Add libc++ and libc++abi to third-party.

third_party/libcxx/include/complex

+// -*- C++ -*-
+//===--------------------------- complex ----------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP_COMPLEX
+#define _LIBCPP_COMPLEX
+
+/*
+    complex synopsis
+
+namespace std
+{
+
+template<class T>
+class complex
+{
+public:
+    typedef T value_type;
+
+    complex(const T& re = T(), const T& im = T()); // constexpr in C++14
+    complex(const complex&);  // constexpr in C++14
+    template<class X> complex(const complex<X>&);  // constexpr in C++14
+
+    T real() const; // constexpr in C++14
+    T imag() const; // constexpr in C++14
+
+    void real(T);
+    void imag(T);
+
+    complex<T>& operator= (const T&);
+    complex<T>& operator+=(const T&);
+    complex<T>& operator-=(const T&);
+    complex<T>& operator*=(const T&);
+    complex<T>& operator/=(const T&);
+
+    complex& operator=(const complex&);
+    template<class X> complex<T>& operator= (const complex<X>&);
+    template<class X> complex<T>& operator+=(const complex<X>&);
+    template<class X> complex<T>& operator-=(const complex<X>&);
+    template<class X> complex<T>& operator*=(const complex<X>&);
+    template<class X> complex<T>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<float>
+{
+public:
+    typedef float value_type;
+
+    constexpr complex(float re = 0.0f, float im = 0.0f);
+    explicit constexpr complex(const complex<double>&);
+    explicit constexpr complex(const complex<long double>&);
+
+    constexpr float real() const;
+    void real(float);
+    constexpr float imag() const;
+    void imag(float);
+
+    complex<float>& operator= (float);
+    complex<float>& operator+=(float);
+    complex<float>& operator-=(float);
+    complex<float>& operator*=(float);
+    complex<float>& operator/=(float);
+
+    complex<float>& operator=(const complex<float>&);
+    template<class X> complex<float>& operator= (const complex<X>&);
+    template<class X> complex<float>& operator+=(const complex<X>&);
+    template<class X> complex<float>& operator-=(const complex<X>&);
+    template<class X> complex<float>& operator*=(const complex<X>&);
+    template<class X> complex<float>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<double>
+{
+public:
+    typedef double value_type;
+
+    constexpr complex(double re = 0.0, double im = 0.0);
+    constexpr complex(const complex<float>&);
+    explicit constexpr complex(const complex<long double>&);
+
+    constexpr double real() const;
+    void real(double);
+    constexpr double imag() const;
+    void imag(double);
+
+    complex<double>& operator= (double);
+    complex<double>& operator+=(double);
+    complex<double>& operator-=(double);
+    complex<double>& operator*=(double);
+    complex<double>& operator/=(double);
+    complex<double>& operator=(const complex<double>&);
+
+    template<class X> complex<double>& operator= (const complex<X>&);
+    template<class X> complex<double>& operator+=(const complex<X>&);
+    template<class X> complex<double>& operator-=(const complex<X>&);
+    template<class X> complex<double>& operator*=(const complex<X>&);
+    template<class X> complex<double>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<long double>
+{
+public:
+    typedef long double value_type;
+
+    constexpr complex(long double re = 0.0L, long double im = 0.0L);
+    constexpr complex(const complex<float>&);
+    constexpr complex(const complex<double>&);
+
+    constexpr long double real() const;
+    void real(long double);
+    constexpr long double imag() const;
+    void imag(long double);
+
+    complex<long double>& operator=(const complex<long double>&);
+    complex<long double>& operator= (long double);
+    complex<long double>& operator+=(long double);
+    complex<long double>& operator-=(long double);
+    complex<long double>& operator*=(long double);
+    complex<long double>& operator/=(long double);
+
+    template<class X> complex<long double>& operator= (const complex<X>&);
+    template<class X> complex<long double>& operator+=(const complex<X>&);
+    template<class X> complex<long double>& operator-=(const complex<X>&);
+    template<class X> complex<long double>& operator*=(const complex<X>&);
+    template<class X> complex<long double>& operator/=(const complex<X>&);
+};
+
+// 26.3.6 operators:
+template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator+(const complex<T>&, const T&);
+template<class T> complex<T> operator+(const T&, const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&, const T&);
+template<class T> complex<T> operator-(const T&, const complex<T>&);
+template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator*(const complex<T>&, const T&);
+template<class T> complex<T> operator*(const T&, const complex<T>&);
