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Edit File: complex

// The template and inlines for the -*- C++ -*- complex number classes. // Copyright (C) 1997-2021 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 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> class complex { public: /// 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_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 times @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 divided by @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 = __x; __r /= __y; return __r; } ///@} /// Return @a x. template<typename _Tp> inline _GLIBCXX20_CONSTEXPR complex<_Tp> operator+(const complex<_Tp>& __x) { return __x; } /// Return complex negation of @a x. template<typename _Tp> inline _GLIBCXX20_CONSTEXPR complex<_Tp> operator-(const complex<_Tp>& __x) { return complex<_Tp>(-__x.real(), -__x.imag()); } ///@{ /// Return true if @a x is equal to @a y. template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x.real() == __y.real() && __x.imag() == __y.imag(); } template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator==(const complex<_Tp>& __x, const _Tp& __y) { return __x.real() == __y && __x.imag() == _Tp(); } #if !(__cpp_impl_three_way_comparison >= 201907L) template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator==(const _Tp& __x, const complex<_Tp>& __y) { return __x == __y.real() && _Tp() == __y.imag(); } ///@} ///@{ /// Return false if @a x is equal to @a y. template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x.real() != __y.real() || __x.imag() != __y.imag(); } template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator!=(const complex<_Tp>& __x, const _Tp& __y) { return __x.real() != __y || __x.imag() != _Tp(); } template<typename _Tp> inline _GLIBCXX_CONSTEXPR bool operator!=(const _Tp& __x, const complex<_Tp>& __y) { return __x != __y.real() || _Tp() != __y.imag(); } #endif ///@} /// Extraction operator for complex values. template<typename _Tp, typename _CharT, class _Traits> basic_istream<_CharT, _Traits>& operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) { bool __fail = true; _CharT __ch; if (__is >> __ch) { if (_Traits::eq(__ch, __is.widen('('))) { _Tp __u; if (__is >> __u >> __ch) { const _CharT __rparen = __is.widen(')'); if (_Traits::eq(__ch, __rparen)) { __x = __u; __fail = false; } else if (_Traits::eq(__ch, __is.widen(','))) { _Tp __v; if (__is >> __v >> __ch) { if (_Traits::eq(__ch, __rparen)) { __x = complex<_Tp>(__u, __v); __fail = false; } else __is.putback(__ch); } } else __is.putback(__ch); } } else { __is.putback(__ch); _Tp __u; if (__is >> __u) { __x = __u; __fail = false; } } } if (__fail) __is.setstate(ios_base::failbit); return __is; } /// Insertion operator for complex values. template<typename _Tp, typename _CharT, class _Traits> basic_ostream<_CharT, _Traits>& operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) { basic_ostringstream<_CharT, _Traits> __s; __s.flags(__os.flags()); __s.imbue(__os.getloc()); __s.precision(__os.precision()); __s << '(' << __x.real() << ',' << __x.imag() << ')'; return __os << __s.str(); } // Values #if __cplusplus >= 201103L template<typename _Tp> constexpr _Tp real(const complex<_Tp>& __z) { return __z.real(); } template<typename _Tp> constexpr _Tp imag(const complex<_Tp>& __z) { return __z.imag(); } #else template<typename _Tp> inline _Tp& real(complex<_Tp>& __z) { return __z.real(); } template<typename _Tp> inline const _Tp& real(const complex<_Tp>& __z) { return __z.real(); } template<typename _Tp> inline _Tp& imag(complex<_Tp>& __z) { return __z.imag(); } template<typename _Tp> inline const _Tp& imag(const complex<_Tp>& __z) { return __z.imag(); } #endif // 26.2.7/3 abs(__z): Returns the magnitude of __z. template<typename _Tp> inline _Tp __complex_abs(const complex<_Tp>& __z) { _Tp __x = __z.real(); _Tp __y = __z.imag(); const _Tp __s = std::max(abs(__x), abs(__y)); if (__s == _Tp()) // well ... return __s; __x /= __s; __y /= __s; return __s * sqrt(__x * __x + __y * __y); } #if _GLIBCXX_USE_C99_COMPLEX inline float __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } inline double __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } inline long double __complex_abs(const __complex__ long double& __z) { return __builtin_cabsl(__z); } template<typename _Tp> inline _Tp abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } #else template<typename _Tp> inline _Tp abs(const complex<_Tp>& __z) { return __complex_abs(__z); } #endif // 26.2.7/4: arg(__z): Returns the phase angle of __z. template<typename _Tp> inline _Tp __complex_arg(const complex<_Tp>& __z) { return atan2(__z.imag(), __z.real()); } #if _GLIBCXX_USE_C99_COMPLEX