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 /* boost random/uniform_int_distribution.hpp header file
  *
  * Copyright Jens Maurer 2000-2001
  * Copyright Steven Watanabe 2011
  * Distributed under the Boost Software License, Version 1.0. (See
  * accompanying file LICENSE_1_0.txt or copy at
  * http://www.boost.org/LICENSE_1_0.txt)
  *
  * See http://www.boost.org for most recent version including documentation.
  *
  * $Id$
  *
  * Revision history
  *  2001-04-08  added min<max assertion (N. Becker)
  *  2001-02-18  moved to individual header files
  */
 
 #ifndef BOOST_RANDOM_UNIFORM_INT_DISTRIBUTION_HPP
 #define BOOST_RANDOM_UNIFORM_INT_DISTRIBUTION_HPP
 
 #include <iosfwd>
 #include <ios>
 #include <istream>
 #include <boost/config.hpp>
 #include <boost/limits.hpp>
 #include <boost/assert.hpp>
 #include <boost/random/detail/config.hpp>
 #include <boost/random/detail/operators.hpp>
 #include <boost/random/detail/uniform_int_float.hpp>
 #include <boost/random/detail/signed_unsigned_tools.hpp>
 #include <boost/random/traits.hpp>
 #include <boost/type_traits/integral_constant.hpp>
 #ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
 #include <boost/type_traits/conditional.hpp>
 #endif
 
 namespace boost {
 namespace random {
 namespace detail {
     
 
 #ifdef BOOST_MSVC
 #pragma warning(push)
 // disable division by zero warning, since we can't
 // actually divide by zero.
 #pragma warning(disable:4723)
 #endif
 
 template<class Engine, class T>
 T generate_uniform_int(
     Engine& eng, T min_value, T max_value,
     boost::true_type /** is_integral<Engine::result_type> */)
 {
     typedef T result_type;
     typedef typename boost::random::traits::make_unsigned_or_unbounded<T>::type range_type;
     typedef typename Engine::result_type base_result;
     // ranges are always unsigned or unbounded
     typedef typename boost::random::traits::make_unsigned_or_unbounded<base_result>::type base_unsigned;
     const range_type range = random::detail::subtract<result_type>()(max_value, min_value);
     const base_result bmin = (eng.min)();
     const base_unsigned brange =
       random::detail::subtract<base_result>()((eng.max)(), (eng.min)());
 
     if(range == 0) {
       return min_value;    
     } else if(brange == range) {
       // this will probably never happen in real life
       // basically nothing to do; just take care we don't overflow / underflow
       base_unsigned v = random::detail::subtract<base_result>()(eng(), bmin);
       return random::detail::add<base_unsigned, result_type>()(v, min_value);
     } else if(brange < range) {
       // use rejection method to handle things like 0..3 --> 0..4
       for(;;) {
         // concatenate several invocations of the base RNG
         // take extra care to avoid overflows
 
         //  limit == floor((range+1)/(brange+1))
         //  Therefore limit*(brange+1) <= range+1
         range_type limit;
         if(range == (std::numeric_limits<range_type>::max)()) {
           limit = range/(range_type(brange)+1);
           if(range % (range_type(brange)+1) == range_type(brange))
             ++limit;
         } else {
           limit = (range+1)/(range_type(brange)+1);
         }
 
         // We consider "result" as expressed to base (brange+1):
         // For every power of (brange+1), we determine a random factor
         range_type result = range_type(0);
         range_type mult = range_type(1);
 
         // loop invariants:
         //  result < mult
         //  mult <= range
         while(mult <= limit) {
           // Postcondition: result <= range, thus no overflow
           //
           // limit*(brange+1)<=range+1                   def. of limit       (1)
           // eng()-bmin<=brange                          eng() post.         (2)
           // and mult<=limit.                            loop condition      (3)
           // Therefore mult*(eng()-bmin+1)<=range+1      by (1),(2),(3)      (4)
           // Therefore mult*(eng()-bmin)+mult<=range+1   rearranging (4)     (5)
           // result<mult                                 loop invariant      (6)
           // Therefore result+mult*(eng()-bmin)<range+1  by (5), (6)         (7)
           //
           // Postcondition: result < mult*(brange+1)
           //
           // result<mult                                 loop invariant      (1)
           // eng()-bmin<=brange                          eng() post.         (2)
           // Therefore result+mult*(eng()-bmin) <
           //           mult+mult*(eng()-bmin)            by (1)              (3)
           // Therefore result+(eng()-bmin)*mult <
           //           mult+mult*brange                  by (2), (3)         (4)
           // Therefore result+(eng()-bmin)*mult <
           //           mult*(brange+1)                   by (4)
           result += static_cast<range_type>(static_cast<range_type>(random::detail::subtract<base_result>()(eng(), bmin)) * mult);
 
           // equivalent to (mult * (brange+1)) == range+1, but avoids overflow.
           if(mult * range_type(brange) == range - mult + 1) {
               // The destination range is an integer power of
               // the generator's range.
               return(result);
           }
 
