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// random number generation -*- C++ -*-
// Copyright (C) 2009-2020 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 tr1/random.h
* This is an internal header file, included by other library headers.
* Do not attempt to use it directly. @headername{tr1/random}
*/
#ifndef _GLIBCXX_TR1_RANDOM_H
#define _GLIBCXX_TR1_RANDOM_H 1
#pragma GCC system_header
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
namespace tr1
{
// [5.1] Random number generation
/**
* @addtogroup tr1_random Random Number Generation
* A facility for generating random numbers on selected distributions.
* @{
*/
/*
* Implementation-space details.
*/
namespace __detail
{
template<typename _UIntType, int __w,
bool = __w < std::numeric_limits<_UIntType>::digits>
struct _Shift
{ static const _UIntType __value = 0; };
template<typename _UIntType, int __w>
struct _Shift<_UIntType, __w, true>
{ static const _UIntType __value = _UIntType(1) << __w; };
template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
struct _Mod;
// Dispatch based on modulus value to prevent divide-by-zero compile-time
// errors when m == 0.
template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
inline _Tp
__mod(_Tp __x)
{ return _Mod<_Tp, __a, __c, __m, __m == 0>::__calc(__x); }
typedef __gnu_cxx::__conditional_type<(sizeof(unsigned) == 4),
unsigned, unsigned long>::__type _UInt32Type;
/*
* An adaptor class for converting the output of any Generator into
* the input for a specific Distribution.
*/
template<typename _Engine, typename _Distribution>
struct _Adaptor
{
typedef typename remove_reference<_Engine>::type _BEngine;
typedef typename _BEngine::result_type _Engine_result_type;
typedef typename _Distribution::input_type result_type;
public:
_Adaptor(const _Engine& __g)
: _M_g(__g) { }
result_type
min() const
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = _M_g.min();
else
__return_value = result_type(0);
return __return_value;
}
result_type
max() const
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = _M_g.max();
else if (!is_integral<result_type>::value)
__return_value = result_type(1);
else
__return_value = std::numeric_limits<result_type>::max() - 1;
return __return_value;
}
/*
* Converts a value generated by the adapted random number generator
* into a value in the input domain for the dependent random number
* distribution.
*
* Because the type traits are compile time constants only the
* appropriate clause of the if statements will actually be emitted
* by the compiler.
*/
result_type
operator()()
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = _M_g();
else if (!is_integral<_Engine_result_type>::value
&& !is_integral<result_type>::value)
__return_value = result_type(_M_g() - _M_g.min())
/ result_type(_M_g.max() - _M_g.min());
else if (is_integral<_Engine_result_type>::value
&& !is_integral<result_type>::value)
__return_value = result_type(_M_g() - _M_g.min())
/ result_type(_M_g.max() - _M_g.min() + result_type(1));
else
__return_value = (((_M_g() - _M_g.min())
/ (_M_g.max() - _M_g.min()))
* std::numeric_limits<result_type>::max());
return __return_value;
}
private:
_Engine _M_g;
};
// Specialization for _Engine*.
template<typename _Engine, typename _Distribution>
struct _Adaptor<_Engine*, _Distribution>
{
typedef typename _Engine::result_type _Engine_result_type;
typedef typename _Distribution::input_type result_type;
public:
_Adaptor(_Engine* __g)
: _M_g(__g) { }
result_type
min() const
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = _M_g->min();
else
__return_value = result_type(0);
return __return_value;
}
result_type
max() const
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = _M_g->max();
else if (!is_integral<result_type>::value)
__return_value = result_type(1);
else
__return_value = std::numeric_limits<result_type>::max() - 1;
return __return_value;
}
result_type
operator()()
{
result_type __return_value;
if (is_integral<_Engine_result_type>::value
&& is_integral<result_type>::value)
__return_value = (*_M_g)();
else if (!is_integral<_Engine_result_type>::value
&& !is_integral<result_type>::value)
__return_value = result_type((*_M_g)() - _M_g->min())
/ result_type(_M_g->max() - _M_g->min());
else if (is_integral<_Engine_result_type>::value
&& !is_integral<result_type>::value)
__return_value = result_type((*_M_g)() - _M_g->min())
/ result_type(_M_g->max() - _M_g->min() + result_type(1));
else
__return_value = ((((*_M_g)() - _M_g->min())
/ (_M_g->max() - _M_g->min()))
* std::numeric_limits<result_type>::max());
return __return_value;
}
private:
_Engine* _M_g;
};
} // namespace __detail
/**
* Produces random numbers on a given distribution function using a
* non-uniform random number generation engine.
*
* @todo the engine_value_type needs to be studied more carefully.
*/
template<typename _Engine, typename _Dist>
class variate_generator
{
// Concept requirements.
__glibcxx_class_requires(_Engine, _CopyConstructibleConcept)
// __glibcxx_class_requires(_Engine, _EngineConcept)
// __glibcxx_class_requires(_Dist, _EngineConcept)
public:
typedef _Engine engine_type;
typedef __detail::_Adaptor<_Engine, _Dist> engine_value_type;
typedef _Dist distribution_type;
typedef typename _Dist::result_type result_type;
// tr1:5.1.1 table 5.1 requirement
typedef typename __gnu_cxx::__enable_if<
is_arithmetic<result_type>::value, result_type>::__type _IsValidType;
/**
* Constructs a variate generator with the uniform random number
* generator @p __eng for the random distribution @p __dist.
*
* @throws Any exceptions which may thrown by the copy constructors of
* the @p _Engine or @p _Dist objects.
*/
variate_generator(engine_type __eng, distribution_type __dist)
: _M_engine(__eng), _M_dist(__dist) { }
/**
* Gets the next generated value on the distribution.
*/
result_type
operator()()
{ return _M_dist(_M_engine); }
/**
* WTF?
