// -*- C++ -*-
//===--------------------------- complex ----------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_COMPLEX
#define _LIBCPP_COMPLEX
#if defined _GLIBCXX_COMPLEX
#error monkey patching of <complex> failed
#endif

/*
    complex synopsis

namespace std
{

template<class T>
class complex
{
public:
    typedef T value_type;

    complex(const T& re = T(), const T& im = T()); // constexpr in C++14
    complex(const complex&);  // constexpr in C++14
    template<class X> complex(const complex<X>&);  // constexpr in C++14

    T real() const; // constexpr in C++14
    T imag() const; // constexpr in C++14

    void real(T);
    void imag(T);

    complex<T>& operator= (const T&);
    complex<T>& operator+=(const T&);
    complex<T>& operator-=(const T&);
    complex<T>& operator*=(const T&);
    complex<T>& operator/=(const T&);

    complex& operator=(const complex&);
    template<class X> complex<T>& operator= (const complex<X>&);
    template<class X> complex<T>& operator+=(const complex<X>&);
    template<class X> complex<T>& operator-=(const complex<X>&);
    template<class X> complex<T>& operator*=(const complex<X>&);
    template<class X> complex<T>& operator/=(const complex<X>&);
};

template<>
class complex<float>
{
public:
    typedef float value_type;

    constexpr complex(float re = 0.0f, float im = 0.0f);
    explicit constexpr complex(const complex<double>&);
    explicit constexpr complex(const complex<long double>&);

    constexpr float real() const;
    void real(float);
    constexpr float imag() const;
    void imag(float);

    complex<float>& operator= (float);
    complex<float>& operator+=(float);
    complex<float>& operator-=(float);
    complex<float>& operator*=(float);
    complex<float>& operator/=(float);

    complex<float>& operator=(const complex<float>&);
    template<class X> complex<float>& operator= (const complex<X>&);
    template<class X> complex<float>& operator+=(const complex<X>&);
    template<class X> complex<float>& operator-=(const complex<X>&);
    template<class X> complex<float>& operator*=(const complex<X>&);
    template<class X> complex<float>& operator/=(const complex<X>&);
};

template<>
class complex<double>
{
public:
    typedef double value_type;

    constexpr complex(double re = 0.0, double im = 0.0);
    constexpr complex(const complex<float>&);
    explicit constexpr complex(const complex<long double>&);

    constexpr double real() const;
    void real(double);
    constexpr double imag() const;
    void imag(double);

    complex<double>& operator= (double);
    complex<double>& operator+=(double);
    complex<double>& operator-=(double);
    complex<double>& operator*=(double);
    complex<double>& operator/=(double);
    complex<double>& operator=(const complex<double>&);

    template<class X> complex<double>& operator= (const complex<X>&);
    template<class X> complex<double>& operator+=(const complex<X>&);
    template<class X> complex<double>& operator-=(const complex<X>&);
    template<class X> complex<double>& operator*=(const complex<X>&);
    template<class X> complex<double>& operator/=(const complex<X>&);
};

template<>
class complex<long double>
{
public:
    typedef long double value_type;

    constexpr complex(long double re = 0.0L, long double im = 0.0L);
    constexpr complex(const complex<float>&);
    constexpr complex(const complex<double>&);

    constexpr long double real() const;
    void real(long double);
    constexpr long double imag() const;
    void imag(long double);

    complex<long double>& operator=(const complex<long double>&);
    complex<long double>& operator= (long double);
    complex<long double>& operator+=(long double);
    complex<long double>& operator-=(long double);
    complex<long double>& operator*=(long double);
    complex<long double>& operator/=(long double);

    template<class X> complex<long double>& operator= (const complex<X>&);
    template<class X> complex<long double>& operator+=(const complex<X>&);
    template<class X> complex<long double>& operator-=(const complex<X>&);
    template<class X> complex<long double>& operator*=(const complex<X>&);
    template<class X> complex<long double>& operator/=(const complex<X>&);
};

// 26.3.6 operators:
template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&, const T&);
template<class T> complex<T> operator+(const T&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const T&);
template<class T> complex<T> operator-(const T&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const T&);
template<class T> complex<T> operator*(const T&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const T&);
template<class T> complex<T> operator/(const T&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&);
template<class T> bool operator==(const complex<T>&, const complex<T>&); //
constexpr in C++14
template<class T> bool operator==(const complex<T>&, const T&); // constexpr in
C++14
template<class T> bool operator==(const T&, const complex<T>&); // constexpr in
C++14
template<class T> bool operator!=(const complex<T>&, const complex<T>&); //
constexpr in C++14
template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in
C++14
template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in
C++14

template<class T, class charT, class traits>
  basic_istream<charT, traits>&
  operator>>(basic_istream<charT, traits>&, complex<T>&);
template<class T, class charT, class traits>
  basic_ostream<charT, traits>&
  operator<<(basic_ostream<charT, traits>&, const complex<T>&);

