[2229] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2229] | 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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[2372] | 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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| 24 | * |
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| 25 | * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, |
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| 26 | * All rights reserved. |
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| 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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| 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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| 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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[2229] | 62 | #ifndef LEMON_RANDOM_H |
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| 63 | #define LEMON_RANDOM_H |
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| 64 | |
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| 65 | #include <algorithm> |
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[2242] | 66 | #include <iterator> |
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| 67 | #include <vector> |
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[2229] | 68 | |
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| 69 | #include <ctime> |
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| 70 | #include <cmath> |
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| 71 | |
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[2374] | 72 | #include <lemon/dim2.h> |
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[2229] | 73 | ///\ingroup misc |
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| 74 | ///\file |
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| 75 | ///\brief Mersenne Twister random number generator |
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| 76 | /// |
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| 77 | ///\author Balazs Dezso |
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| 78 | |
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| 79 | namespace lemon { |
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| 80 | |
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[2242] | 81 | namespace _random_bits { |
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| 82 | |
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| 83 | template <typename _Word, int _bits = std::numeric_limits<_Word>::digits> |
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| 84 | struct RandomTraits {}; |
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| 85 | |
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| 86 | template <typename _Word> |
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| 87 | struct RandomTraits<_Word, 32> { |
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| 88 | |
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| 89 | typedef _Word Word; |
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| 90 | static const int bits = 32; |
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| 91 | |
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| 92 | static const int length = 624; |
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| 93 | static const int shift = 397; |
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| 94 | |
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| 95 | static const Word mul = 0x6c078965u; |
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| 96 | static const Word arrayInit = 0x012BD6AAu; |
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| 97 | static const Word arrayMul1 = 0x0019660Du; |
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| 98 | static const Word arrayMul2 = 0x5D588B65u; |
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| 99 | |
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| 100 | static const Word mask = 0x9908B0DFu; |
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| 101 | static const Word loMask = (1u << 31) - 1; |
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| 102 | static const Word hiMask = ~loMask; |
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| 103 | |
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| 104 | |
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| 105 | static Word tempering(Word rnd) { |
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| 106 | rnd ^= (rnd >> 11); |
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| 107 | rnd ^= (rnd << 7) & 0x9D2C5680u; |
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| 108 | rnd ^= (rnd << 15) & 0xEFC60000u; |
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| 109 | rnd ^= (rnd >> 18); |
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| 110 | return rnd; |
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| 111 | } |
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| 112 | |
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| 113 | }; |
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| 114 | |
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| 115 | template <typename _Word> |
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| 116 | struct RandomTraits<_Word, 64> { |
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| 117 | |
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| 118 | typedef _Word Word; |
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| 119 | static const int bits = 64; |
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| 120 | |
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| 121 | static const int length = 312; |
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| 122 | static const int shift = 156; |
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| 123 | |
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[2386] | 124 | static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du); |
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| 125 | static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu); |
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| 126 | static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u); |
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| 127 | static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu); |
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[2242] | 128 | |
