[209] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[10] | 2 | * |
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[209] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[10] | 4 | * |
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[463] | 5 | * Copyright (C) 2003-2009 |
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[10] | 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | /* |
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| 20 | * This file contains the reimplemented version of the Mersenne Twister |
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| 21 | * Generator of Matsumoto and Nishimura. |
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| 22 | * |
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| 23 | * See the appropriate copyright notice below. |
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[209] | 24 | * |
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[10] | 25 | * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, |
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[209] | 26 | * All rights reserved. |
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[10] | 27 | * |
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| 28 | * Redistribution and use in source and binary forms, with or without |
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| 29 | * modification, are permitted provided that the following conditions |
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| 30 | * are met: |
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| 31 | * |
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| 32 | * 1. Redistributions of source code must retain the above copyright |
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| 33 | * notice, this list of conditions and the following disclaimer. |
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| 34 | * |
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| 35 | * 2. Redistributions in binary form must reproduce the above copyright |
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| 36 | * notice, this list of conditions and the following disclaimer in the |
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| 37 | * documentation and/or other materials provided with the distribution. |
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| 38 | * |
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[209] | 39 | * 3. The names of its contributors may not be used to endorse or promote |
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| 40 | * products derived from this software without specific prior written |
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[10] | 41 | * permission. |
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| 42 | * |
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| 43 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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| 44 | * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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| 45 | * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
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| 46 | * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
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| 47 | * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, |
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| 48 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
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| 49 | * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
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| 50 | * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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| 51 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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| 52 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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| 53 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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| 54 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
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| 55 | * |
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| 56 | * |
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| 57 | * Any feedback is very welcome. |
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| 58 | * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html |
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| 59 | * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space) |
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| 60 | */ |
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| 61 | |
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| 62 | #ifndef LEMON_RANDOM_H |
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| 63 | #define LEMON_RANDOM_H |
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| 64 | |
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[1340] | 65 | #include <lemon/config.h> |
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| 66 | |
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[10] | 67 | #include <algorithm> |
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| 68 | #include <iterator> |
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| 69 | #include <vector> |
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[110] | 70 | #include <limits> |
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[177] | 71 | #include <fstream> |
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[10] | 72 | |
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[68] | 73 | #include <lemon/math.h> |
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[10] | 74 | #include <lemon/dim2.h> |
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[68] | 75 | |
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[1340] | 76 | #ifndef LEMON_WIN32 |
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[177] | 77 | #include <sys/time.h> |
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| 78 | #include <ctime> |
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| 79 | #include <sys/types.h> |
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| 80 | #include <unistd.h> |
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| 81 | #else |
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[511] | 82 | #include <lemon/bits/windows.h> |
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[177] | 83 | #endif |
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| 84 | |
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[10] | 85 | ///\ingroup misc |
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| 86 | ///\file |
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| 87 | ///\brief Mersenne Twister random number generator |
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| 88 | |
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| 89 | namespace lemon { |
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| 90 | |
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| 91 | namespace _random_bits { |
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[209] | 92 | |
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[10] | 93 | template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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| 94 | struct RandomTraits {}; |
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| 95 | |
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| 96 | template <typename _Word> |
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| 97 | struct RandomTraits<_Word, 32> { |
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| 98 | |
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| 99 | typedef _Word Word; |
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| 100 | static const int bits = 32; |
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| 101 | |
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| 102 | static const int length = 624; |
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| 103 | static const int shift = 397; |
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[209] | 104 | |
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[10] | 105 | static const Word mul = 0x6c078965u; |
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| 106 | static const Word arrayInit = 0x012BD6AAu; |
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| 107 | static const Word arrayMul1 = 0x0019660Du; |
