424 lines
14 KiB
C++
424 lines
14 KiB
C++
// 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 = 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 )
|
|
{ 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 = ( 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
|