deba@2229: /* -*- C++ -*-
deba@2229:  *
deba@2229:  * This file is a part of LEMON, a generic C++ optimization library
deba@2229:  *
alpar@2553:  * Copyright (C) 2003-2008
deba@2229:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2229:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2229:  *
deba@2229:  * Permission to use, modify and distribute this software is granted
deba@2229:  * provided that this copyright notice appears in all copies. For
deba@2229:  * precise terms see the accompanying LICENSE file.
deba@2229:  *
deba@2229:  * This software is provided "AS IS" with no warranty of any kind,
deba@2229:  * express or implied, and with no claim as to its suitability for any
deba@2229:  * purpose.
deba@2229:  *
deba@2229:  */
deba@2229: 
deba@2372: /*
deba@2372:  * This file contains the reimplemented version of the Mersenne Twister
deba@2372:  * Generator of Matsumoto and Nishimura.
deba@2372:  *
deba@2372:  * See the appropriate copyright notice below.
deba@2372:  * 
deba@2372:  * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
deba@2372:  * All rights reserved.                          
deba@2372:  *
deba@2372:  * Redistribution and use in source and binary forms, with or without
deba@2372:  * modification, are permitted provided that the following conditions
deba@2372:  * are met:
deba@2372:  *
deba@2372:  * 1. Redistributions of source code must retain the above copyright
deba@2372:  *    notice, this list of conditions and the following disclaimer.
deba@2372:  *
deba@2372:  * 2. Redistributions in binary form must reproduce the above copyright
deba@2372:  *    notice, this list of conditions and the following disclaimer in the
deba@2372:  *    documentation and/or other materials provided with the distribution.
deba@2372:  *
deba@2372:  * 3. The names of its contributors may not be used to endorse or promote 
deba@2372:  *    products derived from this software without specific prior written 
deba@2372:  *    permission.
deba@2372:  *
deba@2372:  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
deba@2372:  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
deba@2372:  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
deba@2372:  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
deba@2372:  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
deba@2372:  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
deba@2372:  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
deba@2372:  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
deba@2372:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
deba@2372:  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
deba@2372:  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
deba@2372:  * OF THE POSSIBILITY OF SUCH DAMAGE.
deba@2372:  *
deba@2372:  *
deba@2372:  * Any feedback is very welcome.
deba@2372:  * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
deba@2372:  * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
deba@2372:  */
deba@2372: 
deba@2229: #ifndef LEMON_RANDOM_H
deba@2229: #define LEMON_RANDOM_H
deba@2229: 
deba@2229: #include <algorithm>
deba@2242: #include <iterator>
deba@2242: #include <vector>
deba@2229: 
deba@2229: #include <ctime>
deba@2229: 
alpar@2570: #include <lemon/math.h>
alpar@2374: #include <lemon/dim2.h>
deba@2229: ///\ingroup misc
deba@2229: ///\file
deba@2229: ///\brief Mersenne Twister random number generator
deba@2229: ///
deba@2229: ///\author Balazs Dezso
deba@2229: 
deba@2229: namespace lemon {
deba@2229: 
deba@2242:   namespace _random_bits {
deba@2242:     
deba@2242:     template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
deba@2242:     struct RandomTraits {};
deba@2242: 
deba@2242:     template <typename _Word>
deba@2242:     struct RandomTraits<_Word, 32> {
deba@2242: 
deba@2242:       typedef _Word Word;
deba@2242:       static const int bits = 32;
deba@2242: 
deba@2242:       static const int length = 624;
deba@2242:       static const int shift = 397;
deba@2242:       
deba@2242:       static const Word mul = 0x6c078965u;
deba@2242:       static const Word arrayInit = 0x012BD6AAu;
deba@2242:       static const Word arrayMul1 = 0x0019660Du;
deba@2242:       static const Word arrayMul2 = 0x5D588B65u;
deba@2242: 
deba@2242:       static const Word mask = 0x9908B0DFu;
deba@2242:       static const Word loMask = (1u << 31) - 1;
deba@2242:       static const Word hiMask = ~loMask;
deba@2242: 
deba@2242: 
deba@2242:       static Word tempering(Word rnd) {
deba@2242:         rnd ^= (rnd >> 11);
deba@2242:         rnd ^= (rnd << 7) & 0x9D2C5680u;
deba@2242:         rnd ^= (rnd << 15) & 0xEFC60000u;
deba@2242:         rnd ^= (rnd >> 18);
deba@2242:         return rnd;
deba@2242:       }
deba@2242: 
deba@2242:     };
