308 lines
12 KiB
Plaintext
308 lines
12 KiB
Plaintext
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/* boost random/uniform_smallint.hpp header file
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*
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* Copyright Jens Maurer 2000-2001
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id$
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*
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* Revision history
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* 2001-04-08 added min<max assertion (N. Becker)
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* 2001-02-18 moved to individual header files
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*/
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#ifndef BOOST_RANDOM_UNIFORM_SMALLINT_HPP
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#define BOOST_RANDOM_UNIFORM_SMALLINT_HPP
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#include <istream>
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#include <iosfwd>
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#include <boost/assert.hpp>
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#include <boost/config.hpp>
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#include <boost/limits.hpp>
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#include <boost/type_traits/is_integral.hpp>
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#include <boost/random/detail/config.hpp>
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#include <boost/random/detail/operators.hpp>
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#include <boost/random/detail/signed_unsigned_tools.hpp>
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#include <boost/random/uniform_01.hpp>
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#include <boost/detail/workaround.hpp>
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#include <boost/mpl/bool.hpp>
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#ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
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#include <boost/mpl/if.hpp>
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#endif
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namespace boost {
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namespace random {
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// uniform integer distribution on a small range [min, max]
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/**
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* The distribution function uniform_smallint models a \random_distribution.
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* On each invocation, it returns a random integer value uniformly distributed
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* in the set of integer numbers {min, min+1, min+2, ..., max}. It assumes
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* that the desired range (max-min+1) is small compared to the range of the
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* underlying source of random numbers and thus makes no attempt to limit
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* quantization errors.
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*
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* Let \f$r_{\mathtt{out}} = (\mbox{max}-\mbox{min}+1)\f$ the desired range of
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* integer numbers, and
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* let \f$r_{\mathtt{base}}\f$ be the range of the underlying source of random
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* numbers. Then, for the uniform distribution, the theoretical probability
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* for any number i in the range \f$r_{\mathtt{out}}\f$ will be
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* \f$\displaystyle p_{\mathtt{out}}(i) = \frac{1}{r_{\mathtt{out}}}\f$.
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* Likewise, assume a uniform distribution on \f$r_{\mathtt{base}}\f$ for
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* the underlying source of random numbers, i.e.
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* \f$\displaystyle p_{\mathtt{base}}(i) = \frac{1}{r_{\mathtt{base}}}\f$.
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* Let \f$p_{\mathtt{out\_s}}(i)\f$ denote the random
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* distribution generated by @c uniform_smallint. Then the sum over all
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* i in \f$r_{\mathtt{out}}\f$ of
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* \f$\displaystyle
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* \left(\frac{p_{\mathtt{out\_s}}(i)}{p_{\mathtt{out}}(i)} - 1\right)^2\f$
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* shall not exceed
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* \f$\displaystyle \frac{r_{\mathtt{out}}}{r_{\mathtt{base}}^2}
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* (r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})
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* (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$.
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*
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* The template parameter IntType shall denote an integer-like value type.
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*
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* @xmlnote
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* The property above is the square sum of the relative differences
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* in probabilities between the desired uniform distribution
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* \f$p_{\mathtt{out}}(i)\f$ and the generated distribution
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* \f$p_{\mathtt{out\_s}}(i)\f$.
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* The property can be fulfilled with the calculation
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* \f$(\mbox{base\_rng} \mbox{ mod } r_{\mathtt{out}})\f$, as follows:
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* Let \f$r = r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}}\f$.
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* The base distribution on \f$r_{\mathtt{base}}\f$ is folded onto the
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* range \f$r_{\mathtt{out}}\f$. The numbers i < r have assigned
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* \f$\displaystyle
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* \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor+1\f$
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* numbers of the base distribution, the rest has only \f$\displaystyle
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* \left\lfloor\frac{r_{\mathtt{base}}}{r_{\mathtt{out}}}\right\rfloor\f$.