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[2386] | 129 | static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u); |
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| 130 | static const Word loMask = (Word(1u) << 31) - 1; |
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[2242] | 131 | static const Word hiMask = ~loMask; |
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| 132 | |
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| 133 | static Word tempering(Word rnd) { |
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[2386] | 134 | rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u)); |
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| 135 | rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u)); |
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| 136 | rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u)); |
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[2242] | 137 | rnd ^= (rnd >> 43); |
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| 138 | return rnd; |
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| 139 | } |
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| 140 | |
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| 141 | }; |
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| 142 | |
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| 143 | template <typename _Word> |
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| 144 | class RandomCore { |
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| 145 | public: |
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| 146 | |
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| 147 | typedef _Word Word; |
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| 148 | |
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| 149 | private: |
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| 150 | |
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| 151 | static const int bits = RandomTraits<Word>::bits; |
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| 152 | |
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| 153 | static const int length = RandomTraits<Word>::length; |
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| 154 | static const int shift = RandomTraits<Word>::shift; |
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| 155 | |
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| 156 | public: |
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| 157 | |
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| 158 | void initState() { |
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| 159 | static const Word seedArray[4] = { |
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| 160 | 0x12345u, 0x23456u, 0x34567u, 0x45678u |
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| 161 | }; |
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| 162 | |
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| 163 | initState(seedArray, seedArray + 4); |
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| 164 | } |
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| 165 | |
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| 166 | void initState(Word seed) { |
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| 167 | |
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| 168 | static const Word mul = RandomTraits<Word>::mul; |
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| 169 | |
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| 170 | current = state; |
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| 171 | |
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| 172 | Word *curr = state + length - 1; |
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| 173 | curr[0] = seed; --curr; |
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| 174 | for (int i = 1; i < length; ++i) { |
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| 175 | curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i); |
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| 176 | --curr; |
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| 177 | } |
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| 178 | } |
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| 179 | |
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| 180 | template <typename Iterator> |
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| 181 | void initState(Iterator begin, Iterator end) { |
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| 182 | |
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| 183 | static const Word init = RandomTraits<Word>::arrayInit; |
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| 184 | static const Word mul1 = RandomTraits<Word>::arrayMul1; |
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| 185 | static const Word mul2 = RandomTraits<Word>::arrayMul2; |
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| 186 | |
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| 187 | |
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| 188 | Word *curr = state + length - 1; --curr; |
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| 189 | Iterator it = begin; int cnt = 0; |
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| 190 | int num; |
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| 191 | |
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| 192 | initState(init); |
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| 193 | |
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| 194 | num = length > end - begin ? length : end - begin; |
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| 195 | while (num--) { |
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| 196 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) |
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| 197 | + *it + cnt; |
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| 198 | ++it; ++cnt; |
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| 199 | if (it == end) { |
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| 200 | it = begin; cnt = 0; |
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| 201 | } |
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| 202 | if (curr == state) { |
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| 203 | curr = state + length - 1; curr[0] = state[0]; |
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| 204 | } |
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| 205 | --curr; |
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| 206 | } |
