diff options
Diffstat (limited to 'third_party/libcxx/include/c++/v1/complex')
| -rw-r--r-- | third_party/libcxx/include/c++/v1/complex | 1494 |
1 files changed, 1494 insertions, 0 deletions
diff --git a/third_party/libcxx/include/c++/v1/complex b/third_party/libcxx/include/c++/v1/complex new file mode 100644 index 0000000..49ab388 --- /dev/null +++ b/third_party/libcxx/include/c++/v1/complex @@ -0,0 +1,1494 @@ +// -*- 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 T> +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<class X> complex(const complex<X>&); // 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<T>& operator= (const T&); // constexpr in C++20 + complex<T>& operator+=(const T&); // constexpr in C++20 + complex<T>& operator-=(const T&); // constexpr in C++20 + complex<T>& operator*=(const T&); // constexpr in C++20 + complex<T>& operator/=(const T&); // constexpr in C++20 + + complex& operator=(const complex&); // constexpr in C++20 + template<class X> complex<T>& operator= (const complex<X>&); // constexpr in C++20 + template<class X> complex<T>& operator+=(const complex<X>&); // constexpr in C++20 + template<class X> complex<T>& operator-=(const complex<X>&); // constexpr in C++20 + template<class X> complex<T>& operator*=(const complex<X>&); // constexpr in C++20 + template<class X> complex<T>& operator/=(const complex<X>&); // constexpr in C++20 +}; + +template<> +class complex<float> +{ +public: + typedef float value_type; + + constexpr complex(float re = 0.0f, float im = 0.0f); + explicit constexpr complex(const complex<double>&); + explicit constexpr complex(const complex<long double>&); + + constexpr float real() const; + void real(float); // constexpr in C++20 + constexpr float imag() const; + void imag(float); // constexpr in C++20 + + complex<float>& operator= (float); // constexpr in C++20 + complex<float>& operator+=(float); // constexpr in C++20 + complex<float>& operator-=(float); // constexpr in C++20 + complex<float>& operator*=(float); // constexpr in C++20 + complex<float>& operator/=(float); // constexpr in C++20 + + complex<float>& operator=(const complex<float>&); // constexpr in C++20 + template<class X> complex<float>& operator= (const complex<X>&); // constexpr in C++20 + template<class X> complex<float>& operator+=(const complex<X>&); // constexpr in C++20 + template<class X> complex<float>& operator-=(const complex<X>&); // constexpr in C++20 + template<class X> complex<float>& operator*=(const complex<X>&); // constexpr in C++20 + template<class X> complex<float>& operator/=(const complex<X>&); // constexpr in C++20 +}; + +template<> +class complex<double> +{ +public: + typedef double value_type; + + constexpr complex(double re = 0.0, double im = 0.0); + constexpr complex(const complex<float>&); + explicit constexpr complex(const complex<long double>&); + + constexpr double real() const; + void real(double); // constexpr in C++20 + constexpr double imag() const; + void imag(double); // constexpr in C++20 + + complex<double>& operator= (double); // constexpr in C++20 + complex<double>& operator+=(double); // constexpr in C++20 + complex<double>& operator-=(double); // constexpr in C++20 + complex<double>& operator*=(double); // constexpr in C++20 + complex<double>& operator/=(double); // constexpr in C++20 + complex<double>& operator=(const complex<double>&); // constexpr in C++20 + + template<class X> complex<double>& operator= (const complex<X>&); // constexpr in C++20 + template<class X> complex<double>& operator+=(const complex<X>&); // constexpr in C++20 + template<class X> complex<double>& operator-=(const complex<X>&); // constexpr in C++20 + template<class X> complex<double>& operator*=(const complex<X>&); // constexpr in C++20 + template<class X> complex<double>& operator/=(const complex<X>&); // constexpr in C++20 +}; + +template<> +class complex<long double> +{ +public: + typedef long double value_type; + + constexpr complex(long double re = 0.0L, long double im = 0.0L); + constexpr complex(const complex<float>&); + constexpr complex(const complex<double>&); + + 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<long double>& operator=(const complex<long double>&); // constexpr in C++20 + complex<long double>& operator= (long double); // constexpr in C++20 + complex<long double>& operator+=(long double); // constexpr in C++20 + complex<long double>& operator-=(long double); // constexpr in C++20 + complex<long double>& operator*=(long double); // constexpr in C++20 + complex<long double>& operator/=(long double); // constexpr in C++20 + + template<class X> complex<long double>& operator= (const complex<X>&); // constexpr in C++20 + template<class X> complex<long double>& operator+=(const complex<X>&); // constexpr in C++20 + template<class X> complex<long double>& operator-=(const complex<X>&); // constexpr in C++20 + template<class X> complex<long double>& operator*=(const complex<X>&); // constexpr in C++20 + template<class X> complex<long double>& operator/=(const complex<X>&); // constexpr in C++20 +}; + +// 26.3.6 operators: +template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator+(const complex<T>&, const T&); // constexpr in C++20 +template<class T> complex<T> operator+(const