lemon/random.h
changeset 2242 16523135943d
parent 2230 67af33b34394
child 2245 f09b1ea5c249
     1.1 --- a/lemon/random.h	Fri Oct 13 15:10:50 2006 +0000
     1.2 +++ b/lemon/random.h	Sat Oct 14 15:26:05 2006 +0000
     1.3 @@ -20,6 +20,8 @@
     1.4  #define LEMON_RANDOM_H
     1.5  
     1.6  #include <algorithm>
     1.7 +#include <iterator>
     1.8 +#include <vector>
     1.9  
    1.10  #include <ctime>
    1.11  #include <cmath>
    1.12 @@ -33,46 +35,460 @@
    1.13  
    1.14  namespace lemon {
    1.15  
    1.16 -#if WORD_BIT == 32
    1.17 +  namespace _random_bits {
    1.18 +    
    1.19 +    template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
    1.20 +    struct RandomTraits {};
    1.21 +
    1.22 +    template <typename _Word>
    1.23 +    struct RandomTraits<_Word, 32> {
    1.24 +
    1.25 +      typedef _Word Word;
    1.26 +      static const int bits = 32;
    1.27 +
    1.28 +      static const int length = 624;
    1.29 +      static const int shift = 397;
    1.30 +      
    1.31 +      static const Word mul = 0x6c078965u;
    1.32 +      static const Word arrayInit = 0x012BD6AAu;
    1.33 +      static const Word arrayMul1 = 0x0019660Du;
    1.34 +      static const Word arrayMul2 = 0x5D588B65u;
    1.35 +
    1.36 +      static const Word mask = 0x9908B0DFu;
    1.37 +      static const Word loMask = (1u << 31) - 1;
    1.38 +      static const Word hiMask = ~loMask;
    1.39 +
    1.40 +
    1.41 +      static Word tempering(Word rnd) {
    1.42 +        rnd ^= (rnd >> 11);
    1.43 +        rnd ^= (rnd << 7) & 0x9D2C5680u;
    1.44 +        rnd ^= (rnd << 15) & 0xEFC60000u;
    1.45 +        rnd ^= (rnd >> 18);
    1.46 +        return rnd;
    1.47 +      }
    1.48 +
    1.49 +    };
    1.50 +
    1.51 +    template <typename _Word>
    1.52 +    struct RandomTraits<_Word, 64> {
    1.53 +
    1.54 +      typedef _Word Word;
    1.55 +      static const int bits = 64;
    1.56 +
    1.57 +      static const int length = 312;
    1.58 +      static const int shift = 156;
    1.59 +
    1.60 +      static const Word mul = (Word)0x5851F42Du << 32 | (Word)0x4C957F2Du;
    1.61 +      static const Word arrayInit = (Word)0x00000000u << 32 |(Word)0x012BD6AAu;
    1.62 +      static const Word arrayMul1 = (Word)0x369DEA0Fu << 32 |(Word)0x31A53F85u;
    1.63 +      static const Word arrayMul2 = (Word)0x27BB2EE6u << 32 |(Word)0x87B0B0FDu;
    1.64 +
    1.65 +      static const Word mask = (Word)0xB5026F5Au << 32 | (Word)0xA96619E9u;
    1.66 +      static const Word loMask = ((Word)1u << 31) - 1;
    1.67 +      static const Word hiMask = ~loMask;
    1.68 +
    1.69 +      static Word tempering(Word rnd) {
    1.70 +        rnd ^= (rnd >> 29) & ((Word)0x55555555u << 32 | (Word)0x55555555u);
    1.71 +        rnd ^= (rnd << 17) & ((Word)0x71D67FFFu << 32 | (Word)0xEDA60000u);
    1.72 +        rnd ^= (rnd << 37) & ((Word)0xFFF7EEE0u << 32 | (Word)0x00000000u);
    1.73 +        rnd ^= (rnd >> 43);
    1.74 +        return rnd;
    1.75 +      }
    1.76 +
    1.77 +    };
    1.78 +
    1.79 +    template <typename _Word>
    1.80 +    class RandomCore {
    1.81 +    public:
    1.82 +
    1.83 +      typedef _Word Word;
    1.84 +
    1.85 +    private:
    1.86 +
    1.87 +      static const int bits = RandomTraits<Word>::bits;
    1.88 +
    1.89 +      static const int length = RandomTraits<Word>::length;
    1.90 +      static const int shift = RandomTraits<Word>::shift;
    1.91 +
    1.92 +    public:
    1.93 +
    1.94 +      void initState() {
    1.95 +        static const Word seedArray[4] = {
    1.96 +          0x12345u, 0x23456u, 0x34567u, 0x45678u
    1.97 +        };
    1.98 +    
    1.99 +        initState(seedArray, seedArray + 4);
   1.100 +      }
   1.101 +
   1.102 +      void initState(Word seed) {
   1.103 +
   1.104 +        static const Word mul = RandomTraits<Word>::mul;
   1.105 +
   1.106 +        current = state; 
   1.107 +
   1.108 +        Word *curr = state + length - 1;
   1.109 +        curr[0] = seed; --curr;
   1.110 +        for (int i = 1; i < length; ++i) {
   1.111 +          curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
   1.112 +          --curr;
   1.113 +        }
   1.114 +      }
   1.115 +
   1.116 +      template <typename Iterator>
   1.117 +      void initState(Iterator begin, Iterator end) {
   1.118 +
   1.119 +        static const Word init = RandomTraits<Word>::arrayInit;
   1.120 +        static const Word mul1 = RandomTraits<Word>::arrayMul1;
   1.121 +        static const Word mul2 = RandomTraits<Word>::arrayMul2;
   1.122 +
   1.123 +
   1.124 +        Word *curr = state + length - 1; --curr;
   1.125 +        Iterator it = begin; int cnt = 0;
   1.126 +        int num;
   1.127 +
   1.128 +        initState(init);
   1.129 +
   1.130 +        num = length > end - begin ? length : end - begin;
   1.131 +        while (num--) {
   1.132 +          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1)) 
   1.133 +            + *it + cnt;
   1.134 +          ++it; ++cnt;
   1.135 +          if (it == end) {
   1.136 +            it = begin; cnt = 0;
