// -*-c++-*- 
/*****************************************************************
 * file lacomplex Locally modified copy of stdc++'s file complex
 *  -------------------
 * begin                : 2004-01-14
 * copyright            : (C) 2004 by Christian Stimming
 * email                : stimming@tuhh.de
 *
 * (Almost) All changes by Christian are marked with "CS:".
***************************************************************************/

// The template and inlines for the -*- C++ -*- complex number classes.

// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; 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, or (at your option)
// any later version.

// This library 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 General Public License for more details.

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

//
// ISO C++ 14882: 26.2  Complex Numbers
// Note: this is not a conforming implementation.
// Initially implemented by Ulrich Drepper <drepper@cygnus.com>
// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
//

/** \file lacomplex 
 * \brief Complex data type that can be used from the application.
 * 
 * This file has been heavily copied from the Standard
 *  C++ Library header <\c complex >. See the explanations at la::complex
 *  for the reasons.
 */

#ifndef LACOMPLEX_CPPHEADER
#define LACOMPLEX_CPPHEADER

//#pragma GCC system_header

#if LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H
// This is for gcc >= 3.0.0
#  include <bits/c++config.h>
#  include <bits/cpp_type_traits.h>
#endif // LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H

#include <cmath>
#include <iosfwd>
#include <sstream>
#include <complex>

#if defined __GNUC__ && (__GNUC__ < 3)
// This is for gcc2.95
#  include <iostream>
#endif


/** \brief Namespace of Lapack++.
 *
 * This namespace defines the complex data type that can be used
 * from the application, and also various matrix template
 * functions.
 * 
 * This namespace defines the complex data type that is used for
 * passing scalars in and out of LAPACK++. It is a copy of the \c
 * std::complex<double> and it includes automatic conversion from and
 * to \c std::complex<double>. Additionally it includes automatic
 * conversion from and to the internal FORTRAN type \ref COMPLEX,
 * which is why this class is needed to pass complex values into
 * Lapack++.
 *
 * This file has been heavily copied from the Standard C++ Library
 * header <\c complex >. See the explanations at la::complex for the
 * reasons.
 */
namespace la
{
  /** \name Functions for Lapack++ complex number type */
  //@{
#if LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H
  using std::ios_base;
#else
  typedef std::ios ios_base;
#endif

  // Forward declarations
  template<typename _Tp> class complex;
  //template<> class complex<float>;
#if defined __GNUC__ && (__GNUC__ > 2)
  template<> class complex<double>;
#endif
  //template<> class complex<long double>;

  template<typename _Tp> _Tp abs(const complex<_Tp>&);
  template<typename _Tp> _Tp arg(const complex<_Tp>&);
  template<typename _Tp> _Tp norm(const complex<_Tp>&);


  // Transcendentals:
    
    
/** @brief Complex data type that can be used from the application.
 *
 * This type is used for passing scalars in and out of LAPACK++. It is
 * a copy of the \c std::complex<double> and it includes automatic
 * conversion from and to \c std::complex<double>. Additionally it
 * includes automatic conversion from and to the internal FORTRAN type
 * \ref COMPLEX, which is why this class is needed to pass complex
 * values into Lapack++.
 *
 * Again: If you get errors when passing a \c std::complex<double>
 * into Lapack++, then you first need to convert your \c
 * std::complex<double> into this \c LaComplex value.
 */
  // 26.2.2  Primary template class complex
  template<typename _Tp>
    class complex
    {
    public:
      typedef _Tp value_type;
      
      complex(const _Tp& = _Tp(), const _Tp & = _Tp());

      // Let's the compiler synthetize the copy constructor   
      // complex (const complex<_Tp>&);
      template<typename _Up>
        complex(const complex<_Up>&);
      // CS: Additionally add conversion *from* stdc++ type.
      complex(const std::complex<_Tp>&);
      // CS: end
        
      _Tp real() const;
      _Tp imag() const;

