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// random number generation -*- 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/random.h
* This is an internal header file, included by other library headers.
* Do not attempt to use it directly. @headername{random}
*/
#ifndef _RANDOM_H
#define _RANDOM_H 1
#include <vector>
#include <bits/uniform_int_dist.h>
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
// [26.4] Random number generation
/**
* @defgroup random Random Number Generation
* @ingroup numerics
*
* A facility for generating random numbers on selected distributions.
* @{
*/
// std::uniform_random_bit_generator is defined in <bits/uniform_int_dist.h>
/**
* @brief A function template for converting the output of a (integral)
* uniform random number generator to a floatng point result in the range
* [0-1).
*/
template<typename _RealType, size_t __bits,
typename _UniformRandomNumberGenerator>
_RealType
generate_canonical(_UniformRandomNumberGenerator& __g);
/// @cond undocumented
// Implementation-space details.
namespace __detail
{
template<typename _UIntType, size_t __w,
bool = __w < static_cast<size_t>
(std::numeric_limits<_UIntType>::digits)>
struct _Shift
{ static constexpr _UIntType __value = 0; };
template<typename _UIntType, size_t __w>
struct _Shift<_UIntType, __w, true>
{ static constexpr _UIntType __value = _UIntType(1) << __w; };
template<int __s,
int __which = ((__s <= __CHAR_BIT__ * sizeof (int))
+ (__s <= __CHAR_BIT__ * sizeof (long))
+ (__s <= __CHAR_BIT__ * sizeof (long long))
/* assume long long no bigger than __int128 */
+ (__s <= 128))>
struct _Select_uint_least_t
{
static_assert(__which < 0, /* needs to be dependent */
"sorry, would be too much trouble for a slow result");
};
template<int __s>
struct _Select_uint_least_t<__s, 4>
{ using type = unsigned int; };
template<int __s>
struct _Select_uint_least_t<__s, 3>
{ using type = unsigned long; };
template<int __s>
struct _Select_uint_least_t<__s, 2>
{ using type = unsigned long long; };
#if __SIZEOF_INT128__ > __SIZEOF_LONG_LONG__
template<int __s>
struct _Select_uint_least_t<__s, 1>
{ __extension__ using type = unsigned __int128; };
#endif
// Assume a != 0, a < m, c < m, x < m.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c,
bool __big_enough = (!(__m & (__m - 1))
|| (_Tp(-1) - __c) / __a >= __m - 1),
bool __schrage_ok = __m % __a < __m / __a>
struct _Mod
{
static _Tp
__calc(_Tp __x)
{
using _Tp2
= typename _Select_uint_least_t<std::__lg(__a)
+ std::__lg(__m) + 2>::type;
return static_cast<_Tp>((_Tp2(__a) * __x + __c) % __m);
}
};
// Schrage.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
struct _Mod<_Tp, __m, __a, __c, false, true>
{
static _Tp
__calc(_Tp __x);
};
// Special cases:
// - for m == 2^n or m == 0, unsigned integer overflow is safe.
// - a * (m - 1) + c fits in _Tp, there is no overflow.
template<typename _Tp, _Tp __m, _Tp __a, _Tp __c, bool __s>
struct _Mod<_Tp, __m, __a, __c, true, __s>
{
static _Tp
__calc(_Tp __x)
{
_Tp __res = __a * __x + __c;
if (__m)
__res %= __m;
return __res;
}
};
template<typename _Tp, _Tp __m, _Tp __a = 1, _Tp __c = 0>
inline _Tp
__mod(_Tp __x)
{
if _GLIBCXX17_CONSTEXPR (__a == 0)
return __c;
else
{
// _Mod must not be instantiated with a == 0
constexpr _Tp __a1 = __a ? __a : 1;
return _Mod<_Tp, __m, __a1, __c>::__calc(__x);
}
}
/*
* An adaptor class for converting the output of any Generator into
* the input for a specific Distribution.
*/
template<typename _Engine, typename _DInputType>
struct _Adaptor
{
static_assert(std::is_floating_point<_DInputType>::value,
"template argument must be a floating point type");
public:
_Adaptor(_Engine& __g)
: _M_g(__g) { }
_DInputType
min() const
{ return _DInputType(0); }
_DInputType
max() const
{ return _DInputType(1); }
/*
* Converts a value generated by the adapted random number generator
* into a value in the input domain for the dependent random number
* distribution.
*/
_DInputType
operator()()
{
return std::generate_canonical<_DInputType,
std::numeric_limits<_DInputType>::digits,
_Engine>(_M_g);
}
private:
_Engine& _M_g;
};
template<typename _Sseq>
using __seed_seq_generate_t = decltype(
std::declval<_Sseq&>().generate(std::declval<uint_least32_t*>(),
std::declval<uint_least32_t*>()));
// Detect whether _Sseq is a valid seed sequence for
// a random number engine _Engine with result type _Res.
template<typename _Sseq, typename _Engine, typename _Res,
typename _GenerateCheck = __seed_seq_generate_t<_Sseq>>
using __is_seed_seq = __and_<
__not_<is_same<__remove_cvref_t<_Sseq>, _Engine>>,
is_unsigned<typename _Sseq::result_type>,
__not_<is_convertible<_Sseq, _Res>>
>;
} // namespace __detail
/// @endcond
/**
* @addtogroup random_generators Random Number Generators
* @ingroup random
*
* These classes define objects which provide random or pseudorandom
* numbers, either from a discrete or a continuous interval. The
* random number generator supplied as a part of this library are
* all uniform random number generators which provide a sequence of
* random number uniformly distributed over their range.
*
* A number generator is a function object with an operator() that
* takes zero arguments and returns a number.
*
* A compliant random number generator must satisfy the following
* requirements. <table border=1 cellpadding=10 cellspacing=0>
* <caption align=top>Random Number Generator Requirements</caption>
* <tr><td>To be documented.</td></tr> </table>
*
* @{
*/
/**
* @brief A model of a linear congruential random number generator.
*
* A random number generator that produces pseudorandom numbers via
* linear function:
* @f[
* x_{i+1}\leftarrow(ax_{i} + c) \bmod m
* @f]
*
* The template parameter @p _UIntType must be an unsigned integral type
* large enough to store values up to (__m-1). If the template parameter
* @p __m is 0, the modulus @p __m used is
* std::numeric_limits<_UIntType>::max() plus 1. Otherwise, the template
* parameters @p __a and @p __c must be less than @p __m.
*
* The size of the state is @f$1@f$.
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
class linear_congruential_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(__m == 0u || (__a < __m && __c < __m),
"template argument substituting __m out of bounds");
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, linear_congruential_engine, _UIntType>::value>::type;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
/** The multiplier. */
static constexpr result_type multiplier = __a;
/** An increment. */
static constexpr result_type increment = __c;
/** The modulus. */
static constexpr result_type modulus = __m;
static constexpr result_type default_seed = 1u;
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine with seed 1.
