include/__random/piecewise_linear_distribution.h - llvm-project/libcxx - Git at Google

 //===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//

 #ifndef _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H
 #define _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H

 #include <__algorithm/upper_bound.h>
 #include <__config>
 #include <__random/is_valid.h>
 #include <__random/uniform_real_distribution.h>
 #include <cmath>
 #include <iosfwd>
 #include <vector>

 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
 #endif

 _LIBCPP_PUSH_MACROS
 #include <__undef_macros>

 _LIBCPP_BEGIN_NAMESPACE_STD

 template <class _RealType = double>
 class _LIBCPP_TEMPLATE_VIS piecewise_linear_distribution {
   static_assert(__libcpp_random_is_valid_realtype<_RealType>::value,
                 "RealType must be a supported floating-point type");

 public:
   // types
   typedef _RealType result_type;

   class _LIBCPP_TEMPLATE_VIS param_type {
     vector<result_type> __b_;
     vector<result_type> __densities_;
     vector<result_type> __areas_;

   public:
     typedef piecewise_linear_distribution distribution_type;

     _LIBCPP_HIDE_FROM_ABI param_type();
     template <class _InputIteratorB, class _InputIteratorW>
     _LIBCPP_HIDE_FROM_ABI param_type(_InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w);
 #ifndef _LIBCPP_CXX03_LANG
     template <class _UnaryOperation>
     _LIBCPP_HIDE_FROM_ABI param_type(initializer_list<result_type> __bl, _UnaryOperation __fw);
 #endif // _LIBCPP_CXX03_LANG
     template <class _UnaryOperation>
     _LIBCPP_HIDE_FROM_ABI param_type(size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw);
     _LIBCPP_HIDE_FROM_ABI param_type(param_type const&) = default;
     _LIBCPP_HIDE_FROM_ABI param_type& operator=(const param_type& __rhs);

     _LIBCPP_HIDE_FROM_ABI vector<result_type> intervals() const { return __b_; }
     _LIBCPP_HIDE_FROM_ABI vector<result_type> densities() const { return __densities_; }

     friend _LIBCPP_HIDE_FROM_ABI bool operator==(const param_type& __x, const param_type& __y) {
       return __x.__densities_ == __y.__densities_ && __x.__b_ == __y.__b_;
     }
     friend _LIBCPP_HIDE_FROM_ABI bool operator!=(const param_type& __x, const param_type& __y) { return !(__x == __y); }

   private:
     _LIBCPP_HIDE_FROM_ABI void __init();

     friend class piecewise_linear_distribution;

     template <class _CharT, class _Traits, class _RT>
     friend basic_ostream<_CharT, _Traits>&
     operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x);

     template <class _CharT, class _Traits, class _RT>
     friend basic_istream<_CharT, _Traits>&
     operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x);
   };

 private:
   param_type __p_;

 public:
   // constructor and reset functions
   _LIBCPP_HIDE_FROM_ABI piecewise_linear_distribution() {}
   template <class _InputIteratorB, class _InputIteratorW>
   _LIBCPP_HIDE_FROM_ABI
   piecewise_linear_distribution(_InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w)
       : __p_(__f_b, __l_b, __f_w) {}

 #ifndef _LIBCPP_CXX03_LANG
   template <class _UnaryOperation>
   _LIBCPP_HIDE_FROM_ABI piecewise_linear_distribution(initializer_list<result_type> __bl, _UnaryOperation __fw)
       : __p_(__bl, __fw) {}
 #endif // _LIBCPP_CXX03_LANG

   template <class _UnaryOperation>
   _LIBCPP_HIDE_FROM_ABI
   piecewise_linear_distribution(size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw)
       : __p_(__nw, __xmin, __xmax, __fw) {}

   _LIBCPP_HIDE_FROM_ABI explicit piecewise_linear_distribution(const param_type& __p) : __p_(__p) {}

   _LIBCPP_HIDE_FROM_ABI void reset() {}

   // generating functions
   template <class _URNG>
   _LIBCPP_HIDE_FROM_ABI result_type operator()(_URNG& __g) {
     return (*this)(__g, __p_);
   }
   template <class _URNG>
   _LIBCPP_HIDE_FROM_ABI result_type operator()(_URNG& __g, const param_type& __p);

