lemon/random.h
author Peter Kovacs <kpeter@inf.elte.hu>
Tue, 28 Oct 2008 14:47:57 +0100
changeset 352 0badf3bb38c2
parent 351 2593e163e407
child 392 80ec623f529f
permissions -rw-r--r--
Minor doc improvements
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/* -*- 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) 2003-2008
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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/*
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 * This file contains the reimplemented version of the Mersenne Twister
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 * Generator of Matsumoto and Nishimura.
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 *
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 * See the appropriate copyright notice below.
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 *
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 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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 * All rights reserved.
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 *
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 * Redistribution and use in source and binary forms, with or without
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 * modification, are permitted provided that the following conditions
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 * are met:
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 *
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 * 1. Redistributions of source code must retain the above copyright
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 *    notice, this list of conditions and the following disclaimer.
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 *
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 * 2. Redistributions in binary form must reproduce the above copyright
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 *    notice, this list of conditions and the following disclaimer in the
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 *    documentation and/or other materials provided with the distribution.
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 *
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 * 3. The names of its contributors may not be used to endorse or promote
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 *    products derived from this software without specific prior written
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 *    permission.
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 *
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
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 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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 * OF THE POSSIBILITY OF SUCH DAMAGE.
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 *
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 *
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 * Any feedback is very welcome.
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 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
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 */
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#ifndef LEMON_RANDOM_H
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#define LEMON_RANDOM_H
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#include <algorithm>
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#include <iterator>
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#include <vector>
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#include <limits>
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#include <fstream>
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#include <lemon/math.h>
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#include <lemon/dim2.h>
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#ifndef WIN32
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#include <sys/time.h>
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#include <ctime>
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#include <sys/types.h>
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#include <unistd.h>
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#else
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#include <windows.h>
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#endif
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///\ingroup misc
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///\file
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///\brief Mersenne Twister random number generator
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namespace lemon {
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  namespace _random_bits {
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    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
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    struct RandomTraits {};
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    template <typename _Word>
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    struct RandomTraits<_Word, 32> {
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      typedef _Word Word;
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      static const int bits = 32;
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      static const int length = 624;
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      static const int shift = 397;
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      static const Word mul = 0x6c078965u;
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      static const Word arrayInit = 0x012BD6AAu;
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      static const Word arrayMul1 = 0x0019660Du;
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      static const Word arrayMul2 = 0x5D588B65u;
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      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, bool pos = (exp >= 0)>
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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>(2.0);
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        return res;