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| 108 | static const Word arrayMul2 = 0x5D588B65u; |
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| 109 | |
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| 110 | static const Word mask = 0x9908B0DFu; |
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| 111 | static const Word loMask = (1u << 31) - 1; |
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| 112 | static const Word hiMask = ~loMask; |
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| 113 | |
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| 114 | |
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| 115 | static Word tempering(Word rnd) { |
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| 116 | rnd ^= (rnd >> 11); |
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| 117 | rnd ^= (rnd << 7) & 0x9D2C5680u; |
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| 118 | rnd ^= (rnd << 15) & 0xEFC60000u; |
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| 119 | rnd ^= (rnd >> 18); |
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| 120 | return rnd; |
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| 121 | } |
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| 122 | |
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| 123 | }; |
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| 124 | |
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| 125 | template <typename _Word> |
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| 126 | struct RandomTraits<_Word, 64> { |
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| 127 | |
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| 128 | typedef _Word Word; |
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| 129 | static const int bits = 64; |
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| 130 | |
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| 131 | static const int length = 312; |
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| 132 | static const int shift = 156; |
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| 133 | |
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| 134 | static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du); |
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| 135 | static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu); |
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| 136 | static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u); |
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| 137 | static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu); |
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| 138 | |
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| 139 | static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u); |
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| 140 | static const Word loMask = (Word(1u) << 31) - 1; |
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| 141 | static const Word hiMask = ~loMask; |
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| 142 | |
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| 143 | static Word tempering(Word rnd) { |
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| 144 | rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u)); |
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| 145 | rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u)); |
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| 146 | rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u)); |
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| 147 | rnd ^= (rnd >> 43); |
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| 148 | return rnd; |
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| 149 | } |
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| 150 | |
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| 151 | }; |
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| 152 | |
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| 153 | template <typename _Word> |
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| 154 | class RandomCore { |
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| 155 | public: |
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| 156 | |
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| 157 | typedef _Word Word; |
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| 158 | |
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| 159 | private: |
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| 160 | |
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| 161 | static const int bits = RandomTraits<Word>::bits; |
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| 162 | |
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| 163 | static const int length = RandomTraits<Word>::length; |
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| 164 | static const int shift = RandomTraits<Word>::shift; |
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| 165 | |
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| 166 | public: |
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| 167 | |
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| 168 | void initState() { |
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| 169 | static const Word seedArray[4] = { |
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| 170 | 0x12345u, 0x23456u, 0x34567u, 0x45678u |
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| 171 | }; |
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[209] | 172 | |
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[10] | 173 | initState(seedArray, seedArray + 4); |
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| 174 | } |
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| 175 | |
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| 176 | void initState(Word seed) { |
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| 177 | |
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| 178 | static const Word mul = RandomTraits<Word>::mul; |
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| 179 | |
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[209] | 180 | current = state; |
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[10] | 181 | |
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| 182 | Word *curr = state + length - 1; |
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| 183 | curr[0] = seed; --curr; |
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| 184 | for (int i = 1; i < length; ++i) { |
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| 185 | curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); |
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| 186 | --curr; |
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| 187 | } |
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| 188 | } |
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| 189 | |
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| 190 | template <typename Iterator> |
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| 191 | void initState(Iterator begin, Iterator end) { |
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| 192 | |
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| 193 | static const Word init = RandomTraits<Word>::arrayInit; |
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| 194 | static const Word mul1 = RandomTraits<Word>::arrayMul1; |
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| 195 | static const Word mul2 = RandomTraits<Word>::arrayMul2; |
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| 196 | |
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| 197 | |
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| 198 | Word *curr = state + length - 1; --curr; |
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| 199 | Iterator it = begin; int cnt = 0; |
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| 200 | int num; |
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| 201 | |
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| 202 | initState(init); |
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| 203 | |
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[1328] | 204 | num = static_cast<int>(length > end - begin ? length : end - begin); |
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[10] | 205 | while (num--) { |
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[209] | 206 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) |
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[10] | 207 | + *it + cnt; |