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| 207 | |
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| 208 | num = length - 1; cnt = length - (curr - state) - 1; |
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| 209 | while (num--) { |
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| 210 | curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2)) |
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| 211 | - cnt; |
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| 212 | --curr; ++cnt; |
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| 213 | if (curr == state) { |
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| 214 | curr = state + length - 1; curr[0] = state[0]; --curr; |
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| 215 | cnt = 1; |
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| 216 | } |
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| 217 | } |
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| 218 | |
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[2386] | 219 | state[length - 1] = Word(1) << (bits - 1); |
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[2242] | 220 | } |
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| 221 | |
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| 222 | void copyState(const RandomCore& other) { |
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| 223 | std::copy(other.state, other.state + length, state); |
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| 224 | current = state + (other.current - other.state); |
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| 225 | } |
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| 226 | |
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| 227 | Word operator()() { |
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| 228 | if (current == state) fillState(); |
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| 229 | --current; |
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| 230 | Word rnd = *current; |
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| 231 | return RandomTraits<Word>::tempering(rnd); |
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| 232 | } |
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| 233 | |
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| 234 | private: |
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| 235 | |
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| 236 | |
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| 237 | void fillState() { |
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| 238 | static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask }; |
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| 239 | static const Word loMask = RandomTraits<Word>::loMask; |
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| 240 | static const Word hiMask = RandomTraits<Word>::hiMask; |
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| 241 | |
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| 242 | current = state + length; |
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| 243 | |
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| 244 | register Word *curr = state + length - 1; |
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| 245 | register long num; |
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| 246 | |
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| 247 | num = length - shift; |
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| 248 | while (num--) { |
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| 249 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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| 250 | curr[- shift] ^ mask[curr[-1] & 1ul]; |
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| 251 | --curr; |
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| 252 | } |
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| 253 | num = shift - 1; |
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| 254 | while (num--) { |
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| 255 | curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^ |
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| 256 | curr[length - shift] ^ mask[curr[-1] & 1ul]; |
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| 257 | --curr; |
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| 258 | } |
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| 259 | curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^ |
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[2545] | 260 | curr[length - shift] ^ mask[int(curr[length - 1] & 1ul)]; |
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[2242] | 261 | |
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| 262 | } |
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| 263 | |
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| 264 | |
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| 265 | Word *current; |
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| 266 | Word state[length]; |
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| 267 | |
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| 268 | }; |
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| 269 | |
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| 270 | |
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| 271 | template <typename Result, |
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| 272 | int shift = (std::numeric_limits<Result>::digits + 1) / 2> |
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| 273 | struct Masker { |
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| 274 | static Result mask(const Result& result) { |
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| 275 | return Masker<Result, (shift + 1) / 2>:: |
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[2386] | 276 | mask(static_cast<Result>(result | (result >> shift))); |
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[2242] | 277 | } |
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| 278 | }; |
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| 279 | |
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| 280 | template <typename Result> |
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| 281 | struct Masker<Result, 1> { |
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| 282 | static Result mask(const Result& result) { |
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[2386] | 283 | return static_cast<Result>(result | (result >> 1)); |