+template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator/(const complex<T>&, const T&);
+template<class T> complex<T> operator/(const T&, const complex<T>&);
+template<class T> complex<T> operator+(const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&);
+template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14
+template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14
+template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14
+template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14
+template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14
+template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14
+
+template<class T, class charT, class traits>
+  basic_istream<charT, traits>&
+  operator>>(basic_istream<charT, traits>&, complex<T>&);
+template<class T, class charT, class traits>
+  basic_ostream<charT, traits>&
+  operator<<(basic_ostream<charT, traits>&, const complex<T>&);
+
+// 26.3.7 values:
+
+template<class T>              T real(const complex<T>&); // constexpr in C++14
+                     long double real(long double);       // constexpr in C++14
+                          double real(double);            // constexpr in C++14
+template<Integral T>      double real(T);                 // constexpr in C++14
+                          float  real(float);             // constexpr in C++14
+
+template<class T>              T imag(const complex<T>&); // constexpr in C++14
+                     long double imag(long double);       // constexpr in C++14
+                          double imag(double);            // constexpr in C++14
+template<Integral T>      double imag(T);                 // constexpr in C++14
+                          float  imag(float);             // constexpr in C++14
+
+template<class T> T abs(const complex<T>&);
+
+template<class T>              T arg(const complex<T>&);
+                     long double arg(long double);
+                          double arg(double);
+template<Integral T>      double arg(T);
+                          float  arg(float);
+
+template<class T>              T norm(const complex<T>&);
+                     long double norm(long double);
+                          double norm(double);
+template<Integral T>      double norm(T);
+                          float  norm(float);
+
+template<class T>      complex<T>           conj(const complex<T>&);
+                       complex<long double> conj(long double);
+                       complex<double>      conj(double);
+template<Integral T>   complex<double>      conj(T);
+                       complex<float>       conj(float);
+
+template<class T>    complex<T>           proj(const complex<T>&);
+                     complex<long double> proj(long double);
+                     complex<double>      proj(double);
+template<Integral T> complex<double>      proj(T);
+                     complex<float>       proj(float);
+
+template<class T> complex<T> polar(const T&, const T& = 0);
+
+// 26.3.8 transcendentals:
+template<class T> complex<T> acos(const complex<T>&);
+template<class T> complex<T> asin(const complex<T>&);
+template<class T> complex<T> atan(const complex<T>&);
+template<class T> complex<T> acosh(const complex<T>&);
+template<class T> complex<T> asinh(const complex<T>&);
+template<class T> complex<T> atanh(const complex<T>&);
+template<class T> complex<T> cos (const complex<T>&);
+template<class T> complex<T> cosh (const complex<T>&);
+template<class T> complex<T> exp (const complex<T>&);
+template<class T> complex<T> log (const complex<T>&);
+template<class T> complex<T> log10(const complex<T>&);
+
+template<class T> complex<T> pow(const complex<T>&, const T&);
+template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
+template<class T> complex<T> pow(const T&, const complex<T>&);
+
+template<class T> complex<T> sin (const complex<T>&);
+template<class T> complex<T> sinh (const complex<T>&);
+template<class T> complex<T> sqrt (const complex<T>&);
+template<class T> complex<T> tan (const complex<T>&);
+template<class T> complex<T> tanh (const complex<T>&);
+
+template<class T, class charT, class traits>
+  basic_istream<charT, traits>&
+  operator>>(basic_istream<charT, traits>& is, complex<T>& x);
+
+template<class T, class charT, class traits>
+  basic_ostream<charT, traits>&
+  operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
+
+}  // std
+
+*/
+
+#include <__config>
+#include <type_traits>
+#include <stdexcept>
+#include <cmath>
+#include <sstream>
+#if defined(_LIBCPP_NO_EXCEPTIONS)
+    #include <cassert>
+#endif
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+template<class _Tp> class _LIBCPP_TYPE_VIS_ONLY complex;
+
+template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
+template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
