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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;
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 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