   1.137 +          }
   1.138 +          if (curr == state) {
   1.139 +            curr = state + length - 1; curr[0] = state[0];
   1.140 +          }
   1.141 +          --curr;
   1.142 +        }
   1.143 +
   1.144 +        num = length - 1; cnt = length - (curr - state) - 1;
   1.145 +        while (num--) {
   1.146 +          curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
   1.147 +            - cnt;
   1.148 +          --curr; ++cnt;
   1.149 +          if (curr == state) {
   1.150 +            curr = state + length - 1; curr[0] = state[0]; --curr;
   1.151 +            cnt = 1;
   1.152 +          }
   1.153 +        }
   1.154 +        
   1.155 +        state[length - 1] = (Word)1 << (bits - 1);
   1.156 +      }
   1.157 +      
   1.158 +      void copyState(const RandomCore& other) {
   1.159 +        std::copy(other.state, other.state + length, state);
   1.160 +        current = state + (other.current - other.state);
   1.161 +      }
   1.162 +
   1.163 +      Word operator()() {
   1.164 +        if (current == state) fillState();
   1.165 +        --current;
   1.166 +        Word rnd = *current;
   1.167 +        return RandomTraits<Word>::tempering(rnd);
   1.168 +      }
   1.169 +
   1.170 +    private:
   1.171 +
   1.172 +  
   1.173 +      void fillState() {
   1.174 +        static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
   1.175 +        static const Word loMask = RandomTraits<Word>::loMask;
   1.176 +        static const Word hiMask = RandomTraits<Word>::hiMask;
   1.177 +
   1.178 +        current = state + length; 
   1.179 +
   1.180 +        register Word *curr = state + length - 1;
   1.181 +        register long num;
   1.182 +      
   1.183 +        num = length - shift;
   1.184 +        while (num--) {
   1.185 +          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.186 +            curr[- shift] ^ mask[curr[-1] & 1ul];
   1.187 +          --curr;
   1.188 +        }
   1.189 +        num = shift - 1;
   1.190 +        while (num--) {
   1.191 +          curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.192 +            curr[length - shift] ^ mask[curr[-1] & 1ul];
   1.193 +          --curr;
   1.194 +        }
   1.195 +        curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   1.196 +          curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   1.197 +
   1.198 +      }
   1.199 +
   1.200 +  
   1.201 +      Word *current;
   1.202 +      Word state[length];
   1.203 +      
   1.204 +    };
   1.205 +
   1.206 +
   1.207 +    template <typename Result, 
   1.208 +              int shift = (std::numeric_limits<Result>::digits + 1) / 2>
   1.209 +    struct Masker {
   1.210 +      static Result mask(const Result& result) {
   1.211 +        return Masker<Result, (shift + 1) / 2>::
   1.212 +          mask((Result)(result | (result >> shift)));
   1.213 +      }
   1.214 +    };
   1.215 +    
   1.216 +    template <typename Result>
   1.217 +    struct Masker<Result, 1> {
   1.218 +      static Result mask(const Result& result) {
   1.219 +        return (Result)(result | (result >> 1));
   1.220 +      }
   1.221 +    };
   1.222 +
   1.223 +    template <typename Result, typename Word, 
   1.224 +              int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   1.225 +              bool last = rest <= std::numeric_limits<Word>::digits>
   1.226 +    struct IntConversion {
   1.227 +      static const int bits = std::numeric_limits<Word>::digits;
   1.228 +    
   1.229 +      static Result convert(RandomCore<Word>& rnd) {
   1.230 +        return (Result)(rnd() >> (bits - rest)) << shift;
   1.231 +      }
   1.232 +      
   1.233 +    }; 
   1.234 +
   1.235 +    template <typename Result, typename Word, int rest, int shift> 
   1.236 +    struct IntConversion<Result, Word, rest, shift, false> {
   1.237 +      static const int bits = std::numeric_limits<Word>::digits;
   1.238 +
   1.239 +      static Result convert(RandomCore<Word>& rnd) {
   1.240 +        return ((Result)rnd() << shift) | 
   1.241 +          IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
   1.242 +      }
   1.243 +    };
   1.244 +
   1.245 +
   1.246 +    template <typename Result, typename Word,
   1.247 +              bool one_word = std::numeric_limits<Word>::digits < 
   1.248 +                              std::numeric_limits<Result>::digits>
   1.249 +    struct Mapping {
   1.250 +      static Result map(RandomCore<Word>& rnd, const Result& bound) {
   1.251 +        Word max = (Word)(bound - 1);
   1.252 +        Result mask = Masker<Result>::mask(bound - 1);
   1.253 +        Result num;
   1.254 +        do {
   1.255 +          num = IntConversion<Result, Word>::convert(rnd) & mask; 
   1.256 +        } while (num > max);
   1.257 +        return num;
   1.258 +      }
   1.259 +    };
   1.260 +
   1.261 +    template <typename Result, typename Word>
   1.262 +    struct Mapping<Result, Word, false> {
   1.263 +      static Result map(RandomCore<Word>& rnd, const Result& bound) {
   1.264 +        Word max = (Word)(bound - 1);