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      }
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    };
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    template <typename Result, int exp>
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    struct ShiftMultiplier<Result, exp, false> {
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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, true> {
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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, true> {
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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, true> {
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      static const Result multiplier() {
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        return static_cast<Result>(1.0/424967296.0);
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      }
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    };
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    template <typename Result>
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    struct ShiftMultiplier<Result, -53, true> {
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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, true> {
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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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   406
      }
alpar@10
   407
    };
alpar@10
   408
alpar@10
   409
    template <typename Result, typename Word,
alpar@209
   410
              int rest = std::numeric_limits<Result>::digits, int shift = 0,
alpar@10
   411
              bool last = rest <= std::numeric_limits<Word>::digits>
alpar@209
   412
    struct RealConversion{
alpar@10
   413
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   414
alpar@10
   415
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   416
        return Shifting<Result, - shift - rest>::
alpar@10
   417
          shift(static_cast<Result>(rnd() >> (bits - rest)));
alpar@10
   418
      }
alpar@10
   419
    };
alpar@10
   420
alpar@10
   421
    template <typename Result, typename Word, int rest, int shift>
alpar@209
   422
    struct RealConversion<Result, Word, rest, shift, false> {
alpar@10
   423
      static const int bits = std::numeric_limits<Word>::digits;
alpar@10
   424
alpar@10
   425
      static Result convert(RandomCore<Word>& rnd) {
alpar@10
   426
        return Shifting<Result, - shift - bits>::
alpar@10
   427
          shift(static_cast<Result>(rnd())) +
alpar@10
   428
          RealConversion<Result, Word, rest-bits, shift + bits>::
alpar@10
   429
          convert(rnd);
alpar@10
   430
      }
alpar@10
   431
    };
alpar@10
   432
alpar@10
   433
    template <typename Result, typename Word>
alpar@10
   434
    struct Initializer {
alpar@10
   435
alpar@10
   436
      template <typename Iterator>
alpar@10
   437
      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
alpar@10
   438
        std::vector<Word> ws;
alpar@10
   439
        for (Iterator it = begin; it != end; ++it) {
alpar@10
   440
          ws.push_back(Word(*it));
alpar@10
   441
        }
alpar@10
   442
        rnd.initState(ws.begin(), ws.end());
alpar@10
   443
      }
alpar@10
   444
alpar@10
   445
      static void init(RandomCore<Word>& rnd, Result seed) {
alpar@10
   446
        rnd.initState(seed);
alpar@10
   447
      }
alpar@10
   448
    };
alpar@10
   449
alpar@10
   450
    template <typename Word>
alpar@10
   451
    struct BoolConversion {
alpar@10
   452
      static bool convert(RandomCore<Word>& rnd) {
alpar@10
   453
        return (rnd() & 1) == 1;
alpar@10
   454
      }
alpar@10
   455
    };
alpar@10
   456
alpar@10
   457
    template <typename Word>
alpar@10
   458
    struct BoolProducer {
alpar@10
   459
      Word buffer;
alpar@10
   460
      int num;
alpar@209
   461
alpar@10
   462
      BoolProducer() : num(0) {}
alpar@10
   463
alpar@10
   464
      bool convert(RandomCore<Word>& rnd) {
alpar@10
   465
        if (num == 0) {
alpar@10
   466
          buffer = rnd();
alpar@10
   467
          num = RandomTraits<Word>::bits;
alpar@10
   468
        }
alpar@10
   469
        bool r = (buffer & 1);
alpar@10
   470
        buffer >>= 1;
alpar@10
   471
        --num;
alpar@10
   472
        return r;
alpar@10
   473
      }
alpar@10
   474
    };
alpar@10
   475
alpar@10
   476
  }
alpar@10
   477
alpar@10
   478
  /// \ingroup misc
alpar@10
   479
  ///
alpar@10
   480
  /// \brief Mersenne Twister random number generator
alpar@10
   481
  ///
alpar@10
   482
  /// The Mersenne Twister is a twisted generalized feedback
alpar@10
   483
  /// shift-register generator of Matsumoto and Nishimura. The period
alpar@10
   484
  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
alpar@10
   485
  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
alpar@10
   486
  /// performance of this generator is comparable to the commonly used
alpar@10
   487
  /// generators.
alpar@10
   488
  ///
alpar@10
   489
  /// This implementation is specialized for both 32-bit and 64-bit
alpar@10
   490
  /// architectures. The generators differ sligthly in the
alpar@10
   491
  /// initialization and generation phase so they produce two
alpar@10
   492
  /// completly different sequences.
alpar@10
   493
  ///
alpar@10
   494
  /// The generator gives back random numbers of serveral types. To
alpar@10
   495
  /// get a random number from a range of a floating point type you
alpar@10
   496
  /// can use one form of the \c operator() or the \c real() member
alpar@10
   497
  /// function. If you want to get random number from the {0, 1, ...,
alpar@10
   498
  /// n-1} integer range use the \c operator[] or the \c integer()
alpar@10
   499
  /// method. And to get random number from the whole range of an
alpar@10
   500
  /// integer type you can use the argumentless \c integer() or \c
alpar@10
   501
  /// uinteger() functions. After all you can get random bool with
alpar@10
   502
  /// equal chance of true and false or given probability of true
alpar@10
   503
  /// result with the \c boolean() member functions.