*/
template<typename _Tp>
result_type
operator()(_Tp __value)
{ return _M_dist(_M_engine, __value); }
/**
* Gets a reference to the underlying uniform random number generator
* object.
*/
engine_value_type&
engine()
{ return _M_engine; }
/**
* Gets a const reference to the underlying uniform random number
* generator object.
*/
const engine_value_type&
engine() const
{ return _M_engine; }
/**
* Gets a reference to the underlying random distribution.
*/
distribution_type&
distribution()
{ return _M_dist; }
/**
* Gets a const reference to the underlying random distribution.
*/
const distribution_type&
distribution() const
{ return _M_dist; }
/**
* Gets the closed lower bound of the distribution interval.
*/
result_type
min() const
{ return this->distribution().min(); }
/**
* Gets the closed upper bound of the distribution interval.
*/
result_type
max() const
{ return this->distribution().max(); }
private:
engine_value_type _M_engine;
distribution_type _M_dist;
};
/**
* @addtogroup tr1_random_generators Random Number Generators
* @ingroup tr1_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 using the
* 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<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
class linear_congruential
{
__glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
// __glibcpp_class_requires(__a < __m && __c < __m)
public:
/** The type of the generated random value. */
typedef _UIntType result_type;
/** The multiplier. */
static const _UIntType multiplier = __a;
/** An increment. */
static const _UIntType increment = __c;
/** The modulus. */
static const _UIntType modulus = __m;
/**
* Constructs a %linear_congruential random number generator engine with
* seed @p __s. The default seed value is 1.
*
* @param __s The initial seed value.
*/
explicit
linear_congruential(unsigned long __x0 = 1)
{ this->seed(__x0); }
/**
* Constructs a %linear_congruential random number generator engine
* seeded from the generator function @p __g.
*
* @param __g The seed generator function.
*/
template<class _Gen>
linear_congruential(_Gen& __g)
{ this->seed(__g); }
/**
* Reseeds the %linear_congruential random number generator engine
* sequence to the seed @g __s.
*
* @param __s The new seed.
*/
void
seed(unsigned long __s = 1);
/**
* Reseeds the %linear_congruential random number generator engine
* sequence using values from the generator function @p __g.
*
* @param __g the seed generator function.
*/
template<class _Gen>
void
seed(_Gen& __g)
{ seed(__g, typename is_fundamental<_Gen>::type()); }
/**
* 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.
*/
result_type
min() const
{ return (__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0) ? 1 : 0; }
/**
* Gets the largest possible value in the output range.
*/
result_type
max() const
{ return __m - 1; }
/**
* Gets the next random number in the sequence.
*/
result_type
operator()();
/**
* 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 obj.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const linear_congruential& __lhs,
const linear_congruential& __rhs)
{ return __lhs._M_x == __rhs._M_x; }
/**
* 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 obj.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const linear_congruential& __lhs,
const linear_congruential& __rhs)
{ return !(__lhs == __rhs); }
/**
* Writes the textual representation of the state x(i) of x to @p __os.
*
* @param __os The output stream.
* @param __lcr A % linear_congruential random number generator.
* @returns __os.
*/
template<class _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 linear_congruential<_UIntType1, __a1, __c1,
__m1>& __lcr);
/**
* 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 random number generator.
* @returns __is.
*/
template<class _UIntType1, _UIntType1 __a1, _UIntType1 __c1,
_UIntType1 __m1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
linear_congruential<_UIntType1, __a1, __c1, __m1>& __lcr);
private:
template<class _Gen>
void
seed(_Gen& __g, true_type)
{ return seed(static_cast<unsigned long>(__g)); }
template<class _Gen>
void
seed(_Gen& __g, false_type);
_UIntType _M_x;
};
/**
* The classic Minimum Standard rand0 of Lewis, Goodman, and Miller.
*/
typedef linear_congruential<unsigned long, 16807, 0, 2147483647> minstd_rand0;
/**
* An alternative LCR (Lehmer Generator function) .
*/
typedef linear_congruential<unsigned long, 48271, 0, 2147483647> minstd_rand;
/**
* 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.
*
* @var word_size The number of bits in each element of the state vector.
* @var state_size The degree of recursion.
* @var shift_size The period parameter.
* @var mask_bits The separation point bit index.
* @var parameter_a The last row of the twist matrix.
* @var output_u The first right-shift tempering matrix parameter.
* @var output_s The first left-shift tempering matrix parameter.
* @var output_b The first left-shift tempering matrix mask.
* @var output_t The second left-shift tempering matrix parameter.
* @var output_c The second left-shift tempering matrix mask.
* @var output_l The second right-shift tempering matrix parameter.
*/
template<class _UIntType, int __w, int __n, int __m, int __r,
_UIntType __a, int __u, int __s, _UIntType __b, int __t,
_UIntType __c, int __l>
class mersenne_twister
{
__glibcxx_class_requires(_UIntType, _UnsignedIntegerConcept)
public:
// types
typedef _UIntType result_type;
// parameter values
static const int word_size = __w;
static const int state_size = __n;
static const int shift_size = __m;
static const int mask_bits = __r;
static const _UIntType parameter_a = __a;
static const int output_u = __u;
static const int output_s = __s;
static const _UIntType output_b = __b;
static const int output_t = __t;
static const _UIntType output_c = __c;
static const int output_l = __l;
// constructors and member function
mersenne_twister()
{ seed(); }
explicit
mersenne_twister(unsigned long __value)
{ seed(__value); }
template<class _Gen>
mersenne_twister(_Gen& __g)
{ seed(__g); }
void
seed()
{ seed(5489UL); }
void
seed(unsigned long __value);
template<class _Gen>
void
seed(_Gen& __g)
{ seed(__g, typename is_fundamental<_Gen>::type()); }
result_type
min() const
{ return 0; }
result_type
max() const
{ return __detail::_Shift<_UIntType, __w>::__value - 1; }
result_type
operator()();
/**
* Compares two % mersenne_twister random number generator objects of
* the same type for equality.
