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
concepts
concept_check.h
std::bool_constant
integral_constant< bool, __v > bool_constant
Alias template for compile-time boolean constant types.
Definition: type_traits:99
std::max
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:254
std::min
constexpr const _Tp & min(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:230
std
ISO C++ entities toplevel namespace is std.
__gnu_cxx::__int_traits
__numeric_traits_integer< _Tp > __int_traits
Convenience alias for __numeric_traits<integer-type>.
Definition: ext/numeric_traits.h:136
std::is_integral
is_integral
Definition: type_traits:394
std::uniform_int_distribution
Uniform discrete distribution for random numbers. A discrete random distribution on the range with e...
Definition: uniform_int_dist.h:78
std::uniform_int_distribution::reset
void reset()
Resets the distribution state.
Definition: uniform_int_dist.h:148
std::uniform_int_distribution::uniform_int_distribution
uniform_int_distribution()
Constructs a uniform distribution object.
Definition: uniform_int_dist.h:125
std::uniform_int_distribution::param
void param(const param_type &__param)
Sets the parameter set of the distribution.
Definition: uniform_int_dist.h:170
std::uniform_int_distribution::min
result_type min() const
Returns the inclusive lower bound of the distribution range.
Definition: uniform_int_dist.h:177
std::uniform_int_distribution::result_type
_IntType result_type
Definition: uniform_int_dist.h:80
std::uniform_int_distribution::operator==
friend bool operator==(const uniform_int_distribution &__d1, const uniform_int_distribution &__d2)
Return true if two uniform integer distributions have the same parameters.
Definition: uniform_int_dist.h:227
std::uniform_int_distribution::max
result_type max() const
Returns the inclusive upper bound of the distribution range.
Definition: uniform_int_dist.h:184
std::uniform_int_distribution::operator()
result_type operator()(_UniformRandomBitGenerator &__urng)
Generating functions.
Definition: uniform_int_dist.h:192
std::uniform_int_distribution::uniform_int_distribution
uniform_int_distribution(_IntType __a, _IntType __b=__gnu_cxx::__int_traits< _IntType >::__max)
Constructs a uniform distribution object.
Definition: uniform_int_dist.h:131
std::uniform_int_distribution::param
param_type param() const
Returns the parameter set of the distribution.
Definition: uniform_int_dist.h:162
std::uniform_int_distribution::param_type
Definition: uniform_int_dist.h:87
numeric_traits.h
type_traits