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/* -*- C++ -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library
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*
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* Copyright (C) 2003-2008
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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deba@2372
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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 <ctime>
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#include <lemon/math.h>
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#include <lemon/dim2.h>
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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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///
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///\author Balazs Dezso
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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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deba@2242
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deba@2242
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void fillState() {
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deba@2242
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static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
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deba@2242
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static const Word loMask = RandomTraits<Word>::loMask;
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deba@2242
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static const Word hiMask = RandomTraits<Word>::hiMask;
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deba@2242
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deba@2242
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current = state + length;
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deba@2242
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deba@2242
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register Word *curr = state + length - 1;
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deba@2242
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register long num;
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deba@2242
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deba@2242
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num = length - shift;
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deba@2242
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while (num--) {
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deba@2242
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curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
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deba@2242
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curr[- shift] ^ mask[curr[-1] & 1ul];
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deba@2242
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--curr;
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deba@2242
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}
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deba@2242
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num = shift - 1;
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deba@2242
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254 |
while (num--) {
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deba@2242
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curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
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deba@2242
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curr[length - shift] ^ mask[curr[-1] & 1ul];
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deba@2242
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--curr;
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deba@2242
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}
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state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
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deba@2545
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curr[length - shift] ^ mask[int(curr[length - 1] & 1ul)];
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deba@2242
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261 |
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deba@2242
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262 |
}
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deba@2242
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263 |
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deba@2242
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264 |
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deba@2242
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265 |
Word *current;
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deba@2242
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266 |
Word state[length];
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deba@2242
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267 |
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deba@2242
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};
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deba@2242
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deba@2242
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deba@2242
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271 |
template <typename Result,
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deba@2242
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272 |
int shift = (std::numeric_limits<Result>::digits + 1) / 2>
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deba@2242
|
273 |
struct Masker {
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deba@2242
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274 |
