alpar@209: /* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@10:  *
alpar@209:  * This file is a part of LEMON, a generic C++ optimization library.
alpar@10:  *
alpar@463:  * Copyright (C) 2003-2009
alpar@10:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@10:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@10:  *
alpar@10:  * Permission to use, modify and distribute this software is granted
alpar@10:  * provided that this copyright notice appears in all copies. For
alpar@10:  * precise terms see the accompanying LICENSE file.
alpar@10:  *
alpar@10:  * This software is provided "AS IS" with no warranty of any kind,
alpar@10:  * express or implied, and with no claim as to its suitability for any
alpar@10:  * purpose.
alpar@10:  *
alpar@10:  */
alpar@10: 
alpar@10: /*
alpar@10:  * This file contains the reimplemented version of the Mersenne Twister
alpar@10:  * Generator of Matsumoto and Nishimura.
alpar@10:  *
alpar@10:  * See the appropriate copyright notice below.
alpar@209:  *
alpar@10:  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
alpar@209:  * All rights reserved.
alpar@10:  *
alpar@10:  * Redistribution and use in source and binary forms, with or without
alpar@10:  * modification, are permitted provided that the following conditions
alpar@10:  * are met:
alpar@10:  *
alpar@10:  * 1. Redistributions of source code must retain the above copyright
alpar@10:  *    notice, this list of conditions and the following disclaimer.
alpar@10:  *
alpar@10:  * 2. Redistributions in binary form must reproduce the above copyright
alpar@10:  *    notice, this list of conditions and the following disclaimer in the
alpar@10:  *    documentation and/or other materials provided with the distribution.
alpar@10:  *
alpar@209:  * 3. The names of its contributors may not be used to endorse or promote
alpar@209:  *    products derived from this software without specific prior written
alpar@10:  *    permission.
alpar@10:  *
alpar@10:  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
alpar@10:  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
alpar@10:  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
alpar@10:  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
alpar@10:  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
alpar@10:  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
alpar@10:  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
alpar@10:  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
alpar@10:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
alpar@10:  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
alpar@10:  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
alpar@10:  * OF THE POSSIBILITY OF SUCH DAMAGE.
alpar@10:  *
alpar@10:  *
alpar@10:  * Any feedback is very welcome.
alpar@10:  * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
alpar@10:  * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
alpar@10:  */
alpar@10: 
alpar@10: #ifndef LEMON_RANDOM_H
alpar@10: #define LEMON_RANDOM_H
alpar@10: 
alpar@1340: #include <lemon/config.h>
alpar@1340: 
alpar@10: #include <algorithm>
alpar@10: #include <iterator>
alpar@10: #include <vector>
deba@110: #include <limits>
deba@177: #include <fstream>
alpar@10: 
alpar@68: #include <lemon/math.h>
alpar@10: #include <lemon/dim2.h>
alpar@68: 
alpar@1340: #ifndef LEMON_WIN32
deba@177: #include <sys/time.h>
deba@177: #include <ctime>
deba@177: #include <sys/types.h>
deba@177: #include <unistd.h>
deba@177: #else
alpar@511: #include <lemon/bits/windows.h>
deba@177: #endif
deba@177: 
alpar@10: ///\ingroup misc
alpar@10: ///\file
alpar@10: ///\brief Mersenne Twister random number generator
alpar@10: 
alpar@10: namespace lemon {
alpar@10: 
alpar@10:   namespace _random_bits {
alpar@209: 
alpar@10:     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
alpar@10:     struct RandomTraits {};
alpar@10: 
alpar@10:     template <typename _Word>
alpar@10:     struct RandomTraits<_Word, 32> {
alpar@10: 
alpar@10:       typedef _Word Word;
alpar@10:       static const int bits = 32;
alpar@10: 
alpar@10:       static const int length = 624;
alpar@10:       static const int shift = 397;
alpar@209: 
alpar@10:       static const Word mul = 0x6c078965u;
alpar@10:       static const Word arrayInit = 0x012BD6AAu;
alpar@10:       static const Word arrayMul1 = 0x0019660Du;
alpar@10:       static const Word arrayMul2 = 0x5D588B65u;
alpar@10: 
alpar@10:       static const Word mask = 0x9908B0DFu;
alpar@10:       static const Word loMask = (1u << 31) - 1;
alpar@10:       static const Word hiMask = ~loMask;
alpar@10: 
alpar@10:       static Word tempering(Word rnd) {
alpar@10:         rnd ^= (rnd >> 11);
alpar@10:         rnd ^= (rnd << 7) & 0x9D2C5680u;
alpar@10:         rnd ^= (rnd << 15) & 0xEFC60000u;
alpar@10:         rnd ^= (rnd >> 18);
alpar@10:         return rnd;
alpar@10:       }
alpar@10: 
alpar@10:     };
alpar@10: 
alpar@10:     template <typename _Word>
alpar@10:     struct RandomTraits<_Word, 64> {
alpar@10: 
alpar@10:       typedef _Word Word;
alpar@10:       static const int bits = 64;
alpar@10: 
alpar@10:       static const int length = 312;
alpar@10:       static const int shift = 156;
alpar@10: 
alpar@10:       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
alpar@10:       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
alpar@10:       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
alpar@10:       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
alpar@10: 
alpar@10:       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
alpar@10:       static const Word loMask = (Word(1u) << 31) - 1;
alpar@10:       static const Word hiMask = ~loMask;
alpar@10: 
alpar@10:       static Word tempering(Word rnd) {
alpar@10:         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
alpar@10:         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
alpar@10:         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
alpar@10:         rnd ^= (rnd >> 43);
alpar@10:         return rnd;
alpar@10:       }
alpar@10: 
alpar@10:     };
alpar@10: 
alpar@10:     template <typename _Word>