inline float __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } inline double __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } inline long double __complex_arg(const __complex__ long double& __z) { return __builtin_cargl(__z); } template<typename _Tp> inline _Tp arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } #else template<typename _Tp> inline _Tp arg(const complex<_Tp>& __z) { return __complex_arg(__z); } #endif // 26.2.7/5: norm(__z) returns the squared magnitude of __z. // As defined, norm() is -not- a norm is the common mathematical // sense 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 _GLIBCXX20_CONSTEXPR _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 _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) { //_Tp __res = std::abs(__z); //return __res * __res; const _Tp __x = __z.real(); const _Tp __y = __z.imag(); return __x * __x + __y * __y; } }; template<typename _Tp> inline _GLIBCXX20_CONSTEXPR _Tp norm(const complex<_Tp>& __z) { return _Norm_helper<__is_floating<_Tp>::__value && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); } template<typename _Tp> inline complex<_Tp> polar(const _Tp& __rho, const _Tp& __theta) { __glibcxx_assert( __rho >= 0 ); return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } template<typename _Tp> inline _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>& __z) { return complex<_Tp>(__z.real(), -__z.imag()); } // Transcendentals // 26.2.8/1 cos(__z): Returns the cosine of __z. template<typename _Tp> inline complex<_Tp> __complex_cos(const complex<_Tp>& __z) { const _Tp __x = __z.real(); const _Tp __y = __z.imag(); return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } inline __complex__ double __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } inline __complex__ long double __complex_cos(const __complex__ long double& __z) { return __builtin_ccosl(__z); } template<typename _Tp> inline complex<_Tp> cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> cos(const complex<_Tp>& __z) { return __complex_cos(__z); } #endif // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. template<typename _Tp> inline complex<_Tp> __complex_cosh(const complex<_Tp>& __z) { const _Tp __x = __z.real(); const _Tp __y = __z.imag(); return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } inline __complex__ double __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } inline __complex__ long double __complex_cosh(const __complex__ long double& __z) { return __builtin_ccoshl(__z); } template<typename _Tp> inline complex<_Tp> cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } #endif // 26.2.8/3 exp(__z): Returns the complex base e exponential of x template<typename _Tp> inline complex<_Tp> __complex_exp(const complex<_Tp>& __z) { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } inline __complex__ double __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } inline __complex__ long double __complex_exp(const __complex__ long double& __z) { return __builtin_cexpl(__z); } template<typename _Tp> inline complex<_Tp> exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> exp(const complex<_Tp>& __z) { return __complex_exp(__z); } #endif // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. // The branch cut is along the negative axis. template<typename _Tp> inline complex<_Tp> __complex_log(const complex<_Tp>& __z) { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } inline __complex__ double __complex_log(__complex__ double __z) { return __builtin_clog(__z); } inline __complex__ long double __complex_log(const __complex__ long double& __z) { return __builtin_clogl(__z); } template<typename _Tp> inline complex<_Tp> log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> log(const complex<_Tp>& __z) { return __complex_log(__z); } #endif template<typename _Tp> inline complex<_Tp> log10(const complex<_Tp>& __z) { return std::log(__z) / log(_Tp(10.0)); } // 26.2.8/10 sin(__z): Returns the sine of __z. template<typename _Tp> inline complex<_Tp> __complex_sin(const complex<_Tp>& __z) { const _Tp __x = __z.real(); const _Tp __y = __z.imag(); return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } inline __complex__ double __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } inline __complex__ long double __complex_sin(const __complex__ long double& __z) { return __builtin_csinl(__z); } template<typename _Tp> inline complex<_Tp> sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> sin(const complex<_Tp>& __z) { return __complex_sin(__z); } #endif // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. template<typename _Tp> inline complex<_Tp> __complex_sinh(const complex<_Tp>& __z) { const _Tp __x = __z.real(); const _Tp __y = __z.imag(); return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } inline __complex__ double __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } inline __complex__ long double __complex_sinh(const __complex__ long double& __z) { return __builtin_csinhl(__z); } template<typename _Tp> inline complex<_Tp> sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } #endif // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. // The branch cut is on the negative axis. template<typename _Tp> complex<_Tp> __complex_sqrt(const complex<_Tp>& __z) { _Tp __x = __z.real(); _Tp __y = __z.imag(); if (__x == _Tp()) { _Tp __t = sqrt(abs(__y) / 2); return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); } else { _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); _Tp __u = __t / 2; return __x > _Tp() ? complex<_Tp>(__u, __y / __t) : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); } } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } inline __complex__ double __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } inline __complex__ long double __complex_sqrt(const __complex__ long double& __z) { return __builtin_csqrtl(__z); } template<typename _Tp> inline complex<_Tp> sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } #endif // 26.2.8/14 tan(__z): Return the complex tangent of __z. template<typename _Tp> inline complex<_Tp> __complex_tan(const complex<_Tp>& __z) { return std::sin(__z) / std::cos(__z); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } inline __complex__ double __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } inline __complex__ long double __complex_tan(const __complex__ long double& __z) { return __builtin_ctanl(__z); } template<typename _Tp> inline complex<_Tp> tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> tan(const complex<_Tp>& __z) { return __complex_tan(__z); } #endif // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. template<typename _Tp> inline complex<_Tp> __complex_tanh(const complex<_Tp>& __z) { return std::sinh(__z) / std::cosh(__z); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } inline __complex__ double __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } inline __complex__ long double __complex_tanh(const __complex__ long double& __z) { return __builtin_ctanhl(__z); } template<typename _Tp> inline complex<_Tp> tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } #else template<typename _Tp> inline complex<_Tp> tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } #endif // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x // raised to the __y-th power. The branch // cut is on the negative axis. template<typename _Tp> complex<_Tp> __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) { complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); while (__n >>= 1) { __x *= __x; if (__n % 2) __y *= __x; } return __y; } // In C++11 mode we used to implement the resolution of // DR 844. complex pow return type is ambiguous. // thus the following overload was disabled in that mode. However, doing // that causes all sorts of issues, see, for example: // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html // and also PR57974. template<typename _Tp> inline complex<_Tp> pow(const complex<_Tp>& __z, int __n) { return __n < 0 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) : std::__complex_pow_unsigned(__z, __n); } template<typename _Tp> complex<_Tp> pow(const complex<_Tp>& __x, const _Tp& __y) { #if ! _GLIBCXX_USE_C99_COMPLEX if (__x == _Tp()) return _Tp(); #endif if (__x.imag() == _Tp() && __x.real() > _Tp()) return pow(__x.real(), __y); complex<_Tp> __t = std::log(__x); return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); } template<typename _Tp> inline complex<_Tp> __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } #if _GLIBCXX_USE_C99_COMPLEX inline __complex__ float __complex_pow(__complex__ float __x, __complex__ float __y) { return __builtin_cpowf(__x, __y); } inline __complex__ double __complex_pow(__complex__ double __x, __complex__ double __y) { return __builtin_cpow(__x, __y); } inline __complex__ long double __complex_pow(const __complex__ long double& __x, const __complex__ long double& __y) { return __builtin_cpowl(__x, __y); } template<typename _Tp> inline complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __complex_pow(__x.__rep(), __y.