uniform_int_dist.h

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// Class template uniform_int_distribution -*- C++ -*-
 
// Copyright (C) 2009-2021 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/**
 * @file bits/uniform_int_dist.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{random}
 */
 
#ifndef _GLIBCXX_BITS_UNIFORM_INT_DIST_H
#define _GLIBCXX_BITS_UNIFORM_INT_DIST_H
 
#include <type_traits>
#include <ext/numeric_traits.h>
#if __cplusplus > 201703L
# include <concepts>
#endif
#include <bits/concept_check.h> // __glibcxx_function_requires
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
 
#ifdef __cpp_lib_concepts
  /// Requirements for a uniform random bit generator.
  template<typename _Gen>
    concept uniform_random_bit_generator
      = invocable<_Gen&> && unsigned_integral<invoke_result_t<_Gen&>>
      && requires
      {
        { _Gen::min() } -> same_as<invoke_result_t<_Gen&>>;
        { _Gen::max() } -> same_as<invoke_result_t<_Gen&>>;
        requires bool_constant<(_Gen::min() < _Gen::max())>::value;
      };
#endif
 
  namespace __detail
  {
    // Determine whether number is a power of two.
    // This is true for zero, which is OK because we want _Power_of_2(n+1)
    // to be true if n==numeric_limits<_Tp>::max() and so n+1 wraps around.
    template<typename _Tp>
      constexpr bool
      _Power_of_2(_Tp __x)
      {
        return ((__x - 1) & __x) == 0;
      }
  }
 
  /**
   * @brief Uniform discrete distribution for random numbers.
   * A discrete random distribution on the range @f$[min, max]@f$ with equal
   * probability throughout the range.
   */
  template<typename _IntType = int>
    class uniform_int_distribution
    {
      static_assert(std::is_integral<_IntType>::value,
                    "template argument must be an integral type");
 
    public:
      /** The type of the range of the distribution. */
      typedef _IntType result_type;
      /** Parameter type. */
      struct param_type
      {
        typedef uniform_int_distribution<_IntType> distribution_type;
 
        param_type() : param_type(0) { }
 
        explicit
        param_type(_IntType __a,
                   _IntType __b = __gnu_cxx::__int_traits<_IntType>::__max)
        : _M_a(__a), _M_b(__b)
        {
          __glibcxx_assert(_M_a <= _M_b);
        }
 
        result_type
        a() const
        { return _M_a; }
 
        result_type
        b() const
        { return _M_b; }
 
        friend bool
        operator==(const param_type& __p1, const param_type& __p2)
        { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
 
        friend bool
        operator!=(const param_type& __p1, const param_type& __p2)
        { return !(__p1 == __p2); }
 
      private:
        _IntType _M_a;
        _IntType _M_b;
      };
 
    public:
      /**
       * @brief Constructs a uniform distribution object.
       */
      uniform_int_distribution() : uniform_int_distribution(0) { }
 
      /**
       * @brief Constructs a uniform distribution object.
       */
      explicit
      uniform_int_distribution(_IntType __a,
                               _IntType __b
                                 = __gnu_cxx::__int_traits<_IntType>::__max)
      : _M_param(__a, __b)
      { }
 
      explicit
      uniform_int_distribution(const param_type& __p)
      : _M_param(__p)
      { }
 
      /**
       * @brief Resets the distribution state.
       *
       * Does nothing for the uniform integer distribution.
       */
      void
      reset() { }
 
      result_type
      a() const
      { return _M_param.a(); }
 
      result_type
      b() const
      { return _M_param.b(); }
 
      /**
       * @brief Returns the parameter set of the distribution.
       */
      param_type
      param() const
      { return _M_param; }
 
      /**
       * @brief Sets the parameter set of the distribution.
       * @param __param The new parameter set of the distribution.
       */
      void
      param(const param_type& __param)
      { _M_param = __param; }
 
      /**
       * @brief Returns the inclusive lower bound of the distribution range.
       */
      result_type
      min() const
      { return this->a(); }
 
      /**
       * @brief Returns the inclusive upper bound of the distribution range.
       */
      result_type
      max() const
      { return this->b(); }
 