alpar@10:     class RandomCore {
alpar@10:     public:
alpar@10: 
alpar@10:       typedef _Word Word;
alpar@10: 
alpar@10:     private:
alpar@10: 
alpar@10:       static const int bits = RandomTraits<Word>::bits;
alpar@10: 
alpar@10:       static const int length = RandomTraits<Word>::length;
alpar@10:       static const int shift = RandomTraits<Word>::shift;
alpar@10: 
alpar@10:     public:
alpar@10: 
alpar@10:       void initState() {
alpar@10:         static const Word seedArray[4] = {
alpar@10:           0x12345u, 0x23456u, 0x34567u, 0x45678u
alpar@10:         };
alpar@209: 
alpar@10:         initState(seedArray, seedArray + 4);
alpar@10:       }
alpar@10: 
alpar@10:       void initState(Word seed) {
alpar@10: 
alpar@10:         static const Word mul = RandomTraits<Word>::mul;
alpar@10: 
alpar@209:         current = state;
alpar@10: 
alpar@10:         Word *curr = state + length - 1;
alpar@10:         curr[0] = seed; --curr;
alpar@10:         for (int i = 1; i < length; ++i) {
alpar@10:           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
alpar@10:           --curr;
alpar@10:         }
alpar@10:       }
alpar@10: 
alpar@10:       template <typename Iterator>
alpar@10:       void initState(Iterator begin, Iterator end) {
alpar@10: 
alpar@10:         static const Word init = RandomTraits<Word>::arrayInit;
alpar@10:         static const Word mul1 = RandomTraits<Word>::arrayMul1;
alpar@10:         static const Word mul2 = RandomTraits<Word>::arrayMul2;
alpar@10: 
alpar@10: 
alpar@10:         Word *curr = state + length - 1; --curr;
alpar@10:         Iterator it = begin; int cnt = 0;
alpar@10:         int num;
alpar@10: 
alpar@10:         initState(init);
alpar@10: 
alpar@1328:         num = static_cast<int>(length > end - begin ? length : end - begin);
alpar@10:         while (num--) {
alpar@209:           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
alpar@10:             + *it + cnt;
alpar@10:           ++it; ++cnt;
alpar@10:           if (it == end) {
alpar@10:             it = begin; cnt = 0;
alpar@10:           }
alpar@10:           if (curr == state) {
alpar@10:             curr = state + length - 1; curr[0] = state[0];
alpar@10:           }
alpar@10:           --curr;
alpar@10:         }
alpar@10: 
alpar@1328:         num = length - 1; cnt = static_cast<int>(length - (curr - state) - 1);
alpar@10:         while (num--) {
alpar@10:           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
alpar@10:             - cnt;
alpar@10:           --curr; ++cnt;
alpar@10:           if (curr == state) {
alpar@10:             curr = state + length - 1; curr[0] = state[0]; --curr;
alpar@10:             cnt = 1;
alpar@10:           }
alpar@10:         }
alpar@209: 
alpar@10:         state[length - 1] = Word(1) << (bits - 1);
alpar@10:       }
alpar@209: 
alpar@10:       void copyState(const RandomCore& other) {
alpar@10:         std::copy(other.state, other.state + length, state);
alpar@10:         current = state + (other.current - other.state);
alpar@10:       }
alpar@10: 
alpar@10:       Word operator()() {
alpar@10:         if (current == state) fillState();
alpar@10:         --current;
alpar@10:         Word rnd = *current;
alpar@10:         return RandomTraits<Word>::tempering(rnd);
alpar@10:       }
alpar@10: 
alpar@10:     private:
alpar@10: 
alpar@10:       void fillState() {
alpar@10:         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
alpar@10:         static const Word loMask = RandomTraits<Word>::loMask;
alpar@10:         static const Word hiMask = RandomTraits<Word>::hiMask;
alpar@10: 
alpar@209:         current = state + length;
alpar@10: 
alpar@1338:         Word *curr = state + length - 1;
alpar@1338:         long num;
alpar@209: 
alpar@10:         num = length - shift;
alpar@10:         while (num--) {
alpar@10:           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
alpar@10:             curr[- shift] ^ mask[curr[-1] & 1ul];
alpar@10:           --curr;
alpar@10:         }
alpar@10:         num = shift - 1;
alpar@10:         while (num--) {
alpar@10:           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
alpar@10:             curr[length - shift] ^ mask[curr[-1] & 1ul];
alpar@10:           --curr;
alpar@10:         }
deba@62:         state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
alpar@10:           curr[length - shift] ^ mask[curr[length - 1] & 1ul];
alpar@10: 
alpar@10:       }
alpar@10: 
alpar@10:       Word *current;
alpar@10:       Word state[length];
alpar@209: 
alpar@10:     };
alpar@10: 
alpar@10: 
alpar@209:     template <typename Result,
alpar@10:               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
alpar@10:     struct Masker {
alpar@10:       static Result mask(const Result& result) {
alpar@10:         return Masker<Result, (shift + 1) / 2>::
alpar@10:           mask(static_cast<Result>(result | (result >> shift)));
alpar@10:       }
alpar@10:     };
alpar@209: 
alpar@10:     template <typename Result>
alpar@10:     struct Masker<Result, 1> {
alpar@10:       static Result mask(const Result& result) {
alpar@10:         return static_cast<Result>(result | (result >> 1));
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@209:     template <typename Result, typename Word,
alpar@209:               int rest = std::numeric_limits<Result>::digits, int shift = 0,
alpar@1379:               bool last = (rest <= std::numeric_limits<Word>::digits)>
alpar@10:     struct IntConversion {
alpar@10:       static const int bits = std::numeric_limits<Word>::digits;
alpar@209: 
alpar@10:       static Result convert(RandomCore<Word>& rnd) {
alpar@10:         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
alpar@10:       }
alpar@10: 
alpar@209:     };
alpar@209: 
alpar@209:     template <typename Result, typename Word, int rest, int shift>
alpar@10:     struct IntConversion<Result, Word, rest, shift, false> {
alpar@10:       static const int bits = std::numeric_limits<Word>::digits;
alpar@10: 
alpar@10:       static Result convert(RandomCore<Word>& rnd) {
alpar@209:         return (static_cast<Result>(rnd()) << shift) |
