diff options
Diffstat (limited to 'boost/random/uniform_smallint.hpp')
| -rw-r--r-- | boost/random/uniform_smallint.hpp | 288 |
1 files changed, 288 insertions, 0 deletions
diff --git a/boost/random/uniform_smallint.hpp b/boost/random/uniform_smallint.hpp new file mode 100644 index 0000000000..745fa8e93b --- /dev/null +++ b/boost/random/uniform_smallint.hpp @@ -0,0 +1,288 @@ +/* boost random/uniform_smallint.hpp header file + * + * Copyright Jens Maurer 2000-2001 + * 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: uniform_smallint.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $ + * + * Revision history + * 2001-04-08 added min<max assertion (N. Becker) + * 2001-02-18 moved to individual header files + */ + +#ifndef BOOST_RANDOM_UNIFORM_SMALLINT_HPP +#define BOOST_RANDOM_UNIFORM_SMALLINT_HPP + +#include <istream> +#include <iosfwd> +#include <boost/assert.hpp> +#include <boost/config.hpp> +#include <boost/limits.hpp> +#include <boost/type_traits/is_integral.hpp> +#include <boost/random/detail/config.hpp> +#include <boost/random/detail/operators.hpp> +#include <boost/random/detail/signed_unsigned_tools.hpp> +#include <boost/random/uniform_01.hpp> +#include <boost/detail/workaround.hpp> + +namespace boost { +namespace random { + +// uniform integer distribution on a small range [min, max] + +/** + * The distribution function uniform_smallint models a \random_distribution. + * On each invocation, it returns a random integer value uniformly distributed + * in the set of integer numbers {min, min+1, min+2, ..., max}. It assumes + * that the desired range (max-min+1) is small compared to the range of the + * underlying source of random numbers and thus makes no attempt to limit + * quantization errors. + * + * Let \f$r_{\mathtt{out}} = (\mbox{max}-\mbox{min}+1)\f$ the desired range of + * integer numbers, and + * let \f$r_{\mathtt{base}}\f$ be the range of the underlying source of random + * numbers. Then, for the uniform distribution, the theoretical probability + * for any number i in the range \f$r_{\mathtt{out}}\f$ will be + * \f$\displaystyle p_{\mathtt{out}}(i) = \frac{1}{r_{\mathtt{out}}}\f$. + * Likewise, assume a uniform distribution on \f$r_{\mathtt{base}}\f$ for + * the underlying source of random numbers, i.e. + * \f$\displaystyle p_{\mathtt{base}}(i) = \frac{1}{r_{\mathtt{base}}}\f$. + * Let \f$p_{\mathtt{out\_s}}(i)\f$ denote the random + * distribution generated by @c uniform_smallint. Then the sum over all + * i in \f$r_{\mathtt{out}}\f$ of + * \f$\displaystyle + * \left(\frac{p_{\mathtt{out\_s}}(i)}{p_{\mathtt{out}}(i)} - 1\right)^2\f$ + * shall not exceed + * \f$\displaystyle \frac{r_{\mathtt{out}}}{r_{\mathtt{base}}^2} + * (r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}}) + * (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$. + * + * The template parameter IntType shall denote an integer-like value type. + * + * @xmlnote + * The property above is the square sum of the relative differences + * in probabilities between the desired uniform distribution + * \f$p_{\mathtt{out}}(i)\f$ and the generated distribution + * \f$p_{\mathtt{out\_s}}(i)\f$. + * The property can be fulfilled with the calculation + * \f$(\mbox{base\_rng} \mbox{ mod } r_{\mathtt{out}})\f$, as follows: + * Let \f$r = r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}}\f$. + * The base distribution on \f$r_{\mathtt{base}}\f$ is folded onto the + * range \f$r_{\mathtt{out}}\f$. The numbers i < r have assigned + * \f$\displaystyle + * \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor+1\f$ + * numbers of the base distribution, the rest has only \f$\displaystyle + * \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor\f$. + * Therefore, + * \f$\displaystyle p_{\mathtt{out\_s}}(i) = + * \left(\left\lfloor\frac{r_{\mathtt{base}}} + * {r_{\mathtt{out}}}\right\rfloor+1\right) / + * r_{\mathtt{base}}\f$ for i < r and \f$\displaystyle p_{\mathtt{out\_s}}(i) = + * \left\lfloor\frac{r_{\mathtt{base}}} + * {r_{\mathtt{out}}}\right\rfloor/r_{\mathtt{base}}\f$ otherwise. + * Substituting this in the + * above sum formula leads to the desired result. + * @endxmlnote + * + * Note: The upper bound for + * \f$(r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}}) + * (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$ is + * \f$\displaystyle \frac{r_{\mathtt{out}}^2}{4}\f$. Regarding the upper bound + * for the square sum of the relative quantization error of + * \f$\displaystyle \frac{r_\mathtt{out}^3}{4r_{\mathtt{base}}^2}\f$, it + * seems wise to either choose \f$r_{\mathtt{base}}\f$ so that + * \f$r_{\mathtt{base}} > 10r_{\mathtt{out}}^2\f$ or ensure that + * \f$r_{\mathtt{base}}\f$ is + * divisible by \f$r_{\mathtt{out}}\f$. + */ +template<class IntType = int> +class uniform_smallint +{ +public: + typedef IntType