// -*- C++ -*- //===----------------------------------------------------------------------===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// #ifndef _LIBCPP_COMPLEX #define _LIBCPP_COMPLEX /* complex synopsis namespace std { template class complex { public: typedef T value_type; complex(const T& re = T(), const T& im = T()); // constexpr in C++14 complex(const complex&); // constexpr in C++14 template complex(const complex&); // constexpr in C++14 T real() const; // constexpr in C++14 T imag() const; // constexpr in C++14 void real(T); // constexpr in C++20 void imag(T); // constexpr in C++20 complex& operator= (const T&); // constexpr in C++20 complex& operator+=(const T&); // constexpr in C++20 complex& operator-=(const T&); // constexpr in C++20 complex& operator*=(const T&); // constexpr in C++20 complex& operator/=(const T&); // constexpr in C++20 complex& operator=(const complex&); // constexpr in C++20 template complex& operator= (const complex&); // constexpr in C++20 template complex& operator+=(const complex&); // constexpr in C++20 template complex& operator-=(const complex&); // constexpr in C++20 template complex& operator*=(const complex&); // constexpr in C++20 template complex& operator/=(const complex&); // constexpr in C++20 }; template<> class complex { public: typedef float value_type; constexpr complex(float re = 0.0f, float im = 0.0f); explicit constexpr complex(const complex&); explicit constexpr complex(const complex&); constexpr float real() const; void real(float); // constexpr in C++20 constexpr float imag() const; void imag(float); // constexpr in C++20 complex& operator= (float); // constexpr in C++20 complex& operator+=(float); // constexpr in C++20 complex& operator-=(float); // constexpr in C++20 complex& operator*=(float); // constexpr in C++20 complex& operator/=(float); // constexpr in C++20 complex& operator=(const complex&); // constexpr in C++20 template complex& operator= (const complex&); // constexpr in C++20 template complex& operator+=(const complex&); // constexpr in C++20 template complex& operator-=(const complex&); // constexpr in C++20 template complex& operator*=(const complex&); // constexpr in C++20 template complex& operator/=(const complex&); // constexpr in C++20 }; template<> class complex { public: typedef double value_type; constexpr complex(double re = 0.0, double im = 0.0); constexpr complex(const complex&); explicit constexpr complex(const complex&); constexpr double real() const; void real(double); // constexpr in C++20 constexpr double imag() const; void imag(double); // constexpr in C++20 complex& operator= (double); // constexpr in C++20 complex& operator+=(double); // constexpr in C++20 complex& operator-=(double); // constexpr in C++20 complex& operator*=(double); // constexpr in C++20 complex& operator/=(double); // constexpr in C++20 complex& operator=(const complex&); // constexpr in C++20 template complex& operator= (const complex&); // constexpr in C++20 template complex& operator+=(const complex&); // constexpr in C++20 template complex& operator-=(const complex&); // constexpr in C++20 template complex& operator*=(const complex&); // constexpr in C++20 template complex& operator/=(const complex&); // constexpr in C++20 }; template<> class complex { public: typedef long double value_type; constexpr complex(long double re = 0.0L, long double im = 0.0L); constexpr complex(const complex&); constexpr complex(const complex&); constexpr long double real() const; void real(long double); // constexpr in C++20 constexpr long double imag() const; void imag(long double); // constexpr in C++20 complex& operator=(const complex&); // constexpr in C++20 complex& operator= (long double); // constexpr in C++20 complex& operator+=(long double); // constexpr in C++20 complex& operator-=(long double); // constexpr in C++20 complex& operator*=(long double); // constexpr in C++20 complex& operator/=(long double); // constexpr in C++20 template complex& operator= (const complex&); // constexpr in C++20 template complex& operator+=(const complex&); // constexpr in C++20 template complex& operator-=(const complex&); // constexpr in C++20 template complex& operator*=(const complex&); // constexpr in C++20 template complex& operator/=(const complex&); // constexpr in C++20 }; // 26.3.6 operators: template complex operator+(const complex&, const complex&); // constexpr in C++20 template complex operator+(const complex&, const T&); // constexpr in C++20 template complex operator+(const T&, const complex&); // constexpr in C++20 template complex