alpar@10:           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10: 
alpar@10:     template <typename Result, typename Word,
alpar@209:               bool one_word = (std::numeric_limits<Word>::digits <
alpar@209:                                std::numeric_limits<Result>::digits) >
alpar@10:     struct Mapping {
alpar@10:       static Result map(RandomCore<Word>& rnd, const Result& bound) {
alpar@10:         Word max = Word(bound - 1);
alpar@10:         Result mask = Masker<Result>::mask(bound - 1);
alpar@10:         Result num;
alpar@10:         do {
alpar@209:           num = IntConversion<Result, Word>::convert(rnd) & mask;
alpar@10:         } while (num > max);
alpar@10:         return num;
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result, typename Word>
alpar@10:     struct Mapping<Result, Word, false> {
alpar@10:       static Result map(RandomCore<Word>& rnd, const Result& bound) {
alpar@10:         Word max = Word(bound - 1);
alpar@10:         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
alpar@10:           ::mask(max);
alpar@10:         Word num;
alpar@10:         do {
alpar@10:           num = rnd() & mask;
alpar@10:         } while (num > max);
alpar@1396:         return static_cast<Result>(num);
alpar@10:       }
alpar@10:     };
alpar@10: 
kpeter@517:     template <typename Result, int exp>
alpar@10:     struct ShiftMultiplier {
alpar@10:       static const Result multiplier() {
alpar@10:         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
alpar@10:         res *= res;
alpar@10:         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
alpar@209:         return res;
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result>
kpeter@517:     struct ShiftMultiplier<Result, 0> {
alpar@10:       static const Result multiplier() {
alpar@209:         return static_cast<Result>(1.0);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result>
kpeter@517:     struct ShiftMultiplier<Result, 20> {
alpar@10:       static const Result multiplier() {
alpar@209:         return static_cast<Result>(1.0/1048576.0);
alpar@10:       }
alpar@10:     };
alpar@209: 
alpar@10:     template <typename Result>
kpeter@517:     struct ShiftMultiplier<Result, 32> {
alpar@10:       static const Result multiplier() {
kpeter@517:         return static_cast<Result>(1.0/4294967296.0);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result>
kpeter@517:     struct ShiftMultiplier<Result, 53> {
alpar@10:       static const Result multiplier() {
alpar@209:         return static_cast<Result>(1.0/9007199254740992.0);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result>
kpeter@517:     struct ShiftMultiplier<Result, 64> {
alpar@10:       static const Result multiplier() {
alpar@209:         return static_cast<Result>(1.0/18446744073709551616.0);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result, int exp>
alpar@10:     struct Shifting {
alpar@10:       static Result shift(const Result& result) {
alpar@10:         return result * ShiftMultiplier<Result, exp>::multiplier();
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result, typename Word,
alpar@209:               int rest = std::numeric_limits<Result>::digits, int shift = 0,
alpar@10:               bool last = rest <= std::numeric_limits<Word>::digits>
alpar@209:     struct RealConversion{
alpar@10:       static const int bits = std::numeric_limits<Word>::digits;
alpar@10: 
alpar@10:       static Result convert(RandomCore<Word>& rnd) {
kpeter@517:         return Shifting<Result, shift + rest>::
alpar@10:           shift(static_cast<Result>(rnd() >> (bits - rest)));
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result, typename Word, int rest, int shift>
alpar@209:     struct RealConversion<Result, Word, rest, shift, false> {
alpar@10:       static const int bits = std::numeric_limits<Word>::digits;
alpar@10: 
alpar@10:       static Result convert(RandomCore<Word>& rnd) {
kpeter@517:         return Shifting<Result, shift + bits>::
alpar@10:           shift(static_cast<Result>(rnd())) +
alpar@10:           RealConversion<Result, Word, rest-bits, shift + bits>::
alpar@10:           convert(rnd);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Result, typename Word>
alpar@10:     struct Initializer {
alpar@10: 
alpar@10:       template <typename Iterator>
alpar@10:       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
alpar@10:         std::vector<Word> ws;
alpar@10:         for (Iterator it = begin; it != end; ++it) {
alpar@10:           ws.push_back(Word(*it));
alpar@10:         }
alpar@10:         rnd.initState(ws.begin(), ws.end());
alpar@10:       }
alpar@10: 
alpar@10:       static void init(RandomCore<Word>& rnd, Result seed) {
alpar@10:         rnd.initState(seed);
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Word>
alpar@10:     struct BoolConversion {
alpar@10:       static bool convert(RandomCore<Word>& rnd) {
alpar@10:         return (rnd() & 1) == 1;
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@10:     template <typename Word>
alpar@10:     struct BoolProducer {
alpar@10:       Word buffer;
alpar@10:       int num;
alpar@209: 
alpar@10:       BoolProducer() : num(0) {}
alpar@10: 
alpar@10:       bool convert(RandomCore<Word>& rnd) {
alpar@10:         if (num == 0) {
alpar@10:           buffer = rnd();
alpar@10:           num = RandomTraits<Word>::bits;
alpar@10:         }
alpar@10:         bool r = (buffer & 1);
alpar@10:         buffer >>= 1;
alpar@10:         --num;
alpar@10:         return r;
alpar@10:       }
alpar@10:     };
alpar@10: 
alpar@1379:     /// \ingroup misc
alpar@1379:     ///
alpar@1379:     /// \brief Mersenne Twister random number generator
alpar@1379:     ///
alpar@1379:     /// The Mersenne Twister is a twisted generalized feedback
alpar@1379:     /// shift-register generator of Matsumoto and Nishimura. The period
kpeter@1380:     /// of this generator is \f$ 2^{19937} - 1\f$ and it is
alpar@1379:     /// equi-distributed in 623 dimensions for 32-bit numbers. The time
alpar@1379:     /// performance of this generator is comparable to the commonly used
alpar@1379:     /// generators.
