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/* -*- C++ -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library
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*
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* Copyright (C) 2003-2008
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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/*
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* This file contains the reimplemented version of the Mersenne Twister
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* Generator of Matsumoto and Nishimura.
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*
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* See the appropriate copyright notice below.
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*
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* Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* 3. The names of its contributors may not be used to endorse or promote
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* products derived from this software without specific prior written
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* permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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*
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* Any feedback is very welcome.
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* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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* email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
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*/
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#ifndef LEMON_RANDOM_H
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#define LEMON_RANDOM_H
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#include <algorithm>
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#include <iterator>
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#include <vector>
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#include <limits>
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#include <fstream>
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#include <lemon/math.h>
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#include <lemon/dim2.h>
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#ifndef WIN32
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#include <sys/time.h>
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#include <ctime>
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#include <sys/types.h>
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#include <unistd.h>
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#else
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#include <windows.h>
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#endif
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///\ingroup misc
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///\file
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///\brief Mersenne Twister random number generator
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namespace lemon {
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namespace _random_bits {
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template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
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struct RandomTraits {};
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template <typename _Word>
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struct RandomTraits<_Word, 32> {
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typedef _Word Word;
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static const int bits = 32;
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static const int length = 624;
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static const int shift = 397;
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static const Word mul = 0x6c078965u;
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static const Word arrayInit = 0x012BD6AAu;
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static const Word arrayMul1 = 0x0019660Du;
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static const Word arrayMul2 = 0x5D588B65u;
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107 |
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static const Word mask = 0x9908B0DFu;
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static const Word loMask = (1u << 31) - 1;
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static const Word hiMask = ~loMask;
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static Word tempering(Word rnd) {
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rnd ^= (rnd >> 11);
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rnd ^= (rnd << 7) & 0x9D2C5680u;
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rnd ^= (rnd << 15) & 0xEFC60000u;
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rnd ^= (rnd >> 18);
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return rnd;
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}
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};
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template <typename _Word>
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struct RandomTraits<_Word, 64> {
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typedef _Word Word;
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static const int bits = 64;
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static const int length = 312;
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static const int shift = 156;
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static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
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static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
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static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
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static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
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136 |
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static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
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static const Word loMask = (Word(1u) << 31) - 1;
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static const Word hiMask = ~loMask;
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static Word tempering(Word rnd) {
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rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
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rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
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rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
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rnd ^= (rnd >> 43);
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return rnd;
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}
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148 |
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};
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template <typename _Word>
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class RandomCore {
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public:
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typedef _Word Word;
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private:
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158 |
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static const int bits = RandomTraits<Word>::bits;
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160 |
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static const int length = RandomTraits<Word>::length;
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static const int shift = RandomTraits<Word>::shift;
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public:
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165 |
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void initState() {
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static const Word seedArray[4] = {
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0x12345u, 0x23456u, 0x34567u, 0x45678u
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};
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initState(seedArray, seedArray + 4);
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}
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void initState(Word seed) {
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175 |
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static const Word mul = RandomTraits<Word>::mul;
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current = state;
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| ... |
... |
@@ -433,375 +443,460 @@
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}
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static void init(RandomCore<Word>& rnd, Result seed) {
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rnd.initState(seed);
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}
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};
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template <typename Word>
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struct BoolConversion {
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static bool convert(RandomCore<Word>& rnd) {
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return (rnd() & 1) == 1;
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454 |
}
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455 |
};
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template <typename Word>
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struct BoolProducer {
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Word buffer;
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int num;
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461 |
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BoolProducer() : num(0) {}
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463 |
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bool convert(RandomCore<Word>& rnd) {
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465 |
if (num == 0) {
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buffer = rnd();
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467 |
num = RandomTraits<Word>::bits;
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468 |
}
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469 |
bool r = (buffer & 1);
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470 |
buffer >>= 1;
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--num;
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return r;
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473 |
}
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| 464 |
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};
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}
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477 |
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/// \ingroup misc
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479 |
///
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/// \brief Mersenne Twister random number generator
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| 471 |
481 |
///
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| 472 |
482 |
/// The Mersenne Twister is a twisted generalized feedback
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| 473 |
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/// shift-register generator of Matsumoto and Nishimura. The period
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| 474 |
484 |
/// of this generator is \f$ 2^{19937} - 1 \f$ and it is
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| 475 |
485 |
/// equi-distributed in 623 dimensions for 32-bit numbers. The time
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| 476 |
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/// performance of this generator is comparable to the commonly used
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| 477 |
487 |
/// generators.