operator-(const complex&, const complex&); // constexpr in C++20 template complex operator-(const complex&, const T&); // constexpr in C++20 template complex operator-(const T&, const complex&); // constexpr in C++20 template complex operator*(const complex&, const complex&); // constexpr in C++20 template complex operator*(const complex&, const T&); // constexpr in C++20 template complex operator*(const T&, const complex&); // constexpr in C++20 template complex operator/(const complex&, const complex&); // constexpr in C++20 template complex operator/(const complex&, const T&); // constexpr in C++20 template complex operator/(const T&, const complex&); // constexpr in C++20 template complex operator+(const complex&); // constexpr in C++20 template complex operator-(const complex&); // constexpr in C++20 template bool operator==(const complex&, const complex&); // constexpr in C++14 template bool operator==(const complex&, const T&); // constexpr in C++14 template bool operator==(const T&, const complex&); // constexpr in C++14, removed in C++20 template bool operator!=(const complex&, const complex&); // constexpr in C++14, removed in C++20 template bool operator!=(const complex&, const T&); // constexpr in C++14, removed in C++20 template bool operator!=(const T&, const complex&); // constexpr in C++14, removed in C++20 template basic_istream& operator>>(basic_istream&, complex&); template basic_ostream& operator<<(basic_ostream&, const complex&); // 26.3.7 values: template T real(const complex&); // constexpr in C++14 long double real(long double); // constexpr in C++14 double real(double); // constexpr in C++14 template double real(T); // constexpr in C++14 float real(float); // constexpr in C++14 template T imag(const complex&); // constexpr in C++14 long double imag(long double); // constexpr in C++14 double imag(double); // constexpr in C++14 template double imag(T); // constexpr in C++14 float imag(float); // constexpr in C++14 template T abs(const complex&); template T arg(const complex&); long double arg(long double); double arg(double); template double arg(T); float arg(float); template T norm(const complex&); // constexpr in C++20 long double norm(long double); // constexpr in C++20 double norm(double); // constexpr in C++20 template double norm(T); // constexpr in C++20 float norm(float); // constexpr in C++20 template complex conj(const complex&); // constexpr in C++20 complex conj(long double); // constexpr in C++20 complex conj(double); // constexpr in C++20 template complex conj(T); // constexpr in C++20 complex conj(float); // constexpr in C++20 template complex proj(const complex&); complex proj(long double); complex proj(double); template complex proj(T); complex proj(float); template complex polar(const T&, const T& = T()); // 26.3.8 transcendentals: template complex acos(const complex&); template complex asin(const complex&); template complex atan(const complex&); template complex acosh(const complex&); template complex asinh(const complex&); template complex atanh(const complex&); template complex cos (const complex&); template complex cosh (const complex&); template complex exp (const complex&); template complex log (const complex&); template complex log10(const complex&); template complex pow(const complex&, const T&); template complex pow(const complex&, const complex&); template complex pow(const T&, const complex&); template complex sin (const complex&); template complex sinh (const complex&); template complex sqrt (const complex&); template complex tan (const complex&); template complex tanh (const complex&); } // std */ #include <__assert> // all public C++ headers provide the assertion handler #include <__config> #include #include #include #include #if !defined(_LIBCPP_HAS_NO_LOCALIZATION) # include // for std::basic_ostringstream #endif #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) # pragma GCC system_header #endif _LIBCPP_BEGIN_NAMESPACE_STD template class _LIBCPP_TEMPLATE_VIS complex; template _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); template _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); template class _LIBCPP_TEMPLATE_VIS complex { public: typedef _Tp value_type; private: value_type __re_; value_type __im_; public: _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 complex(const value_type& __re = value_type(), const value_type& __im = value_type()) : __re_(__re), __im_(__im) {} template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 complex(const complex<_Xp>& __c) : __re_(__c.real()), __im_(__c.imag()) {} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type