1006 lines
30 KiB
C++
Executable File
1006 lines
30 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2009
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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/*
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* This file contains the reimplemented version of the Mersenne Twister
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* Generator of Matsumoto and Nishimura.
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*
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* See the appropriate copyright notice below.
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*
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* Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* 3. The names of its contributors may not be used to endorse or promote
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* products derived from this software without specific prior written
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* permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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*
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* Any feedback is very welcome.
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* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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* email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
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*/
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#ifndef LEMON_RANDOM_H
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#define LEMON_RANDOM_H
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#include <algorithm>
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#include <iterator>
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#include <vector>
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#include <limits>
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#include <fstream>
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#include <lemon/math.h>
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#include <lemon/dim2.h>
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#ifndef WIN32
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#include <sys/time.h>
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#include <ctime>
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#include <sys/types.h>
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#include <unistd.h>
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#else
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#include <lemon/bits/windows.h>
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#endif
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///\ingroup misc
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///\file
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///\brief Mersenne Twister random number generator
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namespace lemon {
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namespace _random_bits {
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template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
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struct RandomTraits {};
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template <typename _Word>
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struct RandomTraits<_Word, 32> {
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typedef _Word Word;
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static const int bits = 32;
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static const int length = 624;
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static const int shift = 397;
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static const Word mul = 0x6c078965u;
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static const Word arrayInit = 0x012BD6AAu;
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static const Word arrayMul1 = 0x0019660Du;
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static const Word arrayMul2 = 0x5D588B65u;
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static const Word mask = 0x9908B0DFu;
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static const Word loMask = (1u << 31) - 1;
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static const Word hiMask = ~loMask;
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static Word tempering(Word rnd) {
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rnd ^= (rnd >> 11);
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rnd ^= (rnd << 7) & 0x9D2C5680u;
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rnd ^= (rnd << 15) & 0xEFC60000u;
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rnd ^= (rnd >> 18);
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return rnd;
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}
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};
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template <typename _Word>
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struct RandomTraits<_Word, 64> {
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typedef _Word Word;
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static const int bits = 64;
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static const int length = 312;
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static const int shift = 156;
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static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
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static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
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static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
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static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
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static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
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static const Word loMask = (Word(1u) << 31) - 1;
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static const Word hiMask = ~loMask;
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static Word tempering(Word rnd) {
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rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
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rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
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rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
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rnd ^= (rnd >> 43);
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return rnd;
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}
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};
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template <typename _Word>
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class RandomCore {
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public:
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typedef _Word Word;
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private:
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static const int bits = RandomTraits<Word>::bits;
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static const int length = RandomTraits<Word>::length;
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static const int shift = RandomTraits<Word>::shift;
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public:
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void initState() {
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static const Word seedArray[4] = {
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0x12345u, 0x23456u, 0x34567u, 0x45678u
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};
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initState(seedArray, seedArray + 4);
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}
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void initState(Word seed) {
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static const Word mul = RandomTraits<Word>::mul;
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current = state;
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Word *curr = state + length - 1;
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curr[0] = seed; --curr;
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for (int i = 1; i < length; ++i) {
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curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
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--curr;
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}
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}
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template <typename Iterator>
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void initState(Iterator begin, Iterator end) {
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static const Word init = RandomTraits<Word>::arrayInit;
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static const Word mul1 = RandomTraits<Word>::arrayMul1;
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static const Word mul2 = RandomTraits<Word>::arrayMul2;
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Word *curr = state + length - 1; --curr;
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Iterator it = begin; int cnt = 0;
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int num;
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initState(init);
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num = length > end - begin ? length : end - begin;
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while (num--) {
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curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
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+ *it + cnt;
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++it; ++cnt;
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if (it == end) {
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it = begin; cnt = 0;
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}
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if (curr == state) {
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curr = state + length - 1; curr[0] = state[0];
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}
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--curr;
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}
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num = length - 1; cnt = length - (curr - state) - 1;