// 26.3.7 values:

template<class T>              T real(const complex<T>&); // constexpr in C++14
                     long double real(long double);       // constexpr in C++14
                          double real(double);            // constexpr in C++14
template<Integral T>      double real(T);                 // constexpr in C++14
                          float  real(float);             // constexpr in C++14

template<class T>              T imag(const complex<T>&); // constexpr in C++14
                     long double imag(long double);       // constexpr in C++14
                          double imag(double);            // constexpr in C++14
template<Integral T>      double imag(T);                 // constexpr in C++14
                          float  imag(float);             // constexpr in C++14

template<class T> T abs(const complex<T>&);

template<class T>              T arg(const complex<T>&);
                     long double arg(long double);
                          double arg(double);
template<Integral T>      double arg(T);
                          float  arg(float);

template<class T>              T norm(const complex<T>&);
                     long double norm(long double);
                          double norm(double);
template<Integral T>      double norm(T);
                          float  norm(float);

template<class T>      complex<T>           conj(const complex<T>&);
                       complex<long double> conj(long double);
                       complex<double>      conj(double);
template<Integral T>   complex<double>      conj(T);
                       complex<float>       conj(float);

template<class T>    complex<T>           proj(const complex<T>&);
                     complex<long double> proj(long double);
                     complex<double>      proj(double);
template<Integral T> complex<double>      proj(T);
                     complex<float>       proj(float);

template<class T> complex<T> polar(const T&, const T& = 0);

// 26.3.8 transcendentals:
template<class T> complex<T> acos(const complex<T>&);
template<class T> complex<T> asin(const complex<T>&);
template<class T> complex<T> atan(const complex<T>&);
template<class T> complex<T> acosh(const complex<T>&);
template<class T> complex<T> asinh(const complex<T>&);
template<class T> complex<T> atanh(const complex<T>&);
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10(const complex<T>&);

template<class T> complex<T> pow(const complex<T>&, const T&);
template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
template<class T> complex<T> pow(const T&, const complex<T>&);

template<class T> complex<T> sin (const complex<T>&);
template<class T> complex<T> sinh (const complex<T>&);
template<class T> complex<T> sqrt (const complex<T>&);
template<class T> complex<T> tan (const complex<T>&);
template<class T> complex<T> tanh (const complex<T>&);

template<class T, class charT, class traits>
  basic_istream<charT, traits>&
  operator>>(basic_istream<charT, traits>& is, complex<T>& x);

template<class T, class charT, class traits>
  basic_ostream<charT, traits>&
  operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);

}  // std

*/

// pythran #include <__config>
#define _LIBCPP_BEGIN_NAMESPACE_STD                                            \
  namespace std                                                                \
  {
#define _LIBCPP_END_NAMESPACE_STD }
#define _LIBCPP_TYPE_VIS_ONLY
#define _VSTD std
#define _LIBCPP_INLINE_VISIBILITY
#define _LIBCPP_CONSTEXPR_AFTER_CXX11 constexpr
#define _LIBCPP_CONSTEXPR

#include <type_traits>
#include <stdexcept>
#include <cmath>
#include <sstream>
#if defined(_LIBCPP_NO_EXCEPTIONS)
#include <cassert>
#endif

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

_LIBCPP_BEGIN_NAMESPACE_STD

template <class U, class V>
struct __promote {
  typedef decltype(std::declval<U>() + std::declval<V>()) type;
};

template <class _Tp>
class _LIBCPP_TYPE_VIS_ONLY complex;

template <class _Tp>
complex<_Tp> operator*(const complex<_Tp> &__z, const complex<_Tp> &__w);
template <class _Tp>
complex<_Tp> operator/(const complex<_Tp> &__x, const complex<_Tp> &__y);

template <class _Tp>
class _LIBCPP_TYPE_VIS_ONLY complex
{
public:
  typedef _Tp value_type;

private:
  value_type __re_;
  value_type __im_;

public:
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
  complex(const value_type &__re = value_type(),
          const value_type &__im = value_type())
      : __re_(__re), __im_(__im)
  {
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
  complex(const complex<_Xp> &__c)
      : __re_(__c.real()), __im_(__c.imag())
  {
  }

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type
  real() const
  {
    return __re_;
  }
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type
  imag() const
  {
    return __im_;
  }

  _LIBCPP_INLINE_VISIBILITY void real(value_type __re)
  {
    __re_ = __re;
  }
  _LIBCPP_INLINE_VISIBILITY void imag(value_type __im)
  {
    __im_ = __im;
  }