alpar@10
   504
  ///
alpar@10
   505
  ///\code
alpar@10
   506
  /// // The commented code is identical to the other
alpar@10
   507
  /// double a = rnd();                     // [0.0, 1.0)
alpar@10
   508
  /// // double a = rnd.real();             // [0.0, 1.0)
alpar@10
   509
  /// double b = rnd(100.0);                // [0.0, 100.0)
alpar@10
   510
  /// // double b = rnd.real(100.0);        // [0.0, 100.0)
alpar@10
   511
  /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
alpar@10
   512
  /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
alpar@10
   513
  /// int d = rnd[100000];                  // 0..99999
alpar@10
   514
  /// // int d = rnd.integer(100000);       // 0..99999
alpar@10
   515
  /// int e = rnd[6] + 1;                   // 1..6
alpar@10
   516
  /// // int e = rnd.integer(1, 1 + 6);     // 1..6
alpar@10
   517
  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
alpar@10
   518
  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
alpar@10
   519
  /// bool g = rnd.boolean();               // P(g = true) = 0.5
alpar@10
   520
  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
alpar@10
   521
  ///\endcode
alpar@10
   522
  ///
kpeter@49
   523
  /// LEMON provides a global instance of the random number
alpar@10
   524
  /// generator which name is \ref lemon::rnd "rnd". Usually it is a
alpar@10
   525
  /// good programming convenience to use this global generator to get
alpar@10
   526
  /// random numbers.
alpar@10
   527
  class Random {
alpar@10
   528
  private:
alpar@10
   529
kpeter@16
   530
    // Architecture word
alpar@10
   531
    typedef unsigned long Word;
alpar@209
   532
alpar@10
   533
    _random_bits::RandomCore<Word> core;
alpar@10
   534
    _random_bits::BoolProducer<Word> bool_producer;
alpar@209
   535
alpar@10
   536
alpar@10
   537
  public:
alpar@10
   538
deba@177
   539
    ///\name Initialization
deba@177
   540
    ///
deba@177
   541
    /// @{
deba@177
   542
kpeter@49
   543
    /// \brief Default constructor
alpar@10
   544
    ///
alpar@10
   545
    /// Constructor with constant seeding.
alpar@10
   546
    Random() { core.initState(); }
alpar@10
   547
kpeter@49
   548
    /// \brief Constructor with seed
alpar@10
   549
    ///
alpar@10
   550
    /// Constructor with seed. The current number type will be converted
alpar@10
   551
    /// to the architecture word type.
alpar@10
   552
    template <typename Number>
alpar@209
   553
    Random(Number seed) {
alpar@10
   554
      _random_bits::Initializer<Number, Word>::init(core, seed);
alpar@10
   555
    }
alpar@10
   556
kpeter@49
   557
    /// \brief Constructor with array seeding
alpar@10
   558
    ///
alpar@10
   559
    /// Constructor with array seeding. The given range should contain
alpar@10
   560
    /// any number type and the numbers will be converted to the
alpar@10
   561
    /// architecture word type.
alpar@10
   562
    template <typename Iterator>
alpar@209
   563
    Random(Iterator begin, Iterator end) {
alpar@10
   564
      typedef typename std::iterator_traits<Iterator>::value_type Number;
alpar@10
   565
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
alpar@10
   566
    }
alpar@10
   567
alpar@10
   568
    /// \brief Copy constructor
alpar@10
   569
    ///
alpar@10
   570
    /// Copy constructor. The generated sequence will be identical to
alpar@10
   571
    /// the other sequence. It can be used to save the current state
alpar@10
   572
    /// of the generator and later use it to generate the same
alpar@10
   573
    /// sequence.
alpar@10
   574
    Random(const Random& other) {
alpar@10
   575
      core.copyState(other.core);
alpar@10
   576
    }
alpar@10
   577
alpar@10
   578
    /// \brief Assign operator
alpar@10
   579
    ///
alpar@10
   580
    /// Assign operator. The generated sequence will be identical to
alpar@10
   581
    /// the other sequence. It can be used to save the current state
alpar@10
   582
    /// of the generator and later use it to generate the same
alpar@10
   583
    /// sequence.
alpar@10
   584
    Random& operator=(const Random& other) {
alpar@10
   585
      if (&other != this) {
alpar@10
   586
        core.copyState(other.core);
alpar@10
   587
      }
alpar@10
   588
      return *this;
alpar@10
   589
    }
alpar@10
   590
deba@102
   591
    /// \brief Seeding random sequence
deba@102
   592
    ///
deba@102
   593
    /// Seeding the random sequence. The current number type will be
deba@102
   594
    /// converted to the architecture word type.
deba@102
   595
    template <typename Number>
alpar@209
   596
    void seed(Number seed) {
deba@102
   597
      _random_bits::Initializer<Number, Word>::init(core, seed);
deba@102
   598
    }
deba@102
   599
deba@102
   600
    /// \brief Seeding random sequence
deba@102
   601
    ///
deba@102
   602
    /// Seeding the random sequence. The given range should contain
deba@102
   603
    /// any number type and the numbers will be converted to the
deba@102
   604
    /// architecture word type.