+
+template<class _Tp>
+class _LIBCPP_TYPE_VIS_ONLY complex
+{
+public:
+    typedef _Tp value_type;
+private:
+    value_type __re_;
+    value_type __im_;
+public:
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+    complex(const value_type& __re = value_type(), const value_type& __im = value_type())
+        : __re_(__re), __im_(__im) {}
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+    complex(const complex<_Xp>& __c)
+        : __re_(__c.real()), __im_(__c.imag()) {}
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
+
+    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+    _LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re)
+        {__re_ = __re; __im_ = value_type(); return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+        {
+            __re_ = __c.real();
+            __im_ = __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+        {
+            __re_ += __c.real();
+            __im_ += __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+        {
+            __re_ -= __c.real();
+            __im_ -= __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+        {
+            *this = *this * complex(__c.real(), __c.imag());
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+        {
+            *this = *this / complex(__c.real(), __c.imag());
+            return *this;
+        }
+};
+
+template<> class _LIBCPP_TYPE_VIS_ONLY complex<double>;
+template<> class _LIBCPP_TYPE_VIS_ONLY complex<long double>;
+
+template<>
+class _LIBCPP_TYPE_VIS_ONLY complex<float>
+{
+    float __re_;
+    float __im_;
+public:
+    typedef float value_type;
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
+        : __re_(__re), __im_(__im) {}
+    explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
+    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
+
+    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+    _LIBCPP_INLINE_VISIBILITY complex& operator= (float __re)
+        {__re_ = __re; __im_ = value_type(); return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+        {
+            __re_ = __c.real();
+            __im_ = __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+        {
+            __re_ += __c.real();
+            __im_ += __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+        {
+            __re_ -= __c.real();
+            __im_ -= __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+        {
+            *this = *this * complex(__c.real(), __c.imag());
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+        {
+            *this = *this / complex(__c.real(), __c.imag());
+            return *this;
+        }
+};
+
+template<>
+class _LIBCPP_TYPE_VIS_ONLY complex<double>
+{
+    double __re_;
+    double __im_;
+public:
+    typedef double value_type;
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
+        : __re_(__re), __im_(__im) {}
+    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
+    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
+
+    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+    _LIBCPP_INLINE_VISIBILITY complex& operator= (double __re)
+        {__re_ = __re; __im_ = value_type(); return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+        {
+            __re_ = __c.real();
+            __im_ = __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+        {
+            __re_ += __c.real();
+            __im_ += __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+        {
+            __re_ -= __c.real();
+            __im_ -= __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+        {
+            *this = *this * complex(__c.real(), __c.imag());
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+        {
+            *this = *this / complex(__c.real(), __c.imag());
+            return *this;
+        }
+};
+
+template<>
+class _LIBCPP_TYPE_VIS_ONLY complex<long double>
+{
+    long double __re_;
+    long double __im_;
+public:
+    typedef long double value_type;
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
+        : __re_(__re), __im_(__im) {}
+    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
+    _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
+
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
+
+    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+    _LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
+        {__re_ = __re; __im_ = value_type(); return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
+    _LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+        {
+            __re_ = __c.real();
+            __im_ = __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+        {
+            __re_ += __c.real();