   1.265 +        Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
   1.266 +          ::mask(max);
   1.267 +        Word num;
   1.268 +        do {
   1.269 +          num = rnd() & mask;
   1.270 +        } while (num > max);
   1.271 +        return num;
   1.272 +      }
   1.273 +    };
   1.274 +
   1.275 +    template <typename Result, int exp, bool pos = (exp >= 0)>
   1.276 +    struct ShiftMultiplier {
   1.277 +      static const Result multiplier() {
   1.278 +        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   1.279 +        res *= res;
   1.280 +        if ((exp & 1) == 1) res *= (Result)2.0;
   1.281 +        return res; 
   1.282 +      }
   1.283 +    };
   1.284 +
   1.285 +    template <typename Result, int exp>
   1.286 +    struct ShiftMultiplier<Result, exp, false> {
   1.287 +      static const Result multiplier() {
   1.288 +        Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
   1.289 +        res *= res;
   1.290 +        if ((exp & 1) == 1) res *= (Result)0.5;
   1.291 +        return res; 
   1.292 +      }
   1.293 +    };
   1.294 +
   1.295 +    template <typename Result>
   1.296 +    struct ShiftMultiplier<Result, 0, true> {
   1.297 +      static const Result multiplier() {
   1.298 +        return (Result)1.0; 
   1.299 +      }
   1.300 +    };
   1.301 +
   1.302 +    template <typename Result>
   1.303 +    struct ShiftMultiplier<Result, -20, true> {
   1.304 +      static const Result multiplier() {
   1.305 +        return (Result)(1.0/1048576.0); 
   1.306 +      }
   1.307 +    };
   1.308 +    
   1.309 +    template <typename Result>
   1.310 +    struct ShiftMultiplier<Result, -32, true> {
   1.311 +      static const Result multiplier() {
   1.312 +        return (Result)(1.0/424967296.0); 
   1.313 +      }
   1.314 +    };
   1.315 +
   1.316 +    template <typename Result>
   1.317 +    struct ShiftMultiplier<Result, -53, true> {
   1.318 +      static const Result multiplier() {
   1.319 +        return (Result)(1.0/9007199254740992.0); 
   1.320 +      }
   1.321 +    };
   1.322 +
   1.323 +    template <typename Result>
   1.324 +    struct ShiftMultiplier<Result, -64, true> {
   1.325 +      static const Result multiplier() {
   1.326 +        return (Result)(1.0/18446744073709551616.0); 
   1.327 +      }
   1.328 +    };
   1.329 +
   1.330 +    template <typename Result, int exp>
   1.331 +    struct Shifting {
   1.332 +      static Result shift(const Result& result) {
   1.333 +        return result * ShiftMultiplier<Result, exp>::multiplier();
   1.334 +      }
   1.335 +    };
   1.336 +
   1.337 +    template <typename Result, typename Word,
   1.338 +              int rest = std::numeric_limits<Result>::digits, int shift = 0, 
   1.339 +              bool last = rest <= std::numeric_limits<Word>::digits>
   1.340 +    struct RealConversion{ 
   1.341 +      static const int bits = std::numeric_limits<Word>::digits;
   1.342 +
   1.343 +      static Result convert(RandomCore<Word>& rnd) {
   1.344 +        return Shifting<Result, - shift - rest>::
   1.345 +          shift((Result)(rnd() >> (bits - rest)));
   1.346 +      }
   1.347 +    };
   1.348 +
   1.349 +    template <typename Result, typename Word, int rest, int shift>
   1.350 +    struct RealConversion<Result, Word, rest, shift, false> { 
   1.351 +      static const int bits = std::numeric_limits<Word>::digits;
   1.352 +
   1.353 +      static Result convert(RandomCore<Word>& rnd) {
   1.354 +        return Shifting<Result, - shift - bits>::shift((Result)rnd()) +
   1.355 +          RealConversion<Result, Word, rest-bits, shift + bits>::convert(rnd);
   1.356 +      }
   1.357 +    };
   1.358 +
   1.359 +    template <typename Result, typename Word>
   1.360 +    struct Initializer {
   1.361 +
   1.362 +      template <typename Iterator>
   1.363 +      static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
   1.364 +        std::vector<Word> ws;
   1.365 +        for (Iterator it = begin; it != end; ++it) {
   1.366 +          ws.push_back((Word)*it);
   1.367 +        }
   1.368 +        rnd.initState(ws.begin(), ws.end());
   1.369 +      }
   1.370 +
   1.371 +      template <typename Iterator>
   1.372 +      static void init(RandomCore<Word>& rnd, Result seed) {
   1.373 +        rnd.initState(seed);
   1.374 +      }
   1.375 +    };
   1.376 +
   1.377 +    template <typename Word>
   1.378 +    struct BoolConversion {
   1.379 +      static bool convert(RandomCore<Word>& rnd) {
   1.380 +        return (rnd() & 1) == 1;
   1.381 +      }
   1.382 +    };
   1.383 +
   1.384 +  }
   1.385  
   1.386    /// \ingroup misc
   1.387    ///
   1.388    /// \brief Mersenne Twister random number generator
   1.389    ///
   1.390    /// The Mersenne Twister is a twisted generalized feedback
   1.391 -  /// shift-register generator of Matsumoto and Nishimura. The period of
   1.392 -  /// this generator is \f$ 2^{19937} - 1 \f$ and it is equi-distributed in
   1.393 -  /// 623 dimensions. The time performance of this generator is comparable
   1.394 -  /// to the commonly used generators.
