| // -*- 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>&); |
| |
| } // std |
| |
| */ |
| |
| #include <__assert> // all public C++ headers provide the assertion handler |
| #include <__config> |
| #include <cmath> |
| #include <iosfwd> |
| #include <stdexcept> |
| #include <version> |
| |
| #if !defined(_LIBCPP_HAS_NO_LOCALIZATION) |
| # include <sstream> // for std::basic_ostringstream |
| #endif |
| |
| #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
| # pragma GCC system_header |
| #endif |
| |
| _LIBCPP_BEGIN_NAMESPACE_STD |
| |
| template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex; |
| |
| template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); |
| template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); |
| |
| template<class _Tp> |
| 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<class _Xp> _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<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) |
| { |
| __re_ = __c.real(); |
| __im_ = __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) |
| { |
| __re_ += __c.real(); |
| __im_ += __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) |
| { |
| __re_ -= __c.real(); |
| __im_ -= __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) |
| { |
| *this = *this * complex(__c.real(), __c.imag()); |
| return *this; |
| } |
| template<class _Xp> _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>; |
| template<> class _LIBCPP_TEMPLATE_VIS complex<long double>; |
| |
| template<> |
| class _LIBCPP_TEMPLATE_VIS complex<float> |
| { |
| 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<double>& __c); |
| _LIBCPP_INLINE_VISIBILITY |
| explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __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<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) |
| { |
| __re_ = __c.real(); |
| __im_ = __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) |
| { |
| __re_ += __c.real(); |
| __im_ += __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) |
| { |
| __re_ -= __c.real(); |
| __im_ -= __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) |
| { |
| *this = *this * complex(__c.real(), __c.imag()); |
| return *this; |
| } |
| template<class _Xp> _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> |
| { |
| 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<float>& __c); |
| _LIBCPP_INLINE_VISIBILITY |
| explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __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<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) |
| { |
| __re_ = __c.real(); |
| __im_ = __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) |
| { |
| __re_ += __c.real(); |
| __im_ += __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) |
| { |
| __re_ -= __c.real(); |
| __im_ -= __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) |
| { |
| *this = *this * complex(__c.real(), __c.imag()); |
| return *this; |
| } |
| template<class _Xp> _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> |
| { |
| 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<float>& __c); |
| _LIBCPP_INLINE_VISIBILITY |
| _LIBCPP_CONSTEXPR complex(const complex<double>& __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<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c) |
| { |
| __re_ = __c.real(); |
| __im_ = __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) |
| { |
| __re_ += __c.real(); |
| __im_ += __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) |
| { |
| __re_ -= __c.real(); |
| __im_ -= __c.imag(); |
| return *this; |
| } |
| template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) |
| { |
| *this = *this * complex(__c.real(), __c.imag()); |
| return *this; |
| } |
| template<class _Xp> _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<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> |
| 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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| _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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| _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<int>(__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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 |
| complex<_Tp> |
| operator+(const complex<_Tp>& __x) |
| { |
| return __x; |
| } |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 |
| complex<_Tp> |
| operator-(const complex<_Tp>& __x) |
| { |
| return complex<_Tp>(-__x.real(), -__x.imag()); |
| } |
| |
| template<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| 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<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| bool |
| operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| { |
| return !(__x == __y); |
| } |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| bool |
| operator!=(const complex<_Tp>& __x, const _Tp& __y) |
| { |
| return !(__x == __y); |
| } |
| |
| template<class _Tp> |
| 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 <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> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| _Tp |
| real(const complex<_Tp>& __c) |
| { |
| return __c.real(); |
| } |
| |
| template <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| typename __libcpp_complex_overload_traits<_Tp>::_ValueType |
| real(_Tp __re) |
| { |
| return __re; |
| } |
| |
| // imag |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| _Tp |
| imag(const complex<_Tp>& __c) |
| { |
| return __c.imag(); |
| } |
| |
| template <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX14 |
| typename __libcpp_complex_overload_traits<_Tp>::_ValueType |