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| 208 | ++it; ++cnt; |
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| 209 | if (it == end) { |
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| 210 | it = begin; cnt = 0; |
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| 211 | } |
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| 212 | if (curr == state) { |
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| 213 | curr = state + length - 1; curr[0] = state[0]; |
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| 214 | } |
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| 215 | --curr; |
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| 216 | } |
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| 217 | |
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[1328] | 218 | num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1); |
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[10] | 219 | while (num--) { |
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| 220 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) |
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| 221 | - cnt; |
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| 222 | --curr; ++cnt; |
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| 223 | if (curr == state) { |
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| 224 | curr = state + length - 1; curr[0] = state[0]; --curr; |
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| 225 | cnt = 1; |
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| 226 | } |
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| 227 | } |
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[209] | 228 | |
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[10] | 229 | state[length - 1] = Word(1) << (bits - 1); |
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| 230 | } |
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[209] | 231 | |
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[10] | 232 | void copyState(const RandomCore& other) { |
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| 233 | std::copy(other.state, other.state + length, state); |
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| 234 | current = state + (other.current - other.state); |
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| 235 | } |
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| 236 | |
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| 237 | Word operator()() { |
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| 238 | if (current == state) fillState(); |
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| 239 | --current; |
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| 240 | Word rnd = *current; |
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| 241 | return RandomTraits<Word>::tempering(rnd); |
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| 242 | } |
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| 243 | |
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| 244 | private: |
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| 245 | |
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[209] | 246 | |
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[10] | 247 | void fillState() { |
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| 248 | static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; |
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| 249 | static const Word loMask = RandomTraits<Word>::loMask; |
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| 250 | static const Word hiMask = RandomTraits<Word>::hiMask; |
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| 251 | |
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[209] | 252 | current = state + length; |
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[10] | 253 | |
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[1338] | 254 | Word *curr = state + length - 1; |
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| 255 | long num; |
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[209] | 256 | |
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[10] | 257 | num = length - shift; |
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| 258 | while (num--) { |
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| 259 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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| 260 | curr[- shift] ^ mask[curr[-1] & 1ul]; |
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| 261 | --curr; |
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| 262 | } |
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| 263 | num = shift - 1; |
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| 264 | while (num--) { |
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| 265 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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| 266 | curr[length - shift] ^ mask[curr[-1] & 1ul]; |
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| 267 | --curr; |
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| 268 | } |
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[62] | 269 | state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ |
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[10] | 270 | curr[length - shift] ^ mask[curr[length - 1] & 1ul]; |
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| 271 | |
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| 272 | } |
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| 273 | |
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[209] | 274 | |
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[10] | 275 | Word *current; |
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| 276 | Word state[length]; |
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[209] | 277 | |
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[10] | 278 | }; |
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| 279 | |
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| 280 | |
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[209] | 281 | template <typename Result, |
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[10] | 282 | int shift = (std::numeric_limits<Result>::digits + 1) / 2> |
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| 283 | struct Masker { |
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| 284 | static Result mask(const Result& result) { |
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| 285 | return Masker<Result, (shift + 1) / 2>:: |
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| 286 | mask(static_cast<Result>(result | (result >> shift))); |
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| 287 | } |
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| 288 | }; |
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[209] | 289 | |
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[10] | 290 | template <typename Result> |
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| 291 | struct Masker<Result, 1> { |
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| 292 | static Result mask(const Result& result) { |
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| 293 | return static_cast<Result>(result | (result >> 1)); |
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| 294 | } |
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| 295 | }; |
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| 296 | |
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[209] | 297 | template <typename Result, typename Word, |
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| 298 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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[10] | 299 | bool last = rest <= std::numeric_limits<Word>::digits> |
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| 300 | struct IntConversion { |
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| 301 | static const int bits = std::numeric_limits<Word>::digits; |
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[209] | 302 | |
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[10] | 303 | static Result convert(RandomCore<Word>& rnd) { |
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| 304 | return static_cast<Result>(rnd() >> (bits - rest)) << shift; |
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| 305 | } |
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| 306 | |
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[209] | 307 | }; |