deba@102
   605
    template <typename Iterator>
alpar@209
   606
    void seed(Iterator begin, Iterator end) {
deba@102
   607
      typedef typename std::iterator_traits<Iterator>::value_type Number;
deba@102
   608
      _random_bits::Initializer<Number, Word>::init(core, begin, end);
deba@102
   609
    }
deba@102
   610
deba@177
   611
    /// \brief Seeding from file or from process id and time
deba@177
   612
    ///
deba@177
   613
    /// By default, this function calls the \c seedFromFile() member
alpar@178
   614
    /// function with the <tt>/dev/urandom</tt> file. If it does not success,
deba@177
   615
    /// it uses the \c seedFromTime().
deba@177
   616
    /// \return Currently always true.
deba@177
   617
    bool seed() {
deba@177
   618
#ifndef WIN32
deba@177
   619
      if (seedFromFile("/dev/urandom", 0)) return true;
deba@177
   620
#endif
deba@177
   621
      if (seedFromTime()) return true;
deba@177
   622
      return false;
deba@177
   623
    }
alpar@209
   624
deba@177
   625
    /// \brief Seeding from file
deba@177
   626
    ///
deba@177
   627
    /// Seeding the random sequence from file. The linux kernel has two
deba@177
   628
    /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
deba@177
   629
    /// could give good seed values for pseudo random generators (The
deba@177
   630
    /// difference between two devices is that the <tt>random</tt> may
deba@177
   631
    /// block the reading operation while the kernel can give good
deba@177
   632
    /// source of randomness, while the <tt>urandom</tt> does not
deba@177
   633
    /// block the input, but it could give back bytes with worse
deba@177
   634
    /// entropy).
deba@177
   635
    /// \param file The source file
deba@177
   636
    /// \param offset The offset, from the file read.
alpar@178
   637
    /// \return True when the seeding successes.
deba@177
   638
#ifndef WIN32
alpar@209
   639
    bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
deba@177
   640
#else
alpar@209
   641
    bool seedFromFile(const std::string& file = "", int offset = 0)
deba@177
   642
#endif
deba@177
   643
    {
deba@177
   644
      std::ifstream rs(file.c_str());
deba@177
   645
      const int size = 4;
deba@177
   646
      Word buf[size];
deba@177
   647
      if (offset != 0 && !rs.seekg(offset)) return false;
deba@177
   648
      if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
deba@177
   649
      seed(buf, buf + size);
deba@177
   650
      return true;
deba@177
   651
    }
deba@177
   652
deba@177
   653
    /// \brief Seding from process id and time
deba@177
   654
    ///
deba@177
   655
    /// Seding from process id and time. This function uses the
deba@177
   656
    /// current process id and the current time for initialize the
deba@177
   657
    /// random sequence.
deba@177
   658
    /// \return Currently always true.
alpar@209
   659
    bool seedFromTime() {
deba@177
   660
#ifndef WIN32
deba@177
   661
      timeval tv;
deba@177
   662
      gettimeofday(&tv, 0);
deba@177
   663
      seed(getpid() + tv.tv_sec + tv.tv_usec);
deba@177
   664
#else
deba@177
   665
      FILETIME time;
deba@177
   666
      GetSystemTimeAsFileTime(&time);
deba@177
   667
      seed(GetCurrentProcessId() + time.dwHighDateTime + time.dwLowDateTime);
deba@177
   668
#endif
deba@177
   669
      return true;
deba@177
   670
    }
deba@177
   671
deba@177
   672
    /// @}
deba@177
   673
deba@177
   674
    ///\name Uniform distributions
deba@177
   675
    ///
deba@177
   676
    /// @{
deba@177
   677
alpar@10
   678
    /// \brief Returns a random real number from the range [0, 1)
alpar@10
   679
    ///
alpar@10
   680
    /// It returns a random real number from the range [0, 1). The
kpeter@49
   681
    /// default Number type is \c double.