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while (num--) {
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curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
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- cnt;
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--curr; ++cnt;
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if (curr == state) {
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curr = state + length - 1; curr[0] = state[0]; --curr;
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cnt = 1;
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}
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}
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state[length - 1] = Word(1) << (bits - 1);
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}
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void copyState(const RandomCore& other) {
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std::copy(other.state, other.state + length, state);
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current = state + (other.current - other.state);
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}
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Word operator()() {
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if (current == state) fillState();
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--current;
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Word rnd = *current;
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return RandomTraits<Word>::tempering(rnd);
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}
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private:
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void fillState() {
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static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
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static const Word loMask = RandomTraits<Word>::loMask;
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static const Word hiMask = RandomTraits<Word>::hiMask;
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current = state + length;
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register Word *curr = state + length - 1;
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register long num;
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num = length - shift;
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while (num--) {
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curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
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curr[- shift] ^ mask[curr[-1] & 1ul];
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--curr;
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}
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num = shift - 1;
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while (num--) {
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curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
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curr[length - shift] ^ mask[curr[-1] & 1ul];
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--curr;
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}
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state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
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curr[length - shift] ^ mask[curr[length - 1] & 1ul];
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}
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Word *current;
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Word state[length];
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};
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template <typename Result,
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int shift = (std::numeric_limits<Result>::digits + 1) / 2>
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struct Masker {
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static Result mask(const Result& result) {
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return Masker<Result, (shift + 1) / 2>::
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mask(static_cast<Result>(result | (result >> shift)));
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}
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};
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template <typename Result>
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struct Masker<Result, 1> {
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static Result mask(const Result& result) {
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return static_cast<Result>(result | (result >> 1));
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}
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};
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template <typename Result, typename Word,
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int rest = std::numeric_limits<Result>::digits, int shift = 0,
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bool last = rest <= std::numeric_limits<Word>::digits>
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struct IntConversion {
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static const int bits = std::numeric_limits<Word>::digits;
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static Result convert(RandomCore<Word>& rnd) {
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return static_cast<Result>(rnd() >> (bits - rest)) << shift;
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}
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};
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template <typename Result, typename Word, int rest, int shift>
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struct IntConversion<Result, Word, rest, shift, false> {
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static const int bits = std::numeric_limits<Word>::digits;
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static Result convert(RandomCore<Word>& rnd) {
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return (static_cast<Result>(rnd()) << shift) |
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IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
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}
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};
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template <typename Result, typename Word,
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bool one_word = (std::numeric_limits<Word>::digits <
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std::numeric_limits<Result>::digits) >
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struct Mapping {
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static Result map(RandomCore<Word>& rnd, const Result& bound) {
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Word max = Word(bound - 1);
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Result mask = Masker<Result>::mask(bound - 1);
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Result num;
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do {
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num = IntConversion<Result, Word>::convert(rnd) & mask;
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} while (num > max);
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return num;
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}
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};
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template <typename Result, typename Word>
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struct Mapping<Result, Word, false> {
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static Result map(RandomCore<Word>& rnd, const Result& bound) {
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Word max = Word(bound - 1);
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Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
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::mask(max);
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Word num;
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do {
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num = rnd() & mask;
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} while (num > max);
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return num;
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}
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};
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template <typename Result, int exp>
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struct ShiftMultiplier {
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static const Result multiplier() {
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Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
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res *= res;
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if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
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return res;
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}
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};
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template <typename Result>
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struct ShiftMultiplier<Result, 0> {
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static const Result multiplier() {
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return static_cast<Result>(1.0);
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}
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};
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template <typename Result>
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struct ShiftMultiplier<Result, 20> {
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static const Result multiplier() {
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return static_cast<Result>(1.0/1048576.0);
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}
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};
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template <typename Result>
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struct ShiftMultiplier<Result, 32> {
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static const Result multiplier() {
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return static_cast<Result>(1.0/4294967296.0);
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}
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};
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template <typename Result>