*/
linear_congruential_engine() : linear_congruential_engine(default_seed)
{ }
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine with seed @p __s. The default seed value
* is 1.
*
* @param __s The initial seed value.
*/
explicit
linear_congruential_engine(result_type __s)
{ seed(__s); }
/**
* @brief Constructs a %linear_congruential_engine random number
* generator engine seeded from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
linear_congruential_engine(_Sseq& __q)
{ seed(__q); }
/**
* @brief Reseeds the %linear_congruential_engine random number generator
* engine sequence to the seed @p __s.
*
* @param __s The new seed.
*/
void
seed(result_type __s = default_seed);
/**
* @brief Reseeds the %linear_congruential_engine random number generator
* engine
* sequence using values from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q);
/**
* @brief Gets the smallest possible value in the output range.
*
* The minimum depends on the @p __c parameter: if it is zero, the
* minimum generated must be > 0, otherwise 0 is allowed.
*/
static constexpr result_type
min()
{ return __c == 0u ? 1u : 0u; }
/**
* @brief Gets the largest possible value in the output range.
*/
static constexpr result_type
max()
{ return __m - 1u; }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* @brief Gets the next random number in the sequence.
*/
result_type
operator()()
{
_M_x = __detail::__mod<_UIntType, __m, __a, __c>(_M_x);
return _M_x;
}
/**
* @brief Compares two linear congruential random number generator
* objects of the same type for equality.
*
* @param __lhs A linear congruential random number generator object.
* @param __rhs Another linear congruential random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const linear_congruential_engine& __lhs,
const linear_congruential_engine& __rhs)
{ return __lhs._M_x == __rhs._M_x; }
/**
* @brief Writes the textual representation of the state x(i) of x to
* @p __os.
*
* @param __os The output stream.
* @param __lcr A % linear_congruential_engine random number generator.
* @returns __os.
*/
template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
_UIntType1 __m1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::linear_congruential_engine<_UIntType1,
__a1, __c1, __m1>& __lcr);
/**
* @brief Sets the state of the engine by reading its textual
* representation from @p __is.
*
* The textual representation must have been previously written using
* an output stream whose imbued locale and whose type's template
* specialization arguments _CharT and _Traits were the same as those
* of @p __is.
*
* @param __is The input stream.
* @param __lcr A % linear_congruential_engine random number generator.
* @returns __is.
*/
template<typename _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
_UIntType1 __m1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::linear_congruential_engine<_UIntType1, __a1,
__c1, __m1>& __lcr);
private:
_UIntType _M_x;
};
/**
* @brief Compares two linear congruential random number generator
* objects of the same type for inequality.
*
* @param __lhs A linear congruential random number generator object.
* @param __rhs Another linear congruential random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
inline bool
operator!=(const std::linear_congruential_engine<_UIntType, __a,
__c, __m>& __lhs,
const std::linear_congruential_engine<_UIntType, __a,
__c, __m>& __rhs)
{ return !(__lhs == __rhs); }
/**
* A generalized feedback shift register discrete random number generator.
*
* This algorithm avoids multiplication and division and is designed to be
* friendly to a pipelined architecture. If the parameters are chosen
* correctly, this generator will produce numbers with a very long period and
* fairly good apparent entropy, although still not cryptographically strong.
*
* The best way to use this generator is with the predefined mt19937 class.
*
* This algorithm was originally invented by Makoto Matsumoto and
* Takuji Nishimura.
*
* @tparam __w Word size, the number of bits in each element of
* the state vector.
* @tparam __n The degree of recursion.
* @tparam __m The period parameter.
* @tparam __r The separation point bit index.
* @tparam __a The last row of the twist matrix.
* @tparam __u The first right-shift tempering matrix parameter.
* @tparam __d The first right-shift tempering matrix mask.
* @tparam __s The first left-shift tempering matrix parameter.
* @tparam __b The first left-shift tempering matrix mask.
* @tparam __t The second left-shift tempering matrix parameter.
* @tparam __c The second left-shift tempering matrix mask.
* @tparam __l The second right-shift tempering matrix parameter.
* @tparam __f Initialization multiplier.
*/
template<typename _UIntType, size_t __w,
size_t __n, size_t __m, size_t __r,
_UIntType __a, size_t __u, _UIntType __d, size_t __s,
_UIntType __b, size_t __t,
_UIntType __c, size_t __l, _UIntType __f>
class mersenne_twister_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(1u <= __m && __m <= __n,
"template argument substituting __m out of bounds");
static_assert(__r <= __w, "template argument substituting "
"__r out of bound");
static_assert(__u <= __w, "template argument substituting "
"__u out of bound");
static_assert(__s <= __w, "template argument substituting "
"__s out of bound");
static_assert(__t <= __w, "template argument substituting "
"__t out of bound");
static_assert(__l <= __w, "template argument substituting "
"__l out of bound");
static_assert(__w <= std::numeric_limits<_UIntType>::digits,
"template argument substituting __w out of bound");
static_assert(__a <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __a out of bound");
static_assert(__b <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __b out of bound");
static_assert(__c <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __c out of bound");
static_assert(__d <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __d out of bound");
static_assert(__f <= (__detail::_Shift<_UIntType, __w>::__value - 1),
"template argument substituting __f out of bound");
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, mersenne_twister_engine, _UIntType>::value>::type;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
// parameter values
static constexpr size_t word_size = __w;
static constexpr size_t state_size = __n;
static constexpr size_t shift_size = __m;
static constexpr size_t mask_bits = __r;
static constexpr result_type xor_mask = __a;
static constexpr size_t tempering_u = __u;
static constexpr result_type tempering_d = __d;
static constexpr size_t tempering_s = __s;
static constexpr result_type tempering_b = __b;
static constexpr size_t tempering_t = __t;
static constexpr result_type tempering_c = __c;
static constexpr size_t tempering_l = __l;
static constexpr result_type initialization_multiplier = __f;
static constexpr result_type default_seed = 5489u;
// constructors and member functions
mersenne_twister_engine() : mersenne_twister_engine(default_seed) { }
explicit
mersenne_twister_engine(result_type __sd)
{ seed(__sd); }
/**
* @brief Constructs a %mersenne_twister_engine random number generator
* engine seeded from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
mersenne_twister_engine(_Sseq& __q)
{ seed(__q); }
void
seed(result_type __sd = default_seed);
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q);
/**
* @brief Gets the smallest possible value in the output range.
*/
static constexpr result_type
min()
{ return 0; }
/**
* @brief Gets the largest possible value in the output range.
*/
static constexpr result_type
max()
{ return __detail::_Shift<_UIntType, __w>::__value - 1; }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z);
result_type
operator()();
/**
* @brief Compares two % mersenne_twister_engine random number generator
* objects of the same type for equality.