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| 308 | |
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| 309 | template <typename Result, typename Word, int rest, int shift> |
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[10] | 310 | struct IntConversion<Result, Word, rest, shift, false> { |
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| 311 | static const int bits = std::numeric_limits<Word>::digits; |
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| 312 | |
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| 313 | static Result convert(RandomCore<Word>& rnd) { |
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[209] | 314 | return (static_cast<Result>(rnd()) << shift) | |
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[10] | 315 | IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); |
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| 316 | } |
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| 317 | }; |
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| 318 | |
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| 319 | |
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| 320 | template <typename Result, typename Word, |
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[209] | 321 | bool one_word = (std::numeric_limits<Word>::digits < |
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| 322 | std::numeric_limits<Result>::digits) > |
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[10] | 323 | struct Mapping { |
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| 324 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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| 325 | Word max = Word(bound - 1); |
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| 326 | Result mask = Masker<Result>::mask(bound - 1); |
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| 327 | Result num; |
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| 328 | do { |
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[209] | 329 | num = IntConversion<Result, Word>::convert(rnd) & mask; |
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[10] | 330 | } while (num > max); |
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| 331 | return num; |
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| 332 | } |
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| 333 | }; |
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| 334 | |
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| 335 | template <typename Result, typename Word> |
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| 336 | struct Mapping<Result, Word, false> { |
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| 337 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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| 338 | Word max = Word(bound - 1); |
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| 339 | Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> |
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| 340 | ::mask(max); |
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| 341 | Word num; |
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| 342 | do { |
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| 343 | num = rnd() & mask; |
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| 344 | } while (num > max); |
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| 345 | return num; |
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| 346 | } |
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| 347 | }; |
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| 348 | |
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[517] | 349 | template <typename Result, int exp> |
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[10] | 350 | struct ShiftMultiplier { |
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| 351 | static const Result multiplier() { |
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| 352 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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| 353 | res *= res; |
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| 354 | if ((exp & 1) == 1) res *= static_cast<Result>(0.5); |
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[209] | 355 | return res; |
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[10] | 356 | } |
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| 357 | }; |
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| 358 | |
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| 359 | template <typename Result> |
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[517] | 360 | struct ShiftMultiplier<Result, 0> { |
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[10] | 361 | static const Result multiplier() { |
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[209] | 362 | return static_cast<Result>(1.0); |
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[10] | 363 | } |
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| 364 | }; |
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| 365 | |
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| 366 | template <typename Result> |
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[517] | 367 | struct ShiftMultiplier<Result, 20> { |
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[10] | 368 | static const Result multiplier() { |
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[209] | 369 | return static_cast<Result>(1.0/1048576.0); |
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[10] | 370 | } |
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| 371 | }; |
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[209] | 372 | |
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[10] | 373 | template <typename Result> |
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[517] | 374 | struct ShiftMultiplier<Result, 32> { |
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[10] | 375 | static const Result multiplier() { |
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[517] | 376 | return static_cast<Result>(1.0/4294967296.0); |
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[10] | 377 | } |
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| 378 | }; |
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| 379 | |
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| 380 | template <typename Result> |
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[517] | 381 | struct ShiftMultiplier<Result, 53> { |
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[10] | 382 | static const Result multiplier() { |
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[209] | 383 | return static_cast<Result>(1.0/9007199254740992.0); |
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[10] | 384 | } |
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| 385 | }; |
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| 386 | |
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| 387 | template <typename Result> |
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[517] | 388 | struct ShiftMultiplier<Result, 64> { |
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[10] | 389 | static const Result multiplier() { |
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[209] | 390 | return static_cast<Result>(1.0/18446744073709551616.0); |
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[10] | 391 | } |
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| 392 | }; |
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| 393 | |
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| 394 | template <typename Result, int exp> |
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| 395 | struct Shifting { |
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| 396 | static Result shift(const Result& result) { |
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| 397 | return result * ShiftMultiplier<Result, exp>::multiplier(); |
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| 398 | } |
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| 399 | }; |
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| 400 | |
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| 401 | template <typename Result, typename Word, |
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[209] | 402 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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[10] | 403 | bool last = rest <= std::numeric_limits<Word>::digits> |
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[209] | 404 | struct RealConversion{ |