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| 478 |
488 |
///
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| 479 |
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/// This implementation is specialized for both 32-bit and 64-bit
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| 480 |
490 |
/// architectures. The generators differ sligthly in the
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| 481 |
491 |
/// initialization and generation phase so they produce two
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/// completly different sequences.
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| 483 |
493 |
///
|
| 484 |
494 |
/// The generator gives back random numbers of serveral types. To
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495 |
/// get a random number from a range of a floating point type you
|
| 486 |
496 |
/// can use one form of the \c operator() or the \c real() member
|
| 487 |
497 |
/// function. If you want to get random number from the {0, 1, ...,
|
| 488 |
498 |
/// n-1} integer range use the \c operator[] or the \c integer()
|
| 489 |
499 |
/// method. And to get random number from the whole range of an
|
| 490 |
500 |
/// integer type you can use the argumentless \c integer() or \c
|
| 491 |
501 |
/// uinteger() functions. After all you can get random bool with
|
| 492 |
502 |
/// equal chance of true and false or given probability of true
|
| 493 |
503 |
/// result with the \c boolean() member functions.
|
| 494 |
504 |
///
|
| 495 |
505 |
///\code
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| 496 |
506 |
/// // The commented code is identical to the other
|
| 497 |
507 |
/// double a = rnd(); // [0.0, 1.0)
|
| 498 |
508 |
/// // double a = rnd.real(); // [0.0, 1.0)
|
| 499 |
509 |
/// double b = rnd(100.0); // [0.0, 100.0)
|
| 500 |
510 |
/// // double b = rnd.real(100.0); // [0.0, 100.0)
|
| 501 |
511 |
/// double c = rnd(1.0, 2.0); // [1.0, 2.0)
|
| 502 |
512 |
/// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
|
| 503 |
513 |
/// int d = rnd[100000]; // 0..99999
|
| 504 |
514 |
/// // int d = rnd.integer(100000); // 0..99999
|
| 505 |
515 |
/// int e = rnd[6] + 1; // 1..6
|
| 506 |
516 |
/// // int e = rnd.integer(1, 1 + 6); // 1..6
|
| 507 |
517 |
/// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
|
| 508 |
518 |
/// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
|
| 509 |
519 |
/// bool g = rnd.boolean(); // P(g = true) = 0.5
|
| 510 |
520 |
/// bool h = rnd.boolean(0.8); // P(h = true) = 0.8
|
| 511 |
521 |
///\endcode
|
| 512 |
522 |
///
|
| 513 |
523 |
/// LEMON provides a global instance of the random number
|
| 514 |
524 |
/// generator which name is \ref lemon::rnd "rnd". Usually it is a
|
| 515 |
525 |
/// good programming convenience to use this global generator to get
|
| 516 |
526 |
/// random numbers.
|
| 517 |
527 |
class Random {
|
| 518 |
528 |
private:
|
| 519 |
529 |
|
| 520 |
530 |
// Architecture word
|
| 521 |
531 |
typedef unsigned long Word;
|
| 522 |
532 |
|
| 523 |
533 |
_random_bits::RandomCore<Word> core;
|
| 524 |
534 |
_random_bits::BoolProducer<Word> bool_producer;
|
| 525 |
535 |
|
| 526 |
536 |
|
| 527 |
537 |
public:
|
| 528 |
538 |
|
|
539 |
///\name Initialization
|
|
540 |
///
|
|
541 |
/// @{
|
|
542 |
|
|
543 |
///\name Initialization
|
|
544 |
///
|
|
545 |
/// @{
|
|
546 |
|
| 529 |
547 |
/// \brief Default constructor
|
| 530 |
548 |
///
|
| 531 |
549 |
/// Constructor with constant seeding.
|
| 532 |
550 |
Random() { core.initState(); }
|
| 533 |
551 |
|
| 534 |
552 |
/// \brief Constructor with seed
|
| 535 |
553 |
///
|
| 536 |
554 |
/// Constructor with seed. The current number type will be converted
|
| 537 |
555 |
/// to the architecture word type.
|
| 538 |
556 |
template <typename Number>
|
| 539 |
557 |
Random(Number seed) {
|
| 540 |
558 |
_random_bits::Initializer<Number, Word>::init(core, seed);
|
| 541 |
559 |
}
|
| 542 |
560 |
|
| 543 |
561 |
/// \brief Constructor with array seeding
|
| 544 |
562 |
///
|
| 545 |
563 |
/// Constructor with array seeding. The given range should contain
|
| 546 |
564 |
/// any number type and the numbers will be converted to the
|
| 547 |
565 |
/// architecture word type.