static Result mask(const Result& result) {
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deba@2242
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275 |
return Masker<Result, (shift + 1) / 2>::
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deba@2386
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276 |
mask(static_cast<Result>(result | (result >> shift)));
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deba@2242
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277 |
}
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deba@2242
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278 |
};
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deba@2242
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279 |
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deba@2242
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280 |
template <typename Result>
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deba@2242
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281 |
struct Masker<Result, 1> {
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deba@2242
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282 |
static Result mask(const Result& result) {
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deba@2386
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283 |
return static_cast<Result>(result | (result >> 1));
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deba@2242
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284 |
}
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deba@2242
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285 |
};
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deba@2242
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286 |
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deba@2242
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287 |
template <typename Result, typename Word,
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deba@2242
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288 |
int rest = std::numeric_limits<Result>::digits, int shift = 0,
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deba@2242
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289 |
bool last = rest <= std::numeric_limits<Word>::digits>
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deba@2242
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290 |
struct IntConversion {
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deba@2242
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291 |
static const int bits = std::numeric_limits<Word>::digits;
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deba@2242
|
292 |
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deba@2242
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293 |
static Result convert(RandomCore<Word>& rnd) {
|
deba@2386
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294 |
return static_cast<Result>(rnd() >> (bits - rest)) << shift;
|
deba@2242
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295 |
}
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deba@2242
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296 |
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deba@2242
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297 |
};
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deba@2242
|
298 |
|
deba@2242
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299 |
template <typename Result, typename Word, int rest, int shift>
|
deba@2242
|
300 |
struct IntConversion<Result, Word, rest, shift, false> {
|
deba@2242
|
301 |
static const int bits = std::numeric_limits<Word>::digits;
|
deba@2242
|
302 |
|
deba@2242
|
303 |
static Result convert(RandomCore<Word>& rnd) {
|
deba@2386
|
304 |
return (static_cast<Result>(rnd()) << shift) |
|
deba@2242
|
305 |
IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
|
deba@2242
|
306 |
}
|
deba@2242
|
307 |
};
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deba@2242
|
308 |
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deba@2242
|
309 |
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deba@2242
|
310 |
template <typename Result, typename Word,
|
alpar@2387
|
311 |
bool one_word = (std::numeric_limits<Word>::digits <
|
alpar@2387
|
312 |
std::numeric_limits<Result>::digits) >
|
deba@2242
|
313 |
struct Mapping {
|
deba@2242
|
314 |
static Result map(RandomCore<Word>& rnd, const Result& bound) {
|
deba@2386
|
315 |
Word max = Word(bound - 1);
|
deba@2242
|
316 |
Result mask = Masker<Result>::mask(bound - 1);
|
deba@2242
|
317 |
Result num;
|
deba@2242
|
318 |
do {
|
deba@2242
|
319 |
num = IntConversion<Result, Word>::convert(rnd) & mask;
|
deba@2242
|
320 |
} while (num > max);
|
deba@2242
|
321 |
return num;
|
deba@2242
|
322 |
}
|
deba@2242
|
323 |
};
|
deba@2242
|
324 |
|
deba@2242
|
325 |
template <typename Result, typename Word>
|
deba@2242
|
326 |
struct Mapping<Result, Word, false> {
|
deba@2242
|
327 |
static Result map(RandomCore<Word>& rnd, const Result& bound) {
|
deba@2386
|
328 |
Word max = Word(bound - 1);
|
deba@2242
|
329 |
Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
|
deba@2242
|
330 |
::mask(max);
|
deba@2242
|
331 |
Word num;
|
deba@2242
|
332 |
do {
|
deba@2242
|
333 |
num = rnd() & mask;
|
deba@2242
|
334 |
} while (num > max);
|
deba@2242
|
335 |
return num;
|
deba@2242
|
336 |
}
|
deba@2242
|
337 |
};
|
deba@2242
|
338 |
|
deba@2242
|
339 |
template <typename Result, int exp, bool pos = (exp >= 0)>
|
deba@2242
|
340 |
struct ShiftMultiplier {
|
deba@2242
|
341 |
static const Result multiplier() {
|
deba@2242
|
342 |
Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
|
deba@2242
|
343 |
res *= res;
|
deba@2386
|
344 |
if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
|
deba@2242
|
345 |
return res;
|
deba@2242
|
346 |
}
|
deba@2242
|
347 |
};
|
deba@2242
|
348 |
|
deba@2242
|
349 |
template <typename Result, int exp>
|
deba@2242
|
350 |