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[10] | 405 | static const int bits = std::numeric_limits<Word>::digits; |
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| 406 | |
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| 407 | static Result convert(RandomCore<Word>& rnd) { |
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[517] | 408 | return Shifting<Result, shift + rest>:: |
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[10] | 409 | shift(static_cast<Result>(rnd() >> (bits - rest))); |
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| 410 | } |
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| 411 | }; |
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| 412 | |
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| 413 | template <typename Result, typename Word, int rest, int shift> |
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[209] | 414 | struct RealConversion<Result, Word, rest, shift, false> { |
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[10] | 415 | static const int bits = std::numeric_limits<Word>::digits; |
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| 416 | |
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| 417 | static Result convert(RandomCore<Word>& rnd) { |
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[517] | 418 | return Shifting<Result, shift + bits>:: |
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[10] | 419 | shift(static_cast<Result>(rnd())) + |
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| 420 | RealConversion<Result, Word, rest-bits, shift + bits>:: |
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| 421 | convert(rnd); |
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| 422 | } |
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| 423 | }; |
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| 424 | |
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| 425 | template <typename Result, typename Word> |
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| 426 | struct Initializer { |
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| 427 | |
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| 428 | template <typename Iterator> |
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| 429 | static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) { |
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| 430 | std::vector<Word> ws; |
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| 431 | for (Iterator it = begin; it != end; ++it) { |
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| 432 | ws.push_back(Word(*it)); |
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| 433 | } |
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| 434 | rnd.initState(ws.begin(), ws.end()); |
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| 435 | } |
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| 436 | |
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| 437 | static void init(RandomCore<Word>& rnd, Result seed) { |
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| 438 | rnd.initState(seed); |
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| 439 | } |
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| 440 | }; |
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| 441 | |
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| 442 | template <typename Word> |
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| 443 | struct BoolConversion { |
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| 444 | static bool convert(RandomCore<Word>& rnd) { |
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| 445 | return (rnd() & 1) == 1; |
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| 446 | } |
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| 447 | }; |
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| 448 | |
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| 449 | template <typename Word> |
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| 450 | struct BoolProducer { |
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| 451 | Word buffer; |
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| 452 | int num; |
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[209] | 453 | |
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[10] | 454 | BoolProducer() : num(0) {} |
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| 455 | |
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| 456 | bool convert(RandomCore<Word>& rnd) { |
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| 457 | if (num == 0) { |
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| 458 | buffer = rnd(); |
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| 459 | num = RandomTraits<Word>::bits; |
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| 460 | } |
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| 461 | bool r = (buffer & 1); |
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| 462 | buffer >>= 1; |
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| 463 | --num; |
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| 464 | return r; |
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| 465 | } |
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| 466 | }; |
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| 467 | |
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| 468 | } |
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| 469 | |
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| 470 | /// \ingroup misc |
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| 471 | /// |
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| 472 | /// \brief Mersenne Twister random number generator |
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| 473 | /// |
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| 474 | /// The Mersenne Twister is a twisted generalized feedback |
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| 475 | /// shift-register generator of Matsumoto and Nishimura. The period |
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| 476 | /// of this generator is \f$ 2^{19937} - 1 \f$ and it is |
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| 477 | /// equi-distributed in 623 dimensions for 32-bit numbers. The time |
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| 478 | /// performance of this generator is comparable to the commonly used |
---|
| 479 | /// generators. |
---|
| 480 | /// |
---|
| 481 | /// This implementation is specialized for both 32-bit and 64-bit |
---|
| 482 | /// architectures. The generators differ sligthly in the |
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| 483 | /// initialization and generation phase so they produce two |
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| 484 | /// completly different sequences. |
---|
| 485 | /// |
---|
| 486 | /// The generator gives back random numbers of serveral types. To |
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| 487 | /// get a random number from a range of a floating point type you |
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| 488 | /// can use one form of the \c operator() or the \c real() member |
---|
| 489 | /// function. If you want to get random number from the {0, 1, ..., |
---|
| 490 | /// n-1} integer range use the \c operator[] or the \c integer() |
---|
| 491 | /// method. And to get random number from the whole range of an |
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| 492 | /// integer type you can use the argumentless \c integer() or \c |
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| 493 | /// uinteger() functions. After all you can get random bool with |
---|
| 494 | /// equal chance of true and false or given probability of true |
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| 495 | /// result with the \c boolean() member functions. |
---|
| 496 | /// |
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| 497 | ///\code |
---|
| 498 | /// // The commented code is identical to the other |
---|
| 499 | /// double a = rnd(); // [0.0, 1.0) |
---|
| 500 | /// // double a = rnd.real(); // [0.0, 1.0) |
---|
| 501 | /// double b = rnd(100.0); // [0.0, 100.0) |
---|
| 502 | /// // double b = rnd.real(100.0); // [0.0, 100.0) |
---|
| 503 | /// double c = rnd(1.0, 2.0); // [1.0, 2.0) |
---|
| 504 | /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) |
---|
| 505 | /// int d = rnd[100000]; // 0..99999 |
---|
| 506 | /// // int d = rnd.integer(100000); // 0..99999 |