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[2242] | 284 | } |
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| 285 | }; |
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| 286 | |
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| 287 | template <typename Result, typename Word, |
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| 288 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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| 289 | bool last = rest <= std::numeric_limits<Word>::digits> |
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| 290 | struct IntConversion { |
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| 291 | static const int bits = std::numeric_limits<Word>::digits; |
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| 292 | |
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| 293 | static Result convert(RandomCore<Word>& rnd) { |
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[2386] | 294 | return static_cast<Result>(rnd() >> (bits - rest)) << shift; |
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[2242] | 295 | } |
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| 296 | |
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| 297 | }; |
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| 298 | |
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| 299 | template <typename Result, typename Word, int rest, int shift> |
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| 300 | struct IntConversion<Result, Word, rest, shift, false> { |
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| 301 | static const int bits = std::numeric_limits<Word>::digits; |
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| 302 | |
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| 303 | static Result convert(RandomCore<Word>& rnd) { |
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[2386] | 304 | return (static_cast<Result>(rnd()) << shift) | |
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[2242] | 305 | IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd); |
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| 306 | } |
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| 307 | }; |
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| 308 | |
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| 309 | |
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| 310 | template <typename Result, typename Word, |
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[2387] | 311 | bool one_word = (std::numeric_limits<Word>::digits < |
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| 312 | std::numeric_limits<Result>::digits) > |
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[2242] | 313 | struct Mapping { |
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| 314 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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[2386] | 315 | Word max = Word(bound - 1); |
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[2242] | 316 | Result mask = Masker<Result>::mask(bound - 1); |
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| 317 | Result num; |
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| 318 | do { |
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| 319 | num = IntConversion<Result, Word>::convert(rnd) & mask; |
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| 320 | } while (num > max); |
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| 321 | return num; |
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| 322 | } |
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| 323 | }; |
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| 324 | |
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| 325 | template <typename Result, typename Word> |
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| 326 | struct Mapping<Result, Word, false> { |
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| 327 | static Result map(RandomCore<Word>& rnd, const Result& bound) { |
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[2386] | 328 | Word max = Word(bound - 1); |
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[2242] | 329 | Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2> |
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| 330 | ::mask(max); |
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| 331 | Word num; |
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| 332 | do { |
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| 333 | num = rnd() & mask; |
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| 334 | } while (num > max); |
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| 335 | return num; |
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| 336 | } |
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| 337 | }; |
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| 338 | |
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| 339 | template <typename Result, int exp, bool pos = (exp >= 0)> |
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| 340 | struct ShiftMultiplier { |
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| 341 | static const Result multiplier() { |
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| 342 | Result res = ShiftMultiplier<Result, exp / 2>::multiplier(); |
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| 343 | res *= res; |
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[2386] | 344 | if ((exp & 1) == 1) res *= static_cast<Result>(2.0); |
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[2242] | 345 | return res; |
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| 346 | } |
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| 347 | }; |
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| 348 | |
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| 349 | template <typename Result, int exp> |
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| 350 | struct ShiftMultiplier<Result, exp, false> { |
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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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[2386] | 354 | if ((exp & 1) == 1) res *= static_cast<Result>(0.5); |
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[2242] | 355 | return res; |
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| 356 | } |
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| 357 | }; |
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| 358 | |
