Chris@16: ///////////////////////////////////////////////////////////////
Chris@16: //  Copyright Jens Maurer 2006-1011
Chris@16: //  Copyright Steven Watanabe 2011
Chris@16: //  Copyright 2012 John Maddock. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
Chris@16: 
Chris@16: #ifndef BOOST_MP_RANDOM_HPP
Chris@16: #define BOOST_MP_RANDOM_HPP
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: #pragma warning(push)
Chris@16: #pragma warning(disable:4127)
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/multiprecision/number.hpp>
Chris@16: 
Chris@16: namespace boost{ namespace random{ namespace detail{
Chris@16: //
Chris@16: // This is a horrible hack: this declaration has to appear before the definition of
Chris@16: // uniform_int_distribution, otherwise it won't be used...
Chris@16: // Need to find a better solution, like make Boost.Random safe to use with
Chris@16: // UDT's and depricate/remove this header altogether.
Chris@16: //
Chris@16: template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: boost::multiprecision::number<Backend, ExpressionTemplates> 
Chris@16:    generate_uniform_int(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value);
Chris@16: 
Chris@16: }}}
Chris@16: 
Chris@16: #include <boost/random.hpp>
Chris@16: #include <boost/mpl/eval_if.hpp>
Chris@16: 
Chris@16: namespace boost{
Chris@16: namespace random{
Chris@16: namespace detail{
Chris@16: 
Chris@16: template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct subtract<boost::multiprecision::number<Backend, ExpressionTemplates>, true> 
Chris@16: { 
Chris@16:   typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type;
Chris@16:   result_type operator()(result_type const& x, result_type const& y) { return x - y; }
Chris@16: };
Chris@16: 
Chris@16: }
Chris@16: 
Chris@16: template<class Engine, std::size_t w, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: class independent_bits_engine<Engine, w, boost::multiprecision::number<Backend, ExpressionTemplates> >
Chris@16: {
Chris@16: public:
Chris@16:     typedef Engine base_type;
Chris@16:     typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type;
Chris@16: 
Chris@16:     static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return 0; }
Chris@16:     // This is the only function we modify compared to the primary template:
Chris@16:     static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     {
Chris@16:        // This expression allows for the possibility that w == std::numeric_limits<result_type>::digits:
Chris@16:        return (((result_type(1) << (w - 1)) - 1) << 1) + 1; 
Chris@16:     }
Chris@16: 
Chris@16:     independent_bits_engine() { }
Chris@16: 
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(independent_bits_engine,
Chris@16:         result_type, seed_arg)
Chris@16:     {
Chris@16:         _base.seed(seed_arg);
Chris@16:     }
Chris@16: 
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(independent_bits_engine,
Chris@16:         SeedSeq, seq)
Chris@16:     { _base.seed(seq); }
Chris@16: 
Chris@16:     independent_bits_engine(const base_type& base_arg) : _base(base_arg) {}
Chris@16: 
Chris@16:     template<class It>
Chris@16:     independent_bits_engine(It& first, It last) : _base(first, last) { }
Chris@16: 
Chris@16:     void seed() { _base.seed(); }
Chris@16: 
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(independent_bits_engine,
Chris@16:         result_type, seed_arg)
Chris@16:     { _base.seed(seed_arg); }
Chris@16: 
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(independent_bits_engine,
Chris@16:         SeedSeq, seq)
Chris@16:     { _base.seed(seq); }
Chris@16: 
Chris@16:     template<class It> void seed(It& first, It last)
Chris@16:     { _base.seed(first, last); }
Chris@16: 
Chris@16:     result_type operator()()
Chris@16:     {
Chris@16:         // While it may seem wasteful to recalculate this
Chris@16:         // every time, both msvc and gcc can propagate
Chris@16:         // constants, resolving this at compile time.
