Restoring authorship annotation for Andrey Khalyavin <[email protected]>. Commit 1 of 2.

1 files changed, 1488 insertions, 1488 deletions

diff --git a/contrib/libs/cxxsupp/libcxx/include/complex b/contrib/libs/cxxsupp/libcxx/include/complex
index e4c59193bce..8013b02b452 100644
--- a/contrib/libs/cxxsupp/libcxx/include/complex
+++ b/contrib/libs/cxxsupp/libcxx/include/complex
@@ -1,1495 +1,1495 @@
-// -*- C++ -*-
-//===--------------------------- complex ----------------------------------===//
-//
+// -*- C++ -*- 
+//===--------------------------- complex ----------------------------------===// 
+// 
 // 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_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& = T());
-
-// 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>&);
-
-}  // std
-
-*/
-
-#include <__config>
-#include <cmath>
-#include <iosfwd>
-#include <stdexcept>
-#include <type_traits>
+// 
+//===----------------------------------------------------------------------===// 
+ 
+#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& = T()); 
+ 
+// 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>&); 
+ 
+}  // std 
+ 
+*/ 
+ 
+#include <__config> 
+#include <cmath> 
+#include <iosfwd> 
+#include <stdexcept> 
+#include <type_traits> 
 #include <version>
-
-#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
-#   include <sstream> // for std::basic_ostringstream
-#endif
-
-#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
-#pragma GCC system_header
-#endif
-
-_LIBCPP_BEGIN_NAMESPACE_STD
-
-template<class _Tp> class _LIBCPP_TEMPLATE_VIS 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_TEMPLATE_VIS 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_TEMPLATE_VIS complex<double>;
-template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
-
-template<>
-class _LIBCPP_TEMPLATE_VIS 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) {}
-    _LIBCPP_INLINE_VISIBILITY
-    explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
-    _LIBCPP_INLINE_VISIBILITY
-    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_TEMPLATE_VIS 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_INLINE_VISIBILITY
-    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
-    _LIBCPP_INLINE_VISIBILITY
-    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_TEMPLATE_VIS 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_INLINE_VISIBILITY
-    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
-    _LIBCPP_INLINE_VISIBILITY
-    _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_CONSTEXPR
-complex<float>::complex(const complex<double>& __c)
-    : __re_(__c.real()), __im_(__c.imag()) {}
-
-inline
-_LIBCPP_CONSTEXPR
-complex<float>::complex(const complex<long double>& __c)
-    : __re_(__c.real()), __im_(__c.imag()) {}
-
-inline
-_LIBCPP_CONSTEXPR
-complex<double>::complex(const complex<float>& __c)
-    : __re_(__c.real()), __im_(__c.imag()) {}
-
-inline
-_LIBCPP_CONSTEXPR
-complex<double>::complex(const complex<long double>& __c)
-    : __re_(__c.real()), __im_(__c.imag()) {}
-
-inline
-_LIBCPP_CONSTEXPR
-complex<long double>::complex(const complex<float>& __c)
-    : __re_(__c.real()), __im_(__c.imag()) {}
-
-inline
-_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 (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
-    {
-        bool __recalc = false;
-        if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
-        {
-            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
-            if (__libcpp_isnan_or_builtin(__c))
-                __c = copysign(_Tp(0), __c);
-            if (__libcpp_isnan_or_builtin(__d))
-                __d = copysign(_Tp(0), __d);
-            __recalc = true;
-        }
-        if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
-        {
-            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
-            if (__libcpp_isnan_or_builtin(__a))
-                __a = copysign(_Tp(0), __a);
-            if (__libcpp_isnan_or_builtin(__b))
-                __b = copysign(_Tp(0), __b);
-            __recalc = true;
-        }
-        if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
-                          __libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
-        {
-            if (__libcpp_isnan_or_builtin(__a))
-                __a = copysign(_Tp(0), __a);
-            if (__libcpp_isnan_or_builtin(__b))
-                __b = copysign(_Tp(0), __b);
-            if (__libcpp_isnan_or_builtin(__c))
-                __c = copysign(_Tp(0), __c);
-            if (__libcpp_isnan_or_builtin(__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 (__libcpp_isfinite_or_builtin(__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 (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
-    {
-        if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
-        {
-            __x = copysign(_Tp(INFINITY), __c) * __a;
-            __y = copysign(_Tp(INFINITY), __c) * __b;
-        }
-        else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
-        {