*
* @param __lhs A % mersenne_twister_engine random number generator
* object.
* @param __rhs Another % mersenne_twister_engine random number
* generator object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const mersenne_twister_engine& __lhs,
const mersenne_twister_engine& __rhs)
{ return (std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x)
&& __lhs._M_p == __rhs._M_p); }
/**
* @brief Inserts the current state of a % mersenne_twister_engine
* random number generator engine @p __x into the output stream
* @p __os.
*
* @param __os An output stream.
* @param __x A % mersenne_twister_engine random number generator
* engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _UIntType1,
size_t __w1, size_t __n1,
size_t __m1, size_t __r1,
_UIntType1 __a1, size_t __u1,
_UIntType1 __d1, size_t __s1,
_UIntType1 __b1, size_t __t1,
_UIntType1 __c1, size_t __l1, _UIntType1 __f1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::mersenne_twister_engine<_UIntType1, __w1, __n1,
__m1, __r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1,
__l1, __f1>& __x);
/**
* @brief Extracts the current state of a % mersenne_twister_engine
* random number generator engine @p __x from the input stream
* @p __is.
*
* @param __is An input stream.
* @param __x A % mersenne_twister_engine random number generator
* engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _UIntType1,
size_t __w1, size_t __n1,
size_t __m1, size_t __r1,
_UIntType1 __a1, size_t __u1,
_UIntType1 __d1, size_t __s1,
_UIntType1 __b1, size_t __t1,
_UIntType1 __c1, size_t __l1, _UIntType1 __f1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::mersenne_twister_engine<_UIntType1, __w1, __n1, __m1,
__r1, __a1, __u1, __d1, __s1, __b1, __t1, __c1,
__l1, __f1>& __x);
private:
void _M_gen_rand();
_UIntType _M_x[state_size];
size_t _M_p;
};
/**
* @brief Compares two % mersenne_twister_engine random number generator
* objects of the same type for inequality.
*
* @param __lhs A % mersenne_twister_engine random number generator
* object.
* @param __rhs Another % mersenne_twister_engine random number
* generator object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _UIntType, size_t __w,
size_t __n, size_t __m, size_t __r,
_UIntType __a, size_t __u, _UIntType __d, size_t __s,
_UIntType __b, size_t __t,
_UIntType __c, size_t __l, _UIntType __f>
inline bool
operator!=(const std::mersenne_twister_engine<_UIntType, __w, __n, __m,
__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __lhs,
const std::mersenne_twister_engine<_UIntType, __w, __n, __m,
__r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __rhs)
{ return !(__lhs == __rhs); }
/**
* @brief The Marsaglia-Zaman generator.
*
* This is a model of a Generalized Fibonacci discrete random number
* generator, sometimes referred to as the SWC generator.
*
* A discrete random number generator that produces pseudorandom
* numbers using:
* @f[
* x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m
* @f]
*
* The size of the state is @f$r@f$
* and the maximum period of the generator is @f$(m^r - m^s - 1)@f$.
*/
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
class subtract_with_carry_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(0u < __s && __s < __r,
"0 < s < r");
static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits,
"template argument substituting __w out of bounds");
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, subtract_with_carry_engine, _UIntType>::value>::type;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
// parameter values
static constexpr size_t word_size = __w;
static constexpr size_t short_lag = __s;
static constexpr size_t long_lag = __r;
static constexpr result_type default_seed = 19780503u;
subtract_with_carry_engine() : subtract_with_carry_engine(default_seed)
{ }
/**
* @brief Constructs an explicitly seeded %subtract_with_carry_engine
* random number generator.
*/
explicit
subtract_with_carry_engine(result_type __sd)
{ seed(__sd); }
/**
* @brief Constructs a %subtract_with_carry_engine random number engine
* seeded from the seed sequence @p __q.
*
* @param __q the seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
subtract_with_carry_engine(_Sseq& __q)
{ seed(__q); }
/**
* @brief Seeds the initial state @f$x_0@f$ of the random number
* generator.
*
* N1688[4.19] modifies this as follows. If @p __value == 0,
* sets value to 19780503. In any case, with a linear
* congruential generator lcg(i) having parameters @f$ m_{lcg} =
* 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value
* @f$, sets @f$ x_{-r} \dots x_{-1} @f$ to @f$ lcg(1) \bmod m
* \dots lcg(r) \bmod m @f$ respectively. If @f$ x_{-1} = 0 @f$
* set carry to 1, otherwise sets carry to 0.
*/
void
seed(result_type __sd = default_seed);
/**
* @brief Seeds the initial state @f$x_0@f$ of the
* % subtract_with_carry_engine random number generator.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q);
/**
* @brief Gets the inclusive minimum value of the range of random
* integers returned by this generator.
*/
static constexpr result_type
min()
{ return 0; }
/**
* @brief Gets the inclusive maximum value of the range of random
* integers returned by this generator.
*/
static constexpr result_type
max()
{ return __detail::_Shift<_UIntType, __w>::__value - 1; }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* @brief Gets the next random number in the sequence.
*/
result_type
operator()();
/**
* @brief Compares two % subtract_with_carry_engine random number
* generator objects of the same type for equality.
*
* @param __lhs A % subtract_with_carry_engine random number generator
* object.
* @param __rhs Another % subtract_with_carry_engine random number
* generator object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const subtract_with_carry_engine& __lhs,
const subtract_with_carry_engine& __rhs)
{ return (std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x)
&& __lhs._M_carry == __rhs._M_carry
&& __lhs._M_p == __rhs._M_p); }
/**
* @brief Inserts the current state of a % subtract_with_carry_engine
* random number generator engine @p __x into the output stream
* @p __os.
*
* @param __os An output stream.
* @param __x A % subtract_with_carry_engine random number generator
* engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::subtract_with_carry_engine<_UIntType1, __w1,
__s1, __r1>& __x);
/**
* @brief Extracts the current state of a % subtract_with_carry_engine
* random number generator engine @p __x from the input stream
* @p __is.
*
* @param __is An input stream.
* @param __x A % subtract_with_carry_engine random number generator
* engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _UIntType1, size_t __w1, size_t __s1, size_t __r1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::subtract_with_carry_engine<_UIntType1, __w1,
__s1, __r1>& __x);
private:
/// The state of the generator. This is a ring buffer.
_UIntType _M_x[long_lag];
_UIntType _M_carry; ///< The carry
size_t _M_p; ///< Current index of x(i - r).
};
/**
* @brief Compares two % subtract_with_carry_engine random number
* generator objects of the same type for inequality.
*
* @param __lhs A % subtract_with_carry_engine random number generator
* object.