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struct ShiftMultiplier<Result, 53> {
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static const Result multiplier() {
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return static_cast<Result>(1.0/9007199254740992.0);
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}
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};
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template <typename Result>
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struct ShiftMultiplier<Result, 64> {
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static const Result multiplier() {
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return static_cast<Result>(1.0/18446744073709551616.0);
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}
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};
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template <typename Result, int exp>
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struct Shifting {
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static Result shift(const Result& result) {
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return result * ShiftMultiplier<Result, exp>::multiplier();
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}
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};
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template <typename Result, typename Word,
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int rest = std::numeric_limits<Result>::digits, int shift = 0,
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bool last = rest <= std::numeric_limits<Word>::digits>
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struct RealConversion{
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static const int bits = std::numeric_limits<Word>::digits;
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static Result convert(RandomCore<Word>& rnd) {
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return Shifting<Result, shift + rest>::
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shift(static_cast<Result>(rnd() >> (bits - rest)));
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}
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};
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template <typename Result, typename Word, int rest, int shift>
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struct RealConversion<Result, Word, rest, shift, false> {
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static const int bits = std::numeric_limits<Word>::digits;
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static Result convert(RandomCore<Word>& rnd) {
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return Shifting<Result, shift + bits>::
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shift(static_cast<Result>(rnd())) +
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RealConversion<Result, Word, rest-bits, shift + bits>::
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convert(rnd);
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}
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};
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template <typename Result, typename Word>
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struct Initializer {
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template <typename Iterator>
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static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
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std::vector<Word> ws;
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for (Iterator it = begin; it != end; ++it) {
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ws.push_back(Word(*it));
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}
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rnd.initState(ws.begin(), ws.end());
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}
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static void init(RandomCore<Word>& rnd, Result seed) {
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rnd.initState(seed);
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}
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};
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template <typename Word>
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struct BoolConversion {
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static bool convert(RandomCore<Word>& rnd) {
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return (rnd() & 1) == 1;
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}
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};
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template <typename Word>
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struct BoolProducer {
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Word buffer;
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int num;
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BoolProducer() : num(0) {}
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bool convert(RandomCore<Word>& rnd) {
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if (num == 0) {
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buffer = rnd();
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num = RandomTraits<Word>::bits;
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}
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bool r = (buffer & 1);
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buffer >>= 1;
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--num;
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return r;
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}
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};
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}
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/// \ingroup misc
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///
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/// \brief Mersenne Twister random number generator
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///
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/// The Mersenne Twister is a twisted generalized feedback
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/// shift-register generator of Matsumoto and Nishimura. The period
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/// of this generator is \f$ 2^{19937} - 1 \f$ and it is
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/// equi-distributed in 623 dimensions for 32-bit numbers. The time
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/// performance of this generator is comparable to the commonly used
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/// generators.
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///
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/// This implementation is specialized for both 32-bit and 64-bit
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/// architectures. The generators differ sligthly in the
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/// initialization and generation phase so they produce two
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/// completly different sequences.
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///
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/// The generator gives back random numbers of serveral types. To
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/// get a random number from a range of a floating point type you
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/// can use one form of the \c operator() or the \c real() member
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/// function. If you want to get random number from the {0, 1, ...,
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/// n-1} integer range use the \c operator[] or the \c integer()
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/// method. And to get random number from the whole range of an
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/// integer type you can use the argumentless \c integer() or \c
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/// uinteger() functions. After all you can get random bool with
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/// equal chance of true and false or given probability of true
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/// result with the \c boolean() member functions.
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///
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///\code
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/// // The commented code is identical to the other
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/// double a = rnd(); // [0.0, 1.0)
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/// // double a = rnd.real(); // [0.0, 1.0)
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/// double b = rnd(100.0); // [0.0, 100.0)
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/// // double b = rnd.real(100.0); // [0.0, 100.0)
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/// double c = rnd(1.0, 2.0); // [1.0, 2.0)
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/// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
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/// int d = rnd[100000]; // 0..99999
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/// // int d = rnd.integer(100000); // 0..99999
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/// int e = rnd[6] + 1; // 1..6
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/// // int e = rnd.integer(1, 1 + 6); // 1..6
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/// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
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/// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
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/// bool g = rnd.boolean(); // P(g = true) = 0.5
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/// bool h = rnd.boolean(0.8); // P(h = true) = 0.8
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///\endcode
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///
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/// LEMON provides a global instance of the random number
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/// generator which name is \ref lemon::rnd "rnd". Usually it is a
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/// good programming convenience to use this global generator to get
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/// random numbers.