-            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
-            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
-            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
-        }
-        else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
-        {
-            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = copysign(__libcpp_isinf_or_builtin(__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:
-
-template <class _Tp, bool = is_integral<_Tp>::value,
-                     bool = is_floating_point<_Tp>::value
-                     >
-struct __libcpp_complex_overload_traits {};
-
-// Integral Types
-template <class _Tp>
-struct __libcpp_complex_overload_traits<_Tp, true, false>
-{
-    typedef double _ValueType;
-    typedef complex<double> _ComplexType;
-};
-
-// Floating point types
-template <class _Tp>
-struct __libcpp_complex_overload_traits<_Tp, false, true>
-{
-    typedef _Tp _ValueType;
-    typedef complex<_Tp> _ComplexType;
-};
-
-// real
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
-_Tp
-real(const complex<_Tp>& __c)
-{
-    return __c.real();
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
-typename __libcpp_complex_overload_traits<_Tp>::_ValueType
-real(_Tp __re)
-{
-    return __re;
-}
-
-// imag
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
-_Tp
-imag(const complex<_Tp>& __c)
-{
-    return __c.imag();
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
-typename __libcpp_complex_overload_traits<_Tp>::_ValueType
-imag(_Tp)
-{
-    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());
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename enable_if<
-    is_same<_Tp, long double>::value,
-    long double
->::type
-arg(_Tp __re)
-{
-    return atan2l(0.L, __re);
-}
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename enable_if
-<
-    is_integral<_Tp>::value || is_same<_Tp, double>::value,
-    double
->::type
-arg(_Tp __re)
-{
-    return atan2(0., __re);
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename enable_if<
-    is_same<_Tp, float>::value,
-    float
->::type
-arg(_Tp __re)
-{
-    return atan2f(0.F, __re);
-}
-
-// norm
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-_Tp
-norm(const complex<_Tp>& __c)
-{
-    if (__libcpp_isinf_or_builtin(__c.real()))
-        return abs(__c.real());
-    if (__libcpp_isinf_or_builtin(__c.imag()))
-        return abs(__c.imag());
-    return __c.real() * __c.real() + __c.imag() * __c.imag();
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename __libcpp_complex_overload_traits<_Tp>::_ValueType
-norm(_Tp __re)
-{
-    typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
-    return static_cast<_ValueType>(__re) * __re;
-}
-
-// conj
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-complex<_Tp>
-conj(const complex<_Tp>& __c)
-{
-    return complex<_Tp>(__c.real(), -__c.imag());
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
-conj(_Tp __re)
-{
-    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
-    return _ComplexType(__re);
-}
-
-
-
-// proj
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-complex<_Tp>
-proj(const complex<_Tp>& __c)
-{
-    complex<_Tp> __r = __c;
-    if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
-        __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
-    return __r;
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename enable_if
-<
-    is_floating_point<_Tp>::value,
-    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
->::type
-proj(_Tp __re)
-{
-    if (__libcpp_isinf_or_builtin(__re))
-        __re = abs(__re);
-    return complex<_Tp>(__re);
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-typename enable_if
-<
-    is_integral<_Tp>::value,
-    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
->::type
-proj(_Tp __re)
-{
-    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
-    return _ComplexType(__re);
-}
-
-// polar
-
-template<class _Tp>
-complex<_Tp>
-polar(const _Tp& __rho, const _Tp& __theta = _Tp())
-{
-    if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
-        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
-    if (__libcpp_isnan_or_builtin(__theta))
-    {
-        if (__libcpp_isinf_or_builtin(__rho))
-            return complex<_Tp>(__rho, __theta);
-        return complex<_Tp>(__theta, __theta);
-    }
-    if (__libcpp_isinf_or_builtin(__theta))
-    {
-        if (__libcpp_isinf_or_builtin(__rho))
-            return complex<_Tp>(__rho, _Tp(NAN));
-        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
-    }
-    _Tp __x = __rho * cos(__theta);
-    if (__libcpp_isnan_or_builtin(__x))
-        __x = 0;
-    _Tp __y = __rho * sin(__theta);
-    if (__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.imag()))
-        return complex<_Tp>(_Tp(INFINITY), __x.imag());
-    if (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (__x.real() > _Tp(0))
-            return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
-        return complex<_Tp>(__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (__x.real() < _Tp(0))