struct ShiftMultiplier<Result, exp, false> {
|
deba@2242
|
351 |
static const Result multiplier() {
|
deba@2242
|
352 |
Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
|
deba@2242
|
353 |
res *= res;
|
deba@2386
|
354 |
if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
|
deba@2242
|
355 |
return res;
|
deba@2242
|
356 |
}
|
deba@2242
|
357 |
};
|
deba@2242
|
358 |
|
deba@2242
|
359 |
template <typename Result>
|
deba@2242
|
360 |
struct ShiftMultiplier<Result, 0, true> {
|
deba@2242
|
361 |
static const Result multiplier() {
|
deba@2386
|
362 |
return static_cast<Result>(1.0);
|
deba@2242
|
363 |
}
|
deba@2242
|
364 |
};
|
deba@2242
|
365 |
|
deba@2242
|
366 |
template <typename Result>
|
deba@2242
|
367 |
struct ShiftMultiplier<Result, -20, true> {
|
deba@2242
|
368 |
static const Result multiplier() {
|
deba@2386
|
369 |
return static_cast<Result>(1.0/1048576.0);
|
deba@2242
|
370 |
}
|
deba@2242
|
371 |
};
|
deba@2242
|
372 |
|
deba@2242
|
373 |
template <typename Result>
|
deba@2242
|
374 |
struct ShiftMultiplier<Result, -32, true> {
|
deba@2242
|
375 |
static const Result multiplier() {
|
deba@2386
|
376 |
return static_cast<Result>(1.0/424967296.0);
|
deba@2242
|
377 |
}
|
deba@2242
|
378 |
};
|
deba@2242
|
379 |
|
deba@2242
|
380 |
template <typename Result>
|
deba@2242
|
381 |
struct ShiftMultiplier<Result, -53, true> {
|
deba@2242
|
382 |
static const Result multiplier() {
|
deba@2386
|
383 |
return static_cast<Result>(1.0/9007199254740992.0);
|
deba@2242
|
384 |
}
|
deba@2242
|
385 |
};
|
deba@2242
|
386 |
|
deba@2242
|
387 |
template <typename Result>
|
deba@2242
|
388 |
struct ShiftMultiplier<Result, -64, true> {
|
deba@2242
|
389 |
static const Result multiplier() {
|
deba@2386
|
390 |
return static_cast<Result>(1.0/18446744073709551616.0);
|
deba@2242
|
391 |
}
|
deba@2242
|
392 |
};
|
deba@2242
|
393 |
|
deba@2242
|
394 |
template <typename Result, int exp>
|
deba@2242
|
395 |
struct Shifting {
|
deba@2242
|
396 |
static Result shift(const Result& result) {
|
deba@2242
|
397 |
return result * ShiftMultiplier<Result, exp>::multiplier();
|
deba@2242
|
398 |
}
|
deba@2242
|
399 |
};
|
deba@2242
|
400 |
|
deba@2242
|
401 |
template <typename Result, typename Word,
|
deba@2242
|
402 |
int rest = std::numeric_limits<Result>::digits, int shift = 0,
|
deba@2242
|
403 |
bool last = rest <= std::numeric_limits<Word>::digits>
|
deba@2242
|
404 |
struct RealConversion{
|
deba@2242
|
405 |
static const int bits = std::numeric_limits<Word>::digits;
|
deba@2242
|
406 |
|
deba@2242
|
407 |
static Result convert(RandomCore<Word>& rnd) {
|
deba@2242
|
408 |
return Shifting<Result, - shift - rest>::
|
deba@2386
|
409 |
shift(static_cast<Result>(rnd() >> (bits - rest)));
|
deba@2242
|
410 |
}
|
deba@2242
|
411 |
};
|
deba@2242
|
412 |
|
deba@2242
|
413 |
template <typename Result, typename Word, int rest, int shift>
|
deba@2242
|
414 |
struct RealConversion<Result, Word, rest, shift, false> {
|
deba@2242
|
415 |
static const int bits = std::numeric_limits<Word>::digits;
|
deba@2242
|
416 |
|
deba@2242
|
417 |
static Result convert(RandomCore<Word>& rnd) {
|
deba@2386
|
418 |
return Shifting<Result, - shift - bits>::
|
deba@2386
|
419 |
shift(static_cast<Result>(rnd())) +
|
deba@2386
|
420 |
RealConversion<Result, Word, rest-bits, shift + bits>::
|
deba@2386
|
421 |
convert(rnd);
|
deba@2242
|
422 |
}
|
deba@2242
|
423 |
};
|
deba@2242
|
424 |
|
deba@2242
|
425 |
template <typename Result, typename Word>
|
deba@2242
|
426 |
struct Initializer {
|
deba@2242
|
427 |
|
deba@2242
|
428 |
template <typename Iterator>
|
deba@2242
|
429 |
static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
|
deba@2242
|
430 |
std::vector<Word> ws;
|
deba@2242
|
431 |
for (Iterator it = begin; it != end; ++it) {
|
deba@2386
|
432 |
ws.push_back(Word(*it));
|
deba@2242
|
433 |
}
|
deba@2242
|
434 |
rnd.initState(ws.begin(), ws.end());
|
deba@2242
|
435 |
}
|
deba@2242
|
436 |
|
deba@2242
|
437 |
static void init(RandomCore<Word>& rnd, Result seed) {
|
deba@2242
|
438 |
rnd.initState(seed);
|
deba@2242
|
439 |
}
|
deba@2242
|
440 |
};
|
deba@2242
|
441 |
|
deba@2242
|
442 |
template <typename Word>
|
deba@2242
|
443 |
struct BoolConversion {
|
deba@2242
|
444 |
static bool convert(RandomCore<Word>& rnd) {
|
deba@2242
|
445 |
return (rnd() & 1) == 1;
|
deba@2242
|
446 |
}
|
deba@2242
|
447 |
};
|
deba@2242
|
448 |
|
deba@2372
|
449 |
template <typename Word>
|
deba@2372
|
450 |
struct BoolProducer {
|
deba@2372
|
451 |
Word buffer;
|
deba@2372
|
452 |
int num;
|
deba@2372
|
453 |
|
deba@2372
|
454 |
BoolProducer() : num(0) {}
|
deba@2372
|
455 |
|
deba@2372
|
456 |
bool convert(RandomCore<Word>& rnd) {
|
deba@2372
|
457 |
if (num == 0) {
|
deba@2372
|
458 |
buffer = rnd();
|
deba@2372
|
459 |
num = RandomTraits<Word>::bits;
|
deba@2372
|
460 |
}
|
deba@2372
|
461 |
bool r = (buffer & 1);
|
deba@2372
|
462 |
buffer >>= 1;
|
deba@2372
|
463 |
--num;
|
deba@2372
|
464 |
return r;
|
deba@2372
|
465 |
}
|
deba@2372
|
466 |
};
|
deba@2372
|
467 |
|
deba@2242
|
468 |
}
|
deba@2229
|
469 |
|
deba@2229
|
470 |
/// \ingroup misc
|
deba@2229
|
471 |
///
|
deba@2229
|
472 |
/// \brief Mersenne Twister random number generator
|
deba@2229
|
473 |
///
|
deba@2229
|
474 |
/// The Mersenne Twister is a twisted generalized feedback
|
deba@2242
|
475 |
/// shift-register generator of Matsumoto and Nishimura. The period
|
deba@2242
|
476 |
/// of this generator is \f$ 2^{19937} - 1 \f$ and it is
|
deba@2242
|
477 |
/// equi-distributed in 623 dimensions for 32-bit numbers. The time
|
deba@2242
|
478 |
/// performance of this generator is comparable to the commonly used
|
deba@2242
|
479 |
/// generators.
|
deba@2242
|
480 |
///
|
deba@2242
|
481 |
/// This implementation is specialized for both 32-bit and 64-bit
|
deba@2242
|
482 |
/// architectures. The generators differ sligthly in the
|
deba@2242
|
483 |
/// initialization and generation phase so they produce two
|
deba@2242
|
484 |
/// completly different sequences.