---|
| 507 | /// int e = rnd[6] + 1; // 1..6 |
---|
| 508 | /// // int e = rnd.integer(1, 1 + 6); // 1..6 |
---|
| 509 | /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 |
---|
| 510 | /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 |
---|
| 511 | /// bool g = rnd.boolean(); // P(g = true) = 0.5 |
---|
| 512 | /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 |
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| 513 | ///\endcode |
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| 514 | /// |
---|
[49] | 515 | /// LEMON provides a global instance of the random number |
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[10] | 516 | /// generator which name is \ref lemon::rnd "rnd". Usually it is a |
---|
| 517 | /// good programming convenience to use this global generator to get |
---|
| 518 | /// random numbers. |
---|
| 519 | class Random { |
---|
| 520 | private: |
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| 521 | |
---|
[16] | 522 | // Architecture word |
---|
[10] | 523 | typedef unsigned long Word; |
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[209] | 524 | |
---|
[10] | 525 | _random_bits::RandomCore<Word> core; |
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| 526 | _random_bits::BoolProducer<Word> bool_producer; |
---|
[209] | 527 | |
---|
[10] | 528 | |
---|
| 529 | public: |
---|
| 530 | |
---|
[177] | 531 | ///\name Initialization |
---|
| 532 | /// |
---|
| 533 | /// @{ |
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| 534 | |
---|
[49] | 535 | /// \brief Default constructor |
---|
[10] | 536 | /// |
---|
| 537 | /// Constructor with constant seeding. |
---|
| 538 | Random() { core.initState(); } |
---|
| 539 | |
---|
[49] | 540 | /// \brief Constructor with seed |
---|
[10] | 541 | /// |
---|
| 542 | /// Constructor with seed. The current number type will be converted |
---|
| 543 | /// to the architecture word type. |
---|
| 544 | template <typename Number> |
---|
[209] | 545 | Random(Number seed) { |
---|
[10] | 546 | _random_bits::Initializer<Number, Word>::init(core, seed); |
---|
| 547 | } |
---|
| 548 | |
---|
[49] | 549 | /// \brief Constructor with array seeding |
---|
[10] | 550 | /// |
---|
| 551 | /// Constructor with array seeding. The given range should contain |
---|
| 552 | /// any number type and the numbers will be converted to the |
---|
| 553 | /// architecture word type. |
---|
| 554 | template <typename Iterator> |
---|
[209] | 555 | Random(Iterator begin, Iterator end) { |
---|
[10] | 556 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
---|
| 557 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
---|
| 558 | } |
---|
| 559 | |
---|
| 560 | /// \brief Copy constructor |
---|
| 561 | /// |
---|
| 562 | /// Copy constructor. The generated sequence will be identical to |
---|
| 563 | /// the other sequence. It can be used to save the current state |
---|
| 564 | /// of the generator and later use it to generate the same |
---|
| 565 | /// sequence. |
---|
| 566 | Random(const Random& other) { |
---|
| 567 | core.copyState(other.core); |
---|
| 568 | } |
---|
| 569 | |
---|
| 570 | /// \brief Assign operator |
---|
| 571 | /// |
---|
| 572 | /// Assign operator. The generated sequence will be identical to |
---|
| 573 | /// the other sequence. It can be used to save the current state |
---|
| 574 | /// of the generator and later use it to generate the same |
---|
| 575 | /// sequence. |
---|
| 576 | Random& operator=(const Random& other) { |
---|
| 577 | if (&other != this) { |
---|
| 578 | core.copyState(other.core); |
---|
| 579 | } |
---|
| 580 | return *this; |
---|
| 581 | } |
---|
| 582 | |
---|
[102] | 583 | /// \brief Seeding random sequence |
---|
| 584 | /// |
---|
| 585 | /// Seeding the random sequence. The current number type will be |
---|
| 586 | /// converted to the architecture word type. |
---|
| 587 | template <typename Number> |
---|
[209] | 588 | void seed(Number seed) { |
---|
[102] | 589 | _random_bits::Initializer<Number, Word>::init(core, seed); |
---|
| 590 | } |
---|
| 591 | |
---|
| 592 | /// \brief Seeding random sequence |
---|
| 593 | /// |
---|
| 594 | /// Seeding the random sequence. The given range should contain |
---|
| 595 | /// any number type and the numbers will be converted to the |
---|
| 596 | /// architecture word type. |
---|
| 597 | template <typename Iterator> |
---|
[209] | 598 | void seed(Iterator begin, Iterator end) { |
---|
[102] | 599 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
---|
| 600 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
---|
| 601 | } |
---|
| 602 | |
---|
[177] | 603 | /// \brief Seeding from file or from process id and time |
---|
| 604 | /// |
---|
| 605 | /// By default, this function calls the \c seedFromFile() member |
---|
[178] | 606 | /// function with the <tt>/dev/urandom</tt> file. If it does not success, |
---|
[177] | 607 | /// it uses the \c seedFromTime(). |
---|
[606] | 608 | /// \return Currently always \c true. |
---|
[177] | 609 | bool seed() { |
---|
[1340] | 610 | #ifndef LEMON_WIN32 |
---|
[177] | 611 | if (seedFromFile("/dev/urandom", 0)) return true; |
---|
| 612 | #endif |
---|
| 613 | if (seedFromTime()) return true; |
---|
| 614 | return false; |
---|
| 615 | } |
---|
[209] | 616 | |
---|
[177] | 617 | /// \brief Seeding from file |
---|
| 618 | /// |
---|
| 619 | /// Seeding the random sequence from file. The linux kernel has two |
---|
| 620 | /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which |
---|
| 621 | /// could give good seed values for pseudo random generators (The |
---|
| 622 | /// difference between two devices is that the <tt>random</tt> may |
---|
| 623 | /// block the reading operation while the kernel can give good |
---|
| 624 | /// source of randomness, while the <tt>urandom</tt> does not |
---|
| 625 | /// block the input, but it could give back bytes with worse |
---|
| 626 | /// entropy). |
---|
| 627 | /// \param file The source file |
---|
| 628 | /// \param offset The offset, from the file read. |
---|
[606] | 629 | /// \return \c true when the seeding successes. |
---|
[1340] | 630 | #ifndef LEMON_WIN32 |
---|
[209] | 631 | bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0) |
---|
[177] | 632 | #else |
---|
[209] | 633 | bool seedFromFile(const std::string& file = "", int offset = 0) |
---|
[177] | 634 | #endif |
---|
| 635 | { |
---|
| 636 | std::ifstream rs(file.c_str()); |
---|
| 637 | const int size = 4; |
---|
| 638 | Word buf[size]; |
---|
| 639 | if (offset != 0 && !rs.seekg(offset)) return false; |
---|
| 640 | if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false; |
---|
| 641 | seed(buf, buf + size); |
---|
| 642 | return true; |
---|
| 643 | } |
---|
| 644 | |
---|
| 645 | /// \brief Seding from process id and time |
---|
| 646 | /// |
---|
| 647 | /// Seding from process id and time. This function uses the |
---|
| 648 | /// current process id and the current time for initialize the |
---|
| 649 | /// random sequence. |
---|
[606] | 650 | /// \return Currently always \c true. |
---|
[209] | 651 | bool seedFromTime() { |
---|
[1340] | 652 | #ifndef LEMON_WIN32 |
---|
[177] | 653 | timeval tv; |
---|
| 654 | gettimeofday(&tv, 0); |
---|
| 655 | seed(getpid() + tv.tv_sec + tv.tv_usec); |
---|
| 656 | #else |
---|
[511] | 657 | seed(bits::getWinRndSeed()); |
---|
[177] | 658 | #endif |
---|
| 659 | return true; |
---|
| 660 | } |
---|
| 661 | |
---|
| 662 | /// @} |
---|
| 663 | |
---|
[631] | 664 | ///\name Uniform Distributions |
---|
[177] | 665 | /// |
---|
| 666 | /// @{ |
---|
| 667 | |
---|
[10] | 668 | /// \brief Returns a random real number from the range [0, 1) |
---|
| 669 | /// |
---|
| 670 | /// It returns a random real number from the range [0, 1). The |
---|
[49] | 671 | /// default Number type is \c double. |
---|
[10] | 672 | template <typename Number> |
---|
| 673 | Number real() { |
---|
| 674 | return _random_bits::RealConversion<Number, Word>::convert(core); |
---|
| 675 | } |
---|
| 676 | |
---|
| 677 | double real() { |
---|
| 678 | return real<double>(); |
---|
| 679 | } |
---|
| 680 | |
---|
| 681 | /// \brief Returns a random real number from the range [0, 1) |
---|
| 682 | /// |
---|
| 683 | /// It returns a random double from the range [0, 1). |
---|
| 684 | double operator()() { |
---|
| 685 | return real<double>(); |
---|
| 686 | } |
---|
| 687 | |
---|
| 688 | /// \brief Returns a random real number from the range [0, b) |
---|
| 689 | /// |
---|
| 690 | /// It returns a random real number from the range [0, b). |