-        {
-            if (!__libcpp_isfinite_or_builtin(__i))
-                __i = _Tp(1);
-        }
-        else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i))
-        {
-            if (__libcpp_isinf_or_builtin(__i))
-                __i = _Tp(NAN);
-            return complex<_Tp>(__x.real(), __i);
-        }
-    }
-    else if (__libcpp_isnan_or_builtin(__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));
-}
-
-// __sqr, computes pow(x, 2)
-
-template<class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-complex<_Tp>
-__sqr(const complex<_Tp>& __x)
-{
-    return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
-                        _Tp(2) * __x.real() * __x.imag());
-}
-
-// asinh
-
-template<class _Tp>
-complex<_Tp>
-asinh(const complex<_Tp>& __x)
-{
-    const _Tp __pi(atan2(+0., -0.));
-    if (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (__libcpp_isnan_or_builtin(__x.imag()))
-            return __x;
-        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real()))
-    {
-        if (__libcpp_isinf_or_builtin(__x.imag()))
-            return complex<_Tp>(__x.imag(), __x.real());
-        if (__x.imag() == 0)
-            return __x;
-        return complex<_Tp>(__x.real(), __x.real());
-    }
-    if (__libcpp_isinf_or_builtin(__x.imag()))
-        return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
-    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _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 (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (__libcpp_isnan_or_builtin(__x.imag()))
-            return complex<_Tp>(abs(__x.real()), __x.imag());
-        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real()))
-    {
-        if (__libcpp_isinf_or_builtin(__x.imag()))
-            return complex<_Tp>(abs(__x.imag()), __x.real());
-        return complex<_Tp>(__x.real(), __x.real());
-    }
-    if (__libcpp_isinf_or_builtin(__x.imag()))
-        return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
-    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _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 (__libcpp_isinf_or_builtin(__x.imag()))
-    {
-        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
-    }
-    if (__libcpp_isnan_or_builtin(__x.imag()))
-    {
-        if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0)
-            return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
-        return complex<_Tp>(__x.imag(), __x.imag());
-    }
-    if (__libcpp_isnan_or_builtin(__x.real()))
-    {
-        return complex<_Tp>(__x.real(), __x.real());
-    }
-    if (__libcpp_isinf_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
-        return complex<_Tp>(__x.real(), _Tp(NAN));
-    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
-        return complex<_Tp>(__x.real(), _Tp(NAN));
-    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
-        return complex<_Tp>(abs(__x.real()), _Tp(NAN));
-    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__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 && !__libcpp_isfinite_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (!__libcpp_isfinite_or_builtin(__x.imag()))
-            return complex<_Tp>(_Tp(1), _Tp(0));
-        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
-    }
-    if (__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()))
-    {
-        if (__libcpp_isnan_or_builtin(__x.imag()))
-            return complex<_Tp>(__x.imag(), __x.real());
-        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real()))
-    {
-        if (__libcpp_isinf_or_builtin(__x.imag()))
-            return complex<_Tp>(__x.real(), -__x.imag());
-        return complex<_Tp>(__x.real(), __x.real());
-    }
-    if (__libcpp_isinf_or_builtin(__x.imag()))
-        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
-    if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
-        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
-    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _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(__is.failbit);
-                    }
-                    else
-                        __is.setstate(__is.failbit);
-                }
-                else if (__c == _CharT(')'))
-                {
-                    __is.get();
-                    __x = complex<_Tp>(__r, _Tp(0));
-                }
-                else
-                    __is.setstate(__is.failbit);
-            }
-            else
-                __is.setstate(__is.failbit);
-        }
-        else
-        {
-            _Tp __r;
-            __is >> __r;
-            if (!__is.fail())
-                __x = complex<_Tp>(__r, _Tp(0));
-            else
-                __is.setstate(__is.failbit);
-        }
-    }
-    else
-        __is.setstate(__is.failbit);
-    return __is;
-}
-
-#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
-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();
-}