Chris@16:         base_unsigned range =
Chris@16:             detail::subtract<base_result>()((_base.max)(), (_base.min)());
Chris@16:         std::size_t m =
Chris@16:             (range == (std::numeric_limits<base_unsigned>::max)()) ?
Chris@16:                 std::numeric_limits<base_unsigned>::digits :
Chris@16:                 detail::integer_log2(range + 1);
Chris@16:         std::size_t n = (w + m - 1) / m;
Chris@16:         std::size_t w0, n0;
Chris@16:         base_unsigned y0, y1;
Chris@16:         base_unsigned y0_mask, y1_mask;
Chris@16:         calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask);
Chris@16:         if(base_unsigned(range - y0 + 1) > y0 / n) {
Chris@16:             // increment n and try again.
Chris@16:             ++n;
Chris@16:             calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask);
Chris@16:         }
Chris@16: 
Chris@16:         BOOST_ASSERT(n0*w0 + (n - n0)*(w0 + 1) == w);
Chris@16: 
Chris@16:         result_type S = 0;
Chris@16:         for(std::size_t k = 0; k < n0; ++k) {
Chris@16:             base_unsigned u;
Chris@16:             do {
Chris@16:                 u = detail::subtract<base_result>()(_base(), (_base.min)());
Chris@16:             } while(u > base_unsigned(y0 - 1));
Chris@16:             S = (S << w0) + (u & y0_mask);
Chris@16:         }
Chris@16:         for(std::size_t k = 0; k < (n - n0); ++k) {
Chris@16:             base_unsigned u;
Chris@16:             do {
Chris@16:                 u = detail::subtract<base_result>()(_base(), (_base.min)());
Chris@16:             } while(u > base_unsigned(y1 - 1));
Chris@16:             S = (S << (w0 + 1)) + (u & y1_mask);
Chris@16:         }
Chris@16:         return S;
Chris@16:     }
Chris@16:   
Chris@16:     /** Fills a range with random values */
Chris@16:     template<class Iter>
Chris@16:     void generate(Iter first, Iter last)
Chris@16:     { detail::generate_from_int(*this, first, last); }
Chris@16: 
Chris@16:     /** Advances the state of the generator by @c z. */
Chris@16:     void discard(boost::uintmax_t z)
Chris@16:     {
Chris@16:         for(boost::uintmax_t i = 0; i < z; ++i) {
Chris@16:             (*this)();
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     const base_type& base() const { return _base; }
Chris@16: 
Chris@16:     /**
Chris@16:      * Writes the textual representation if the generator to a @c std::ostream.
Chris@16:      * The textual representation of the engine is the textual representation
Chris@16:      * of the base engine.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, independent_bits_engine, r)
Chris@16:     {
Chris@16:         os << r._base;
Chris@16:         return os;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Reads the state of an @c independent_bits_engine from a
Chris@16:      * @c std::istream.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, independent_bits_engine, r)
Chris@16:     {
Chris@16:         is >> r._base;
Chris@16:         return is;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns: true iff the two @c independent_bits_engines will
Chris@16:      * produce the same sequence of values.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(independent_bits_engine, x, y)
Chris@16:     { return x._base == y._base; }
Chris@16:     /**
Chris@16:      * Returns: true iff the two @c independent_bits_engines will
Chris@16:      * produce different sequences of values.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(independent_bits_engine)
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     /// \cond show_private
Chris@16:     typedef typename base_type::result_type base_result;
Chris@16:     typedef typename make_unsigned<base_result>::type base_unsigned;
Chris@16: 
Chris@16:     void calc_params(
Chris@16:         std::size_t n, base_unsigned range,
Chris@16:         std::size_t& w0, std::size_t& n0,
Chris@16:         base_unsigned& y0, base_unsigned& y1,
Chris@16:         base_unsigned& y0_mask, base_unsigned& y1_mask)
Chris@16:     {
Chris@16:         BOOST_ASSERT(w >= n);
Chris@16:         w0 = w/n;
Chris@16:         n0 = n - w % n;
Chris@16:         y0_mask = (base_unsigned(2) << (w0 - 1)) - 1;