|
| 548 |
566 |
template <typename Iterator>
|
| 549 |
567 |
Random(Iterator begin, Iterator end) {
|
| 550 |
568 |
typedef typename std::iterator_traits<Iterator>::value_type Number;
|
| 551 |
569 |
_random_bits::Initializer<Number, Word>::init(core, begin, end);
|
| 552 |
570 |
}
|
| 553 |
571 |
|
| 554 |
572 |
/// \brief Copy constructor
|
| 555 |
573 |
///
|
| 556 |
574 |
/// Copy constructor. The generated sequence will be identical to
|
| 557 |
575 |
/// the other sequence. It can be used to save the current state
|
| 558 |
576 |
/// of the generator and later use it to generate the same
|
| 559 |
577 |
/// sequence.
|
| 560 |
578 |
Random(const Random& other) {
|
| 561 |
579 |
core.copyState(other.core);
|
| 562 |
580 |
}
|
| 563 |
581 |
|
| 564 |
582 |
/// \brief Assign operator
|
| 565 |
583 |
///
|
| 566 |
584 |
/// Assign operator. The generated sequence will be identical to
|
| 567 |
585 |
/// the other sequence. It can be used to save the current state
|
| 568 |
586 |
/// of the generator and later use it to generate the same
|
| 569 |
587 |
/// sequence.
|
| 570 |
588 |
Random& operator=(const Random& other) {
|
| 571 |
589 |
if (&other != this) {
|
| 572 |
590 |
core.copyState(other.core);
|
| 573 |
591 |
}
|
| 574 |
592 |
return *this;
|
| 575 |
593 |
}
|
| 576 |
594 |
|
| 577 |
595 |
/// \brief Seeding random sequence
|
| 578 |
596 |
///
|
| 579 |
597 |
/// Seeding the random sequence. The current number type will be
|
| 580 |
598 |
/// converted to the architecture word type.
|
| 581 |
599 |
template <typename Number>
|
| 582 |
600 |
void seed(Number seed) {
|
| 583 |
601 |
_random_bits::Initializer<Number, Word>::init(core, seed);
|
| 584 |
602 |
}
|
| 585 |
603 |
|
| 586 |
604 |
/// \brief Seeding random sequence
|
| 587 |
605 |
///
|
| 588 |
606 |
/// Seeding the random sequence. The given range should contain
|
| 589 |
607 |
/// any number type and the numbers will be converted to the
|
| 590 |
608 |
/// architecture word type.
|
| 591 |
609 |
template <typename Iterator>
|
| 592 |
610 |
void seed(Iterator begin, Iterator end) {
|
| 593 |
611 |
typedef typename std::iterator_traits<Iterator>::value_type Number;
|
| 594 |
612 |
_random_bits::Initializer<Number, Word>::init(core, begin, end);
|
| 595 |
613 |
}
|
| 596 |
614 |
|
|
615 |
/// \brief Seeding from file or from process id and time
|
|
616 |
///
|
|
617 |
/// By default, this function calls the \c seedFromFile() member
|
|
618 |
/// function with the <tt>/dev/urandom</tt> file. If it does not success,
|
|
619 |
/// it uses the \c seedFromTime().
|
|
620 |
/// \return Currently always true.
|
|
621 |
bool seed() {
|
|
622 |
#ifndef WIN32
|
|
623 |
if (seedFromFile("/dev/urandom", 0)) return true;
|
|
624 |
#endif
|
|
625 |
if (seedFromTime()) return true;
|
|
626 |
return false;
|
|
627 |
}
|
|
628 |
|
|
629 |
/// \brief Seeding from file
|
|
630 |
///
|
|
631 |
/// Seeding the random sequence from file. The linux kernel has two
|
|
632 |
/// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
|
|
633 |
/// could give good seed values for pseudo random generators (The
|
|
634 |
/// difference between two devices is that the <tt>random</tt> may
|
|
635 |
/// block the reading operation while the kernel can give good
|
|
636 |
/// source of randomness, while the <tt>urandom</tt> does not
|
|
637 |
/// block the input, but it could give back bytes with worse
|
|
638 |
/// entropy).
|
|
639 |
/// \param file The source file
|
|
640 |
/// \param offset The offset, from the file read.
|
|
641 |
/// \return True when the seeding successes.
