// 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 v0.6 14 February 2001 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) 2001 Richard J. Wagner
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
// The original code included the following notice:
//
// Copyright (C) 1997, 1999 Makoto Matsumoto and Takuji Nishimura.
// 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 <stdio.h>
#include <ctime>
#include <climits>
#include <iostream>
using namespace std;
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
enum { MAGIC = 0x9908b0dfU }; // magic constant
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 ); // initialize with an array of N uint32's
MTRand(); // auto-initialize with /dev/urandom or time() and clock()
// Access to 32-bit random numbers
// Do NOT use for CRYPTOGRAPHY without securely hashing several returned
// values together, otherwise the generator state can be learned after
// reading 624 consecutive values.
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)
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()
// Re-seeding functions with same behavior as initializers
void seed( uint32 oneSeed );
void seed( uint32 *const bigSeed );
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 ostream& operator<<( ostream& os, const MTRand& mtrand );
friend istream& operator>>( istream& is, MTRand& mtrand );
protected:
void reload();
uint32 hiBit( const uint32& u ) const { return u & 0x80000000U; }
uint32 loBit( const uint32& u ) const { return u & 0x00000001U; }
uint32 loBits( const uint32& u ) const { return u & 0x7fffffffU; }
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) ? MAGIC : 0U); }
static uint32 hash( time_t t, clock_t c );
};
inline MTRand::MTRand( const uint32& oneSeed )
{ seed(oneSeed); }
inline MTRand::MTRand( uint32 *const bigSeed )
{ seed(bigSeed); }
inline MTRand::MTRand()
{ seed(); }
inline double MTRand::rand()
{ return double(randInt()) * 2.3283064370807974e-10; }
inline double MTRand::rand( const double& n )
{ return rand() * n; }
inline double MTRand::randExc()
{ return double(randInt()) * 2.3283064365386963e-10; }
inline double MTRand::randExc( const double& n )
{ return randExc() * n; }
inline MTRand::uint32 MTRand::randInt()
{
if( left == 0 ) reload();
--left;
register uint32 s1;
s1 = *pNext++;
s1 ^= (s1 >> 11);
s1 ^= (s1 << 7) & 0x9d2c5680U;
s1 ^= (s1 << 15) & 0xefc60000U;
return ( s1 ^ (s1 >> 18) );
}
inline MTRand::uint32 MTRand::randInt( const uint32& n )
{
// Find which bits are used in n
uint32 used = ~0;
for( uint32 m = n; m; used <<= 1, m >>= 1 ) {}
used = ~used;
// 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( uint32 oneSeed )
{
// Seed the generator with a simple uint32
register uint32 *s;
register int i;
for( i = N, s = state;
i--;
*s = oneSeed & 0xffff0000,
*s++ |= ( (oneSeed *= 69069U)++ & 0xffff0000 ) >> 16,
(oneSeed *= 69069U)++ ) {} // hard to read, but fast
reload();
}
inline void MTRand::seed( uint32 *const bigSeed )
{
// Seed the generator with an array of 624 uint32's
// There are 2^19937-1 possible initial states. This function allows
// any one of those to be chosen by providing 19937 bits. The lower
// 31 bits of the first element, bigSeed[0], are discarded. Any bits
// above the lower 32 in each element are also discarded. Theoretically,
// the rest of the array can contain any values except all zeroes.
// Just call seed() if you want to get array from /dev/urandom
register uint32 *s = state, *b = bigSeed;
register int i = N;
for( ; i--; *s++ = *b++ & 0xffffffff ) {}
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 )
{
register uint32 *s = state;
register int i = N;
register bool success = true;
while( success && i-- )
{
success = fread( s, sizeof(uint32), 1, urandom );
*s++ &= 0xffffffff; // filter in case uint32 > 32 bits
}
fclose(urandom);
if( success )
{
// There is a 1 in 2^19937 chance that a working urandom gave
// 19937 consecutive zeroes and will make the generator fail
// Ignore that case and continue with initialization
reload();
return;
}
}
// Was not successful, so use time() and clock() instead
seed( hash( time(NULL), clock() ) );
}
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++ = twist( p[M], p[0], p[1] );
for( i = M; --i; )
*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 ostream& operator<<( 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 istream& operator>>( 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 0xffffffff instead
//
// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
// - Changed integer [0,n] generator to give better uniformity
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