   1.395 +  /// shift-register generator of Matsumoto and Nishimura. The period
   1.396 +  /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
   1.397 +  /// equi-distributed in 623 dimensions for 32-bit numbers. The time
   1.398 +  /// performance of this generator is comparable to the commonly used
   1.399 +  /// generators.
   1.400 +  ///
   1.401 +  /// This implementation is specialized for both 32-bit and 64-bit
   1.402 +  /// architectures. The generators differ sligthly in the
   1.403 +  /// initialization and generation phase so they produce two
   1.404 +  /// completly different sequences.
   1.405 +  ///
   1.406 +  /// The generator gives back random numbers of serveral types. To
   1.407 +  /// get a random number from a range of a floating point type you
   1.408 +  /// can use one form of the \c operator(). If you want to get random
   1.409 +  /// number from a the {0, 1, ..., n-1} integer range use the \c
   1.410 +  /// operator[]. And to get random number from the whole range of an
   1.411 +  /// integer type you can use the \c integer() or \c uinteger()
   1.412 +  /// functions. After all you can get random bool with equal chance
   1.413 +  /// or given probability with the \c boolean() member function.
   1.414 +  ///
   1.415 +  ///\code
   1.416 +  /// int a = rnd[100000];                  // 0..99999
   1.417 +  /// int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
   1.418 +  /// int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
   1.419 +  /// double d = rnd();                     // [0.0, 1.0)
   1.420 +  /// double e = rnd(100.0);                // [0.0, 100.0)
   1.421 +  /// double f = rnd(1.0, 2.0);             // [1.0, 2.0)
   1.422 +  /// bool g = rnd.boolean();               // P(g = true) = 0.5
   1.423 +  /// bool h = rnd.boolean(0.8);            // P(h = true) = 0.8
   1.424 +  ///\endcode
   1.425 +  ///
   1.426 +  /// The lemon provides a global instance of the random number generator
   1.427 +  /// which name is \c rnd. Usually it is a good programming convenience
   1.428 +  /// to use this global generator to get random numbers.
   1.429    ///
   1.430    /// \author Balazs Dezso
   1.431    class Random {
   1.432 +  private:
   1.433  
   1.434 -    static const int length = 624;
   1.435 -    static const int shift = 397;
   1.436 +#if WORD_BIT == 32
   1.437 +    typedef unsigned int Word;
   1.438 +#elif WORD_BIT == 64
   1.439 +    typedef unsigned long Word;
   1.440 +#endif
   1.441 +    
   1.442 +    _random_bits::RandomCore<Word> core;
   1.443  
   1.444    public:
   1.445  
   1.446 -    static const unsigned long min = 0ul;
   1.447 -    static const unsigned long max = ~0ul;
   1.448 -  
   1.449      /// \brief Constructor
   1.450      ///
   1.451 -    /// Constructor with time dependent seeding.
   1.452 -    Random() { initState(std::time(0)); }
   1.453 +    /// Constructor with constant seeding.
   1.454 +    Random() { core.initState(); }
   1.455  
   1.456      /// \brief Constructor
   1.457      ///
   1.458 -    /// Constructor
   1.459 -    Random(unsigned long seed) { initState(seed); }
   1.460 +    /// Constructor with seed. The current number type will be converted
   1.461 +    /// to the architecture word type.
   1.462 +    template <typename Number>
   1.463 +    Random(Number seed) { 
   1.464 +      _random_bits::Initializer<Number, Word>::init(core, seed);
   1.465 +    }
   1.466 +
   1.467 +    /// \brief Constructor
   1.468 +    ///
   1.469 +    /// Constructor with array seeding. The given range should contain
   1.470 +    /// any number type and the numbers will be converted to the
   1.471 +    /// architecture word type.
   1.472 +    template <typename Iterator>
   1.473 +    Random(Iterator begin, Iterator end) { 
   1.474 +      typedef typename std::iterator_traits<Iterator>::value_type Number;
   1.475 +      _random_bits::Initializer<Number, Word>::init(core, begin, end);
   1.476 +    }
   1.477  
   1.478      /// \brief Copy constructor
   1.479      ///
   1.480      /// Copy constructor. The generated sequence will be identical to
   1.481      /// the other sequence.
   1.482 -    Random(const Random& other) { 
   1.483 -      std::copy(other.state, other.state + length, state);
   1.484 -      current = state + (other.current - other.state);
   1.485 +    Random(const Random& other) {
   1.486 +      core.copyState(other.core);
   1.487      }
   1.488  
   1.489      /// \brief Assign operator
   1.490 @@ -81,429 +497,94 @@
   1.491      /// the other sequence.
   1.492      Random& operator=(const Random& other) {
   1.493        if (&other != this) {
   1.494 -        std::copy(other.state, other.state + length, state);
   1.495 -        current = state + (other.current - other.state);
   1.496 +        core.copyState(other.core);
   1.497        }
   1.498        return *this;
   1.499      }
   1.500  
   1.501 -    /// \brief Returns an unsigned random number
   1.502 +    /// \brief Returns a random real number
   1.503      ///
   1.504 -    /// It returns an unsigned integer random number from the range 
   1.505 -    /// \f$ \{0, 1, \dots, 2^{32} - 1\} \f$.
