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>

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, nstrides = 1, stride = 0);  // initialize with a simple uint32
        MTRand( uint32 *const bigSeed, uint32 const seedLength = N, nstrides = 1, stride = 0);  // or an array
        MTRand(nstrides = 1, stride = 0);  // 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]
        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();
        
        // 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);
}

inline MTRand::uint32 MTRand::randInt()
{
        // Pull a 32-bit integer from the generator state
        // Every other access function simply transforms the numbers extracted here

        uint32 ranNums[nstrides];

        for (int i = 0; i < nstrides; ++i) {
            if( left == 0 ) {
                reload();
            }
            
            --left;

            register uint32 s1;
            s1 = *pNext++;
            s1 ^= (s1 >> 11);
            s1 ^= (s1 <<  7) & 0x9d2c5680UL;
            s1 ^= (s1 << 15) & 0xefc60000UL;
            ranNums[i] = s1 ^ (s1 >> 18) );
        }

        return ranNums[stride];
}

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()
{
        // Seed the generator with an array from /dev/urandom if available
        // Otherwise use a hash of time() and clock() values
        
        // First try getting an array from /dev/urandom
        FILE* urandom = fopen( "/dev/urandom", "rb" );
        if( urandom )
        {
                uint32 bigSeed[N];
                register uint32 *s = bigSeed;
                register int i = N;
                register bool success = true;
                while( success && i-- )
                        success = fread( s++, sizeof(uint32), 1, urandom );
                fclose(urandom);
                if( success ) { seed( bigSeed, N );  return; }
        }
        
        // Was not successful, so use time() and clock() instead
        seed( hash( time(NULL), clock() ) );
}