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

      // Let's the compiler synthetize the
      // copy and assignment operator
      // complex<_Tp>& operator= (const complex<_Tp>&);
      template<typename _Up>
        complex<_Tp>& operator=(const complex<_Up>&);
      template<typename _Up>
        complex<_Tp>& operator+=(const complex<_Up>&);
      template<typename _Up>
        complex<_Tp>& operator-=(const complex<_Up>&);
      template<typename _Up>
        complex<_Tp>& operator*=(const complex<_Up>&);
      template<typename _Up>
        complex<_Tp>& operator/=(const complex<_Up>&);

      // CS: Additionally add converstions to old C-style complex type
      complex(COMPLEX);
      operator COMPLEX() const;
      COMPLEX toCOMPLEX() const;
      operator std::complex<_Tp>() const;
      // CS: end additions

    private:
      _Tp _M_real, _M_imag;
    };

  template<typename _Tp>
    inline _Tp
    complex<_Tp>::real() const { return _M_real; }

  template<typename _Tp>
    inline _Tp
    complex<_Tp>::imag() const { return _M_imag; }

  template<typename _Tp>
    inline 
    complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
    : _M_real(__r), _M_imag(__i) { }

  template<typename _Tp>
    template<typename _Up>
    inline 
    complex<_Tp>::complex(const complex<_Up>& __z)
    : _M_real(__z.real()), _M_imag(__z.imag()) { }
        
  // CS: addition
  template<typename _Tp>
    inline 
    complex<_Tp>::complex(const std::complex<_Tp>& __z)
    : _M_real(__z.real()), _M_imag(__z.imag()) { }
  // CS: end addition

  template<typename _Tp>
    complex<_Tp>&
    complex<_Tp>::operator=(const _Tp& __t)
    {
     _M_real = __t;
     _M_imag = _Tp();
     return *this;
    } 

  // 26.2.5/1
  template<typename _Tp>
    inline complex<_Tp>&
    complex<_Tp>::operator+=(const _Tp& __t)
    {
      _M_real += __t;
      return *this;
    }

  // 26.2.5/3
  template<typename _Tp>
    inline complex<_Tp>&
    complex<_Tp>::operator-=(const _Tp& __t)
    {
      _M_real -= __t;
      return *this;
    }

  // 26.2.5/5
  template<typename _Tp>
    complex<_Tp>&
    complex<_Tp>::operator*=(const _Tp& __t)
    {
      _M_real *= __t;
      _M_imag *= __t;
      return *this;
    }

  // 26.2.5/7
  template<typename _Tp>
    complex<_Tp>&
    complex<_Tp>::operator/=(const _Tp& __t)
    {
      _M_real /= __t;
      _M_imag /= __t;
      return *this;
    }

  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator=(const complex<_Up>& __z)
    {
      _M_real = __z.real();
      _M_imag = __z.imag();
      return *this;
    }

  // 26.2.5/9
  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator+=(const complex<_Up>& __z)
    {
      _M_real += __z.real();
      _M_imag += __z.imag();
      return *this;
    }

  // 26.2.5/11
  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator-=(const complex<_Up>& __z)
    {
      _M_real -= __z.real();
      _M_imag -= __z.imag();
      return *this;
    }

  // 26.2.5/13
  // XXX: This is a grammar school implementation.
  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator*=(const complex<_Up>& __z)
    {
      const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
      _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
      _M_real = __r;
      return *this;
    }

  // 26.2.5/15
  // XXX: This is a grammar school implementation.
  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator/=(const complex<_Up>& __z)
    {
      const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
      const _Tp __n = norm(__z);
      _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
      _M_real = __r / __n;
      return *this;
    }

