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

// Copyright (C) 1997-2019 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 3, 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.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
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/** @file include/complex
 *  This is a Standard C++ Library header.
 */

//
// 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>
//

#ifndef _GLIBCXX_COMPLEX
#define _GLIBCXX_COMPLEX 1

#pragma GCC system_header

#include <bits/c++config.h>
#include <bits/cpp_type_traits.h>
#include <ext/type_traits.h>
#include <cmath>
#include <sstream>

// Get rid of a macro possibly defined in <complex.h>
#undef complex

#if __cplusplus > 201703L
# define __cpp_lib_constexpr_complex 201711L
#endif

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  /**
   * @defgroup complex_numbers Complex Numbers
   * @ingroup numerics
   *
   * Classes and functions for complex numbers.
   * @{
   */

  // Forward declarations.
  template<typename _Tp> class complex;
  template<> class complex<float>;
  template<> class complex<double>;
  template<> class complex<long double>;

  ///  Return magnitude of @a z.
  template<typename _Tp> _Tp abs(const complex<_Tp>&);
  ///  Return phase angle of @a z.
  template<typename _Tp> _Tp arg(const complex<_Tp>&);
  ///  Return @a z magnitude squared.
  template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);

  ///  Return complex conjugate of @a z.
  template<typename _Tp>
    _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&);
  ///  Return complex with magnitude @a rho and angle @a theta.
  template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);

  // Transcendentals:
  /// Return complex cosine of @a z.
  template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  /// Return complex hyperbolic cosine of @a z.
  template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  /// Return complex base e exponential of @a z.
  template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  /// Return complex natural logarithm of @a z.
  template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  /// Return complex base 10 logarithm of @a z.
  template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  /// Return @a x to the @a y'th power.
  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  /// Return @a x to the @a y'th power.
  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
  /// Return @a x to the @a y'th power.
  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
                                          const complex<_Tp>&);
  /// Return @a x to the @a y'th power.
  template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
  /// Return complex sine of @a z.
  template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
  /// Return complex hyperbolic sine of @a z.
  template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
  /// Return complex square root of @a z.
  template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
  /// Return complex tangent of @a z.
  template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
  /// Return complex hyperbolic tangent of @a z.
  template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);


  // 26.2.2  Primary template class complex
  /**
   *  Template to represent complex numbers.
   *
   *  Specializations for float, double, and long double are part of the
   *  library.  Results with any other type are not guaranteed.
   *
   *  @param  Tp  Type of real and imaginary values.
  */
  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.
      _GLIBCXX20_CONSTEXPR void
      real(_Tp __val) { _M_real = __val; }

      _GLIBCXX20_CONSTEXPR void
      imag(_Tp __val) { _M_imag = __val; }

      /// Assign a scalar to this complex number.
      _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);

      /// Add a scalar to this complex number.
      // 26.2.5/1
      _GLIBCXX20_CONSTEXPR complex<_Tp>&
      operator+=(const _Tp& __t)
      {
	_M_real += __t;
	return *this;
      }

      /// Subtract a scalar from this complex number.
      // 26.2.5/3
      _GLIBCXX20_CONSTEXPR complex<_Tp>&
      operator-=(const _Tp& __t)
      {
	_M_real -= __t;
	return *this;
      }

      /// Multiply this complex number by a scalar.
      _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
      /// Divide this complex number by a scalar.
      _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);

      // Let the compiler synthesize the copy assignment operator
#if __cplusplus >= 201103L
      _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
#endif

      /// Assign another complex number to this one.
      template<typename _Up>
        _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
      /// Add another complex number to this one.
      template<typename _Up>
        _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
      /// Subtract another complex number from this one.
      template<typename _Up>
        _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
      /// Multiply this complex number by another.
      template<typename _Up>
        _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
      /// Divide this complex number by another.
      template<typename _Up>
        _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);

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

    private:
      _Tp _M_real;
      _Tp _M_imag;
    };

  template<typename _Tp>
    _GLIBCXX20_CONSTEXPR complex<_Tp>&
    complex<_Tp>::operator=(const _Tp& __t)
    {
     _M_real = __t;
     _M_imag = _Tp();
     return *this;
    }

  // 26.2.5/5
  template<typename _Tp>
    _GLIBCXX20_CONSTEXPR complex<_Tp>&
    complex<_Tp>::operator*=(const _Tp& __t)
    {
      _M_real *= __t;
      _M_imag *= __t;
      return *this;
    }

  // 26.2.5/7
  template<typename _Tp>
    _GLIBCXX20_CONSTEXPR complex<_Tp>&
    complex<_Tp>::operator/=(const _Tp& __t)
    {
      _M_real /= __t;
      _M_imag /= __t;
      return *this;
    }

  template<typename _Tp>
    template<typename _Up>
    _GLIBCXX20_CONSTEXPR 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>
    _GLIBCXX20_CONSTEXPR 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>
    _GLIBCXX20_CONSTEXPR 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>
    _GLIBCXX20_CONSTEXPR 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>
    _GLIBCXX20_CONSTEXPR complex<_Tp>&
    complex<_Tp>::operator/=(const complex<_Up>& __z)
    {
      const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
      const _Tp __n = std::norm(__z);
      _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
      _M_real = __r / __n;
      return *this;
    }

  // Operators:
  //@{
  ///  Return new complex value @a x plus @a y.
  template<typename _Tp>
    inline _GLIBCXX20_CONSTEXPR complex<_Tp>
    operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r += __y;
      return __r;
    }

  template<typename _Tp>
    inline _GLIBCXX20_CONSTEXPR complex<_Tp>
    operator+(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r += __y;
      return __r;
    }

  template<typename _Tp>
    inline _GLIBCXX20_CONSTEXPR 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 _GLIBCXX20_CONSTEXPR complex<_Tp>
    operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r -= __y;
      return __r;
    }

  template<typename _Tp>
    inline _GLIBCXX20_CONSTEXP                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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