-#endif // !_LIBCPP_HAS_NO_LOCALIZATION
-
+ 
+#if !defined(_LIBCPP_HAS_NO_LOCALIZATION) 
+#   include <sstream> // for std::basic_ostringstream 
+#endif 
+ 
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 
+#pragma GCC system_header 
+#endif 
+ 
+_LIBCPP_BEGIN_NAMESPACE_STD 
+ 
+template<class _Tp> class _LIBCPP_TEMPLATE_VIS 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_TEMPLATE_VIS 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_TEMPLATE_VIS complex<double>; 
+template<> class _LIBCPP_TEMPLATE_VIS complex<long double>; 
+ 
+template<> 
+class _LIBCPP_TEMPLATE_VIS 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) {} 
+    _LIBCPP_INLINE_VISIBILITY 
+    explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c); 
+    _LIBCPP_INLINE_VISIBILITY 
+    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_TEMPLATE_VIS 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_INLINE_VISIBILITY 
+    _LIBCPP_CONSTEXPR complex(const complex<float>& __c); 
+    _LIBCPP_INLINE_VISIBILITY 
+    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_TEMPLATE_VIS 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_INLINE_VISIBILITY 
+    _LIBCPP_CONSTEXPR complex(const complex<float>& __c); 
+    _LIBCPP_INLINE_VISIBILITY 
+    _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_CONSTEXPR 
+complex<float>::complex(const complex<double>& __c) 
+    : __re_(__c.real()), __im_(__c.imag()) {} 
+ 
+inline 
+_LIBCPP_CONSTEXPR 
+complex<float>::complex(const complex<long double>& __c) 
+    : __re_(__c.real()), __im_(__c.imag()) {} 
+ 
+inline 
+_LIBCPP_CONSTEXPR 
+complex<double>::complex(const complex<float>& __c) 
+    : __re_(__c.real()), __im_(__c.imag()) {} 
+ 
+inline 
+_LIBCPP_CONSTEXPR 
+complex<double>::complex(const complex<long double>& __c) 
+    : __re_(__c.real()), __im_(__c.imag()) {} 
+ 
+inline 
+_LIBCPP_CONSTEXPR 
+complex<long double>::complex(const complex<float>& __c) 
+    : __re_(__c.real()), __im_(__c.imag()) {} 
+ 
+inline 
+_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 (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y)) 
+    { 
+        bool __recalc = false; 
+        if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) 
+        { 
+            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a); 
+            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b); 
+            if (__libcpp_isnan_or_builtin(__c)) 
+                __c = copysign(_Tp(0), __c); 
+            if (__libcpp_isnan_or_builtin(__d)) 
+                __d = copysign(_Tp(0), __d); 
+            __recalc = true; 
+        } 
+        if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d)) 
+        { 
+            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c); 
+            __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d); 
+            if (__libcpp_isnan_or_builtin(__a)) 
+                __a = copysign(_Tp(0), __a); 
+            if (__libcpp_isnan_or_builtin(__b)) 
+                __b = copysign(_Tp(0), __b); 
+            __recalc = true; 
+        } 
+        if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) || 
+                          __libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc))) 
+        { 
+            if (__libcpp_isnan_or_builtin(__a)) 
+                __a = copysign(_Tp(0), __a); 
+            if (__libcpp_isnan_or_builtin(__b)) 
+                __b = copysign(_Tp(0), __b); 
+            if (__libcpp_isnan_or_builtin(__c)) 
+                __c = copysign(_Tp(0), __c); 
+            if (__libcpp_isnan_or_builtin(__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 (__libcpp_isfinite_or_builtin(__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 (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y)) 
+    { 
+        if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b))) 
+        { 
+            __x = copysign(_Tp(INFINITY), __c) * __a; 
+            __y = copysign(_Tp(INFINITY), __c) * __b; 
+        } 
+        else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d)) 
+        { 
+            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a); 
+            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b); 
+            __x = _Tp(INFINITY) * (__a * __c + __b * __d); 
+            __y = _Tp(INFINITY) * (__b * __c - __a * __d); 
+        } 
+        else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b)) 
+        { 
+            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c); 
+            __d = copysign(__libcpp_isinf_or_builtin(__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: 
+ 
+template <class _Tp, bool = is_integral<_Tp>::value, 
+                     bool = is_floating_point<_Tp>::value 
+                     > 
+struct __libcpp_complex_overload_traits {}; 
+ 
+// Integral Types 
+template <class _Tp> 
+struct __libcpp_complex_overload_traits<_Tp, true, false> 
+{ 
+    typedef double _ValueType; 
+    typedef complex<double> _ComplexType; 
+}; 
+ 
+// Floating point types 
+template <class _Tp> 
+struct __libcpp_complex_overload_traits<_Tp, false, true> 