   // property functions
   _LIBCPP_HIDE_FROM_ABI vector<result_type> intervals() const { return __p_.intervals(); }
   _LIBCPP_HIDE_FROM_ABI vector<result_type> densities() const { return __p_.densities(); }

   _LIBCPP_HIDE_FROM_ABI param_type param() const { return __p_; }
   _LIBCPP_HIDE_FROM_ABI void param(const param_type& __p) { __p_ = __p; }

   _LIBCPP_HIDE_FROM_ABI result_type min() const { return __p_.__b_.front(); }
   _LIBCPP_HIDE_FROM_ABI result_type max() const { return __p_.__b_.back(); }

   friend _LIBCPP_HIDE_FROM_ABI bool
   operator==(const piecewise_linear_distribution& __x, const piecewise_linear_distribution& __y) {
     return __x.__p_ == __y.__p_;
   }
   friend _LIBCPP_HIDE_FROM_ABI bool
   operator!=(const piecewise_linear_distribution& __x, const piecewise_linear_distribution& __y) {
     return !(__x == __y);
   }

   template <class _CharT, class _Traits, class _RT>
   friend basic_ostream<_CharT, _Traits>&
   operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x);

   template <class _CharT, class _Traits, class _RT>
   friend basic_istream<_CharT, _Traits>&
   operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x);
 };

 template <class _RealType>
 typename piecewise_linear_distribution<_RealType>::param_type&
 piecewise_linear_distribution<_RealType>::param_type::operator=(const param_type& __rhs) {
   //  These can throw
   __b_.reserve(__rhs.__b_.size());
   __densities_.reserve(__rhs.__densities_.size());
   __areas_.reserve(__rhs.__areas_.size());

   //  These can not throw
   __b_         = __rhs.__b_;
   __densities_ = __rhs.__densities_;
   __areas_     = __rhs.__areas_;
   return *this;
 }

 template <class _RealType>
 void piecewise_linear_distribution<_RealType>::param_type::__init() {
   __areas_.assign(__densities_.size() - 1, result_type());
   result_type __sp = 0;
   for (size_t __i = 0; __i < __areas_.size(); ++__i) {
     __areas_[__i] = (__densities_[__i + 1] + __densities_[__i]) * (__b_[__i + 1] - __b_[__i]) * .5;
     __sp += __areas_[__i];
   }
   for (size_t __i = __areas_.size(); __i > 1;) {
     --__i;
     __areas_[__i] = __areas_[__i - 1] / __sp;
   }
   __areas_[0] = 0;
   for (size_t __i = 1; __i < __areas_.size(); ++__i)
     __areas_[__i] += __areas_[__i - 1];
   for (size_t __i = 0; __i < __densities_.size(); ++__i)
     __densities_[__i] /= __sp;
 }

 template <class _RealType>
 piecewise_linear_distribution<_RealType>::param_type::param_type() : __b_(2), __densities_(2, 1.0), __areas_(1, 0.0) {
   __b_[1] = 1;
 }

 template <class _RealType>
 template <class _InputIteratorB, class _InputIteratorW>
 piecewise_linear_distribution<_RealType>::param_type::param_type(
     _InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w)
     : __b_(__f_b, __l_b) {
   if (__b_.size() < 2) {
     __b_.resize(2);
     __b_[0] = 0;
     __b_[1] = 1;
     __densities_.assign(2, 1.0);
     __areas_.assign(1, 0.0);
   } else {
     __densities_.reserve(__b_.size());
     for (size_t __i = 0; __i < __b_.size(); ++__i, ++__f_w)
       __densities_.push_back(*__f_w);
     __init();
   }
 }

 #ifndef _LIBCPP_CXX03_LANG

 template <class _RealType>
 template <class _UnaryOperation>
 piecewise_linear_distribution<_RealType>::param_type::param_type(
     initializer_list<result_type> __bl, _UnaryOperation __fw)
     : __b_(__bl.begin(), __bl.end()) {
   if (__b_.size() < 2) {
     __b_.resize(2);
     __b_[0] = 0;
     __b_[1] = 1;
     __densities_.assign(2, 1.0);
     __areas_.assign(1, 0.0);
   } else {
     __densities_.reserve(__b_.size());
     for (size_t __i = 0; __i < __b_.size(); ++__i)
       __densities_.push_back(__fw(__b_[__i]));
     __init();
   }
 }