*
* @param __lhs A % mersenne_twister random number generator object.
* @param __rhs Another % mersenne_twister random number generator
* object.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const mersenne_twister& __lhs,
const mersenne_twister& __rhs)
{ return std::equal(__lhs._M_x, __lhs._M_x + state_size, __rhs._M_x); }
/**
* Compares two % mersenne_twister random number generator objects of
* the same type for inequality.
*
* @param __lhs A % mersenne_twister random number generator object.
* @param __rhs Another % mersenne_twister random number generator
* object.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const mersenne_twister& __lhs,
const mersenne_twister& __rhs)
{ return !(__lhs == __rhs); }
/**
* Inserts the current state of a % mersenne_twister random number
* generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A % mersenne_twister random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
_UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
_UIntType1 __c1, int __l1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
__a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
/**
* Extracts the current state of a % mersenne_twister random number
* generator engine @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A % mersenne_twister random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<class _UIntType1, int __w1, int __n1, int __m1, int __r1,
_UIntType1 __a1, int __u1, int __s1, _UIntType1 __b1, int __t1,
_UIntType1 __c1, int __l1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
mersenne_twister<_UIntType1, __w1, __n1, __m1, __r1,
__a1, __u1, __s1, __b1, __t1, __c1, __l1>& __x);
private:
template<class _Gen>
void
seed(_Gen& __g, true_type)
{ return seed(static_cast<unsigned long>(__g)); }
template<class _Gen>
void
seed(_Gen& __g, false_type);
_UIntType _M_x[state_size];
int _M_p;
};
/**
* 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<
unsigned long, 32, 624, 397, 31,
0x9908b0dful, 11, 7,
0x9d2c5680ul, 15,
0xefc60000ul, 18
> mt19937;
/**
* @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$.
*
* N1688[4.13] says <em>the template parameter _IntType shall denote
* an integral type large enough to store values up to m</em>.
*
* @var _M_x The state of the generator. This is a ring buffer.
* @var _M_carry The carry.
* @var _M_p Current index of x(i - r).
*/
template<typename _IntType, _IntType __m, int __s, int __r>
class subtract_with_carry
{
__glibcxx_class_requires(_IntType, _IntegerConcept)
public:
/** The type of the generated random value. */
typedef _IntType result_type;
// parameter values
static const _IntType modulus = __m;
static const int long_lag = __r;
static const int short_lag = __s;
/**
* Constructs a default-initialized % subtract_with_carry random number
* generator.
*/
subtract_with_carry()
{ this->seed(); }
/**
* Constructs an explicitly seeded % subtract_with_carry random number
* generator.
*/
explicit
subtract_with_carry(unsigned long __value)
{ this->seed(__value); }
/**
* Constructs a %subtract_with_carry random number generator engine
* seeded from the generator function @p __g.
*
* @param __g The seed generator function.
*/
template<class _Gen>
subtract_with_carry(_Gen& __g)
{ this->seed(__g); }
/**
* Seeds the initial state @f$ 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(unsigned long __value = 19780503);
/**
* Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry
* random number generator.
*/
template<class _Gen>
void
seed(_Gen& __g)
{ seed(__g, typename is_fundamental<_Gen>::type()); }
/**
* Gets the inclusive minimum value of the range of random integers
* returned by this generator.
*/
result_type
min() const
{ return 0; }
/**
* Gets the inclusive maximum value of the range of random integers
* returned by this generator.
*/
result_type
max() const
{ return this->modulus - 1; }
/**
* Gets the next random number in the sequence.
*/
result_type
operator()();
/**
* Compares two % subtract_with_carry random number generator objects of
* the same type for equality.
*
* @param __lhs A % subtract_with_carry random number generator object.
* @param __rhs Another % subtract_with_carry random number generator
* object.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const subtract_with_carry& __lhs,
const subtract_with_carry& __rhs)
{ return std::equal(__lhs._M_x, __lhs._M_x + long_lag, __rhs._M_x); }
/**
* Compares two % subtract_with_carry random number generator objects of
* the same type for inequality.
*
* @param __lhs A % subtract_with_carry random number generator object.
* @param __rhs Another % subtract_with_carry random number generator
* object.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const subtract_with_carry& __lhs,
const subtract_with_carry& __rhs)
{ return !(__lhs == __rhs); }
/**
* Inserts the current state of a % subtract_with_carry random number
* generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A % subtract_with_carry random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const subtract_with_carry<_IntType1, __m1, __s1,
__r1>& __x);
/**
* Extracts the current state of a % subtract_with_carry random number
* generator engine @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A % subtract_with_carry random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _IntType1, _IntType1 __m1, int __s1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
subtract_with_carry<_IntType1, __m1, __s1, __r1>& __x);
private:
template<class _Gen>
void
seed(_Gen& __g, true_type)
{ return seed(static_cast<unsigned long>(__g)); }
template<class _Gen>
void
seed(_Gen& __g, false_type);
typedef typename __gnu_cxx::__add_unsigned<_IntType>::__type _UIntType;
_UIntType _M_x[long_lag];
_UIntType _M_carry;
int _M_p;
};
/**
* @brief The Marsaglia-Zaman generator (floats version).
*
* @var _M_x The state of the generator. This is a ring buffer.
* @var _M_carry The carry.
* @var _M_p Current index of x(i - r).
* @var _M_npows Precomputed negative powers of 2.
*/
template<typename _RealType, int __w, int __s, int __r>
class subtract_with_carry_01
{
public:
/** The type of the generated random value. */
typedef _RealType result_type;
// parameter values
static const int word_size = __w;
static const int long_lag = __r;
static const int short_lag = __s;
/**
* Constructs a default-initialized % subtract_with_carry_01 random
* number generator.