  _LIBCPP_INLINE_VISIBILITY complex &operator=(const value_type &__re)
  {
    __re_ = __re;
    __im_ = value_type();
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(const value_type &__re)
  {
    __re_ += __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(const value_type &__re)
  {
    __re_ -= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(const value_type &__re)
  {
    __re_ *= __re;
    __im_ *= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(const value_type &__re)
  {
    __re_ /= __re;
    __im_ /= __re;
    return *this;
  }

  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator=(const complex<_Xp> &__c)
  {
    __re_ = __c.real();
    __im_ = __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(const complex<_Xp> &__c)
  {
    __re_ += __c.real();
    __im_ += __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(const complex<_Xp> &__c)
  {
    __re_ -= __c.real();
    __im_ -= __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(const complex<_Xp> &__c)
  {
    *this = *this *complex(__c.real(), __c.imag());
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(const complex<_Xp> &__c)
  {
    *this = *this / complex(__c.real(), __c.imag());
    return *this;
  }
};

template <>
class _LIBCPP_TYPE_VIS_ONLY complex<double>;
template <>
class _LIBCPP_TYPE_VIS_ONLY complex<long double>;

template <>
class _LIBCPP_TYPE_VIS_ONLY complex<float>
{
  float __re_;
  float __im_;

public:
  typedef float value_type;

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
  complex(float __re = 0.0f, float __im = 0.0f)
      : __re_(__re), __im_(__im)
  {
  }
  explicit _LIBCPP_CONSTEXPR complex(const complex<double> &__c);
  explicit _LIBCPP_CONSTEXPR complex(const complex<long double> &__c);

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const
  {
    return __re_;
  }
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const
  {
    return __im_;
  }

  _LIBCPP_INLINE_VISIBILITY void real(value_type __re)
  {
    __re_ = __re;
  }
  _LIBCPP_INLINE_VISIBILITY void imag(value_type __im)
  {
    __im_ = __im;
  }

  _LIBCPP_INLINE_VISIBILITY complex &operator=(float __re)
  {
    __re_ = __re;
    __im_ = value_type();
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(float __re)
  {
    __re_ += __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(float __re)
  {
    __re_ -= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(float __re)
  {
    __re_ *= __re;
    __im_ *= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(float __re)
  {
    __re_ /= __re;
    __im_ /= __re;
    return *this;
  }

  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator=(const complex<_Xp> &__c)
  {
    __re_ = __c.real();
    __im_ = __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(const complex<_Xp> &__c)
  {
    __re_ += __c.real();
    __im_ += __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(const complex<_Xp> &__c)
  {
    __re_ -= __c.real();
    __im_ -= __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(const complex<_Xp> &__c)
  {
    *this = *this *complex(__c.real(), __c.imag());
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(const complex<_Xp> &__c)
  {
    *this = *this / complex(__c.real(), __c.imag());
    return *this;
  }
};

template <>
class _LIBCPP_TYPE_VIS_ONLY complex<double>
{
  double __re_;
  double __im_;

public:
  typedef double value_type;

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
  complex(double __re = 0.0, double __im = 0.0)
      : __re_(__re), __im_(__im)
  {
  }
  _LIBCPP_CONSTEXPR complex(const complex<float> &__c);
  explicit _LIBCPP_CONSTEXPR complex(const complex<long double> &__c);

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const
  {
    return __re_;
  }
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const
  {
    return __im_;
  }

  _LIBCPP_INLINE_VISIBILITY void real(value_type __re)
  {
    __re_ = __re;
  }
  _LIBCPP_INLINE_VISIBILITY void imag(value_type __im)
  {
    __im_ = __im;
  }

  _LIBCPP_INLINE_VISIBILITY complex &operator=(double __re)
  {
    __re_ = __re;
    __im_ = value_type();
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(double __re)
  {
    __re_ += __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(double __re)
  {
    __re_ -= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(double __re)
  {
    __re_ *= __re;
    __im_ *= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(double __re)
  {
    __re_ /= __re;
    __im_ /= __re;
    return *this;
  }

  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator=(const complex<_Xp> &__c)
  {
    __re_ = __c.real();
    __im_ = __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(const complex<_Xp> &__c)
  {
    __re_ += __c.real();
    __im_ += __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(const complex<_Xp> &__c)
  {
    __re_ -= __c.real();
    __im_ -= __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(const complex<_Xp> &__c)
  {
    *this = *this *complex(__c.real(), __c.imag());
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(const complex<_Xp> &__c)
  {
    *this = *this / complex(__c.real(), __c.imag());
    return *this;
  }
};

template <>
class _LIBCPP_TYPE_VIS_ONLY complex<long double>
{
  long double __re_;
  long double __im_;

public:
  typedef long double value_type;