+            __im_ += __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+        {
+            __re_ -= __c.real();
+            __im_ -= __c.imag();
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+        {
+            *this = *this * complex(__c.real(), __c.imag());
+            return *this;
+        }
+    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+        {
+            *this = *this / complex(__c.real(), __c.imag());
+            return *this;
+        }
+};
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<float>::complex(const complex<double>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<float>::complex(const complex<long double>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<double>::complex(const complex<float>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<double>::complex(const complex<long double>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<long double>::complex(const complex<float>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
+complex<long double>::complex(const complex<double>& __c)
+    : __re_(__c.real()), __im_(__c.imag()) {}
+
+// 26.3.6 operators:
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(__x);
+    __t += __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x, const _Tp& __y)
+{
+    complex<_Tp> __t(__x);
+    __t += __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const _Tp& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(__y);
+    __t += __x;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(__x);
+    __t -= __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x, const _Tp& __y)
+{
+    complex<_Tp> __t(__x);
+    __t -= __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const _Tp& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(-__y);
+    __t += __x;
+    return __t;
+}
+
+template<class _Tp>
+complex<_Tp>
+operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
+{
+    _Tp __a = __z.real();
+    _Tp __b = __z.imag();
+    _Tp __c = __w.real();
+    _Tp __d = __w.imag();
+    _Tp __ac = __a * __c;
+    _Tp __bd = __b * __d;
+    _Tp __ad = __a * __d;
+    _Tp __bc = __b * __c;
+    _Tp __x = __ac - __bd;
+    _Tp __y = __ad + __bc;
+    if (isnan(__x) && isnan(__y))
+    {
+        bool __recalc = false;
+        if (isinf(__a) || isinf(__b))
+        {
+            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
+            __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
+            if (isnan(__c))
+                __c = copysign(_Tp(0), __c);
+            if (isnan(__d))
+                __d = copysign(_Tp(0), __d);
+            __recalc = true;
+        }
+        if (isinf(__c) || isinf(__d))
+        {
+            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
+            __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
+            if (isnan(__a))
+                __a = copysign(_Tp(0), __a);
+            if (isnan(__b))
+                __b = copysign(_Tp(0), __b);
+            __recalc = true;
+        }
+        if (!__recalc && (isinf(__ac) || isinf(__bd) ||
+                          isinf(__ad) || isinf(__bc)))
+        {
+            if (isnan(__a))
+                __a = copysign(_Tp(0), __a);
+            if (isnan(__b))
+                __b = copysign(_Tp(0), __b);
+            if (isnan(__c))
+                __c = copysign(_Tp(0), __c);
+            if (isnan(__d))
+                __d = copysign(_Tp(0), __d);
+            __recalc = true;
+        }
+        if (__recalc)
+        {
+            __x = _Tp(INFINITY) * (__a * __c - __b * __d);
+            __y = _Tp(INFINITY) * (__a * __d + __b * __c);
+        }
+    }
+    return complex<_Tp>(__x, __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator*(const complex<_Tp>& __x, const _Tp& __y)
+{
+    complex<_Tp> __t(__x);
+    __t *= __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator*(const _Tp& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(__y);
+    __t *= __x;
+    return __t;
+}
+
+template<class _Tp>
+complex<_Tp>
+operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
+{
+    int __ilogbw = 0;
+    _Tp __a = __z.real();
+    _Tp __b = __z.imag();
+    _Tp __c = __w.real();
+    _Tp __d = __w.imag();
+    _Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
+    if (isfinite(__logbw))
+    {
+        __ilogbw = static_cast<int>(__logbw);
+        __c = scalbn(__c, -__ilogbw);
+        __d = scalbn(__d, -__ilogbw);
+    }
+    _Tp __denom = __c * __c + __d * __d;
+    _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
+    _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
+    if (isnan(__x) && isnan(__y))
+    {
+        if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
+        {
+            __x = copysign(_Tp(INFINITY), __c) * __a;
+            __y = copysign(_Tp(INFINITY), __c) * __b;