*/
subtract_with_carry_01()
{
this->seed();
_M_initialize_npows();
}
/**
* Constructs an explicitly seeded % subtract_with_carry_01 random number
* generator.
*/
explicit
subtract_with_carry_01(unsigned long __value)
{
this->seed(__value);
_M_initialize_npows();
}
/**
* Constructs a % subtract_with_carry_01 random number generator engine
* seeded from the generator function @p __g.
*
* @param __g The seed generator function.
*/
template<class _Gen>
subtract_with_carry_01(_Gen& __g)
{
this->seed(__g);
_M_initialize_npows();
}
/**
* Seeds the initial state @f$ x_0 @f$ of the random number generator.
*/
void
seed(unsigned long __value = 19780503);
/**
* Seeds the initial state @f$ x_0 @f$ of the % subtract_with_carry_01
* random number generator.
*/
template<class _Gen>
void
seed(_Gen& __g)
{ seed(__g, typename is_fundamental<_Gen>::type()); }
/**
* Gets the minimum value of the range of random floats
* returned by this generator.
*/
result_type
min() const
{ return 0.0; }
/**
* Gets the maximum value of the range of random floats
* returned by this generator.
*/
result_type
max() const
{ return 1.0; }
/**
* Gets the next random number in the sequence.
*/
result_type
operator()();
/**
* Compares two % subtract_with_carry_01 random number generator objects
* of the same type for equality.
*
* @param __lhs A % subtract_with_carry_01 random number
* generator object.
* @param __rhs Another % subtract_with_carry_01 random number generator
* object.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const subtract_with_carry_01& __lhs,
const subtract_with_carry_01& __rhs)
{
for (int __i = 0; __i < long_lag; ++__i)
if (!std::equal(__lhs._M_x[__i], __lhs._M_x[__i] + __n,
__rhs._M_x[__i]))
return false;
return true;
}
/**
* Compares two % subtract_with_carry_01 random number generator objects
* of the same type for inequality.
*
* @param __lhs A % subtract_with_carry_01 random number
* generator object.
*
* @param __rhs Another % subtract_with_carry_01 random number generator
* object.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const subtract_with_carry_01& __lhs,
const subtract_with_carry_01& __rhs)
{ return !(__lhs == __rhs); }
/**
* Inserts the current state of a % subtract_with_carry_01 random number
* generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A % subtract_with_carry_01 random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, int __w1, int __s1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const subtract_with_carry_01<_RealType1, __w1, __s1,
__r1>& __x);
/**
* Extracts the current state of a % subtract_with_carry_01 random number
* generator engine @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A % subtract_with_carry_01 random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<typename _RealType1, int __w1, int __s1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
subtract_with_carry_01<_RealType1, __w1, __s1, __r1>& __x);
private:
template<class _Gen>
void
seed(_Gen& __g, true_type)
{ return seed(static_cast<unsigned long>(__g)); }
template<class _Gen>
void
seed(_Gen& __g, false_type);
void
_M_initialize_npows();
static const int __n = (__w + 31) / 32;
typedef __detail::_UInt32Type _UInt32Type;
_UInt32Type _M_x[long_lag][__n];
_RealType _M_npows[__n];
_UInt32Type _M_carry;
int _M_p;
};
typedef subtract_with_carry_01<float, 24, 10, 24> ranlux_base_01;
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// 508. Bad parameters for ranlux64_base_01.
typedef subtract_with_carry_01<double, 48, 5, 12> ranlux64_base_01;
/**
* Produces random numbers from some base engine by discarding blocks of
* data.
*
* 0 <= @p __r <= @p __p
*/
template<class _UniformRandomNumberGenerator, int __p, int __r>
class discard_block
{
// __glibcxx_class_requires(typename base_type::result_type,
// ArithmeticTypeConcept)
public:
/** The type of the underlying generator engine. */
typedef _UniformRandomNumberGenerator base_type;
/** The type of the generated random value. */
typedef typename base_type::result_type result_type;
// parameter values
static const int block_size = __p;
static const int used_block = __r;
/**
* Constructs a default %discard_block engine.
*
* The underlying engine is default constructed as well.
*/
discard_block()
: _M_n(0) { }
/**
* Copy constructs a %discard_block engine.
*
* Copies an existing base class random number generator.
* @param rng An existing (base class) engine object.
*/
explicit
discard_block(const base_type& __rng)
: _M_b(__rng), _M_n(0) { }
/**
* Seed constructs a %discard_block engine.
*
* Constructs the underlying generator engine seeded with @p __s.
* @param __s A seed value for the base class engine.
*/
explicit
discard_block(unsigned long __s)
: _M_b(__s), _M_n(0) { }
/**
* Generator construct a %discard_block engine.
*
* @param __g A seed generator function.
*/
template<class _Gen>
discard_block(_Gen& __g)
: _M_b(__g), _M_n(0) { }
/**
* Reseeds the %discard_block object with the default seed for the
* underlying base class generator engine.
*/
void seed()
{
_M_b.seed();
_M_n = 0;
}
/**
* Reseeds the %discard_block object with the given seed generator
* function.
* @param __g A seed generator function.
*/
template<class _Gen>
void seed(_Gen& __g)
{
_M_b.seed(__g);
_M_n = 0;
}
/**
* Gets a const reference to the underlying generator engine object.
*/
const base_type&
base() const
{ return _M_b; }
/**
* Gets the minimum value in the generated random number range.
*/
result_type
min() const
{ return _M_b.min(); }
/**
* Gets the maximum value in the generated random number range.
*/
result_type
max() const
{ return _M_b.max(); }
/**
* Gets the next value in the generated random number sequence.
*/
result_type
operator()();
/**
* Compares two %discard_block random number generator objects of
* the same type for equality.
*
* @param __lhs A %discard_block random number generator object.