Chris@16:         y1_mask = (y0_mask << 1) | 1;
Chris@16:         y0 = (range + 1) & ~y0_mask;
Chris@16:         y1 = (range + 1) & ~y1_mask;
Chris@16:         BOOST_ASSERT(y0 != 0 || base_unsigned(range + 1) == 0);
Chris@16:     }
Chris@16:     /// \endcond
Chris@16: 
Chris@16:     Engine _base;
Chris@16: };
Chris@16: 
Chris@16: template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: class uniform_smallint<boost::multiprecision::number<Backend, ExpressionTemplates> >
Chris@16: {
Chris@16: public:
Chris@16:     typedef boost::multiprecision::number<Backend, ExpressionTemplates> input_type;
Chris@16:     typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type;
Chris@16: 
Chris@16:     class param_type
Chris@16:     {
Chris@16:     public:
Chris@16: 
Chris@16:         typedef uniform_smallint distribution_type;
Chris@16: 
Chris@16:         /** constructs the parameters of a @c uniform_smallint distribution. */
Chris@16:         param_type(result_type const& min_arg = 0, result_type const& max_arg = 9)
Chris@16:           : _min(min_arg), _max(max_arg)
Chris@16:         {
Chris@16:             BOOST_ASSERT(_min <= _max);
Chris@16:         }
Chris@16: 
Chris@16:         /** Returns the minimum value. */
Chris@16:         result_type a() const { return _min; }
Chris@16:         /** Returns the maximum value. */
Chris@16:         result_type b() const { return _max; }
Chris@16:         
Chris@16: 
Chris@16:         /** Writes the parameters to a @c std::ostream. */
Chris@16:         BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
Chris@16:         {
Chris@16:             os << parm._min << " " << parm._max;
Chris@16:             return os;
Chris@16:         }
Chris@16:     
Chris@16:         /** Reads the parameters from a @c std::istream. */
Chris@16:         BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
Chris@16:         {
Chris@16:             is >> parm._min >> std::ws >> parm._max;
Chris@16:             return is;
Chris@16:         }
Chris@16: 
Chris@16:         /** Returns true if the two sets of parameters are equal. */
Chris@16:         BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
Chris@16:         { return lhs._min == rhs._min && lhs._max == rhs._max; }
Chris@16: 
Chris@16:         /** Returns true if the two sets of parameters are different. */
Chris@16:         BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
Chris@16: 
Chris@16:     private:
Chris@16:         result_type _min;
Chris@16:         result_type _max;
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c uniform_smallint. @c min and @c max are the
Chris@16:      * lower and upper bounds of the output range, respectively.
Chris@16:      */
Chris@16:     explicit uniform_smallint(result_type const& min_arg = 0, result_type const& max_arg = 9)
Chris@16:       : _min(min_arg), _max(max_arg) {}
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c uniform_smallint from its parameters.
Chris@16:      */
Chris@16:     explicit uniform_smallint(const param_type& parm)
Chris@16:       : _min(parm.a()), _max(parm.b()) {}
Chris@16: 
Chris@16:     /** Returns the minimum value of the distribution. */
Chris@16:     result_type a() const { return _min; }
Chris@16:     /** Returns the maximum value of the distribution. */
Chris@16:     result_type b() const { return _max; }
Chris@16:     /** Returns the minimum value of the distribution. */
Chris@16:     result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; }
Chris@16:     /** Returns the maximum value of the distribution. */
Chris@16:     result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; }
Chris@16: 
Chris@16:     /** Returns the parameters of the distribution. */
Chris@16:     param_type param() const { return param_type(_min, _max); }
Chris@16:     /** Sets the parameters of the distribution. */
Chris@16:     void param(const param_type& parm)
Chris@16:     {
Chris@16:         _min = parm.a();
Chris@16:         _max = parm.b();
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Effects: Subsequent uses of the distribution do not depend
Chris@16:      * on values produced by any engine prior to invoking reset.