alpar@10
   682
    template <typename Number>
alpar@10
   683
    Number real() {
alpar@10
   684
      return _random_bits::RealConversion<Number, Word>::convert(core);
alpar@10
   685
    }
alpar@10
   686
alpar@10
   687
    double real() {
alpar@10
   688
      return real<double>();
alpar@10
   689
    }
alpar@10
   690
alpar@10
   691
    /// \brief Returns a random real number the range [0, b)
alpar@10
   692
    ///
alpar@10
   693
    /// It returns a random real number from the range [0, b).
alpar@10
   694
    template <typename Number>
alpar@209
   695
    Number real(Number b) {
alpar@209
   696
      return real<Number>() * b;
alpar@10
   697
    }
alpar@10
   698
alpar@10
   699
    /// \brief Returns a random real number from the range [a, b)
alpar@10
   700
    ///
alpar@10
   701
    /// It returns a random real number from the range [a, b).
alpar@10
   702
    template <typename Number>
alpar@209
   703
    Number real(Number a, Number b) {
alpar@209
   704
      return real<Number>() * (b - a) + a;
alpar@10
   705
    }
alpar@10
   706
alpar@10
   707
    /// \brief Returns a random real number from the range [0, 1)
alpar@10
   708
    ///
alpar@10
   709
    /// It returns a random double from the range [0, 1).
alpar@10
   710
    double operator()() {
alpar@10
   711
      return real<double>();
alpar@10
   712
    }
alpar@10
   713
alpar@10
   714
    /// \brief Returns a random real number from the range [0, b)
alpar@10
   715
    ///
alpar@10
   716
    /// It returns a random real number from the range [0, b).
alpar@10
   717
    template <typename Number>
alpar@209
   718
    Number operator()(Number b) {
alpar@209
   719
      return real<Number>() * b;
alpar@10
   720
    }
alpar@10
   721
alpar@10
   722
    /// \brief Returns a random real number from the range [a, b)
alpar@10
   723
    ///
alpar@10
   724
    /// It returns a random real number from the range [a, b).
alpar@10
   725
    template <typename Number>
alpar@209
   726
    Number operator()(Number a, Number b) {
alpar@209
   727
      return real<Number>() * (b - a) + a;
alpar@10
   728
    }
alpar@10
   729
alpar@10
   730
    /// \brief Returns a random integer from a range
alpar@10
   731
    ///
alpar@10
   732
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@10
   733
    template <typename Number>
alpar@10
   734
    Number integer(Number b) {
alpar@10
   735
      return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@10
   736
    }
alpar@10
   737
alpar@10
   738
    /// \brief Returns a random integer from a range
alpar@10
   739
    ///
alpar@10
   740
    /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
alpar@10
   741
    template <typename Number>
alpar@10
   742
    Number integer(Number a, Number b) {
alpar@10
   743
      return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
alpar@10
   744
    }
alpar@10
   745
alpar@10
   746
    /// \brief Returns a random integer from a range
alpar@10
   747
    ///
alpar@10
   748
    /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@10
   749
    template <typename Number>
alpar@10
   750
    Number operator[](Number b) {
alpar@10
   751
      return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@10
   752
    }
alpar@10
   753
alpar@10
   754
    /// \brief Returns a random non-negative integer
alpar@10
   755
    ///
alpar@10
   756
    /// It returns a random non-negative integer uniformly from the
kpeter@49
   757
    /// whole range of the current \c Number type. The default result
kpeter@49
   758
    /// type of this function is <tt>unsigned int</tt>.
alpar@10
   759
    template <typename Number>
alpar@10
   760
    Number uinteger() {
alpar@10
   761
      return _random_bits::IntConversion<Number, Word>::convert(core);
alpar@10
   762
    }
alpar@10
   763
alpar@10
   764
    unsigned int uinteger() {
alpar@10
   765
      return uinteger<unsigned int>();
alpar@10
   766
    }
alpar@10
   767
alpar@10
   768
    /// \brief Returns a random integer
alpar@10
   769
    ///
alpar@10
   770
    /// It returns a random integer uniformly from the whole range of
alpar@10
   771
    /// the current \c Number type. The default result type of this
kpeter@49
   772
    /// function is \c int.
