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// -*- C++ -*- |
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//===--------------------------- complex ----------------------------------===// |
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// |
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// The LLVM Compiler Infrastructure |
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// |
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// This file is dual licensed under the MIT and the University of Illinois Open |
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// Source Licenses. See LICENSE.TXT for details. |
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// |
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//===----------------------------------------------------------------------===// |
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|
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#ifndef _LIBCPP_COMPLEX |
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#define _LIBCPP_COMPLEX |
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|
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/* |
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complex synopsis |
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|
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namespace std |
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{
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template<class T> |
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class complex |
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{
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public: |
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typedef T value_type; |
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complex(const T& re = T(), const T& im = T()); // constexpr in C++14 |
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complex(const complex&); // constexpr in C++14 |
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template<class X> complex(const complex<X>&); // constexpr in C++14 |
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T real() const; // constexpr in C++14 |
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T imag() const; // constexpr in C++14 |
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|
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void real(T); |
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void imag(T); |
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complex<T>& operator= (const T&); |
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complex<T>& operator+=(const T&); |
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complex<T>& operator-=(const T&); |
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complex<T>& operator*=(const T&); |
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complex<T>& operator/=(const T&); |
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complex& operator=(const complex&); |
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template<class X> complex<T>& operator= (const complex<X>&); |
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template<class X> complex<T>& operator+=(const complex<X>&); |
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template<class X> complex<T>& operator-=(const complex<X>&); |
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template<class X> complex<T>& operator*=(const complex<X>&); |
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template<class X> complex<T>& operator/=(const complex<X>&); |
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}; |
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template<> |
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class complex<float> |
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{
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public: |
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typedef float value_type; |
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constexpr complex(float re = 0.0f, float im = 0.0f); |
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explicit constexpr complex(const complex<double>&); |
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explicit constexpr complex(const complex<long double>&); |
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constexpr float real() const; |
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void real(float); |
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constexpr float imag() const; |
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void imag(float); |
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complex<float>& operator= (float); |
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complex<float>& operator+=(float); |
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complex<float>& operator-=(float); |
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complex<float>& operator*=(float); |
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complex<float>& operator/=(float); |
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complex<float>& operator=(const complex<float>&); |
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template<class X> complex<float>& operator= (const complex<X>&); |
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template<class X> complex<float>& operator+=(const complex<X>&); |
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template<class X> complex<float>& operator-=(const complex<X>&); |
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template<class X> complex<float>& operator*=(const complex<X>&); |
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template<class X> complex<float>& operator/=(const complex<X>&); |
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}; |
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template<> |
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class complex<double> |
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{
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public: |
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typedef double value_type; |
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constexpr complex(double re = 0.0, double im = 0.0); |
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constexpr complex(const complex<float>&); |
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explicit constexpr complex(const complex<long double>&); |
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constexpr double real() const; |
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void real(double); |
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constexpr double imag() const; |
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void imag(double); |
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complex<double>& operator= (double); |
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complex<double>& operator+=(double); |
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complex<double>& operator-=(double); |
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complex<double>& operator*=(double); |
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complex<double>& operator/=(double); |