   1.506 -    unsigned long getUnsigned() {
   1.507 -      if (current == state) fillState();
   1.508 -      --current;
   1.509 -      unsigned long rnd = *current;
   1.510 -      rnd ^= (rnd >> 11);
   1.511 -      rnd ^= (rnd << 7) & 0x9D2C5680ul;
   1.512 -      rnd ^= (rnd << 15) & 0xEFC60000ul;
   1.513 -      rnd ^= (rnd >> 18);
   1.514 -      return rnd;
   1.515 +    /// It returns a random real number from the range [0, 1). The default
   1.516 +    /// result type of this function is double.
   1.517 +    template <typename Number>
   1.518 +    Number operator()() {
   1.519 +      return _random_bits::RealConversion<Number, Word>::convert(core);
   1.520      }
   1.521  
   1.522 -    /// \brief Returns a random number
   1.523 +    double operator()() {
   1.524 +      return operator()<double>();
   1.525 +    }
   1.526 +
   1.527 +    /// \brief Returns a random real number
   1.528      ///
   1.529 -    /// It returns an integer random number from the range 
   1.530 -    /// \f$ \{-2^{31}, \dots, 2^{31} - 1\} \f$.
   1.531 -    long getInt() {
   1.532 -      return (long)getUnsigned();
   1.533 +    /// It returns a random real number from the range [0, b).
   1.534 +    template <typename Number>
   1.535 +    Number operator()(Number b) { 
   1.536 +      return operator()<Number>() * b; 
   1.537 +    }
   1.538 +
   1.539 +    /// \brief Returns a random real number
   1.540 +    ///
   1.541 +    /// It returns a random real number from the range [a, b).
   1.542 +    template <typename Number>
   1.543 +    Number operator()(Number a, Number b) { 
   1.544 +      return operator()<Number>() * (b - a) + a; 
   1.545 +    }
   1.546 +
   1.547 +    /// \brief Returns a random integer from a range
   1.548 +    ///
   1.549 +    /// It returns a random integer from the range {0, 1, ..., bound - 1}.
   1.550 +    template <typename Number>
   1.551 +    Number operator[](const Number& bound) {
   1.552 +      return _random_bits::Mapping<Number, Word>::map(core, bound);
   1.553 +    }
   1.554 +
   1.555 +    /// \brief Returns a random non-negative integer
   1.556 +    ///
   1.557 +    /// It returns a random non-negative integer uniformly from the
   1.558 +    /// whole range of the current \c Number type.  The default result
   1.559 +    /// type of this function is unsigned int.
   1.560 +    template <typename Number>
   1.561 +    Number uinteger() {
   1.562 +      return _random_bits::IntConversion<Number, Word>::convert(core);
   1.563 +    }
   1.564 +
   1.565 +    unsigned int uinteger() {
   1.566 +      return uinteger<unsigned int>();
   1.567 +    }
   1.568 +
   1.569 +    /// \brief Returns a random integer
   1.570 +    ///
   1.571 +    /// It returns a random integer uniformly from the whole range of
   1.572 +    /// the current \c Number type. The default result type of this
   1.573 +    /// function is int.
   1.574 +    template <typename Number>
   1.575 +    Number integer() {
   1.576 +      static const int nb = std::numeric_limits<Number>::digits + 
   1.577 +        (std::numeric_limits<Number>::is_signed ? 1 : 0);
   1.578 +      return _random_bits::IntConversion<Number, Word, nb>::convert(core);
   1.579 +    }
   1.580 +
   1.581 +    int integer() {
   1.582 +      return integer<int>();
   1.583      }
   1.584      
   1.585 -    /// \brief Returns an unsigned integer random number
   1.586 +    /// \brief Returns a random bool
   1.587      ///
   1.588 -    /// It returns an unsigned integer random number from the range 
   1.589 -    /// \f$ \{0, 1, \dots, 2^{31} - 1\} \f$.
   1.590 -    long getNatural() {
   1.591 -      return (long)(getUnsigned() >> 1);
   1.592 +    /// It returns a random bool
   1.593 +    bool boolean() {
   1.594 +      return _random_bits::BoolConversion<Word>::convert(core);
   1.595      }
   1.596  
   1.597      /// \brief Returns a random bool
   1.598      ///
   1.599 -    /// It returns a random bool.
   1.600 -    bool getBool() {
   1.601 -      return (bool)(getUnsigned() & 1);
   1.602 +    /// It returns a random bool with given probability of true result
   1.603 +    bool boolean(double p) {
   1.604 +      return operator()() < p;
   1.605      }
   1.606 -
   1.607 -    /// \brief Returns a real random number
   1.608 -    ///
   1.609 -    /// It returns a real random number from the range 
   1.610 -    /// \f$ [0, 1) \f$. The double will have 32 significant bits.
   1.611 -    double getReal() {
   1.612 -      return std::ldexp((double)getUnsigned(), -32);
   1.613 -    }
   1.614 -
   1.615 -    /// \brief Returns a real random number
   1.616 -    ///
   1.617 -    /// It returns a real random number from the range 
   1.618 -    /// \f$ [0, 1) \f$. The double will have 53 significant bits,
   1.619 -    /// but it is slower than the \c getReal().