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class Random {
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private:
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// Architecture word
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typedef unsigned long Word;
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_random_bits::RandomCore<Word> core;
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_random_bits::BoolProducer<Word> bool_producer;
|
|
|
|
|
|
public:
|
|
|
|
///\name Initialization
|
|
///
|
|
/// @{
|
|
|
|
/// \brief Default constructor
|
|
///
|
|
/// Constructor with constant seeding.
|
|
Random() { core.initState(); }
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|
|
|
/// \brief Constructor with seed
|
|
///
|
|
/// Constructor with seed. The current number type will be converted
|
|
/// to the architecture word type.
|
|
template <typename Number>
|
|
Random(Number seed) {
|
|
_random_bits::Initializer<Number, Word>::init(core, seed);
|
|
}
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|
|
|
/// \brief Constructor with array seeding
|
|
///
|
|
/// Constructor with array seeding. The given range should contain
|
|
/// any number type and the numbers will be converted to the
|
|
/// architecture word type.
|
|
template <typename Iterator>
|
|
Random(Iterator begin, Iterator end) {
|
|
typedef typename std::iterator_traits<Iterator>::value_type Number;
|
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_random_bits::Initializer<Number, Word>::init(core, begin, end);
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|
}
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|
|
|
/// \brief Copy constructor
|
|
///
|
|
/// Copy constructor. The generated sequence will be identical to
|
|
/// the other sequence. It can be used to save the current state
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|
/// of the generator and later use it to generate the same
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|
/// sequence.
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|
Random(const Random& other) {
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|
core.copyState(other.core);
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|
}
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|
|
|
/// \brief Assign operator
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|
///
|
|
/// Assign operator. The generated sequence will be identical to
|
|
/// the other sequence. It can be used to save the current state
|
|
/// of the generator and later use it to generate the same
|
|
/// sequence.
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|
Random& operator=(const Random& other) {
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|
if (&other != this) {
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|
core.copyState(other.core);
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|
}
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|
return *this;
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|
}
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|
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|
/// \brief Seeding random sequence
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|
///
|
|
/// Seeding the random sequence. The current number type will be
|
|
/// converted to the architecture word type.
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|
template <typename Number>
|
|
void seed(Number seed) {
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|
_random_bits::Initializer<Number, Word>::init(core, seed);
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|
}
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|
|
|
/// \brief Seeding random sequence
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|
///
|
|
/// Seeding the random sequence. The given range should contain
|
|
/// any number type and the numbers will be converted to the
|
|
/// architecture word type.
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|
template <typename Iterator>
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|
void seed(Iterator begin, Iterator end) {
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|
typedef typename std::iterator_traits<Iterator>::value_type Number;
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|
_random_bits::Initializer<Number, Word>::init(core, begin, end);
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|
}
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|
/// \brief Seeding from file or from process id and time
|
|
///
|
|
/// By default, this function calls the \c seedFromFile() member
|
|
/// function with the <tt>/dev/urandom</tt> file. If it does not success,
|
|
/// it uses the \c seedFromTime().
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|
/// \return Currently always \c true.
|
|
bool seed() {
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|
#ifndef WIN32
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|
if (seedFromFile("/dev/urandom", 0)) return true;
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|
#endif
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|
if (seedFromTime()) return true;
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|
return false;
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|
}
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|
|
|
/// \brief Seeding from file
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|
///
|
|
/// Seeding the random sequence from file. The linux kernel has two
|
|
/// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
|
|
/// could give good seed values for pseudo random generators (The
|
|
/// difference between two devices is that the <tt>random</tt> may
|
|
/// block the reading operation while the kernel can give good
|
|
/// source of randomness, while the <tt>urandom</tt> does not
|
|
/// block the input, but it could give back bytes with worse
|
|
/// entropy).
|
|
/// \param file The source file
|
|
/// \param offset The offset, from the file read.
|
|
/// \return \c true when the seeding successes.