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complex<double>& operator=(const complex<double>&); |
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template<class X> complex<double>& operator= (const complex<X>&); |
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template<class X> complex<double>& operator+=(const complex<X>&); |
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template<class X> complex<double>& operator-=(const complex<X>&); |
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template<class X> complex<double>& operator*=(const complex<X>&); |
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template<class X> complex<double>& operator/=(const complex<X>&); |
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}; |
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template<> |
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class complex<long double> |
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{
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public: |
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typedef long double value_type; |
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constexpr complex(long double re = 0.0L, long double im = 0.0L); |
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constexpr complex(const complex<float>&); |
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constexpr complex(const complex<double>&); |
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constexpr long double real() const; |
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void real(long double); |
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constexpr long double imag() const; |
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void imag(long double); |
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complex<long double>& operator=(const complex<long double>&); |
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complex<long double>& operator= (long double); |
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complex<long double>& operator+=(long double); |
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complex<long double>& operator-=(long double); |
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complex<long double>& operator*=(long double); |
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complex<long double>& operator/=(long double); |
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template<class X> complex<long double>& operator= (const complex<X>&); |
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template<class X> complex<long double>& operator+=(const complex<X>&); |
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template<class X> complex<long double>& operator-=(const complex<X>&); |
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template<class X> complex<long double>& operator*=(const complex<X>&); |
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template<class X> complex<long double>& operator/=(const complex<X>&); |
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}; |
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// 26.3.6 operators: |
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template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); |
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template<class T> complex<T> operator+(const complex<T>&, const T&); |
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template<class T> complex<T> operator+(const T&, const complex<T>&); |
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template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); |
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template<class T> complex<T> operator-(const complex<T>&, const T&); |
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template<class T> complex<T> operator-(const T&, const complex<T>&); |
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template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); |
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template<class T> complex<T> operator*(const complex<T>&, const T&); |
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template<class T> complex<T> operator*(const T&, const complex<T>&); |
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template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); |
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template<class T> complex<T> operator/(const complex<T>&, const T&); |
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template<class T> complex<T> operator/(const T&, const complex<T>&); |
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template<class T> complex<T> operator+(const complex<T>&); |
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template<class T> complex<T> operator-(const complex<T>&); |
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template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14 |
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template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14 |
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template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14 |
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template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14 |
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template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14 |
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template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14 |
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template<class T, class charT, class traits> |
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basic_istream<charT, traits>& |
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operator>>(basic_istream<charT, traits>&, complex<T>&); |
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template<class T, class charT, class traits> |
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basic_ostream<charT, traits>& |
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operator<<(basic_ostream<charT, traits>&, const complex<T>&); |
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// 26.3.7 values: |
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template<class T> T real(const complex<T>&); // constexpr in C++14 |
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long double real(long double); // constexpr in C++14 |
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double real(double); // constexpr in C++14 |
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template<Integral T> double real(T); // constexpr in C++14 |
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float real(float); // constexpr in C++14 |
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template<class T> T imag(const complex<T>&); // constexpr in C++14 |
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long double imag(long double); // constexpr in C++14 |
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double imag(double); // constexpr in C++14 |
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template<Integral T> double imag(T); // constexpr in C++14 |