+        }
+        else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
+        {
+            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
+            __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
+            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
+            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
+        }
+        else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
+        {
+            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
+            __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
+            __x = _Tp(0) * (__a * __c + __b * __d);
+            __y = _Tp(0) * (__b * __c - __a * __d);
+        }
+    }
+    return complex<_Tp>(__x, __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator/(const complex<_Tp>& __x, const _Tp& __y)
+{
+    return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator/(const _Tp& __x, const complex<_Tp>& __y)
+{
+    complex<_Tp> __t(__x);
+    __t /= __y;
+    return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x)
+{
+    return __x;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x)
+{
+    return complex<_Tp>(-__x.real(), -__x.imag());
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+    return __x.real() == __y.real() && __x.imag() == __y.imag();
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator==(const complex<_Tp>& __x, const _Tp& __y)
+{
+    return __x.real() == __y && __x.imag() == 0;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator==(const _Tp& __x, const complex<_Tp>& __y)
+{
+    return __x == __y.real() && 0 == __y.imag();
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+    return !(__x == __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator!=(const complex<_Tp>& __x, const _Tp& __y)
+{
+    return !(__x == __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+bool
+operator!=(const _Tp& __x, const complex<_Tp>& __y)
+{
+    return !(__x == __y);
+}
+
+// 26.3.7 values:
+
+// real
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+_Tp
+real(const complex<_Tp>& __c)
+{
+    return __c.real();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+long double
+real(long double __re)
+{
+    return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+double
+real(double __re)
+{
+    return __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    double
+>::type
+real(_Tp  __re)
+{
+    return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+float
+real(float  __re)
+{
+    return __re;
+}
+
+// imag
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+_Tp
+imag(const complex<_Tp>& __c)
+{
+    return __c.imag();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+long double
+imag(long double __re)
+{
+    return 0;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+double
+imag(double __re)
+{
+    return 0;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    double
+>::type
+imag(_Tp  __re)
+{
+    return 0;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
+float
+imag(float  __re)
+{
+    return 0;
+}
+
+// abs
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+abs(const complex<_Tp>& __c)
+{
+    return hypot(__c.real(), __c.imag());
+}
+
+// arg
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+arg(const complex<_Tp>& __c)
+{
+    return atan2(__c.imag(), __c.real());
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+arg(long double __re)
+{
+    return atan2l(0.L, __re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+arg(double __re)
+{
+    return atan2(0., __re);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    double
+>::type
+arg(_Tp __re)
+{
+    return atan2(0., __re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+arg(float __re)
+{
+    return atan2f(0.F, __re);
+}
+
+// norm
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+norm(const complex<_Tp>& __c)
+{
+    if (isinf(__c.real()))
+        return abs(__c.real());
+    if (isinf(__c.imag()))
+        return abs(__c.imag());
+    return __c.real() * __c.real() + __c.imag() * __c.imag();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+norm(long double __re)
+{
+    return __re * __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+norm(double __re)
+{
+    return __re * __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    double
+>::type
+norm(_Tp __re)
+{
+    return (double)__re * __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+norm(float __re)
+{
+    return __re * __re;
+}
+
+// conj
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+conj(const complex<_Tp>& __c)
+{
+    return complex<_Tp>(__c.real(), -__c.imag());
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<long double>
+conj(long double __re)
+{
+    return complex<long double>(__re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<double>