alpar@1379:     ///
kpeter@1380:     /// This is a template implementation of both 32-bit and
alpar@1379:     /// 64-bit architecture optimized versions. The generators differ
alpar@1379:     /// sligthly in the initialization and generation phase so they
alpar@1379:     /// produce two completly different sequences.
alpar@1379:     ///
alpar@1379:     /// \alert Do not use this class directly, but instead one of \ref
alpar@1379:     /// Random, \ref Random32 or \ref Random64.
alpar@1379:     ///
alpar@1379:     /// The generator gives back random numbers of serveral types. To
kpeter@1380:     /// get a random number from a range of a floating point type, you
alpar@1379:     /// can use one form of the \c operator() or the \c real() member
alpar@1379:     /// function. If you want to get random number from the {0, 1, ...,
kpeter@1380:     /// n-1} integer range, use the \c operator[] or the \c integer()
alpar@1379:     /// method. And to get random number from the whole range of an
kpeter@1380:     /// integer type, you can use the argumentless \c integer() or
kpeter@1380:     /// \c uinteger() functions. Finally, you can get random bool with
kpeter@1380:     /// equal chance of true and false or with given probability of true
kpeter@1380:     /// result using the \c boolean() member functions.
kpeter@1380:     ///
kpeter@1380:     /// Various non-uniform distributions are also supported: normal (Gauss),
kpeter@1380:     /// exponential, gamma, Poisson, etc.; and a few two-dimensional
kpeter@1380:     /// distributions, too.
alpar@1379:     ///
alpar@1379:     ///\code
alpar@1379:     /// // The commented code is identical to the other
alpar@1379:     /// double a = rnd();                     // [0.0, 1.0)
alpar@1379:     /// // double a = rnd.real();             // [0.0, 1.0)
alpar@1379:     /// double b = rnd(100.0);                // [0.0, 100.0)
alpar@1379:     /// // double b = rnd.real(100.0);        // [0.0, 100.0)
alpar@1379:     /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
alpar@1379:     /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
alpar@1379:     /// int d = rnd[100000];                  // 0..99999
alpar@1379:     /// // int d = rnd.integer(100000);       // 0..99999
alpar@1379:     /// int e = rnd[6] + 1;                   // 1..6
alpar@1379:     /// // int e = rnd.integer(1, 1 + 6);     // 1..6
alpar@1379:     /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
alpar@1379:     /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
alpar@1379:     /// bool g = rnd.boolean();               // P(g = true) = 0.5
alpar@1379:     /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
alpar@1379:     ///\endcode
alpar@1379:     ///
kpeter@1380:     /// LEMON provides a global instance of the random number generator:
kpeter@1380:     /// \ref lemon::rnd "rnd". In most cases, it is a good practice
kpeter@1380:     /// to use this global generator to get random numbers.
alpar@1379:     ///
alpar@1379:     /// \sa \ref Random, \ref Random32 or \ref Random64.
alpar@1379:     template<class Word>
alpar@1379:     class Random {
alpar@1379:     private:
alpar@1379: 
alpar@1379:       _random_bits::RandomCore<Word> core;
alpar@1379:       _random_bits::BoolProducer<Word> bool_producer;
alpar@1379: 
alpar@1379: 
alpar@1379:     public:
alpar@1379: 
alpar@1379:       ///\name Initialization
alpar@1379:       ///
alpar@1379:       /// @{
alpar@1379: 
alpar@1379:       /// \brief Default constructor
alpar@1379:       ///
alpar@1379:       /// Constructor with constant seeding.
alpar@1379:       Random() { core.initState(); }
alpar@1379: 
alpar@1379:       /// \brief Constructor with seed
alpar@1379:       ///
alpar@1379:       /// Constructor with seed. The current number type will be converted
alpar@1379:       /// to the architecture word type.