|
deba@2242
|
485 |
///
|
deba@2242
|
486 |
/// The generator gives back random numbers of serveral types. To
|
deba@2242
|
487 |
/// get a random number from a range of a floating point type you
|
deba@2245
|
488 |
/// can use one form of the \c operator() or the \c real() member
|
deba@2245
|
489 |
/// function. If you want to get random number from the {0, 1, ...,
|
deba@2245
|
490 |
/// n-1} integer range use the \c operator[] or the \c integer()
|
deba@2245
|
491 |
/// method. And to get random number from the whole range of an
|
deba@2245
|
492 |
/// integer type you can use the argumentless \c integer() or \c
|
deba@2245
|
493 |
/// uinteger() functions. After all you can get random bool with
|
deba@2245
|
494 |
/// equal chance of true and false or given probability of true
|
deba@2245
|
495 |
/// result with the \c boolean() member functions.
|
deba@2242
|
496 |
///
|
deba@2242
|
497 |
///\code
|
deba@2245
|
498 |
/// // The commented code is identical to the other
|
deba@2245
|
499 |
/// double a = rnd(); // [0.0, 1.0)
|
deba@2245
|
500 |
/// // double a = rnd.real(); // [0.0, 1.0)
|
deba@2245
|
501 |
/// double b = rnd(100.0); // [0.0, 100.0)
|
deba@2245
|
502 |
/// // double b = rnd.real(100.0); // [0.0, 100.0)
|
deba@2245
|
503 |
/// double c = rnd(1.0, 2.0); // [1.0, 2.0)
|
deba@2245
|
504 |
/// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
|
deba@2245
|
505 |
/// int d = rnd[100000]; // 0..99999
|
deba@2245
|
506 |
/// // int d = rnd.integer(100000); // 0..99999
|
deba@2245
|
507 |
/// int e = rnd[6] + 1; // 1..6
|
deba@2245
|
508 |
/// // int e = rnd.integer(1, 1 + 6); // 1..6
|
deba@2242
|
509 |
/// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
|
deba@2242
|
510 |
/// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
|
deba@2242
|
511 |
/// bool g = rnd.boolean(); // P(g = true) = 0.5
|
deba@2242
|
512 |
/// bool h = rnd.boolean(0.8); // P(h = true) = 0.8
|
deba@2242
|
513 |
///\endcode
|
deba@2242
|
514 |
///
|
deba@2245
|
515 |
/// The lemon provides a global instance of the random number
|
deba@2245
|
516 |
/// generator which name is \ref lemon::rnd "rnd". Usually it is a
|
deba@2245
|
517 |
/// good programming convenience to use this global generator to get
|
deba@2245
|
518 |
/// random numbers.
|
deba@2229
|
519 |
///
|
deba@2229
|
520 |
/// \author Balazs Dezso
|
deba@2229
|
521 |
class Random {
|
deba@2242
|
522 |
private:
|
deba@2229
|
523 |
|
deba@2245
|
524 |
// architecture word
|
deba@2242
|
525 |
typedef unsigned long Word;
|
deba@2242
|
526 |
|
deba@2242
|
527 |
_random_bits::RandomCore<Word> core;
|
deba@2372
|
528 |
_random_bits::BoolProducer<Word> bool_producer;
|
deba@2372
|
529 |
|
deba@2229
|
530 |
|
deba@2229
|
531 |
public:
|
deba@2229
|
532 |
|
deba@2229
|
533 |
/// \brief Constructor
|
deba@2229
|
534 |
///
|
deba@2242
|
535 |
/// Constructor with constant seeding.
|
deba@2242
|
536 |
Random() { core.initState(); }
|
deba@2229
|
537 |
|
deba@2229
|
538 |
/// \brief Constructor
|
deba@2229
|
539 |
///
|
deba@2242
|
540 |
/// Constructor with seed. The current number type will be converted
|
deba@2242
|
541 |
/// to the architecture word type.
|
deba@2242
|
542 |
template <typename Number>
|
deba@2242
|
543 |
Random(Number seed) {
|
deba@2242
|
544 |
_random_bits::Initializer<Number, Word>::init(core, seed);
|
deba@2242
|
545 |
}
|
deba@2242
|
546 |
|
deba@2242
|
547 |
/// \brief Constructor
|
deba@2242
|
548 |
///
|
deba@2242
|
549 |
/// Constructor with array seeding. The given range should contain
|
deba@2242
|
550 |
/// any number type and the numbers will be converted to the
|
deba@2242
|
551 |
/// architecture word type.