Chris@16:      */
Chris@16:     void reset() { }
Chris@16: 
Chris@16:     /** Returns a value uniformly distributed in the range [min(), max()]. */
Chris@16:     template<class Engine>
Chris@16:     result_type operator()(Engine& eng) const
Chris@16:     {
Chris@16:         typedef typename Engine::result_type base_result;
Chris@16:         return generate(eng, boost::is_integral<base_result>());
Chris@16:     }
Chris@16: 
Chris@16:     /** Returns a value uniformly distributed in the range [param.a(), param.b()]. */
Chris@16:     template<class Engine>
Chris@16:     result_type operator()(Engine& eng, const param_type& parm) const
Chris@16:     { return uniform_smallint(parm)(eng); }
Chris@16: 
Chris@16:     /** Writes the distribution to a @c std::ostream. */
Chris@16:     BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_smallint, ud)
Chris@16:     {
Chris@16:         os << ud._min << " " << ud._max;
Chris@16:         return os;
Chris@16:     }
Chris@16:     
Chris@16:     /** Reads the distribution from a @c std::istream. */
Chris@16:     BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_smallint, ud)
Chris@16:     {
Chris@16:         is >> ud._min >> std::ws >> ud._max;
Chris@16:         return is;
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two distributions will produce identical
Chris@16:      * sequences of values given equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_smallint, lhs, rhs)
Chris@16:     { return lhs._min == rhs._min && lhs._max == rhs._max; }
Chris@16:     
Chris@16:     /**
Chris@16:      * Returns true if the two distributions may produce different
Chris@16:      * sequences of values given equal generators.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_smallint)
Chris@16: 
Chris@16: private:
Chris@16:     
Chris@16:     // \cond show_private
Chris@16:     template<class Engine>
Chris@16:     result_type generate(Engine& eng, boost::mpl::true_) const
Chris@16:     {
Chris@16:         // equivalent to (eng() - eng.min()) % (_max - _min + 1) + _min,
Chris@16:         // but guarantees no overflow.
Chris@16:         typedef typename Engine::result_type base_result;
Chris@16:         typedef typename boost::make_unsigned<base_result>::type base_unsigned;
Chris@16:         typedef result_type  range_type;
Chris@16:         range_type range = random::detail::subtract<result_type>()(_max, _min);
Chris@16:         base_unsigned base_range =
Chris@16:             random::detail::subtract<result_type>()((eng.max)(), (eng.min)());
Chris@16:         base_unsigned val =
Chris@16:             random::detail::subtract<base_result>()(eng(), (eng.min)());
Chris@16:         if(range >= base_range) {
Chris@16:             return boost::random::detail::add<range_type, result_type>()(
Chris@16:                 static_cast<range_type>(val), _min);
Chris@16:         } else {
Chris@16:             base_unsigned modulus = static_cast<base_unsigned>(range) + 1;
Chris@16:             return boost::random::detail::add<range_type, result_type>()(
Chris@16:                 static_cast<range_type>(val % modulus), _min);
Chris@16:         }
Chris@16:     }
Chris@16:     
Chris@16:     template<class Engine>
Chris@16:     result_type generate(Engine& eng, boost::mpl::false_) const
Chris@16:     {
Chris@16:         typedef typename Engine::result_type base_result;
Chris@16:         typedef result_type                  range_type;
Chris@16:         range_type range = random::detail::subtract<result_type>()(_max, _min);
Chris@16:         base_result val = boost::uniform_01<base_result>()(eng);
Chris@16:         // what is the worst that can possibly happen here?
Chris@16:         // base_result may not be able to represent all the values in [0, range]
Chris@16:         // exactly.  If this happens, it will cause round off error and we
Chris@16:         // won't be able to produce all the values in the range.  We don't
Chris@16:         // care about this because the user has already told us not to by
Chris@16:         // using uniform_smallint.  However, we do need to be careful
Chris@16:         // to clamp the result, or floating point rounding can produce
Chris@16:         // an out of range result.