 #endif // _LIBCPP_CXX03_LANG

 template <class _RealType>
 template <class _UnaryOperation>
 piecewise_linear_distribution<_RealType>::param_type::param_type(
     size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw)
     : __b_(__nw == 0 ? 2 : __nw + 1) {
   size_t __n      = __b_.size() - 1;
   result_type __d = (__xmax - __xmin) / __n;
   __densities_.reserve(__b_.size());
   for (size_t __i = 0; __i < __n; ++__i) {
     __b_[__i] = __xmin + __i * __d;
     __densities_.push_back(__fw(__b_[__i]));
   }
   __b_[__n] = __xmax;
   __densities_.push_back(__fw(__b_[__n]));
   __init();
 }

 template <class _RealType>
 template <class _URNG>
 _RealType piecewise_linear_distribution<_RealType>::operator()(_URNG& __g, const param_type& __p) {
   static_assert(__libcpp_random_is_valid_urng<_URNG>::value, "");
   typedef uniform_real_distribution<result_type> _Gen;
   result_type __u = _Gen()(__g);
   ptrdiff_t __k   = std::upper_bound(__p.__areas_.begin(), __p.__areas_.end(), __u) - __p.__areas_.begin() - 1;
   __u -= __p.__areas_[__k];
   const result_type __dk     = __p.__densities_[__k];
   const result_type __dk1    = __p.__densities_[__k + 1];
   const result_type __deltad = __dk1 - __dk;
   const result_type __bk     = __p.__b_[__k];
   if (__deltad == 0)
     return __u / __dk + __bk;
   const result_type __bk1    = __p.__b_[__k + 1];
   const result_type __deltab = __bk1 - __bk;
   return (__bk * __dk1 - __bk1 * __dk + std::sqrt(__deltab * (__deltab * __dk * __dk + 2 * __deltad * __u))) / __deltad;
 }

 template <class _CharT, class _Traits, class _RT>
 _LIBCPP_HIDE_FROM_ABI basic_ostream<_CharT, _Traits>&
 operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x) {
   __save_flags<_CharT, _Traits> __lx(__os);
   typedef basic_ostream<_CharT, _Traits> _OStream;
   __os.flags(_OStream::dec | _OStream::left | _OStream::fixed | _OStream::scientific);
   _CharT __sp = __os.widen(' ');
   __os.fill(__sp);
   size_t __n = __x.__p_.__b_.size();
   __os << __n;
   for (size_t __i = 0; __i < __n; ++__i)
     __os << __sp << __x.__p_.__b_[__i];
   __n = __x.__p_.__densities_.size();
   __os << __sp << __n;
   for (size_t __i = 0; __i < __n; ++__i)
     __os << __sp << __x.__p_.__densities_[__i];
   __n = __x.__p_.__areas_.size();
   __os << __sp << __n;
   for (size_t __i = 0; __i < __n; ++__i)
     __os << __sp << __x.__p_.__areas_[__i];
   return __os;
 }

 template <class _CharT, class _Traits, class _RT>
 _LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>&
 operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x) {
   typedef piecewise_linear_distribution<_RT> _Eng;
   typedef typename _Eng::result_type result_type;
   __save_flags<_CharT, _Traits> __lx(__is);
   typedef basic_istream<_CharT, _Traits> _Istream;
   __is.flags(_Istream::dec | _Istream::skipws);
   size_t __n;
   __is >> __n;
   vector<result_type> __b(__n);
   for (size_t __i = 0; __i < __n; ++__i)
     __is >> __b[__i];
   __is >> __n;
   vector<result_type> __densities(__n);
   for (size_t __i = 0; __i < __n; ++__i)
     __is >> __densities[__i];
   __is >> __n;
   vector<result_type> __areas(__n);
   for (size_t __i = 0; __i < __n; ++__i)
     __is >> __areas[__i];
   if (!__is.fail()) {
     swap(__x.__p_.__b_, __b);
     swap(__x.__p_.__densities_, __densities);
     swap(__x.__p_.__areas_, __areas);
   }
   return __is;
 }

 _LIBCPP_END_NAMESPACE_STD

 _LIBCPP_POP_MACROS

 #endif // _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H
	//===----------------------------------------------------------------------===//
	//
	// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
	// See https://llvm.org/LICENSE.txt for license information.
	// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
	//
	//===----------------------------------------------------------------------===//

	#ifndef _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H
	#define _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H