|
|
642 |
#ifndef WIN32
|
|
643 |
bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
|
|
644 |
#else
|
|
645 |
bool seedFromFile(const std::string& file = "", int offset = 0)
|
|
646 |
#endif
|
|
647 |
{
|
|
648 |
std::ifstream rs(file.c_str());
|
|
649 |
const int size = 4;
|
|
650 |
Word buf[size];
|
|
651 |
if (offset != 0 && !rs.seekg(offset)) return false;
|
|
652 |
if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
|
|
653 |
seed(buf, buf + size);
|
|
654 |
return true;
|
|
655 |
}
|
|
656 |
|
|
657 |
/// \brief Seding from process id and time
|
|
658 |
///
|
|
659 |
/// Seding from process id and time. This function uses the
|
|
660 |
/// current process id and the current time for initialize the
|
|
661 |
/// random sequence.
|
|
662 |
/// \return Currently always true.
|
|
663 |
bool seedFromTime() {
|
|
664 |
#ifndef WIN32
|
|
665 |
timeval tv;
|
|
666 |
gettimeofday(&tv, 0);
|
|
667 |
seed(getpid() + tv.tv_sec + tv.tv_usec);
|
|
668 |
#else
|
|
669 |
FILETIME time;
|
|
670 |
GetSystemTimeAsFileTime(&time);
|
|
671 |
seed(GetCurrentProcessId() + time.dwHighDateTime + time.dwLowDateTime);
|
|
672 |
#endif
|
|
673 |
return true;
|
|
674 |
}
|
|
675 |
|
|
676 |
/// @}
|
|
677 |
|
|
678 |
///\name Uniform distributions
|
|
679 |
///
|
|
680 |
/// @{
|
|
681 |
|
| 597 |
682 |
/// \brief Returns a random real number from the range [0, 1)
|
| 598 |
683 |
///
|
| 599 |
684 |
/// It returns a random real number from the range [0, 1). The
|
| 600 |
685 |
/// default Number type is \c double.
|
| 601 |
686 |
template <typename Number>
|
| 602 |
687 |
Number real() {
|
| 603 |
688 |
return _random_bits::RealConversion<Number, Word>::convert(core);
|
| 604 |
689 |
}
|
| 605 |
690 |
|
| 606 |
691 |
double real() {
|
| 607 |
692 |
return real<double>();
|
| 608 |
693 |
}
|
| 609 |
694 |
|
| 610 |
695 |
/// \brief Returns a random real number the range [0, b)
|
| 611 |
696 |
///
|
| 612 |
697 |
/// It returns a random real number from the range [0, b).
|
| 613 |
698 |
template <typename Number>
|
| 614 |
699 |
Number real(Number b) {
|
| 615 |
700 |
return real<Number>() * b;
|
| 616 |
701 |
}
|
| 617 |
702 |
|
| 618 |
703 |
/// \brief Returns a random real number from the range [a, b)
|
| 619 |
704 |
///
|
| 620 |
705 |
/// It returns a random real number from the range [a, b).
|
| 621 |
706 |
template <typename Number>
|
| 622 |
707 |
Number real(Number a, Number b) {
|
| 623 |
708 |
return real<Number>() * (b - a) + a;
|
| 624 |
709 |
}
|
| 625 |
710 |
|
|
711 |
/// @}
|
|
712 |
|
|
713 |
///\name Uniform distributions
|
|
714 |
///
|
|
715 |
/// @{
|
|
716 |
|
| 626 |
717 |
/// \brief Returns a random real number from the range [0, 1)
|
| 627 |
718 |
///
|
| 628 |
719 |
/// It returns a random double from the range [0, 1).
|
| 629 |
720 |
double operator()() {
|
| 630 |
721 |
return real<double>();
|
| 631 |
722 |
}
|
| 632 |
723 |
|
| 633 |
724 |
/// \brief Returns a random real number from the range [0, b)
|
| 634 |
725 |
///
|
| 635 |
726 |
/// It returns a random real number from the range [0, b).
|
| 636 |
727 |
template <typename Number>
|
| 637 |
728 |
Number operator()(Number b) {
|
| 638 |
729 |
return real<Number>() * b;
|
| 639 |
730 |
}
|
| 640 |
731 |
|
| 641 |
732 |
/// \brief Returns a random real number from the range [a, b)
|
| 642 |
733 |
///
|
| 643 |
734 |
/// It returns a random real number from the range [a, b).