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
  complex(long double __re = 0.0L, long double __im = 0.0L)
      : __re_(__re), __im_(__im)
  {
  }
  _LIBCPP_CONSTEXPR complex(const complex<float> &__c);
  _LIBCPP_CONSTEXPR complex(const complex<double> &__c);

  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const
  {
    return __re_;
  }
  _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const
  {
    return __im_;
  }

  _LIBCPP_INLINE_VISIBILITY void real(value_type __re)
  {
    __re_ = __re;
  }
  _LIBCPP_INLINE_VISIBILITY void imag(value_type __im)
  {
    __im_ = __im;
  }

  _LIBCPP_INLINE_VISIBILITY complex &operator=(long double __re)
  {
    __re_ = __re;
    __im_ = value_type();
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(long double __re)
  {
    __re_ += __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(long double __re)
  {
    __re_ -= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(long double __re)
  {
    __re_ *= __re;
    __im_ *= __re;
    return *this;
  }
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(long double __re)
  {
    __re_ /= __re;
    __im_ /= __re;
    return *this;
  }

  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator=(const complex<_Xp> &__c)
  {
    __re_ = __c.real();
    __im_ = __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator+=(const complex<_Xp> &__c)
  {
    __re_ += __c.real();
    __im_ += __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator-=(const complex<_Xp> &__c)
  {
    __re_ -= __c.real();
    __im_ -= __c.imag();
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator*=(const complex<_Xp> &__c)
  {
    *this = *this *complex(__c.real(), __c.imag());
    return *this;
  }
  template <class _Xp>
  _LIBCPP_INLINE_VISIBILITY complex &operator/=(const complex<_Xp> &__c)
  {
    *this = *this / complex(__c.real(), __c.imag());
    return *this;
  }
};

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<float>::complex(const complex<double> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<float>::complex(const complex<long double> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<double>::complex(const complex<float> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<double>::complex(const complex<long double> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<long double>::complex(const complex<float> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
complex<long double>::complex(const complex<double> &__c)
    : __re_(__c.real()), __im_(__c.imag())
{
}

// 26.3.6 operators:

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator+(const complex<_Tp> &__x,
                                                        const complex<_Tp> &__y)
{
  complex<_Tp> __t(__x);
  __t += __y;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator+(const complex<_Tp> &__x,
                                                        const _Tp &__y)
{
  complex<_Tp> __t(__x);
  __t += __y;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator+(const _Tp &__x,
                                                        const complex<_Tp> &__y)
{
  complex<_Tp> __t(__y);
  __t += __x;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator-(const complex<_Tp> &__x,
                                                        const complex<_Tp> &__y)
{
  complex<_Tp> __t(__x);
  __t -= __y;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator-(const complex<_Tp> &__x,
                                                        const _Tp &__y)
{
  complex<_Tp> __t(__x);
  __t -= __y;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator-(const _Tp &__x,
                                                        const complex<_Tp> &__y)
{
  complex<_Tp> __t(-__y);
  __t += __x;
  return __t;
}