__rep()); } #else template<typename _Tp> inline complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __complex_pow(__x, __y); } #endif template<typename _Tp> inline complex<_Tp> pow(const _Tp& __x, const complex<_Tp>& __y) { return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), __y.imag() * log(__x)) : std::pow(complex<_Tp>(__x), __y); } /// 26.2.3 complex specializations /// complex<float> specialization template<> class complex<float> { public: typedef float value_type; typedef __complex__ float _ComplexT; _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) #if __cplusplus >= 201103L : _M_value{ __r, __i } { } #else { __real__ _M_value = __r; __imag__ _M_value = __i; } #endif explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); #if __cplusplus >= 201103L // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. __attribute ((__abi_tag__ ("cxx11"))) constexpr float real() const { return __real__ _M_value; } __attribute ((__abi_tag__ ("cxx11"))) constexpr float imag() const { return __imag__ _M_value; } #else float& real() { return __real__ _M_value; } const float& real() const { return __real__ _M_value; } float& imag() { return __imag__ _M_value; } const float& imag() const { return __imag__ _M_value; } #endif // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. _GLIBCXX20_CONSTEXPR void real(float __val) { __real__ _M_value = __val; } _GLIBCXX20_CONSTEXPR void imag(float __val) { __imag__ _M_value = __val; } _GLIBCXX20_CONSTEXPR complex& operator=(float __f) { _M_value = __f; return *this; } _GLIBCXX20_CONSTEXPR complex& operator+=(float __f) { _M_value += __f; return *this; } _GLIBCXX20_CONSTEXPR complex& operator-=(float __f) { _M_value -= __f; return *this; } _GLIBCXX20_CONSTEXPR complex& operator*=(float __f) { _M_value *= __f; return *this; } _GLIBCXX20_CONSTEXPR complex& operator/=(float __f) { _M_value /= __f; return *this; } // Let the compiler synthesize the copy and assignment // operator. It always does a pretty good job. #if __cplusplus >= 201103L _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; #endif template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator=(const complex<_Tp>& __z) { __real__ _M_value = __z.real(); __imag__ _M_value = __z.imag(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator+=(const complex<_Tp>& __z) { _M_value += __z.__rep(); return *this; } template<class _Tp> _GLIBCXX20_CONSTEXPR complex& operator-=(const complex<_Tp>& __z) { _M_value -= __z.__rep(); return *this; } template<class _Tp> _GLIBCXX20_CONSTEXPR complex& operator*=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value *= __t; return *this; } template<class _Tp> _GLIBCXX20_CONSTEXPR complex& operator/=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value /= __t; return *this; } _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } private: _ComplexT _M_value; }; /// 26.2.3 complex specializations /// complex<double> specialization template<> class complex<double> { public: typedef double value_type; typedef __complex__ double _ComplexT; _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) #if __cplusplus >= 201103L : _M_value{ __r, __i } { } #else { __real__ _M_value = __r; __imag__ _M_value = __i; } #endif _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) : _M_value(__z.__rep()) { } explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); #if __cplusplus >= 201103L // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. __attribute ((__abi_tag__ ("cxx11"))) constexpr double real() const { return __real__ _M_value; } __attribute ((__abi_tag__ ("cxx11"))) constexpr double imag() const { return __imag__ _M_value; } #else double& real() { return __real__ _M_value; } const double& real() const { return __real__ _M_value; } double& imag() { return __imag__ _M_value; } const double& imag() const { return __imag__ _M_value; } #endif // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. _GLIBCXX20_CONSTEXPR void real(double __val) { __real__ _M_value = __val; } _GLIBCXX20_CONSTEXPR void imag(double __val) { __imag__ _M_value = __val; } _GLIBCXX20_CONSTEXPR complex& operator=(double __d) { _M_value = __d; return *this; } _GLIBCXX20_CONSTEXPR complex& operator+=(double __d) { _M_value += __d; return *this; } _GLIBCXX20_CONSTEXPR complex& operator-=(double __d) { _M_value -= __d; return *this; } _GLIBCXX20_CONSTEXPR complex& operator*=(double __d) { _M_value *= __d; return *this; } _GLIBCXX20_CONSTEXPR complex& operator/=(double __d) { _M_value /= __d; return *this; } // The compiler will synthesize this, efficiently. #if __cplusplus >= 201103L _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; #endif template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator=(const complex<_Tp>& __z) { _M_value = __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator+=(const complex<_Tp>& __z) { _M_value += __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator-=(const complex<_Tp>& __z) { _M_value -= __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator*=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value *= __t; return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator/=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value /= __t; return *this; } _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } private: _ComplexT _M_value; }; /// 26.2.3 complex specializations /// complex<long double> specialization template<> class complex<long double> { public: typedef long double value_type; typedef __complex__ long double _ComplexT; _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, long double __i = 0.0L) #if __cplusplus >= 201103L : _M_value{ __r, __i } { } #else { __real__ _M_value = __r; __imag__ _M_value = __i; } #endif _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) : _M_value(__z.__rep()) { } _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) : _M_value(__z.__rep()) { } #if __cplusplus >= 201103L // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. __attribute ((__abi_tag__ ("cxx11"))) constexpr long double real() const { return __real__ _M_value; } __attribute ((__abi_tag__ ("cxx11"))) constexpr long double imag() const { return __imag__ _M_value; } #else long double& real() { return __real__ _M_value; } const long double& real() const { return __real__ _M_value; } long double& imag() { return __imag__ _M_value; } const long double& imag() const { return __imag__ _M_value; } #endif // _GLIBCXX_RESOLVE_LIB_DEFECTS // DR 387. std::complex over-encapsulated. _GLIBCXX20_CONSTEXPR void real(long double __val) { __real__ _M_value = __val; } _GLIBCXX20_CONSTEXPR void imag(long double __val) { __imag__ _M_value = __val; } _GLIBCXX20_CONSTEXPR complex& operator=(long double __r) { _M_value = __r; return *this; } _GLIBCXX20_CONSTEXPR complex& operator+=(long double __r) { _M_value += __r; return *this; } _GLIBCXX20_CONSTEXPR complex& operator-=(long double __r) { _M_value -= __r; return *this; } _GLIBCXX20_CONSTEXPR complex& operator*=(long double __r) { _M_value *= __r; return *this; } _GLIBCXX20_CONSTEXPR complex& operator/=(long double __r) { _M_value /= __r; return *this; } // The compiler knows how to do this efficiently #if __cplusplus >= 201103L _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; #endif template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator=(const complex<_Tp>& __z) { _M_value = __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator+=(const complex<_Tp>& __z) { _M_value += __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator-=(const complex<_Tp>& __z) { _M_value -= __z.__rep(); return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator*=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value *= __t; return *this; } template<typename _Tp> _GLIBCXX20_CONSTEXPR complex& operator/=(const complex<_Tp>& __z) { const _ComplexT __t = __z.__rep(); _M_value /= __t; return *this; } _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } private: _ComplexT _M_value; }; // These bits have to be at the end of this file, so that the // specializations have all been defined. inline _GLIBCXX_CONSTEXPR complex<float>::complex(const complex<double>& __z) : _M_value(__z.__rep()) { } inline _GLIBCXX_CONSTEXPR complex<float>::complex(const complex<long double>& __z) : _M_value(__z.__rep()) { } inline _GLIBCXX_CONSTEXPR complex<double>::complex(const complex<long double>& __z) : _M_value(__z.__rep()) { } // Inhibit implicit instantiations for required instantiations, // which are defined via explicit instantiations elsewhere. // NB: This syntax is a GNU extension. #if _GLIBCXX_EXTERN_TEMPLATE extern template istream& operator>>(istream&, complex<float>&); extern template ostream& operator<<(ostream&, const complex<float>&); extern template istream& operator>>(istream&, complex<double>&); extern template ostream& operator<<(ostream&, const complex<double>&); extern template istream& operator>>(istream&, complex<long double>&); extern template ostream& operator<<(ostream&, const complex<long double>&); #ifdef _GLIBCXX_USE_WCHAR_T extern template wistream& operator>>(wistream&, complex<float>&); extern template wostream& operator<<(wostream&, const complex<float>&); extern template wistream& operator>>(wistream&, complex<double>&); extern template wostream& operator<<(wostream&, const complex<double>&); extern template wistream& operator>>(wistream&, complex<long double>&); extern template wostream& operator<<(wostream&, const complex<long double>&); #endif #endif /// @} group complex_numbers _GLIBCXX_END_NAMESPACE_VERSION } // namespace namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) { _GLIBCXX_BEGIN_NAMESPACE_VERSION // See ext/type_traits.h for the primary template. template<typename _Tp, typename _Up> struct __promote_2<std::complex<_Tp>, _Up> { public: typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; }; template<typename _Tp, typename _Up> struct __promote_2<_Tp, std::complex<_Up> > { public: typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; }; template<typename _Tp, typename _Up> struct __promote_2<std::complex<_Tp>, std::complex<_Up> > { public: typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; }; _GLIBCXX_END_NAMESPACE_VERSION } // namespace #if __cplusplus >= 201103L namespace std _GLIBCXX_VISIBILITY(default) { _GLIBCXX_BEGIN_NAMESPACE_VERSION // Forward declarations. 