deba@2242: 
deba@2242:     template <typename _Word>
deba@2242:     struct RandomTraits<_Word, 64> {
deba@2242: 
deba@2242:       typedef _Word Word;
deba@2242:       static const int bits = 64;
deba@2242: 
deba@2242:       static const int length = 312;
deba@2242:       static const int shift = 156;
deba@2242: 
deba@2386:       static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
deba@2386:       static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
deba@2386:       static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
deba@2386:       static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
deba@2242: 
deba@2386:       static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
deba@2386:       static const Word loMask = (Word(1u) << 31) - 1;
deba@2242:       static const Word hiMask = ~loMask;
deba@2242: 
deba@2242:       static Word tempering(Word rnd) {
deba@2386:         rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
deba@2386:         rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
deba@2386:         rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
deba@2242:         rnd ^= (rnd >> 43);
deba@2242:         return rnd;
deba@2242:       }
deba@2242: 
deba@2242:     };
deba@2242: 
deba@2242:     template <typename _Word>
deba@2242:     class RandomCore {
deba@2242:     public:
deba@2242: 
deba@2242:       typedef _Word Word;
deba@2242: 
deba@2242:     private:
deba@2242: 
deba@2242:       static const int bits = RandomTraits<Word>::bits;
deba@2242: 
deba@2242:       static const int length = RandomTraits<Word>::length;
deba@2242:       static const int shift = RandomTraits<Word>::shift;
deba@2242: 
deba@2242:     public:
deba@2242: 
deba@2242:       void initState() {
deba@2242:         static const Word seedArray[4] = {
deba@2242:           0x12345u, 0x23456u, 0x34567u, 0x45678u
deba@2242:         };
deba@2242:     
deba@2242:         initState(seedArray, seedArray + 4);
deba@2242:       }
deba@2242: 
deba@2242:       void initState(Word seed) {
deba@2242: 
deba@2242:         static const Word mul = RandomTraits<Word>::mul;
deba@2242: 
deba@2242:         current = state; 
deba@2242: 
deba@2242:         Word *curr = state + length - 1;
deba@2242:         curr[0] = seed; --curr;
deba@2242:         for (int i = 1; i < length; ++i) {
deba@2242:           curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
deba@2242:           --curr;
deba@2242:         }
deba@2242:       }
deba@2242: 
deba@2242:       template <typename Iterator>
deba@2242:       void initState(Iterator begin, Iterator end) {
deba@2242: 
deba@2242:         static const Word init = RandomTraits<Word>::arrayInit;
deba@2242:         static const Word mul1 = RandomTraits<Word>::arrayMul1;
deba@2242:         static const Word mul2 = RandomTraits<Word>::arrayMul2;
deba@2242: 
deba@2242: 
deba@2242:         Word *curr = state + length - 1; --curr;
deba@2242:         Iterator it = begin; int cnt = 0;
deba@2242:         int num;
deba@2242: 
deba@2242:         initState(init);
deba@2242: 
deba@2242:         num = length > end - begin ? length : end - begin;
deba@2242:         while (num--) {
deba@2242:           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
deba@2242:             + *it + cnt;
deba@2242:           ++it; ++cnt;
deba@2242:           if (it == end) {
deba@2242:             it = begin; cnt = 0;
deba@2242:           }
deba@2242:           if (curr == state) {
deba@2242:             curr = state + length - 1; curr[0] = state[0];
deba@2242:           }
deba@2242:           --curr;
deba@2242:         }
deba@2242: 
deba@2242:         num = length - 1; cnt = length - (curr - state) - 1;
deba@2242:         while (num--) {
deba@2242:           curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
deba@2242:             - cnt;
deba@2242:           --curr; ++cnt;
deba@2242:           if (curr == state) {
deba@2242:             curr = state + length - 1; curr[0] = state[0]; --curr;
deba@2242:             cnt = 1;
deba@2242:           }
deba@2242:         }
deba@2242:         
deba@2386:         state[length - 1] = Word(1) << (bits - 1);
deba@2242:       }
deba@2242:       
deba@2242:       void copyState(const RandomCore& other) {
deba@2242:         std::copy(other.state, other.state + length, state);
deba@2242:         current = state + (other.current - other.state);
deba@2242:       }
deba@2242: 
deba@2242:       Word operator()() {
deba@2242:         if (current == state) fillState();
deba@2242:         --current;
deba@2242:         Word rnd = *current;
deba@2242:         return RandomTraits<Word>::tempering(rnd);
deba@2242:       }
deba@2242: 
deba@2242:     private:
deba@2242: 
deba@2242:   
deba@2242:       void fillState() {