* @param __rhs Another % subtract_with_carry_engine random number
* generator object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _UIntType, size_t __w, size_t __s, size_t __r>
inline bool
operator!=(const std::subtract_with_carry_engine<_UIntType, __w,
__s, __r>& __lhs,
const std::subtract_with_carry_engine<_UIntType, __w,
__s, __r>& __rhs)
{ return !(__lhs == __rhs); }
/**
* Produces random numbers from some base engine by discarding blocks of
* data.
*
* 0 <= @p __r <= @p __p
*/
template<typename _RandomNumberEngine, size_t __p, size_t __r>
class discard_block_engine
{
static_assert(1 <= __r && __r <= __p,
"template argument substituting __r out of bounds");
public:
/** The type of the generated random value. */
typedef typename _RandomNumberEngine::result_type result_type;
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, discard_block_engine, result_type>::value>::type;
// parameter values
static constexpr size_t block_size = __p;
static constexpr size_t used_block = __r;
/**
* @brief Constructs a default %discard_block_engine engine.
*
* The underlying engine is default constructed as well.
*/
discard_block_engine()
: _M_b(), _M_n(0) { }
/**
* @brief Copy constructs a %discard_block_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
discard_block_engine(const _RandomNumberEngine& __rng)
: _M_b(__rng), _M_n(0) { }
/**
* @brief Move constructs a %discard_block_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
discard_block_engine(_RandomNumberEngine&& __rng)
: _M_b(std::move(__rng)), _M_n(0) { }
/**
* @brief Seed constructs a %discard_block_engine engine.
*
* Constructs the underlying generator engine seeded with @p __s.
* @param __s A seed value for the base class engine.
*/
explicit
discard_block_engine(result_type __s)
: _M_b(__s), _M_n(0) { }
/**
* @brief Generator construct a %discard_block_engine engine.
*
* @param __q A seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
discard_block_engine(_Sseq& __q)
: _M_b(__q), _M_n(0)
{ }
/**
* @brief Reseeds the %discard_block_engine object with the default
* seed for the underlying base class generator engine.
*/
void
seed()
{
_M_b.seed();
_M_n = 0;
}
/**
* @brief Reseeds the %discard_block_engine object with the default
* seed for the underlying base class generator engine.
*/
void
seed(result_type __s)
{
_M_b.seed(__s);
_M_n = 0;
}
/**
* @brief Reseeds the %discard_block_engine object with the given seed
* sequence.
* @param __q A seed generator function.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q)
{
_M_b.seed(__q);
_M_n = 0;
}
/**
* @brief Gets a const reference to the underlying generator engine
* object.
*/
const _RandomNumberEngine&
base() const noexcept
{ return _M_b; }
/**
* @brief Gets the minimum value in the generated random number range.
*/
static constexpr result_type
min()
{ return _RandomNumberEngine::min(); }
/**
* @brief Gets the maximum value in the generated random number range.
*/
static constexpr result_type
max()
{ return _RandomNumberEngine::max(); }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* @brief Gets the next value in the generated random number sequence.
*/
result_type
operator()();
/**
* @brief Compares two %discard_block_engine random number generator
* objects of the same type for equality.
*
* @param __lhs A %discard_block_engine random number generator object.
* @param __rhs Another %discard_block_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const discard_block_engine& __lhs,
const discard_block_engine& __rhs)
{ return __lhs._M_b == __rhs._M_b && __lhs._M_n == __rhs._M_n; }
/**
* @brief Inserts the current state of a %discard_block_engine random
* number generator engine @p __x into the output stream
* @p __os.
*
* @param __os An output stream.
* @param __x A %discard_block_engine random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RandomNumberEngine1, size_t __p1, size_t __r1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::discard_block_engine<_RandomNumberEngine1,
__p1, __r1>& __x);
/**
* @brief Extracts the current state of a % subtract_with_carry_engine
* random number generator engine @p __x from the input stream
* @p __is.
*
* @param __is An input stream.
* @param __x A %discard_block_engine random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _RandomNumberEngine1, size_t __p1, size_t __r1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::discard_block_engine<_RandomNumberEngine1,
__p1, __r1>& __x);
private:
_RandomNumberEngine _M_b;
size_t _M_n;
};
/**
* @brief Compares two %discard_block_engine random number generator
* objects of the same type for inequality.
*
* @param __lhs A %discard_block_engine random number generator object.
* @param __rhs Another %discard_block_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _RandomNumberEngine, size_t __p, size_t __r>
inline bool
operator!=(const std::discard_block_engine<_RandomNumberEngine, __p,
__r>& __lhs,
const std::discard_block_engine<_RandomNumberEngine, __p,
__r>& __rhs)
{ return !(__lhs == __rhs); }
/**
* Produces random numbers by combining random numbers from some base
* engine to produce random numbers with a specified number of bits @p __w.
*/
template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
class independent_bits_engine
{
static_assert(std::is_unsigned<_UIntType>::value,
"result_type must be an unsigned integral type");
static_assert(0u < __w && __w <= std::numeric_limits<_UIntType>::digits,
"template argument substituting __w out of bounds");
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, independent_bits_engine, _UIntType>::value>::type;
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
/**
* @brief Constructs a default %independent_bits_engine engine.
*
* The underlying engine is default constructed as well.
*/
independent_bits_engine()
: _M_b() { }
/**
* @brief Copy constructs a %independent_bits_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
independent_bits_engine(const _RandomNumberEngine& __rng)
: _M_b(__rng) { }
/**
* @brief Move constructs a %independent_bits_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
independent_bits_engine(_RandomNumberEngine&& __rng)
: _M_b(std::move(__rng)) { }
/**
* @brief Seed constructs a %independent_bits_engine engine.
*
* Constructs the underlying generator engine seeded with @p __s.
* @param __s A seed value for the base class engine.
*/
explicit
independent_bits_engine(result_type __s)
: _M_b(__s) { }
/**
* @brief Generator construct a %independent_bits_engine engine.
*
* @param __q A seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
independent_bits_engine(_Sseq& __q)
: _M_b(__q)
{ }
/**
* @brief Reseeds the %independent_bits_engine object with the default
* seed for the underlying base class generator engine.
*/
void
seed()
{ _M_b.seed(); }
/**
* @brief Reseeds the %independent_bits_engine object with the default
* seed for the underlying base class generator engine.
*/
void
seed(result_type __s)
{ _M_b.seed(__s); }
/**
* @brief Reseeds the %independent_bits_engine object with the given
* seed sequence.
* @param __q A seed generator function.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q)
{ _M_b.seed(__q); }
/**
* @brief Gets a const reference to the underlying generator engine
* object.
*/
const _RandomNumberEngine&
base() const noexcept
{ return _M_b; }
/**
* @brief Gets the minimum value in the generated random number range.
*/
static constexpr result_type
min()
{ return 0U; }
/**
* @brief Gets the maximum value in the generated random number range.
*/
static constexpr result_type
max()
{ return __detail::_Shift<_UIntType, __w>::__value - 1; }
/**
* @brief Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* @brief Gets the next value in the generated random number sequence.