* @param __rhs Another %discard_block random number generator
* object.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const discard_block& __lhs, const discard_block& __rhs)
{ return (__lhs._M_b == __rhs._M_b) && (__lhs._M_n == __rhs._M_n); }
/**
* Compares two %discard_block random number generator objects of
* the same type for inequality.
*
* @param __lhs A %discard_block random number generator object.
* @param __rhs Another %discard_block random number generator
* object.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const discard_block& __lhs, const discard_block& __rhs)
{ return !(__lhs == __rhs); }
/**
* Inserts the current state of a %discard_block random number
* generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %discard_block random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const discard_block<_UniformRandomNumberGenerator1,
__p1, __r1>& __x);
/**
* Extracts the current state of a % subtract_with_carry random number
* generator engine @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %discard_block random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<class _UniformRandomNumberGenerator1, int __p1, int __r1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
discard_block<_UniformRandomNumberGenerator1,
__p1, __r1>& __x);
private:
base_type _M_b;
int _M_n;
};
/**
* James's luxury-level-3 integer adaptation of Luescher's generator.
*/
typedef discard_block<
subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
223,
24
> ranlux3;
/**
* James's luxury-level-4 integer adaptation of Luescher's generator.
*/
typedef discard_block<
subtract_with_carry<unsigned long, (1UL << 24), 10, 24>,
389,
24
> ranlux4;
typedef discard_block<
subtract_with_carry_01<float, 24, 10, 24>,
223,
24
> ranlux3_01;
typedef discard_block<
subtract_with_carry_01<float, 24, 10, 24>,
389,
24
> ranlux4_01;
/**
* A random number generator adaptor class that combines two random number
* generator engines into a single output sequence.
*/
template<class _UniformRandomNumberGenerator1, int __s1,
class _UniformRandomNumberGenerator2, int __s2>
class xor_combine
{
// __glibcxx_class_requires(typename _UniformRandomNumberGenerator1::
// result_type, ArithmeticTypeConcept)
// __glibcxx_class_requires(typename _UniformRandomNumberGenerator2::
// result_type, ArithmeticTypeConcept)
public:
/** The type of the first underlying generator engine. */
typedef _UniformRandomNumberGenerator1 base1_type;
/** The type of the second underlying generator engine. */
typedef _UniformRandomNumberGenerator2 base2_type;
private:
typedef typename base1_type::result_type _Result_type1;
typedef typename base2_type::result_type _Result_type2;
public:
/** The type of the generated random value. */
typedef typename __gnu_cxx::__conditional_type<(sizeof(_Result_type1)
> sizeof(_Result_type2)),
_Result_type1, _Result_type2>::__type result_type;
// parameter values
static const int shift1 = __s1;
static const int shift2 = __s2;
// constructors and member function
xor_combine()
: _M_b1(), _M_b2()
{ _M_initialize_max(); }
xor_combine(const base1_type& __rng1, const base2_type& __rng2)
: _M_b1(__rng1), _M_b2(__rng2)
{ _M_initialize_max(); }
xor_combine(unsigned long __s)
: _M_b1(__s), _M_b2(__s + 1)
{ _M_initialize_max(); }
template<class _Gen>
xor_combine(_Gen& __g)
: _M_b1(__g), _M_b2(__g)
{ _M_initialize_max(); }
void
seed()
{
_M_b1.seed();
_M_b2.seed();
}
template<class _Gen>
void
seed(_Gen& __g)
{
_M_b1.seed(__g);
_M_b2.seed(__g);
}
const base1_type&
base1() const
{ return _M_b1; }
const base2_type&
base2() const
{ return _M_b2; }
result_type
min() const
{ return 0; }
result_type
max() const
{ return _M_max; }
/**
* Gets the next random number in the sequence.
*/
// NB: Not exactly the TR1 formula, per N2079 instead.
result_type
operator()()
{
return ((result_type(_M_b1() - _M_b1.min()) << shift1)
^ (result_type(_M_b2() - _M_b2.min()) << shift2));
}
/**
* Compares two %xor_combine random number generator objects of
* the same type for equality.
*
* @param __lhs A %xor_combine random number generator object.
* @param __rhs Another %xor_combine random number generator
* object.
*
* @returns true if the two objects are equal, false otherwise.
*/
friend bool
operator==(const xor_combine& __lhs, const xor_combine& __rhs)
{
return (__lhs.base1() == __rhs.base1())
&& (__lhs.base2() == __rhs.base2());
}
/**
* Compares two %xor_combine random number generator objects of
* the same type for inequality.
*
* @param __lhs A %xor_combine random number generator object.
* @param __rhs Another %xor_combine random number generator
* object.
*
* @returns true if the two objects are not equal, false otherwise.
*/
friend bool
operator!=(const xor_combine& __lhs, const xor_combine& __rhs)
{ return !(__lhs == __rhs); }
/**
* Inserts the current state of a %xor_combine random number
* generator engine @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %xor_combine random number generator engine.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<class _UniformRandomNumberGenerator11, int __s11,
class _UniformRandomNumberGenerator21, int __s21,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const xor_combine<_UniformRandomNumberGenerator11, __s11,
_UniformRandomNumberGenerator21, __s21>& __x);
/**
* Extracts the current state of a %xor_combine random number
* generator engine @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %xor_combine random number generator engine.
*
* @returns The input stream with the state of @p __x extracted or in
* an error state.
*/
template<class _UniformRandomNumberGenerator11, int __s11,
class _UniformRandomNumberGenerator21, int __s21,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
xor_combine<_UniformRandomNumberGenerator11, __s11,
_UniformRandomNumberGenerator21, __s21>& __x);
private:
void
_M_initialize_max();
result_type
_M_initialize_max_aux(result_type, result_type, int);
base1_type _M_b1;
base2_type _M_b2;
result_type _M_max;
};
/**
* A standard interface to a platform-specific non-deterministic
* random number generator (if any are available).