deba@2242:         static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
deba@2242:         static const Word loMask = RandomTraits<Word>::loMask;
deba@2242:         static const Word hiMask = RandomTraits<Word>::hiMask;
deba@2242: 
deba@2242:         current = state + length; 
deba@2242: 
deba@2242:         register Word *curr = state + length - 1;
deba@2242:         register long num;
deba@2242:       
deba@2242:         num = length - shift;
deba@2242:         while (num--) {
deba@2242:           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
deba@2242:             curr[- shift] ^ mask[curr[-1] & 1ul];
deba@2242:           --curr;
deba@2242:         }
deba@2242:         num = shift - 1;
deba@2242:         while (num--) {
deba@2242:           curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
deba@2242:             curr[length - shift] ^ mask[curr[-1] & 1ul];
deba@2242:           --curr;
deba@2242:         }
deba@2242:         curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
deba@2545:           curr[length - shift] ^ mask[int(curr[length - 1] & 1ul)];
deba@2242: 
deba@2242:       }
deba@2242: 
deba@2242:   
deba@2242:       Word *current;
deba@2242:       Word state[length];
deba@2242:       
deba@2242:     };
deba@2242: 
deba@2242: 
deba@2242:     template <typename Result, 
deba@2242:               int shift = (std::numeric_limits<Result>::digits + 1) / 2>
deba@2242:     struct Masker {
deba@2242:       static Result mask(const Result& result) {
deba@2242:         return Masker<Result, (shift + 1) / 2>::
deba@2386:           mask(static_cast<Result>(result | (result >> shift)));
deba@2242:       }
deba@2242:     };
deba@2242:     
deba@2242:     template <typename Result>
deba@2242:     struct Masker<Result, 1> {
deba@2242:       static Result mask(const Result& result) {
deba@2386:         return static_cast<Result>(result | (result >> 1));
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, typename Word, 
deba@2242:               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
deba@2242:               bool last = rest <= std::numeric_limits<Word>::digits>
deba@2242:     struct IntConversion {
deba@2242:       static const int bits = std::numeric_limits<Word>::digits;
deba@2242:     
deba@2242:       static Result convert(RandomCore<Word>& rnd) {
deba@2386:         return static_cast<Result>(rnd() >> (bits - rest)) << shift;
deba@2242:       }
deba@2242:       
deba@2242:     }; 
deba@2242: 
deba@2242:     template <typename Result, typename Word, int rest, int shift> 
deba@2242:     struct IntConversion<Result, Word, rest, shift, false> {
deba@2242:       static const int bits = std::numeric_limits<Word>::digits;
deba@2242: 
deba@2242:       static Result convert(RandomCore<Word>& rnd) {
deba@2386:         return (static_cast<Result>(rnd()) << shift) | 
deba@2242:           IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242: 
deba@2242:     template <typename Result, typename Word,
alpar@2387:               bool one_word = (std::numeric_limits<Word>::digits < 
alpar@2387: 			       std::numeric_limits<Result>::digits) >
deba@2242:     struct Mapping {
deba@2242:       static Result map(RandomCore<Word>& rnd, const Result& bound) {
deba@2386:         Word max = Word(bound - 1);
deba@2242:         Result mask = Masker<Result>::mask(bound - 1);
deba@2242:         Result num;
deba@2242:         do {
deba@2242:           num = IntConversion<Result, Word>::convert(rnd) & mask; 
deba@2242:         } while (num > max);
deba@2242:         return num;
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, typename Word>
deba@2242:     struct Mapping<Result, Word, false> {
deba@2242:       static Result map(RandomCore<Word>& rnd, const Result& bound) {
deba@2386:         Word max = Word(bound - 1);
deba@2242:         Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
deba@2242:           ::mask(max);
deba@2242:         Word num;
deba@2242:         do {
deba@2242:           num = rnd() & mask;
deba@2242:         } while (num > max);
deba@2242:         return num;
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, int exp, bool pos = (exp >= 0)>
deba@2242:     struct ShiftMultiplier {
deba@2242:       static const Result multiplier() {
deba@2242:         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
deba@2242:         res *= res;
deba@2386:         if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
deba@2242:         return res; 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, int exp>
deba@2242:     struct ShiftMultiplier<Result, exp, false> {
deba@2242:       static const Result multiplier() {
deba@2242:         Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
deba@2242:         res *= res;