|
|
#ifndef WIN32
|
|
bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
|
|
#else
|
|
bool seedFromFile(const std::string& file = "", int offset = 0)
|
|
#endif
|
|
{
|
|
std::ifstream rs(file.c_str());
|
|
const int size = 4;
|
|
Word buf[size];
|
|
if (offset != 0 && !rs.seekg(offset)) return false;
|
|
if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
|
|
seed(buf, buf + size);
|
|
return true;
|
|
}
|
|
|
|
/// \brief Seding from process id and time
|
|
///
|
|
/// Seding from process id and time. This function uses the
|
|
/// current process id and the current time for initialize the
|
|
/// random sequence.
|
|
/// \return Currently always \c true.
|
|
bool seedFromTime() {
|
|
#ifndef WIN32
|
|
timeval tv;
|
|
gettimeofday(&tv, 0);
|
|
seed(getpid() + tv.tv_sec + tv.tv_usec);
|
|
#else
|
|
seed(bits::getWinRndSeed());
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
/// @}
|
|
|
|
///\name Uniform Distributions
|
|
///
|
|
/// @{
|
|
|
|
/// \brief Returns a random real number from the range [0, 1)
|
|
///
|
|
/// It returns a random real number from the range [0, 1). The
|
|
/// default Number type is \c double.
|
|
template <typename Number>
|
|
Number real() {
|
|
return _random_bits::RealConversion<Number, Word>::convert(core);
|
|
}
|
|
|
|
double real() {
|
|
return real<double>();
|
|
}
|
|
|
|
/// \brief Returns a random real number from the range [0, 1)
|
|
///
|
|
/// It returns a random double from the range [0, 1).
|
|
double operator()() {
|
|
return real<double>();
|
|
}
|
|
|
|
/// \brief Returns a random real number from the range [0, b)
|
|
///
|
|
/// It returns a random real number from the range [0, b).
|
|
double operator()(double b) {
|
|
return real<double>() * b;
|
|
}
|
|
|
|
/// \brief Returns a random real number from the range [a, b)
|
|
///
|
|
/// It returns a random real number from the range [a, b).
|
|
double operator()(double a, double b) {
|
|
return real<double>() * (b - a) + a;
|
|
}
|
|
|
|
/// \brief Returns a random integer from a range
|
|
///
|
|
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
|
template <typename Number>
|
|
Number integer(Number b) {
|
|
return _random_bits::Mapping<Number, Word>::map(core, b);
|
|
}
|
|
|
|
/// \brief Returns a random integer from a range
|
|
///
|
|
/// It returns a random integer from the range {a, a + 1, ..., b - 1}.
|
|
template <typename Number>
|
|
Number integer(Number a, Number b) {
|
|
return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
|
|
}
|
|
|
|
/// \brief Returns a random integer from a range
|
|
///
|
|
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
|
template <typename Number>
|
|
Number operator[](Number b) {
|
|
return _random_bits::Mapping<Number, Word>::map(core, b);
|
|
}
|
|
|
|
/// \brief Returns a random non-negative integer
|
|
///
|
|
/// It returns a random non-negative integer uniformly from the
|
|
/// whole range of the current \c Number type. The default result
|
|
/// type of this function is <tt>unsigned int</tt>.
|
|
template <typename Number>
|
|
Number uinteger() {
|
|
return _random_bits::IntConversion<Number, Word>::convert(core);
|
|
}
|
|
|
|
unsigned int uinteger() {
|
|
return uinteger<unsigned int>();
|
|
}
|
|
|
|
/// \brief Returns a random integer
|
|
///
|
|
/// It returns a random integer uniformly from the whole range of
|
|
/// the current \c Number type. The default result type of this
|
|
/// function is \c int.
|
|
template <typename Number>
|
|
Number integer() {
|
|
static const int nb = std::numeric_limits<Number>::digits +
|
|
(std::numeric_limits<Number>::is_signed ? 1 : 0);
|
|
return _random_bits::IntConversion<Number, Word, nb>::convert(core);
|
|
}
|
|
|
|
int integer() {
|
|
return integer<int>();
|
|
}
|
|
|
|
/// \brief Returns a random bool
|
|
///
|
|
/// It returns a random bool. The generator holds a buffer for
|
|
/// random bits. Every time when it become empty the generator makes
|
|
/// a new random word and fill the buffer up.