*/
class random_device
{
public:
// types
typedef unsigned int result_type;
// constructors, destructors and member functions
#ifdef _GLIBCXX_USE_RANDOM_TR1
explicit
random_device(const std::string& __token = "/dev/urandom")
{
if ((__token != "/dev/urandom" && __token != "/dev/random")
|| !(_M_file = std::fopen(__token.c_str(), "rb")))
std::__throw_runtime_error(__N("random_device::"
"random_device(const std::string&)"));
}
~random_device()
{ std::fclose(_M_file); }
#else
explicit
random_device(const std::string& __token = "mt19937")
: _M_mt(_M_strtoul(__token)) { }
private:
static unsigned long
_M_strtoul(const std::string& __str)
{
unsigned long __ret = 5489UL;
if (__str != "mt19937")
{
const char* __nptr = __str.c_str();
char* __endptr;
__ret = std::strtoul(__nptr, &__endptr, 0);
if (*__nptr == '\0' || *__endptr != '\0')
std::__throw_runtime_error(__N("random_device::_M_strtoul"
"(const std::string&)"));
}
return __ret;
}
public:
#endif
result_type
min() const
{ return std::numeric_limits<result_type>::min(); }
result_type
max() const
{ return std::numeric_limits<result_type>::max(); }
double
entropy() const
{ return 0.0; }
result_type
operator()()
{
#ifdef _GLIBCXX_USE_RANDOM_TR1
result_type __ret;
std::fread(reinterpret_cast<void*>(&__ret), sizeof(result_type),
1, _M_file);
return __ret;
#else
return _M_mt();
#endif
}
private:
random_device(const random_device&);
void operator=(const random_device&);
#ifdef _GLIBCXX_USE_RANDOM_TR1
FILE* _M_file;
#else
mt19937 _M_mt;
#endif
};
/* @} */ // group tr1_random_generators
/**
* @addtogroup tr1_random_distributions Random Number Distributions
* @ingroup tr1_random
* @{
*/
/**
* @addtogroup tr1_random_distributions_discrete Discrete Distributions
* @ingroup tr1_random_distributions
* @{
*/
/**
* @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
{
__glibcxx_class_requires(_IntType, _IntegerConcept)
public:
/** The type of the parameters of the distribution. */
typedef _IntType input_type;
/** The type of the range of the distribution. */
typedef _IntType result_type;
public:
/**
* Constructs a uniform distribution object.
*/
explicit
uniform_int(_IntType __min = 0, _IntType __max = 9)
: _M_min(__min), _M_max(__max)
{
_GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
}
/**
* Gets the inclusive lower bound of the distribution range.
*/
result_type
min() const
{ return _M_min; }
/**
* Gets the inclusive upper bound of the distribution range.
*/
result_type
max() const
{ return _M_max; }
/**
* Resets the distribution state.
*
* Does nothing for the uniform integer distribution.
*/
void
reset() { }
/**
* Gets a uniformly distributed random number in the range
* @f$(min, max)@f$.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{
typedef typename _UniformRandomNumberGenerator::result_type
_UResult_type;
return _M_call(__urng, _M_min, _M_max,
typename is_integral<_UResult_type>::type());
}
/**
* Gets a uniform random number in the range @f$[0, n)@f$.
*
* This function is aimed at use with std::random_shuffle.
*/
template<typename _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng, result_type __n)
{
typedef typename _UniformRandomNumberGenerator::result_type
_UResult_type;
return _M_call(__urng, 0, __n - 1,
typename is_integral<_UResult_type>::type());
}
/**
* Inserts a %uniform_int random number distribution @p __x into the
* output stream @p os.
*
* @param __os An output stream.
* @param __x A %uniform_int random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const uniform_int<_IntType1>& __x);
/**
* Extracts a %uniform_int random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %uniform_int random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _IntType1, typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
uniform_int<_IntType1>& __x);
private:
template<typename _UniformRandomNumberGenerator>
result_type
_M_call(_UniformRandomNumberGenerator& __urng,
result_type __min, result_type __max, true_type);
template<typename _UniformRandomNumberGenerator>
result_type
_M_call(_UniformRandomNumberGenerator& __urng,
result_type __min, result_type __max, false_type)
{
return result_type((__urng() - __urng.min())
/ (__urng.max() - __urng.min())
* (__max - __min + 1)) + __min;
}
_IntType _M_min;
_IntType _M_max;
};
/**
* @brief A Bernoulli random number distribution.
*
* Generates a sequence of true and false values with likelihood @f$ p @f$
* that true will come up and @f$ (1 - p) @f$ that false will appear.
*/
class bernoulli_distribution
{
public:
typedef int input_type;
typedef bool result_type;
public:
/**
* Constructs a Bernoulli distribution with likelihood @p p.
*
* @param __p [IN] The likelihood of a true result being returned. Must
* be in the interval @f$ [0, 1] @f$.
*/
explicit
bernoulli_distribution(double __p = 0.5)
: _M_p(__p)
{
_GLIBCXX_DEBUG_ASSERT((_M_p >= 0.0) && (_M_p <= 1.0));
}
/**
* Gets the @p p parameter of the distribution.
*/
double
p() const
{ return _M_p; }
/**
* Resets the distribution state.
*
* Does nothing for a Bernoulli distribution.
*/
void
reset() { }
/**
* Gets the next value in the Bernoullian sequence.
*/
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{
if ((__urng() - __urng.min()) < _M_p * (__urng.max() - __urng.min()))
return true;
return false;
}
/**
* Inserts a %bernoulli_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %bernoulli_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const bernoulli_distribution& __x);
/**
* Extracts a %bernoulli_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %bernoulli_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
bernoulli_distribution& __x)
{ return __is >> __x._M_p; }
private:
double _M_p;
};
/**
* @brief A discrete geometric random number distribution.