real() const {return __re_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type imag() const {return __im_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const value_type& __re) {__re_ = __re; __im_ = value_type(); return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const value_type& __re) {__re_ += __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;} template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) { __re_ = __c.real(); __im_ = __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { __re_ += __c.real(); __im_ += __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { __re_ -= __c.real(); __im_ -= __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { *this = *this * complex(__c.real(), __c.imag()); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { *this = *this / complex(__c.real(), __c.imag()); return *this; } }; template<> class _LIBCPP_TEMPLATE_VIS complex; template<> class _LIBCPP_TEMPLATE_VIS complex; template<> class _LIBCPP_TEMPLATE_VIS complex { float __re_; float __im_; public: typedef float value_type; _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) : __re_(__re), __im_(__im) {} _LIBCPP_INLINE_VISIBILITY explicit _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY explicit _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (float __re) {__re_ = __re; __im_ = value_type(); return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) {__re_ += __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) {__re_ -= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;} template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) { __re_ = __c.real(); __im_ = __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { __re_ += __c.real(); __im_ += __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { __re_ -= __c.real(); __im_ -= __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { *this = *this * complex(__c.real(), __c.imag()); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { *this = *this / complex(__c.real(), __c.imag()); return *this; } }; template<> class _LIBCPP_TEMPLATE_VIS complex { double __re_; double __im_; public: typedef double value_type; _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) : __re_(__re), __im_(__im) {} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY explicit _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (double __re) {__re_ = __re; __im_ = value_type(); return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) {__re_ += __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) {__re_ -= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;} template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) { __re_ = __c.real(); __im_ = __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { __re_ += __c.real(); __im_ += __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { __re_ -= __c.real(); __im_ -= __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { *this = *this * complex(__c.real(), __c.imag()); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { *this = *this / complex(__c.real(), __c.imag()); return *this; } }; template<> class _LIBCPP_TEMPLATE_VIS complex { long double __re_; long double __im_; public: typedef long double value_type; _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L) : __re_(__re), __im_(__im) {} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(const complex& __c); _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (long double __re) {__re_ = __re; __im_ = value_type(); return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) {__re_ += __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) {__re_ -= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;} _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;} template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) { __re_ = __c.real(); __im_ = __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { __re_ += __c.real(); __im_ += __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { __re_ -= __c.real(); __im_ -= __c.imag(); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { *this = *this * complex(__c.real(), __c.imag()); return *this; } template _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { *this = *this / complex(__c.real(), __c.imag()); return *this; } }; inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} inline _LIBCPP_CONSTEXPR complex::complex(const complex& __c) : __re_(__c.real()), __im_(__c.imag()) {} // 26.3.6 operators: template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __t(__x); __t += __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __t(__x); __t += __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __t(__y); __t += __x; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) { complex<_Tp> __t(__x); __t -= __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __t(__x); __t -= __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __t(-__y); __t += __x; return __t; } template _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) { _Tp __a = __z.real(); _Tp __b = __z.imag(); _Tp __c = __w.real(); _Tp __d = __w.imag(); // Avoid floating point operations that are invalid during constant evaluation if (__libcpp_is_constant_evaluated()) { bool __z_zero = __a == _Tp(0) && __b == _Tp(0); bool __w_zero = __c == _Tp(0) && __d == _Tp(0); bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b); bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d); bool __z_nan = !__z_inf && ( (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b)) || (std::__constexpr_isnan(__a) && __b == _Tp(0)) || (__a == _Tp(0) && std::__constexpr_isnan(__b)) ); bool __w_nan = !__w_inf && ( (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d)) || (std::__constexpr_isnan(__c) && __d == _Tp(0)) || (__c == _Tp(0) && std::__constexpr_isnan(__d)) ); if (__z_nan || __w_nan) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } if (__z_inf || __w_inf) { if (__z_zero || __w_zero) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity())); } bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b)); bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d)); if (__z_nonzero_nan || __w_nonzero_nan) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } } _Tp __ac = __a * __c; _Tp __bd = __b * __d; _Tp __ad = __a * __d; _Tp __bc = __b * __c; _Tp __x = __ac - __bd; _Tp __y = __ad + __bc; if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y)) { bool __recalc = false; if (std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b)) { __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a); __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b); if (std::__constexpr_isnan(__c)) __c = std::__constexpr_copysign(_Tp(0), __c); if (std::__constexpr_isnan(__d)) __d = std::__constexpr_copysign(_Tp(0), __d); __recalc = true; } if (std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d)) { __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c); __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d); if (std::__constexpr_isnan(__a)) __a = std::__constexpr_copysign(_Tp(0), __a); if (std::__constexpr_isnan(__b)) __b = std::__constexpr_copysign(_Tp(0), __b); __recalc = true; } if (!__recalc && (std::__constexpr_isinf(__ac) || std::__constexpr_isinf(__bd) || std::__constexpr_isinf(__ad) || std::__constexpr_isinf(__bc))) { if (std::__constexpr_isnan(__a)) __a = std::__constexpr_copysign(_Tp(0), __a); if (std::__constexpr_isnan(__b)) __b = std::__constexpr_copysign(_Tp(0), __b); if (std::__constexpr_isnan(__c)) __c = std::__constexpr_copysign(_Tp(0), __c); if (std::__constexpr_isnan(__d)) __d = std::__constexpr_copysign(_Tp(0), __d); __recalc = true; } if (__recalc) { __x = _Tp(INFINITY) * (__a * __c - __b * __d); __y = _Tp(INFINITY) * (__a * __d + __b * __c); } } return complex<_Tp>(__x, __y); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __x, const _Tp& __y) { complex<_Tp> __t(__x); __t *= __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __t(__y); __t *= __x; return __t; } template _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) { int __ilogbw = 0; _Tp __a = __z.real(); _Tp __b = __z.imag(); _Tp __c = __w.real(); _Tp __d = __w.imag(); _Tp __logbw = std::__constexpr_logb(std::__constexpr_fmax(std::__constexpr_fabs(__c), std::__constexpr_fabs(__d))); if (std::__constexpr_isfinite(__logbw)) { __ilogbw = static_cast(__logbw); __c = std::__constexpr_scalbn(__c, -__ilogbw); __d = std::__constexpr_scalbn(__d, -__ilogbw); } // Avoid floating point operations that are invalid during constant evaluation if (__libcpp_is_constant_evaluated()) { bool __z_zero = __a == _Tp(0) && __b == _Tp(0); bool __w_zero = __c == _Tp(0) && __d == _Tp(0); bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b); bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d); bool __z_nan = !__z_inf && ( (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b)) || (std::__constexpr_isnan(__a) && __b == _Tp(0)) || (__a == _Tp(0) && std::__constexpr_isnan(__b)) ); bool __w_nan = !