T&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator-(const complex<T>&, const T&); // constexpr in C++20 +template<class T> complex<T> operator-(const T&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator*(const complex<T>&, const T&); // constexpr in C++20 +template<class T> complex<T> operator*(const T&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator/(const complex<T>&, const T&); // constexpr in C++20 +template<class T> complex<T> operator/(const T&, const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator+(const complex<T>&); // constexpr in C++20 +template<class T> complex<T> operator-(const complex<T>&); // constexpr in C++20 +template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14 +template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14 +template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14, removed in C++20 +template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14, removed in C++20 +template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14, removed in C++20 +template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14, removed in C++20 + +template<class T, class charT, class traits> + basic_istream<charT, traits>& + operator>>(basic_istream<charT, traits>&, complex<T>&); +template<class T, class charT, class traits> + basic_ostream<charT, traits>& + operator<<(basic_ostream<charT, traits>&, const complex<T>&); + +// 26.3.7 values: + +template<class T> T real(const complex<T>&); // constexpr in C++14 + long double real(long double); // constexpr in C++14 + double real(double); // constexpr in C++14 +template<Integral T> double real(T); // constexpr in C++14 + float real(float); // constexpr in C++14 + +template<class T> T imag(const complex<T>&); // constexpr in C++14 + long double imag(long double); // constexpr in C++14 + double imag(double); // constexpr in C++14 +template<Integral T> double imag(T); // constexpr in C++14 + float imag(float); // constexpr in C++14 + +template<class T> T abs(const complex<T>&); + +template<class T> T arg(const complex<T>&); + long double arg(long double); + double arg(double); +template<Integral T> double arg(T); + float arg(float); + +template<class T> T norm(const complex<T>&); // constexpr in C++20 + long double norm(long double); // constexpr in C++20 + double norm(double); // constexpr in C++20 +template<Integral T> double norm(T); // constexpr in C++20 + float norm(float); // constexpr in C++20 + +template<class T> complex<T> conj(const complex<T>&); // constexpr in C++20 + complex<long double> conj(long double); // constexpr in C++20 + complex<double> conj(double); // constexpr in C++20 +template<Integral T> complex<double> conj(T); // constexpr in C++20 + complex<float> conj(float); // constexpr in C++20 + +template<class T> complex<T> proj(const complex<T>&); + complex<long double> proj(long double); + complex<double> proj(double); +template<Integral T> complex<double> proj(T); + complex<float> proj(float); + +template<class T> complex<T> polar(const T&, const T& = T()); + +// 26.3.8 transcendentals: +template<class T> complex<T> acos(const complex<T>&); +template<class T> complex<T> asin(const complex<T>&); +template<class T> complex<T> atan(const complex<T>&); +template<class T> complex<T> acosh(const complex<T>&); +template<class T> complex<T> asinh(const complex<T>&); +template<class T> complex<T> atanh(const complex<T>&); +template<class T> complex<T> cos (const complex<T>&); +template<class T> complex<T> cosh (const complex<T>&); +template<class T> complex<T> exp (const complex<T>&); +template<class T> complex<T> log (const complex<T>&); +template<class T> complex<T> log10(const complex<T>&); + +template<class T> complex<T> pow(const complex<T>&, const T&); +template<class T> complex<T> pow(const complex<T>&, const complex<T>&); +template<class T> complex<T> pow(const T&, const complex<T>&); + +template<class T> complex<T> sin (const complex<T>&); +template<class T> complex<T> sinh (const complex<T>&); +template<class T> complex<T> sqrt (const complex<T>&); +template<class T> complex<T> tan (const complex<T>&); +template<class T> complex<T> tanh (const complex<T>&); + + // [complex.tuple], tuple interface + template<class T> struct tuple_size; // Since C++26 + template<size_t I, class T> struct tuple_element; // Since C++26 + template<class T> struct tuple_size<complex<T>>; // Since C++26 + template<size_t I, class T> struct tuple_element<I, complex<T>>; // Since C++26 + template<size_t I, class T> + constexpr T& get(complex<T>&) noexcept; // Since C++26 + template<size_t I, class T> + constexpr T&& get(complex<T>&&) noexcept; // Since C++26 + template<size_t I, class T> + constexpr const T& get(const complex<T>&) noexcept; // Since C++26 + template<size_t I, class T> + constexpr const T&& get(const complex<T>&&) noexcept; // Since C++26 + + // [complex.literals], complex literals + inline namespace literals { + inline namespace complex_literals { + constexpr complex<long double> operator""il(long double); // Since C++14 + constexpr complex<long double> operator""il(unsigned long long); // Since C++14 + constexpr complex<double> operator""i(long double); // Since C++14 + constexpr complex<double> operator""i(unsigned long long); // Since C++14 + constexpr complex<float> operator""if(long