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:	2064
Committed:	Tue Mar 1 03:55:13 2005 UTC (19 years, 4 months ago) by tim
File size:	14861 byte(s)
Log Message:	Adding a modified version of MersenneTwister.hpp
#	User	Rev	Content
1	tim	2064	// 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
70			class MTRand {
71			// Data
72			public:
73			typedef unsigned long uint32; // unsigned integer type, at least 32 bits
74
75			enum { N = 624 }; // length of state vector
76			enum { SAVE = N + 1 }; // length of array for save()
77
78			private:
79			enum { M = 397 }; // period parameter
80
81			uint32 state[N]; // internal state
82			uint32 *pNext; // next value to get from state
83			int left; // number of values left before reload needed
84			int nstrides_;
85			int stride_;
86
87			//Methods
88			public:
89			MTRand( const uint32& oneSeed, nstrides = 1, stride = 0); // initialize with a simple uint32
90			MTRand( uint32 *const bigSeed, uint32 const seedLength = N, nstrides = 1, stride = 0); // or an array
91			MTRand(nstrides = 1, stride = 0); // auto-initialize with /dev/urandom or time() and clock()
92
93			// Do NOT use for CRYPTOGRAPHY without securely hashing several returned
94			// values together, otherwise the generator state can be learned after
95			// reading 624 consecutive values.
96
97			// Access to 32-bit random numbers
98			double rand(); // real number in [0,1]
99			double rand( const double& n ); // real number in [0,n]
100			double randExc(); // real number in [0,1)
101			double randExc( const double& n ); // real number in [0,n)
102			double randDblExc(); // real number in (0,1)
103			double randDblExc( const double& n ); // real number in (0,n)
104			uint32 randInt(); // integer in [0,2^32-1]
105			uint32 randInt( const uint32& n ); // integer in [0,n] for n < 2^32
106			double operator()() { return rand(); } // same as rand()
107
108			// Access to 53-bit random numbers (capacity of IEEE double precision)
109			double rand53(); // real number in [0,1)
110
111			// Access to nonuniform random number distributions
112			double randNorm( const double& mean = 0.0, const double& variance = 0.0 );
113
114			// Re-seeding functions with same behavior as initializers
115			void seed( const uint32 oneSeed );
116			void seed( uint32 *const bigSeed, const uint32 seedLength = N );
117			void seed();
118
119			// Saving and loading generator state
120			void save( uint32* saveArray ) const; // to array of size SAVE
121			void load( uint32 *const loadArray ); // from such array
122			friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
123			friend std::istream& operator>>( std::istream& is, MTRand& mtrand );
124
125			protected:
126			void initialize( const uint32 oneSeed );
127			void reload();
128			uint32 hiBit( const uint32& u ) const { return u & 0x80000000UL; }
129			uint32 loBit( const uint32& u ) const { return u & 0x00000001UL; }
130			uint32 loBits( const uint32& u ) const { return u & 0x7fffffffUL; }
131			uint32 mixBits( const uint32& u, const uint32& v ) const
132			{ return hiBit(u) \| loBits(v); }
133			uint32 twist( const uint32& m, const uint32& s0, const uint32& s1 ) const
134			{ return m ^ (mixBits(s0,s1)>>1) ^ (-loBit(s1) & 0x9908b0dfUL); }
135			static uint32 hash( time_t t, clock_t c );
136			};
137
138
139			inline MTRand::MTRand( const uint32& oneSeed, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
140			assert(stride_ < nstrides_ && stride_ >= 0);
141			seed(oneSeed);
142			}
143
144			inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength, int nstrides, int stride) : nstrides_(nstrides), stride_(stride) {
145			assert(stride_ < nstrides_ && stride_ >= 0);
146			seed(bigSeed,seedLength);
147			}
148
149			inline MTRand::MTRand(int nstrides, int stride) : nstrides_(nstrides), stride_(stride){
150			assert(stride_ < nstrides_ && stride_ >= 0);
151			seed();
152			}
153
154			inline double MTRand::rand()
155			{ return double(randInt()) * (1.0/4294967295.0); }
156
157			inline double MTRand::rand( const double& n )
158			{ return rand() * n; }
159
160			inline double MTRand::randExc()
161			{ return double(randInt()) * (1.0/4294967296.0); }
162
163			inline double MTRand::randExc( const double& n )
164			{ return randExc() * n; }
165
166			inline double MTRand::randDblExc()
167			{ return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }
168
169			inline double MTRand::randDblExc( const double& n )
170			{ return randDblExc() * n; }
171
172			inline double MTRand::rand53()
173			{
174			uint32 a = randInt() >> 5, b = randInt() >> 6;
175			return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0); // by Isaku Wada
176			}
177
178			inline double MTRand::randNorm( const double& mean, const double& variance )
179			{
180			// Return a real number from a normal (Gaussian) distribution with given
181			// mean and variance by Box-Muller method
182			double r = sqrt( -2.0 * log( 1.0-randDblExc()) ) * variance;
183			double phi = 2.0 * 3.14159265358979323846264338328 * randExc();
184			return mean + r * cos(phi);
185			}
186
187			inline MTRand::uint32 MTRand::randInt()
188			{
189			// Pull a 32-bit integer from the generator state
190			// Every other access function simply transforms the numbers extracted here
191
192			uint32 ranNums[nstrides];
193
194			for (int i = 0; i < nstrides; ++i) {
195			if( left == 0 ) {
196			reload();
197			}
198
199			--left;
200
201			register uint32 s1;
202			s1 = *pNext++;
203			s1 ^= (s1 >> 11);
204			s1 ^= (s1 << 7) & 0x9d2c5680UL;
205			s1 ^= (s1 << 15) & 0xefc60000UL;
206			ranNums[i] = s1 ^ (s1 >> 18) );
207			}
208
209			return ranNums[stride];
210			}
211
212			inline MTRand::uint32 MTRand::randInt( const uint32& n )
213			{
214			// Find which bits are used in n
215			// Optimized by Magnus Jonsson (magnus@smartelectronix.com)
216			uint32 used = n;
217			used \|= used >> 1;
218			used \|= used >> 2;
219			used \|= used >> 4;
220			used \|= used >> 8;
221			used \|= used >> 16;
222
223			// Draw numbers until one is found in [0,n]
224			uint32 i;
225			do
226			i = randInt() & used; // toss unused bits to shorten search
227			while( i > n );
228			return i;
229			}
230
231
232			inline void MTRand::seed( const uint32 oneSeed )
233			{
234			// Seed the generator with a simple uint32
235			initialize(oneSeed);
236			reload();
237			}
238
239
240			inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
241			{
242			// Seed the generator with an array of uint32's
243			// There are 2^19937-1 possible initial states. This function allows
