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// 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  v1.1  28 September 2009  wagnerr@umich.edu

// 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.sci.hiroshima-u.ac.jp/~m-mat/MT/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 - 2009, 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: m-mat@math.sci.hiroshima-u.ac.jp

//     with an appropriate reference to your work.

// 

// It would be nice to CC: wagnerr@umich.edu 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 <iostream>

#include <climits>

#include <cstdio>

#include <ctime>

#include <cmath>

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()

protected:

        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

// Methods

public:

        MTRand( const uint32 oneSeed );  // initialize with a simple uint32

        MTRand( uint32 *const bigSeed, uint32 const seedLength = N );  // or array

        MTRand();  // auto-initialize with /dev/urandom or time() and clock()

        MTRand( const MTRand& o );  // copy

        // 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

        uint32 randInt();                     // integer in [0,2^32-1]

        uint32 randInt( const uint32 n );     // integer in [0,n] for n < 2^32

        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)

        double operator()();                  // 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 stddev = 1.0 );

        // 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 );

        MTRand& operator=( const MTRand& o );

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 magic( const uint32 u ) const

                { return loBit(u) ? 0x9908b0dfUL : 0x0UL; }

        uint32 twist( const uint32 m, const uint32 s0, const uint32 s1 ) const

                { return m ^ (mixBits(s0,s1)>>1) ^ magic(s1); }

        static uint32 hash( time_t t, clock_t c );

};

// Functions are defined in order of usage to assist inlining

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::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)

        static const int MmN = int(M) - int(N);  // in case enums are unsigned

        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[MmN], p[0], p[1] );

        *p = twist( p[MmN], p[0], state[0] );

        left = N, pNext = state;

}

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;

    // orig: register int k = ( N > seedLength ? N : seedLength );

    register int k = ( uint32(N) > seedLength ? uint32(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

#if defined(Q_CC_INTEL) || defined(Q_CC_GNU)

    FILE* urandom = fopen( "/dev/urandom", "rb" );

#else

    FILE* urandom;

    fopen_s(&urandom, "/dev/urandom", "rb" );

#endif

        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 MTRand::MTRand( const uint32 oneSeed )

        { seed(oneSeed); }

inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )

        { seed(bigSeed,seedLength); }

inline MTRand::MTRand()

        { seed(); }

inline MTRand::MTRand( const MTRand& o )

{

        register const uint32 *t = o.state;

        register uint32 *s = state;

        register int i = N;

        for( ; i--; *s++ = *t++ ) {}

        left = o.left;

        pNext = &state[N-left];

}

inline MTRand::uint32 MTRand::randInt()

{

        // 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 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 stddev )

{

        // Return a real number from a normal (Gaussian) distribution with given

        // mean and standard deviation by polar form of Box-Muller transformation

        double x, y, r;

        do

        {

                x = 2.0 * rand() - 1.0;

                y = 2.0 * rand() - 1.0;

                r = x * x + y * y;

        }

        while ( r >= 1.0 || r == 0.0 );

        double s = sqrt( -2.0 * log(r) / r );

        return mean + x * s * stddev;

}

inline double MTRand::operator()()

{

        return rand();

}

inline void MTRand::save( uint32* saveArray ) const

{

        register const uint32 *s = state;

        register uint32 *sa = saveArray;

        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;

}

inline MTRand& MTRand::operator=( const MTRand& o )

{

        if( this == &o ) return (*this);

        register const uint32 *t = o.state;

        register uint32 *s = state;

        register int i = N;

        for( ; i--; *s++ = *t++ ) {}

        left = o.left;

        pNext = &state[N-left];

        return (*this);

}

#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

//

// v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"

//      - Changed randNorm algorithm from basic to polar form for efficiency

//      - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms

//      - Cleaned declarations and definitions to please Intel compiler

//      - Revised twist() operator to work on ones'-complement machines

//      - Fixed reload() function to work when N and M are unsigned

//      - Added copy constructor and copy operator from Salvador Espana