alpar@1379:       template <typename Number>
alpar@1379:       Random(Number seed) {
alpar@1379:         _random_bits::Initializer<Number, Word>::init(core, seed);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Constructor with array seeding
alpar@1379:       ///
alpar@1379:       /// Constructor with array seeding. The given range should contain
alpar@1379:       /// any number type and the numbers will be converted to the
alpar@1379:       /// architecture word type.
alpar@1379:       template <typename Iterator>
alpar@1379:       Random(Iterator begin, Iterator end) {
alpar@1379:         typedef typename std::iterator_traits<Iterator>::value_type Number;
alpar@1379:         _random_bits::Initializer<Number, Word>::init(core, begin, end);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Copy constructor
alpar@1379:       ///
alpar@1379:       /// Copy constructor. The generated sequence will be identical to
alpar@1379:       /// the other sequence. It can be used to save the current state
alpar@1379:       /// of the generator and later use it to generate the same
alpar@1379:       /// sequence.
alpar@1379:       Random(const Random& other) {
alpar@1379:         core.copyState(other.core);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Assign operator
alpar@1379:       ///
alpar@1379:       /// Assign operator. The generated sequence will be identical to
alpar@1379:       /// the other sequence. It can be used to save the current state
alpar@1379:       /// of the generator and later use it to generate the same
alpar@1379:       /// sequence.
alpar@1379:       Random& operator=(const Random& other) {
alpar@1379:         if (&other != this) {
alpar@1379:           core.copyState(other.core);
alpar@1379:         }
alpar@1379:         return *this;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Seeding random sequence
alpar@1379:       ///
alpar@1379:       /// Seeding the random sequence. The current number type will be
alpar@1379:       /// converted to the architecture word type.
alpar@1379:       template <typename Number>
alpar@1379:       void seed(Number seed) {
alpar@1379:         _random_bits::Initializer<Number, Word>::init(core, seed);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Seeding random sequence
alpar@1379:       ///
alpar@1379:       /// Seeding the random sequence. The given range should contain
alpar@1379:       /// any number type and the numbers will be converted to the
alpar@1379:       /// architecture word type.
alpar@1379:       template <typename Iterator>
alpar@1379:       void seed(Iterator begin, Iterator end) {
alpar@1379:         typedef typename std::iterator_traits<Iterator>::value_type Number;
alpar@1379:         _random_bits::Initializer<Number, Word>::init(core, begin, end);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Seeding from file or from process id and time
alpar@1379:       ///
alpar@1379:       /// By default, this function calls the \c seedFromFile() member
alpar@1379:       /// function with the <tt>/dev/urandom</tt> file. If it does not success,
alpar@1379:       /// it uses the \c seedFromTime().
alpar@1379:       /// \return Currently always \c true.
alpar@1379:       bool seed() {
alpar@1379: #ifndef LEMON_WIN32
alpar@1379:         if (seedFromFile("/dev/urandom", 0)) return true;
alpar@1379: #endif
alpar@1379:         if (seedFromTime()) return true;
alpar@1379:         return false;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Seeding from file
alpar@1379:       ///
alpar@1379:       /// Seeding the random sequence from file. The linux kernel has two
alpar@1379:       /// devices, <tt>/dev/random</tt> and <tt>/dev/urandom</tt> which
alpar@1379:       /// could give good seed values for pseudo random generators (The
alpar@1379:       /// difference between two devices is that the <tt>random</tt> may
alpar@1379:       /// block the reading operation while the kernel can give good
alpar@1379:       /// source of randomness, while the <tt>urandom</tt> does not
alpar@1379:       /// block the input, but it could give back bytes with worse
alpar@1379:       /// entropy).
alpar@1379:       /// \param file The source file
alpar@1379:       /// \param offset The offset, from the file read.
alpar@1379:       /// \return \c true when the seeding successes.
alpar@1379: #ifndef LEMON_WIN32
alpar@1379:       bool seedFromFile(const std::string& file = "/dev/urandom", int offset = 0)
alpar@1379: #else
alpar@1379:         bool seedFromFile(const std::string& file = "", int offset = 0)
alpar@1379: #endif
alpar@1379:       {
alpar@1379:         std::ifstream rs(file.c_str());
alpar@1379:         const int size = 4;
alpar@1379:         Word buf[size];
alpar@1379:         if (offset != 0 && !rs.seekg(offset)) return false;
alpar@1379:         if (!rs.read(reinterpret_cast<char*>(buf), sizeof(buf))) return false;
alpar@1379:         seed(buf, buf + size);
alpar@1379:         return true;
alpar@1379:       }
alpar@1379: 
kpeter@1380:       /// \brief Seeding from process id and time
alpar@1379:       ///
kpeter@1380:       /// Seeding from process id and time. This function uses the
alpar@1379:       /// current process id and the current time for initialize the
alpar@1379:       /// random sequence.
alpar@1379:       /// \return Currently always \c true.
alpar@1379:       bool seedFromTime() {
alpar@1379: #ifndef LEMON_WIN32
alpar@1379:         timeval tv;
alpar@1379:         gettimeofday(&tv, 0);
alpar@1379:         seed(getpid() + tv.tv_sec + tv.tv_usec);
alpar@1379: #else
alpar@1379:         seed(bits::getWinRndSeed());
alpar@1379: #endif
alpar@1379:         return true;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// @}
alpar@1379: 
alpar@1379:       ///\name Uniform Distributions
alpar@1379:       ///
alpar@1379:       /// @{
alpar@1379: 
alpar@1379:       /// \brief Returns a random real number from the range [0, 1)
alpar@1379:       ///
alpar@1379:       /// It returns a random real number from the range [0, 1). The
alpar@1379:       /// default Number type is \c double.