|
deba@2242
|
552 |
template <typename Iterator>
|
deba@2242
|
553 |
Random(Iterator begin, Iterator end) {
|
deba@2242
|
554 |
typedef typename std::iterator_traits<Iterator>::value_type Number;
|
deba@2242
|
555 |
_random_bits::Initializer<Number, Word>::init(core, begin, end);
|
deba@2242
|
556 |
}
|
deba@2229
|
557 |
|
deba@2229
|
558 |
/// \brief Copy constructor
|
deba@2229
|
559 |
///
|
deba@2229
|
560 |
/// Copy constructor. The generated sequence will be identical to
|
deba@2245
|
561 |
/// the other sequence. It can be used to save the current state
|
deba@2245
|
562 |
/// of the generator and later use it to generate the same
|
deba@2245
|
563 |
/// sequence.
|
deba@2242
|
564 |
Random(const Random& other) {
|
deba@2242
|
565 |
core.copyState(other.core);
|
deba@2229
|
566 |
}
|
deba@2229
|
567 |
|
deba@2229
|
568 |
/// \brief Assign operator
|
deba@2229
|
569 |
///
|
deba@2229
|
570 |
/// Assign operator. The generated sequence will be identical to
|
deba@2245
|
571 |
/// the other sequence. It can be used to save the current state
|
deba@2245
|
572 |
/// of the generator and later use it to generate the same
|
deba@2245
|
573 |
/// sequence.
|
deba@2229
|
574 |
Random& operator=(const Random& other) {
|
deba@2229
|
575 |
if (&other != this) {
|
deba@2242
|
576 |
core.copyState(other.core);
|
deba@2229
|
577 |
}
|
deba@2229
|
578 |
return *this;
|
deba@2229
|
579 |
}
|
deba@2229
|
580 |
|
deba@2596
|
581 |
/// \brief Seeding random sequence
|
deba@2596
|
582 |
///
|
deba@2596
|
583 |
/// Seeding the random sequence. The current number type will be
|
deba@2596
|
584 |
/// converted to the architecture word type.
|
deba@2596
|
585 |
template <typename Number>
|
deba@2596
|
586 |
void seed(Number seed) {
|
deba@2596
|
587 |
_random_bits::Initializer<Number, Word>::init(core, seed);
|
deba@2596
|
588 |
}
|
deba@2596
|
589 |
|
deba@2596
|
590 |
/// \brief Seeding random sequence
|
deba@2596
|
591 |
///
|
deba@2596
|
592 |
/// Seeding the random sequence. The given range should contain
|
deba@2596
|
593 |
/// any number type and the numbers will be converted to the
|
deba@2596
|
594 |
/// architecture word type.
|
deba@2596
|
595 |
template <typename Iterator>
|
deba@2596
|
596 |
void seed(Iterator begin, Iterator end) {
|
deba@2596
|
597 |
typedef typename std::iterator_traits<Iterator>::value_type Number;
|
deba@2596
|
598 |
_random_bits::Initializer<Number, Word>::init(core, begin, end);
|
deba@2596
|
599 |
}
|
deba@2596
|
600 |
|
alpar@2257
|
601 |
/// \brief Returns a random real number from the range [0, 1)
|
deba@2229
|
602 |
///
|
deba@2245
|
603 |
/// It returns a random real number from the range [0, 1). The
|
deba@2245
|
604 |
/// default Number type is double.
|
deba@2242
|
605 |
template <typename Number>
|
deba@2245
|
606 |
Number real() {
|
deba@2242
|
607 |
return _random_bits::RealConversion<Number, Word>::convert(core);
|
deba@2229
|
608 |
}
|
deba@2229
|
609 |
|
deba@2245
|
610 |
double real() {
|
deba@2245
|
611 |
return real<double>();
|
deba@2245
|
612 |
}
|
deba@2245
|
613 |
|
alpar@2257
|
614 |
/// \brief Returns a random real number the range [0, b)
|
deba@2245
|
615 |
///
|
deba@2245
|
616 |
/// It returns a random real number from the range [0, b).
|
deba@2245
|
617 |
template <typename Number>
|
deba@2245
|
618 |
Number real(Number b) {
|
deba@2245
|
619 |
return real<Number>() * b;
|
deba@2245
|
620 |
}
|
deba@2245
|
621 |
|
alpar@2257
|
622 |
/// \brief Returns a random real number from the range [a, b)
|
deba@2245
|
623 |
///
|
deba@2245
|
624 |
/// It returns a random real number from the range [a, b).
|
deba@2245
|
625 |
template <typename Number>
|
deba@2245
|
626 |
Number real(Number a, Number b) {
|
deba@2245
|
627 |
return real<Number>() * (b - a) + a;
|
deba@2245
|
628 |
}
|
deba@2245
|
629 |
|
alpar@2257
|
630 |
/// \brief Returns a random real number from the range [0, 1)
|
deba@2245
|
631 |
///
|
deba@2245
|
632 |
/// It returns a random double from the range [0, 1).
