unsupported/Eigen/Complex

#ifndef EIGEN_COMPLEX_H
#define EIGEN_COMPLEX_H

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

// Eigen::Complex reuses as much as possible from std::complex
// and allows easy conversion to and from, even at the pointer level.

/** \ingroup Unsupported_modules
  * \defgroup Complex_Module Complex module
  *
  * \code
  * #include <unsupported/Eigen/Complex>
  * \endcode
  *
  * The C++ complex type has some severe limitations that prevent an
  * optimal use within Eigen. This (still unsupported) module is an attempt
  * to fix this.
  */
 
#include <complex>

namespace Eigen {

template <typename _NativeData,typename _PunnedData>
struct castable_pointer
{
    castable_pointer(_NativeData * ptr) : _ptr(ptr) { }
    operator _NativeData * ()  {return _ptr;}
    operator _PunnedData * ()  {return reinterpret_cast<_PunnedData*>(_ptr);}
    operator const _NativeData * () const {return _ptr;}
    operator const _PunnedData * () const {return reinterpret_cast<_PunnedData*>(_ptr);}
    private: 
    _NativeData *  _ptr;
};

template <typename _NativeData,typename _PunnedData>
struct const_castable_pointer
{
    const_castable_pointer(_NativeData * ptr) : _ptr(ptr) { }
    operator const _NativeData * () const {return _ptr;}
    operator const _PunnedData * () const {return reinterpret_cast<_PunnedData*>(_ptr);}
    private: 
    _NativeData * _ptr;
};

template <typename T>
struct Complex
{
    typedef typename std::complex<T> StandardComplex;
    typedef T value_type;

    // constructors
    Complex() {}
    Complex(const T& re, const T& im = T()) : _re(re),_im(im) { }
    Complex(const Complex&other ): _re(other.real()) ,_im(other.imag()) {}

    template<class X> 
    Complex(const Complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
    template<class X> 
    Complex(const std::complex<X>&other): _re(other.real()) ,_im(other.imag()) {}

    // allow binary access to the object as a std::complex
    typedef castable_pointer< Complex<T>, StandardComplex > pointer_type;
    typedef const_castable_pointer< Complex<T>, StandardComplex > const_pointer_type;

    inline
    pointer_type operator & () {return pointer_type(this);}

    inline
    const_pointer_type operator & () const {return const_pointer_type(this);}

    inline
    operator StandardComplex () const {return std_type();}
    inline
    operator StandardComplex & () {return std_type();}

    inline
    const StandardComplex & std_type() const {return *reinterpret_cast<const StandardComplex*>(this);}

    inline
    StandardComplex & std_type() {return *reinterpret_cast<StandardComplex*>(this);}


    // every sort of accessor and mutator that has ever been in fashion.
    // For a brief history, search for "std::complex over-encapsulated"
    // http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-defects.html#387
    inline
    const T & real() const {return _re;}
    inline
    const T & imag() const {return _im;}
    inline
    T & real() {return _re;}
    inline
    T & imag() {return _im;}
    inline
    T & real(const T & x) {return _re=x;}
    inline
    T & imag(const T & x) {return _im=x;}
    inline
    void set_real(const T & x) {_re = x;}
    inline
    void set_imag(const T & x) {_im = x;}

    // *** complex member functions: ***
    inline
    Complex<T>& operator= (const T& val) { _re=val;_im=0;return *this;  }
    inline
    Complex<T>& operator+= (const T& val) {_re+=val;return *this;}
    inline
    Complex<T>& operator-= (const T& val) {_re-=val;return *this;}
    inline
    Complex<T>& operator*= (const T& val) {_re*=val;_im*=val;return *this;  }
    inline
    Complex<T>& operator/= (const T& val) {_re/=val;_im/=val;return *this;  }

    inline
    Complex& operator= (const Complex& rhs) {_re=rhs._re;_im=rhs._im;return *this;}
    inline
    Complex& operator= (const StandardComplex& rhs) {_re=rhs.real();_im=rhs.imag();return *this;}

    template<class X> Complex<T>& operator= (const Complex<X>& rhs) { _re=rhs._re;_im=rhs._im;return *this;}
    template<class X> Complex<T>& operator+= (const Complex<X>& rhs) { _re+=rhs._re;_im+=rhs._im;return *this;}
    template<class X> Complex<T>& operator-= (const Complex<X>& rhs) { _re-=rhs._re;_im-=rhs._im;return *this;}
    template<class X> Complex<T>& operator*= (const Complex<X>& rhs) { this->std_type() *= rhs.std_type(); return *this; }
    template<class X> Complex<T>& operator/= (const Complex<X>& rhs) { this->std_type() /= rhs.std_type(); return *this; }

    private:
    T _re;
    T _im;
};