__w_inf && ( (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d)) || (std::__constexpr_isnan(__c) && __d == _Tp(0)) || (__c == _Tp(0) && std::__constexpr_isnan(__d)) ); if ((__z_nan || __w_nan) || (__z_inf && __w_inf)) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b)); bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d)); if (__z_nonzero_nan || __w_nonzero_nan) { if (__w_zero) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity())); } return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } if (__w_inf) { return complex<_Tp>(_Tp(0), _Tp(0)); } if (__z_inf) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity())); } if (__w_zero) { if (__z_zero) { return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0)); } return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity())); } } _Tp __denom = __c * __c + __d * __d; _Tp __x = std::__constexpr_scalbn((__a * __c + __b * __d) / __denom, -__ilogbw); _Tp __y = std::__constexpr_scalbn((__b * __c - __a * __d) / __denom, -__ilogbw); if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y)) { if ((__denom == _Tp(0)) && (!std::__constexpr_isnan(__a) || !std::__constexpr_isnan(__b))) { __x = std::__constexpr_copysign(_Tp(INFINITY), __c) * __a; __y = std::__constexpr_copysign(_Tp(INFINITY), __c) * __b; } else if ((std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b)) && std::__constexpr_isfinite(__c) && std::__constexpr_isfinite(__d)) { __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a); __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b); __x = _Tp(INFINITY) * (__a * __c + __b * __d); __y = _Tp(INFINITY) * (__b * __c - __a * __d); } else if (std::__constexpr_isinf(__logbw) && __logbw > _Tp(0) && std::__constexpr_isfinite(__a) && std::__constexpr_isfinite(__b)) { __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c); __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d); __x = _Tp(0) * (__a * __c + __b * __d); __y = _Tp(0) * (__b * __c - __a * __d); } } return complex<_Tp>(__x, __y); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __x, const _Tp& __y) { return complex<_Tp>(__x.real() / __y, __x.imag() / __y); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const _Tp& __x, const complex<_Tp>& __y) { complex<_Tp> __t(__x); __t /= __y; return __t; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const complex<_Tp>& __x) { return __x; } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const complex<_Tp>& __x) { return complex<_Tp>(-__x.real(), -__x.imag()); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) { return __x.real() == __y.real() && __x.imag() == __y.imag(); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const complex<_Tp>& __x, const _Tp& __y) { return __x.real() == __y && __x.imag() == 0; } #if _LIBCPP_STD_VER <= 17 template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const _Tp& __x, const complex<_Tp>& __y) { return __x == __y.real() && 0 == __y.imag(); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) { return !(__x == __y); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const complex<_Tp>& __x, const _Tp& __y) { return !(__x == __y); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const _Tp& __x, const complex<_Tp>& __y) { return !(__x == __y); } #endif // 26.3.7 values: template ::value, bool = is_floating_point<_Tp>::value > struct __libcpp_complex_overload_traits {}; // Integral Types template struct __libcpp_complex_overload_traits<_Tp, true, false> { typedef double _ValueType; typedef complex _ComplexType; }; // Floating point types template struct __libcpp_complex_overload_traits<_Tp, false, true> { typedef _Tp _ValueType; typedef complex<_Tp> _ComplexType; }; // real template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp real(const complex<_Tp>& __c) { return __c.real(); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType real(_Tp __re) { return __re; } // imag template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp imag(const complex<_Tp>& __c) { return __c.imag(); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType imag(_Tp) { return 0; } // abs template inline _LIBCPP_INLINE_VISIBILITY _Tp abs(const complex<_Tp>& __c) { return std::hypot(__c.real(), __c.imag()); } // arg template inline _LIBCPP_INLINE_VISIBILITY _Tp arg(const complex<_Tp>& __c) { return std::atan2(__c.imag(), __c.real()); } template ::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY long double arg(_Tp __re) { return std::atan2l(0.L, __re); } template::value || is_same<_Tp, double>::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY double arg(_Tp __re) { return std::atan2(0., __re); } template ::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY float arg(_Tp __re) { return std::atan2f(0.F, __re); } // norm template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp norm(const complex<_Tp>& __c) { if (std::__constexpr_isinf(__c.real())) return std::abs(__c.real()); if (std::__constexpr_isinf(__c.imag())) return std::abs(__c.imag()); return __c.real() * __c.real() + __c.imag() * __c.imag(); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ValueType norm(_Tp __re) { typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType; return static_cast<_ValueType>(__re) * __re; } // conj template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> conj(const complex<_Tp>& __c) { return complex<_Tp>(__c.real(), -__c.imag()); } template inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ComplexType conj(_Tp __re) { typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; return _ComplexType(__re); } // proj template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> proj(const complex<_Tp>& __c) { complex<_Tp> __r = __c; if (std::__constexpr_isinf(__c.real()) || std::__constexpr_isinf(__c.imag())) __r = complex<_Tp>(INFINITY, std::copysign(_Tp(0), __c.imag())); return __r; } template ::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) { if (std::__constexpr_isinf(__re)) __re = std::abs(__re); return complex<_Tp>(__re); } template ::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) { typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; return _ComplexType(__re); } // polar template _LIBCPP_HIDE_FROM_ABI complex<_Tp> polar(const _Tp& __rho, const _Tp& __theta = _Tp()) { if (std::__constexpr_isnan(__rho) || std::signbit(__rho)) return complex<_Tp>(_Tp(NAN), _Tp(NAN)); if (std::__constexpr_isnan(__theta)) { if (std::__constexpr_isinf(__rho)) return complex<_Tp>(__rho, __theta); return complex<_Tp>(__theta, __theta); } if (std::__constexpr_isinf(__theta)) { if (std::__constexpr_isinf(__rho)) return complex<_Tp>(__rho, _Tp(NAN)); return complex<_Tp>(_Tp(NAN), _Tp(NAN)); } _Tp __x = __rho * std::cos(__theta); if (std::__constexpr_isnan(__x)) __x = 0; _Tp __y = __rho * std::sin(__theta); if (std::__constexpr_isnan(__y)) __y = 0; return complex<_Tp>(__x, __y); } // log template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> log(const complex<_Tp>& __x) { return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x)); } // log10 template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> log10(const complex<_Tp>& __x) { return std::log(__x) / std::log(_Tp(10)); } // sqrt template _LIBCPP_HIDE_FROM_ABI complex<_Tp> sqrt(const complex<_Tp>& __x) { if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(_Tp(INFINITY), __x.imag()); if (std::__constexpr_isinf(__x.real())) { if (__x.real() > _Tp(0)) return complex<_Tp>(__x.real(), std::__constexpr_isnan(__x.imag()) ? __x.imag() : std::copysign(_Tp(0), __x.imag())); return complex<_Tp>(std::__constexpr_isnan(__x.imag()) ? __x.imag() : _Tp(0), std::copysign(__x.real(), __x.imag())); } return std::polar(std::sqrt(std::abs(__x)), std::arg(__x) / _Tp(2)); } // exp template _LIBCPP_HIDE_FROM_ABI complex<_Tp> exp(const complex<_Tp>& __x) { _Tp __i = __x.imag(); if (__i == 0) { return complex<_Tp>(std::exp(__x.real()), std::copysign(_Tp(0), __x.imag())); } if (std::__constexpr_isinf(__x.real())) { if (__x.real() < _Tp(0)) { if (!std::__constexpr_isfinite(__i)) __i = _Tp(1); } else if (__i == 0 || !std::__constexpr_isfinite(__i)) { if (std::__constexpr_isinf(__i)) __i = _Tp(NAN); return complex<_Tp>(__x.real(), __i); } } _Tp __e = std::exp(__x.real()); return complex<_Tp>(__e * std::cos(__i), __e * std::sin(__i)); } // pow template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { return std::exp(__y * std::log(__x)); } template inline _LIBCPP_INLINE_VISIBILITY complex::type> pow(const complex<_Tp>& __x, const complex<_Up>& __y) { typedef complex::type> result_type; return _VSTD::pow(result_type(__x), result_type(__y)); } template::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY complex::type> pow(const complex<_Tp>& __x, const _Up& __y) { typedef complex::type> result_type; return _VSTD::pow(result_type(__x), result_type(__y)); } template::value, int> = 0> inline _LIBCPP_INLINE_VISIBILITY complex::type> pow(const _Tp& __x, const complex<_Up>& __y) { typedef complex::type> result_type; return _VSTD::pow(result_type(__x), result_type(__y)); } // __sqr, computes pow(x, 2) template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> __sqr(const complex<_Tp>& __x) { return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()), _Tp(2) * __x.real() * __x.imag()); } // asinh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> asinh(const