template <class _Tp>
complex<_Tp> operator*(const complex<_Tp> &__z, const complex<_Tp> &__w)
{
  _Tp __a = __z.real();
  _Tp __b = __z.imag();
  _Tp __c = __w.real();
  _Tp __d = __w.imag();
  _Tp __ac = __a * __c;
  _Tp __bd = __b * __d;
  _Tp __ad = __a * __d;
  _Tp __bc = __b * __c;
  _Tp __x = __ac - __bd;
  _Tp __y = __ad + __bc;
#if 0 // not required by numpy!
    if (isnan(__x) && isnan(__y))
    {
        bool __recalc = false;
        if (isinf(__a) || isinf(__b))
        {
            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
            __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
            if (isnan(__c))
                __c = copysign(_Tp(0), __c);
            if (isnan(__d))
                __d = copysign(_Tp(0), __d);
            __recalc = true;
        }
        if (isinf(__c) || isinf(__d))
        {
            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
            __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
            if (isnan(__a))
                __a = copysign(_Tp(0), __a);
            if (isnan(__b))
                __b = copysign(_Tp(0), __b);
            __recalc = true;
        }
        if (!__recalc && (isinf(__ac) || isinf(__bd) ||
                          isinf(__ad) || isinf(__bc)))
        {
            if (isnan(__a))
                __a = copysign(_Tp(0), __a);
            if (isnan(__b))
                __b = copysign(_Tp(0), __b);
            if (isnan(__c))
                __c = copysign(_Tp(0), __c);
            if (isnan(__d))
                __d = copysign(_Tp(0), __d);
            __recalc = true;
        }
        if (__recalc)
        {
            __x = _Tp(INFINITY) * (__a * __c - __b * __d);
            __y = _Tp(INFINITY) * (__a * __d + __b * __c);
        }
    }
#endif
  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();
#if 0 // not required by numpy
    _Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
    if (isfinite(__logbw))
    {
        __ilogbw = static_cast<int>(__logbw);
        __c = scalbn(__c, -__ilogbw);
        __d = scalbn(__d, -__ilogbw);
    }
    _Tp __denom = __c * __c + __d * __d;
    _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
    _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
    if (isnan(__x) && isnan(__y))
    {
        if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
        {
            __x = copysign(_Tp(INFINITY), __c) * __a;
            __y = copysign(_Tp(INFINITY), __c) * __b;
        }
        else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
        {
            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
            __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
        }
        else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
        {
            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
            __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
            __x = _Tp(0) * (__a * __c + __b * __d);
            __y = _Tp(0) * (__b * __c - __a * __d);
        }
    }
    return complex<_Tp>(__x, __y);
#else
  _Tp __e = __c * __c + __d * __d;
  return complex<_Tp>(__c * __a + __d * __b, __c * __b - __d * __a) / __e;
#endif
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator/(const complex<_Tp> &__x,
                                                        const _Tp &__y)
{
  return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator/(const _Tp &__x,
                                                        const complex<_Tp> &__y)
{
  complex<_Tp> __t(__x);
  __t /= __y;
  return __t;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator+(const complex<_Tp> &__x)
{
  return __x;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> operator-(const complex<_Tp> &__x)
{
  return complex<_Tp>(-__x.real(), -__x.imag());
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator==(const complex<_Tp> &__x, const complex<_Tp> &__y)
{
  return __x.real() == __y.real() && __x.imag() == __y.imag();
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator==(const complex<_Tp> &__x, const _Tp &__y)
{
  return __x.real() == __y && __x.imag() == 0;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator==(const _Tp &__x, const complex<_Tp> &__y)
{
  return __x == __y.real() && 0 == __y.imag();
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator!=(const complex<_Tp> &__x, const complex<_Tp> &__y)
{
  return !(__x == __y);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator!=(const complex<_Tp> &__x, const _Tp &__y)
{
  return !(__x == __y);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 bool
operator!=(const _Tp &__x, const complex<_Tp> &__y)
{
  return !(__x == __y);
}

// 26.3.7 values:

// real

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 _Tp
real(const complex<_Tp> &__c)
{
  return __c.real();
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 long double
real(long double __re)
{
  return __re;
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 double
real(double __re)
{
  return __re;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
    typename enable_if<is_integral<_Tp>::value, double>::type
    real(_Tp __re)
{
  return __re;
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 float
real(float __re)
{
  return __re;
}

// imag

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 _Tp
imag(const complex<_Tp> &__c)
{
  return __c.imag();
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 long double
imag(long double __re)
{
  return 0;
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 double
imag(double __re)
{
  return 0;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
    typename enable_if<is_integral<_Tp>::value, double>::type
    imag(_Tp __re)
{
  return 0;
}

inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 float
imag(float __re)
{
  return 0;
}

// abs

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _Tp abs(const complex<_Tp> &__c)
{
  return hypot(__c.real(), __c.imag());
}

// arg

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _Tp arg(const complex<_Tp> &__c)
{
  return atan2(__c.imag(), __c.real());
}

inline _LIBCPP_INLINE_VISIBILITY long double arg(long double __re)
{
  return atan2l(0.L, __re);
}

inline _LIBCPP_INLINE_VISIBILITY double arg(double __re)
{
  return atan2(0., __re);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_integral<_Tp>::value, double>::type
    arg(_Tp __re)
{
  return atan2(0., __re);
}

inline _LIBCPP_INLINE_VISIBILITY float arg(float __re)
{
  return atan2f(0.F, __re);
}

// norm

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _Tp norm(const complex<_Tp> &__c)
{
  if (isinf(__c.real()))
    return abs(__c.real());
  if (isinf(__c.imag()))
    return abs(__c.imag());
  return __c.real() * __c.real() + __c.imag() * __c.imag();
}

inline _LIBCPP_INLINE_VISIBILITY long double norm(long double __re)
{
  return __re * __re;
}

inline _LIBCPP_INLINE_VISIBILITY double norm(double __re)
{
  return __re * __re;
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_integral<_Tp>::value, double>::type
    norm(_Tp __re)
{
  return (double)__re * __re;
}

inline _LIBCPP_INLINE_VISIBILITY float norm(float __re)
{
  return __re * __re;
}