deba@2386:         if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
deba@2242:         return res; 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result>
deba@2242:     struct ShiftMultiplier<Result, 0, true> {
deba@2242:       static const Result multiplier() {
deba@2386:         return static_cast<Result>(1.0); 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result>
deba@2242:     struct ShiftMultiplier<Result, -20, true> {
deba@2242:       static const Result multiplier() {
deba@2386:         return static_cast<Result>(1.0/1048576.0); 
deba@2242:       }
deba@2242:     };
deba@2242:     
deba@2242:     template <typename Result>
deba@2242:     struct ShiftMultiplier<Result, -32, true> {
deba@2242:       static const Result multiplier() {
deba@2386:         return static_cast<Result>(1.0/424967296.0); 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result>
deba@2242:     struct ShiftMultiplier<Result, -53, true> {
deba@2242:       static const Result multiplier() {
deba@2386:         return static_cast<Result>(1.0/9007199254740992.0); 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result>
deba@2242:     struct ShiftMultiplier<Result, -64, true> {
deba@2242:       static const Result multiplier() {
deba@2386:         return static_cast<Result>(1.0/18446744073709551616.0); 
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, int exp>
deba@2242:     struct Shifting {
deba@2242:       static Result shift(const Result& result) {
deba@2242:         return result * ShiftMultiplier<Result, exp>::multiplier();
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, typename Word,
deba@2242:               int rest = std::numeric_limits<Result>::digits, int shift = 0, 
deba@2242:               bool last = rest <= std::numeric_limits<Word>::digits>
deba@2242:     struct RealConversion{ 
deba@2242:       static const int bits = std::numeric_limits<Word>::digits;
deba@2242: 
deba@2242:       static Result convert(RandomCore<Word>& rnd) {
deba@2242:         return Shifting<Result, - shift - rest>::
deba@2386:           shift(static_cast<Result>(rnd() >> (bits - rest)));
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, typename Word, int rest, int shift>
deba@2242:     struct RealConversion<Result, Word, rest, shift, false> { 
deba@2242:       static const int bits = std::numeric_limits<Word>::digits;
deba@2242: 
deba@2242:       static Result convert(RandomCore<Word>& rnd) {
deba@2386:         return Shifting<Result, - shift - bits>::
deba@2386:           shift(static_cast<Result>(rnd())) +
deba@2386:           RealConversion<Result, Word, rest-bits, shift + bits>::
deba@2386:           convert(rnd);
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Result, typename Word>
deba@2242:     struct Initializer {
deba@2242: 
deba@2242:       template <typename Iterator>
deba@2242:       static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
deba@2242:         std::vector<Word> ws;
deba@2242:         for (Iterator it = begin; it != end; ++it) {
deba@2386:           ws.push_back(Word(*it));
deba@2242:         }
deba@2242:         rnd.initState(ws.begin(), ws.end());
deba@2242:       }
deba@2242: 
deba@2242:       static void init(RandomCore<Word>& rnd, Result seed) {
deba@2242:         rnd.initState(seed);
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2242:     template <typename Word>
deba@2242:     struct BoolConversion {
deba@2242:       static bool convert(RandomCore<Word>& rnd) {
deba@2242:         return (rnd() & 1) == 1;
deba@2242:       }
deba@2242:     };
deba@2242: 
deba@2372:     template <typename Word>
deba@2372:     struct BoolProducer {
deba@2372:       Word buffer;
deba@2372:       int num;
deba@2372:       
deba@2372:       BoolProducer() : num(0) {}
deba@2372: 
deba@2372:       bool convert(RandomCore<Word>& rnd) {
deba@2372:         if (num == 0) {
deba@2372:           buffer = rnd();
deba@2372:           num = RandomTraits<Word>::bits;
deba@2372:         }
deba@2372:         bool r = (buffer & 1);
deba@2372:         buffer >>= 1;
deba@2372:         --num;
deba@2372:         return r;
deba@2372:       }
deba@2372:     };
deba@2372: 
deba@2242:   }
deba@2229: 
deba@2229:   /// \ingroup misc
deba@2229:   ///
deba@2229:   /// \brief Mersenne Twister random number generator
deba@2229:   ///
deba@2229:   /// The Mersenne Twister is a twisted generalized feedback
deba@2242:   /// shift-register generator of Matsumoto and Nishimura. The period
deba@2242:   /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
deba@2242:   /// equi-distributed in 623 dimensions for 32-bit numbers. The time
deba@2242:   /// performance of this generator is comparable to the commonly used
deba@2242:   /// generators.