*
* The formula for the geometric probability mass function is
* @f$ p(i) = (1 - p)p^{i-1} @f$ where @f$ p @f$ is the parameter of the
* distribution.
*/
template<typename _IntType = int, typename _RealType = double>
class geometric_distribution
{
public:
// types
typedef _RealType input_type;
typedef _IntType result_type;
// constructors and member function
explicit
geometric_distribution(const _RealType& __p = _RealType(0.5))
: _M_p(__p)
{
_GLIBCXX_DEBUG_ASSERT((_M_p > 0.0) && (_M_p < 1.0));
_M_initialize();
}
/**
* Gets the distribution parameter @p p.
*/
_RealType
p() const
{ return _M_p; }
void
reset() { }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng);
/**
* Inserts a %geometric_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %geometric_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType1, typename _RealType1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const geometric_distribution<_IntType1, _RealType1>& __x);
/**
* Extracts a %geometric_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %geometric_distribution random number generator engine.
*
* @returns The input stream with @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,
geometric_distribution& __x)
{
__is >> __x._M_p;
__x._M_initialize();
return __is;
}
private:
void
_M_initialize()
{ _M_log_p = std::log(_M_p); }
_RealType _M_p;
_RealType _M_log_p;
};
template<typename _RealType>
class normal_distribution;
/**
* @brief A discrete Poisson random number distribution.
*
* The formula for the Poisson probability mass function is
* @f$ p(i) = \frac{mean^i}{i!} e^{-mean} @f$ where @f$ mean @f$ is the
* parameter of the distribution.
*/
template<typename _IntType = int, typename _RealType = double>
class poisson_distribution
{
public:
// types
typedef _RealType input_type;
typedef _IntType result_type;
// constructors and member function
explicit
poisson_distribution(const _RealType& __mean = _RealType(1))
: _M_mean(__mean), _M_nd()
{
_GLIBCXX_DEBUG_ASSERT(_M_mean > 0.0);
_M_initialize();
}
/**
* Gets the distribution parameter @p mean.
*/
_RealType
mean() const
{ return _M_mean; }
void
reset()
{ _M_nd.reset(); }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng);
/**
* Inserts a %poisson_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %poisson_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType1, typename _RealType1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const poisson_distribution<_IntType1, _RealType1>& __x);
/**
* Extracts a %poisson_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %poisson_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _IntType1, typename _RealType1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
poisson_distribution<_IntType1, _RealType1>& __x);
private:
void
_M_initialize();
// NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
normal_distribution<_RealType> _M_nd;
_RealType _M_mean;
// Hosts either log(mean) or the threshold of the simple method.
_RealType _M_lm_thr;
#if _GLIBCXX_USE_C99_MATH_TR1
_RealType _M_lfm, _M_sm, _M_d, _M_scx, _M_1cx, _M_c2b, _M_cb;
#endif
};
/**
* @brief A discrete binomial random number distribution.
*
* The formula for the binomial probability mass function is
* @f$ p(i) = \binom{n}{i} p^i (1 - p)^{t - i} @f$ where @f$ t @f$
* and @f$ p @f$ are the parameters of the distribution.
*/
template<typename _IntType = int, typename _RealType = double>
class binomial_distribution
{
public:
// types
typedef _RealType input_type;
typedef _IntType result_type;
// constructors and member function
explicit
binomial_distribution(_IntType __t = 1,
const _RealType& __p = _RealType(0.5))
: _M_t(__t), _M_p(__p), _M_nd()
{
_GLIBCXX_DEBUG_ASSERT((_M_t >= 0) && (_M_p >= 0.0) && (_M_p <= 1.0));
_M_initialize();
}
/**
* Gets the distribution @p t parameter.
*/
_IntType
t() const
{ return _M_t; }
/**
* Gets the distribution @p p parameter.
*/
_RealType
p() const
{ return _M_p; }
void
reset()
{ _M_nd.reset(); }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng);
/**
* Inserts a %binomial_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %binomial_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _IntType1, typename _RealType1,
typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const binomial_distribution<_IntType1, _RealType1>& __x);
/**
* Extracts a %binomial_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %binomial_distribution random number generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _IntType1, typename _RealType1,
typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
binomial_distribution<_IntType1, _RealType1>& __x);
private:
void
_M_initialize();
template<class _UniformRandomNumberGenerator>
result_type
_M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t);
// NB: Unused when _GLIBCXX_USE_C99_MATH_TR1 is undefined.
normal_distribution<_RealType> _M_nd;
_RealType _M_q;
#if _GLIBCXX_USE_C99_MATH_TR1
_RealType _M_d1, _M_d2, _M_s1, _M_s2, _M_c,
_M_a1, _M_a123, _M_s, _M_lf, _M_lp1p;
#endif
_RealType _M_p;
_IntType _M_t;
bool _M_easy;
};
/* @} */ // group tr1_random_distributions_discrete
/**
* @addtogroup tr1_random_distributions_continuous Continuous Distributions
* @ingroup tr1_random_distributions
* @{
*/
/**
* @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
{
public:
// types
typedef _RealType input_type;
typedef _RealType result_type;
public:
/**
* Constructs a uniform_real object.
*
* @param __min [IN] The lower bound of the distribution.
* @param __max [IN] The upper bound of the distribution.
*/
explicit
uniform_real(_RealType __min = _RealType(0),
_RealType __max = _RealType(1))
: _M_min(__min), _M_max(__max)
{
_GLIBCXX_DEBUG_ASSERT(_M_min <= _M_max);
}
result_type
min() const
{ return _M_min; }
result_type
max() const
{ return _M_max; }
void
reset() { }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return (__urng() * (_M_max - _M_min)) + _M_min; }
/**
* Inserts a %uniform_real random number distribution @p __x into the
* output stream @p __os.
*
* @param __os An output stream.