alpar@10
   773
    template <typename Number>
alpar@10
   774
    Number integer() {
alpar@209
   775
      static const int nb = std::numeric_limits<Number>::digits +
alpar@10
   776
        (std::numeric_limits<Number>::is_signed ? 1 : 0);
alpar@10
   777
      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
alpar@10
   778
    }
alpar@10
   779
alpar@10
   780
    int integer() {
alpar@10
   781
      return integer<int>();
alpar@10
   782
    }
alpar@209
   783
alpar@10
   784
    /// \brief Returns a random bool
alpar@10
   785
    ///
alpar@10
   786
    /// It returns a random bool. The generator holds a buffer for
alpar@10
   787
    /// random bits. Every time when it become empty the generator makes
alpar@10
   788
    /// a new random word and fill the buffer up.
alpar@10
   789
    bool boolean() {
alpar@10
   790
      return bool_producer.convert(core);
alpar@10
   791
    }
alpar@10
   792
deba@177
   793
    /// @}
deba@177
   794
kpeter@49
   795
    ///\name Non-uniform distributions
alpar@10
   796
    ///
alpar@10
   797
    ///@{
alpar@209
   798
kpeter@352
   799
    /// \brief Returns a random bool with given probability of true result.
alpar@10
   800
    ///
kpeter@23
   801
    /// It returns a random bool with given probability of true result.
alpar@10
   802
    bool boolean(double p) {
alpar@10
   803
      return operator()() < p;
alpar@10
   804
    }
alpar@10
   805
kpeter@352
   806
    /// Standard normal (Gauss) distribution
alpar@10
   807
kpeter@352
   808
    /// Standard normal (Gauss) distribution.
alpar@10
   809
    /// \note The Cartesian form of the Box-Muller
alpar@10
   810
    /// transformation is used to generate a random normal distribution.
alpar@209
   811
    double gauss()
alpar@10
   812
    {
alpar@10
   813
      double V1,V2,S;
alpar@10
   814
      do {
alpar@209
   815
        V1=2*real<double>()-1;
alpar@209
   816
        V2=2*real<double>()-1;
alpar@209
   817
        S=V1*V1+V2*V2;
alpar@10
   818
      } while(S>=1);
alpar@10
   819
      return std::sqrt(-2*std::log(S)/S)*V1;
alpar@10
   820
    }
kpeter@352
   821
    /// Normal (Gauss) distribution with given mean and standard deviation
alpar@10
   822
kpeter@352
   823
    /// Normal (Gauss) distribution with given mean and standard deviation.
alpar@10
   824
    /// \sa gauss()
alpar@10
   825
    double gauss(double mean,double std_dev)
alpar@10
   826
    {
alpar@10
   827
      return gauss()*std_dev+mean;
alpar@10
   828
    }
alpar@10
   829
alpar@351
   830
    /// Lognormal distribution
alpar@351
   831
alpar@351
   832
    /// Lognormal distribution. The parameters are the mean and the standard
alpar@351
   833
    /// deviation of <tt>exp(X)</tt>.
alpar@351
   834
    ///
alpar@351
   835
    double lognormal(double n_mean,double n_std_dev)
alpar@351
   836
    {
alpar@351
   837
      return std::exp(gauss(n_mean,n_std_dev));
alpar@351
   838
    }
alpar@351
   839
    /// Lognormal distribution
alpar@351
   840
alpar@351
   841
    /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
alpar@351
   842
    /// the mean and the standard deviation of <tt>exp(X)</tt>.
alpar@351
   843
    ///
alpar@351
   844
    double lognormal(const std::pair<double,double> &params)
alpar@351
   845
    {
alpar@351
   846
      return std::exp(gauss(params.first,params.second));
alpar@351
   847
    }
alpar@351
   848
    /// Compute the lognormal parameters from mean and standard deviation
alpar@351
   849
alpar@351
   850
    /// This function computes the lognormal parameters from mean and
alpar@351
   851
    /// standard deviation. The return value can direcly be passed to
alpar@351
   852
    /// lognormal().
alpar@351
   853
    std::pair<double,double> lognormalParamsFromMD(double mean,
kpeter@352
   854
                                                   double std_dev)
alpar@351
   855
    {
alpar@351
   856
      double fr=std_dev/mean;
alpar@351
   857
      fr*=fr;
alpar@351
   858
      double lg=std::log(1+fr);
alpar@351
   859
      return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
alpar@351
   860
    }
alpar@351
   861
    /// Lognormal distribution with given mean and standard deviation
kpeter@352
   862
alpar@351
   863
    /// Lognormal distribution with given mean and standard deviation.