*/
result_type
operator()();
/**
* @brief Compares two %independent_bits_engine random number generator
* objects of the same type for equality.
*
* @param __lhs A %independent_bits_engine random number generator
* object.
* @param __rhs Another %independent_bits_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const independent_bits_engine& __lhs,
const independent_bits_engine& __rhs)
{ return __lhs._M_b == __rhs._M_b; }
/**
* @brief Extracts the current state of a % subtract_with_carry_engine
* random number generator engine @p __x from the input stream
* @p __is.
*
* @param __is An input stream.
* @param __x A %independent_bits_engine random number generator
* engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::independent_bits_engine<_RandomNumberEngine,
__w, _UIntType>& __x)
{
__is >> __x._M_b;
return __is;
}
private:
_RandomNumberEngine _M_b;
};
/**
* @brief Compares two %independent_bits_engine random number generator
* objects of the same type for inequality.
*
* @param __lhs A %independent_bits_engine random number generator
* object.
* @param __rhs Another %independent_bits_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
inline bool
operator!=(const std::independent_bits_engine<_RandomNumberEngine, __w,
_UIntType>& __lhs,
const std::independent_bits_engine<_RandomNumberEngine, __w,
_UIntType>& __rhs)
{ return !(__lhs == __rhs); }
/**
* @brief Inserts the current state of a %independent_bits_engine random
* number generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %independent_bits_engine random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RandomNumberEngine, size_t __w, typename _UIntType,
typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::independent_bits_engine<_RandomNumberEngine,
__w, _UIntType>& __x)
{
__os << __x.base();
return __os;
}
/**
* @brief Produces random numbers by reordering random numbers from some
* base engine.
*
* The values from the base engine are stored in a sequence of size @p __k
* and shuffled by an algorithm that depends on those values.
*/
template<typename _RandomNumberEngine, size_t __k>
class shuffle_order_engine
{
static_assert(1u <= __k, "template argument substituting "
"__k out of bound");
public:
/** The type of the generated random value. */
typedef typename _RandomNumberEngine::result_type result_type;
template<typename _Sseq>
using _If_seed_seq = typename enable_if<__detail::__is_seed_seq<
_Sseq, shuffle_order_engine, result_type>::value>::type;
static constexpr size_t table_size = __k;
/**
* @brief Constructs a default %shuffle_order_engine engine.
*
* The underlying engine is default constructed as well.
*/
shuffle_order_engine()
: _M_b()
{ _M_initialize(); }
/**
* @brief Copy constructs a %shuffle_order_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
shuffle_order_engine(const _RandomNumberEngine& __rng)
: _M_b(__rng)
{ _M_initialize(); }
/**
* @brief Move constructs a %shuffle_order_engine engine.
*
* Copies an existing base class random number generator.
* @param __rng An existing (base class) engine object.
*/
explicit
shuffle_order_engine(_RandomNumberEngine&& __rng)
: _M_b(std::move(__rng))
{ _M_initialize(); }
/**
* @brief Seed constructs a %shuffle_order_engine engine.
*
* Constructs the underlying generator engine seeded with @p __s.
* @param __s A seed value for the base class engine.
*/
explicit
shuffle_order_engine(result_type __s)
: _M_b(__s)
{ _M_initialize(); }
/**
* @brief Generator construct a %shuffle_order_engine engine.
*
* @param __q A seed sequence.
*/
template<typename _Sseq, typename = _If_seed_seq<_Sseq>>
explicit
shuffle_order_engine(_Sseq& __q)
: _M_b(__q)
{ _M_initialize(); }
/**
* @brief Reseeds the %shuffle_order_engine object with the default seed
for the underlying base class generator engine.
*/
void
seed()
{
_M_b.seed();
_M_initialize();
}
/**
* @brief Reseeds the %shuffle_order_engine object with the default seed
* for the underlying base class generator engine.
*/
void
seed(result_type __s)
{
_M_b.seed(__s);
_M_initialize();
}
/**
* @brief Reseeds the %shuffle_order_engine object with the given seed
* sequence.
* @param __q A seed generator function.
*/
template<typename _Sseq>
_If_seed_seq<_Sseq>
seed(_Sseq& __q)
{
_M_b.seed(__q);
_M_initialize();
}
/**
* Gets a const reference to the underlying generator engine object.
*/
const _RandomNumberEngine&
base() const noexcept
{ return _M_b; }
/**
* Gets the minimum value in the generated random number range.
*/
static constexpr result_type
min()
{ return _RandomNumberEngine::min(); }
/**
* Gets the maximum value in the generated random number range.
*/
static constexpr result_type
max()
{ return _RandomNumberEngine::max(); }
/**
* Discard a sequence of random numbers.
*/
void
discard(unsigned long long __z)
{
for (; __z != 0ULL; --__z)
(*this)();
}
/**
* Gets the next value in the generated random number sequence.
*/
result_type
operator()();
/**
* Compares two %shuffle_order_engine random number generator objects
* of the same type for equality.
*
* @param __lhs A %shuffle_order_engine random number generator object.
* @param __rhs Another %shuffle_order_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be equal, false otherwise.
*/
friend bool
operator==(const shuffle_order_engine& __lhs,
const shuffle_order_engine& __rhs)
{ return (__lhs._M_b == __rhs._M_b
&& std::equal(__lhs._M_v, __lhs._M_v + __k, __rhs._M_v)
&& __lhs._M_y == __rhs._M_y); }
/**
* @brief Inserts the current state of a %shuffle_order_engine random
* number generator engine @p __x into the output stream
@p __os.
*
* @param __os An output stream.
* @param __x A %shuffle_order_engine random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RandomNumberEngine1, size_t __k1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::shuffle_order_engine<_RandomNumberEngine1,
__k1>& __x);
/**
* @brief Extracts the current state of a % subtract_with_carry_engine
* random number generator engine @p __x from the input stream
* @p __is.
*
* @param __is An input stream.
* @param __x A %shuffle_order_engine random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _RandomNumberEngine1, size_t __k1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::shuffle_order_engine<_RandomNumberEngine1, __k1>& __x);
private:
void _M_initialize()
{
for (size_t __i = 0; __i < __k; ++__i)
_M_v[__i] = _M_b();
_M_y = _M_b();
}
_RandomNumberEngine _M_b;
result_type _M_v[__k];
result_type _M_y;
};
/**
* Compares two %shuffle_order_engine random number generator objects
* of the same type for inequality.
*
* @param __lhs A %shuffle_order_engine random number generator object.
* @param __rhs Another %shuffle_order_engine random number generator
* object.
*
* @returns true if the infinite sequences of generated values
* would be different, false otherwise.