//template <typename T> T ei_to_std( const T & x) {return x;}

template <typename T>
std::complex<T> ei_to_std( const Complex<T> & x) {return x.std_type();}

// 26.2.6 operators
template<class T> Complex<T> operator+(const Complex<T>& rhs) {return rhs;}
template<class T> Complex<T> operator-(const Complex<T>& rhs) {return -ei_to_std(rhs);}

template<class T> Complex<T> operator+(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) + ei_to_std(rhs);}
template<class T> Complex<T> operator-(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) - ei_to_std(rhs);}
template<class T> Complex<T> operator*(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) * ei_to_std(rhs);}
template<class T> Complex<T> operator/(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) / ei_to_std(rhs);}
template<class T> bool operator==(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) == ei_to_std(rhs);}
template<class T> bool operator!=(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) != ei_to_std(rhs);}

template<class T> Complex<T> operator+(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }

template<class T> Complex<T> operator+(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }

template<class T, class charT, class traits>
std::basic_istream<charT,traits>&
  operator>> (std::basic_istream<charT,traits>& istr, Complex<T>& rhs)
{
    return istr >> rhs.std_type();
}

template<class T, class charT, class traits>
std::basic_ostream<charT,traits>&
operator<< (std::basic_ostream<charT,traits>& ostr, const Complex<T>& rhs)
{
    return ostr << rhs.std_type();
}

 // 26.2.7 values:
 template<class T> T real(const Complex<T>&x) {return real(ei_to_std(x));}
 template<class T> T abs(const Complex<T>&x) {return abs(ei_to_std(x));}
 template<class T> T arg(const Complex<T>&x) {return arg(ei_to_std(x));}
 template<class T> T norm(const Complex<T>&x) {return norm(ei_to_std(x));}

 template<class T> Complex<T> conj(const Complex<T>&x) { return conj(ei_to_std(x));}
 template<class T> Complex<T> polar(const T& x, const T&y) {return polar(ei_to_std(x),ei_to_std(y));} 
 // 26.2.8 transcendentals:
 template<class T> Complex<T> cos (const  Complex<T>&x){return cos(ei_to_std(x));}
 template<class T> Complex<T> cosh (const  Complex<T>&x){return cosh(ei_to_std(x));}
 template<class T> Complex<T> exp (const  Complex<T>&x){return exp(ei_to_std(x));}
 template<class T> Complex<T> log (const  Complex<T>&x){return log(ei_to_std(x));}
 template<class T> Complex<T> log10 (const  Complex<T>&x){return log10(ei_to_std(x));}

 template<class T> Complex<T> pow(const Complex<T>&x, int p) {return pow(ei_to_std(x),p);}
 template<class T> Complex<T> pow(const Complex<T>&x, const T&p) {return pow(ei_to_std(x),ei_to_std(p));}
 template<class T> Complex<T> pow(const Complex<T>&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
 template<class T> Complex<T> pow(const T&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}

 template<class T> Complex<T> sin (const  Complex<T>&x){return sin(ei_to_std(x));}
 template<class T> Complex<T> sinh (const  Complex<T>&x){return sinh(ei_to_std(x));}
 template<class T> Complex<T> sqrt (const  Complex<T>&x){return sqrt(ei_to_std(x));}
 template<class T> Complex<T> tan (const  Complex<T>&x){return tan(ei_to_std(x));}
 template<class T> Complex<T> tanh (const  Complex<T>&x){return tanh(ei_to_std(x));}

  template<typename _Real> struct NumTraits<Complex<_Real> >
  {
    typedef _Real Real;
    typedef Complex<_Real> FloatingPoint;
    enum {
      IsComplex = 1,
      HasFloatingPoint = NumTraits<Real>::HasFloatingPoint,
      ReadCost = 2,
      AddCost = 2 * NumTraits<Real>::AddCost,
      MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
    };
  };
}
#endif
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