deba@2242:   ///
deba@2242:   /// This implementation is specialized for both 32-bit and 64-bit
deba@2242:   /// architectures. The generators differ sligthly in the
deba@2242:   /// initialization and generation phase so they produce two
deba@2242:   /// completly different sequences.
deba@2242:   ///
deba@2242:   /// The generator gives back random numbers of serveral types. To
deba@2242:   /// get a random number from a range of a floating point type you
deba@2245:   /// can use one form of the \c operator() or the \c real() member
deba@2245:   /// function. If you want to get random number from the {0, 1, ...,
deba@2245:   /// n-1} integer range use the \c operator[] or the \c integer()
deba@2245:   /// method. And to get random number from the whole range of an
deba@2245:   /// integer type you can use the argumentless \c integer() or \c
deba@2245:   /// uinteger() functions. After all you can get random bool with
deba@2245:   /// equal chance of true and false or given probability of true
deba@2245:   /// result with the \c boolean() member functions.
deba@2242:   ///
deba@2242:   ///\code
deba@2245:   /// // The commented code is identical to the other
deba@2245:   /// double a = rnd();                     // [0.0, 1.0)
deba@2245:   /// // double a = rnd.real();             // [0.0, 1.0)
deba@2245:   /// double b = rnd(100.0);                // [0.0, 100.0)
deba@2245:   /// // double b = rnd.real(100.0);        // [0.0, 100.0)
deba@2245:   /// double c = rnd(1.0, 2.0);             // [1.0, 2.0)
deba@2245:   /// // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
deba@2245:   /// int d = rnd[100000];                  // 0..99999
deba@2245:   /// // int d = rnd.integer(100000);       // 0..99999
deba@2245:   /// int e = rnd[6] + 1;                   // 1..6
deba@2245:   /// // int e = rnd.integer(1, 1 + 6);     // 1..6
deba@2242:   /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
deba@2242:   /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
deba@2242:   /// bool g = rnd.boolean();               // P(g = true) = 0.5
deba@2242:   /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
deba@2242:   ///\endcode
deba@2242:   ///
deba@2245:   /// The lemon provides a global instance of the random number
deba@2245:   /// generator which name is \ref lemon::rnd "rnd". Usually it is a
deba@2245:   /// good programming convenience to use this global generator to get
deba@2245:   /// random numbers.
deba@2229:   ///
deba@2229:   /// \author Balazs Dezso
deba@2229:   class Random {
deba@2242:   private:
deba@2229: 
deba@2245:     // architecture word
deba@2242:     typedef unsigned long Word;
deba@2242:     
deba@2242:     _random_bits::RandomCore<Word> core;
deba@2372:     _random_bits::BoolProducer<Word> bool_producer;
deba@2372:     
deba@2229: 
deba@2229:   public:
deba@2229: 
deba@2229:     /// \brief Constructor
deba@2229:     ///
deba@2242:     /// Constructor with constant seeding.
deba@2242:     Random() { core.initState(); }
deba@2229: 
deba@2229:     /// \brief Constructor
deba@2229:     ///
deba@2242:     /// Constructor with seed. The current number type will be converted
deba@2242:     /// to the architecture word type.
deba@2242:     template <typename Number>
deba@2242:     Random(Number seed) { 
deba@2242:       _random_bits::Initializer<Number, Word>::init(core, seed);
deba@2242:     }
deba@2242: 
deba@2242:     /// \brief Constructor
deba@2242:     ///
deba@2242:     /// Constructor with array seeding. The given range should contain
deba@2242:     /// any number type and the numbers will be converted to the
deba@2242:     /// architecture word type.