Chris@16:         range_type offset = static_cast<range_type>(val * (range + 1));
Chris@16:         if(offset > range) return _max;
Chris@16:         return boost::random::detail::add<range_type, result_type>()(offset , _min);
Chris@16:     }
Chris@16:     // \endcond
Chris@16: 
Chris@16:     result_type _min;
Chris@16:     result_type _max;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: struct select_uniform_01<boost::multiprecision::number<Backend, ExpressionTemplates> >
Chris@16: {
Chris@16:   template<class RealType>
Chris@16:   struct apply
Chris@16:   {
Chris@16:     typedef new_uniform_01<boost::multiprecision::number<Backend, ExpressionTemplates> > type;
Chris@16:   };
Chris@16: };
Chris@16: 
Chris@16: template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: boost::multiprecision::number<Backend, ExpressionTemplates> 
Chris@16:    generate_uniform_int(
Chris@16:     Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value,
Chris@16:     boost::mpl::true_ /** is_integral<Engine::result_type> */)
Chris@16: {
Chris@16:     typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type;
Chris@16:     // Since we're using big-numbers, use the result type for all internal calculations:
Chris@16:     typedef result_type range_type;
Chris@16:     typedef result_type base_result;
Chris@16:     typedef result_type base_unsigned;
Chris@16:     const range_type range = random::detail::subtract<result_type>()(max_value, min_value);
Chris@16:     const base_result bmin = (eng.min)();
Chris@16:     const base_unsigned brange =
Chris@16:       random::detail::subtract<base_result>()((eng.max)(), (eng.min)());
Chris@16: 
Chris@16:     if(range == 0) {
Chris@16:       return min_value;    
Chris@16:     } else if(brange == range) {
Chris@16:       // this will probably never happen in real life
Chris@16:       // basically nothing to do; just take care we don't overflow / underflow
Chris@16:       base_unsigned v = random::detail::subtract<base_result>()(eng(), bmin);
Chris@16:       return random::detail::add<base_unsigned, result_type>()(v, min_value);
Chris@16:     } else if(brange < range) {
Chris@16:       // use rejection method to handle things like 0..3 --> 0..4
Chris@16:       for(;;) {
Chris@16:         // concatenate several invocations of the base RNG
Chris@16:         // take extra care to avoid overflows
Chris@16: 
Chris@16:         //  limit == floor((range+1)/(brange+1))
Chris@16:         //  Therefore limit*(brange+1) <= range+1
Chris@16:         range_type limit;
Chris@16:         if(std::numeric_limits<range_type>::is_bounded && (range == (std::numeric_limits<range_type>::max)())) {
Chris@16:           limit = range/(range_type(brange)+1);
Chris@16:           if(range % (range_type(brange)+1) == range_type(brange))
Chris@16:             ++limit;
Chris@16:         } else {
Chris@16:           limit = (range+1)/(range_type(brange)+1);
Chris@16:         }
Chris@16: 
Chris@16:         // We consider "result" as expressed to base (brange+1):
Chris@16:         // For every power of (brange+1), we determine a random factor
Chris@16:         range_type result = range_type(0);
Chris@16:         range_type mult = range_type(1);
Chris@16: 
Chris@16:         // loop invariants:
Chris@16:         //  result < mult
Chris@16:         //  mult <= range
Chris@16:         while(mult <= limit) {
Chris@16:           // Postcondition: result <= range, thus no overflow
Chris@16:           //
Chris@16:           // limit*(brange+1)<=range+1                   def. of limit       (1)
Chris@16:           // eng()-bmin<=brange                          eng() post.         (2)
Chris@16:           // and mult<=limit.                            loop condition      (3)
Chris@16:           // Therefore mult*(eng()-bmin+1)<=range+1      by (1),(2),(3)      (4)
Chris@16:           // Therefore mult*(eng()-bmin)+mult<=range+1   rearranging (4)     (5)
Chris@16:           // result<mult                                 loop invariant      (6)