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* Therefore,
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* \f$\displaystyle p_{\mathtt{out\_s}}(i) =
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* \left(\left\lfloor\frac{r_{\mathtt{base}}}
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* {r_{\mathtt{out}}}\right\rfloor+1\right) /
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* r_{\mathtt{base}}\f$ for i < r and \f$\displaystyle p_{\mathtt{out\_s}}(i) =
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* \left\lfloor\frac{r_{\mathtt{base}}}
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* {r_{\mathtt{out}}}\right\rfloor/r_{\mathtt{base}}\f$ otherwise.
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* Substituting this in the
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* above sum formula leads to the desired result.
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* @endxmlnote
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*
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* Note: The upper bound for
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* \f$(r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})
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* (r_{\mathtt{out}} - r_{\mathtt{base}} \mbox{ mod } r_{\mathtt{out}})\f$ is
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* \f$\displaystyle \frac{r_{\mathtt{out}}^2}{4}\f$. Regarding the upper bound
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* for the square sum of the relative quantization error of
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* \f$\displaystyle \frac{r_\mathtt{out}^3}{4r_{\mathtt{base}}^2}\f$, it
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* seems wise to either choose \f$r_{\mathtt{base}}\f$ so that
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* \f$r_{\mathtt{base}} > 10r_{\mathtt{out}}^2\f$ or ensure that
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* \f$r_{\mathtt{base}}\f$ is
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* divisible by \f$r_{\mathtt{out}}\f$.
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*/
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template<class IntType = int>
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class uniform_smallint
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{
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public:
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typedef IntType input_type;
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typedef IntType result_type;
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class param_type
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{
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public:
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typedef uniform_smallint distribution_type;
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/** constructs the parameters of a @c uniform_smallint distribution. */
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param_type(IntType min_arg = 0, IntType max_arg = 9)
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: _min(min_arg), _max(max_arg)
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{
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BOOST_ASSERT(_min <= _max);
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}
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/** Returns the minimum value. */
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IntType a() const { return _min; }
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/** Returns the maximum value. */
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IntType b() const { return _max; }
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/** Writes the parameters to a @c std::ostream. */
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
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{
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os << parm._min << " " << parm._max;
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return os;
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}
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/** Reads the parameters from a @c std::istream. */
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
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{
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is >> parm._min >> std::ws >> parm._max;
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return is;
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}
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/** Returns true if the two sets of parameters are equal. */
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
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{ return lhs._min == rhs._min && lhs._max == rhs._max; }
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/** Returns true if the two sets of parameters are different. */
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
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private:
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IntType _min;
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IntType _max;
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};
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/**
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* Constructs a @c uniform_smallint. @c min and @c max are the
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* lower and upper bounds of the output range, respectively.
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*/
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explicit uniform_smallint(IntType min_arg = 0, IntType max_arg = 9)
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: _min(min_arg), _max(max_arg) {}
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/**
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* Constructs a @c uniform_smallint from its parameters.
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*/
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explicit uniform_smallint(const param_type& parm)
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: _min(parm.a()), _max(parm.b()) {}
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/** Returns the minimum value of the distribution. */
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result_type a() const { return _min; }
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/** Returns the maximum value of the distribution. */
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result_type b() const { return _max; }
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/** Returns the minimum value of the distribution. */
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result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; }
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/** Returns the maximum value of the distribution. */
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result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; }
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/** Returns the parameters of the distribution. */
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param_type param() const { return param_type(_min, _max); }
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/** Sets the parameters of the distribution. */
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void param(const param_type& parm)
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{
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_min = parm.a();
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_max = parm.b();
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}
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/**
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* Effects: Subsequent uses of the distribution do not depend
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* on values produced by any engine prior to invoking reset.