complex<_Tp>& __x) { const _Tp __pi(atan2(+0., -0.)); if (std::__constexpr_isinf(__x.real())) { if (std::__constexpr_isnan(__x.imag())) return __x; if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag())); return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag())); } if (std::__constexpr_isnan(__x.real())) { if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(__x.imag(), __x.real()); if (__x.imag() == 0) return __x; return complex<_Tp>(__x.real(), __x.real()); } if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(std::copysign(__x.imag(), __x.real()), std::copysign(__pi/_Tp(2), __x.imag())); complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) + _Tp(1))); return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag())); } // acosh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> acosh(const complex<_Tp>& __x) { const _Tp __pi(atan2(+0., -0.)); if (std::__constexpr_isinf(__x.real())) { if (std::__constexpr_isnan(__x.imag())) return complex<_Tp>(std::abs(__x.real()), __x.imag()); if (std::__constexpr_isinf(__x.imag())) { if (__x.real() > 0) return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag())); else return complex<_Tp>(-__x.real(), std::copysign(__pi * _Tp(0.75), __x.imag())); } if (__x.real() < 0) return complex<_Tp>(-__x.real(), std::copysign(__pi, __x.imag())); return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag())); } if (std::__constexpr_isnan(__x.real())) { if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(std::abs(__x.imag()), __x.real()); return complex<_Tp>(__x.real(), __x.real()); } if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(std::abs(__x.imag()), std::copysign(__pi/_Tp(2), __x.imag())); complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1))); return complex<_Tp>(std::copysign(__z.real(), _Tp(0)), std::copysign(__z.imag(), __x.imag())); } // atanh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> atanh(const complex<_Tp>& __x) { const _Tp __pi(atan2(+0., -0.)); if (std::__constexpr_isinf(__x.imag())) { return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi/_Tp(2), __x.imag())); } if (std::__constexpr_isnan(__x.imag())) { if (std::__constexpr_isinf(__x.real()) || __x.real() == 0) return complex<_Tp>(std::copysign(_Tp(0), __x.real()), __x.imag()); return complex<_Tp>(__x.imag(), __x.imag()); } if (std::__constexpr_isnan(__x.real())) { return complex<_Tp>(__x.real(), __x.real()); } if (std::__constexpr_isinf(__x.real())) { return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi/_Tp(2), __x.imag())); } if (std::abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) { return complex<_Tp>(std::copysign(_Tp(INFINITY), __x.real()), std::copysign(_Tp(0), __x.imag())); } complex<_Tp> __z = std::log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2); return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag())); } // sinh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> sinh(const complex<_Tp>& __x) { if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag())) return complex<_Tp>(__x.real(), _Tp(NAN)); if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag())) return complex<_Tp>(__x.real(), _Tp(NAN)); if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real())) return __x; return complex<_Tp>(std::sinh(__x.real()) * std::cos(__x.imag()), std::cosh(__x.real()) * std::sin(__x.imag())); } // cosh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> cosh(const complex<_Tp>& __x) { if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag())) return complex<_Tp>(std::abs(__x.real()), _Tp(NAN)); if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag())) return complex<_Tp>(_Tp(NAN), __x.real()); if (__x.real() == 0 && __x.imag() == 0) return complex<_Tp>(_Tp(1), __x.imag()); if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real())) return complex<_Tp>(std::abs(__x.real()), __x.imag()); return complex<_Tp>(std::cosh(__x.real()) * std::cos(__x.imag()), std::sinh(__x.real()) * std::sin(__x.imag())); } // tanh template _LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) { if (std::__constexpr_isinf(__x.real())) { if (!std::__constexpr_isfinite(__x.imag())) return complex<_Tp>(std::copysign(_Tp(1), __x.real()), _Tp(0)); return complex<_Tp>(std::copysign(_Tp(1), __x.real()), std::copysign(_Tp(0), std::sin(_Tp(2) * __x.imag()))); } if (std::__constexpr_isnan(__x.real()) && __x.imag() == 0) return __x; _Tp __2r(_Tp(2) * __x.real()); _Tp __2i(_Tp(2) * __x.imag()); _Tp __d(std::cosh(__2r) + std::cos(__2i)); _Tp __2rsh(std::sinh(__2r)); if (std::__constexpr_isinf(__2rsh) && std::__constexpr_isinf(__d)) return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), __2i > _Tp(0) ? _Tp(0) : _Tp(-0.)); return complex<_Tp>(__2rsh/__d, std::sin(__2i)/__d); } // asin template _LIBCPP_HIDE_FROM_ABI complex<_Tp> asin(const complex<_Tp>& __x) { complex<_Tp> __z = std::asinh(complex<_Tp>(-__x.imag(), __x.real())); return complex<_Tp>(__z.imag(), -__z.real()); } // acos template _LIBCPP_HIDE_FROM_ABI complex<_Tp> acos(const complex<_Tp>& __x) { const _Tp __pi(atan2(+0., -0.)); if (std::__constexpr_isinf(__x.real())) { if (std::__constexpr_isnan(__x.imag())) return complex<_Tp>(__x.imag(), __x.real()); if (std::__constexpr_isinf(__x.imag())) { if (__x.real() < _Tp(0)) return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag()); return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag()); } if (__x.real() < _Tp(0)) return complex<_Tp>(__pi, std::signbit(__x.imag()) ? -__x.real() : __x.real()); return complex<_Tp>(_Tp(0), std::signbit(__x.imag()) ? __x.real() : -__x.real()); } if (std::__constexpr_isnan(__x.real())) { if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(__x.real(), -__x.imag()); return complex<_Tp>(__x.real(), __x.real()); } if (std::__constexpr_isinf(__x.imag())) return complex<_Tp>(__pi/_Tp(2), -__x.imag()); // Somehow isnan can be a macro, so we use __constexpr_isnan if (__x.real() == 0 && (__x.imag() == 0 || std::__constexpr_isnan(__x.imag()))) return complex<_Tp>(__pi/_Tp(2), -__x.imag()); complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1))); if (std::signbit(__x.imag())) return complex<_Tp>(std::abs(__z.imag()), std::abs(__z.real())); return complex<_Tp>(std::abs(__z.imag()), -std::abs(__z.real())); } // atan template _LIBCPP_HIDE_FROM_ABI complex<_Tp> atan(const complex<_Tp>& __x) { complex<_Tp> __z = std::atanh(complex<_Tp>(-__x.imag(), __x.real())); return complex<_Tp>(__z.imag(), -__z.real()); } // sin template _LIBCPP_HIDE_FROM_ABI complex<_Tp> sin(const complex<_Tp>& __x) { complex<_Tp> __z = std::sinh(complex<_Tp>(-__x.imag(), __x.real())); return complex<_Tp>(__z.imag(), -__z.real()); } // cos template inline _LIBCPP_INLINE_VISIBILITY complex<_Tp> cos(const complex<_Tp>& __x) { return std::cosh(complex<_Tp>(-__x.imag(), __x.real())); } // tan template _LIBCPP_HIDE_FROM_ABI complex<_Tp> tan(const complex<_Tp>& __x) { complex<_Tp> __z = std::tanh(complex<_Tp>(-__x.imag(), __x.real())); return complex<_Tp>(__z.imag(), -__z.real()); } #if !defined(_LIBCPP_HAS_NO_LOCALIZATION) template _LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>& operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) { if (__is.good()) { std::ws(__is); if (__is.peek() == _CharT('(')) { __is.get(); _Tp __r; __is >> __r; if (!__is.fail()) { std::ws(__is); _CharT __c = __is.peek(); if (__c == _CharT(',')) { __is.get(); _Tp __i; __is >> __i; if (!__is.fail()) { std::ws(__is); __c = __is.peek(); if (__c == _CharT(')')) { __is.get(); __x = complex<_Tp>(__r, __i); } else __is.setstate(__is.failbit); } else __is.setstate(__is.failbit); } else if (__c == _CharT(')')) { __is.get(); __x = complex<_Tp>(__r, _Tp(0)); } else __is.setstate(__is.failbit); } else __is.setstate(__is.failbit); } else { _Tp __r; __is >> __r; if (!__is.fail()) __x = complex<_Tp>(__r, _Tp(0)); else __is.setstate(__is.failbit); } } else __is.setstate(__is.failbit); return __is; } template _LIBCPP_HIDE_FROM_ABI 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(); } #endif // !_LIBCPP_HAS_NO_LOCALIZATION #if _LIBCPP_STD_VER >= 14 // Literal suffix for complex number literals [complex.literals] inline namespace literals { inline namespace complex_literals { _LIBCPP_HIDE_FROM_ABI constexpr complex operator""il(long double __im) { return { 0.0l, __im }; } _LIBCPP_HIDE_FROM_ABI constexpr complex operator""il(unsigned long long __im) { return { 0.0l, static_cast(__im) }; } _LIBCPP_HIDE_FROM_ABI constexpr complex operator""i(long double __im) { return { 0.0, static_cast(__im) }; } _LIBCPP_HIDE_FROM_ABI constexpr complex operator""i(unsigned long long __im) { return { 0.0, static_cast(__im) }; } #if !defined(__CUDACC__) _LIBCPP_HIDE_FROM_ABI constexpr complex operator""if(long double __im) { return { 0.0f, static_cast(__im) }; } _LIBCPP_HIDE_FROM_ABI constexpr complex operator""if(unsigned long long __im) { return { 0.0f, static_cast(__im) }; } #endif } // namespace complex_literals } // namespace literals #endif _LIBCPP_END_NAMESPACE_STD #if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 # include #endif #endif // _LIBCPP_COMPLEX