| imag(_Tp) |
| { |
| return 0; |
| } |
| |
| // abs |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| _Tp |
| abs(const complex<_Tp>& __c) |
| { |
| return std::hypot(__c.real(), __c.imag()); |
| } |
| |
| // arg |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| _Tp |
| arg(const complex<_Tp>& __c) |
| { |
| return std::atan2(__c.imag(), __c.real()); |
| } |
| |
| template <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if< |
| is_same<_Tp, long double>::value, |
| long double |
| >::type |
| arg(_Tp __re) |
| { |
| return std::atan2l(0.L, __re); |
| } |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if |
| < |
| is_integral<_Tp>::value || is_same<_Tp, double>::value, |
| double |
| >::type |
| arg(_Tp __re) |
| { |
| return std::atan2(0., __re); |
| } |
| |
| template <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if< |
| is_same<_Tp, float>::value, |
| float |
| >::type |
| arg(_Tp __re) |
| { |
| return std::atan2f(0.F, __re); |
| } |
| |
| // norm |
| |
| template<class _Tp> |
| 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 <class _Tp> |
| 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<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 |
| complex<_Tp> |
| conj(const complex<_Tp>& __c) |
| { |
| return complex<_Tp>(__c.real(), -__c.imag()); |
| } |
| |
| template <class _Tp> |
| 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<class _Tp> |
| 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 <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if |
| < |
| is_floating_point<_Tp>::value, |
| typename __libcpp_complex_overload_traits<_Tp>::_ComplexType |
| >::type |
| proj(_Tp __re) |
| { |
| if (std::__constexpr_isinf(__re)) |
| __re = std::abs(__re); |
| return complex<_Tp>(__re); |
| } |
| |
| template <class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if |
| < |
| is_integral<_Tp>::value, |
| typename __libcpp_complex_overload_traits<_Tp>::_ComplexType |
| >::type |
| proj(_Tp __re) |
| { |
| typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType; |
| return _ComplexType(__re); |
| } |
| |
| // polar |
| |
| template<class _Tp> |
| _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<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| complex<_Tp> |
| log(const complex<_Tp>& __x) |
| { |
| return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x)); |
| } |
| |
| // log10 |
| |
| template<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| complex<_Tp> |
| log10(const complex<_Tp>& __x) |
| { |
| return std::log(__x) / std::log(_Tp(10)); |
| } |
| |
| // sqrt |
| |
| template<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| inline _LIBCPP_INLINE_VISIBILITY |
| complex<_Tp> |
| pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| { |
| return std::exp(__y * std::log(__x)); |
| } |
| |
| template<class _Tp, class _Up> |
| inline _LIBCPP_INLINE_VISIBILITY |
| complex<typename __promote<_Tp, _Up>::type> |
| pow(const complex<_Tp>& __x, const complex<_Up>& __y) |
| { |
| typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| return _VSTD::pow(result_type(__x), result_type(__y)); |
| } |
| |
| template<class _Tp, class _Up> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if |
| < |
| is_arithmetic<_Up>::value, |
| complex<typename __promote<_Tp, _Up>::type> |
| >::type |
| pow(const complex<_Tp>& __x, const _Up& __y) |
| { |
| typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| return _VSTD::pow(result_type(__x), result_type(__y)); |
| } |
| |
| template<class _Tp, class _Up> |
| inline _LIBCPP_INLINE_VISIBILITY |
| typename enable_if |
| < |
| is_arithmetic<_Tp>::value, |
| complex<typename __promote<_Tp, _Up>::type> |
| >::type |
| pow(const _Tp& __x, const complex<_Up>& __y) |
| { |
| typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| return _VSTD::pow(result_type(__x), result_type(__y)); |
| } |
| |
| // __sqr, computes pow(x, 2) |
| |
| template<class _Tp> |
| 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<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| _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<class _Tp> |
| _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> |
| _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()); |
| 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> |
| _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> |
| _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> |
| inline _LIBCPP_INLINE_VISIBILITY |
| complex<_Tp> |
| cos(const complex<_Tp>& __x) |
| { |
| return std::cosh(complex<_Tp>(-__x.imag(), __x.real())); |
| } |
| |
| // tan |
| |
| template<class _Tp> |
| _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<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_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<long double> operator""il(long double __im) |
| { |
| return { 0.0l, __im }; |
| } |
| |
| _LIBCPP_HIDE_FROM_ABI constexpr complex<long double> operator""il(unsigned long long __im) |
| { |
| return { 0.0l, static_cast<long double>(__im) }; |
| } |
| |
| |
| _LIBCPP_HIDE_FROM_ABI constexpr complex<double> operator""i(long double __im) |
| { |
| return { 0.0, static_cast<double>(__im) }; |
| } |
| |
| _LIBCPP_HIDE_FROM_ABI constexpr complex<double> operator""i(unsigned long long __im) |
| { |
| return { 0.0, static_cast<double>(__im) }; |
| } |
| |
| |
| _LIBCPP_HIDE_FROM_ABI constexpr complex<float> operator""if(long double __im) |
| { |
| return { 0.0f, static_cast<float>(__im) }; |
| } |
| |
| _LIBCPP_HIDE_FROM_ABI 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 |
| |
| #if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20 |
| # include <type_traits> |
| #endif |
| |
| #endif // _LIBCPP_COMPLEX |