double); // Since C++14 + constexpr complex<float> operator""if(unsigned long long); // Since C++14 + } + } +} // std + +*/ + +#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) +# include <__cxx03/complex> +#else +# include <__config> +# include <__cstddef/size_t.h> +# include <__fwd/complex.h> +# include <__fwd/tuple.h> +# include <__tuple/tuple_element.h> +# include <__tuple/tuple_size.h> +# include <__type_traits/conditional.h> +# include <__utility/move.h> +# include <cmath> +# include <version> + +# if _LIBCPP_HAS_LOCALIZATION +# include <sstream> // for std::basic_ostringstream +# endif + +# if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) +# pragma GCC system_header +# endif + +_LIBCPP_PUSH_MACROS +# include <__undef_macros> + +_LIBCPP_BEGIN_NAMESPACE_STD + +template <class _Tp> +class complex; + +template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> +_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); + +template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0> +_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); + +template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> +_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); + +template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0> +_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); + +template <class _Tp> +class complex { +public: + typedef _Tp value_type; + +private: + value_type __re_; + value_type __im_; + +public: + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 + complex(const value_type& __re = value_type(), const value_type& __im = value_type()) + : __re_(__re), __im_(__im) {} + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 complex(const complex<_Xp>& __c) + : __re_(__c.real()), __im_(__c.imag()) {} + + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type real() const { return __re_; } + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type imag() const { return __im_; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const value_type& __re) { + __re_ = __re; + __im_ = value_type(); + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const value_type& __re) { + __re_ += __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const value_type& __re) { + __re_ -= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const value_type& __re) { + __re_ *= __re; + __im_ *= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const value_type& __re) { + __re_ /= __re; + __im_ /= __re; + return *this; + } + + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { + __re_ = __c.real(); + __im_ = __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { + __re_ += __c.real(); + __im_ += __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { + __re_ -= __c.real(); + __im_ -= __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { + *this = *this * complex(__c.real(), __c.imag()); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { + *this = *this / complex(__c.real(), __c.imag()); + return *this; + } + +# if _LIBCPP_STD_VER >= 26 + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; +# endif +}; + +template <> +class complex<double>; +template <> +class complex<long double>; + +struct __from_builtin_tag {}; + +template <class _Tp> +using __complex_t _LIBCPP_NODEBUG = + __conditional_t<is_same<_Tp, float>::value, + _Complex float, + __conditional_t<is_same<_Tp, double>::value, _Complex double, _Complex long double> >; + +template <class _Tp> +_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR __complex_t<_Tp> __make_complex(_Tp __re, _Tp __im) { +# if __has_builtin(__builtin_complex) + return __builtin_complex(__re, __im); +# else + return __complex_t<_Tp>{__re, __im}; +# endif +} + +template <> +class complex<float> { + float __re_; + float __im_; + +public: + typedef float value_type; + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) : __re_(__re), __im_(__im) {} + + template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex float __v) + : __re_(__real__ __v), __im_(__imag__ __v) {} + + _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c); + _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); + + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float real() const { return __re_; } + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float imag() const { return __im_; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex float __builtin() const { return std::__make_complex(__re_, __im_); } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex float __f) { + __re_ = __real__ __f; + __im_ = __imag__ __f; + } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(float __re) { + __re_ = __re; + __im_ = value_type(); + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) { + __re_ += __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) { + __re_ -= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) { + __re_ *= __re; + __im_ *= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) { + __re_ /= __re; + __im_ /= __re; + return *this; + } + + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { + __re_ = __c.real(); + __im_ = __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { + __re_ += __c.real(); + __im_ += __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { + __re_ -= __c.real(); + __im_ -= __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { + *this = *this * complex(__c.real(), __c.imag()); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { + *this = *this / complex(__c.real(), __c.imag()); + return *this; + } + +# if _LIBCPP_STD_VER >= 26 + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; +# endif +}; + +template <> +class complex<double> { + double __re_; + double __im_; + +public: + typedef double value_type; + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) : __re_(__re), __im_(__im) {} + + template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex double __v) + : __re_(__real__ __v), __im_(__imag__ __v) {} + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c); + _LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); + + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double real() const { return __re_; } + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double imag() const { return __im_; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex double __builtin() const { + return std::__make_complex(__re_, __im_); + } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex double __f) { + __re_ = __real__ __f; + __im_ = __imag__ __f; + } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(double __re) { + __re_ = __re; + __im_ = value_type(); + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) { + __re_ += __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) { + __re_ -= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) { + __re_ *= __re; + __im_ *= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) { + __re_ /= __re; + __im_ /= __re; + return *this; + } + + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { + __re_ = __c.real(); + __im_ = __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { + __re_ += __c.real(); + __im_ += __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { + __re_ -= __c.real(); + __im_ -= __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { + *this = *this * complex(__c.real(), __c.imag()); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { + *this = *this / complex(__c.real(), __c.imag()); + return *this; + } + +# if _LIBCPP_STD_VER >= 26 + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; +# endif +}; + +template <> +class complex<long double> { + long double __re_; + long double __im_; + +public: + typedef long double value_type; + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L) + : __re_(__re), __im_(__im) {} + + template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex long double __v) + : __re_(__real__ __v), __im_(__imag__ __v) {} + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c); + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<double>& __c); + + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double real() const { return __re_; } + [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double imag() const { return __im_; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex long double __builtin() const { + return std::__make_complex(__re_, __im_); + } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex long double __f) { + __re_ = __real__ __f; + __im_ = __imag__ __f; + } + + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(long double __re) { + __re_ = __re; + __im_ = value_type(); + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) { + __re_ += __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) { + __re_ -= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) { + __re_ *= __re; + __im_ *= __re; + return *this; + } + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) { + __re_ /= __re; + __im_ /= __re; + return *this; + } + + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) { + __re_ = __c.real(); + __im_ = __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) { + __re_ += __c.real(); + __im_ += __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) { + __re_ -= __c.real(); + __im_ -= __c.imag(); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) { + *this = *this * complex(__c.real(), __c.imag()); + return *this; + } + template <class _Xp> + _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) { + *this = *this / complex(__c.real(), __c.imag()); + return *this; + } + +# if _LIBCPP_STD_VER >= 26 + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept; + + template <size_t _Ip, class _Xp> + friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept; +# endif +}; + +inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<double>& __c) : __re_(__c.real()), __im_(__c.imag()) {} + +inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<long double>& __c) + : __re_(__c.real()), __im_(__c.imag()) {} + +inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<float>& __c) : __re_(__c.real()), __im_(__c.imag()) {} + +inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<long double>& __c) + : __re_(__c.real()), __im_(__c.imag()) {} + +inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<float>& __c) + : __re_(__c.real()), __im_(__c.imag()) {} + +inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<double>& __c) + : __re_(__c.real()), __im_(__c.imag()) {} + +// 26.3.6 operators: + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(__x); + __t += __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator+(const