alpar@1379:       template <typename Number>
alpar@1379:       Number real() {
alpar@1379:         return _random_bits::RealConversion<Number, Word>::convert(core);
alpar@1379:       }
alpar@1379: 
alpar@1379:       double real() {
alpar@1379:         return real<double>();
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random real number from the range [0, 1)
alpar@1379:       ///
alpar@1379:       /// It returns a random double from the range [0, 1).
alpar@1379:       double operator()() {
alpar@1379:         return real<double>();
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random real number from the range [0, b)
alpar@1379:       ///
alpar@1379:       /// It returns a random real number from the range [0, b).
alpar@1379:       double operator()(double b) {
alpar@1379:         return real<double>() * b;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random real number from the range [a, b)
alpar@1379:       ///
alpar@1379:       /// It returns a random real number from the range [a, b).
alpar@1379:       double operator()(double a, double b) {
alpar@1379:         return real<double>() * (b - a) + a;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random integer from a range
alpar@1379:       ///
alpar@1379:       /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@1379:       template <typename Number>
alpar@1379:       Number integer(Number b) {
alpar@1379:         return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random integer from a range
alpar@1379:       ///
alpar@1379:       /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
alpar@1379:       template <typename Number>
alpar@1379:       Number integer(Number a, Number b) {
alpar@1379:         return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random integer from a range
alpar@1379:       ///
alpar@1379:       /// It returns a random integer from the range {0, 1, ..., b - 1}.
alpar@1379:       template <typename Number>
alpar@1379:       Number operator[](Number b) {
alpar@1379:         return _random_bits::Mapping<Number, Word>::map(core, b);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random non-negative integer
alpar@1379:       ///
alpar@1379:       /// It returns a random non-negative integer uniformly from the
alpar@1379:       /// whole range of the current \c Number type. The default result
alpar@1379:       /// type of this function is <tt>unsigned int</tt>.
alpar@1379:       template <typename Number>
alpar@1379:       Number uinteger() {
alpar@1379:         return _random_bits::IntConversion<Number, Word>::convert(core);
alpar@1379:       }
alpar@1379: 
alpar@1379:       unsigned int uinteger() {
alpar@1379:         return uinteger<unsigned int>();
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random integer
alpar@1379:       ///
alpar@1379:       /// It returns a random integer uniformly from the whole range of
alpar@1379:       /// the current \c Number type. The default result type of this
alpar@1379:       /// function is \c int.
alpar@1379:       template <typename Number>
alpar@1379:       Number integer() {
alpar@1379:         static const int nb = std::numeric_limits<Number>::digits +
alpar@1379:           (std::numeric_limits<Number>::is_signed ? 1 : 0);
alpar@1379:         return _random_bits::IntConversion<Number, Word, nb>::convert(core);
alpar@1379:       }
alpar@1379: 
alpar@1379:       int integer() {
alpar@1379:         return integer<int>();
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// \brief Returns a random bool
alpar@1379:       ///
alpar@1379:       /// It returns a random bool. The generator holds a buffer for
alpar@1379:       /// random bits. Every time when it become empty the generator makes
alpar@1379:       /// a new random word and fill the buffer up.
alpar@1379:       bool boolean() {
alpar@1379:         return bool_producer.convert(core);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// @}
alpar@1379: 
alpar@1379:       ///\name Non-uniform Distributions
alpar@1379:       ///
alpar@1379:       ///@{
alpar@1379: 
alpar@1379:       /// \brief Returns a random bool with given probability of true result.
alpar@1379:       ///
alpar@1379:       /// It returns a random bool with given probability of true result.
alpar@1379:       bool boolean(double p) {
alpar@1379:         return operator()() < p;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Standard normal (Gauss) distribution
alpar@1379: 
alpar@1379:       /// Standard normal (Gauss) distribution.
alpar@1379:       /// \note The Cartesian form of the Box-Muller
alpar@1379:       /// transformation is used to generate a random normal distribution.
alpar@1379:       double gauss()
alpar@1379:       {
alpar@1379:         double V1,V2,S;
alpar@1379:         do {
alpar@1379:           V1=2*real<double>()-1;
alpar@1379:           V2=2*real<double>()-1;
alpar@1379:           S=V1*V1+V2*V2;
alpar@1379:         } while(S>=1);
alpar@1379:         return std::sqrt(-2*std::log(S)/S)*V1;
alpar@1379:       }
alpar@1379:       /// Normal (Gauss) distribution with given mean and standard deviation
alpar@1379: 
alpar@1379:       /// Normal (Gauss) distribution with given mean and standard deviation.
alpar@1379:       /// \sa gauss()
alpar@1379:       double gauss(double mean,double std_dev)
alpar@1379:       {
alpar@1379:         return gauss()*std_dev+mean;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Lognormal distribution
alpar@1379: 
alpar@1379:       /// Lognormal distribution. The parameters are the mean and the standard
alpar@1379:       /// deviation of <tt>exp(X)</tt>.
alpar@1379:       ///
alpar@1379:       double lognormal(double n_mean,double n_std_dev)
alpar@1379:       {
alpar@1379:         return std::exp(gauss(n_mean,n_std_dev));
alpar@1379:       }
alpar@1379:       /// Lognormal distribution
alpar@1379: 
alpar@1379:       /// Lognormal distribution. The parameter is an <tt>std::pair</tt> of
alpar@1379:       /// the mean and the standard deviation of <tt>exp(X)</tt>.