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| 359 | template <typename Result> |
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| 360 | struct ShiftMultiplier<Result, 0, true> { |
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| 361 | static const Result multiplier() { |
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[2386] | 362 | return static_cast<Result>(1.0); |
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[2242] | 363 | } |
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| 364 | }; |
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| 365 | |
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| 366 | template <typename Result> |
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| 367 | struct ShiftMultiplier<Result, -20, true> { |
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| 368 | static const Result multiplier() { |
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[2386] | 369 | return static_cast<Result>(1.0/1048576.0); |
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[2242] | 370 | } |
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| 371 | }; |
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| 372 | |
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| 373 | template <typename Result> |
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| 374 | struct ShiftMultiplier<Result, -32, true> { |
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| 375 | static const Result multiplier() { |
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[2386] | 376 | return static_cast<Result>(1.0/424967296.0); |
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[2242] | 377 | } |
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| 378 | }; |
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| 379 | |
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| 380 | template <typename Result> |
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| 381 | struct ShiftMultiplier<Result, -53, true> { |
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| 382 | static const Result multiplier() { |
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[2386] | 383 | return static_cast<Result>(1.0/9007199254740992.0); |
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[2242] | 384 | } |
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| 385 | }; |
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| 386 | |
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| 387 | template <typename Result> |
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| 388 | struct ShiftMultiplier<Result, -64, true> { |
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| 389 | static const Result multiplier() { |
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[2386] | 390 | return static_cast<Result>(1.0/18446744073709551616.0); |
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[2242] | 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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| 402 | int rest = std::numeric_limits<Result>::digits, int shift = 0, |
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| 403 | bool last = rest <= std::numeric_limits<Word>::digits> |
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| 404 | struct RealConversion{ |
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| 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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| 408 | return Shifting<Result, - shift - rest>:: |
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[2386] | 409 | shift(static_cast<Result>(rnd() >> (bits - rest))); |
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[2242] | 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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| 414 | struct RealConversion<Result, Word, rest, shift, false> { |
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| 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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[2386] | 418 | return Shifting<Result, - shift - bits>:: |
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| 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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[2242] | 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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[2386] | 432 | ws.push_back(Word(*it)); |
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[2242] | 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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[2372] | 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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| 453 | |
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| 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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[2242] | 468 | } |
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[2229] | 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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[2242] | 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 |
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| 479 | /// generators. |
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| 480 | /// |
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| 481 | /// This implementation is specialized for both 32-bit and 64-bit |
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| 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. |
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| 485 | /// |
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| 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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[2245] | 488 | /// can use one form of the \c operator() or the \c real() member |
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| 489 | /// function. If you want to get random number from the {0, 1, ..., |
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| 490 | /// n-1} integer range use the \c operator[] or the \c integer() |
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| 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 |
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| 494 | /// equal chance of true and false or given probability of true |
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| 495 | /// result with the \c boolean() member functions. |
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[2242] | 496 | /// |
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| 497 | ///\code |