Chris@16:           // Therefore result+mult*(eng()-bmin)<range+1  by (5), (6)         (7)
Chris@16:           //
Chris@16:           // Postcondition: result < mult*(brange+1)
Chris@16:           //
Chris@16:           // result<mult                                 loop invariant      (1)
Chris@16:           // eng()-bmin<=brange                          eng() post.         (2)
Chris@16:           // Therefore result+mult*(eng()-bmin) <
Chris@16:           //           mult+mult*(eng()-bmin)            by (1)              (3)
Chris@16:           // Therefore result+(eng()-bmin)*mult <
Chris@16:           //           mult+mult*brange                  by (2), (3)         (4)
Chris@16:           // Therefore result+(eng()-bmin)*mult <
Chris@16:           //           mult*(brange+1)                   by (4)
Chris@16:           result += static_cast<range_type>(random::detail::subtract<base_result>()(eng(), bmin) * mult);
Chris@16: 
Chris@16:           // equivalent to (mult * (brange+1)) == range+1, but avoids overflow.
Chris@16:           if(mult * range_type(brange) == range - mult + 1) {
Chris@16:               // The destination range is an integer power of
Chris@16:               // the generator's range.
Chris@16:               return(result);
Chris@16:           }
Chris@16: 
Chris@16:           // Postcondition: mult <= range
Chris@16:           // 
Chris@16:           // limit*(brange+1)<=range+1                   def. of limit       (1)
Chris@16:           // mult<=limit                                 loop condition      (2)
Chris@16:           // Therefore mult*(brange+1)<=range+1          by (1), (2)         (3)
Chris@16:           // mult*(brange+1)!=range+1                    preceding if        (4)
Chris@16:           // Therefore mult*(brange+1)<range+1           by (3), (4)         (5)
Chris@16:           // 
Chris@16:           // Postcondition: result < mult
Chris@16:           //
Chris@16:           // See the second postcondition on the change to result. 
Chris@16:           mult *= range_type(brange)+range_type(1);
Chris@16:         }
Chris@16:         // loop postcondition: range/mult < brange+1
Chris@16:         //
Chris@16:         // mult > limit                                  loop condition      (1)
Chris@16:         // Suppose range/mult >= brange+1                Assumption          (2)
Chris@16:         // range >= mult*(brange+1)                      by (2)              (3)
Chris@16:         // range+1 > mult*(brange+1)                     by (3)              (4)
Chris@16:         // range+1 > (limit+1)*(brange+1)                by (1), (4)         (5)
Chris@16:         // (range+1)/(brange+1) > limit+1                by (5)              (6)
Chris@16:         // limit < floor((range+1)/(brange+1))           by (6)              (7)
Chris@16:         // limit==floor((range+1)/(brange+1))            def. of limit       (8)
Chris@16:         // not (2)                                       reductio            (9)
Chris@16:         //
Chris@16:         // loop postcondition: (range/mult)*mult+(mult-1) >= range
Chris@16:         //
Chris@16:         // (range/mult)*mult + range%mult == range       identity            (1)
Chris@16:         // range%mult < mult                             def. of %           (2)
Chris@16:         // (range/mult)*mult+mult > range                by (1), (2)         (3)
Chris@16:         // (range/mult)*mult+(mult-1) >= range           by (3)              (4)
Chris@16:         //
Chris@16:         // Note that the maximum value of result at this point is (mult-1),
Chris@16:         // so after this final step, we generate numbers that can be
Chris@16:         // at least as large as range.  We have to really careful to avoid
Chris@16:         // overflow in this final addition and in the rejection.  Anything
Chris@16:         // that overflows is larger than range and can thus be rejected.