---|
[391] | 691 | double operator()(double b) { |
---|
| 692 | return real<double>() * b; |
---|
[10] | 693 | } |
---|
| 694 | |
---|
| 695 | /// \brief Returns a random real number from the range [a, b) |
---|
| 696 | /// |
---|
| 697 | /// It returns a random real number from the range [a, b). |
---|
[391] | 698 | double operator()(double a, double b) { |
---|
| 699 | return real<double>() * (b - a) + a; |
---|
[10] | 700 | } |
---|
| 701 | |
---|
| 702 | /// \brief Returns a random integer from a range |
---|
| 703 | /// |
---|
| 704 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
| 705 | template <typename Number> |
---|
| 706 | Number integer(Number b) { |
---|
| 707 | return _random_bits::Mapping<Number, Word>::map(core, b); |
---|
| 708 | } |
---|
| 709 | |
---|
| 710 | /// \brief Returns a random integer from a range |
---|
| 711 | /// |
---|
| 712 | /// It returns a random integer from the range {a, a + 1, ..., b - 1}. |
---|
| 713 | template <typename Number> |
---|
| 714 | Number integer(Number a, Number b) { |
---|
| 715 | return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; |
---|
| 716 | } |
---|
| 717 | |
---|
| 718 | /// \brief Returns a random integer from a range |
---|
| 719 | /// |
---|
| 720 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
| 721 | template <typename Number> |
---|
| 722 | Number operator[](Number b) { |
---|
| 723 | return _random_bits::Mapping<Number, Word>::map(core, b); |
---|
| 724 | } |
---|
| 725 | |
---|
| 726 | /// \brief Returns a random non-negative integer |
---|
| 727 | /// |
---|
| 728 | /// It returns a random non-negative integer uniformly from the |
---|
[49] | 729 | /// whole range of the current \c Number type. The default result |
---|
| 730 | /// type of this function is <tt>unsigned int</tt>. |
---|
[10] | 731 | template <typename Number> |
---|
| 732 | Number uinteger() { |
---|
| 733 | return _random_bits::IntConversion<Number, Word>::convert(core); |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | unsigned int uinteger() { |
---|
| 737 | return uinteger<unsigned int>(); |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | /// \brief Returns a random integer |
---|
| 741 | /// |
---|
| 742 | /// It returns a random integer uniformly from the whole range of |
---|
| 743 | /// the current \c Number type. The default result type of this |
---|
[49] | 744 | /// function is \c int. |
---|
[10] | 745 | template <typename Number> |
---|
| 746 | Number integer() { |
---|
[209] | 747 | static const int nb = std::numeric_limits<Number>::digits + |
---|
[10] | 748 | (std::numeric_limits<Number>::is_signed ? 1 : 0); |
---|
| 749 | return _random_bits::IntConversion<Number, Word, nb>::convert(core); |
---|
| 750 | } |
---|
| 751 | |
---|
| 752 | int integer() { |
---|
| 753 | return integer<int>(); |
---|
| 754 | } |
---|
[209] | 755 | |
---|
[10] | 756 | /// \brief Returns a random bool |
---|
| 757 | /// |
---|
| 758 | /// It returns a random bool. The generator holds a buffer for |
---|
| 759 | /// random bits. Every time when it become empty the generator makes |
---|
| 760 | /// a new random word and fill the buffer up. |
---|
| 761 | bool boolean() { |
---|
| 762 | return bool_producer.convert(core); |
---|
| 763 | } |
---|
| 764 | |
---|
[177] | 765 | /// @} |
---|
| 766 | |
---|
[631] | 767 | ///\name Non-uniform Distributions |
---|
[10] | 768 | /// |
---|
| 769 | ///@{ |
---|
[209] | 770 | |
---|
[352] | 771 | /// \brief Returns a random bool with given probability of true result. |
---|
[10] | 772 | /// |
---|
[23] | 773 | /// It returns a random bool with given probability of true result. |
---|
[10] | 774 | bool boolean(double p) { |
---|
| 775 | return operator()() < p; |
---|
| 776 | } |
---|
| 777 | |
---|
[352] | 778 | /// Standard normal (Gauss) distribution |
---|
[10] | 779 | |
---|
[352] | 780 | /// Standard normal (Gauss) distribution. |
---|
[10] | 781 | /// \note The Cartesian form of the Box-Muller |
---|
| 782 | /// transformation is used to generate a random normal distribution. |
---|
[209] | 783 | double gauss() |
---|
[10] | 784 | { |
---|
| 785 | double V1,V2,S; |
---|
| 786 | do { |
---|
[209] | 787 | V1=2*real<double>()-1; |
---|
| 788 | V2=2*real<double>()-1; |
---|
| 789 | S=V1*V1+V2*V2; |
---|
[10] | 790 | } while(S>=1); |
---|
| 791 | return std::sqrt(-2*std::log(S)/S)*V1; |
---|
| 792 | } |
---|
[352] | 793 | /// Normal (Gauss) distribution with given mean and standard deviation |
---|
[10] | 794 | |
---|
[352] | 795 | /// Normal (Gauss) distribution with given mean and standard deviation. |
---|
[10] | 796 | /// \sa gauss() |
---|
| 797 | double gauss(double mean,double std_dev) |
---|
| 798 | { |
---|
| 799 | return gauss()*std_dev+mean; |
---|
| 800 | } |
---|
| 801 | |
---|
[351] | 802 | /// Lognormal distribution |
---|
| 803 | |
---|
| 804 | /// Lognormal distribution. The parameters are the mean and the standard |
---|
| 805 | /// deviation of <tt>exp(X)</tt>. |
---|
| 806 | /// |
---|
| 807 | double lognormal(double n_mean,double n_std_dev) |
---|
| 808 | { |
---|
| 809 | return std::exp(gauss(n_mean,n_std_dev)); |
---|
| 810 | } |
---|
| 811 | /// Lognormal distribution |
---|
| 812 | |
---|
| 813 | /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of |
---|
| 814 | /// the mean and the standard deviation of <tt>exp(X)</tt>. |
---|
| 815 | /// |
---|
| 816 | double lognormal(const std::pair<double,double> ¶ms) |
---|
| 817 | { |
---|
| 818 | return std::exp(gauss(params.first,params.second)); |
---|
| 819 | } |
---|
| 820 | /// Compute the lognormal parameters from mean and standard deviation |
---|
| 821 | |
---|
| 822 | /// This function computes the lognormal parameters from mean and |
---|
| 823 | /// standard deviation. The return value can direcly be passed to |
---|
| 824 | /// lognormal(). |
---|
| 825 | std::pair<double,double> lognormalParamsFromMD(double mean, |
---|
[352] | 826 | double std_dev) |
---|
[351] | 827 | { |
---|
| 828 | double fr=std_dev/mean; |
---|
| 829 | fr*=fr; |
---|
| 830 | double lg=std::log(1+fr); |
---|
| 831 | return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg)); |
---|
| 832 | } |
---|
| 833 | /// Lognormal distribution with given mean and standard deviation |
---|
[352] | 834 | |
---|
[351] | 835 | /// Lognormal distribution with given mean and standard deviation. |
---|
| 836 | /// |
---|
| 837 | double lognormalMD(double mean,double std_dev) |
---|
| 838 | { |
---|
| 839 | return lognormal(lognormalParamsFromMD(mean,std_dev)); |
---|
| 840 | } |
---|
[352] | 841 | |
---|
[10] | 842 | /// Exponential distribution with given mean |
---|
| 843 | |
---|
| 844 | /// This function generates an exponential distribution random number |
---|
| 845 | /// with mean <tt>1/lambda</tt>. |
---|
| 846 | /// |
---|
| 847 | double exponential(double lambda=1.0) |
---|
| 848 | { |
---|
[11] | 849 | return -std::log(1.0-real<double>())/lambda; |
---|
[10] | 850 | } |
---|
| 851 | |
---|
| 852 | /// Gamma distribution with given integer shape |
---|
| 853 | |
---|
| 854 | /// This function generates a gamma distribution random number. |
---|
[209] | 855 | /// |
---|
[10] | 856 | ///\param k shape parameter (<tt>k>0</tt> integer) |
---|
[209] | 857 | double gamma(int k) |
---|
[10] | 858 | { |
---|
| 859 | double s = 0; |
---|
| 860 | for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); |
---|
| 861 | return s; |
---|
| 862 | } |
---|
[209] | 863 | |
---|
[10] | 864 | /// Gamma distribution with given shape and scale parameter |
---|
| 865 | |
---|
| 866 | /// This function generates a gamma distribution random number. |
---|
[209] | 867 | /// |
---|
[10] | 868 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
| 869 | ///\param theta scale parameter |
---|
| 870 | /// |
---|
| 871 | double gamma(double k,double theta=1.0) |
---|
| 872 | { |
---|
| 873 | double xi,nu; |
---|
| 874 | const double delta = k-std::floor(k); |
---|
[68] | 875 | const double v0=E/(E-delta); |
---|
[10] | 876 | do { |
---|
[209] | 877 | double V0=1.0-real<double>(); |
---|
| 878 | double V1=1.0-real<double>(); |
---|
| 879 | double V2=1.0-real<double>(); |
---|
| 880 | if(V2<=v0) |
---|
| 881 | { |
---|
| 882 | xi=std::pow(V1,1.0/delta); |
---|
| 883 | nu=V0*std::pow(xi,delta-1.0); |
---|
| 884 | } |
---|
| 885 | else |
---|
| 886 | { |
---|
| 887 | xi=1.0-std::log(V1); |
---|
| 888 | nu=V0*std::exp(-xi); |
---|
| 889 | } |
---|
[10] | 890 | } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); |
---|
[116] | 891 | return theta*(xi+gamma(int(std::floor(k)))); |
---|
