// TR1 complex -*- C++ -*-

// Copyright (C) 2006-2021 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
// <http://www.gnu.org/licenses/>.

/** @file tr1/complex
 *  This is a TR1 C++ Library header. 
 */

#ifndef _GLIBCXX_TR1_COMPLEX
#define _GLIBCXX_TR1_COMPLEX 1

#pragma GCC system_header

#include <complex>

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

namespace tr1
{
  /**
   * @addtogroup complex_numbers
   * @{
   */

#if __cplusplus >= 201103L
  using std::acos;
  using std::asin;
  using std::atan;
  using std::acosh;
  using std::asinh;
  using std::atanh;
#else
  template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
#endif

  // The std::fabs return type in C++11 mode is different (just _Tp).
  template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);

#if __cplusplus < 201103L
  template<typename _Tp>
    inline std::complex<_Tp>
    __complex_acos(const std::complex<_Tp>& __z)
    {
      const std::complex<_Tp> __t = std::tr1::asin(__z);
      const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
      return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_acos(__complex__ float __z)
  { return __builtin_cacosf(__z); }

  inline __complex__ double
  __complex_acos(__complex__ double __z)
  { return __builtin_cacos(__z); }

  inline __complex__ long double
  __complex_acos(const __complex__ long double& __z)
  { return __builtin_cacosl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    acos(const std::complex<_Tp>& __z)
    { return __complex_acos(__z.__rep()); }
#else
  /// acos(__z) [8.1.2].
  //  Effects:  Behaves the same as C99 function cacos, defined
  //            in subclause 7.3.5.1.
  template<typename _Tp>
    inline std::complex<_Tp>
    acos(const std::complex<_Tp>& __z)
    { return __complex_acos(__z); }
#endif

  template<typename _Tp>
    inline std::complex<_Tp>
    __complex_asin(const std::complex<_Tp>& __z)
    {
      std::complex<_Tp> __t(-__z.imag(), __z.real());
      __t = std::tr1::asinh(__t);
      return std::complex<_Tp>(__t.imag(), -__t.real());
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_asin(__complex__ float __z)
  { return __builtin_casinf(__z); }

  inline __complex__ double
  __complex_asin(__complex__ double __z)
  { return __builtin_casin(__z); }

  inline __complex__ long double
  __complex_asin(const __complex__ long double& __z)
  { return __builtin_casinl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    asin(const std::complex<_Tp>& __z)
    { return __complex_asin(__z.__rep()); }
#else
  /// asin(__z) [8.1.3].
  //  Effects:  Behaves the same as C99 function casin, defined
  //            in subclause 7.3.5.2.
  template<typename _Tp>
    inline std::complex<_Tp>
    asin(const std::complex<_Tp>& __z)
    { return __complex_asin(__z); }
#endif
  
  template<typename _Tp>
    std::complex<_Tp>
    __complex_atan(const std::complex<_Tp>& __z)
    {
      const _Tp __r2 = __z.real() * __z.real();
      const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();

      _Tp __num = __z.imag() + _Tp(1.0);
      _Tp __den = __z.imag() - _Tp(1.0);

      __num = __r2 + __num * __num;
      __den = __r2 + __den * __den;

      return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
			       _Tp(0.25) * log(__num / __den));
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_atan(__complex__ float __z)
  { return __builtin_catanf(__z); }

  inline __complex__ double
  __complex_atan(__complex__ double __z)
  { return __builtin_catan(__z); }

  inline __complex__ long double
  __complex_atan(const __complex__ long double& __z)
  { return __builtin_catanl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    atan(const std::complex<_Tp>& __z)
    { return __complex_atan(__z.__rep()); }
#else
  /// atan(__z) [8.1.4].
  //  Effects:  Behaves the same as C99 function catan, defined
  //            in subclause 7.3.5.3.
  template<typename _Tp>
    inline std::complex<_Tp>
    atan(const std::complex<_Tp>& __z)
    { return __complex_atan(__z); }
#endif

  template<typename _Tp>
    std::complex<_Tp>
    __complex_acosh(const std::complex<_Tp>& __z)
    {
      // Kahan's formula.
      return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
				 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_acosh(__complex__ float __z)
  { return __builtin_cacoshf(__z); }

  inline __complex__ double
  __complex_acosh(__complex__ double __z)
  { return __builtin_cacosh(__z); }

  inline __complex__ long double
  __complex_acosh(const __complex__ long double& __z)
  { return __builtin_cacoshl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    acosh(const std::complex<_Tp>& __z)
    { return __complex_acosh(__z.__rep()); }
#else
  /// acosh(__z) [8.1.5].
  //  Effects:  Behaves the same as C99 function cacosh, defined
  //            in subclause 7.3.6.1.
  template<typename _Tp>
    inline std::complex<_Tp>
    acosh(const std::complex<_Tp>& __z)
    { return __complex_acosh(__z); }
#endif