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*/
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void reset() { }
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/** Returns a value uniformly distributed in the range [min(), max()]. */
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template<class Engine>
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result_type operator()(Engine& eng) const
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{
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typedef typename Engine::result_type base_result;
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return generate(eng, boost::random::traits::is_integral<base_result>());
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}
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/** Returns a value uniformly distributed in the range [param.a(), param.b()]. */
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template<class Engine>
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result_type operator()(Engine& eng, const param_type& parm) const
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{ return uniform_smallint(parm)(eng); }
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/** Writes the distribution to a @c std::ostream. */
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_smallint, ud)
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{
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os << ud._min << " " << ud._max;
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return os;
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}
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/** Reads the distribution from a @c std::istream. */
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_smallint, ud)
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{
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is >> ud._min >> std::ws >> ud._max;
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return is;
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}
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/**
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* Returns true if the two distributions will produce identical
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* sequences of values given equal generators.
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*/
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_smallint, lhs, rhs)
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{ return lhs._min == rhs._min && lhs._max == rhs._max; }
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/**
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* Returns true if the two distributions may produce different
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* sequences of values given equal generators.
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*/
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_smallint)
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private:
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// \cond show_private
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template<class Engine>
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result_type generate(Engine& eng, boost::mpl::true_) const
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{
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// equivalent to (eng() - eng.min()) % (_max - _min + 1) + _min,
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// but guarantees no overflow.
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typedef typename Engine::result_type base_result;
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typedef typename boost::random::traits::make_unsigned<base_result>::type base_unsigned;
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typedef typename boost::random::traits::make_unsigned_or_unbounded<result_type>::type range_type;
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#ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
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typedef typename mpl::if_c<
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std::numeric_limits<range_type>::is_specialized && std::numeric_limits<base_unsigned>::is_specialized
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&& (std::numeric_limits<range_type>::digits >= std::numeric_limits<base_unsigned>::digits),
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range_type, base_unsigned>::type mixed_range_type;
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#else
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typedef base_unsigned mixed_range_type;
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#endif
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range_type range = random::detail::subtract<result_type>()(_max, _min);
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base_unsigned base_range =
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random::detail::subtract<base_result>()((eng.max)(), (eng.min)());
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base_unsigned val =
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random::detail::subtract<base_result>()(eng(), (eng.min)());
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if(range >= base_range) {
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return boost::random::detail::add<range_type, result_type>()(
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static_cast<range_type>(val), _min);
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} else {
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// This involves mixed arithmetic between the base generators range
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// type, and the result_type's range type. mixed_range_type is
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// normally the same as base_unsigned which is the most efficient
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// option, but requires a narrowing explcit cast if result_type
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// is a multiprecision type. If no such casts are available then use
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// multiprecision arithmetic throughout instead.
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mixed_range_type modulus = static_cast<mixed_range_type>(range)+1;
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return boost::random::detail::add<range_type, result_type>()(
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static_cast<mixed_range_type>(val) % modulus, _min);
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}
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}
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template<class Engine>
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result_type generate(Engine& eng, boost::mpl::false_) const
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{
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typedef typename Engine::result_type base_result;
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typedef typename boost::random::traits::make_unsigned<result_type>::type range_type;
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range_type range = random::detail::subtract<result_type>()(_max, _min);
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base_result val = boost::uniform_01<base_result>()(eng);
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// what is the worst that can possibly happen here?
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// base_result may not be able to represent all the values in [0, range]
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// exactly. If this happens, it will cause round off error and we
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// won't be able to produce all the values in the range. We don't
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// care about this because the user has already told us not to by
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// using uniform_smallint. However, we do need to be careful
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// to clamp the result, or floating point rounding can produce
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// an out of range result.
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range_type offset = static_cast<range_type>(val * (static_cast<base_result>(range) + 1));
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if(offset > range) return _max;
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return boost::random::detail::add<range_type, result_type>()(offset , _min);
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}
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// \endcond
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result_type _min;
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result_type _max;
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};
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} // namespace random
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using random::uniform_smallint;
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} // namespace boost
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#endif // BOOST_RANDOM_UNIFORM_SMALLINT_HPP
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