支离破碎的C++学习——std::complex

 刚刚在看《C++语言导学》看到了complex库，还以为是什么新特性去向室友宣传，之后才知道是我学艺不精了。所以特意去看了cppreference和microsoft文档去学习了一下。以下简单记录一下个人想法
先贴一下gcc中的部分源码

  template<typename _Tp>
    struct complex
    {
      /// Value typedef.
      typedef _Tp value_type;

      ///  Default constructor.  First parameter is x, second parameter is y.
      ///  Unspecified parameters default to 0.
      _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
      : _M_real(__r), _M_imag(__i) { }

      // Let the compiler synthesize the copy constructor
#if __cplusplus >= 201103L
      constexpr complex(const complex&) = default;
#endif

      ///  Converting constructor.
      template<typename _Up>
        _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
    : _M_real(__z.real()), _M_imag(__z.imag()) { }

#if __cplusplus >= 201103L
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // DR 387. std::complex over-encapsulated.
      _GLIBCXX_ABI_TAG_CXX11
      constexpr _Tp
      real() const { return _M_real; }

      _GLIBCXX_ABI_TAG_CXX11
      constexpr _Tp
      imag() const { return _M_imag; }
#else
      ///  Return real part of complex number.
      _Tp&
      real() { return _M_real; }

      ///  Return real part of complex number.
      const _Tp&
      real() const { return _M_real; }

      ///  Return imaginary part of complex number.
      _Tp&
      imag() { return _M_imag; }

      ///  Return imaginary part of complex number.
      const _Tp&
      imag() const { return _M_imag; }
#endif

      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // DR 387. std::complex over-encapsulated.
      void
      real(_Tp __val) { _M_real = __val; }

      void
      imag(_Tp __val) { _M_imag = __val; }

      /// Assign a scalar to this complex number.
      complex<_Tp>& operator=(const _Tp&);

      /// Add a scalar to this complex number.
      // 26.2.5/1
      complex<_Tp>&
      operator+=(const _Tp& __t)
      {
    _M_real += __t;
    return *this;
      }

      /// Subtract a scalar from this complex number.
      // 26.2.5/3
      complex<_Tp>&
      operator-=(const _Tp& __t)
      {
    _M_real -= __t;
    return *this;
      }

      /// Multiply this complex number by a scalar.
      complex<_Tp>& operator*=(const _Tp&);
      /// Divide this complex number by a scalar.
      complex<_Tp>& operator/=(const _Tp&);

      // Let the compiler synthesize the copy assignment operator
#if __cplusplus >= 201103L
      complex& operator=(const complex&) = default;
#endif

      /// Assign another complex number to this one.
      template<typename _Up>
        complex<_Tp>& operator=(const complex<_Up>&);
      /// Add another complex number to this one.
      template<typename _Up>
        complex<_Tp>& operator+=(const complex<_Up>&);
      /// Subtract another complex number from this one.
      template<typename _Up>
        complex<_Tp>& operator-=(const complex<_Up>&);
      /// Multiply this complex number by another.
      template<typename _Up>
        complex<_Tp>& operator*=(const complex<_Up>&);
      /// Divide this complex number by another.
      template<typename _Up>
        complex<_Tp>& operator/=(const complex<_Up>&);

      _GLIBCXX_CONSTEXPR complex __rep() const
      { return *this; }

    private:
      _Tp _M_real;
      _Tp _M_imag;
    };

可以发现std::complex的value_type类型为_Tp。_M_real存放实数，_M_imag存放虚数。使用公有成员函数real和imag可以访问到。
公有成员函数还包括构造函数，赋值运算符，+=，-=，*=，/=等。
 

  ///  Return @a x.
  template<typename _Tp>
    inline complex<_Tp>
    operator+(const complex<_Tp>& __x)
    { return __x; }

  ///  Return complex negation of @a x.
  template<typename _Tp>
    inline complex<_Tp>
    operator-(const complex<_Tp>& __x)
    {  return complex<_Tp>(-__x.real(), -__x.imag()); }

非成员函数有，有返回复数的值的重载运算符+、与取反的重载运算符-
 

  //@{
  ///  Return new complex value @a x plus @a y.
  template<typename _Tp>
    inline complex<_Tp>
    operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r += __y;
      return __r;
    }

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

  template<typename _Tp>
    inline complex<_Tp>
    operator+(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __y;
      __r += __x;
      return __r;
    }
  //@}

  //@{
  ///  Return new complex value @a x minus @a y.
  template<typename _Tp>
    inline complex<_Tp>
    operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r -= __y;
      return __r;
    }

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

  template<typename _Tp>
    inline complex<_Tp>
    operator-(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r(__x, -__y.imag());
      __r -= __y.real();
      return __r;
    }
  //@}

  //@{
  ///  Return new complex value @a x times @a y.
  template<typename _Tp>
    inline complex<_Tp>
    operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r *= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator*(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r *= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator*(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __y;
      __r *= __x;
      return __r;
    }
  //@}

  //@{
  ///  Return new complex value @a x divided by @a y.
  template<typename _Tp>
    inline complex<_Tp>
    operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r /= __y;
      return __r;
    }

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

  template<typename _Tp>
    inline complex<_Tp>
    operator/(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r /= __y;
      return __r;
    }
  //@}

非成员函数存在复数和标量，复数与复数之间进行运算的+、-、*、/的重载运算符。由于复数和标量类型不同，所以有复数和标量交换位置两种情况，加上复数和复数则4个重载运算符有12个重载式。
 
剩下的函数建议直接看文档或者stl源码std::complex - cppreference.com