+conj(double __re)
+{
+    return complex<double>(__re);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    complex<double>
+>::type
+conj(_Tp __re)
+{
+    return complex<double>(__re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<float>
+conj(float __re)
+{
+    return complex<float>(__re);
+}
+
+// proj
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+proj(const complex<_Tp>& __c)
+{
+    std::complex<_Tp> __r = __c;
+    if (isinf(__c.real()) || isinf(__c.imag()))
+        __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
+    return __r;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<long double>
+proj(long double __re)
+{
+    if (isinf(__re))
+        __re = abs(__re);
+    return complex<long double>(__re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<double>
+proj(double __re)
+{
+    if (isinf(__re))
+        __re = abs(__re);
+    return complex<double>(__re);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_integral<_Tp>::value,
+    complex<double>
+>::type
+proj(_Tp __re)
+{
+    return complex<double>(__re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+complex<float>
+proj(float __re)
+{
+    if (isinf(__re))
+        __re = abs(__re);
+    return complex<float>(__re);
+}
+
+// polar
+
+template<class _Tp>
+complex<_Tp>
+polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
+{
+    if (isnan(__rho) || signbit(__rho))
+        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
+    if (isnan(__theta))
+    {
+        if (isinf(__rho))
+            return complex<_Tp>(__rho, __theta);
+        return complex<_Tp>(__theta, __theta);
+    }
+    if (isinf(__theta))
+    {
+        if (isinf(__rho))
+            return complex<_Tp>(__rho, _Tp(NAN));
+        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
+    }
+    _Tp __x = __rho * cos(__theta);
+    if (isnan(__x))
+        __x = 0;
+    _Tp __y = __rho * sin(__theta);
+    if (isnan(__y))
+        __y = 0;
+    return complex<_Tp>(__x, __y);
+}
+
+// log
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+log(const complex<_Tp>& __x)
+{
+    return complex<_Tp>(log(abs(__x)), arg(__x));
+}
+
+// log10
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+log10(const complex<_Tp>& __x)
+{
+    return log(__x) / log(_Tp(10));
+}
+
+// sqrt
+
+template<class _Tp>
+complex<_Tp>
+sqrt(const complex<_Tp>& __x)
+{
+    if (isinf(__x.imag()))
+        return complex<_Tp>(_Tp(INFINITY), __x.imag());
+    if (isinf(__x.real()))
+    {
+        if (__x.real() > _Tp(0))
+            return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
+        return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
+    }
+    return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
+}
+
+// exp
+
+template<class _Tp>
+complex<_Tp>
+exp(const complex<_Tp>& __x)
+{
+    _Tp __i = __x.imag();
+    if (isinf(__x.real()))
+    {
+        if (__x.real() < _Tp(0))
+        {
+            if (!isfinite(__i))
+                __i = _Tp(1);
+        }
+        else if (__i == 0 || !isfinite(__i))
+        {
+            if (isinf(__i))
+                __i = _Tp(NAN);
+            return complex<_Tp>(__x.real(), __i);
+        }
+    }
+    else if (isnan(__x.real()) && __x.imag() == 0)
+        return __x;
+    _Tp __e = exp(__x.real());
+    return complex<_Tp>(__e * cos(__i), __e * sin(__i));
+}
+
+// pow
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+    return exp(__y * log(__x));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<typename __promote<_Tp, _Up>::type>
+pow(const complex<_Tp>& __x, const complex<_Up>& __y)
+{
+    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+    return _VSTD::pow(result_type(__x), result_type(__y));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_arithmetic<_Up>::value,
+    complex<typename __promote<_Tp, _Up>::type>
+>::type
+pow(const complex<_Tp>& __x, const _Up& __y)
+{
+    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+    return _VSTD::pow(result_type(__x), result_type(__y));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+    is_arithmetic<_Tp>::value,
+    complex<typename __promote<_Tp, _Up>::type>
+>::type
+pow(const _Tp& __x, const complex<_Up>& __y)
+{
+    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+    return _VSTD::pow(result_type(__x), result_type(__y));
+}
+
+// asinh
+
+template<class _Tp>
+complex<_Tp>
+asinh(const complex<_Tp>& __x)
+{
+    const _Tp __pi(atan2(+0., -0.));
+    if (isinf(__x.real()))
+    {
+        if (isnan(__x.imag()))
+            return __x;
+        if (isinf(__x.imag()))
+            return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
+        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+    }
+    if (isnan(__x.real()))
+    {