[10] | 892 | } |
---|
[209] | 893 | |
---|
[11] | 894 | /// Weibull distribution |
---|
| 895 | |
---|
| 896 | /// This function generates a Weibull distribution random number. |
---|
[209] | 897 | /// |
---|
[11] | 898 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
| 899 | ///\param lambda scale parameter (<tt>lambda>0</tt>) |
---|
| 900 | /// |
---|
| 901 | double weibull(double k,double lambda) |
---|
| 902 | { |
---|
| 903 | return lambda*pow(-std::log(1.0-real<double>()),1.0/k); |
---|
[209] | 904 | } |
---|
| 905 | |
---|
[11] | 906 | /// Pareto distribution |
---|
| 907 | |
---|
| 908 | /// This function generates a Pareto distribution random number. |
---|
[209] | 909 | /// |
---|
[12] | 910 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
[11] | 911 | ///\param x_min location parameter (<tt>x_min>0</tt>) |
---|
| 912 | /// |
---|
[12] | 913 | double pareto(double k,double x_min) |
---|
[11] | 914 | { |
---|
[116] | 915 | return exponential(gamma(k,1.0/x_min))+x_min; |
---|
[209] | 916 | } |
---|
| 917 | |
---|
[92] | 918 | /// Poisson distribution |
---|
| 919 | |
---|
| 920 | /// This function generates a Poisson distribution random number with |
---|
| 921 | /// parameter \c lambda. |
---|
[209] | 922 | /// |
---|
[92] | 923 | /// The probability mass function of this distribusion is |
---|
| 924 | /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f] |
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| 925 | /// \note The algorithm is taken from the book of Donald E. Knuth titled |
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| 926 | /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the |
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| 927 | /// return value. |
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[209] | 928 | |
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[92] | 929 | int poisson(double lambda) |
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| 930 | { |
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| 931 | const double l = std::exp(-lambda); |
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| 932 | int k=0; |
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| 933 | double p = 1.0; |
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| 934 | do { |
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[209] | 935 | k++; |
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| 936 | p*=real<double>(); |
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[92] | 937 | } while (p>=l); |
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| 938 | return k-1; |
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[209] | 939 | } |
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| 940 | |
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[10] | 941 | ///@} |
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[209] | 942 | |
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[631] | 943 | ///\name Two Dimensional Distributions |
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[10] | 944 | /// |
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| 945 | ///@{ |
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[209] | 946 | |
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[23] | 947 | /// Uniform distribution on the full unit circle |
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[16] | 948 | |
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| 949 | /// Uniform distribution on the full unit circle. |
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| 950 | /// |
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[209] | 951 | dim2::Point<double> disc() |
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[10] | 952 | { |
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| 953 | double V1,V2; |
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| 954 | do { |
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[209] | 955 | V1=2*real<double>()-1; |
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| 956 | V2=2*real<double>()-1; |
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| 957 | |
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[10] | 958 | } while(V1*V1+V2*V2>=1); |
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| 959 | return dim2::Point<double>(V1,V2); |
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| 960 | } |
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[352] | 961 | /// A kind of two dimensional normal (Gauss) distribution |
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[10] | 962 | |
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| 963 | /// This function provides a turning symmetric two-dimensional distribution. |
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| 964 | /// Both coordinates are of standard normal distribution, but they are not |
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| 965 | /// independent. |
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| 966 | /// |
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| 967 | /// \note The coordinates are the two random variables provided by |
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| 968 | /// the Box-Muller method. |
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| 969 | dim2::Point<double> gauss2() |
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| 970 | { |
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| 971 | double V1,V2,S; |
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| 972 | do { |
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[209] | 973 | V1=2*real<double>()-1; |
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| 974 | V2=2*real<double>()-1; |
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| 975 | S=V1*V1+V2*V2; |
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[10] | 976 | } while(S>=1); |
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| 977 | double W=std::sqrt(-2*std::log(S)/S); |
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| 978 | return dim2::Point<double>(W*V1,W*V2); |
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| 979 | } |
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| 980 | /// A kind of two dimensional exponential distribution |
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| 981 | |
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| 982 | /// This function provides a turning symmetric two-dimensional distribution. |
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| 983 | /// The x-coordinate is of conditionally exponential distribution |
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[209] | 984 | /// with the condition that x is positive and y=0. If x is negative and |
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[10] | 985 | /// y=0 then, -x is of exponential distribution. The same is true for the |
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| 986 | /// y-coordinate. |
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[209] | 987 | dim2::Point<double> exponential2() |
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[10] | 988 | { |
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| 989 | double V1,V2,S; |
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| 990 | do { |
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[209] | 991 | V1=2*real<double>()-1; |
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| 992 | V2=2*real<double>()-1; |
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| 993 | S=V1*V1+V2*V2; |
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[10] | 994 | } while(S>=1); |
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| 995 | double W=-std::log(S)/S; |
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| 996 | return dim2::Point<double>(W*V1,W*V2); |
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| 997 | } |
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| 998 | |
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[209] | 999 | ///@} |
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[10] | 1000 | }; |
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| 1001 | |
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| 1002 | |
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| 1003 | extern Random rnd; |
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| 1004 | |
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| 1005 | } |
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| 1006 | |
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| 1007 | #endif |
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