*/
template<typename _RandomNumberEngine, size_t __k>
inline bool
operator!=(const std::shuffle_order_engine<_RandomNumberEngine,
__k>& __lhs,
const std::shuffle_order_engine<_RandomNumberEngine,
__k>& __rhs)
{ return !(__lhs == __rhs); }
/**
* The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
*/
typedef linear_congruential_engine<uint_fast32_t, 16807UL, 0UL, 2147483647UL>
minstd_rand0;
/**
* An alternative LCR (Lehmer Generator function).
*/
typedef linear_congruential_engine<uint_fast32_t, 48271UL, 0UL, 2147483647UL>
minstd_rand;
/**
* The classic Mersenne Twister.
*
* Reference:
* M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-Dimensionally
* Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions
* on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.
*/
typedef mersenne_twister_engine<
uint_fast32_t,
32, 624, 397, 31,
0x9908b0dfUL, 11,
0xffffffffUL, 7,
0x9d2c5680UL, 15,
0xefc60000UL, 18, 1812433253UL> mt19937;
/**
* An alternative Mersenne Twister.
*/
typedef mersenne_twister_engine<
uint_fast64_t,
64, 312, 156, 31,
0xb5026f5aa96619e9ULL, 29,
0x5555555555555555ULL, 17,
0x71d67fffeda60000ULL, 37,
0xfff7eee000000000ULL, 43,
6364136223846793005ULL> mt19937_64;
typedef subtract_with_carry_engine<uint_fast32_t, 24, 10, 24>
ranlux24_base;
typedef subtract_with_carry_engine<uint_fast64_t, 48, 5, 12>
ranlux48_base;
typedef discard_block_engine<ranlux24_base, 223, 23> ranlux24;
typedef discard_block_engine<ranlux48_base, 389, 11> ranlux48;
typedef shuffle_order_engine<minstd_rand0, 256> knuth_b;
typedef minstd_rand0 default_random_engine;
/**
* A standard interface to a platform-specific non-deterministic
* random number generator (if any are available).
*/
class random_device
{
public:
/** The type of the generated random value. */
typedef unsigned int result_type;
// constructors, destructors and member functions
random_device() { _M_init("default"); }
explicit
random_device(const std::string& __token) { _M_init(__token); }
#if defined _GLIBCXX_USE_DEV_RANDOM
~random_device()
{ _M_fini(); }
#endif
static constexpr result_type
min()
{ return std::numeric_limits<result_type>::min(); }
static constexpr result_type
max()
{ return std::numeric_limits<result_type>::max(); }
double
entropy() const noexcept
{
#ifdef _GLIBCXX_USE_DEV_RANDOM
return this->_M_getentropy();
#else
return 0.0;
#endif
}
result_type
operator()()
{ return this->_M_getval(); }
// No copy functions.
random_device(const random_device&) = delete;
void operator=(const random_device&) = delete;
private:
void _M_init(const std::string& __token);
void _M_init_pretr1(const std::string& __token);
void _M_fini();
result_type _M_getval();
result_type _M_getval_pretr1();
double _M_getentropy() const noexcept;
void _M_init(const char*, size_t); // not exported from the shared library
__extension__ union
{
struct
{
void* _M_file;
result_type (*_M_func)(void*);
int _M_fd;
};
mt19937 _M_mt;
};
};
/// @} group random_generators
/**
* @addtogroup random_distributions Random Number Distributions
* @ingroup random
* @{
*/
/**
* @addtogroup random_distributions_uniform Uniform Distributions
* @ingroup random_distributions
* @{
*/
// std::uniform_int_distribution is defined in <bits/uniform_int_dist.h>
/**
* @brief Return true if two uniform integer distributions have
* different parameters.
*/
template<typename _IntType>
inline bool
operator!=(const std::uniform_int_distribution<_IntType>& __d1,
const std::uniform_int_distribution<_IntType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief Inserts a %uniform_int_distribution random number
* distribution @p __x into the output stream @p os.
*
* @param __os An output stream.
* @param __x A %uniform_int_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>&,
const std::uniform_int_distribution<_IntType>&);
/**
* @brief Extracts a %uniform_int_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %uniform_int_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _IntType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>&,
std::uniform_int_distribution<_IntType>&);
/**
* @brief Uniform continuous distribution for random numbers.
*
* A continuous random distribution on the range [min, max) with equal
* probability throughout the range. The URNG should be real-valued and
* deliver number in the range [0, 1).
*/
template<typename _RealType = double>
class uniform_real_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef uniform_real_distribution<_RealType> distribution_type;
param_type() : param_type(0) { }
explicit
param_type(_RealType __a, _RealType __b = _RealType(1))
: _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:
_RealType _M_a;
_RealType _M_b;
};
public:
/**
* @brief Constructs a uniform_real_distribution object.
*
* The lower bound is set to 0.0 and the upper bound to 1.0
*/
uniform_real_distribution() : uniform_real_distribution(0.0) { }
/**
* @brief Constructs a uniform_real_distribution object.
*
* @param __a [IN] The lower bound of the distribution.
* @param __b [IN] The upper bound of the distribution.
*/
explicit
uniform_real_distribution(_RealType __a, _RealType __b = _RealType(1))
: _M_param(__a, __b)
{ }
explicit
uniform_real_distribution(const param_type& __p)
: _M_param(__p)
{ }
/**
* @brief Resets the distribution state.
*
* Does nothing for the uniform real 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 _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return this->operator()(__urng, _M_param); }
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
__aurng(__urng);
return (__aurng() * (__p.b() - __p.a())) + __p.a();
}
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate(__f, __t, __urng, _M_param); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
/**
* @brief Return true if two uniform real distributions have
* the same parameters.
*/
friend bool
operator==(const uniform_real_distribution& __d1,
const uniform_real_distribution& __d2)
{ return __d1._M_param == __d2._M_param; }
private:
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p);
param_type _M_param;
};
/**
* @brief Return true if two uniform real distributions have
* different parameters.
*/
template<typename _IntType>
inline bool
operator!=(const std::uniform_real_distribution<_IntType>& __d1,
const std::uniform_real_distribution<_IntType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief Inserts a %uniform_real_distribution random number
* distribution @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %uniform_real_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>&,
const std::uniform_real_distribution<_RealType>&);
/**
* @brief Extracts a %uniform_real_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %uniform_real_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _RealType, typename _CharT, typename _Traits>
std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>&,
std::uniform_real_distribution<_RealType>&);
/// @} group random_distributions_uniform
/**
* @addtogroup random_distributions_normal Normal Distributions
* @ingroup random_distributions
* @{
*/
/**
* @brief A normal continuous distribution for random numbers.