+{ 
+    typedef _Tp _ValueType; 
+    typedef complex<_Tp> _ComplexType; 
+}; 
+ 
+// real 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 
+_Tp 
+real(const complex<_Tp>& __c) 
+{ 
+    return __c.real(); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 
+typename __libcpp_complex_overload_traits<_Tp>::_ValueType 
+real(_Tp __re) 
+{ 
+    return __re; 
+} 
+ 
+// imag 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 
+_Tp 
+imag(const complex<_Tp>& __c) 
+{ 
+    return __c.imag(); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 
+typename __libcpp_complex_overload_traits<_Tp>::_ValueType 
+imag(_Tp) 
+{ 
+    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()); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename enable_if< 
+    is_same<_Tp, long double>::value, 
+    long double 
+>::type 
+arg(_Tp __re) 
+{ 
+    return atan2l(0.L, __re); 
+} 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename enable_if 
+< 
+    is_integral<_Tp>::value || is_same<_Tp, double>::value, 
+    double 
+>::type 
+arg(_Tp __re) 
+{ 
+    return atan2(0., __re); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename enable_if< 
+    is_same<_Tp, float>::value, 
+    float 
+>::type 
+arg(_Tp __re) 
+{ 
+    return atan2f(0.F, __re); 
+} 
+ 
+// norm 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+_Tp 
+norm(const complex<_Tp>& __c) 
+{ 
+    if (__libcpp_isinf_or_builtin(__c.real())) 
+        return abs(__c.real()); 
+    if (__libcpp_isinf_or_builtin(__c.imag())) 
+        return abs(__c.imag()); 
+    return __c.real() * __c.real() + __c.imag() * __c.imag(); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename __libcpp_complex_overload_traits<_Tp>::_ValueType 
+norm(_Tp __re) 
+{ 
+    typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType; 
+    return static_cast<_ValueType>(__re) * __re; 
+} 
+ 
+// conj 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+complex<_Tp> 
+conj(const complex<_Tp>& __c) 
+{ 
+    return complex<_Tp>(__c.real(), -__c.imag()); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename __libcpp_complex_overload_traits<_Tp>::_ComplexType 
+conj(_Tp __re) 
+{ 
+    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; 
+    return _ComplexType(__re); 
+} 
+ 
+ 
+ 
+// proj 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+complex<_Tp> 
+proj(const complex<_Tp>& __c) 
+{ 
+    complex<_Tp> __r = __c; 
+    if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag())) 
+        __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag())); 
+    return __r; 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename enable_if 
+< 
+    is_floating_point<_Tp>::value, 
+    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType 
+>::type 
+proj(_Tp __re) 
+{ 
+    if (__libcpp_isinf_or_builtin(__re)) 
+        __re = abs(__re); 
+    return complex<_Tp>(__re); 
+} 
+ 
+template <class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+typename enable_if 
+< 
+    is_integral<_Tp>::value, 
+    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType 
+>::type 
+proj(_Tp __re) 
+{ 
+    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; 
+    return _ComplexType(__re); 
+} 
+ 
+// polar 
+ 
+template<class _Tp> 
+complex<_Tp> 
+polar(const _Tp& __rho, const _Tp& __theta = _Tp()) 
+{ 
+    if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho)) 
+        return complex<_Tp>(_Tp(NAN), _Tp(NAN)); 
+    if (__libcpp_isnan_or_builtin(__theta)) 
+    { 
+        if (__libcpp_isinf_or_builtin(__rho)) 
+            return complex<_Tp>(__rho, __theta); 
+        return complex<_Tp>(__theta, __theta); 
+    } 
+    if (__libcpp_isinf_or_builtin(__theta)) 
+    { 
+        if (__libcpp_isinf_or_builtin(__rho)) 
+            return complex<_Tp>(__rho, _Tp(NAN)); 
+        return complex<_Tp>(_Tp(NAN), _Tp(NAN)); 
+    } 
+    _Tp __x = __rho * cos(__theta); 
+    if (__libcpp_isnan_or_builtin(__x)) 
+        __x = 0; 
+    _Tp __y = __rho * sin(__theta); 
+    if (__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.imag())) 
+        return complex<_Tp>(_Tp(INFINITY), __x.imag()); 
+    if (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (__x.real() > _Tp(0)) 
+            return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag())); 
+        return complex<_Tp>(__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (__x.real() < _Tp(0)) 
+        { 
+            if (!__libcpp_isfinite_or_builtin(__i)) 
+                __i = _Tp(1); 
+        } 
+        else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i)) 
+        { 
+            if (__libcpp_isinf_or_builtin(__i)) 
+                __i = _Tp(NAN); 
+            return complex<_Tp>(__x.real(), __i); 
+        } 
+    } 
+    else if (__libcpp_isnan_or_builtin(__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)); 
+} 
+ 
+// __sqr, computes pow(x, 2) 
+ 
+template<class _Tp> 
+inline _LIBCPP_INLINE_VISIBILITY 
+complex<_Tp> 
+__sqr(const complex<_Tp>& __x) 
+{ 
+    return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()), 
