pymt: MersenneTwister.h comparison

comparison MersenneTwister.h @ 0:0fa810263337

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author	Peter Meerwald <pmeerw@cosy.sbg.ac.at>
date	Thu, 06 Sep 2007 13:58:46 +0200
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+:0fa810263337
+// 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

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comparison MersenneTwister.h @ 0:0fa810263337