   1.620 -    double getPrecReal() {
   1.621 -      return std::ldexp((double)(getUnsigned() >> 5), -27) + 
   1.622 -        std::ldexp((double)(getUnsigned() >> 6), -53);
   1.623 -    }
   1.624 -
   1.625 -    /// \brief Returns an unsigned random number from a given range
   1.626 -    ///
   1.627 -    /// It returns an unsigned integer random number from the range 
   1.628 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.629 -    unsigned long getUnsigned(unsigned long n) {
   1.630 -      unsigned long mask = n - 1, rnd;
   1.631 -      mask |= mask >> 1;
   1.632 -      mask |= mask >> 2;
   1.633 -      mask |= mask >> 4;
   1.634 -      mask |= mask >> 8;
   1.635 -      mask |= mask >> 16;
   1.636 -      do rnd = getUnsigned() & mask; while (rnd >= n);
   1.637 -      return rnd;
   1.638 -    }
   1.639 -
   1.640 -    /// \brief Returns a random number from a given range
   1.641 -    ///
   1.642 -    /// It returns an unsigned integer random number from the range 
   1.643 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.644 -    long getInt(long n) {
   1.645 -      long mask = n - 1, rnd;
   1.646 -      mask |= mask >> 1;
   1.647 -      mask |= mask >> 2;
   1.648 -      mask |= mask >> 4;
   1.649 -      mask |= mask >> 8;
   1.650 -      mask |= mask >> 16;
   1.651 -      do rnd = getUnsigned() & mask; while (rnd >= n);
   1.652 -      return rnd;
   1.653 -    }
   1.654 -
   1.655 -  private:
   1.656 -
   1.657 -    void initState(unsigned long seed) {
   1.658 -      static const unsigned long mul = 0x6c078965ul;
   1.659 -
   1.660 -      current = state; 
   1.661 -
   1.662 -      unsigned long *curr = state + length - 1;
   1.663 -      curr[0] = seed; --curr;
   1.664 -      for (int i = 1; i < length; ++i) {
   1.665 -        curr[0] = (mul * ( curr[1] ^ (curr[1] >> 30) ) + i);
   1.666 -        --curr;
   1.667 -      }
   1.668 -    }
   1.669 -  
   1.670 -    void fillState() {
   1.671 -      static const unsigned long mask[2] = { 0x0ul, 0x9908B0DFul };
   1.672 -      static const unsigned long loMask = (1ul << 31) - 1;
   1.673 -      static const unsigned long hiMask = ~loMask;
   1.674 -
   1.675 -      current = state + length; 
   1.676 -
   1.677 -      register unsigned long *curr = state + length - 1;
   1.678 -      register long num;
   1.679 -      
   1.680 -      num = length - shift;
   1.681 -      while (num--) {
   1.682 -        curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.683 -          curr[- shift] ^ mask[curr[-1] & 1ul];
   1.684 -        --curr;
   1.685 -      }
   1.686 -      num = shift - 1;
   1.687 -      while (num--) {
   1.688 -        curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.689 -          curr[length - shift] ^ mask[curr[-1] & 1ul];
   1.690 -        --curr;
   1.691 -      }
   1.692 -      curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   1.693 -        curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   1.694 -
   1.695 -    }
   1.696 -  
   1.697 -    unsigned long *current;
   1.698 -    unsigned long state[length];
   1.699      
   1.700    };
   1.701  
   1.702 -#elif WORD_BIT == 64
   1.703 -
   1.704 -  /// \ingroup misc
   1.705 -  ///
   1.706 -  /// \brief Mersenne Twister random number generator
   1.707 -  ///
   1.708 -  /// The Mersenne Twister is a twisted generalized feedback
   1.709 -  /// shift-register generator of Matsumoto and Nishimura. The period of
   1.710 -  /// this generator is \f$ 2^{19937} - 1 \f$ and it is equi-distributed in
   1.711 -  /// 311 dimensions. The time performance of this generator is comparable
   1.712 -  /// to the commonly used generators.
   1.713 -  class Random {
   1.714 -
   1.715 -    static const int length = 312;
   1.716 -    static const int shift = 156;
   1.717 -
   1.718 -  public:
   1.719 -
   1.720 -    static const unsigned long min = 0ul;
   1.721 -    static const unsigned long max = ~0ul;
   1.722 -  
   1.723 -    /// \brief Constructor
   1.724 -    ///
   1.725 -    /// Constructor with time dependent seeding.
   1.726 -    Random() { initState(std::time(0)); }
   1.727 -
   1.728 -    /// \brief Constructor
   1.729 -    ///
   1.730 -    /// Constructor
   1.731 -    Random(unsigned long seed) { initState(seed); }
   1.732 -
   1.733 -    /// \brief Copy constructor
   1.734 -    ///
   1.735 -    /// Copy constructor. The generated sequence will be identical to
   1.736 -    /// the other sequence.
   1.737 -    Random(const Random& other) { 
   1.738 -      std::copy(other.state, other.state + length, state);
   1.739 -      current = state + (other.current - other.state);
   1.740 -    }
   1.741 -
   1.742 -    /// \brief Assign operator
   1.743 -    ///
   1.744 -    /// Assign operator. The generated sequence will be identical to
   1.745 -    /// the other sequence.