+                        _Tp(2) * __x.real() * __x.imag()); 
+} 
+ 
+// asinh 
+ 
+template<class _Tp> 
+complex<_Tp> 
+asinh(const complex<_Tp>& __x) 
+{ 
+    const _Tp __pi(atan2(+0., -0.)); 
+    if (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isnan_or_builtin(__x.imag())) 
+            return __x; 
+        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isinf_or_builtin(__x.imag())) 
+            return complex<_Tp>(__x.imag(), __x.real()); 
+        if (__x.imag() == 0) 
+            return __x; 
+        return complex<_Tp>(__x.real(), __x.real()); 
+    } 
+    if (__libcpp_isinf_or_builtin(__x.imag())) 
+        return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag())); 
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _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 (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isnan_or_builtin(__x.imag())) 
+            return complex<_Tp>(abs(__x.real()), __x.imag()); 
+        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isinf_or_builtin(__x.imag())) 
+            return complex<_Tp>(abs(__x.imag()), __x.real()); 
+        return complex<_Tp>(__x.real(), __x.real()); 
+    } 
+    if (__libcpp_isinf_or_builtin(__x.imag())) 
+        return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag())); 
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _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 (__libcpp_isinf_or_builtin(__x.imag())) 
+    { 
+        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag())); 
+    } 
+    if (__libcpp_isnan_or_builtin(__x.imag())) 
+    { 
+        if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0) 
+            return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag()); 
+        return complex<_Tp>(__x.imag(), __x.imag()); 
+    } 
+    if (__libcpp_isnan_or_builtin(__x.real())) 
+    { 
+        return complex<_Tp>(__x.real(), __x.real()); 
+    } 
+    if (__libcpp_isinf_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag())) 
+        return complex<_Tp>(__x.real(), _Tp(NAN)); 
+    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag())) 
+        return complex<_Tp>(__x.real(), _Tp(NAN)); 
+    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag())) 
+        return complex<_Tp>(abs(__x.real()), _Tp(NAN)); 
+    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__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 && !__libcpp_isfinite_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (!__libcpp_isfinite_or_builtin(__x.imag())) 
+            return complex<_Tp>(_Tp(1), _Tp(0)); 
+        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag()))); 
+    } 
+    if (__libcpp_isnan_or_builtin(__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 (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__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 (__libcpp_isinf_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isnan_or_builtin(__x.imag())) 
+            return complex<_Tp>(__x.imag(), __x.real()); 
+        if (__libcpp_isinf_or_builtin(__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 (__libcpp_isnan_or_builtin(__x.real())) 
+    { 
+        if (__libcpp_isinf_or_builtin(__x.imag())) 
+            return complex<_Tp>(__x.real(), -__x.imag()); 
+        return complex<_Tp>(__x.real(), __x.real()); 
+    } 
+    if (__libcpp_isinf_or_builtin(__x.imag())) 
+        return complex<_Tp>(__pi/_Tp(2), -__x.imag()); 
+    if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag()))) 
+        return complex<_Tp>(__pi/_Tp(2), -__x.imag()); 
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _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(__is.failbit); 
+                    } 
+                    else 
+                        __is.setstate(__is.failbit); 
+                } 
+                else if (__c == _CharT(')')) 
+                { 
+                    __is.get(); 
+                    __x = complex<_Tp>(__r, _Tp(0)); 
+                } 
+                else 
+                    __is.setstate(__is.failbit); 
+            } 
+            else 
+                __is.setstate(__is.failbit); 
+        } 
+        else 
+        { 
+            _Tp __r; 
+            __is >> __r; 
+            if (!__is.fail()) 
+                __x = complex<_Tp>(__r, _Tp(0)); 
+            else 
+                __is.setstate(__is.failbit); 
+        } 
+    } 
+    else 
+        __is.setstate(__is.failbit); 
+    return __is; 
+} 
+ 
+#if !defined(_LIBCPP_HAS_NO_LOCALIZATION) 
+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(); 
+} 
+#endif // !_LIBCPP_HAS_NO_LOCALIZATION 
+ 
 #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) };
-    }
-
-
+// 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) }; 
+    } 
+ 
+ 
 #if !defined(__CUDACC__)
-    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
-  }
-}
+    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
+  } 
+} 
+#endif 
+ 
+_LIBCPP_END_NAMESPACE_STD 
+ 
+#endif // _LIBCPP_COMPLEX