input_type; + typedef IntType result_type; + + class param_type + { + public: + + typedef uniform_smallint distribution_type; + + /** constructs the parameters of a @c uniform_smallint distribution. */ + param_type(IntType min_arg = 0, IntType max_arg = 9) + : _min(min_arg), _max(max_arg) + { + BOOST_ASSERT(_min <= _max); + } + + /** Returns the minimum value. */ + IntType a() const { return _min; } + /** Returns the maximum value. */ + 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) + { + is >> parm._min >> std::ws >> parm._max; + 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 @c uniform_smallint. @c min and @c max are the + * lower and upper bounds of the output range, respectively. + */ + explicit uniform_smallint(IntType min_arg = 0, IntType max_arg = 9) + : _min(min_arg), _max(max_arg) {} + + /** + * Constructs a @c uniform_smallint from its parameters. + */ + explicit uniform_smallint(const param_type& parm) + : _min(parm.a()), _max(parm.b()) {} + + /** Returns the minimum value of the distribution. */ + result_type a() const { return _min; } + /** Returns the maximum value of the distribution. */ + result_type b() const { return _max; } + /** Returns the minimum value of the distribution. */ + result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; } + /** Returns the maximum value of the distribution. */ + result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () 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 a value uniformly distributed in the range [min(), max()]. */ + template<class Engine> + result_type operator()(Engine& eng) const + { + typedef typename Engine::result_type base_result; + return generate(eng, boost::is_integral<base_result>()); + } + + /** Returns a value uniformly distributed in the range [param.a(), param.b()]. */ + template<class Engine> + result_type operator()(Engine& eng, const param_type& parm) const + { return uniform_smallint(parm)(eng); } + + /** Writes the distribution to a @c std::ostream. */ + BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_smallint, ud) + { + os << ud._min << " " << ud._max; + return os; + } + + /** Reads the distribution from a @c std::istream. */ + BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_smallint, ud) + { + is >> ud._min >> std::ws >> ud._max; + return is; + } + + /** + * Returns true if the two distributions will produce identical + * sequences of values given equal generators. + */ + BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_smallint, 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_smallint) + +private: + + // \cond show_private + template<class Engine> + result_type generate(Engine& eng, boost::mpl::true_) const + { + // equivalent to (eng() - eng.min()) % (_max - _min + 1) + _min, + // but guarantees no overflow. + typedef typename Engine::result_type base_result; + typedef typename boost::make_unsigned<base_result>::type base_unsigned; + typedef typename boost::make_unsigned<result_type>::type range_type; + range_type range = random::detail::subtract<result_type>()(_max, _min); + base_unsigned base_range = + random::detail::subtract<result_type>()((eng.max)(), (eng.min)()); + base_unsigned val = + random::detail::subtract<base_result>()(eng(), (eng.min)()); + if(range >= base_range) { + return boost::random::detail::add<range_type, result_type>()( + static_cast<range_type>(val), _min); + } else { + base_unsigned modulus = static_cast<base_unsigned>(range) + 1; + return boost::random::detail::add<range_type, result_type>()( + static_cast<range_type>(val % modulus), _min); + } + } + + template<class Engine> + result_type generate(Engine& eng, boost::mpl::false_) const + { + typedef typename Engine::result_type base_result; + typedef typename boost::make_unsigned<result_type>::type range_type; + range_type range = random::detail::subtract<result_type>()(_max, _min); + base_result val = boost::uniform_01<base_result>()(eng); + // what is the worst that can possibly happen here? + // base_result may not be able to represent all the values in [0, range] + // exactly. If this happens, it will cause round off error and we + // won't be able to produce all the values in the range. We don't + // care about this because the user has already told us not to by + // using uniform_smallint. However, we do need to be careful + // to clamp the result, or floating point rounding can produce + // an out of range result. + range_type offset = static_cast<range_type>(val * (static_cast<base_result>(range) + 1)); + if(offset > range) return _max; + return boost::random::detail::add<range_type, result_type>()(offset , _min); + } + // \endcond + + result_type _min; + result_type _max; +}; + +} // namespace random + +using random::uniform_smallint; + +} // namespace boost + +#endif // BOOST_RANDOM_UNIFORM_SMALLINT_HPP |