Chris@16: /* boost random/uniform_smallint.hpp header file
Chris@16:  *
Chris@16:  * Copyright Jens Maurer 2000-2001
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  * See http://www.boost.org for most recent version including documentation.
Chris@16:  *
Chris@101:  * $Id$
Chris@16:  *
Chris@16:  * Revision history
Chris@16:  *  2001-04-08  added min<max assertion (N. Becker)
Chris@16:  *  2001-02-18  moved to individual header files
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_UNIFORM_SMALLINT_HPP
Chris@16: #define BOOST_RANDOM_UNIFORM_SMALLINT_HPP
Chris@16: 
Chris@16: #include <istream>
Chris@16: #include <iosfwd>
Chris@16: #include <boost/assert.hpp>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/limits.hpp>
Chris@16: #include <boost/type_traits/is_integral.hpp>
Chris@16: #include <boost/random/detail/config.hpp>
Chris@16: #include <boost/random/detail/operators.hpp>
Chris@16: #include <boost/random/detail/signed_unsigned_tools.hpp>
Chris@16: #include <boost/random/uniform_01.hpp>
Chris@16: #include <boost/detail/workaround.hpp>
Chris@101: #include <boost/mpl/bool.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace random {
Chris@16: 
Chris@16: // uniform integer distribution on a small range [min, max]
Chris@16: 
Chris@16: /**
Chris@16:  * The distribution function uniform_smallint models a \random_distribution.
Chris@16:  * On each invocation, it returns a random integer value uniformly distributed
Chris@16:  * in the set of integer numbers {min, min+1, min+2, ..., max}. It assumes
Chris@16:  * that the desired range (max-min+1) is small compared to the range of the
Chris@16:  * underlying source of random numbers and thus makes no attempt to limit
Chris@16:  * quantization errors.
Chris@16:  *
Chris@16:  * Let \f$r_{\mathtt{out}} = (\mbox{max}-\mbox{min}+1)\f$ the desired range of
Chris@16:  * integer numbers, and
Chris@16:  * let \f$r_{\mathtt{base}}\f$ be the range of the underlying source of random
Chris@16:  * numbers. Then, for the uniform distribution, the theoretical probability
Chris@16:  * for any number i in the range \f$r_{\mathtt{out}}\f$ will be
Chris@16:  * \f$\displaystyle p_{\mathtt{out}}(i) = \frac{1}{r_{\mathtt{out}}}\f$.
Chris@16:  * Likewise, assume a uniform distribution on \f$r_{\mathtt{base}}\f$ for
Chris@16:  * the underlying source of random numbers, i.e.
Chris@16:  * \f$\displaystyle p_{\mathtt{base}}(i) = \frac{1}{r_{\mathtt{base}}}\f$.
Chris@16:  * Let \f$p_{\mathtt{out\_s}}(i)\f$ denote the random
Chris@16:  * distribution generated by @c uniform_smallint. Then the sum over all
Chris@16:  * i in \f$r_{\mathtt{out}}\f$ of
Chris@16:  * \f$\displaystyle
Chris@16:  * \left(\frac{p_{\mathtt{out\_s}}(i)}{p_{\mathtt{out}}(i)} - 1\right)^2\f$
Chris@16:  * shall not exceed
Chris@16:  * \f$\displaystyle \frac{r_{\mathtt{out}}}{r_{\mathtt{base}}^2}
Chris@16:  * (r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})
Chris@16:  * (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$.
Chris@16:  *
Chris@16:  * The template parameter IntType shall denote an integer-like value type.
Chris@16:  *
Chris@16:  * @xmlnote
Chris@16:  * The property above is the square sum of the relative differences
Chris@16:  * in probabilities between the desired uniform distribution
Chris@16:  * \f$p_{\mathtt{out}}(i)\f$ and the generated distribution
Chris@16:  * \f$p_{\mathtt{out\_s}}(i)\f$.
Chris@16:  * The property can be fulfilled with the calculation
Chris@16:  * \f$(\mbox{base\_rng} \mbox{ mod } r_{\mathtt{out}})\f$, as follows:
Chris@16:  * Let \f$r = r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}}\f$.
Chris@16:  * The base distribution on \f$r_{\mathtt{base}}\f$ is folded onto the
Chris@16:  * range \f$r_{\mathtt{out}}\f$. The numbers i < r have assigned
Chris@16:  * \f$\displaystyle
Chris@16:  * \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor+1\f$
Chris@16:  * numbers of the base distribution, the rest has only \f$\displaystyle
Chris@16:  * \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor\f$.
Chris@16:  * Therefore,
Chris@16:  * \f$\displaystyle p_{\mathtt{out\_s}}(i) =
Chris@16:  * \left(\left\lfloor\frac{r_{\mathtt{base}}}
Chris@16:  * {r_{\mathtt{out}}}\right\rfloor+1\right) /
Chris@16:  * r_{\mathtt{base}}\f$ for i < r and \f$\displaystyle p_{\mathtt{out\_s}}(i) =
Chris@16:  * \left\lfloor\frac{r_{\mathtt{base}}}
Chris@16:  * {r_{\mathtt{out}}}\right\rfloor/r_{\mathtt{base}}\f$ otherwise.
Chris@16:  * Substituting this in the
Chris@16:  * above sum formula leads to the desired result.
Chris@16:  * @endxmlnote
Chris@16:  *
Chris@16:  * Note: The upper bound for
Chris@16:  * \f$(r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})
Chris@16:  * (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$ is
Chris@16:  * \f$\displaystyle \frac{r_{\mathtt{out}}^2}{4}\f$.  Regarding the upper bound
Chris@16:  * for the square sum of the relative quantization error of
Chris@16:  * \f$\displaystyle \frac{r_\mathtt{out}^3}{4r_{\mathtt{base}}^2}\f$, it
Chris@16:  * seems wise to either choose \f$r_{\mathtt{base}}\f$ so that
Chris@16:  * \f$r_{\mathtt{base}} > 10r_{\mathtt{out}}^2\f$ or ensure that
Chris@16:  * \f$r_{\mathtt{base}}\f$ is
Chris@16:  * divisible by \f$r_{\mathtt{out}}\f$.
Chris@16:  */
Chris@16: template<class IntType = int>
Chris@16: class uniform_smallint
Chris@16: {
Chris@16: public:
Chris@16:     typedef IntType input_type;
Chris@16:     typedef IntType 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(IntType min_arg = 0, IntType 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:         IntType a() const { return _min; }
Chris@16:         /** Returns the maximum value. */
Chris@16:         IntType 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:         IntType _min;
Chris@16:         IntType _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(IntType min_arg = 0, IntType 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 typename boost::make_unsigned<result_type>::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 typename boost::make_unsigned<result_type>::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 * (static_cast<base_result>(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: } // namespace random
Chris@16: 
Chris@16: using random::uniform_smallint;
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_RANDOM_UNIFORM_SMALLINT_HPP