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>&); // DR 595. template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); template<typename _Tp> inline std::complex<_Tp> __complex_acos(const std::complex<_Tp>& __z) { const std::complex<_Tp> __t = std::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::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 template<typename _Tp> inline _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]. template<typename _Tp> inline typename __gnu_cxx::__promote<_Tp>::__type arg(_Tp __x) { typedef typename __gnu_cxx::__promote<_Tp>::__type __type; #if (_GLIBCXX11_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> _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type imag(_Tp) { return _Tp(); } template<typename _Tp> _GLIBCXX20_CONSTEXPR 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> _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type real(_Tp __x) { return __x; } 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)); } // Forward declarations. // DR 781. template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); // Generic implementation of std::proj, does not work for infinities. template<typename _Tp> inline std::complex<_Tp> __complex_proj(const std::complex<_Tp>& __z) { return __z; } #if _GLIBCXX_USE_C99_COMPLEX inline complex<float> __complex_proj(const complex<float>& __z) { return __builtin_cprojf(__z.__rep()); } inline complex<double> __complex_proj(const complex<double>& __z) { return __builtin_cproj(__z.__rep()); } inline complex<long double> __complex_proj(const complex<long double>& __z) { return __builtin_cprojl(__z.__rep()); } #elif defined _GLIBCXX_USE_C99_MATH_TR1 inline complex<float> __complex_proj(const complex<float>& __z) { if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) return complex<float>(__builtin_inff(), __builtin_copysignf(0.0f, __z.imag())); return __z; } inline complex<double> __complex_proj(const complex<double>& __z) { if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) return complex<double>(__builtin_inf(), __builtin_copysign(0.0, __z.imag())); return __z; } inline complex<long double> __complex_proj(const complex<long double>& __z) { if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) return complex<long double>(__builtin_infl(), __builtin_copysignl(0.0l, __z.imag())); return __z; } #endif template<typename _Tp> inline std::complex<_Tp> proj(const std::complex<_Tp>& __z) { return __complex_proj(__z); } // Overload for scalars template<typename _Tp> inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> proj(_Tp __x) { typedef typename __gnu_cxx::__promote<_Tp>::__type __type; return std::proj(std::complex<__type>(__x)); } template<typename _Tp> inline _GLIBCXX20_CONSTEXPR std::complex<typename __gnu_cxx::__promote<_Tp>::__type> conj(_Tp __x) { typedef typename __gnu_cxx::__promote<_Tp>::__type __type; return std::complex<__type>(__x, -__type()); } #if __cplusplus > 201103L inline namespace literals { inline namespace complex_literals { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wliteral-suffix" #define __cpp_lib_complex_udls 201309 constexpr std::complex<float> operator""if(long double __num) { return std::complex<float>{0.0F, static_cast<float>(__num)}; } constexpr std::complex<float> operator""if(unsigned long long __num) { return std::complex<float>{0.0F, static_cast<float>(__num)}; } constexpr std::complex<double> operator""i(long double __num) { return std::complex<double>{0.0, static_cast<double>(__num)}; } constexpr std::complex<double> operator""i(unsigned long long __num) { return std::complex<double>{0.0, static_cast<double>(__num)}; } constexpr std::complex<long double> operator""il(long double __num) { return std::complex<long double>{0.0L, __num}; } constexpr std::complex<long double> operator""il(unsigned long long __num) { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } #pragma GCC diagnostic pop } // inline namespace complex_literals } // inline namespace literals #endif // C++14 _GLIBCXX_END_NAMESPACE_VERSION } // namespace #endif // C++11 #endif /* _GLIBCXX_COMPLEX */