+        if (isinf(__x.imag()))
+            return complex<_Tp>(__x.imag(), __x.real());
+        if (__x.imag() == 0)
+            return __x;
+        return complex<_Tp>(__x.real(), __x.real());
+    }
+    if (isinf(__x.imag()))
+        return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
+    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
+}
+
+// acosh
+
+template<class _Tp>
+complex<_Tp>
+acosh(const complex<_Tp>& __x)
+{
+    const _Tp __pi(atan2(+0., -0.));
+    if (isinf(__x.real()))
+    {
+        if (isnan(__x.imag()))
+            return complex<_Tp>(abs(__x.real()), __x.imag());
+        if (isinf(__x.imag()))
+        {
+            if (__x.real() > 0)
+                return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
+            else
+                return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
+        }
+        if (__x.real() < 0)
+            return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
+        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+    }
+    if (isnan(__x.real()))
+    {
+        if (isinf(__x.imag()))
+            return complex<_Tp>(abs(__x.imag()), __x.real());
+        return complex<_Tp>(__x.real(), __x.real());
+    }
+    if (isinf(__x.imag()))
+        return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
+    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+    return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
+}
+
+// atanh
+
+template<class _Tp>
+complex<_Tp>
+atanh(const complex<_Tp>& __x)
+{
+    const _Tp __pi(atan2(+0., -0.));
+    if (isinf(__x.imag()))
+    {
+        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+    }
+    if (isnan(__x.imag()))
+    {
+        if (isinf(__x.real()) || __x.real() == 0)
+            return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
+        return complex<_Tp>(__x.imag(), __x.imag());
+    }
+    if (isnan(__x.real()))
+    {
+        return complex<_Tp>(__x.real(), __x.real());
+    }
+    if (isinf(__x.real()))
+    {
+        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+    }
+    if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
+    {
+        return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
+    }
+    complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
+    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
+}
+
+// sinh
+
+template<class _Tp>
+complex<_Tp>
+sinh(const complex<_Tp>& __x)
+{
+    if (isinf(__x.real()) && !isfinite(__x.imag()))
+        return complex<_Tp>(__x.real(), _Tp(NAN));
+    if (__x.real() == 0 && !isfinite(__x.imag()))
+        return complex<_Tp>(__x.real(), _Tp(NAN));
+    if (__x.imag() == 0 && !isfinite(__x.real()))
+        return __x;
+    return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
+}
+
+// cosh
+
+template<class _Tp>
+complex<_Tp>
+cosh(const complex<_Tp>& __x)
+{
+    if (isinf(__x.real()) && !isfinite(__x.imag()))
+        return complex<_Tp>(abs(__x.real()), _Tp(NAN));
+    if (__x.real() == 0 && !isfinite(__x.imag()))
+        return complex<_Tp>(_Tp(NAN), __x.real());
+    if (__x.real() == 0 && __x.imag() == 0)
+        return complex<_Tp>(_Tp(1), __x.imag());
+    if (__x.imag() == 0 && !isfinite(__x.real()))
+        return complex<_Tp>(abs(__x.real()), __x.imag());
+    return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
+}
+
+// tanh
+
+template<class _Tp>
+complex<_Tp>
+tanh(const complex<_Tp>& __x)
+{
+    if (isinf(__x.real()))
+    {
+        if (!isfinite(__x.imag()))
+            return complex<_Tp>(_Tp(1), _Tp(0));
+        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
+    }
+    if (isnan(__x.real()) && __x.imag() == 0)
+        return __x;
+    _Tp __2r(_Tp(2) * __x.real());
+    _Tp __2i(_Tp(2) * __x.imag());
+    _Tp __d(cosh(__2r) + cos(__2i));
+    _Tp __2rsh(sinh(__2r));
+    if (isinf(__2rsh) && isinf(__d))
+        return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
+                            __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
+    return  complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
+}
+
+// asin
+
+template<class _Tp>
+complex<_Tp>
+asin(const complex<_Tp>& __x)
+{
+    complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
+    return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// acos
+
+template<class _Tp>
+complex<_Tp>
+acos(const complex<_Tp>& __x)
+{
+    const _Tp __pi(atan2(+0., -0.));
+    if (isinf(__x.real()))
+    {
+        if (isnan(__x.imag()))
+            return complex<_Tp>(__x.imag(), __x.real());
+        if (isinf(__x.imag()))
+        {
+            if (__x.real() < _Tp(0))
+                return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
+            return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
+        }