244			// all of those to be accessed by providing at least 19937 bits (with a
245			// default seed length of N = 624 uint32's). Any bits above the lower 32
246			// in each element are discarded.
247			// Just call seed() if you want to get array from /dev/urandom
248			initialize(19650218UL);
249			register int i = 1;
250			register uint32 j = 0;
251			register int k = ( N > seedLength ? N : seedLength );
252			for( ; k; --k )
253			{
254			state[i] =
255			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
256			state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
257			state[i] &= 0xffffffffUL;
258			++i; ++j;
259			if( i >= N ) { state[0] = state[N-1]; i = 1; }
260			if( j >= seedLength ) j = 0;
261			}
262			for( k = N - 1; k; --k )
263			{
264			state[i] =
265			state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
266			state[i] -= i;
267			state[i] &= 0xffffffffUL;
268			++i;
269			if( i >= N ) { state[0] = state[N-1]; i = 1; }
270			}
271			state[0] = 0x80000000UL; // MSB is 1, assuring non-zero initial array
272			reload();
273			}
274
275
276			inline void MTRand::seed()
277			{
278			// Seed the generator with an array from /dev/urandom if available
279			// Otherwise use a hash of time() and clock() values
280
281			// First try getting an array from /dev/urandom
282			FILE* urandom = fopen( "/dev/urandom", "rb" );
283			if( urandom )
284			{
285			uint32 bigSeed[N];
286			register uint32 *s = bigSeed;
287			register int i = N;
288			register bool success = true;
289			while( success && i-- )
290			success = fread( s++, sizeof(uint32), 1, urandom );
291			fclose(urandom);
292			if( success ) { seed( bigSeed, N ); return; }
293			}
294
295			// Was not successful, so use time() and clock() instead
296			seed( hash( time(NULL), clock() ) );
297			}
298
299
300			inline void MTRand::initialize( const uint32 seed )
301			{
302			// Initialize generator state with seed
303			// See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
304			// In previous versions, most significant bits (MSBs) of the seed affect
305			// only MSBs of the state array. Modified 9 Jan 2002 by Makoto Matsumoto.
306			register uint32 *s = state;
307			register uint32 *r = state;
308			register int i = 1;
309			*s++ = seed & 0xffffffffUL;
310			for( ; i < N; ++i )
311			{
312			s++ = ( 1812433253UL ( r ^ (r >> 30) ) + i ) & 0xffffffffUL;
313			r++;
314			}
315			}
316
317
318			inline void MTRand::reload()
319			{
320			// Generate N new values in state
321			// Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
322			register uint32 *p = state;
323			register int i;
324			for( i = N - M; i--; ++p )
325			*p = twist( p[M], p[0], p[1] );
326			for( i = M; --i; ++p )
327			*p = twist( p[M-N], p[0], p[1] );
328			*p = twist( p[M-N], p[0], state[0] );
329
330			left = N, pNext = state;
331			}
332
333
334			inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
335			{
336			// Get a uint32 from t and c
337			// Better than uint32(x) in case x is floating point in [0,1]
338			// Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)
339
340			static uint32 differ = 0; // guarantee time-based seeds will change
341
342			uint32 h1 = 0;
343			unsigned char p = (unsigned char ) &t;
344			for( size_t i = 0; i < sizeof(t); ++i )
345			{
346			h1 *= UCHAR_MAX + 2U;
347			h1 += p[i];
348			}
349			uint32 h2 = 0;
350			p = (unsigned char *) &c;
351			for( size_t j = 0; j < sizeof(c); ++j )
352			{
353			h2 *= UCHAR_MAX + 2U;
354			h2 += p[j];
355			}
356			return ( h1 + differ++ ) ^ h2;
357			}
358
359
360			inline void MTRand::save( uint32* saveArray ) const
361			{
362			register uint32 *sa = saveArray;
363			register const uint32 *s = state;
364			register int i = N;
365			for( ; i--; sa++ = s++ ) {}
366			*sa = left;
367			}
368
369
370			inline void MTRand::load( uint32 *const loadArray )
371			{
372			register uint32 *s = state;
373			register uint32 *la = loadArray;
374			register int i = N;
375			for( ; i--; s++ = la++ ) {}
376			left = *la;
377			pNext = &state[N-left];
378			}
379
380
381			inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
382			{
383			register const MTRand::uint32 *s = mtrand.state;
384			register int i = mtrand.N;
385			for( ; i--; os << *s++ << "\t" ) {}
386			return os << mtrand.left;
387			}
388
389
390			inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
391			{
392			register MTRand::uint32 *s = mtrand.state;
393			register int i = mtrand.N;
394			for( ; i--; is >> *s++ ) {}
395			is >> mtrand.left;
396			mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
397			return is;
398			}
399
400			#endif // MERSENNETWISTER_H
401
402			// Change log:
403			//
404			// v0.1 - First release on 15 May 2000
405			// - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
406			// - Translated from C to C++
407			// - Made completely ANSI compliant
408			// - Designed convenient interface for initialization, seeding, and
409			// obtaining numbers in default or user-defined ranges
410			// - Added automatic seeding from /dev/urandom or time() and clock()
411			// - Provided functions for saving and loading generator state
412			//
413			// v0.2 - Fixed bug which reloaded generator one step too late
414			//
415			// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
416			//
417			// v0.4 - Removed trailing newline in saved generator format to be consistent
418			// with output format of built-in types
419			//
420			// v0.5 - Improved portability by replacing static const int's with enum's and
421			// clarifying return values in seed(); suggested by Eric Heimburg
422			// - Removed MAXINT constant; use 0xffffffffUL instead
423			//
424			// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
425			// - Changed integer [0,n] generator to give better uniformity
426			//
427			// v0.7 - Fixed operator precedence ambiguity in reload()
428			// - Added access for real numbers in (0,1) and (0,n)
429			//
430			// v0.8 - Included time.h header to properly support time_t and clock_t
431			//
432			// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
433			// - Allowed for seeding with arrays of any length
434			// - Added access for real numbers in [0,1) with 53-bit resolution
435			// - Added access for real numbers from normal (Gaussian) distributions
436			// - Increased overall speed by optimizing twist()
437			// - Doubled speed of integer [0,n] generation
438			// - Fixed out-of-range number generation on 64-bit machines
439			// - Improved portability by substituting literal constants for long enum's
440			// - Changed license from GNU LGPL to BSD