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float imag(float); // constexpr in C++14 |
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template<class T> T abs(const complex<T>&); |
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template<class T> T arg(const complex<T>&); |
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long double arg(long double); |
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double arg(double); |
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template<Integral T> double arg(T); |
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float arg(float); |
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template<class T> T norm(const complex<T>&); |
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long double norm(long double); |
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double norm(double); |
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template<Integral T> double norm(T); |
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float norm(float); |
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template<class T> complex<T> conj(const complex<T>&); |
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complex<long double> conj(long double); |
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complex<double> conj(double); |
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template<Integral T> complex<double> conj(T); |
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complex<float> conj(float); |
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template<class T> complex<T> proj(const complex<T>&); |
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complex<long double> proj(long double); |
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complex<double> proj(double); |
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template<Integral T> complex<double> proj(T); |
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complex<float> proj(float); |
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template<class T> complex<T> polar(const T&, const T& = 0); |
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// 26.3.8 transcendentals: |
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template<class T> complex<T> acos(const complex<T>&); |
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template<class T> complex<T> asin(const complex<T>&); |
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template<class T> complex<T> atan(const complex<T>&); |
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template<class T> complex<T> acosh(const complex<T>&); |
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template<class T> complex<T> asinh(const complex<T>&); |
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template<class T> complex<T> atanh(const complex<T>&); |
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template<class T> complex<T> cos (const complex<T>&); |
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template<class T> complex<T> cosh (const complex<T>&); |
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template<class T> complex<T> exp (const complex<T>&); |
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template<class T> complex<T> log (const complex<T>&); |
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template<class T> complex<T> log10(const complex<T>&); |
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template<class T> complex<T> pow(const complex<T>&, const T&); |
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template<class T> complex<T> pow(const complex<T>&, const complex<T>&); |
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template<class T> complex<T> pow(const T&, const complex<T>&); |
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template<class T> complex<T> sin (const complex<T>&); |
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template<class T> complex<T> sinh (const complex<T>&); |
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template<class T> complex<T> sqrt (const complex<T>&); |
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template<class T> complex<T> tan (const complex<T>&); |
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template<class T> complex<T> tanh (const complex<T>&); |
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template<class T, class charT, class traits> |
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basic_istream<charT, traits>& |
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operator>>(basic_istream<charT, traits>& is, complex<T>& x); |
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template<class T, class charT, class traits> |
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basic_ostream<charT, traits>& |
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operator<<(basic_ostream<charT, traits>& o, const complex<T>& x); |
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} // std |
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*/ |
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#include <__config> |
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#include <type_traits> |
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#include <stdexcept> |
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#include <cmath> |
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#include <sstream> |
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#if defined(_LIBCPP_NO_EXCEPTIONS) |
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#include <cassert> |
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#endif |
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
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#pragma GCC system_header |
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#endif |
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_LIBCPP_BEGIN_NAMESPACE_STD |
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template<class _Tp> class _LIBCPP_TYPE_VIS_ONLY complex; |
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template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); |
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template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); |
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template<class _Tp> |
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class _LIBCPP_TYPE_VIS_ONLY complex |
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{
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public: |
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typedef _Tp value_type; |
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private: |
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value_type __re_; |
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value_type __im_; |
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public: |
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
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complex(const value_type& __re = value_type(), const value_type& __im = value_type()) |
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: __re_(__re), __im_(__im) {}
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