|
|
bool boolean() {
|
|
return bool_producer.convert(core);
|
|
}
|
|
|
|
/// @}
|
|
|
|
///\name Non-uniform Distributions
|
|
///
|
|
///@{
|
|
|
|
/// \brief Returns a random bool with given probability of true result.
|
|
///
|
|
/// It returns a random bool with given probability of true result.
|
|
bool boolean(double p) {
|
|
return operator()() < p;
|
|
}
|
|
|
|
/// Standard normal (Gauss) distribution
|
|
|
|
/// Standard normal (Gauss) distribution.
|
|
/// \note The Cartesian form of the Box-Muller
|
|
/// transformation is used to generate a random normal distribution.
|
|
double gauss()
|
|
{
|
|
double V1,V2,S;
|
|
do {
|
|
V1=2*real<double>()-1;
|
|
V2=2*real<double>()-1;
|
|
S=V1*V1+V2*V2;
|
|
} while(S>=1);
|
|
return std::sqrt(-2*std::log(S)/S)*V1;
|
|
}
|
|
/// Normal (Gauss) distribution with given mean and standard deviation
|
|
|
|
/// Normal (Gauss) distribution with given mean and standard deviation.
|
|
/// \sa gauss()
|
|
double gauss(double mean,double std_dev)
|
|
{
|
|
return gauss()*std_dev+mean;
|
|
}
|
|
|
|
/// Lognormal distribution
|
|
|
|
/// Lognormal distribution. The parameters are the mean and the standard
|
|
/// deviation of <tt>exp(X)</tt>.
|
|
///
|
|
double lognormal(double n_mean,double n_std_dev)
|
|
{
|
|
return std::exp(gauss(n_mean,n_std_dev));
|
|
}
|
|
/// Lognormal distribution
|
|
|
|
/// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
|
|
/// the mean and the standard deviation of <tt>exp(X)</tt>.
|
|
///
|
|
double lognormal(const std::pair<double,double> ¶ms)
|
|
{
|
|
return std::exp(gauss(params.first,params.second));
|
|
}
|
|
/// Compute the lognormal parameters from mean and standard deviation
|
|
|
|
/// This function computes the lognormal parameters from mean and
|
|
/// standard deviation. The return value can direcly be passed to
|
|
/// lognormal().
|
|
std::pair<double,double> lognormalParamsFromMD(double mean,
|
|
double std_dev)
|
|
{
|
|
double fr=std_dev/mean;
|
|
fr*=fr;
|
|
double lg=std::log(1+fr);
|
|
return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
|
|
}
|
|
/// Lognormal distribution with given mean and standard deviation
|
|
|
|
/// Lognormal distribution with given mean and standard deviation.
|
|
///
|
|
double lognormalMD(double mean,double std_dev)
|
|
{
|
|
return lognormal(lognormalParamsFromMD(mean,std_dev));
|
|
}
|
|
|
|
/// Exponential distribution with given mean
|
|
|
|
/// This function generates an exponential distribution random number
|
|
/// with mean <tt>1/lambda</tt>.
|
|
///
|
|
double exponential(double lambda=1.0)
|
|
{
|
|
return -std::log(1.0-real<double>())/lambda;
|
|
}
|
|
|
|
/// Gamma distribution with given integer shape
|
|
|
|
/// This function generates a gamma distribution random number.
|
|
///
|
|
///\param k shape parameter (<tt>k>0</tt> integer)
|
|
double gamma(int k)
|
|
{
|
|
double s = 0;
|
|
for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
|
|
return s;
|
|
}
|
|
|
|
/// Gamma distribution with given shape and scale parameter
|
|
|
|
/// This function generates a gamma distribution random number.
|
|
///
|
|
///\param k shape parameter (<tt>k>0</tt>)
|
|
///\param theta scale parameter
|
|
///
|
|
double gamma(double k,double theta=1.0)
|
|
{
|
|
double xi,nu;
|
|
const double delta = k-std::floor(k);
|
|
const double v0=E/(E-delta);
|
|
do {
|
|
double V0=1.0-real<double>();
|
|
double V1=1.0-real<double>();
|
|
double V2=1.0-real<double>();
|
|
if(V2<=v0)
|
|
{
|
|
xi=std::pow(V1,1.0/delta);
|
|
nu=V0*std::pow(xi,delta-1.0);
|
|
}
|
|
else
|
|
{
|
|
xi=1.0-std::log(V1);
|
|
nu=V0*std::exp(-xi);
|
|
}
|
|
} while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
|
|
return theta*(xi+gamma(int(std::floor(k))));
|
|
}
|
|
|
|
/// Weibull distribution
|
|
|
|
/// This function generates a Weibull distribution random number.