// conj

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> conj(const complex<_Tp> &__c)
{
  return complex<_Tp>(__c.real(), -__c.imag());
}

inline _LIBCPP_INLINE_VISIBILITY complex<long double> conj(long double __re)
{
  return complex<long double>(__re);
}

inline _LIBCPP_INLINE_VISIBILITY complex<double> conj(double __re)
{
  return complex<double>(__re);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_integral<_Tp>::value, complex<double>>::type
    conj(_Tp __re)
{
  return complex<double>(__re);
}

inline _LIBCPP_INLINE_VISIBILITY complex<float> conj(float __re)
{
  return complex<float>(__re);
}

// proj

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> proj(const complex<_Tp> &__c)
{
  std::complex<_Tp> __r = __c;
  if (isinf(__c.real()) || isinf(__c.imag()))
    __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
  return __r;
}

inline _LIBCPP_INLINE_VISIBILITY complex<long double> proj(long double __re)
{
  if (isinf(__re))
    __re = abs(__re);
  return complex<long double>(__re);
}

inline _LIBCPP_INLINE_VISIBILITY complex<double> proj(double __re)
{
  if (isinf(__re))
    __re = abs(__re);
  return complex<double>(__re);
}

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_integral<_Tp>::value, complex<double>>::type
    proj(_Tp __re)
{
  return complex<double>(__re);
}

inline _LIBCPP_INLINE_VISIBILITY complex<float> proj(float __re)
{
  if (isinf(__re))
    __re = abs(__re);
  return complex<float>(__re);
}

// polar

template <class _Tp>
complex<_Tp> polar(const _Tp &__rho, const _Tp &__theta = _Tp(0))
{
  if (isnan(__rho) || signbit(__rho))
    return complex<_Tp>(_Tp(NAN), _Tp(NAN));
  if (isnan(__theta)) {
    if (isinf(__rho))
      return complex<_Tp>(__rho, __theta);
    return complex<_Tp>(__theta, __theta);
  }
  if (isinf(__theta)) {
    if (isinf(__rho))
      return complex<_Tp>(__rho, _Tp(NAN));
    return complex<_Tp>(_Tp(NAN), _Tp(NAN));
  }
  _Tp __x = __rho * cos(__theta);
  if (isnan(__x))
    __x = 0;
  _Tp __y = __rho * sin(__theta);
  if (isnan(__y))
    __y = 0;
  return complex<_Tp>(__x, __y);
}

// log

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> log(const complex<_Tp> &__x)
{
  return complex<_Tp>(log(abs(__x)), arg(__x));
}

// log10

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> log10(const complex<_Tp> &__x)
{
  return log(__x) / log(_Tp(10));
}

// sqrt

template <class _Tp>
complex<_Tp> sqrt(const complex<_Tp> &__x)
{
  if (isinf(__x.imag()))
    return complex<_Tp>(_Tp(INFINITY), __x.imag());
  if (isinf(__x.real())) {
    if (__x.real() > _Tp(0))
      return complex<_Tp>(__x.real(), isnan(__x.imag())
                                          ? __x.imag()
                                          : copysign(_Tp(0), __x.imag()));
    return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0),
                        copysign(__x.real(), __x.imag()));
  }
  return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
}

// exp

template <class _Tp>
complex<_Tp> exp(const complex<_Tp> &__x)
{
  _Tp __i = __x.imag();
  if (isinf(__x.real())) {
    if (__x.real() < _Tp(0)) {
      if (!isfinite(__i))
        __i = _Tp(1);
    } else if (__i == 0 || !isfinite(__i)) {
      if (isinf(__i))
        __i = _Tp(NAN);
      return complex<_Tp>(__x.real(), __i);
    }
  } else if (isnan(__x.real()) && __x.imag() == 0)
    return __x;
  _Tp __e = exp(__x.real());
  return complex<_Tp>(__e * cos(__i), __e * sin(__i));
}

// pow

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> pow(const complex<_Tp> &__x,
                                                  const complex<_Tp> &__y)
{
  return exp(__y * log(__x));
}

template <class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY complex<typename __promote<_Tp, _Up>::type>
pow(const complex<_Tp> &__x, const complex<_Up> &__y)
{
  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
  return _VSTD::pow(result_type(__x), result_type(__y));
}

template <class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_arithmetic<_Up>::value,
                       complex<typename __promote<_Tp, _Up>::type>>::type
    pow(const complex<_Tp> &__x, const _Up &__y)
{
  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
  return _VSTD::pow(result_type(__x), result_type(__y));
}

template <class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
    typename enable_if<is_arithmetic<_Tp>::value,
                       complex<typename __promote<_Tp, _Up>::type>>::type
    pow(const _Tp &__x, const complex<_Up> &__y)
{
  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
  return _VSTD::pow(result_type(__x), result_type(__y));
}