|
deba@2242
|
633 |
double operator()() {
|
deba@2245
|
634 |
return real<double>();
|
deba@2242
|
635 |
}
|
deba@2242
|
636 |
|
alpar@2257
|
637 |
/// \brief Returns a random real number from the range [0, b)
|
deba@2229
|
638 |
///
|
deba@2242
|
639 |
/// It returns a random real number from the range [0, b).
|
deba@2242
|
640 |
template <typename Number>
|
deba@2242
|
641 |
Number operator()(Number b) {
|
deba@2245
|
642 |
return real<Number>() * b;
|
deba@2242
|
643 |
}
|
deba@2242
|
644 |
|
alpar@2257
|
645 |
/// \brief Returns a random real number from the range [a, b)
|
deba@2242
|
646 |
///
|
deba@2242
|
647 |
/// It returns a random real number from the range [a, b).
|
deba@2242
|
648 |
template <typename Number>
|
deba@2242
|
649 |
Number operator()(Number a, Number b) {
|
deba@2245
|
650 |
return real<Number>() * (b - a) + a;
|
deba@2242
|
651 |
}
|
deba@2242
|
652 |
|
deba@2242
|
653 |
/// \brief Returns a random integer from a range
|
deba@2242
|
654 |
///
|
deba@2245
|
655 |
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
deba@2242
|
656 |
template <typename Number>
|
deba@2245
|
657 |
Number integer(Number b) {
|
deba@2245
|
658 |
return _random_bits::Mapping<Number, Word>::map(core, b);
|
deba@2245
|
659 |
}
|
deba@2245
|
660 |
|
deba@2245
|
661 |
/// \brief Returns a random integer from a range
|
deba@2245
|
662 |
///
|
deba@2245
|
663 |
/// It returns a random integer from the range {a, a + 1, ..., b - 1}.
|
deba@2245
|
664 |
template <typename Number>
|
deba@2245
|
665 |
Number integer(Number a, Number b) {
|
deba@2245
|
666 |
return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
|
deba@2245
|
667 |
}
|
deba@2245
|
668 |
|
deba@2245
|
669 |
/// \brief Returns a random integer from a range
|
deba@2245
|
670 |
///
|
deba@2245
|
671 |
/// It returns a random integer from the range {0, 1, ..., b - 1}.
|
deba@2245
|
672 |
template <typename Number>
|
deba@2245
|
673 |
Number operator[](Number b) {
|
deba@2245
|
674 |
return _random_bits::Mapping<Number, Word>::map(core, b);
|
deba@2242
|
675 |
}
|
deba@2242
|
676 |
|
deba@2242
|
677 |
/// \brief Returns a random non-negative integer
|
deba@2242
|
678 |
///
|
deba@2242
|
679 |
/// It returns a random non-negative integer uniformly from the
|
deba@2242
|
680 |
/// whole range of the current \c Number type. The default result
|
deba@2242
|
681 |
/// type of this function is unsigned int.
|
deba@2242
|
682 |
template <typename Number>
|
deba@2242
|
683 |
Number uinteger() {
|
deba@2242
|
684 |
return _random_bits::IntConversion<Number, Word>::convert(core);
|
deba@2242
|
685 |
}
|
deba@2242
|
686 |
|
deba@2242
|
687 |
unsigned int uinteger() {
|
deba@2242
|
688 |
return uinteger<unsigned int>();
|
deba@2242
|
689 |
}
|
deba@2242
|
690 |
|
deba@2242
|
691 |
/// \brief Returns a random integer
|
deba@2242
|
692 |
///
|
deba@2242
|
693 |
/// It returns a random integer uniformly from the whole range of
|
deba@2242
|
694 |
/// the current \c Number type. The default result type of this
|
deba@2242
|
695 |
/// function is int.
|
deba@2242
|
696 |
template <typename Number>
|
deba@2242
|
697 |
Number integer() {
|
deba@2242
|
698 |
static const int nb = std::numeric_limits<Number>::digits +
|
deba@2242
|
699 |
(std::numeric_limits<Number>::is_signed ? 1 : 0);
|
deba@2242
|
700 |
return _random_bits::IntConversion<Number, Word, nb>::convert(core);
|
deba@2242
|
701 |
}
|
deba@2242
|
702 |
|
deba@2242
|
703 |
int integer() {
|
deba@2242
|
704 |
return integer<int>();
|
deba@2229
|
705 |
}
|
deba@2229
|
706 |
|
deba@2242
|
707 |
/// \brief Returns a random bool
|
deba@2229
|
708 |
///
|
deba@2372
|
709 |
/// It returns a random bool. The generator holds a buffer for
|
deba@2372
|
710 |
/// random bits. Every time when it become empty the generator makes
|
deba@2372
|
711 |
/// a new random word and fill the buffer up.