      /**
       * @brief Generating functions.
       */
      template<typename _UniformRandomBitGenerator>
        result_type
        operator()(_UniformRandomBitGenerator& __urng)
        { return this->operator()(__urng, _M_param); }
 
      template<typename _UniformRandomBitGenerator>
        result_type
        operator()(_UniformRandomBitGenerator& __urng,
                   const param_type& __p);
 
      template<typename _ForwardIterator,
               typename _UniformRandomBitGenerator>
        void
        __generate(_ForwardIterator __f, _ForwardIterator __t,
                   _UniformRandomBitGenerator& __urng)
        { this->__generate(__f, __t, __urng, _M_param); }
 
      template<typename _ForwardIterator,
               typename _UniformRandomBitGenerator>
        void
        __generate(_ForwardIterator __f, _ForwardIterator __t,
                   _UniformRandomBitGenerator& __urng,
                   const param_type& __p)
        { this->__generate_impl(__f, __t, __urng, __p); }
 
      template<typename _UniformRandomBitGenerator>
        void
        __generate(result_type* __f, result_type* __t,
                   _UniformRandomBitGenerator& __urng,
                   const param_type& __p)
        { this->__generate_impl(__f, __t, __urng, __p); }
 
      /**
       * @brief Return true if two uniform integer distributions have
       *        the same parameters.
       */
      friend bool
      operator==(const uniform_int_distribution& __d1,
                 const uniform_int_distribution& __d2)
      { return __d1._M_param == __d2._M_param; }
 
    private:
      template<typename _ForwardIterator,
               typename _UniformRandomBitGenerator>
        void
        __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                        _UniformRandomBitGenerator& __urng,
                        const param_type& __p);
 
      param_type _M_param;
 
      // Lemire's nearly divisionless algorithm.
      // Returns an unbiased random number from __g downscaled to [0,__range)
      // using an unsigned type _Wp twice as wide as unsigned type _Up.
      template<typename _Wp, typename _Urbg, typename _Up>
        static _Up
        _S_nd(_Urbg& __g, _Up __range)
        {
          using _Up_traits = __gnu_cxx::__int_traits<_Up>;
          using _Wp_traits = __gnu_cxx::__int_traits<_Wp>;
          static_assert(!_Up_traits::__is_signed, "U must be unsigned");
          static_assert(!_Wp_traits::__is_signed, "W must be unsigned");
          static_assert(_Wp_traits::__digits == (2 * _Up_traits::__digits),
                        "W must be twice as wide as U");
 
          // reference: Fast Random Integer Generation in an Interval
          // ACM Transactions on Modeling and Computer Simulation 29 (1), 2019
          // https://arxiv.org/abs/1805.10941
          _Wp __product = _Wp(__g()) * _Wp(__range);
          _Up __low = _Up(__product);
          if (__low < __range)
            {
              _Up __threshold = -__range % __range;
              while (__low < __threshold)
                {
                  __product = _Wp(__g()) * _Wp(__range);
                  __low = _Up(__product);
                }
            }
          return __product >> _Up_traits::__digits;
        }
    };
 
  template<typename _IntType>
    template<typename _UniformRandomBitGenerator>
      typename uniform_int_distribution<_IntType>::result_type
      uniform_int_distribution<_IntType>::
      operator()(_UniformRandomBitGenerator& __urng,
                 const param_type& __param)
      {
        typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
        typedef typename make_unsigned<result_type>::type __utype;
        typedef typename common_type<_Gresult_type, __utype>::type __uctype;
 
        constexpr __uctype __urngmin = _UniformRandomBitGenerator::min();
        constexpr __uctype __urngmax = _UniformRandomBitGenerator::max();
        static_assert( __urngmin < __urngmax,
            "Uniform random bit generator must define min() < max()");
        constexpr __uctype __urngrange = __urngmax - __urngmin;
 
        const __uctype __urange
          = __uctype(__param.b()) - __uctype(__param.a());
 