|
|
///
|
|
///\param k shape parameter (<tt>k>0</tt>)
|
|
///\param lambda scale parameter (<tt>lambda>0</tt>)
|
|
///
|
|
double weibull(double k,double lambda)
|
|
{
|
|
return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
|
|
}
|
|
|
|
/// Pareto distribution
|
|
|
|
/// This function generates a Pareto distribution random number.
|
|
///
|
|
///\param k shape parameter (<tt>k>0</tt>)
|
|
///\param x_min location parameter (<tt>x_min>0</tt>)
|
|
///
|
|
double pareto(double k,double x_min)
|
|
{
|
|
return exponential(gamma(k,1.0/x_min))+x_min;
|
|
}
|
|
|
|
/// Poisson distribution
|
|
|
|
/// This function generates a Poisson distribution random number with
|
|
/// parameter \c lambda.
|
|
///
|
|
/// The probability mass function of this distribusion is
|
|
/// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
|
|
/// \note The algorithm is taken from the book of Donald E. Knuth titled
|
|
/// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
|
|
/// return value.
|
|
|
|
int poisson(double lambda)
|
|
{
|
|
const double l = std::exp(-lambda);
|
|
int k=0;
|
|
double p = 1.0;
|
|
do {
|
|
k++;
|
|
p*=real<double>();
|
|
} while (p>=l);
|
|
return k-1;
|
|
}
|
|
|
|
///@}
|
|
|
|
///\name Two Dimensional Distributions
|
|
///
|
|
///@{
|
|
|
|
/// Uniform distribution on the full unit circle
|
|
|
|
/// Uniform distribution on the full unit circle.
|
|
///
|
|
dim2::Point<double> disc()
|
|
{
|
|
double V1,V2;
|
|
do {
|
|
V1=2*real<double>()-1;
|
|
V2=2*real<double>()-1;
|
|
|
|
} while(V1*V1+V2*V2>=1);
|
|
return dim2::Point<double>(V1,V2);
|
|
}
|
|
/// A kind of two dimensional normal (Gauss) distribution
|
|
|
|
/// This function provides a turning symmetric two-dimensional distribution.
|
|
/// Both coordinates are of standard normal distribution, but they are not
|
|
/// independent.
|
|
///
|
|
/// \note The coordinates are the two random variables provided by
|
|
/// the Box-Muller method.
|
|
dim2::Point<double> gauss2()
|
|
{
|
|
double V1,V2,S;
|
|
do {
|
|
V1=2*real<double>()-1;
|
|
V2=2*real<double>()-1;
|
|
S=V1*V1+V2*V2;
|
|
} while(S>=1);
|
|
double W=std::sqrt(-2*std::log(S)/S);
|
|
return dim2::Point<double>(W*V1,W*V2);
|
|
}
|
|
/// A kind of two dimensional exponential distribution
|
|
|
|
/// This function provides a turning symmetric two-dimensional distribution.
|
|
/// The x-coordinate is of conditionally exponential distribution
|
|
/// with the condition that x is positive and y=0. If x is negative and
|
|
/// y=0 then, -x is of exponential distribution. The same is true for the
|
|
/// y-coordinate.
|
|
dim2::Point<double> exponential2()
|
|
{
|
|
double V1,V2,S;
|
|
do {
|
|
V1=2*real<double>()-1;
|
|
V2=2*real<double>()-1;
|
|
S=V1*V1+V2*V2;
|
|
} while(S>=1);
|
|
double W=-std::log(S)/S;
|
|
return dim2::Point<double>(W*V1,W*V2);
|
|
}
|
|
|
|
///@}
|
|
};
|
|
|
|
|
|
extern Random rnd;
|
|
|
|
}
|
|
|
|
#endif
|