	#include <__algorithm/upper_bound.h>
	#include <__config>
	#include <__random/is_valid.h>
	#include <__random/uniform_real_distribution.h>
	#include <cmath>
	#include <iosfwd>
	#include <vector>

	#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
	# pragma GCC system_header
	#endif

	_LIBCPP_PUSH_MACROS
	#include <__undef_macros>

	_LIBCPP_BEGIN_NAMESPACE_STD

	template <class _RealType = double>
	class _LIBCPP_TEMPLATE_VIS piecewise_linear_distribution {
	static_assert(__libcpp_random_is_valid_realtype<_RealType>::value,
	"RealType must be a supported floating-point type");

	public:
	// types
	typedef _RealType result_type;

	class _LIBCPP_TEMPLATE_VIS param_type {
	vector<result_type> __b_;
	vector<result_type> __densities_;
	vector<result_type> __areas_;

	public:
	typedef piecewise_linear_distribution distribution_type;

	_LIBCPP_HIDE_FROM_ABI param_type();
	template <class _InputIteratorB, class _InputIteratorW>
	_LIBCPP_HIDE_FROM_ABI param_type(_InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w);
	#ifndef _LIBCPP_CXX03_LANG
	template <class _UnaryOperation>
	_LIBCPP_HIDE_FROM_ABI param_type(initializer_list<result_type> __bl, _UnaryOperation __fw);
	#endif // _LIBCPP_CXX03_LANG
	template <class _UnaryOperation>
	_LIBCPP_HIDE_FROM_ABI param_type(size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw);
	_LIBCPP_HIDE_FROM_ABI param_type(param_type const&) = default;
	_LIBCPP_HIDE_FROM_ABI param_type& operator=(const param_type& __rhs);

	_LIBCPP_HIDE_FROM_ABI vector<result_type> intervals() const { return __b_; }
	_LIBCPP_HIDE_FROM_ABI vector<result_type> densities() const { return __densities_; }

	friend _LIBCPP_HIDE_FROM_ABI bool operator==(const param_type& __x, const param_type& __y) {
	return __x.__densities_ == __y.__densities_ && __x.__b_ == __y.__b_;
	}
	friend _LIBCPP_HIDE_FROM_ABI bool operator!=(const param_type& __x, const param_type& __y) { return !(__x == __y); }

	private:
	_LIBCPP_HIDE_FROM_ABI void __init();

	friend class piecewise_linear_distribution;

	template <class _CharT, class _Traits, class _RT>
	friend basic_ostream<_CharT, _Traits>&
	operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x);

	template <class _CharT, class _Traits, class _RT>
	friend basic_istream<_CharT, _Traits>&
	operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x);
	};

	private:
	param_type __p_;

	public:
	// constructor and reset functions
	_LIBCPP_HIDE_FROM_ABI piecewise_linear_distribution() {}
	template <class _InputIteratorB, class _InputIteratorW>
	_LIBCPP_HIDE_FROM_ABI
	piecewise_linear_distribution(_InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w)
	: __p_(__f_b, __l_b, __f_w) {}

	#ifndef _LIBCPP_CXX03_LANG
	template <class _UnaryOperation>
	_LIBCPP_HIDE_FROM_ABI piecewise_linear_distribution(initializer_list<result_type> __bl, _UnaryOperation __fw)
	: __p_(__bl, __fw) {}
	#endif // _LIBCPP_CXX03_LANG

	template <class _UnaryOperation>
	_LIBCPP_HIDE_FROM_ABI
	piecewise_linear_distribution(size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw)
	: __p_(__nw, __xmin, __xmax, __fw) {}

	_LIBCPP_HIDE_FROM_ABI explicit piecewise_linear_distribution(const param_type& __p) : __p_(__p) {}

	_LIBCPP_HIDE_FROM_ABI void reset() {}

	// generating functions
	template <class _URNG>
	_LIBCPP_HIDE_FROM_ABI result_type operator()(_URNG& __g) {
	return (*this)(__g, __p_);
	}
	template <class _URNG>
	_LIBCPP_HIDE_FROM_ABI result_type operator()(_URNG& __g, const param_type& __p);

	// property functions
	_LIBCPP_HIDE_FROM_ABI vector<result_type> intervals() const { return __p_.intervals(); }
	_LIBCPP_HIDE_FROM_ABI vector<result_type> densities() const { return __p_.densities(); }