// asinh

template <class _Tp>
complex<_Tp> asinh(const complex<_Tp> &__x)
{
  const _Tp __pi(atan2(+0., -0.));
  if (isinf(__x.real())) {
    if (isnan(__x.imag()))
      return __x;
    if (isinf(__x.imag()))
      return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
    return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
  }
  if (isnan(__x.real())) {
    if (isinf(__x.imag()))
      return complex<_Tp>(__x.imag(), __x.real());
    if (__x.imag() == 0)
      return __x;
    return complex<_Tp>(__x.real(), __x.real());
  }
  if (isinf(__x.imag()))
    return complex<_Tp>(copysign(__x.imag(), __x.real()),
                        copysign(__pi / _Tp(2), __x.imag()));
  complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
  return complex<_Tp>(copysign(__z.real(), __x.real()),
                      copysign(__z.imag(), __x.imag()));
}

// acosh

template <class _Tp>
complex<_Tp> acosh(const complex<_Tp> &__x)
{
  const _Tp __pi(atan2(+0., -0.));
  if (isinf(__x.real())) {
    if (isnan(__x.imag()))
      return complex<_Tp>(abs(__x.real()), __x.imag());
    if (isinf(__x.imag())) {
      if (__x.real() > 0)
        return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
      else
        return complex<_Tp>(-__x.real(),
                            copysign(__pi * _Tp(0.75), __x.imag()));
    }
    if (__x.real() < 0)
      return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
    return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
  }
  if (isnan(__x.real())) {
    if (isinf(__x.imag()))
      return complex<_Tp>(abs(__x.imag()), __x.real());
    return complex<_Tp>(__x.real(), __x.real());
  }
  if (isinf(__x.imag()))
    return complex<_Tp>(abs(__x.imag()), copysign(__pi / _Tp(2), __x.imag()));
  complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
  return complex<_Tp>(copysign(__z.real(), _Tp(0)),
                      copysign(__z.imag(), __x.imag()));
}

// atanh

template <class _Tp>
complex<_Tp> atanh(const complex<_Tp> &__x)
{
  const _Tp __pi(atan2(+0., -0.));
  if (isinf(__x.imag())) {
    return complex<_Tp>(copysign(_Tp(0), __x.real()),
                        copysign(__pi / _Tp(2), __x.imag()));
  }
  if (isnan(__x.imag())) {
    if (isinf(__x.real()) || __x.real() == 0)
      return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
    return complex<_Tp>(__x.imag(), __x.imag());
  }
  if (isnan(__x.real())) {
    return complex<_Tp>(__x.real(), __x.real());
  }
  if (isinf(__x.real())) {
    return complex<_Tp>(copysign(_Tp(0), __x.real()),
                        copysign(__pi / _Tp(2), __x.imag()));
  }
  if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) {
    return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()),
                        copysign(_Tp(0), __x.imag()));
  }
  complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
  return complex<_Tp>(copysign(__z.real(), __x.real()),
                      copysign(__z.imag(), __x.imag()));
}

// sinh

template <class _Tp>
complex<_Tp> sinh(const complex<_Tp> &__x)
{
  if (isinf(__x.real()) && !isfinite(__x.imag()))
    return complex<_Tp>(__x.real(), _Tp(NAN));
  if (__x.real() == 0 && !isfinite(__x.imag()))
    return complex<_Tp>(__x.real(), _Tp(NAN));
  if (__x.imag() == 0 && !isfinite(__x.real()))
    return __x;
  return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()),
                      cosh(__x.real()) * sin(__x.imag()));
}

// cosh

template <class _Tp>
complex<_Tp> cosh(const complex<_Tp> &__x)
{
  if (isinf(__x.real()) && !isfinite(__x.imag()))
    return complex<_Tp>(abs(__x.real()), _Tp(NAN));
  if (__x.real() == 0 && !isfinite(__x.imag()))
    return complex<_Tp>(_Tp(NAN), __x.real());
  if (__x.real() == 0 && __x.imag() == 0)
    return complex<_Tp>(_Tp(1), __x.imag());
  if (__x.imag() == 0 && !isfinite(__x.real()))
    return complex<_Tp>(abs(__x.real()), __x.imag());
  return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()),
                      sinh(__x.real()) * sin(__x.imag()));
}

// tanh

template <class _Tp>
complex<_Tp> tanh(const complex<_Tp> &__x)
{
  if (isinf(__x.real())) {
    if (!isfinite(__x.imag()))
      return complex<_Tp>(_Tp(1), _Tp(0));
    return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
  }
  if (isnan(__x.real()) && __x.imag() == 0)
    return __x;
  _Tp __2r(_Tp(2) * __x.real());
  _Tp __2i(_Tp(2) * __x.imag());
  _Tp __d(cosh(__2r) + cos(__2i));
  _Tp __2rsh(sinh(__2r));
  if (isinf(__2rsh) && isinf(__d))
    return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
                        __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
  return complex<_Tp>(__2rsh / __d, sin(__2i) / __d);
}