alpar@1379:       ///
alpar@1379:       double lognormal(const std::pair<double,double> &params)
alpar@1379:       {
alpar@1379:         return std::exp(gauss(params.first,params.second));
alpar@1379:       }
alpar@1379:       /// Compute the lognormal parameters from mean and standard deviation
alpar@1379: 
alpar@1379:       /// This function computes the lognormal parameters from mean and
alpar@1379:       /// standard deviation. The return value can direcly be passed to
alpar@1379:       /// lognormal().
alpar@1379:       std::pair<double,double> lognormalParamsFromMD(double mean,
alpar@1379:                                                      double std_dev)
alpar@1379:       {
alpar@1379:         double fr=std_dev/mean;
alpar@1379:         fr*=fr;
alpar@1379:         double lg=std::log(1+fr);
alpar@1379:         return std::pair<double,double>(std::log(mean)-lg/2.0,std::sqrt(lg));
alpar@1379:       }
alpar@1379:       /// Lognormal distribution with given mean and standard deviation
alpar@1379: 
alpar@1379:       /// Lognormal distribution with given mean and standard deviation.
alpar@1379:       ///
alpar@1379:       double lognormalMD(double mean,double std_dev)
alpar@1379:       {
alpar@1379:         return lognormal(lognormalParamsFromMD(mean,std_dev));
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Exponential distribution with given mean
alpar@1379: 
alpar@1379:       /// This function generates an exponential distribution random number
alpar@1379:       /// with mean <tt>1/lambda</tt>.
alpar@1379:       ///
alpar@1379:       double exponential(double lambda=1.0)
alpar@1379:       {
alpar@1379:         return -std::log(1.0-real<double>())/lambda;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Gamma distribution with given integer shape
alpar@1379: 
alpar@1379:       /// This function generates a gamma distribution random number.
alpar@1379:       ///
alpar@1379:       ///\param k shape parameter (<tt>k>0</tt> integer)
alpar@1379:       double gamma(int k)
alpar@1379:       {
alpar@1379:         double s = 0;
alpar@1379:         for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
alpar@1379:         return s;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Gamma distribution with given shape and scale parameter
alpar@1379: 
alpar@1379:       /// This function generates a gamma distribution random number.
alpar@1379:       ///
alpar@1379:       ///\param k shape parameter (<tt>k>0</tt>)
alpar@1379:       ///\param theta scale parameter
alpar@1379:       ///
alpar@1379:       double gamma(double k,double theta=1.0)
alpar@1379:       {
alpar@1379:         double xi,nu;
alpar@1379:         const double delta = k-std::floor(k);
alpar@1379:         const double v0=E/(E-delta);
alpar@1379:         do {
alpar@1379:           double V0=1.0-real<double>();
alpar@1379:           double V1=1.0-real<double>();
alpar@1379:           double V2=1.0-real<double>();
alpar@1379:           if(V2<=v0)
alpar@1379:             {
alpar@1379:               xi=std::pow(V1,1.0/delta);
alpar@1379:               nu=V0*std::pow(xi,delta-1.0);
alpar@1379:             }
alpar@1379:           else
alpar@1379:             {
alpar@1379:               xi=1.0-std::log(V1);
alpar@1379:               nu=V0*std::exp(-xi);
alpar@1379:             }
alpar@1379:         } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
alpar@1379:         return theta*(xi+gamma(int(std::floor(k))));
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Weibull distribution
alpar@1379: 
alpar@1379:       /// This function generates a Weibull distribution random number.
alpar@1379:       ///
alpar@1379:       ///\param k shape parameter (<tt>k>0</tt>)
alpar@1379:       ///\param lambda scale parameter (<tt>lambda>0</tt>)
alpar@1379:       ///
alpar@1379:       double weibull(double k,double lambda)
alpar@1379:       {
alpar@1379:         return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Pareto distribution
alpar@1379: 
alpar@1379:       /// This function generates a Pareto distribution random number.
alpar@1379:       ///
alpar@1379:       ///\param k shape parameter (<tt>k>0</tt>)
alpar@1379:       ///\param x_min location parameter (<tt>x_min>0</tt>)
alpar@1379:       ///
alpar@1379:       double pareto(double k,double x_min)
alpar@1379:       {
alpar@1379:         return exponential(gamma(k,1.0/x_min))+x_min;
alpar@1379:       }
alpar@1379: 
alpar@1379:       /// Poisson distribution
alpar@1379: 
alpar@1379:       /// This function generates a Poisson distribution random number with
alpar@1379:       /// parameter \c lambda.
alpar@1379:       ///
alpar@1379:       /// The probability mass function of this distribusion is
alpar@1379:       /// \f[ \frac{e^{-\lambda}\lambda^k}{k!} \f]
alpar@1379:       /// \note The algorithm is taken from the book of Donald E. Knuth titled
alpar@1379:       /// ''Seminumerical Algorithms'' (1969). Its running time is linear in the
alpar@1379:       /// return value.
alpar@1379: 
alpar@1379:       int poisson(double lambda)
alpar@1379:       {
alpar@1379:         const double l = std::exp(-lambda);
alpar@1379:         int k=0;
alpar@1379:         double p = 1.0;
alpar@1379:         do {
alpar@1379:           k++;
alpar@1379:           p*=real<double>();
alpar@1379:         } while (p>=l);
alpar@1379:         return k-1;
alpar@1379:       }
alpar@1379: 
alpar@1379:       ///@}
alpar@1379: 
kpeter@1380:       ///\name Two-Dimensional Distributions
alpar@1379:       ///
alpar@1379:       ///@{
alpar@1379: 
alpar@1379:       /// Uniform distribution on the full unit circle
alpar@1379: 
alpar@1379:       /// Uniform distribution on the full unit circle.