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[2245] | 498 | /// // The commented code is identical to the other |
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| 499 | /// double a = rnd(); // [0.0, 1.0) |
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| 500 | /// // double a = rnd.real(); // [0.0, 1.0) |
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| 501 | /// double b = rnd(100.0); // [0.0, 100.0) |
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| 502 | /// // double b = rnd.real(100.0); // [0.0, 100.0) |
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| 503 | /// double c = rnd(1.0, 2.0); // [1.0, 2.0) |
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| 504 | /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0) |
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| 505 | /// int d = rnd[100000]; // 0..99999 |
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| 506 | /// // int d = rnd.integer(100000); // 0..99999 |
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| 507 | /// int e = rnd[6] + 1; // 1..6 |
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| 508 | /// // int e = rnd.integer(1, 1 + 6); // 1..6 |
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[2242] | 509 | /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1 |
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| 510 | /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1 |
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| 511 | /// bool g = rnd.boolean(); // P(g = true) = 0.5 |
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| 512 | /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8 |
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| 513 | ///\endcode |
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| 514 | /// |
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[2245] | 515 | /// The lemon provides a global instance of the random number |
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| 516 | /// generator which name is \ref lemon::rnd "rnd". Usually it is a |
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| 517 | /// good programming convenience to use this global generator to get |
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| 518 | /// random numbers. |
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[2229] | 519 | /// |
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| 520 | /// \author Balazs Dezso |
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| 521 | class Random { |
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[2242] | 522 | private: |
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[2229] | 523 | |
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[2245] | 524 | // architecture word |
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[2242] | 525 | typedef unsigned long Word; |
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| 526 | |
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| 527 | _random_bits::RandomCore<Word> core; |
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[2372] | 528 | _random_bits::BoolProducer<Word> bool_producer; |
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| 529 | |
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[2229] | 530 | |
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| 531 | public: |
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| 532 | |
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| 533 | /// \brief Constructor |
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| 534 | /// |
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[2242] | 535 | /// Constructor with constant seeding. |
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| 536 | Random() { core.initState(); } |
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[2229] | 537 | |
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| 538 | /// \brief Constructor |
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| 539 | /// |
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[2242] | 540 | /// Constructor with seed. The current number type will be converted |
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| 541 | /// to the architecture word type. |
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| 542 | template <typename Number> |
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| 543 | Random(Number seed) { |
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| 544 | _random_bits::Initializer<Number, Word>::init(core, seed); |
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| 545 | } |
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| 546 | |
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| 547 | /// \brief Constructor |
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| 548 | /// |
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| 549 | /// Constructor with array seeding. The given range should contain |
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| 550 | /// any number type and the numbers will be converted to the |
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| 551 | /// architecture word type. |
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| 552 | template <typename Iterator> |
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| 553 | Random(Iterator begin, Iterator end) { |
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| 554 | typedef typename std::iterator_traits<Iterator>::value_type Number; |
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| 555 | _random_bits::Initializer<Number, Word>::init(core, begin, end); |
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| 556 | } |
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[2229] | 557 | |
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| 558 | /// \brief Copy constructor |
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| 559 | /// |
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| 560 | /// Copy constructor. The generated sequence will be identical to |
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[2245] | 561 | /// the other sequence. It can be used to save the current state |
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| 562 | /// of the generator and later use it to generate the same |
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| 563 | /// sequence. |
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[2242] | 564 | Random(const Random& other) { |
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| 565 | core.copyState(other.core); |