// asin

template <class _Tp>
complex<_Tp> asin(const complex<_Tp> &__x)
{
  complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
  return complex<_Tp>(__z.imag(), -__z.real());
}

// acos

template <class _Tp>
complex<_Tp> acos(const complex<_Tp> &__x)
{
  const _Tp __pi(atan2(+0., -0.));
  if (isinf(__x.real())) {
    if (isnan(__x.imag()))
      return complex<_Tp>(__x.imag(), __x.real());
    if (isinf(__x.imag())) {
      if (__x.real() < _Tp(0))
        return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
      return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
    }
    if (__x.real() < _Tp(0))
      return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
    return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
  }
  if (isnan(__x.real())) {
    if (isinf(__x.imag()))
      return complex<_Tp>(__x.real(), -__x.imag());
    return complex<_Tp>(__x.real(), __x.real());
  }
  if (isinf(__x.imag()))
    return complex<_Tp>(__pi / _Tp(2), -__x.imag());
  if (__x.real() == 0)
    return complex<_Tp>(__pi / _Tp(2), -__x.imag());
  complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
  if (signbit(__x.imag()))
    return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
  return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
}

// atan

template <class _Tp>
complex<_Tp> atan(const complex<_Tp> &__x)
{
  complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
  return complex<_Tp>(__z.imag(), -__z.real());
}

// sin

template <class _Tp>
complex<_Tp> sin(const complex<_Tp> &__x)
{
  complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
  return complex<_Tp>(__z.imag(), -__z.real());
}

// cos

template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> cos(const complex<_Tp> &__x)
{
  return cosh(complex<_Tp>(-__x.imag(), __x.real()));
}

// tan

template <class _Tp>
complex<_Tp> tan(const complex<_Tp> &__x)
{
  complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
  return complex<_Tp>(__z.imag(), -__z.real());
}

template <class _Tp, class _CharT, class _Traits>
basic_istream<_CharT, _Traits> &operator>>(basic_istream<_CharT, _Traits> &__is,
                                           complex<_Tp> &__x)
{
  if (__is.good()) {
    ws(__is);
    if (__is.peek() == _CharT('(')) {
      __is.get();
      _Tp __r;
      __is >> __r;
      if (!__is.fail()) {
        ws(__is);
        _CharT __c = __is.peek();
        if (__c == _CharT(',')) {
          __is.get();
          _Tp __i;
          __is >> __i;
          if (!__is.fail()) {
            ws(__is);
            __c = __is.peek();
            if (__c == _CharT(')')) {
              __is.get();
              __x = complex<_Tp>(__r, __i);
            } else
              __is.setstate(ios_base::failbit);
          } else
            __is.setstate(ios_base::failbit);
        } else if (__c == _CharT(')')) {
          __is.get();
          __x = complex<_Tp>(__r, _Tp(0));
        } else
          __is.setstate(ios_base::failbit);
      } else
        __is.setstate(ios_base::failbit);
    } else {
      _Tp __r;
      __is >> __r;
      if (!__is.fail())
        __x = complex<_Tp>(__r, _Tp(0));
      else
        __is.setstate(ios_base::failbit);
    }
  } else
    __is.setstate(ios_base::failbit);
  return __is;
}

template <class _Tp, class _CharT, class _Traits>
basic_ostream<_CharT, _Traits> &operator<<(basic_ostream<_CharT, _Traits> &__os,
                                           const complex<_Tp> &__x)
{
  basic_ostringstream<_CharT, _Traits> __s;
  __s.flags(__os.flags());
  __s.imbue(__os.getloc());
  __s.precision(__os.precision());
  __s << '(' << __x.real() << ',' << __x.imag() << ')';
  return __os << __s.str();
}

#if _LIBCPP_STD_VER > 11
// Literal suffix for complex number literals [complex.literals]
inline namespace literals
{
  inline namespace complex_literals
  {
    constexpr complex<long double> operator""il(long double __im)
    {
      return {0.0l, __im};
    }

    constexpr complex<long double> operator""il(unsigned long long __im)
    {
      return {0.0l, static_cast<long double>(__im)};
    }

    constexpr complex<double> operator""i(long double __im)
    {
      return {0.0, static_cast<double>(__im)};
    }

    constexpr complex<double> operator""i(unsigned long long __im)
    {
      return {0.0, static_cast<double>(__im)};
    }

    constexpr complex<float> operator""if(long double __im)
    {
      return {0.0f, static_cast<float>(__im)};
    }

    constexpr complex<float> operator""if(unsigned long long __im)
    {
      return {0.0f, static_cast<float>(__im)};
    }
  }
}
#endif

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP_COMPLEX