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complex(const complex<_Xp>& __c) |
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: __re_(__c.real()), __im_(__c.imag()) {}
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
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_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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_LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re) |
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{__re_ = __re; __im_ = value_type(); return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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{
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__re_ = __c.real(); |
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__im_ = __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
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{
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__re_ += __c.real(); |
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__im_ += __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
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{
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__re_ -= __c.real(); |
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__im_ -= __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
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{
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*this = *this * complex(__c.real(), __c.imag()); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
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{
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*this = *this / complex(__c.real(), __c.imag()); |
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return *this; |
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} |
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}; |
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template<> class _LIBCPP_TYPE_VIS_ONLY complex<double>; |
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template<> class _LIBCPP_TYPE_VIS_ONLY complex<long double>; |
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template<> |
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class _LIBCPP_TYPE_VIS_ONLY complex<float> |
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{
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float __re_; |
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float __im_; |
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public: |
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typedef float value_type; |
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) |
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: __re_(__re), __im_(__im) {}
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explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c); |
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explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); |
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
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_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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_LIBCPP_INLINE_VISIBILITY complex& operator= (float __re) |
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{__re_ = __re; __im_ = value_type(); return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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{
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__re_ = __c.real(); |
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__im_ = __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
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{
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__re_ += __c.real(); |
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__im_ += __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
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{
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__re_ -= __c.real(); |
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__im_ -= __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
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{
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*this = *this * complex(__c.real(), __c.imag()); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
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{
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*this = *this / complex(__c.real(), __c.imag()); |
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return *this; |
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} |
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}; |
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template<> |
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class _LIBCPP_TYPE_VIS_ONLY complex<double> |
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{
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double __re_; |
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double __im_; |
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public: |
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typedef double value_type; |
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) |
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: __re_(__re), __im_(__im) {}
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_LIBCPP_CONSTEXPR complex(const complex<float>& __c); |
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explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); |
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
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_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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_LIBCPP_INLINE_VISIBILITY complex& operator= (double __re) |
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{__re_ = __re; __im_ = value_type(); return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
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_LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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{
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__re_ = __c.real(); |
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__im_ = __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
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{
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__re_ += __c.real(); |
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__im_ += __c.imag(); |
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return *this; |
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} |
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template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
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{
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__re_ -= __c.real(); |
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__im_ -= __c.imag(); |
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return *this; |
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} |
| 425 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
| 426 |
{
|
| 427 |
*this = *this * complex(__c.real(), __c.imag()); |