Chris@16: 
Chris@16:         // range/mult < brange+1  -> no endless loop
Chris@16:         range_type result_increment =
Chris@16:             generate_uniform_int(
Chris@16:                 eng,
Chris@16:                 static_cast<range_type>(0),
Chris@16:                 static_cast<range_type>(range/mult),
Chris@16:                 boost::mpl::true_());
Chris@16:         if(std::numeric_limits<range_type>::is_bounded && ((std::numeric_limits<range_type>::max)() / mult < result_increment)) {
Chris@16:           // The multiplication would overflow.  Reject immediately.
Chris@16:           continue;
Chris@16:         }
Chris@16:         result_increment *= mult;
Chris@16:         // unsigned integers are guaranteed to wrap on overflow.
Chris@16:         result += result_increment;
Chris@16:         if(result < result_increment) {
Chris@16:           // The addition overflowed.  Reject.
Chris@16:           continue;
Chris@16:         }
Chris@16:         if(result > range) {
Chris@16:           // Too big.  Reject.
Chris@16:           continue;
Chris@16:         }
Chris@16:         return random::detail::add<range_type, result_type>()(result, min_value);
Chris@16:       }
Chris@16:     } else {                   // brange > range
Chris@16:       range_type bucket_size;
Chris@16:       // it's safe to add 1 to range, as long as we cast it first,
Chris@16:       // because we know that it is less than brange.  However,
Chris@16:       // we do need to be careful not to cause overflow by adding 1
Chris@16:       // to brange.
Chris@16:       if(std::numeric_limits<base_unsigned>::is_bounded && (brange == (std::numeric_limits<base_unsigned>::max)())) {
Chris@16:         bucket_size = brange / (range+1);
Chris@16:         if(brange % (range+1) == range) {
Chris@16:           ++bucket_size;
Chris@16:         }
Chris@16:       } else {
Chris@16:         bucket_size = (brange+1) / (range+1);
Chris@16:       }
Chris@16:       for(;;) {
Chris@16:         range_type result =
Chris@16:           random::detail::subtract<base_result>()(eng(), bmin);
Chris@16:         result /= bucket_size;
Chris@16:         // result and range are non-negative, and result is possibly larger
Chris@16:         // than range, so the cast is safe
Chris@16:         if(result <= range)
Chris@16:           return result + min_value;
Chris@16:       }
Chris@16:     }
Chris@16: }
Chris@16: 
Chris@16: template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@16: inline boost::multiprecision::number<Backend, ExpressionTemplates> 
Chris@16:    generate_uniform_int(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value)
Chris@16: {
Chris@16:     typedef typename Engine::result_type base_result;
Chris@16:     typedef typename mpl::or_<boost::is_integral<base_result>, mpl::bool_<boost::multiprecision::number_category<Backend>::value == boost::multiprecision::number_kind_integer> >::type tag_type;
Chris@16:     return generate_uniform_int(eng, min_value, max_value,
Chris@16:         tag_type());
Chris@16: }
Chris@16: 
Chris@101: template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates>
Chris@101: inline boost::multiprecision::number<Backend, ExpressionTemplates> generate_uniform_real(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value)
Chris@101: {
Chris@101:    if(max_value / 2 - min_value / 2 > (std::numeric_limits<boost::multiprecision::number<Backend, ExpressionTemplates> >::max)() / 2)
Chris@101:       return 2 * generate_uniform_real(eng, boost::multiprecision::number<Backend, ExpressionTemplates>(min_value / 2), boost::multiprecision::number<Backend, ExpressionTemplates>(max_value / 2));
Chris@101:    typedef typename Engine::result_type base_result;
Chris@101:    return generate_uniform_real(eng, min_value, max_value,
Chris@101:       boost::is_integral<base_result>());
Chris@101: }
Chris@101: 
Chris@16: } // detail
Chris@16: 
Chris@16: 
Chris@16: }} // namespaces
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: #pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: #endif