|
| 644 |
735 |
template <typename Number>
|
| 645 |
736 |
Number operator()(Number a, Number b) {
|
| 646 |
737 |
return real<Number>() * (b - a) + a;
|
| 647 |
738 |
}
|
| 648 |
739 |
|
| 649 |
740 |
/// \brief Returns a random integer from a range
|
| 650 |
741 |
///
|
| 651 |
742 |
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
| 652 |
743 |
template <typename Number>
|
| 653 |
744 |
Number integer(Number b) {
|
| 654 |
745 |
return _random_bits::Mapping<Number, Word>::map(core, b);
|
| 655 |
746 |
}
|
| 656 |
747 |
|
| 657 |
748 |
/// \brief Returns a random integer from a range
|
| 658 |
749 |
///
|
| 659 |
750 |
/// It returns a random integer from the range {a, a + 1, ..., b - 1}.
|
| 660 |
751 |
template <typename Number>
|
| 661 |
752 |
Number integer(Number a, Number b) {
|
| 662 |
753 |
return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
|
| 663 |
754 |
}
|
| 664 |
755 |
|
| 665 |
756 |
/// \brief Returns a random integer from a range
|
| 666 |
757 |
///
|
| 667 |
758 |
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
| 668 |
759 |
template <typename Number>
|
| 669 |
760 |
Number operator[](Number b) {
|
| 670 |
761 |
return _random_bits::Mapping<Number, Word>::map(core, b);
|
| 671 |
762 |
}
|
| 672 |
763 |
|
| 673 |
764 |
/// \brief Returns a random non-negative integer
|
| 674 |
765 |
///
|
| 675 |
766 |
/// It returns a random non-negative integer uniformly from the
|
| 676 |
767 |
/// whole range of the current \c Number type. The default result
|
| 677 |
768 |
/// type of this function is <tt>unsigned int</tt>.
|
| 678 |
769 |
template <typename Number>
|
| 679 |
770 |
Number uinteger() {
|
| 680 |
771 |
return _random_bits::IntConversion<Number, Word>::convert(core);
|
| 681 |
772 |
}
|
| 682 |
773 |
|
|
774 |
/// @}
|
|
775 |
|
| 683 |
776 |
unsigned int uinteger() {
|
| 684 |
777 |
return uinteger<unsigned int>();
|
| 685 |
778 |
}
|
| 686 |
779 |
|
| 687 |
780 |
/// \brief Returns a random integer
|
| 688 |
781 |
///
|
| 689 |
782 |
/// It returns a random integer uniformly from the whole range of
|
| 690 |
783 |
/// the current \c Number type. The default result type of this
|
| 691 |
784 |
/// function is \c int.
|
| 692 |
785 |
template <typename Number>
|
| 693 |
786 |
Number integer() {
|
| 694 |
787 |
static const int nb = std::numeric_limits<Number>::digits +
|
| 695 |
788 |
(std::numeric_limits<Number>::is_signed ? 1 : 0);
|
| 696 |
789 |
return _random_bits::IntConversion<Number, Word, nb>::convert(core);
|
| 697 |
790 |
}
|
| 698 |
791 |
|
| 699 |
792 |
int integer() {
|
| 700 |
793 |
return integer<int>();
|
| 701 |
794 |
}
|
| 702 |
795 |
|
| 703 |
796 |
/// \brief Returns a random bool
|
| 704 |
797 |
///
|
| 705 |
798 |
/// It returns a random bool. The generator holds a buffer for
|
| 706 |
799 |
/// random bits. Every time when it become empty the generator makes
|
| 707 |
800 |
/// a new random word and fill the buffer up.
|
| 708 |
801 |
bool boolean() {
|
| 709 |
802 |
return bool_producer.convert(core);
|
| 710 |
803 |
}
|
| 711 |
804 |
|
|
805 |
/// @}
|
|
806 |
|
| 712 |
807 |
///\name Non-uniform distributions
|
| 713 |
808 |
///
|
| 714 |
809 |
|
| 715 |
810 |
///@{
|
| 716 |
811 |
|
| 717 |
812 |
/// \brief Returns a random bool
|
| 718 |
813 |
///
|
| 719 |
814 |
/// It returns a random bool with given probability of true result.
|
| 720 |
815 |
bool boolean(double p) {
|
| 721 |
816 |
return operator()() < p;
|
| 722 |
817 |
}
|
| 723 |
818 |
|
| 724 |
819 |
/// Standard Gauss distribution
|
| 725 |
820 |
|
| 726 |
821 |
/// Standard Gauss distribution.