*
* The formula for the normal probability density function is
* @f[
* p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}}
* e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} }
* @f]
*/
template<typename _RealType = double>
class normal_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef normal_distribution<_RealType> distribution_type;
param_type() : param_type(0.0) { }
explicit
param_type(_RealType __mean, _RealType __stddev = _RealType(1))
: _M_mean(__mean), _M_stddev(__stddev)
{
__glibcxx_assert(_M_stddev > _RealType(0));
}
_RealType
mean() const
{ return _M_mean; }
_RealType
stddev() const
{ return _M_stddev; }
friend bool
operator==(const param_type& __p1, const param_type& __p2)
{ return (__p1._M_mean == __p2._M_mean
&& __p1._M_stddev == __p2._M_stddev); }
friend bool
operator!=(const param_type& __p1, const param_type& __p2)
{ return !(__p1 == __p2); }
private:
_RealType _M_mean;
_RealType _M_stddev;
};
public:
normal_distribution() : normal_distribution(0.0) { }
/**
* Constructs a normal distribution with parameters @f$mean@f$ and
* standard deviation.
*/
explicit
normal_distribution(result_type __mean,
result_type __stddev = result_type(1))
: _M_param(__mean, __stddev)
{ }
explicit
normal_distribution(const param_type& __p)
: _M_param(__p)
{ }
/**
* @brief Resets the distribution state.
*/
void
reset()
{ _M_saved_available = false; }
/**
* @brief Returns the mean of the distribution.
*/
_RealType
mean() const
{ return _M_param.mean(); }
/**
* @brief Returns the standard deviation of the distribution.
*/
_RealType
stddev() const
{ return _M_param.stddev(); }
/**
* @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 greatest lower bound value of the distribution.
*/
result_type
min() const
{ return std::numeric_limits<result_type>::lowest(); }
/**
* @brief Returns the least upper bound value of the distribution.
*/
result_type
max() const
{ return std::numeric_limits<result_type>::max(); }
/**
* @brief Generating functions.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return this->operator()(__urng, _M_param); }
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p);
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate(__f, __t, __urng, _M_param); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
/**
* @brief Return true if two normal distributions have
* the same parameters and the sequences that would
* be generated are equal.
*/
template<typename _RealType1>
friend bool
operator==(const std::normal_distribution<_RealType1>& __d1,
const std::normal_distribution<_RealType1>& __d2);
/**
* @brief Inserts a %normal_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %normal_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::normal_distribution<_RealType1>& __x);
/**
* @brief Extracts a %normal_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %normal_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error
* state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::normal_distribution<_RealType1>& __x);
private:
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p);
param_type _M_param;
result_type _M_saved = 0;
bool _M_saved_available = false;
};
/**
* @brief Return true if two normal distributions are different.
*/
template<typename _RealType>
inline bool
operator!=(const std::normal_distribution<_RealType>& __d1,
const std::normal_distribution<_RealType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief A lognormal_distribution random number distribution.
*
* The formula for the normal probability mass function is
* @f[
* p(x|m,s) = \frac{1}{sx\sqrt{2\pi}}
* \exp{-\frac{(\ln{x} - m)^2}{2s^2}}
* @f]
*/
template<typename _RealType = double>
class lognormal_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef lognormal_distribution<_RealType> distribution_type;
param_type() : param_type(0.0) { }
explicit
param_type(_RealType __m, _RealType __s = _RealType(1))
: _M_m(__m), _M_s(__s)
{ }
_RealType
m() const
{ return _M_m; }
_RealType
s() const
{ return _M_s; }
friend bool
operator==(const param_type& __p1, const param_type& __p2)
{ return __p1._M_m == __p2._M_m && __p1._M_s == __p2._M_s; }
friend bool
operator!=(const param_type& __p1, const param_type& __p2)
{ return !(__p1 == __p2); }
private:
_RealType _M_m;
_RealType _M_s;
};
lognormal_distribution() : lognormal_distribution(0.0) { }
explicit
lognormal_distribution(_RealType __m, _RealType __s = _RealType(1))
: _M_param(__m, __s), _M_nd()
{ }
explicit
lognormal_distribution(const param_type& __p)
: _M_param(__p), _M_nd()
{ }
/**
* Resets the distribution state.
*/
void
reset()
{ _M_nd.reset(); }
/**
*
*/
_RealType
m() const
{ return _M_param.m(); }
_RealType
s() const
{ return _M_param.s(); }
/**
* @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 greatest lower bound value of the distribution.
*/
result_type
min() const
{ return result_type(0); }
/**
* @brief Returns the least upper bound value of the distribution.
*/
result_type
max() const
{ return std::numeric_limits<result_type>::max(); }
/**
* @brief Generating functions.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return this->operator()(__urng, _M_param); }
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ return std::exp(__p.s() * _M_nd(__urng) + __p.m()); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate(__f, __t, __urng, _M_param); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
/**
* @brief Return true if two lognormal distributions have
* the same parameters and the sequences that would
* be generated are equal.
*/
friend bool
operator==(const lognormal_distribution& __d1,
const lognormal_distribution& __d2)
{ return (__d1._M_param == __d2._M_param
&& __d1._M_nd == __d2._M_nd); }
/**
* @brief Inserts a %lognormal_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %lognormal_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::lognormal_distribution<_RealType1>& __x);
/**
* @brief Extracts a %lognormal_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %lognormal_distribution random number
* generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::lognormal_distribution<_RealType1>& __x);
private:
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p);
param_type _M_param;
std::normal_distribution<result_type> _M_nd;
};
/**
* @brief Return true if two lognormal distributions are different.
*/
template<typename _RealType>
inline bool
operator!=(const std::lognormal_distribution<_RealType>& __d1,
const std::lognormal_distribution<_RealType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief A gamma continuous distribution for random numbers.
*
* The formula for the gamma probability density function is:
* @f[
* p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)}
* (x/\beta)^{\alpha - 1} e^{-x/\beta}
* @f]
*/
template<typename _RealType = double>
class gamma_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef gamma_distribution<_RealType> distribution_type;
friend class gamma_distribution<_RealType>;
param_type() : param_type(1.0) { }
explicit
param_type(_RealType __alpha_val, _RealType __beta_val = _RealType(1))
: _M_alpha(__alpha_val), _M_beta(__beta_val)
{
__glibcxx_assert(_M_alpha > _RealType(0));
_M_initialize();
}
_RealType
alpha() const
{ return _M_alpha; }
_RealType
beta() const
{ return _M_beta; }
friend bool
operator==(const param_type& __p1, const param_type& __p2)
{ return (__p1._M_alpha == __p2._M_alpha
&& __p1._M_beta == __p2._M_beta); }
friend bool
operator!=(const param_type& __p1, const param_type& __p2)
{ return !(__p1 == __p2); }
private:
void
_M_initialize();
_RealType _M_alpha;
_RealType _M_beta;
_RealType _M_malpha, _M_a2;
};
public:
/**
* @brief Constructs a gamma distribution with parameters 1 and 1.
*/
gamma_distribution() : gamma_distribution(1.0) { }
/**
* @brief Constructs a gamma distribution with parameters
* @f$\alpha@f$ and @f$\beta@f$.
