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+/**
+ * 2Geom developers:
+ * For licence reasons, Do not copy code from this header into other files
+ * */
+// 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 <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()
+
+ 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 an array
+ MTRand(); // 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 = 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 );
+
+ 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 )
+{ seed(oneSeed); }
+
+inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
+{ seed(bigSeed,seedLength); }
+
+inline MTRand::MTRand()
+{ 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
+
+ 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 = ( 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
+ 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
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