|
| 727 |
822 |
/// \note The Cartesian form of the Box-Muller
|
| 728 |
823 |
/// transformation is used to generate a random normal distribution.
|
| 729 |
824 |
/// \todo Consider using the "ziggurat" method instead.
|
| 730 |
825 |
double gauss()
|
| 731 |
826 |
{
|
| 732 |
827 |
double V1,V2,S;
|
| 733 |
828 |
do {
|
| 734 |
829 |
V1=2*real<double>()-1;
|
| 735 |
830 |
V2=2*real<double>()-1;
|
| 736 |
831 |
S=V1*V1+V2*V2;
|
| 737 |
832 |
} while(S>=1);
|
| 738 |
833 |
return std::sqrt(-2*std::log(S)/S)*V1;
|
| 739 |
834 |
}
|
| 740 |
835 |
/// Gauss distribution with given mean and standard deviation
|
| 741 |
836 |
|
| 742 |
837 |
/// Gauss distribution with given mean and standard deviation.
|
| 743 |
838 |
/// \sa gauss()
|
| 744 |
839 |
double gauss(double mean,double std_dev)
|
| 745 |
840 |
{
|
| 746 |
841 |
return gauss()*std_dev+mean;
|
| 747 |
842 |
}
|
| 748 |
843 |
|
| 749 |
844 |
/// Exponential distribution with given mean
|
| 750 |
845 |
|
| 751 |
846 |
/// This function generates an exponential distribution random number
|
| 752 |
847 |
/// with mean <tt>1/lambda</tt>.
|
| 753 |
848 |
///
|
| 754 |
849 |
double exponential(double lambda=1.0)
|
| 755 |
850 |
{
|
| 756 |
851 |
return -std::log(1.0-real<double>())/lambda;
|
| 757 |
852 |
}
|
| 758 |
853 |
|
| 759 |
854 |
/// Gamma distribution with given integer shape
|
| 760 |
855 |
|
| 761 |
856 |
/// This function generates a gamma distribution random number.
|
| 762 |
857 |
///
|
| 763 |
858 |
///\param k shape parameter (<tt>k>0</tt> integer)
|
| 764 |
859 |
double gamma(int k)
|
| 765 |
860 |
{
|
| 766 |
861 |
double s = 0;
|
| 767 |
862 |
for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
|
| 768 |
863 |
return s;
|
| 769 |
864 |
}
|
| 770 |
865 |
|
| 771 |
866 |
/// Gamma distribution with given shape and scale parameter
|
| 772 |
867 |
|
| 773 |
868 |
/// This function generates a gamma distribution random number.
|
| 774 |
869 |
///
|
| 775 |
870 |
///\param k shape parameter (<tt>k>0</tt>)
|
| 776 |
871 |
///\param theta scale parameter
|
| 777 |
872 |
///
|
| 778 |
873 |
double gamma(double k,double theta=1.0)
|
| 779 |
874 |
{
|
| 780 |
875 |
double xi,nu;
|
| 781 |
876 |
const double delta = k-std::floor(k);
|
| 782 |
877 |
const double v0=E/(E-delta);
|
| 783 |
878 |
do {
|
| 784 |
879 |
double V0=1.0-real<double>();
|
| 785 |
880 |
double V1=1.0-real<double>();
|
| 786 |
881 |
double V2=1.0-real<double>();
|
| 787 |
882 |
if(V2<=v0)
|
| 788 |
883 |
{
|
| 789 |
884 |
xi=std::pow(V1,1.0/delta);
|
| 790 |
885 |
nu=V0*std::pow(xi,delta-1.0);
|
| 791 |
886 |
}
|
| 792 |
887 |
else
|
| 793 |
888 |
{
|
| 794 |
889 |
xi=1.0-std::log(V1);
|
| 795 |
890 |
nu=V0*std::exp(-xi);
|
| 796 |
891 |
}
|
| 797 |
892 |
} while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
|
| 798 |
893 |
return theta*(xi+gamma(int(std::floor(k))));
|
| 799 |
894 |
}
|
| 800 |
895 |
|
| 801 |
896 |
/// Weibull distribution
|
| 802 |
897 |
|
| 803 |
898 |
/// This function generates a Weibull distribution random number.
|
| 804 |
899 |
///
|
| 805 |
900 |
///\param k shape parameter (<tt>k>0</tt>)
|
| 806 |
901 |
///\param lambda scale parameter (<tt>lambda>0</tt>)
|
| 807 |
902 |
///
|