           // Postcondition: mult <= range
           // 
           // limit*(brange+1)<=range+1                   def. of limit       (1)
           // mult<=limit                                 loop condition      (2)
           // Therefore mult*(brange+1)<=range+1          by (1), (2)         (3)
           // mult*(brange+1)!=range+1                    preceding if        (4)
           // Therefore mult*(brange+1)<range+1           by (3), (4)         (5)
           // 
           // Postcondition: result < mult
           //
           // See the second postcondition on the change to result. 
           mult *= range_type(brange)+range_type(1);
         }
         // loop postcondition: range/mult < brange+1
         //
         // mult > limit                                  loop condition      (1)
         // Suppose range/mult >= brange+1                Assumption          (2)
         // range >= mult*(brange+1)                      by (2)              (3)
         // range+1 > mult*(brange+1)                     by (3)              (4)
         // range+1 > (limit+1)*(brange+1)                by (1), (4)         (5)
         // (range+1)/(brange+1) > limit+1                by (5)              (6)
         // limit < floor((range+1)/(brange+1))           by (6)              (7)
         // limit==floor((range+1)/(brange+1))            def. of limit       (8)
         // not (2)                                       reductio            (9)
         //
         // loop postcondition: (range/mult)*mult+(mult-1) >= range
         //
         // (range/mult)*mult + range%mult == range       identity            (1)
         // range%mult < mult                             def. of %           (2)
         // (range/mult)*mult+mult > range                by (1), (2)         (3)
         // (range/mult)*mult+(mult-1) >= range           by (3)              (4)
         //
         // Note that the maximum value of result at this point is (mult-1),
         // so after this final step, we generate numbers that can be
         // at least as large as range.  We have to really careful to avoid
         // overflow in this final addition and in the rejection.  Anything
         // that overflows is larger than range and can thus be rejected.
 
         // range/mult < brange+1  -> no endless loop
         range_type result_increment =
             generate_uniform_int(
                 eng,
                 static_cast<range_type>(0),
                 static_cast<range_type>(range/mult),
                 boost::true_type());
         if(std::numeric_limits<range_type>::is_bounded && ((std::numeric_limits<range_type>::max)() / mult < result_increment)) {
           // The multiplcation would overflow.  Reject immediately.
           continue;
         }
         result_increment *= mult;
         // unsigned integers are guaranteed to wrap on overflow.
         result += result_increment;
         if(result < result_increment) {
           // The addition overflowed.  Reject.
           continue;
         }
         if(result > range) {
           // Too big.  Reject.
           continue;
         }
         return random::detail::add<range_type, result_type>()(result, min_value);
       }
     } else {                   // brange > range
 #ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
       typedef typename conditional<
          std::numeric_limits<range_type>::is_specialized && std::numeric_limits<base_unsigned>::is_specialized
          && (std::numeric_limits<range_type>::digits >= std::numeric_limits<base_unsigned>::digits),
          range_type, base_unsigned>::type mixed_range_type;
 #else
       typedef base_unsigned mixed_range_type;
 #endif
 
       mixed_range_type bucket_size;
       // it's safe to add 1 to range, as long as we cast it first,
       // because we know that it is less than brange.  However,
       // we do need to be careful not to cause overflow by adding 1
       // to brange.  We use mixed_range_type throughout for mixed
       // arithmetic between base_unsigned and range_type - in the case
       // that range_type has more bits than base_unsigned it is always
       // safe to use range_type for this albeit it may be more effient
       // to use base_unsigned.  The latter is a narrowing conversion though
       // which may be disallowed if range_type is a multiprecision type
       // and there are no explicit converison operators.
 
       if(brange == (std::numeric_limits<base_unsigned>::max)()) {
         bucket_size = static_cast<mixed_range_type>(brange) / (static_cast<mixed_range_type>(range)+1);
         if(static_cast<mixed_range_type>(brange) % (static_cast<mixed_range_type>(range)+1) == static_cast<mixed_range_type>(range)) {
           ++bucket_size;
         }
       } else {
         bucket_size = static_cast<mixed_range_type>(brange + 1) / (static_cast<mixed_range_type>(range)+1);
       }
       for(;;) {
         mixed_range_type result =
           random::detail::subtract<base_result>()(eng(), bmin);
         result /= bucket_size;
         // result and range are non-negative, and result is possibly larger
         // than range, so the cast is safe
         if(result <= static_cast<mixed_range_type>(range))
           return random::detail::add<mixed_range_type, result_type>()(result, min_value);
       }
     }
 }
 
