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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.
-
-#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 UInt32 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
- uint32 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.
- uint32 *s = state;
- uint32 *r = state;
- uint32 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
- uint32 *p = state;
- 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);
- uint32 i = 1;
- uint32 j = 0;
- uint32 k = ( (uint32)N > seedLength ? (uint32)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
-
- /* // Commented out by FakeTruth because doing this 200 times a tick is SUUUUPEERRR SLOW!!~~!\D5Ne
- 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 )
-{
- const uint32 *t = o.state;
- uint32 *s = state;
- 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;
-
- 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
-{
- const uint32 *s = state;
- uint32 *sa = saveArray;
- int i = N;
- for( ; i--; *sa++ = *s++ ) {}
- *sa = left;
-}
-
-inline void MTRand::load( uint32 *const loadArray )
-{
- uint32 *s = state;
- uint32 *la = loadArray;
- int i = N;
- for( ; i--; *s++ = *la++ ) {}
- left = *la;
- pNext = &state[N-left];
-}
-
-inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
-{
- const MTRand::uint32 *s = mtrand.state;
- int i = mtrand.N;
- for( ; i--; os << *s++ << "\t" ) {}
- return os << mtrand.left;
-}
-
-inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
-{
- MTRand::uint32 *s = mtrand.state;
- 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);
- const uint32 *t = o.state;
- uint32 *s = state;
- 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
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