alpar@1379:       ///
alpar@1379:       dim2::Point<double> disc()
alpar@1379:       {
alpar@1379:         double V1,V2;
alpar@1379:         do {
alpar@1379:           V1=2*real<double>()-1;
alpar@1379:           V2=2*real<double>()-1;
alpar@1379: 
alpar@1379:         } while(V1*V1+V2*V2>=1);
alpar@1379:         return dim2::Point<double>(V1,V2);
alpar@1379:       }
kpeter@1380:       /// A kind of two-dimensional normal (Gauss) distribution
alpar@1379: 
alpar@1379:       /// This function provides a turning symmetric two-dimensional distribution.
alpar@1379:       /// Both coordinates are of standard normal distribution, but they are not
alpar@1379:       /// independent.
alpar@1379:       ///
alpar@1379:       /// \note The coordinates are the two random variables provided by
alpar@1379:       /// the Box-Muller method.
alpar@1379:       dim2::Point<double> gauss2()
alpar@1379:       {
alpar@1379:         double V1,V2,S;
alpar@1379:         do {
alpar@1379:           V1=2*real<double>()-1;
alpar@1379:           V2=2*real<double>()-1;
alpar@1379:           S=V1*V1+V2*V2;
alpar@1379:         } while(S>=1);
alpar@1379:         double W=std::sqrt(-2*std::log(S)/S);
alpar@1379:         return dim2::Point<double>(W*V1,W*V2);
alpar@1379:       }
kpeter@1380:       /// A kind of two-dimensional exponential distribution
alpar@1379: 
alpar@1379:       /// This function provides a turning symmetric two-dimensional distribution.
alpar@1379:       /// The x-coordinate is of conditionally exponential distribution
alpar@1379:       /// with the condition that x is positive and y=0. If x is negative and
alpar@1379:       /// y=0 then, -x is of exponential distribution. The same is true for the
alpar@1379:       /// y-coordinate.
alpar@1379:       dim2::Point<double> exponential2()
alpar@1379:       {
alpar@1379:         double V1,V2,S;
alpar@1379:         do {
alpar@1379:           V1=2*real<double>()-1;
alpar@1379:           V2=2*real<double>()-1;
alpar@1379:           S=V1*V1+V2*V2;
alpar@1379:         } while(S>=1);
alpar@1379:         double W=-std::log(S)/S;
alpar@1379:         return dim2::Point<double>(W*V1,W*V2);
alpar@1379:       }
alpar@1379: 
alpar@1379:       ///@}
alpar@1379:     };
alpar@1379: 
alpar@1379: 
alpar@1379:   };
alpar@10: 
alpar@10:   /// \ingroup misc
alpar@10:   ///
alpar@10:   /// \brief Mersenne Twister random number generator
alpar@10:   ///
kpeter@1380:   /// This class implements either the 32-bit or the 64-bit version of
alpar@1379:   /// the Mersenne Twister random number generator algorithm
kpeter@1380:   /// depending on the system architecture.
alpar@1379:   /// 
kpeter@1380:   /// For the API description, see its base class
kpeter@1380:   /// \ref _random_bits::Random.
alpar@10:   ///
alpar@1379:   /// \sa \ref _random_bits::Random
alpar@1379:   typedef _random_bits::Random<unsigned long> Random;
kpeter@1380: 
alpar@1379:   /// \ingroup misc
alpar@10:   ///
kpeter@1380:   /// \brief Mersenne Twister random number generator (32-bit version)
alpar@10:   ///
kpeter@1380:   /// This class implements the 32-bit version of the Mersenne Twister
alpar@1379:   /// random number generator algorithm. It is recommended to be used
alpar@1379:   /// when someone wants to make sure that the \e same pseudo random
alpar@1379:   /// sequence will be generated on every platfrom.
alpar@10:   ///
kpeter@1380:   /// For the API description, see its base class
kpeter@1380:   /// \ref _random_bits::Random.
alpar@1379:   ///
alpar@1379:   /// \sa \ref _random_bits::Random
kpeter@1380:   typedef _random_bits::Random<unsigned int> Random32;
alpar@10: 
alpar@1379:   /// \ingroup misc
alpar@1379:   ///
kpeter@1380:   /// \brief Mersenne Twister random number generator (64-bit version)
alpar@1379:   ///
kpeter@1380:   /// This class implements the 64-bit version of the Mersenne Twister
kpeter@1380:   /// random number generator algorithm. (Even though it runs
kpeter@1380:   /// on 32-bit architectures, too.) It is recommended to be used when
alpar@1379:   /// someone wants to make sure that the \e same pseudo random sequence
alpar@1379:   /// will be generated on every platfrom.
alpar@1379:   ///
kpeter@1380:   /// For the API description, see its base class
kpeter@1380:   /// \ref _random_bits::Random.
alpar@1379:   ///
alpar@1379:   /// \sa \ref _random_bits::Random
alpar@1379:   typedef _random_bits::Random<unsigned long long> Random64;
alpar@10: 
alpar@10:   extern Random rnd;
alpar@1379:   
alpar@10: }
alpar@10: 
alpar@10: #endif