+        if (__x.real() < _Tp(0))
+            return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
+        return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
+    }
+    if (isnan(__x.real()))
+    {
+        if (isinf(__x.imag()))
+            return complex<_Tp>(__x.real(), -__x.imag());
+        return complex<_Tp>(__x.real(), __x.real());
+    }
+    if (isinf(__x.imag()))
+        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
+    if (__x.real() == 0)
+        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
+    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+    if (signbit(__x.imag()))
+        return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
+    return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
+}
+
+// atan
+
+template<class _Tp>
+complex<_Tp>
+atan(const complex<_Tp>& __x)
+{
+    complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
+    return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// sin
+
+template<class _Tp>
+complex<_Tp>
+sin(const complex<_Tp>& __x)
+{
+    complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
+    return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// cos
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+cos(const complex<_Tp>& __x)
+{
+    return cosh(complex<_Tp>(-__x.imag(), __x.real()));
+}
+
+// tan
+
+template<class _Tp>
+complex<_Tp>
+tan(const complex<_Tp>& __x)
+{
+    complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
+    return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+template<class _Tp, class _CharT, class _Traits>
+basic_istream<_CharT, _Traits>&
+operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
+{
+    if (__is.good())
+    {
+        ws(__is);
+        if (__is.peek() == _CharT('('))
+        {
+            __is.get();
+            _Tp __r;
+            __is >> __r;
+            if (!__is.fail())
+            {
+                ws(__is);
+                _CharT __c = __is.peek();
+                if (__c == _CharT(','))
+                {
+                    __is.get();
+                    _Tp __i;
+                    __is >> __i;
+                    if (!__is.fail())
+                    {
+                        ws(__is);
+                        __c = __is.peek();
+                        if (__c == _CharT(')'))
+                        {
+                            __is.get();
+                            __x = complex<_Tp>(__r, __i);
+                        }
+                        else
+                            __is.setstate(ios_base::failbit);
+                    }
+                    else
+                        __is.setstate(ios_base::failbit);
+                }
+                else if (__c == _CharT(')'))
+                {
+                    __is.get();
+                    __x = complex<_Tp>(__r, _Tp(0));
+                }
+                else
+                    __is.setstate(ios_base::failbit);
+            }
+            else
+                __is.setstate(ios_base::failbit);
+        }
+        else
+        {
+            _Tp __r;
+            __is >> __r;
+            if (!__is.fail())
+                __x = complex<_Tp>(__r, _Tp(0));
+            else
+                __is.setstate(ios_base::failbit);
+        }
+    }
+    else
+        __is.setstate(ios_base::failbit);
+    return __is;
+}
+
+template<class _Tp, class _CharT, class _Traits>
+basic_ostream<_CharT, _Traits>&
+operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
+{
+    basic_ostringstream<_CharT, _Traits> __s;
+    __s.flags(__os.flags());
+    __s.imbue(__os.getloc());
+    __s.precision(__os.precision());
+    __s << '(' << __x.real() << ',' << __x.imag() << ')';
+    return __os << __s.str();
+}
+
+#if _LIBCPP_STD_VER > 11 
+// Literal suffix for complex number literals [complex.literals]
+inline namespace literals
+{ 
+  inline namespace complex_literals
+  {
+    constexpr complex<long double> operator""il(long double __im)
+    {
+        return { 0.0l, __im };
+    }
+
+    constexpr complex<long double> operator""il(unsigned long long __im)
+    {
+        return { 0.0l, static_cast<long double>(__im) };
+    }
+
+
+    constexpr complex<double> operator""i(long double __im)
+    {
+        return { 0.0, static_cast<double>(__im) };
+    }
+
+    constexpr complex<double> operator""i(unsigned long long __im)
+    {
+        return { 0.0, static_cast<double>(__im) };
+    }
+
+
+    constexpr complex<float> operator""if(long double __im)
+    {
+        return { 0.0f, static_cast<float>(__im) };
+    }
+
+    constexpr complex<float> operator""if(unsigned long long __im)
+    {
+        return { 0.0f, static_cast<float>(__im) };
+    }
+  }
+}
+#endif
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif  // _LIBCPP_COMPLEX