|
deba@2242
|
712 |
bool boolean() {
|
deba@2372
|
713 |
return bool_producer.convert(core);
|
deba@2229
|
714 |
}
|
deba@2229
|
715 |
|
alpar@2356
|
716 |
///\name Nonuniform distributions
|
alpar@2356
|
717 |
///
|
alpar@2356
|
718 |
|
alpar@2356
|
719 |
///@{
|
alpar@2356
|
720 |
|
deba@2229
|
721 |
/// \brief Returns a random bool
|
deba@2229
|
722 |
///
|
deba@2242
|
723 |
/// It returns a random bool with given probability of true result
|
deba@2242
|
724 |
bool boolean(double p) {
|
deba@2242
|
725 |
return operator()() < p;
|
deba@2229
|
726 |
}
|
alpar@2355
|
727 |
|
alpar@2355
|
728 |
/// Standard Gauss distribution
|
alpar@2355
|
729 |
|
alpar@2355
|
730 |
/// Standard Gauss distribution.
|
alpar@2356
|
731 |
/// \note The Cartesian form of the Box-Muller
|
alpar@2356
|
732 |
/// transformation is used to generate a random normal distribution.
|
alpar@2356
|
733 |
/// \todo Consider using the "ziggurat" method instead.
|
alpar@2355
|
734 |
double gauss()
|
alpar@2355
|
735 |
{
|
alpar@2355
|
736 |
double V1,V2,S;
|
alpar@2355
|
737 |
do {
|
alpar@2355
|
738 |
V1=2*real<double>()-1;
|
alpar@2355
|
739 |
V2=2*real<double>()-1;
|
alpar@2355
|
740 |
S=V1*V1+V2*V2;
|
alpar@2355
|
741 |
} while(S>=1);
|
alpar@2355
|
742 |
return std::sqrt(-2*std::log(S)/S)*V1;
|
alpar@2355
|
743 |
}
|
alpar@2356
|
744 |
/// Gauss distribution with given standard deviation and mean 0
|
alpar@2356
|
745 |
|
alpar@2356
|
746 |
/// \sa gauss()
|
alpar@2356
|
747 |
///
|
alpar@2356
|
748 |
double gauss(double std_dev)
|
alpar@2355
|
749 |
{
|
alpar@2356
|
750 |
return gauss()*std_dev;
|
alpar@2355
|
751 |
}
|
alpar@2356
|
752 |
/// Gauss distribution with given mean and standard deviation
|
alpar@2356
|
753 |
|
alpar@2356
|
754 |
/// \sa gauss()
|
alpar@2356
|
755 |
///
|
alpar@2356
|
756 |
double gauss(double mean,double std_dev)
|
alpar@2355
|
757 |
{
|
alpar@2356
|
758 |
return gauss()*std_dev+mean;
|
alpar@2355
|
759 |
}
|
alpar@2355
|
760 |
|
alpar@2356
|
761 |
/// Exponential distribution with given mean
|
alpar@2356
|
762 |
|
alpar@2356
|
763 |
/// This function generates an exponential distribution random number
|
alpar@2356
|
764 |
/// with mean <tt>1/lambda</tt>.
|
alpar@2356
|
765 |
///
|
alpar@2356
|
766 |
double exponential(double lambda=1.0)
|
alpar@2355
|
767 |
{
|
alpar@2374
|
768 |
return -std::log(real<double>())/lambda;
|
alpar@2355
|
769 |
}
|
alpar@2356
|
770 |
|
alpar@2483
|
771 |
double gamma(int k)
|
alpar@2483
|
772 |
{
|
alpar@2483
|
773 |
double s = 0;
|
alpar@2483
|
774 |
for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
|
alpar@2483
|
775 |
return s;
|
alpar@2483
|
776 |
}
|
alpar@2483
|
777 |
|
alpar@2483
|
778 |
/// Gamma distribution with given shape and scale parameter
|
alpar@2483
|
779 |
|
alpar@2483
|
780 |
/// This function generates a gamma distribution random number.