	_LIBCPP_HIDE_FROM_ABI param_type param() const { return __p_; }
	_LIBCPP_HIDE_FROM_ABI void param(const param_type& __p) { __p_ = __p; }

	_LIBCPP_HIDE_FROM_ABI result_type min() const { return __p_.__b_.front(); }
	_LIBCPP_HIDE_FROM_ABI result_type max() const { return __p_.__b_.back(); }

	friend _LIBCPP_HIDE_FROM_ABI bool
	operator==(const piecewise_linear_distribution& __x, const piecewise_linear_distribution& __y) {
	return __x.__p_ == __y.__p_;
	}
	friend _LIBCPP_HIDE_FROM_ABI bool
	operator!=(const piecewise_linear_distribution& __x, const piecewise_linear_distribution& __y) {
	return !(__x == __y);
	}

	template <class _CharT, class _Traits, class _RT>
	friend basic_ostream<_CharT, _Traits>&
	operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x);

	template <class _CharT, class _Traits, class _RT>
	friend basic_istream<_CharT, _Traits>&
	operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x);
	};

	template <class _RealType>
	typename piecewise_linear_distribution<_RealType>::param_type&
	piecewise_linear_distribution<_RealType>::param_type::operator=(const param_type& __rhs) {
	// These can throw
	__b_.reserve(__rhs.__b_.size());
	__densities_.reserve(__rhs.__densities_.size());
	__areas_.reserve(__rhs.__areas_.size());

	// These can not throw
	__b_ = __rhs.__b_;
	__densities_ = __rhs.__densities_;
	__areas_ = __rhs.__areas_;
	return *this;
	}

	template <class _RealType>
	void piecewise_linear_distribution<_RealType>::param_type::__init() {
	__areas_.assign(__densities_.size() - 1, result_type());
	result_type __sp = 0;
	for (size_t __i = 0; __i < __areas_.size(); ++__i) {
	__areas_[__i] = (__densities_[__i + 1] + __densities_[__i]) * (__b_[__i + 1] - __b_[__i]) * .5;
	__sp += __areas_[__i];
	}
	for (size_t __i = __areas_.size(); __i > 1;) {
	--__i;
	__areas_[__i] = __areas_[__i - 1] / __sp;
	}
	__areas_[0] = 0;
	for (size_t __i = 1; __i < __areas_.size(); ++__i)
	__areas_[__i] += __areas_[__i - 1];
	for (size_t __i = 0; __i < __densities_.size(); ++__i)
	__densities_[__i] /= __sp;
	}

	template <class _RealType>
	piecewise_linear_distribution<_RealType>::param_type::param_type() : __b_(2), __densities_(2, 1.0), __areas_(1, 0.0) {
	__b_[1] = 1;
	}

	template <class _RealType>
	template <class _InputIteratorB, class _InputIteratorW>
	piecewise_linear_distribution<_RealType>::param_type::param_type(
	_InputIteratorB __f_b, _InputIteratorB __l_b, _InputIteratorW __f_w)
	: __b_(__f_b, __l_b) {
	if (__b_.size() < 2) {
	__b_.resize(2);
	__b_[0] = 0;
	__b_[1] = 1;
	__densities_.assign(2, 1.0);
	__areas_.assign(1, 0.0);
	} else {
	__densities_.reserve(__b_.size());
	for (size_t __i = 0; __i < __b_.size(); ++__i, ++__f_w)
	__densities_.push_back(*__f_w);
	__init();
	}
	}

	#ifndef _LIBCPP_CXX03_LANG

	template <class _RealType>
	template <class _UnaryOperation>
	piecewise_linear_distribution<_RealType>::param_type::param_type(
	initializer_list<result_type> __bl, _UnaryOperation __fw)
	: __b_(__bl.begin(), __bl.end()) {
	if (__b_.size() < 2) {
	__b_.resize(2);
	__b_[0] = 0;
	__b_[1] = 1;
	__densities_.assign(2, 1.0);
	__areas_.assign(1, 0.0);
	} else {
	__densities_.reserve(__b_.size());
	for (size_t __i = 0; __i < __b_.size(); ++__i)
	__densities_.push_back(__fw(__b_[__i]));
	__init();
	}
	}