   1.746 -    Random& operator=(const Random& other) {
   1.747 -      if (&other != this) {
   1.748 -        std::copy(other.state, other.state + length, state);
   1.749 -        current = state + (other.current - other.state);
   1.750 -      }
   1.751 -      return *this;
   1.752 -    }
   1.753 -
   1.754 -    /// \brief Returns an unsigned random number
   1.755 -    ///
   1.756 -    /// It returns an unsigned integer random number from the range 
   1.757 -    /// \f$ \{0, 1, \dots, 2^{64} - 1\} \f$.
   1.758 -    unsigned long getUnsigned() {
   1.759 -      if (current == state) fillState();
   1.760 -      --current;
   1.761 -      unsigned long rnd = *current;
   1.762 -      rnd ^= (rnd >> 29) & 0x5555555555555555ul;
   1.763 -      rnd ^= (rnd << 17) & 0x71D67FFFEDA60000ul;
   1.764 -      rnd ^= (rnd << 37) & 0xFFF7EEE000000000ul;
   1.765 -      rnd ^= (rnd >> 43);
   1.766 -      return rnd;
   1.767 -    }
   1.768 -
   1.769 -    /// \brief Returns a random number
   1.770 -    ///
   1.771 -    /// It returns an integer random number from the range 
   1.772 -    /// \f$ \{-2^{63}, \dots, 2^{63} - 1\} \f$.
   1.773 -    long getInt() {
   1.774 -      return (long)getUnsigned();
   1.775 -    }
   1.776 -    
   1.777 -    /// \brief Returns an unsigned integer random number
   1.778 -    ///
   1.779 -    /// It returns an unsigned integer random number from the range 
   1.780 -    /// \f$ \{0, 1, \dots, 2^{63} - 1\} \f$.
   1.781 -    long getNatural() {
   1.782 -      return (long)(getUnsigned() >> 1);
   1.783 -    }
   1.784 -
   1.785 -    /// \brief Returns a random bool
   1.786 -    ///
   1.787 -    /// It returns a random bool.
   1.788 -    bool getBool() {
   1.789 -      return (bool)(getUnsigned() & 1);
   1.790 -    }
   1.791 -
   1.792 -    /// \brief Returns a real random number
   1.793 -    ///
   1.794 -    /// It returns a real random number from the range 
   1.795 -    /// \f$ [0, 1) \f$.
   1.796 -    double getReal() {
   1.797 -      return std::ldexp((double)(getUnsigned() >> 11), -53);
   1.798 -    }
   1.799 -
   1.800 -    /// \brief Returns a real random number
   1.801 -    ///
   1.802 -    /// It returns a real random number from the range 
   1.803 -    /// \f$ [0, 1) \f$. This function is identical to the \c getReal().
   1.804 -    double getPrecReal() {
   1.805 -      return getReal();
   1.806 -    }
   1.807 -
   1.808 -    /// \brief Returns an unsigned random number from a given range
   1.809 -    ///
   1.810 -    /// It returns an unsigned integer random number from the range 
   1.811 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.812 -    unsigned long getUnsigned(unsigned long n) {
   1.813 -      unsigned long mask = n - 1, rnd;
   1.814 -      mask |= mask >> 1;
   1.815 -      mask |= mask >> 2;
   1.816 -      mask |= mask >> 4;
   1.817 -      mask |= mask >> 8;
   1.818 -      mask |= mask >> 16;
   1.819 -      mask |= mask >> 32;
   1.820 -      do rnd = getUnsigned() & mask; while (rnd >= n);
   1.821 -      return rnd;
   1.822 -    }
   1.823 -
   1.824 -    /// \brief Returns a random number from a given range
   1.825 -    ///
   1.826 -    /// It returns an unsigned integer random number from the range 
   1.827 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.828 -    long getInt(long n) {
   1.829 -      long mask = n - 1, rnd;
   1.830 -      mask |= mask >> 1;
   1.831 -      mask |= mask >> 2;
   1.832 -      mask |= mask >> 4;
   1.833 -      mask |= mask >> 8;
   1.834 -      mask |= mask >> 16;
   1.835 -      mask |= mask >> 32;
   1.836 -      do rnd = getUnsigned() & mask; while (rnd >= n);
   1.837 -      return rnd;
   1.838 -    }
   1.839 -
   1.840 -  private:
   1.841 -
   1.842 -    void initState(unsigned long seed) {
   1.843 -
   1.844 -      static const unsigned long mul = 0x5851F42D4C957F2Dul;
   1.845 -
   1.846 -      current = state; 
   1.847 -
   1.848 -      unsigned long *curr = state + length - 1;
   1.849 -      curr[0] = seed; --curr;
   1.850 -      for (int i = 1; i < length; ++i) {
   1.851 -        curr[0] = (mul * ( curr[1] ^ (curr[1] >> 62) ) + i);
   1.852 -        --curr;
   1.853 -      }
   1.854 -    }
   1.855 -  
   1.856 -    void fillState() {
   1.857 -      static const unsigned long mask[2] = { 0x0ul, 0xB5026F5AA96619E9ul };
   1.858 -      static const unsigned long loMask = (1ul << 31) - 1;
   1.859 -      static const unsigned long hiMask = ~loMask;
   1.860 -
   1.861 -      current = state + length; 
   1.862 -
   1.863 -      register unsigned long *curr = state + length - 1;
   1.864 -      register int num;
   1.865 -      
   1.866 -      num = length - shift;
   1.867 -      while (num--) {
   1.868 -        curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.869 -          curr[- shift] ^ mask[curr[-1] & 1ul];
   1.870 -        --curr;
   1.871 -      }
   1.872 -      num = shift - 1;
   1.873 -      while (num--) {
   1.874 -        curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
   1.875 -          curr[length - shift] ^ mask[curr[-1] & 1ul];
   1.876 -        --curr;
   1.877 -      }
   1.878 -      curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
   1.879 -        curr[length - shift] ^ mask[curr[length - 1] & 1ul];
   1.880 -
   1.881 -    }
   1.882 -  
   1.883 -    unsigned long *current;
   1.884 -    unsigned long state[length];
   1.885 -    
   1.886 -  };
   1.887 -
   1.888 -#else
   1.889 -
   1.890 -  /// \ingroup misc
   1.891 -  ///
   1.892 -  /// \brief Mersenne Twister random number generator
   1.893 -  ///
   1.894 -  /// The Mersenne Twister is a twisted generalized feedback
   1.895 -  /// shift-register generator of Matsumoto and Nishimura. There is
   1.896 -  /// two different implementation in the Lemon library, one for
   1.897 -  /// 32-bit processors and one for 64-bit processors. The period of
   1.898 -  /// the generated sequence is \f$ 2^{19937} - 1 \f$, the generated
   1.899 -  /// sequence of 32-bit random numbers is equi-distributed in 623
   1.900 -  /// dimensions. The time performance of this generator is comparable
   1.901 -  /// to the commonly used generators.