deba@2242:     template <typename Iterator>
deba@2242:     Random(Iterator begin, Iterator end) { 
deba@2242:       typedef typename std::iterator_traits<Iterator>::value_type Number;
deba@2242:       _random_bits::Initializer<Number, Word>::init(core, begin, end);
deba@2242:     }
deba@2229: 
deba@2229:     /// \brief Copy constructor
deba@2229:     ///
deba@2229:     /// Copy constructor. The generated sequence will be identical to
deba@2245:     /// the other sequence. It can be used to save the current state
deba@2245:     /// of the generator and later use it to generate the same
deba@2245:     /// sequence.
deba@2242:     Random(const Random& other) {
deba@2242:       core.copyState(other.core);
deba@2229:     }
deba@2229: 
deba@2229:     /// \brief Assign operator
deba@2229:     ///
deba@2229:     /// Assign operator. The generated sequence will be identical to
deba@2245:     /// the other sequence. It can be used to save the current state
deba@2245:     /// of the generator and later use it to generate the same
deba@2245:     /// sequence.
deba@2229:     Random& operator=(const Random& other) {
deba@2229:       if (&other != this) {
deba@2242:         core.copyState(other.core);
deba@2229:       }
deba@2229:       return *this;
deba@2229:     }
deba@2229: 
alpar@2257:     /// \brief Returns a random real number from the range [0, 1)
deba@2229:     ///
deba@2245:     /// It returns a random real number from the range [0, 1). The
deba@2245:     /// default Number type is double.
deba@2242:     template <typename Number>
deba@2245:     Number real() {
deba@2242:       return _random_bits::RealConversion<Number, Word>::convert(core);
deba@2229:     }
deba@2229: 
deba@2245:     double real() {
deba@2245:       return real<double>();
deba@2245:     }
deba@2245: 
alpar@2257:     /// \brief Returns a random real number the range [0, b)
deba@2245:     ///
deba@2245:     /// It returns a random real number from the range [0, b).
deba@2245:     template <typename Number>
deba@2245:     Number real(Number b) { 
deba@2245:       return real<Number>() * b; 
deba@2245:     }
deba@2245: 
alpar@2257:     /// \brief Returns a random real number from the range [a, b)
deba@2245:     ///
deba@2245:     /// It returns a random real number from the range [a, b).
deba@2245:     template <typename Number>
deba@2245:     Number real(Number a, Number b) { 
deba@2245:       return real<Number>() * (b - a) + a; 
deba@2245:     }
deba@2245: 
alpar@2257:     /// \brief Returns a random real number from the range [0, 1)
deba@2245:     ///
deba@2245:     /// It returns a random double from the range [0, 1).
deba@2242:     double operator()() {
deba@2245:       return real<double>();
deba@2242:     }
deba@2242: 
alpar@2257:     /// \brief Returns a random real number from the range [0, b)
deba@2229:     ///
deba@2242:     /// It returns a random real number from the range [0, b).
deba@2242:     template <typename Number>
deba@2242:     Number operator()(Number b) { 
deba@2245:       return real<Number>() * b; 
deba@2242:     }
deba@2242: 
alpar@2257:     /// \brief Returns a random real number from the range [a, b)
deba@2242:     ///
deba@2242:     /// It returns a random real number from the range [a, b).
deba@2242:     template <typename Number>
deba@2242:     Number operator()(Number a, Number b) { 
deba@2245:       return real<Number>() * (b - a) + a; 
deba@2242:     }
deba@2242: 
deba@2242:     /// \brief Returns a random integer from a range
deba@2242:     ///
deba@2245:     /// It returns a random integer from the range {0, 1, ..., b - 1}.
deba@2242:     template <typename Number>
deba@2245:     Number integer(Number b) {
deba@2245:       return _random_bits::Mapping<Number, Word>::map(core, b);
deba@2245:     }
deba@2245: 
deba@2245:     /// \brief Returns a random integer from a range
deba@2245:     ///
deba@2245:     /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
deba@2245:     template <typename Number>
deba@2245:     Number integer(Number a, Number b) {
deba@2245:       return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
deba@2245:     }
deba@2245: 
deba@2245:     /// \brief Returns a random integer from a range
deba@2245:     ///
deba@2245:     /// It returns a random integer from the range {0, 1, ..., b - 1}.