	#endif // _LIBCPP_CXX03_LANG

	template <class _RealType>
	template <class _UnaryOperation>
	piecewise_linear_distribution<_RealType>::param_type::param_type(
	size_t __nw, result_type __xmin, result_type __xmax, _UnaryOperation __fw)
	: __b_(__nw == 0 ? 2 : __nw + 1) {
	size_t __n = __b_.size() - 1;
	result_type __d = (__xmax - __xmin) / __n;
	__densities_.reserve(__b_.size());
	for (size_t __i = 0; __i < __n; ++__i) {
	__b_[__i] = __xmin + __i * __d;
	__densities_.push_back(__fw(__b_[__i]));
	}
	__b_[__n] = __xmax;
	__densities_.push_back(__fw(__b_[__n]));
	__init();
	}

	template <class _RealType>
	template <class _URNG>
	_RealType piecewise_linear_distribution<_RealType>::operator()(_URNG& __g, const param_type& __p) {
	static_assert(__libcpp_random_is_valid_urng<_URNG>::value, "");
	typedef uniform_real_distribution<result_type> _Gen;
	result_type __u = _Gen()(__g);
	ptrdiff_t __k = std::upper_bound(__p.__areas_.begin(), __p.__areas_.end(), __u) - __p.__areas_.begin() - 1;
	__u -= __p.__areas_[__k];
	const result_type __dk = __p.__densities_[__k];
	const result_type __dk1 = __p.__densities_[__k + 1];
	const result_type __deltad = __dk1 - __dk;
	const result_type __bk = __p.__b_[__k];
	if (__deltad == 0)
	return __u / __dk + __bk;
	const result_type __bk1 = __p.__b_[__k + 1];
	const result_type __deltab = __bk1 - __bk;
	return (__bk * __dk1 - __bk1 * __dk + std::sqrt(__deltab * (__deltab * __dk * __dk + 2 * __deltad * __u))) / __deltad;
	}

	template <class _CharT, class _Traits, class _RT>
	_LIBCPP_HIDE_FROM_ABI basic_ostream<_CharT, _Traits>&
	operator<<(basic_ostream<_CharT, _Traits>& __os, const piecewise_linear_distribution<_RT>& __x) {
	__save_flags<_CharT, _Traits> __lx(__os);
	typedef basic_ostream<_CharT, _Traits> _OStream;
	__os.flags(_OStream::dec \| _OStream::left \| _OStream::fixed \| _OStream::scientific);
	_CharT __sp = __os.widen(' ');
	__os.fill(__sp);
	size_t __n = __x.__p_.__b_.size();
	__os << __n;
	for (size_t __i = 0; __i < __n; ++__i)
	__os << __sp << __x.__p_.__b_[__i];
	__n = __x.__p_.__densities_.size();
	__os << __sp << __n;
	for (size_t __i = 0; __i < __n; ++__i)
	__os << __sp << __x.__p_.__densities_[__i];
	__n = __x.__p_.__areas_.size();
	__os << __sp << __n;
	for (size_t __i = 0; __i < __n; ++__i)
	__os << __sp << __x.__p_.__areas_[__i];
	return __os;
	}

	template <class _CharT, class _Traits, class _RT>
	_LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>&
	operator>>(basic_istream<_CharT, _Traits>& __is, piecewise_linear_distribution<_RT>& __x) {
	typedef piecewise_linear_distribution<_RT> _Eng;
	typedef typename _Eng::result_type result_type;
	__save_flags<_CharT, _Traits> __lx(__is);
	typedef basic_istream<_CharT, _Traits> _Istream;
	__is.flags(_Istream::dec \| _Istream::skipws);
	size_t __n;
	__is >> __n;
	vector<result_type> __b(__n);
	for (size_t __i = 0; __i < __n; ++__i)
	__is >> __b[__i];
	__is >> __n;
	vector<result_type> __densities(__n);
	for (size_t __i = 0; __i < __n; ++__i)
	__is >> __densities[__i];
	__is >> __n;
	vector<result_type> __areas(__n);
	for (size_t __i = 0; __i < __n; ++__i)
	__is >> __areas[__i];
	if (!__is.fail()) {
	swap(__x.__p_.__b_, __b);
	swap(__x.__p_.__densities_, __densities);
	swap(__x.__p_.__areas_, __areas);
	}
	return __is;
	}

	_LIBCPP_END_NAMESPACE_STD

	_LIBCPP_POP_MACROS

	#endif // _LIBCPP___RANDOM_PIECEWISE_LINEAR_DISTRIBUTION_H