 #ifdef BOOST_MSVC
 #pragma warning(pop)
 #endif
 
 template<class Engine, class T>
 inline T generate_uniform_int(
     Engine& eng, T min_value, T max_value,
     boost::false_type /** is_integral<Engine::result_type> */)
 {
     uniform_int_float<Engine> wrapper(eng);
     return generate_uniform_int(wrapper, min_value, max_value, boost::true_type());
 }
 
 template<class Engine, class T>
 inline T generate_uniform_int(Engine& eng, T min_value, T max_value)
 {
     typedef typename Engine::result_type base_result;
     return generate_uniform_int(eng, min_value, max_value,
         boost::random::traits::is_integral<base_result>());
 }
 
 }
 
 /**
  * The class template uniform_int_distribution models a \random_distribution.
  * On each invocation, it returns a random integer value uniformly
  * distributed in the set of integers {min, min+1, min+2, ..., max}.
  *
  * The template parameter IntType shall denote an integer-like value type.
  */
 template<class IntType = int>
 class uniform_int_distribution
 {
 public:
     typedef IntType input_type;
     typedef IntType result_type;
 
     class param_type
     {
     public:
 
         typedef uniform_int_distribution distribution_type;
 
         /**
          * Constructs the parameters of a uniform_int_distribution.
          *
          * Requires min <= max
          */
         explicit param_type(
             IntType min_arg = 0,
             IntType max_arg = (std::numeric_limits<IntType>::max)())
           : _min(min_arg), _max(max_arg)
         {
             BOOST_ASSERT(_min <= _max);
         }
 
         /** Returns the minimum value of the distribution. */
         IntType a() const { return _min; }
         /** Returns the maximum value of the distribution. */
         IntType b() const { return _max; }
 
         /** Writes the parameters to a @c std::ostream. */
         BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
         {
             os << parm._min << " " << parm._max;
             return os;
         }
 
         /** Reads the parameters from a @c std::istream. */
         BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
         {
             IntType min_in, max_in;
             if(is >> min_in >> std::ws >> max_in) {
                 if(min_in <= max_in) {
                     parm._min = min_in;
                     parm._max = max_in;
                 } else {
                     is.setstate(std::ios_base::failbit);
                 }
             }
             return is;
         }
 
         /** Returns true if the two sets of parameters are equal. */
         BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
         { return lhs._min == rhs._min && lhs._max == rhs._max; }
 
         /** Returns true if the two sets of parameters are different. */
         BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
 
     private:
 
         IntType _min;
         IntType _max;
     };
 
     /**
      * Constructs a uniform_int_distribution. @c min and @c max are
      * the parameters of the distribution.
      *
      * Requires: min <= max
      */
     explicit uniform_int_distribution(
         IntType min_arg = 0,
         IntType max_arg = (std::numeric_limits<IntType>::max)())
       : _min(min_arg), _max(max_arg)
     {
         BOOST_ASSERT(min_arg <= max_arg);
     }
     /** Constructs a uniform_int_distribution from its parameters. */
     explicit uniform_int_distribution(const param_type& parm)
       : _min(parm.a()), _max(parm.b()) {}
 
     /**  Returns the minimum value of the distribution */
     IntType min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; }
     /**  Returns the maximum value of the distribution */
     IntType max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; }
 
     /**  Returns the minimum value of the distribution */
     IntType a() const { return _min; }
     /**  Returns the maximum value of the distribution */
     IntType b() const { return _max; }
 
     /** Returns the parameters of the distribution. */
     param_type param() const { return param_type(_min, _max); }
     /** Sets the parameters of the distribution. */
     void param(const param_type& parm)
     {
         _min = parm.a();
         _max = parm.b();
     }
 
     /**
      * Effects: Subsequent uses of the distribution do not depend
      * on values produced by any engine prior to invoking reset.
      */
     void reset() { }
 
     /** Returns an integer uniformly distributed in the range [min, max]. */
     template<class Engine>
     result_type operator()(Engine& eng) const
     { return detail::generate_uniform_int(eng, _min, _max); }
 
     /**
      * Returns an integer uniformly distributed in the range
      * [param.a(), param.b()].
      */
     template<class Engine>
     result_type operator()(Engine& eng, const param_type& parm) const
     { return detail::generate_uniform_int(eng, parm.a(), parm.b()); }
 
     /** Writes the distribution to a @c std::ostream. */
     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_int_distribution, ud)
     {
         os << ud.param();
         return os;
     }
 
     /** Reads the distribution from a @c std::istream. */
     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_int_distribution, ud)
     {
         param_type parm;
         if(is >> parm) {
             ud.param(parm);
         }
         return is;
     }
 
     /**
      * Returns true if the two distributions will produce identical sequences
      * of values given equal generators.
      */
     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_int_distribution, lhs, rhs)
     { return lhs._min == rhs._min && lhs._max == rhs._max; }
     
     /**
      * Returns true if the two distributions may produce different sequences
      * of values given equal generators.
      */
     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_int_distribution)
 
 private:
     IntType _min;
     IntType _max;
 };
 
 } // namespace random
 } // namespace boost
 
 #endif // BOOST_RANDOM_UNIFORM_INT_HPP

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