  // CS: Additionally add converstions to old C-style complex type
  template<typename _Tp>
  inline
  complex<_Tp>::complex(COMPLEX c)
    : _M_real(c.r), _M_imag(c.i) { }

  template<typename _Tp>
  inline
  complex<_Tp>::operator COMPLEX() const
  {
    return toCOMPLEX();
  }

  template<typename _Tp>
  inline COMPLEX
  complex<_Tp>::toCOMPLEX() const
  {
    COMPLEX r;
    r.r = _M_real;
    r.i = _M_imag;
    return r;
  }

  template<typename _Tp>
  inline
  complex<_Tp>::operator std::complex<_Tp>() const
  {
    return std::complex<_Tp>(real(), imag());
  }
  // CS: end 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  template<typename _Tp>
    inline bool
    operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
    { return __x.real() != __y.real() || __x.imag() != __y.imag(); }

  template<typename _Tp>
    inline bool
    operator!=(const complex<_Tp>& __x, const _Tp& __y)
    { return __x.real() != __y || __x.imag() != _Tp(); }

  template<typename _Tp>
    inline bool
    operator!=(const _Tp& __x, const complex<_Tp>& __y)
    { return __x != __y.real() || _Tp() != __y.imag(); }

  template<typename _Tp>
    std::istream&
    operator>>(std::istream& __is, complex<_Tp>& __x)
    {
      _Tp __re_x, __im_x;
      char __ch;
      __is >> __ch;
      if (__ch == '(') 
	{
	  __is >> __re_x >> __ch;
	  if (__ch == ',') 
	    {
	      __is >> __im_x >> __ch;
	      if (__ch == ')') 
		__x = complex<_Tp>(__re_x, __im_x);
	      else
		__is.setstate(ios_base::failbit);
	    }
	  else if (__ch == ')') 
	    __x = complex<_Tp>(__re_x, _Tp(0));
	  else
	    __is.setstate(ios_base::failbit);
	}
      else 
	{
	  __is.putback(__ch);
	  __is >> __re_x;
	  __x = complex<_Tp>(__re_x, _Tp(0));
	}
      return __is;
    }

  template<typename _Tp>
    std::ostream&
    operator<<(std::ostream& __os, const complex<_Tp>& __x)
    {
      std::ostringstream __s;
      __s.flags(__os.flags());
#if defined __GNUC__ && (__GNUC__ > 2)
      __s.imbue(__os.getloc());
#endif
      __s.precision(__os.precision());
      __s << '(' << __x.real() << ',' << __x.imag() << ')';
      return __os << __s.str();
    }

  // Values
  template<typename _Tp>
    inline _Tp
    real(const complex<_Tp>& __z)
    { return __z.real(); }
    
  template<typename _Tp>
    inline _Tp
    imag(const complex<_Tp>& __z)
    { return __z.imag(); }

#ifndef DOXYGEN_IGNORE
  template<typename _Tp>
    inline _Tp
    abs(const complex<_Tp>& __z)
    {
      _Tp __x = __z.real();
      _Tp __y = __z.imag();
      const _Tp __s = std::max(std::abs(__x), std::abs(__y));
      if (__s == _Tp())  // well ...
        return __s;
      __x /= __s; 
      __y /= __s;
      return __s * sqrt(__x * __x + __y * __y);
    }

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

  // 26.2.7/5: norm(__z) returns the squared magintude of __z.
  //     As defined, norm() is -not- a norm is the common mathematical
  //     sens used in numerics.  The helper class _Norm_helper<> tries to
  //     distinguish between builtin floating point and the rest, so as
  //     to deliver an answer as close as possible to the real value.
  template<bool>
    struct _Norm_helper
    {
      template<typename _Tp>
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
        {
          const _Tp __x = __z.real();
          const _Tp __y = __z.imag();
          return __x * __x + __y * __y;
        }
    };

  template<>
    struct _Norm_helper<true>
    {
      template<typename _Tp>
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
        {
          _Tp __res = abs(__z);
          return __res * __res;
        }
    };
  
  template<typename _Tp>
    inline _Tp
    norm(const complex<_Tp>& __z)
    {
	return _Norm_helper<
#if LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H
	    std::__is_floating<_Tp>::
#  if defined __GNUC__ && (__GNUC__ > 3)
	    // This member name is for gcc>=4.0.0
	    __value
#  else
	    // This member name is for gcc 3.x.x
	    _M_type 
#  endif // __GNUC__ > 3
	    && !
#  ifdef _GLIBCXX_FAST_MATH
	    // This macro name is new in gcc3.4
	    _GLIBCXX_FAST_MATH
#  else
	    // This macro name is for gcc3.3
	    _GLIBCPP_FAST_MATH
#  endif // _GLIBCXX_FAST_MATH
#else // LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H
	    false
#endif // LAPACKPP_HAVE_BITS_CPP_TYPE_TRAITS_H
	    >::_S_do_it(__z);
    }

#endif // DOXYGEN_IGNORE
  // much deleted...