  template<typename _Tp>
    std::complex<_Tp>
    __complex_asinh(const std::complex<_Tp>& __z)
    {
      std::complex<_Tp> __t((__z.real() - __z.imag())
			    * (__z.real() + __z.imag()) + _Tp(1.0),
			    _Tp(2.0) * __z.real() * __z.imag());
      __t = std::sqrt(__t);

      return std::log(__t + __z);
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_asinh(__complex__ float __z)
  { return __builtin_casinhf(__z); }

  inline __complex__ double
  __complex_asinh(__complex__ double __z)
  { return __builtin_casinh(__z); }

  inline __complex__ long double
  __complex_asinh(const __complex__ long double& __z)
  { return __builtin_casinhl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    asinh(const std::complex<_Tp>& __z)
    { return __complex_asinh(__z.__rep()); }
#else
  /// asinh(__z) [8.1.6].
  //  Effects:  Behaves the same as C99 function casin, defined
  //            in subclause 7.3.6.2.
  template<typename _Tp>
    inline std::complex<_Tp>
    asinh(const std::complex<_Tp>& __z)
    { return __complex_asinh(__z); }
#endif

  template<typename _Tp>
    std::complex<_Tp>
    __complex_atanh(const std::complex<_Tp>& __z)
    {
      const _Tp __i2 = __z.imag() * __z.imag();
      const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();

      _Tp __num = _Tp(1.0) + __z.real();
      _Tp __den = _Tp(1.0) - __z.real();

      __num = __i2 + __num * __num;
      __den = __i2 + __den * __den;

      return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
			       _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
    }

#if _GLIBCXX_USE_C99_COMPLEX_TR1
  inline __complex__ float
  __complex_atanh(__complex__ float __z)
  { return __builtin_catanhf(__z); }

  inline __complex__ double
  __complex_atanh(__complex__ double __z)
  { return __builtin_catanh(__z); }

  inline __complex__ long double
  __complex_atanh(const __complex__ long double& __z)
  { return __builtin_catanhl(__z); }

  template<typename _Tp>
    inline std::complex<_Tp>
    atanh(const std::complex<_Tp>& __z)
    { return __complex_atanh(__z.__rep()); }
#else
  /// atanh(__z) [8.1.7].
  //  Effects:  Behaves the same as C99 function catanh, defined
  //            in subclause 7.3.6.3.
  template<typename _Tp>
    inline std::complex<_Tp>
    atanh(const std::complex<_Tp>& __z)
    { return __complex_atanh(__z); }
#endif

#endif // C++11

  template<typename _Tp>
    inline std::complex<_Tp>
    /// fabs(__z) [8.1.8].
    //  Effects:  Behaves the same as C99 function cabs, defined
    //            in subclause 7.3.8.1.
    fabs(const std::complex<_Tp>& __z)
    { return std::abs(__z); }

  /// Additional overloads [8.1.9].
#if __cplusplus < 201103L

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    arg(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
      return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
	                       : __type();
#else
      return std::arg(std::complex<__type>(__x));
#endif
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    imag(_Tp)
    { return _Tp(); }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    norm(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __type(__x) * __type(__x);
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    real(_Tp __x)
    { return __x; }

#endif

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const std::complex<_Tp>& __x, const _Up& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(std::complex<__type>(__x), __type(__y));
    }

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const _Tp& __x, const std::complex<_Up>& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(__type(__x), std::complex<__type>(__y));
    }

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(std::complex<__type>(__x),
		      std::complex<__type>(__y));
    }

  using std::arg;

  template<typename _Tp>
    inline std::complex<_Tp>
    conj(const std::complex<_Tp>& __z)
    { return std::conj(__z); }

  template<typename _Tp>
    inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
    conj(_Tp __x)
    { return __x; }

  using std::imag;
  using std::norm;
  using std::polar;

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    polar(const _Tp& __rho, const _Up& __theta)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::polar(__type(__rho), __type(__theta));
    }

  using std::real;

  template<typename _Tp>
    inline std::complex<_Tp>
    pow(const std::complex<_Tp>& __x, const _Tp& __y)
    { return std::pow(__x, __y); }

  template<typename _Tp>
    inline std::complex<_Tp>
    pow(const _Tp& __x, const std::complex<_Tp>& __y)
    { return std::pow(__x, __y); }

  template<typename _Tp>
    inline std::complex<_Tp>
    pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y)
    { return std::pow(__x, __y); }

/// @} group complex_numbers
}

_GLIBCXX_END_NAMESPACE_VERSION
}

#endif // _GLIBCXX_TR1_COMPLEX