alpar@351
   864
    ///
alpar@351
   865
    double lognormalMD(double mean,double std_dev)
alpar@351
   866
    {
alpar@351
   867
      return lognormal(lognormalParamsFromMD(mean,std_dev));
alpar@351
   868
    }
kpeter@352
   869
alpar@10
   870
    /// Exponential distribution with given mean
alpar@10
   871
alpar@10
   872
    /// This function generates an exponential distribution random number
alpar@10
   873
    /// with mean <tt>1/lambda</tt>.
alpar@10
   874
    ///
alpar@10
   875
    double exponential(double lambda=1.0)
alpar@10
   876
    {
alpar@11
   877
      return -std::log(1.0-real<double>())/lambda;
alpar@10
   878
    }
alpar@10
   879
alpar@10
   880
    /// Gamma distribution with given integer shape
alpar@10
   881
alpar@10
   882
    /// This function generates a gamma distribution random number.
alpar@209
   883
    ///
alpar@10
   884
    ///\param k shape parameter (<tt>k>0</tt> integer)
alpar@209
   885
    double gamma(int k)
alpar@10
   886
    {
alpar@10
   887
      double s = 0;
alpar@10
   888
      for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
alpar@10
   889
      return s;
alpar@10
   890
    }
alpar@209
   891
alpar@10
   892
    /// Gamma distribution with given shape and scale parameter
alpar@10
   893
alpar@10
   894
    /// This function generates a gamma distribution random number.
alpar@209
   895
    ///
alpar@10
   896
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@10
   897
    ///\param theta scale parameter
alpar@10
   898
    ///
alpar@10
   899
    double gamma(double k,double theta=1.0)
alpar@10
   900
    {
alpar@10
   901
      double xi,nu;
alpar@10
   902
      const double delta = k-std::floor(k);
alpar@68
   903
      const double v0=E/(E-delta);
alpar@10
   904
      do {
alpar@209
   905
        double V0=1.0-real<double>();
alpar@209
   906
        double V1=1.0-real<double>();
alpar@209
   907
        double V2=1.0-real<double>();
alpar@209
   908
        if(V2<=v0)
alpar@209
   909
          {
alpar@209
   910
            xi=std::pow(V1,1.0/delta);
alpar@209
   911
            nu=V0*std::pow(xi,delta-1.0);
alpar@209
   912
          }
alpar@209
   913
        else
alpar@209
   914
          {
alpar@209
   915
            xi=1.0-std::log(V1);
alpar@209
   916
            nu=V0*std::exp(-xi);
alpar@209
   917
          }
alpar@10
   918
      } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
alpar@116
   919
      return theta*(xi+gamma(int(std::floor(k))));
alpar@10
   920
    }
alpar@209
   921
alpar@11
   922
    /// Weibull distribution
alpar@11
   923
alpar@11
   924
    /// This function generates a Weibull distribution random number.
alpar@209
   925
    ///
alpar@11
   926
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@11
   927
    ///\param lambda scale parameter (<tt>lambda>0</tt>)
alpar@11
   928
    ///
alpar@11
   929
    double weibull(double k,double lambda)
alpar@11
   930
    {
alpar@11
   931
      return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
alpar@209
   932
    }
alpar@209
   933
alpar@11
   934
    /// Pareto distribution
alpar@11
   935
alpar@11
   936
    /// This function generates a Pareto distribution random number.
alpar@209
   937
    ///
alpar@12
   938
    ///\param k shape parameter (<tt>k>0</tt>)
alpar@11
   939
    ///\param x_min location parameter (<tt>x_min>0</tt>)
alpar@11
   940
    ///
alpar@12
   941
    double pareto(double k,double x_min)
alpar@11
   942
    {
alpar@116
   943
      return exponential(gamma(k,1.0/x_min))+x_min;
alpar@209
   944
    }
alpar@209
   945
alpar@92
   946
    /// Poisson distribution
alpar@92
   947
alpar@92
   948
    /// This function generates a Poisson distribution random number with
alpar@92
   949
    /// parameter \c lambda.