   1.902 -  class Random {
   1.903 -  public:
   1.904 -
   1.905 -    static const unsigned long min = 0ul;
   1.906 -    static const unsigned long max = ~0ul;
   1.907 -  
   1.908 -    /// \brief Constructor
   1.909 -    ///
   1.910 -    /// Constructor with time dependent seeding.
   1.911 -    Random() {}
   1.912 -
   1.913 -    /// \brief Constructor
   1.914 -    ///
   1.915 -    /// Constructor
   1.916 -    Random(unsigned long seed) {}
   1.917 -
   1.918 -    /// \brief Copy constructor
   1.919 -    ///
   1.920 -    /// Copy constructor. The generated sequence will be identical to
   1.921 -    /// the other sequence.
   1.922 -    Random(const Random& other) {}
   1.923 -
   1.924 -    /// \brief Assign operator
   1.925 -    ///
   1.926 -    /// Assign operator. The generated sequence will be identical to
   1.927 -    /// the other sequence.
   1.928 -    Random& operator=(const Random& other) { return *this; }
   1.929 -
   1.930 -    /// \brief Returns an unsigned random number
   1.931 -    ///
   1.932 -    /// It returns an unsigned integer random number from the range 
   1.933 -    /// \f$ \{0, 1, \dots, 2^{64} - 1\} \f$ for 64-bit processors and from
   1.934 -    /// \f$ \{0, 1, \dots, 2^{32} - 1\} \f$ for 32-bit processors.
   1.935 -    unsigned long getUnsigned() { return 0ul; }
   1.936 -
   1.937 -    /// \brief Returns a random number
   1.938 -    ///
   1.939 -    /// It returns an integer random number from the range 
   1.940 -    /// \f$ \{-2^{63}, \dots, 2^{63} - 1\} \f$ for 64-bit processors and from
   1.941 -    /// \f$ \{-2^{31}, \dots, 2^{31} - 1\} \f$ for 32-bit processors.
   1.942 -    long getInt() { return 0l; }
   1.943 -    
   1.944 -    /// \brief Returns an unsigned integer random number
   1.945 -    ///
   1.946 -    /// It returns an unsigned integer random number from the range 
   1.947 -    /// \f$ \{0, 1, \dots, 2^{63} - 1\} \f$ for 64-bit processors and
   1.948 -    /// from \f$ \{0, 1, \dots, 2^{31} - 1\} \f$ for 32-bit processors.
   1.949 -    long getNatural() { return 0l; }
   1.950 -
   1.951 -    /// \brief Returns a random bool
   1.952 -    ///
   1.953 -    /// It returns a random bool.
   1.954 -    bool getBool() { return false; }
   1.955 -
   1.956 -    /// \brief Returns a real random number
   1.957 -    ///
   1.958 -    /// It returns a real random number from the range 
   1.959 -    /// \f$ [0, 1) \f$. For 32-bit processors the generated random
   1.960 -    /// number will just have 32 significant bits.
   1.961 -    double getReal() { return 0.0; }
   1.962 -
   1.963 -    /// \brief Returns a real random number
   1.964 -    ///
   1.965 -    /// It returns a real random number from the range 
   1.966 -    /// \f$ [0, 1) \f$. This function returns random numbers with 53
   1.967 -    /// significant bits for 32-bit processors. For 64-bit processors
   1.968 -    /// it is identical to the \c getReal().
   1.969 -    double getPrecReal() { return 0.0; }
   1.970 -
   1.971 -    /// \brief Returns an unsigned random number from a given range
   1.972 -    ///
   1.973 -    /// It returns an unsigned integer random number from the range 
   1.974 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.975 -    unsigned long getUnsigned(unsigned long n) { return 0; }
   1.976 -
   1.977 -    /// \brief Returns a random number from a given range
   1.978 -    ///
   1.979 -    /// It returns an unsigned integer random number from the range 
   1.980 -    /// \f$ \{0, 1, \dots, n - 1\} \f$.
   1.981 -    long getInt(long n) { return 0; }
   1.982 -
   1.983 -  };
   1.984 -
   1.985 -#endif
   1.986  
   1.987    /// \brief Global random number generator instance
   1.988    ///