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[2229] | 566 | } |
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| 567 | |
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| 568 | /// \brief Assign operator |
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| 569 | /// |
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| 570 | /// Assign operator. The generated sequence will be identical to |
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[2245] | 571 | /// the other sequence. It can be used to save the current state |
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| 572 | /// of the generator and later use it to generate the same |
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| 573 | /// sequence. |
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[2229] | 574 | Random& operator=(const Random& other) { |
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| 575 | if (&other != this) { |
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[2242] | 576 | core.copyState(other.core); |
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[2229] | 577 | } |
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| 578 | return *this; |
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| 579 | } |
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| 580 | |
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[2257] | 581 | /// \brief Returns a random real number from the range [0, 1) |
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[2229] | 582 | /// |
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[2245] | 583 | /// It returns a random real number from the range [0, 1). The |
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| 584 | /// default Number type is double. |
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[2242] | 585 | template <typename Number> |
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[2245] | 586 | Number real() { |
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[2242] | 587 | return _random_bits::RealConversion<Number, Word>::convert(core); |
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[2229] | 588 | } |
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| 589 | |
---|
[2245] | 590 | double real() { |
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| 591 | return real<double>(); |
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| 592 | } |
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| 593 | |
---|
[2257] | 594 | /// \brief Returns a random real number the range [0, b) |
---|
[2245] | 595 | /// |
---|
| 596 | /// It returns a random real number from the range [0, b). |
---|
| 597 | template <typename Number> |
---|
| 598 | Number real(Number b) { |
---|
| 599 | return real<Number>() * b; |
---|
| 600 | } |
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| 601 | |
---|
[2257] | 602 | /// \brief Returns a random real number from the range [a, b) |
---|
[2245] | 603 | /// |
---|
| 604 | /// It returns a random real number from the range [a, b). |
---|
| 605 | template <typename Number> |
---|
| 606 | Number real(Number a, Number b) { |
---|
| 607 | return real<Number>() * (b - a) + a; |
---|
| 608 | } |
---|
| 609 | |
---|
[2257] | 610 | /// \brief Returns a random real number from the range [0, 1) |
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[2245] | 611 | /// |
---|
| 612 | /// It returns a random double from the range [0, 1). |
---|
[2242] | 613 | double operator()() { |
---|
[2245] | 614 | return real<double>(); |
---|
[2242] | 615 | } |
---|
| 616 | |
---|
[2257] | 617 | /// \brief Returns a random real number from the range [0, b) |
---|
[2229] | 618 | /// |
---|
[2242] | 619 | /// It returns a random real number from the range [0, b). |
---|
| 620 | template <typename Number> |
---|
| 621 | Number operator()(Number b) { |
---|
[2245] | 622 | return real<Number>() * b; |
---|
[2242] | 623 | } |
---|
| 624 | |
---|
[2257] | 625 | /// \brief Returns a random real number from the range [a, b) |
---|
[2242] | 626 | /// |
---|
| 627 | /// It returns a random real number from the range [a, b). |
---|
| 628 | template <typename Number> |
---|
| 629 | Number operator()(Number a, Number b) { |
---|
[2245] | 630 | return real<Number>() * (b - a) + a; |
---|
[2242] | 631 | } |
---|
| 632 | |
---|
| 633 | /// \brief Returns a random integer from a range |
---|
| 634 | /// |
---|
[2245] | 635 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
[2242] | 636 | template <typename Number> |
---|
[2245] | 637 | Number integer(Number b) { |
---|
| 638 | return _random_bits::Mapping<Number, Word>::map(core, b); |
---|
| 639 | } |
---|
| 640 | |
---|
| 641 | /// \brief Returns a random integer from a range |
---|
| 642 | /// |
---|
| 643 | /// It returns a random integer from the range {a, a + 1, ..., b - 1}. |
---|
| 644 | template <typename Number> |
---|
| 645 | Number integer(Number a, Number b) { |
---|
| 646 | return _random_bits::Mapping<Number, Word>::map(core, b - a) + a; |
---|
| 647 | } |
---|
| 648 | |
---|
| 649 | /// \brief Returns a random integer from a range |
---|
| 650 | /// |
---|
| 651 | /// It returns a random integer from the range {0, 1, ..., b - 1}. |
---|
| 652 | template <typename Number> |
---|
| 653 | Number operator[](Number b) { |
---|
| 654 | return _random_bits::Mapping<Number, Word>::map(core, b); |
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[2242] | 655 | } |
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| 656 | |
---|
| 657 | /// \brief Returns a random non-negative integer |
---|
| 658 | /// |
---|
| 659 | /// It returns a random non-negative integer uniformly from the |
---|
| 660 | /// whole range of the current \c Number type. The default result |
---|
| 661 | /// type of this function is unsigned int. |
---|
| 662 | template <typename Number> |
---|
| 663 | Number uinteger() { |
---|
| 664 | return _random_bits::IntConversion<Number, Word>::convert(core); |
---|
| 665 | } |
---|
| 666 | |
---|
| 667 | unsigned int uinteger() { |
---|
| 668 | return uinteger<unsigned int>(); |
---|
| 669 | } |
---|
| 670 | |
---|
| 671 | /// \brief Returns a random integer |
---|
| 672 | /// |
---|
| 673 | /// It returns a random integer uniformly from the whole range of |
---|
| 674 | /// the current \c Number type. The default result type of this |
---|
| 675 | /// function is int. |
---|
| 676 | template <typename Number> |
---|
| 677 | Number integer() { |
---|
| 678 | static const int nb = std::numeric_limits<Number>::digits + |
---|