|
alpar@2483
|
781 |
///
|
alpar@2483
|
782 |
///\param k shape parameter (<tt>k>0</tt>)
|
alpar@2483
|
783 |
///\param theta scale parameter
|
alpar@2483
|
784 |
///
|
alpar@2483
|
785 |
double gamma(double k,double theta=1.0)
|
alpar@2483
|
786 |
{
|
alpar@2483
|
787 |
double xi,nu;
|
alpar@2483
|
788 |
const double delta = k-std::floor(k);
|
alpar@2568
|
789 |
const double v0=E/(E-delta);
|
alpar@2483
|
790 |
do {
|
alpar@2483
|
791 |
double V0=1.0-real<double>();
|
alpar@2483
|
792 |
double V1=1.0-real<double>();
|
alpar@2483
|
793 |
double V2=1.0-real<double>();
|
alpar@2483
|
794 |
if(V2<=v0)
|
alpar@2483
|
795 |
{
|
alpar@2483
|
796 |
xi=std::pow(V1,1.0/delta);
|
alpar@2483
|
797 |
nu=V0*std::pow(xi,delta-1.0);
|
alpar@2483
|
798 |
}
|
alpar@2483
|
799 |
else
|
alpar@2483
|
800 |
{
|
alpar@2483
|
801 |
xi=1.0-std::log(V1);
|
alpar@2483
|
802 |
nu=V0*std::exp(-xi);
|
alpar@2483
|
803 |
}
|
alpar@2483
|
804 |
} while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
|
alpar@2599
|
805 |
return theta*(xi+gamma(int(std::floor(k))));
|
alpar@2483
|
806 |
}
|
alpar@2483
|
807 |
|
alpar@2483
|
808 |
|
alpar@2356
|
809 |
///@}
|
deba@2229
|
810 |
|
alpar@2374
|
811 |
///\name Two dimensional distributions
|
alpar@2374
|
812 |
///
|
alpar@2374
|
813 |
|
alpar@2374
|
814 |
///@{
|
alpar@2374
|
815 |
|
alpar@2374
|
816 |
/// Uniform distribution on the full unit circle.
|
alpar@2380
|
817 |
dim2::Point<double> disc()
|
alpar@2374
|
818 |
{
|
alpar@2374
|
819 |
double V1,V2;
|
alpar@2374
|
820 |
do {
|
alpar@2374
|
821 |
V1=2*real<double>()-1;
|
alpar@2374
|
822 |
V2=2*real<double>()-1;
|
alpar@2374
|
823 |
|
alpar@2374
|
824 |
} while(V1*V1+V2*V2>=1);
|
alpar@2374
|
825 |
return dim2::Point<double>(V1,V2);
|
alpar@2374
|
826 |
}
|
alpar@2374
|
827 |
/// A kind of two dimensional Gauss distribution
|
alpar@2374
|
828 |
|
alpar@2374
|
829 |
/// This function provides a turning symmetric two-dimensional distribution.
|
alpar@2374
|
830 |
/// Both coordinates are of standard normal distribution, but they are not
|
alpar@2374
|
831 |
/// independent.
|
alpar@2374
|
832 |
///
|
alpar@2374
|
833 |
/// \note The coordinates are the two random variables provided by
|
alpar@2374
|
834 |
/// the Box-Muller method.
|
alpar@2374
|
835 |
dim2::Point<double> gauss2()
|
alpar@2374
|
836 |
{
|
alpar@2374
|
837 |
double V1,V2,S;
|
alpar@2374
|
838 |
do {
|
alpar@2374
|
839 |
V1=2*real<double>()-1;
|
alpar@2374
|
840 |
V2=2*real<double>()-1;
|
alpar@2374
|
841 |
S=V1*V1+V2*V2;
|
alpar@2374
|
842 |
} while(S>=1);
|
alpar@2374
|
843 |
double W=std::sqrt(-2*std::log(S)/S);
|
alpar@2374
|
844 |
return dim2::Point<double>(W*V1,W*V2);
|
alpar@2374
|
845 |
}
|
alpar@2374
|
846 |
/// A kind of two dimensional exponential distribution
|
alpar@2374
|
847 |
|
alpar@2374
|
848 |
/// This function provides a turning symmetric two-dimensional distribution.
|
alpar@2374
|
849 |
/// The x-coordinate is of conditionally exponential distribution
|
alpar@2374
|
850 |
/// with the condition that x is positive and y=0. If x is negative and
|
alpar@2374
|
851 |
/// y=0 then, -x is of exponential distribution. The same is true for the
|
alpar@2374
|
852 |
/// y-coordinate.
|
alpar@2374
|
853 |
dim2::Point<double> exponential2()
|
alpar@2374
|
854 |
{
|
alpar@2374
|
855 |
double V1,V2,S;
|
alpar@2374
|
856 |
do {
|
alpar@2374
|
857 |
V1=2*real<double>()-1;
|
alpar@2374
|
858 |
V2=2*real<double>()-1;
|
alpar@2374
|
859 |
S=V1*V1+V2*V2;
|
alpar@2374
|
860 |
} while(S>=1);
|
alpar@2374
|
861 |
double W=-std::log(S)/S;
|
alpar@2374
|
862 |
return dim2::Point<double>(W*V1,W*V2);
|
alpar@2374
|
863 |
}
|
alpar@2374
|
864 |
|
alpar@2374
|
865 |
///@}
|
deba@2229
|
866 |
};
|
deba@2229
|
867 |
|
deba@2229
|
868 |
|
deba@2229
|
869 |
extern Random rnd;
|
deba@2229
|
870 |
|
deba@2229
|
871 |
}
|
deba@2229
|
872 |
|
deba@2229
|
873 |
#endif
|