alpar@209
   950
    ///
alpar@92
   951
    /// The probability mass function of this distribusion is
alpar@92
   952
    /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
alpar@92
   953
    /// \note The algorithm is taken from the book of Donald E. Knuth titled
alpar@92
   954
    /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
alpar@92
   955
    /// return value.
alpar@209
   956
alpar@92
   957
    int poisson(double lambda)
alpar@92
   958
    {
alpar@92
   959
      const double l = std::exp(-lambda);
alpar@92
   960
      int k=0;
alpar@92
   961
      double p = 1.0;
alpar@92
   962
      do {
alpar@209
   963
        k++;
alpar@209
   964
        p*=real<double>();
alpar@92
   965
      } while (p>=l);
alpar@92
   966
      return k-1;
alpar@209
   967
    }
alpar@209
   968
alpar@10
   969
    ///@}
alpar@209
   970
alpar@10
   971
    ///\name Two dimensional distributions
alpar@10
   972
    ///
alpar@10
   973
    ///@{
alpar@209
   974
kpeter@23
   975
    /// Uniform distribution on the full unit circle
kpeter@16
   976
kpeter@16
   977
    /// Uniform distribution on the full unit circle.
kpeter@16
   978
    ///
alpar@209
   979
    dim2::Point<double> disc()
alpar@10
   980
    {
alpar@10
   981
      double V1,V2;
alpar@10
   982
      do {
alpar@209
   983
        V1=2*real<double>()-1;
alpar@209
   984
        V2=2*real<double>()-1;
alpar@209
   985
alpar@10
   986
      } while(V1*V1+V2*V2>=1);
alpar@10
   987
      return dim2::Point<double>(V1,V2);
alpar@10
   988
    }
kpeter@352
   989
    /// A kind of two dimensional normal (Gauss) distribution
alpar@10
   990
alpar@10
   991
    /// This function provides a turning symmetric two-dimensional distribution.
alpar@10
   992
    /// Both coordinates are of standard normal distribution, but they are not
alpar@10
   993
    /// independent.
alpar@10
   994
    ///
alpar@10
   995
    /// \note The coordinates are the two random variables provided by
alpar@10
   996
    /// the Box-Muller method.
alpar@10
   997
    dim2::Point<double> gauss2()
alpar@10
   998
    {
alpar@10
   999
      double V1,V2,S;
alpar@10
  1000
      do {
alpar@209
  1001
        V1=2*real<double>()-1;
alpar@209
  1002
        V2=2*real<double>()-1;
alpar@209
  1003
        S=V1*V1+V2*V2;
alpar@10
  1004
      } while(S>=1);
alpar@10
  1005
      double W=std::sqrt(-2*std::log(S)/S);
alpar@10
  1006
      return dim2::Point<double>(W*V1,W*V2);
alpar@10
  1007
    }
alpar@10
  1008
    /// A kind of two dimensional exponential distribution
alpar@10
  1009
alpar@10
  1010
    /// This function provides a turning symmetric two-dimensional distribution.
alpar@10
  1011
    /// The x-coordinate is of conditionally exponential distribution
alpar@209
  1012
    /// with the condition that x is positive and y=0. If x is negative and
alpar@10
  1013
    /// y=0 then, -x is of exponential distribution. The same is true for the
alpar@10
  1014
    /// y-coordinate.
alpar@209
  1015
    dim2::Point<double> exponential2()
alpar@10
  1016
    {
alpar@10
  1017
      double V1,V2,S;
alpar@10
  1018
      do {
alpar@209
  1019
        V1=2*real<double>()-1;
alpar@209
  1020
        V2=2*real<double>()-1;
alpar@209
  1021
        S=V1*V1+V2*V2;
alpar@10
  1022
      } while(S>=1);
alpar@10
  1023
      double W=-std::log(S)/S;
alpar@10
  1024
      return dim2::Point<double>(W*V1,W*V2);
alpar@10
  1025
    }
alpar@10
  1026
alpar@209
  1027
    ///@}
alpar@10
  1028
  };
alpar@10
  1029
alpar@10
  1030
alpar@10
  1031
  extern Random rnd;
alpar@10
  1032
alpar@10
  1033
}
alpar@10
  1034
alpar@10
  1035
#endif