deba@2245:     template <typename Number>
deba@2245:     Number operator[](Number b) {
deba@2245:       return _random_bits::Mapping<Number, Word>::map(core, b);
deba@2242:     }
deba@2242: 
deba@2242:     /// \brief Returns a random non-negative integer
deba@2242:     ///
deba@2242:     /// It returns a random non-negative integer uniformly from the
deba@2242:     /// whole range of the current \c Number type.  The default result
deba@2242:     /// type of this function is unsigned int.
deba@2242:     template <typename Number>
deba@2242:     Number uinteger() {
deba@2242:       return _random_bits::IntConversion<Number, Word>::convert(core);
deba@2242:     }
deba@2242: 
deba@2242:     unsigned int uinteger() {
deba@2242:       return uinteger<unsigned int>();
deba@2242:     }
deba@2242: 
deba@2242:     /// \brief Returns a random integer
deba@2242:     ///
deba@2242:     /// It returns a random integer uniformly from the whole range of
deba@2242:     /// the current \c Number type. The default result type of this
deba@2242:     /// function is int.
deba@2242:     template <typename Number>
deba@2242:     Number integer() {
deba@2242:       static const int nb = std::numeric_limits<Number>::digits + 
deba@2242:         (std::numeric_limits<Number>::is_signed ? 1 : 0);
deba@2242:       return _random_bits::IntConversion<Number, Word, nb>::convert(core);
deba@2242:     }
deba@2242: 
deba@2242:     int integer() {
deba@2242:       return integer<int>();
deba@2229:     }
deba@2229:     
deba@2242:     /// \brief Returns a random bool
deba@2229:     ///
deba@2372:     /// It returns a random bool. The generator holds a buffer for
deba@2372:     /// random bits. Every time when it become empty the generator makes
deba@2372:     /// a new random word and fill the buffer up.
deba@2242:     bool boolean() {
deba@2372:       return bool_producer.convert(core);
deba@2229:     }
deba@2229: 
alpar@2356:     ///\name Nonuniform distributions
alpar@2356:     ///
alpar@2356:     
alpar@2356:     ///@{
alpar@2356:     
deba@2229:     /// \brief Returns a random bool
deba@2229:     ///
deba@2242:     /// It returns a random bool with given probability of true result
deba@2242:     bool boolean(double p) {
deba@2242:       return operator()() < p;
deba@2229:     }
alpar@2355: 
alpar@2355:     /// Standard Gauss distribution
alpar@2355: 
alpar@2355:     /// Standard Gauss distribution.
alpar@2356:     /// \note The Cartesian form of the Box-Muller
alpar@2356:     /// transformation is used to generate a random normal distribution.
alpar@2356:     /// \todo Consider using the "ziggurat" method instead.
alpar@2355:     double gauss() 
alpar@2355:     {
alpar@2355:       double V1,V2,S;
alpar@2355:       do {
alpar@2355: 	V1=2*real<double>()-1;
alpar@2355: 	V2=2*real<double>()-1;
alpar@2355: 	S=V1*V1+V2*V2;
alpar@2355:       } while(S>=1);
alpar@2355:       return std::sqrt(-2*std::log(S)/S)*V1;
alpar@2355:     }
alpar@2356:     /// Gauss distribution with given standard deviation and mean 0
alpar@2356: 
alpar@2356:     /// \sa gauss()
alpar@2356:     ///
alpar@2356:     double gauss(double std_dev) 
alpar@2355:     {
alpar@2356:       return gauss()*std_dev;
alpar@2355:     }
alpar@2356:     /// Gauss distribution with given mean and standard deviation
alpar@2356: 
alpar@2356:     /// \sa gauss()
alpar@2356:     ///
alpar@2356:     double gauss(double mean,double std_dev)
alpar@2355:     {
alpar@2356:       return gauss()*std_dev+mean;
alpar@2355:     }
alpar@2355: 
alpar@2356:     /// Exponential distribution with given mean
alpar@2356: 
alpar@2356:     /// This function generates an exponential distribution random number
alpar@2356:     /// with mean <tt>1/lambda</tt>.
alpar@2356:     ///
alpar@2356:     double exponential(double lambda=1.0)
alpar@2355:     {
alpar@2374:       return -std::log(real<double>())/lambda;
alpar@2355:     }
alpar@2356: 
alpar@2483:     double gamma(int k) 
alpar@2483:     {
alpar@2483:       double s = 0;
alpar@2483:       for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
alpar@2483:       return s;
alpar@2483:     }
alpar@2483:     
alpar@2483:     /// Gamma distribution with given shape and scale parameter
alpar@2483: 
alpar@2483:     /// This function generates a gamma distribution random number.