*/
explicit
gamma_distribution(_RealType __alpha_val,
_RealType __beta_val = _RealType(1))
: _M_param(__alpha_val, __beta_val), _M_nd()
{ }
explicit
gamma_distribution(const param_type& __p)
: _M_param(__p), _M_nd()
{ }
/**
* @brief Resets the distribution state.
*/
void
reset()
{ _M_nd.reset(); }
/**
* @brief Returns the @f$\alpha@f$ of the distribution.
*/
_RealType
alpha() const
{ return _M_param.alpha(); }
/**
* @brief Returns the @f$\beta@f$ of the distribution.
*/
_RealType
beta() const
{ return _M_param.beta(); }
/**
* @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 greatest lower bound value of the distribution.
*/
result_type
min() const
{ return result_type(0); }
/**
* @brief Returns the least upper bound value of the distribution.
*/
result_type
max() const
{ return std::numeric_limits<result_type>::max(); }
/**
* @brief Generating functions.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return this->operator()(__urng, _M_param); }
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p);
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate(__f, __t, __urng, _M_param); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ this->__generate_impl(__f, __t, __urng, __p); }
/**
* @brief Return true if two gamma distributions have the same
* parameters and the sequences that would be generated
* are equal.
*/
friend bool
operator==(const gamma_distribution& __d1,
const gamma_distribution& __d2)
{ return (__d1._M_param == __d2._M_param
&& __d1._M_nd == __d2._M_nd); }
/**
* @brief Inserts a %gamma_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %gamma_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::gamma_distribution<_RealType1>& __x);
/**
* @brief Extracts a %gamma_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %gamma_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::gamma_distribution<_RealType1>& __x);
private:
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p);
param_type _M_param;
std::normal_distribution<result_type> _M_nd;
};
/**
* @brief Return true if two gamma distributions are different.
*/
template<typename _RealType>
inline bool
operator!=(const std::gamma_distribution<_RealType>& __d1,
const std::gamma_distribution<_RealType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief A chi_squared_distribution random number distribution.
*
* The formula for the normal probability mass function is
* @f$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}@f$
*/
template<typename _RealType = double>
class chi_squared_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef chi_squared_distribution<_RealType> distribution_type;
param_type() : param_type(1) { }
explicit
param_type(_RealType __n)
: _M_n(__n)
{ }
_RealType
n() const
{ return _M_n; }
friend bool
operator==(const param_type& __p1, const param_type& __p2)
{ return __p1._M_n == __p2._M_n; }
friend bool
operator!=(const param_type& __p1, const param_type& __p2)
{ return !(__p1 == __p2); }
private:
_RealType _M_n;
};
chi_squared_distribution() : chi_squared_distribution(1) { }
explicit
chi_squared_distribution(_RealType __n)
: _M_param(__n), _M_gd(__n / 2)
{ }
explicit
chi_squared_distribution(const param_type& __p)
: _M_param(__p), _M_gd(__p.n() / 2)
{ }
/**
* @brief Resets the distribution state.
*/
void
reset()
{ _M_gd.reset(); }
/**
*
*/
_RealType
n() const
{ return _M_param.n(); }
/**
* @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;
typedef typename std::gamma_distribution<result_type>::param_type
param_type;
_M_gd.param(param_type{__param.n() / 2});
}
/**
* @brief Returns the greatest lower bound value of the distribution.
*/
result_type
min() const
{ return result_type(0); }
/**
* @brief Returns the least upper bound value of the distribution.
*/
result_type
max() const
{ return std::numeric_limits<result_type>::max(); }
/**
* @brief Generating functions.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return 2 * _M_gd(__urng); }
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{
typedef typename std::gamma_distribution<result_type>::param_type
param_type;
return 2 * _M_gd(__urng, param_type(__p.n() / 2));
}
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate_impl(__f, __t, __urng); }
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ typename std::gamma_distribution<result_type>::param_type
__p2(__p.n() / 2);
this->__generate_impl(__f, __t, __urng, __p2); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng)
{ this->__generate_impl(__f, __t, __urng); }
template<typename _UniformRandomNumberGenerator>
void
__generate(result_type* __f, result_type* __t,
_UniformRandomNumberGenerator& __urng,
const param_type& __p)
{ typename std::gamma_distribution<result_type>::param_type
__p2(__p.n() / 2);
this->__generate_impl(__f, __t, __urng, __p2); }
/**
* @brief Return true if two Chi-squared distributions have
* the same parameters and the sequences that would be
* generated are equal.
*/
friend bool
operator==(const chi_squared_distribution& __d1,
const chi_squared_distribution& __d2)
{ return __d1._M_param == __d2._M_param && __d1._M_gd == __d2._M_gd; }
/**
* @brief Inserts a %chi_squared_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %chi_squared_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const std::chi_squared_distribution<_RealType1>& __x);
/**
* @brief Extracts a %chi_squared_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %chi_squared_distribution random number
* generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
std::chi_squared_distribution<_RealType1>& __x);
private:
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng);
template<typename _ForwardIterator,
typename _UniformRandomNumberGenerator>
void
__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
_UniformRandomNumberGenerator& __urng,
const typename
std::gamma_distribution<result_type>::param_type& __p);
param_type _M_param;
std::gamma_distribution<result_type> _M_gd;
};
/**
* @brief Return true if two Chi-squared distributions are different.
*/
template<typename _RealType>
inline bool
operator!=(const std::chi_squared_distribution<_RealType>& __d1,
const std::chi_squared_distribution<_RealType>& __d2)
{ return !(__d1 == __d2); }
/**
* @brief A cauchy_distribution random number distribution.
*
* The formula for the normal probability mass function is
* @f$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}@f$
*/
template<typename _RealType = double>
class cauchy_distribution
{
static_assert(std::is_floating_point<_RealType>::value,
"result_type must be a floating point type");
public:
/** The type of the range of the distribution. */
typedef _RealType result_type;
/** Parameter type. */
struct param_type
{
typedef cauchy_distribution<_RealType> distribution_type;
param_type() : param_type(0) { }
explicit
param_type(_RealType __a, _RealType __b = _RealType(1))
: _M_a(__a), _M_b(__b)
{ }
_RealType
a() const
{ return _M_a; }
_RealType
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:
_RealType _M_a;
_RealType _M_b;
};
cauchy_distribution() : cauchy_distribution(0.0) { }
explicit
cauchy_distribution(_RealType __a, _RealType __b = 1.0)
: _M_param(__a, __b)
{ }
explicit
cauchy_distribution(const param_type& __p)
: _M_param(__p)
{ }
/**
* @brief Resets the distribution state.
*/
void
reset()
{ }
/**
*
*/
_RealType
a() const
{ return _M_param.a(); }
_RealType
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 distrib