#if defined __GNUC__ && (__GNUC__ > 2)
  // 26.2.3  complex specializations
  // complex<double> specialization
  template<> class complex<double>
  {
  public:
    typedef double value_type;

    complex(double  =0.0, double =0.0);
#ifdef _GLIBCPP_BUGGY_COMPLEX
    complex(const complex& __z) : _M_value(__z._M_value) { }
#endif // _GLIBCPP_BUGGY_COMPLEX
    complex(const complex<float>&);
    explicit complex(const complex<long double>&);
    // CS: Additionally add conversion *from* stdc++ type.
    complex(const std::complex<double>&);
    // CS: end
        
    double real() const;
    double imag() const;
        
    complex<double>& operator=(double);
    complex<double>& operator+=(double);
    complex<double>& operator-=(double);
    complex<double>& operator*=(double);
    complex<double>& operator/=(double);

    // The compiler will synthetize this, efficiently.
    // complex& operator= (const complex&);
    template<typename _Tp>
      complex<double>& operator=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator+=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator-=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator*=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator/=(const complex<_Tp>&);

    // CS: Additionally add converstions to old C-style complex type
    complex(COMPLEX);
    operator COMPLEX() const;
    COMPLEX toCOMPLEX() const;
    operator std::complex<double>() const;
    // CS: end additions

  private:
    typedef __complex__ double _ComplexT;
    _ComplexT _M_value;

    complex(_ComplexT __z) : _M_value(__z) { }
        
    friend class complex<float>;
    friend class complex<long double>;
  };

  inline double
  complex<double>::real() const
  { return __real__ _M_value; }

  inline double
  complex<double>::imag() const
  { return __imag__ _M_value; }

  inline
  complex<double>::complex(double __r, double __i)
  {
    __real__ _M_value = __r;
    __imag__ _M_value = __i;
  }
  
  // CS: addition
  inline
  complex<double>::complex(const std::complex<double>&__s)
  {
    __real__ _M_value = __s.real();
    __imag__ _M_value = __s.imag();
  }
  // CS: end addition

  inline complex<double>&
  complex<double>::operator=(double __d)
  {
    __real__ _M_value = __d;
    __imag__ _M_value = 0.0;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator+=(double __d)
  {
    __real__ _M_value += __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator-=(double __d)
  {
    __real__ _M_value -= __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator*=(double __d)
  {
    _M_value *= __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator/=(double __d)
  {
    _M_value /= __d;
    return *this;
  }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator=(const complex<_Tp>& __z)
    {
      __real__ _M_value = __z.real();
      __imag__ _M_value = __z.imag();
      return *this;
    }
    
  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator+=(const complex<_Tp>& __z)
    {
      __real__ _M_value += __z.real();
      __imag__ _M_value += __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator-=(const complex<_Tp>& __z)
    {
      __real__ _M_value -= __z.real();
      __imag__ _M_value -= __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator*=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value *= __t;
      return *this;
    }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator/=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value /= __t;
      return *this;
    }

  // CS: Additionally add converstions to old C-style complex type
  inline
  complex<double>::complex(COMPLEX __c)
  {
    __real__ _M_value = __c.r;
    __imag__ _M_value = __c.i;
  }

  inline
  complex<double>::operator COMPLEX() const
  {
    return toCOMPLEX();
  }

  inline COMPLEX
  complex<double>::toCOMPLEX() const
  {
    COMPLEX r;
    r.r = real();
    r.i = imag();
    return r;
  }

  inline
  complex<double>::operator std::complex<double>() const
  {
    return std::complex<double>(real(), imag());
  }
  // CS: end 
#endif // (__GNUC__ > 2)

  // much deleted...

  //@}
} // namespace std

#endif	/* _CPP_COMPLEX */