Good Random Number generator rutine for print map

include/MersenneTwister.h

+// 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