complex<_Tp>& __x, const _Tp& __y) { + complex<_Tp> __t(__x); + __t += __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator+(const _Tp& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(__y); + __t += __x; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(__x); + __t -= __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator-(const complex<_Tp>& __x, const _Tp& __y) { + complex<_Tp> __t(__x); + __t -= __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator-(const _Tp& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(-__y); + __t += __x; + return __t; +} + +template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> > +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator*(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) { + return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() * __rhs.__builtin()); +} + +template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> > +[[__nodiscard__]] _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(); + + return complex<_Tp>((__a * __c) - (__b * __d), (__a * __d) + (__b * __c)); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator*(const complex<_Tp>& __x, const _Tp& __y) { + complex<_Tp> __t(__x); + __t *= __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator*(const _Tp& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(__y); + __t *= __x; + return __t; +} + +template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> > +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator/(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) { + return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() / __rhs.__builtin()); +} + +template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> > +[[__nodiscard__]] _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(); + + _Tp __denom = __c * __c + __d * __d; + return complex<_Tp>((__a * __c + __b * __d) / __denom, (__b * __c - __a * __d) / __denom); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator/(const complex<_Tp>& __x, const _Tp& __y) { + return complex<_Tp>(__x.real() / __y, __x.imag() / __y); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator/(const _Tp& __x, const complex<_Tp>& __y) { + complex<_Tp> __t(__x); + __t /= __y; + return __t; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator+(const complex<_Tp>& __x) { + return __x; +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +operator-(const complex<_Tp>& __x) { + return complex<_Tp>(-__x.real(), -__x.imag()); +} + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool +operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) { + return __x.real() == __y.real() && __x.imag() == __y.imag(); +} + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _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 <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const _Tp& __x, const complex<_Tp>& __y) { + return __x == __y.real() && 0 == __y.imag(); +} + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool +operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) { + return !(__x == __y); +} + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const complex<_Tp>& __x, const _Tp& __y) { + return !(__x == __y); +} + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const _Tp& __x, const complex<_Tp>& __y) { + return !(__x == __y); +} + +# endif + +// 26.3.7 values: + +template <class _Tp, bool = is_integral<_Tp>::value, bool = is_floating_point<_Tp>::value > +struct __libcpp_complex_overload_traits {}; + +// Integral Types +template <class _Tp> +struct __libcpp_complex_overload_traits<_Tp, true, false> { + typedef double _ValueType; + typedef complex<double> _ComplexType; +}; + +// Floating point types +template <class _Tp> +struct __libcpp_complex_overload_traits<_Tp, false, true> { + typedef _Tp _ValueType; + typedef complex<_Tp> _ComplexType; +}; + +// real + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp real(const complex<_Tp>& __c) { + return __c.real(); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 +typename __libcpp_complex_overload_traits<_Tp>::_ValueType +real(_Tp __re) { + return __re; +} + +// imag + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp imag(const complex<_Tp>& __c) { + return __c.imag(); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 +typename __libcpp_complex_overload_traits<_Tp>::_ValueType +imag(_Tp) { + return 0; +} + +// abs + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _Tp abs(const complex<_Tp>& __c) { + return std::hypot(__c.real(), __c.imag()); +} + +// arg + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _Tp arg(const complex<_Tp>& __c) { + return std::atan2(__c.imag(), __c.real()); +} + +template <class _Tp, __enable_if_t<is_same<_Tp, long double>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI long double arg(_Tp __re) { + return std::atan2l(0.L, __re); +} + +template <class _Tp, __enable_if_t<is_integral<_Tp>::value || is_same<_Tp, double>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI double arg(_Tp __re) { + return std::atan2(0., __re); +} + +template <class _Tp, __enable_if_t<is_same<_Tp, float>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI float arg(_Tp __re) { + return std::atan2f(0.F, __re); +} + +// norm + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _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 <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _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 <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> +conj(const complex<_Tp>& __c) { + return complex<_Tp>(__c.real(), -__c.imag()); +} + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _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 <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> proj(const complex<_Tp>& __c) { + complex<_Tp> __r = __c; + if (std::isinf(__c.real()) || std::isinf(__c.imag())) + __r = complex<_Tp>(INFINITY, std::copysign(_Tp(0), __c.imag())); + return __r; +} + +template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType +proj(_Tp __re) { + if (std::isinf(__re)) + __re = std::abs(__re); + return complex<_Tp>(__re); +} + +template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType +proj(_Tp __re) { + typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; + return _ComplexType(__re); +} + +// polar + +template <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> polar(const _Tp& __rho, const _Tp& __theta = _Tp()) { + if (std::isnan(__rho) || std::signbit(__rho)) + return complex<_Tp>(_Tp(NAN), _Tp(NAN)); + if (std::isnan(__theta)) { + if (std::isinf(__rho)) + return complex<_Tp>(__rho, __theta); + return complex<_Tp>(__theta, __theta); + } + if (std::isinf(__theta)) { + if (std::isinf(__rho)) + return complex<_Tp>(__rho, _Tp(NAN)); + return complex<_Tp>(_Tp(NAN), _Tp(NAN)); + } + _Tp __x = __rho * std::cos(__theta); + if (std::isnan(__x)) + __x = 0; + _Tp __y = __rho * std::sin(__theta); + if (std::isnan(__y)) + __y = 0; + return complex<_Tp>(__x, __y); +} + +// log + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log(const complex<_Tp>& __x) { + return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x)); +} + +// log10 + +template <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log10(const complex<_Tp>& __x) { + return std::log(__x) / std::log(_Tp(10)); +} + +// sqrt + +template <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> sqrt(const complex<_Tp>& __x) { + if (std::isinf(__x.imag())) + return complex<_Tp>(_Tp(INFINITY), __x.imag()); + if (std::isinf(__x.real())) { + if (__x.real() > _Tp(0)) + return complex<_Tp>(__x.real(), std::isnan(__x.imag()) ? __x.imag() : std::copysign(_Tp(0), __x.imag())); + return complex<_Tp>(std::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 <class _Tp> +[[__nodiscard__]] _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::isinf(__x.real())) { + if (__x.real() < _Tp(0)) { + if (!std::isfinite(__i)) + __i = _Tp(1); + } else if (__i == 0 || !std::isfinite(__i)) { + if (std::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 <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) { + return std::exp(__y * std::log(__x)); +} + +template <class _Tp, class _Up, __enable_if_t<is_floating_point<_Tp>::value && is_floating_point<_Up>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<__promote_t<_Tp, _Up> > +pow(const complex<_Tp>& __x, const complex<_Up>& __y) { + typedef complex<__promote_t<_Tp, _Up> > result_type; + return std::pow(result_type(__x), result_type(__y)); +} + +template <class _Tp, class _Up, __enable_if_t<is_floating_point<_Tp>::value && is_arithmetic<_Up>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<__promote_t<_Tp, _Up> > +pow(const complex<_Tp>& __x, const _Up& __y) { + typedef complex<__promote_t<_Tp, _Up> > result_type; + return std::pow(result_type(__x), result_type(__y)); +} + +template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value && is_floating_point<_Up>::value, int> = 0> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<__promote_t<_Tp, _Up> > +pow(const _Tp& __x, const complex<_Up>& __y) { + typedef complex<__promote_t<_Tp, _Up> > result_type; + return std::pow(result_type(__x), result_type(__y)); +} + +// __sqr, computes pow(x, 2) + +template <class _Tp> +inline _LIBCPP_HIDE_FROM_ABI 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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> asinh(const complex<_Tp>& __x) { + const _Tp __pi(atan2(+0., -0.)); + if (std::isinf(__x.real())) { + if (std::isnan(__x.imag())) + return __x; + if (std::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::isnan(__x.real())) { + if (std::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::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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> acosh(const complex<_Tp>& __x) { + const _Tp __pi(atan2(+0., -0.)); + if (std::isinf(__x.real())) { + if (std::isnan(__x.imag())) + return complex<_Tp>(std::abs(__x.real()), __x.imag()); + if (std::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::isnan(__x.real())) { + if (std::isinf(__x.imag())) + return complex<_Tp>(std::abs(__x.imag()), __x.real()); + return complex<_Tp>(__x.real(), __x.real()); + } + if (std::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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> atanh(const complex<_Tp>& __x) { + const _Tp __pi(atan2(+0., -0.)); + if (std::isinf(__x.imag())) { + return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi / _Tp(2), __x.imag())); + } + if (std::isnan(__x.imag())) { + if (std::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::isnan(__x.real())) { + return complex<_Tp>(__x.real(), __x.real()); + } + if (std::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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> sinh(const complex<_Tp>& __x) { + if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) + return complex<_Tp>(__x.real(), _Tp(NAN)); + if (__x.real() == 0 && !std::isfinite(__x.imag())) + return complex<_Tp>(__x.real(), _Tp(NAN)); + if (__x.imag() == 0 && !std::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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> cosh(const complex<_Tp>& __x) { + if (std::isinf(__x.real()) && !std::isfinite(__x.imag())) + return complex<_Tp>(std::abs(__x.real()), _Tp(NAN)); + if (__x.real() == 0 && !std::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::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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) { + if (std::isinf(__x.real())) { + if (!std::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::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::isinf(__2rsh) && std::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 <class _Tp> +[[__nodiscard__]] _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 <class _Tp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI complex<_Tp> acos(const complex<_Tp>& __x) { + const _Tp __pi(atan2(+0., -0.)); + if (std::isinf(__x.real())) { + if (std::isnan(__x.imag())) + return complex<_Tp>(__x.imag(), __x.real()); + if (std::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::isnan(__x.real())) { + if (std::isinf(__x.imag())) + return complex<_Tp>(__x.real(), -__x.imag()); + return complex<_Tp>(__x.real(), __x.real()); + } + if (std::isinf(__x.imag())) + return complex<_Tp>(__pi / _Tp(2), -__x.imag()); + if (__x.real() == 0 && (__x.imag() == 0 || std::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 <class _Tp> +[[__nodiscard__]] _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 <class _Tp> +[[__nodiscard__]] _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 <class _Tp> +[[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> cos(const complex<_Tp>& __x) { + return std::cosh(complex<_Tp>(-__x.imag(), __x.real())); +} + +// tan + +template <class _Tp> +[[__nodiscard__]] _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 _LIBCPP_HAS_LOCALIZATION +template <class _Tp, class _CharT, class _Traits> +_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 <class _Tp, class _CharT, class _Traits> +_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_LOCALIZATION + +# if _LIBCPP_STD_VER >= 26 + +// [complex.tuple], tuple interface + +template <class _Tp> +struct tuple_size<complex<_Tp>> : integral_constant<size_t, 2> {}; + +template <size_t _Ip, class _Tp> +struct tuple_element<_Ip, complex<_Tp>> { + static_assert(_Ip < 2, "Index value is out of range."); + using type _LIBCPP_NODEBUG = _Tp; +}; + +template <size_t _Ip, class _Xp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>& __z) noexcept { + static_assert(_Ip < 2, "Index value is out of range."); + if constexpr (_Ip == 0) { + return __z.__re_; + } else { + return __z.__im_; + } +} + +template <size_t _Ip, class _Xp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&& __z) noexcept { + static_assert(_Ip < 2, "Index value is out of range."); + if constexpr (_Ip == 0) { + return std::move(__z.__re_); + } else { + return std::move(__z.__im_); + } +} + +template <size_t _Ip, class _Xp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>& __z) noexcept { + static_assert(_Ip < 2, "Index value is out of range."); + if constexpr (_Ip == 0) { + return __z.__re_; + } else { + return __z.__im_; + } +} + +template <size_t _Ip, class _Xp> +[[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&& __z) noexcept { + static_assert(_Ip < 2, "Index value is out of range."); + if constexpr (_Ip == 0) { + return std::move(__z.__re_); + } else { + return std::move(__z.__im_); + } +} + +# endif // _LIBCPP_STD_VER >= 26 + +# if _LIBCPP_STD_VER >= 14 +// Literal suffix for complex number literals [complex.literals] +inline namespace literals { +inline namespace complex_literals { +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(long double __im) { return {0.0l, __im}; } + +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(unsigned long long __im) { + return {0.0l, static_cast<long double>(__im)}; +} + +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(long double __im) { + return {0.0, static_cast<double>(__im)}; +} + +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(unsigned long long __im) { + return {0.0, static_cast<double>(__im)}; +} + +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(long double __im) { + return {0.0f, static_cast<float>(__im)}; +} + +_LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(unsigned long long __im) { + return {0.0f, static_cast<float>(__im)}; +} +} // namespace complex_literals +} // namespace literals +# endif + +_LIBCPP_END_NAMESPACE_STD + +_LIBCPP_POP_MACROS + +# if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 +# include <iosfwd> +# include <stdexcept> +# include <type_traits> +# endif +#endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS) + +#endif // _LIBCPP_COMPLEX |