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diff --git a/src/MersenneTwister.h b/src/MersenneTwister.h new file mode 100644 index 000000000..dc7134a93 --- /dev/null +++ b/src/MersenneTwister.h @@ -0,0 +1,456 @@ +// 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 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 + + /* // Commented out by FakeTruth because doing this 200 times a tick is SUUUUPEERRR SLOW!!~~!ÕNe + 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 |