| 679 | (std::numeric_limits<Number>::is_signed ? 1 : 0); |
---|
| 680 | return _random_bits::IntConversion<Number, Word, nb>::convert(core); |
---|
| 681 | } |
---|
| 682 | |
---|
| 683 | int integer() { |
---|
| 684 | return integer<int>(); |
---|
[2229] | 685 | } |
---|
| 686 | |
---|
[2242] | 687 | /// \brief Returns a random bool |
---|
[2229] | 688 | /// |
---|
[2372] | 689 | /// It returns a random bool. The generator holds a buffer for |
---|
| 690 | /// random bits. Every time when it become empty the generator makes |
---|
| 691 | /// a new random word and fill the buffer up. |
---|
[2242] | 692 | bool boolean() { |
---|
[2372] | 693 | return bool_producer.convert(core); |
---|
[2229] | 694 | } |
---|
| 695 | |
---|
[2356] | 696 | ///\name Nonuniform distributions |
---|
| 697 | /// |
---|
| 698 | |
---|
| 699 | ///@{ |
---|
| 700 | |
---|
[2229] | 701 | /// \brief Returns a random bool |
---|
| 702 | /// |
---|
[2242] | 703 | /// It returns a random bool with given probability of true result |
---|
| 704 | bool boolean(double p) { |
---|
| 705 | return operator()() < p; |
---|
[2229] | 706 | } |
---|
[2355] | 707 | |
---|
| 708 | /// Standard Gauss distribution |
---|
| 709 | |
---|
| 710 | /// Standard Gauss distribution. |
---|
[2356] | 711 | /// \note The Cartesian form of the Box-Muller |
---|
| 712 | /// transformation is used to generate a random normal distribution. |
---|
| 713 | /// \todo Consider using the "ziggurat" method instead. |
---|
[2355] | 714 | double gauss() |
---|
| 715 | { |
---|
| 716 | double V1,V2,S; |
---|
| 717 | do { |
---|
| 718 | V1=2*real<double>()-1; |
---|
| 719 | V2=2*real<double>()-1; |
---|
| 720 | S=V1*V1+V2*V2; |
---|
| 721 | } while(S>=1); |
---|
| 722 | return std::sqrt(-2*std::log(S)/S)*V1; |
---|
| 723 | } |
---|
[2356] | 724 | /// Gauss distribution with given standard deviation and mean 0 |
---|
| 725 | |
---|
| 726 | /// \sa gauss() |
---|
| 727 | /// |
---|
| 728 | double gauss(double std_dev) |
---|
[2355] | 729 | { |
---|
[2356] | 730 | return gauss()*std_dev; |
---|
[2355] | 731 | } |
---|
[2356] | 732 | /// Gauss distribution with given mean and standard deviation |
---|
| 733 | |
---|
| 734 | /// \sa gauss() |
---|
| 735 | /// |
---|
| 736 | double gauss(double mean,double std_dev) |
---|
[2355] | 737 | { |
---|
[2356] | 738 | return gauss()*std_dev+mean; |
---|
[2355] | 739 | } |
---|
| 740 | |
---|
[2356] | 741 | /// Exponential distribution with given mean |
---|
| 742 | |
---|
| 743 | /// This function generates an exponential distribution random number |
---|
| 744 | /// with mean <tt>1/lambda</tt>. |
---|
| 745 | /// |
---|
| 746 | double exponential(double lambda=1.0) |
---|
[2355] | 747 | { |
---|
[2374] | 748 | return -std::log(real<double>())/lambda; |
---|
[2355] | 749 | } |
---|
[2356] | 750 | |
---|
[2483] | 751 | double gamma(int k) |
---|
| 752 | { |
---|
| 753 | double s = 0; |
---|
| 754 | for(int i=0;i<k;i++) s-=std::log(1.0-real<double>()); |
---|
| 755 | return s; |
---|
| 756 | } |
---|
| 757 | |
---|
| 758 | /// Gamma distribution with given shape and scale parameter |
---|
| 759 | |
---|
| 760 | /// This function generates a gamma distribution random number. |
---|
| 761 | /// |
---|
| 762 | ///\param k shape parameter (<tt>k>0</tt>) |
---|
| 763 | ///\param theta scale parameter |
---|
| 764 | /// |
---|
| 765 | double gamma(double k,double theta=1.0) |
---|
| 766 | { |
---|
| 767 | double xi,nu; |
---|
| 768 | const double delta = k-std::floor(k); |
---|
| 769 | const double v0=M_E/(M_E-delta); |
---|
| 770 | do { |
---|
| 771 | double V0=1.0-real<double>(); |
---|
| 772 | double V1=1.0-real<double>(); |
---|
| 773 | double V2=1.0-real<double>(); |
---|
| 774 | if(V2<=v0) |
---|
| 775 | { |
---|
| 776 | xi=std::pow(V1,1.0/delta); |
---|
| 777 | nu=V0*std::pow(xi,delta-1.0); |
---|
| 778 | } |
---|
| 779 | else |
---|
| 780 | { |
---|
| 781 | xi=1.0-std::log(V1); |
---|
| 782 | nu=V0*std::exp(-xi); |
---|
| 783 | } |
---|
| 784 | } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi)); |
---|
| 785 | return theta*(xi-gamma(int(std::floor(k)))); |
---|
| 786 | } |
---|
| 787 | |
---|
| 788 | |
---|
[2356] | 789 | ///@} |
---|
[2229] | 790 | |
---|
[2374] | 791 | ///\name Two dimensional distributions |
---|
| 792 | /// |
---|
| 793 | |
---|
| 794 | ///@{ |
---|
| 795 | |
---|
| 796 | /// Uniform distribution on the full unit circle. |
---|
[2380] | 797 | dim2::Point<double> disc() |
---|
[2374] | 798 | { |
---|
| 799 | double V1,V2; |
---|
| 800 | do { |
---|
| 801 | V1=2*real<double>()-1; |
---|
| 802 | V2=2*real<double>()-1; |
---|
| 803 | |
---|
| 804 | } while(V1*V1+V2*V2>=1); |
---|
| 805 | return dim2::Point<double>(V1,V2); |
---|
| 806 | } |
---|
| 807 | /// A kind of two dimensional Gauss distribution |
---|
| 808 | |
---|
| 809 | /// This function provides a turning symmetric two-dimensional distribution. |
---|
| 810 | /// Both coordinates are of standard normal distribution, but they are not |
---|
| 811 | /// independent. |
---|
| 812 | /// |
---|
| 813 | /// \note The coordinates are the two random variables provided by |
---|
| 814 | /// the Box-Muller method. |
---|
| 815 | dim2::Point<double> gauss2() |
---|
| 816 | { |
---|
| 817 | double V1,V2,S; |
---|
| 818 | do { |
---|
| 819 | V1=2*real<double>()-1; |
---|
| 820 | V2=2*real<double>()-1; |
---|
| 821 | S=V1*V1+V2*V2; |
---|
| 822 | } while(S>=1); |
---|
| 823 | double W=std::sqrt(-2*std::log(S)/S); |
---|
| 824 | return dim2::Point<double>(W*V1,W*V2); |
---|
| 825 | } |
---|
| 826 | /// A kind of two dimensional exponential distribution |
---|
| 827 | |
---|
| 828 | /// This function provides a turning symmetric two-dimensional distribution. |
---|
| 829 | /// The x-coordinate is of conditionally exponential distribution |
---|
| 830 | /// with the condition that x is positive and y=0. If x is negative and |
---|
| 831 | /// y=0 then, -x is of exponential distribution. The same is true for the |
---|
| 832 | /// y-coordinate. |
---|
| 833 | dim2::Point<double> exponential2() |
---|
| 834 | { |
---|
| 835 | double V1,V2,S; |
---|
| 836 | do { |
---|
| 837 | V1=2*real<double>()-1; |
---|
| 838 | V2=2*real<double>()-1; |
---|
| 839 | S=V1*V1+V2*V2; |
---|
| 840 | } while(S>=1); |
---|
| 841 | double W=-std::log(S)/S; |
---|
| 842 | return dim2::Point<double>(W*V1,W*V2); |
---|
| 843 | } |
---|
| 844 | |
---|
| 845 | ///@} |
---|
[2229] | 846 | }; |
---|
| 847 | |
---|
| 848 | |
---|
| 849 | extern Random rnd; |
---|
| 850 | |
---|
| 851 | } |
---|
| 852 | |
---|
| 853 | #endif |
---|