alpar@2483:     /// 
alpar@2483:     ///\param k shape parameter (<tt>k>0</tt>)
alpar@2483:     ///\param theta scale parameter
alpar@2483:     ///
alpar@2483:     double gamma(double k,double theta=1.0)
alpar@2483:     {
alpar@2483:       double xi,nu;
alpar@2483:       const double delta = k-std::floor(k);
alpar@2568:       const double v0=E/(E-delta);
alpar@2483:       do {
alpar@2483: 	double V0=1.0-real<double>();
alpar@2483: 	double V1=1.0-real<double>();
alpar@2483: 	double V2=1.0-real<double>();
alpar@2483: 	if(V2<=v0) 
alpar@2483: 	  {
alpar@2483: 	    xi=std::pow(V1,1.0/delta);
alpar@2483: 	    nu=V0*std::pow(xi,delta-1.0);
alpar@2483: 	  }
alpar@2483: 	else 
alpar@2483: 	  {
alpar@2483: 	    xi=1.0-std::log(V1);
alpar@2483: 	    nu=V0*std::exp(-xi);
alpar@2483: 	  }
alpar@2483:       } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
alpar@2483:       return theta*(xi-gamma(int(std::floor(k))));
alpar@2483:     }
alpar@2483:     
alpar@2483:       
alpar@2356:     ///@}
deba@2229:     
alpar@2374:     ///\name Two dimensional distributions
alpar@2374:     ///
alpar@2374: 
alpar@2374:     ///@{
alpar@2374:     
alpar@2374:     /// Uniform distribution on the full unit circle.
alpar@2380:     dim2::Point<double> disc() 
alpar@2374:     {
alpar@2374:       double V1,V2;
alpar@2374:       do {
alpar@2374: 	V1=2*real<double>()-1;
alpar@2374: 	V2=2*real<double>()-1;
alpar@2374: 	
alpar@2374:       } while(V1*V1+V2*V2>=1);
alpar@2374:       return dim2::Point<double>(V1,V2);
alpar@2374:     }
alpar@2374:     /// A kind of two dimensional Gauss distribution
alpar@2374: 
alpar@2374:     /// This function provides a turning symmetric two-dimensional distribution.
alpar@2374:     /// Both coordinates are of standard normal distribution, but they are not
alpar@2374:     /// independent.
alpar@2374:     ///
alpar@2374:     /// \note The coordinates are the two random variables provided by
alpar@2374:     /// the Box-Muller method.
alpar@2374:     dim2::Point<double> gauss2()
alpar@2374:     {
alpar@2374:       double V1,V2,S;
alpar@2374:       do {
alpar@2374: 	V1=2*real<double>()-1;
alpar@2374: 	V2=2*real<double>()-1;
alpar@2374: 	S=V1*V1+V2*V2;
alpar@2374:       } while(S>=1);
alpar@2374:       double W=std::sqrt(-2*std::log(S)/S);
alpar@2374:       return dim2::Point<double>(W*V1,W*V2);
alpar@2374:     }
alpar@2374:     /// A kind of two dimensional exponential distribution
alpar@2374: 
alpar@2374:     /// This function provides a turning symmetric two-dimensional distribution.
alpar@2374:     /// The x-coordinate is of conditionally exponential distribution
alpar@2374:     /// with the condition that x is positive and y=0. If x is negative and 
alpar@2374:     /// y=0 then, -x is of exponential distribution. The same is true for the
alpar@2374:     /// y-coordinate.
alpar@2374:     dim2::Point<double> exponential2() 
alpar@2374:     {
alpar@2374:       double V1,V2,S;
alpar@2374:       do {
alpar@2374: 	V1=2*real<double>()-1;
alpar@2374: 	V2=2*real<double>()-1;
alpar@2374: 	S=V1*V1+V2*V2;
alpar@2374:       } while(S>=1);
alpar@2374:       double W=-std::log(S)/S;
alpar@2374:       return dim2::Point<double>(W*V1,W*V2);
alpar@2374:     }
alpar@2374: 
alpar@2374:     ///@}    
deba@2229:   };
deba@2229: 
deba@2229: 
deba@2229:   extern Random rnd;
deba@2229: 
deba@2229: }
deba@2229: 
deba@2229: #endif