* @param __x A %uniform_real 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 uniform_real<_RealType1>& __x);
/**
* Extracts a %uniform_real random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %uniform_real 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,
uniform_real<_RealType1>& __x);
private:
_RealType _M_min;
_RealType _M_max;
};
/**
* @brief An exponential continuous distribution for random numbers.
*
* The formula for the exponential probability mass function is
* @f$ p(x) = \lambda e^{-\lambda x} @f$.
*
* <table border=1 cellpadding=10 cellspacing=0>
* <caption align=top>Distribution Statistics</caption>
* <tr><td>Mean</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
* <tr><td>Median</td><td>@f$ \frac{\ln 2}{\lambda} @f$</td></tr>
* <tr><td>Mode</td><td>@f$ zero @f$</td></tr>
* <tr><td>Range</td><td>@f$[0, \infty]@f$</td></tr>
* <tr><td>Standard Deviation</td><td>@f$ \frac{1}{\lambda} @f$</td></tr>
* </table>
*/
template<typename _RealType = double>
class exponential_distribution
{
public:
// types
typedef _RealType input_type;
typedef _RealType result_type;
public:
/**
* Constructs an exponential distribution with inverse scale parameter
* @f$ \lambda @f$.
*/
explicit
exponential_distribution(const result_type& __lambda = result_type(1))
: _M_lambda(__lambda)
{
_GLIBCXX_DEBUG_ASSERT(_M_lambda > 0);
}
/**
* Gets the inverse scale parameter of the distribution.
*/
_RealType
lambda() const
{ return _M_lambda; }
/**
* Resets the distribution.
*
* Has no effect on exponential distributions.
*/
void
reset() { }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng)
{ return -std::log(__urng()) / _M_lambda; }
/**
* Inserts a %exponential_distribution random number distribution
* @p __x into the output stream @p __os.
*
* @param __os An output stream.
* @param __x A %exponential_distribution random number distribution.
*
* @returns The output stream with the state of @p __x inserted or in
* an error state.
*/
template<typename _RealType1, typename _CharT, typename _Traits>
friend std::basic_ostream<_CharT, _Traits>&
operator<<(std::basic_ostream<_CharT, _Traits>& __os,
const exponential_distribution<_RealType1>& __x);
/**
* Extracts a %exponential_distribution random number distribution
* @p __x from the input stream @p __is.
*
* @param __is An input stream.
* @param __x A %exponential_distribution random number
* generator engine.
*
* @returns The input stream with @p __x extracted or in an error state.
*/
template<typename _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
exponential_distribution& __x)
{ return __is >> __x._M_lambda; }
private:
result_type _M_lambda;
};
/**
* @brief A normal continuous distribution for random numbers.
*
* The formula for the normal probability mass function is
* @f$ p(x) = \frac{1}{\sigma \sqrt{2 \pi}}
* e^{- \frac{{x - mean}^ {2}}{2 \sigma ^ {2}} } @f$.
*/
template<typename _RealType = double>
class normal_distribution
{
public:
// types
typedef _RealType input_type;
typedef _RealType result_type;
public:
/**
* Constructs a normal distribution with parameters @f$ mean @f$ and
* @f$ \sigma @f$.
*/
explicit
normal_distribution(const result_type& __mean = result_type(0),
const result_type& __sigma = result_type(1))
: _M_mean(__mean), _M_sigma(__sigma), _M_saved_available(false)
{
_GLIBCXX_DEBUG_ASSERT(_M_sigma > 0);
}
/**
* Gets the mean of the distribution.
*/
_RealType
mean() const
{ return _M_mean; }
/**
* Gets the @f$ \sigma @f$ of the distribution.
*/
_RealType
sigma() const
{ return _M_sigma; }
/**
* Resets the distribution.
*/
void
reset()
{ _M_saved_available = false; }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng);
/**
* 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 normal_distribution<_RealType1>& __x);
/**
* 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,
normal_distribution<_RealType1>& __x);
private:
result_type _M_mean;
result_type _M_sigma;
result_type _M_saved;
bool _M_saved_available;
};
/**
* @brief A gamma continuous distribution for random numbers.
*
* The formula for the gamma probability mass function is
* @f$ p(x) = \frac{1}{\Gamma(\alpha)} x^{\alpha - 1} e^{-x} @f$.
*/
template<typename _RealType = double>
class gamma_distribution
{
public:
// types
typedef _RealType input_type;
typedef _RealType result_type;
public:
/**
* Constructs a gamma distribution with parameters @f$ \alpha @f$.
*/
explicit
gamma_distribution(const result_type& __alpha_val = result_type(1))
: _M_alpha(__alpha_val)
{
_GLIBCXX_DEBUG_ASSERT(_M_alpha > 0);
_M_initialize();
}
/**
* Gets the @f$ \alpha @f$ of the distribution.
*/
_RealType
alpha() const
{ return _M_alpha; }
/**
* Resets the distribution.
*/
void
reset() { }
template<class _UniformRandomNumberGenerator>
result_type
operator()(_UniformRandomNumberGenerator& __urng);
/**
* 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 gamma_distribution<_RealType1>& __x);
/**
* 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 _CharT, typename _Traits>
friend std::basic_istream<_CharT, _Traits>&
operator>>(std::basic_istream<_CharT, _Traits>& __is,
gamma_distribution& __x)
{
__is >> __x._M_alpha;
__x._M_initialize();
return __is;
}
private:
void
_M_initialize();
result_type _M_alpha;
// Hosts either lambda of GB or d of modified Vaduva's.
result_type _M_l_d;
};
/* @} */ // group tr1_random_distributions_continuous
/* @} */ // group tr1_random_distributions
/* @} */ // group tr1_random
}
_GLIBCXX_END_NAMESPACE_VERSION
}
#endif // _GLIBCXX_TR1_RANDOM_H
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