        __uctype __ret;
        if (__urngrange > __urange)
          {
            // downscaling
 
            const __uctype __uerange = __urange + 1; // __urange can be zero
 
#if defined __UINT64_TYPE__ && defined __UINT32_TYPE__
#if __SIZEOF_INT128__
            if _GLIBCXX17_CONSTEXPR (__urngrange == __UINT64_MAX__)
              {
                // __urng produces values that use exactly 64-bits,
                // so use 128-bit integers to downscale to desired range.
                __UINT64_TYPE__ __u64erange = __uerange;
                __ret = _S_nd<unsigned __int128>(__urng, __u64erange);
              }
            else
#endif
            if _GLIBCXX17_CONSTEXPR (__urngrange == __UINT32_MAX__)
              {
                // __urng produces values that use exactly 32-bits,
                // so use 64-bit integers to downscale to desired range.
                __UINT32_TYPE__ __u32erange = __uerange;
                __ret = _S_nd<__UINT64_TYPE__>(__urng, __u32erange);
              }
            else
#endif
              {
                // fallback case (2 divisions)
                const __uctype __scaling = __urngrange / __uerange;
                const __uctype __past = __uerange * __scaling;
                do
                  __ret = __uctype(__urng()) - __urngmin;
                while (__ret >= __past);
                __ret /= __scaling;
              }
          }
        else if (__urngrange < __urange)
          {
            // upscaling
            /*
              Note that every value in [0, urange]
              can be written uniquely as
 
              (urngrange + 1) * high + low
 
              where
 
              high in [0, urange / (urngrange + 1)]
 
              and
 
              low in [0, urngrange].
            */
            __uctype __tmp; // wraparound control
            do
              {
                const __uctype __uerngrange = __urngrange + 1;
                __tmp = (__uerngrange * operator()
                         (__urng, param_type(0, __urange / __uerngrange)));
                __ret = __tmp + (__uctype(__urng()) - __urngmin);
              }
            while (__ret > __urange || __ret < __tmp);
          }
        else
          __ret = __uctype(__urng()) - __urngmin;
 
        return __ret + __param.a();
      }
 
 
  template<typename _IntType>
    template<typename _ForwardIterator,
             typename _UniformRandomBitGenerator>
      void
      uniform_int_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
                      _UniformRandomBitGenerator& __urng,
                      const param_type& __param)
      {
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
        typedef typename make_unsigned<result_type>::type __utype;
        typedef typename common_type<_Gresult_type, __utype>::type __uctype;
 
        static_assert( __urng.min() < __urng.max(),
            "Uniform random bit generator must define min() < max()");
 
        constexpr __uctype __urngmin = __urng.min();
        constexpr __uctype __urngmax = __urng.max();
        constexpr __uctype __urngrange = __urngmax - __urngmin;
        const __uctype __urange
          = __uctype(__param.b()) - __uctype(__param.a());
 
        __uctype __ret;
 
        if (__urngrange > __urange)
          {
            if (__detail::_Power_of_2(__urngrange + 1)
                && __detail::_Power_of_2(__urange + 1))
              {
                while (__f != __t)
                  {
                    __ret = __uctype(__urng()) - __urngmin;
                    *__f++ = (__ret & __urange) + __param.a();
                  }
              }
            else
              {
                // downscaling
                const __uctype __uerange = __urange + 1; // __urange can be zero
                const __uctype __scaling = __urngrange / __uerange;
                const __uctype __past = __uerange * __scaling;
                while (__f != __t)
                  {
                    do
                      __ret = __uctype(__urng()) - __urngmin;
                    while (__ret >= __past);
                    *__f++ = __ret / __scaling + __param.a();
                  }
              }
          }
        else if (__urngrange < __urange)
          {
            // upscaling
            /*
              Note that every value in [0, urange]
              can be written uniquely as
 
              (urngrange + 1) * high + low
 
              where
 
              high in [0, urange / (urngrange + 1)]
 
              and
 
              low in [0, urngrange].
            */
            __uctype __tmp; // wraparound control
            while (__f != __t)
              {
                do
                  {
                    constexpr __uctype __uerngrange = __urngrange + 1;
                    __tmp = (__uerngrange * operator()
                             (__urng, param_type(0, __urange / __uerngrange)));
                    __ret = __tmp + (__uctype(__urng()) - __urngmin);
                  }
                while (__ret > __urange || __ret < __tmp);
                *__f++ = __ret;
              }
          }
        else
          while (__f != __t)
            *__f++ = __uctype(__urng()) - __urngmin + __param.a();
      }
 
  // operator!= and operator<< and operator>> are defined in <bits/random.h>
 
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
 
#endif