| 428 |
return *this; |
| 429 |
} |
| 430 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
| 431 |
{
|
| 432 |
*this = *this / complex(__c.real(), __c.imag()); |
| 433 |
return *this; |
| 434 |
} |
| 435 |
}; |
| 436 |
|
| 437 |
template<> |
| 438 |
class _LIBCPP_TYPE_VIS_ONLY complex<long double> |
| 439 |
{
|
| 440 |
long double __re_; |
| 441 |
long double __im_; |
| 442 |
public: |
| 443 |
typedef long double value_type; |
| 444 |
|
| 445 |
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L) |
| 446 |
: __re_(__re), __im_(__im) {}
|
| 447 |
_LIBCPP_CONSTEXPR complex(const complex<float>& __c); |
| 448 |
_LIBCPP_CONSTEXPR complex(const complex<double>& __c); |
| 449 |
|
| 450 |
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
|
| 451 |
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
|
| 452 |
|
| 453 |
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
|
| 454 |
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
|
| 455 |
|
| 456 |
_LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re) |
| 457 |
{__re_ = __re; __im_ = value_type(); return *this;}
|
| 458 |
_LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
|
| 459 |
_LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
|
| 460 |
_LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
|
| 461 |
_LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
|
| 462 |
|
| 463 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
| 464 |
{
|
| 465 |
__re_ = __c.real(); |
| 466 |
__im_ = __c.imag(); |
| 467 |
return *this; |
| 468 |
} |
| 469 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
| 470 |
{
|
| 471 |
__re_ += __c.real(); |
| 472 |
__im_ += __c.imag(); |
| 473 |
return *this; |
| 474 |
} |
| 475 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
| 476 |
{
|
| 477 |
__re_ -= __c.real(); |
| 478 |
__im_ -= __c.imag(); |
| 479 |
return *this; |
| 480 |
} |
| 481 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
| 482 |
{
|
| 483 |
*this = *this * complex(__c.real(), __c.imag()); |
| 484 |
return *this; |
| 485 |
} |
| 486 |
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
| 487 |
{
|
| 488 |
*this = *this / complex(__c.real(), __c.imag()); |
| 489 |
return *this; |
| 490 |
} |
| 491 |
}; |
| 492 |
|
| 493 |
inline _LIBCPP_INLINE_VISIBILITY |
| 494 |
_LIBCPP_CONSTEXPR |
| 495 |
complex<float>::complex(const complex<double>& __c) |
| 496 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 497 |
|
| 498 |
inline _LIBCPP_INLINE_VISIBILITY |
| 499 |
_LIBCPP_CONSTEXPR |
| 500 |
complex<float>::complex(const complex<long double>& __c) |
| 501 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 502 |
|
| 503 |
inline _LIBCPP_INLINE_VISIBILITY |
| 504 |
_LIBCPP_CONSTEXPR |
| 505 |
complex<double>::complex(const complex<float>& __c) |
| 506 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 507 |
|
| 508 |
inline _LIBCPP_INLINE_VISIBILITY |
| 509 |
_LIBCPP_CONSTEXPR |
| 510 |
complex<double>::complex(const complex<long double>& __c) |
| 511 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 512 |
|
| 513 |
inline _LIBCPP_INLINE_VISIBILITY |
| 514 |
_LIBCPP_CONSTEXPR |
| 515 |
complex<long double>::complex(const complex<float>& __c) |
| 516 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 517 |
|
| 518 |
inline _LIBCPP_INLINE_VISIBILITY |
| 519 |
_LIBCPP_CONSTEXPR |
| 520 |
complex<long double>::complex(const complex<double>& __c) |
| 521 |
: __re_(__c.real()), __im_(__c.imag()) {}
|
| 522 |
|
| 523 |
// 26.3.6 operators: |
| 524 |
|
| 525 |
template<class _Tp> |
| 526 |
inline _LIBCPP_INLINE_VISIBILITY |
| 527 |
complex<_Tp> |
| 528 |
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| 529 |
{
|
| 530 |
complex<_Tp> __t(__x); |
| 531 |
__t += __y; |
| 532 |
return __t; |
| 533 |
} |
| 534 |
|
| 535 |
template<class _Tp> |
| 536 |
inline _LIBCPP_INLINE_VISIBILITY |
| 537 |
complex<_Tp> |
| 538 |
operator+(const complex<_Tp>& __x, const _Tp& __y) |
| 539 |
{
|
| 540 |
complex<_Tp> __t(__x); |
| 541 |
__t += __y; |
| 542 |
return __t; |
| 543 |
} |
| 544 |
|
| 545 |
template<class _Tp> |
| 546 |
inline _LIBCPP_INLINE_VISIBILITY |
| 547 |
complex<_Tp> |
| 548 |
operator+(const _Tp& __x, const complex<_Tp>& __y) |
| 549 |
{
|
| 550 |
complex<_Tp> __t(__y); |
| 551 |
__t += __x; |
| 552 |
return __t; |
| 553 |
} |
| 554 |
|
| 555 |
template<class _Tp> |
| 556 |
inline _LIBCPP_INLINE_VISIBILITY |
| 557 |
complex<_Tp> |
| 558 |
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| 559 |
{
|
| 560 |
complex<_Tp> __t(__x); |
| 561 |
__t -= __y; |
| 562 |
return __t; |
| 563 |
} |
| 564 |
|
| 565 |
template<class _Tp> |
| 566 |
inline _LIBCPP_INLINE_VISIBILITY |
| 567 |
complex<_Tp> |
| 568 |
operator-(const complex<_Tp>& __x, const _Tp& __y) |
| 569 |
{
|
| 570 |
complex<_Tp> __t(__x); |
| 571 |
__t -= __y; |
| 572 |
return __t; |
| 573 |
} |
| 574 |
|
| 575 |
template<class _Tp> |
| 576 |
inline _LIBCPP_INLINE_VISIBILITY |
| 577 |
complex<_Tp> |
| 578 |
operator-(const _Tp& __x, const complex<_Tp>& __y) |
| 579 |
{
|
| 580 |
complex<_Tp> __t(-__y); |
| 581 |
__t += __x; |
| 582 |
return __t; |
| 583 |
} |
| 584 |
|
| 585 |
template<class _Tp> |
| 586 |
complex<_Tp> |
| 587 |
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) |
| 588 |
{
|
| 589 |
_Tp __a = __z.real(); |
| 590 |
_Tp __b = __z.imag(); |
| 591 |
_Tp __c = __w.real(); |
| 592 |
_Tp __d = __w.imag(); |
| 593 |
_Tp __ac = __a * __c; |
| 594 |
_Tp __bd = __b * __d; |
| 595 |
_Tp __ad = __a * __d; |
| 596 |
_Tp __bc = __b * __c; |
| 597 |
_Tp __x = __ac - __bd; |
| 598 |
_Tp __y = __ad + __bc; |
| 599 |
if (isnan(__x) && isnan(__y)) |
| 600 |
{
|
| 601 |
bool __recalc = false; |
| 602 |
if (isinf(__a) || isinf(__b)) |
| 603 |
{
|
| 604 |
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a); |
| 605 |
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b); |
| 606 |
if (isnan(__c)) |
| 607 |
__c = copysign(_Tp(0), __c); |
| 608 |
if (isnan(__d)) |
| 609 |
__d = copysign(_Tp(0), __d); |
| 610 |
__recalc = true; |
| 611 |
} |
| 612 |
if (isinf(__c) || isinf(__d)) |
| 613 |
{
|
| 614 |
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c); |
| 615 |
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d); |
| 616 |
if (isnan(__a)) |
| 617 |
__a = copysign(_Tp(0), __a); |
| 618 |
if (isnan(__b)) |
| 619 |
__b = copysign(_Tp(0), __b); |
| 620 |
__recalc = true; |
| 621 |
} |
| 622 |
if (!__recalc && (isinf(__ac) || isinf(__bd) || |
| 623 |
isinf(__ad) || isinf(__bc))) |
| 624 |
{
|
| 625 |
if (isnan(__a)) |
| 626 |
__a = copysign(_Tp(0), __a); |
| 627 |
if (isnan(__b)) |
| 628 |
__b = copysign(_Tp(0), __b); |
| 629 |
if (isnan(__c)) |
| 630 |
__c = copysign(_Tp(0), __c); |
| 631 |
if (isnan(__d)) |
| 632 |
__d = copysign(_Tp(0), __d); |
| 633 |
__recalc = true; |
| 634 |
} |
| 635 |
if (__recalc) |
| 636 |
{
|
| 637 |
__x = _Tp(INFINITY) * (__a * __c - __b * __d); |
| 638 |
__y = _Tp(INFINITY) * (__a * __d + __b * __c); |
| 639 |
} |
| 640 |
} |
| 641 |
return complex<_Tp>(__x, __y); |
| 642 |
} |
| 643 |
|
| 644 |
template<class _Tp> |
| 645 |
inline _LIBCPP_INLINE_VISIBILITY |
| 646 |
complex<_Tp> |
| 647 |
operator*(const complex<_Tp>& __x, const _Tp& __y) |
| 648 |
{
|
| 649 |
complex<_Tp> __t(__x); |
| 650 |
__t *= __y; |
| 651 |
return __t; |
| 652 |
} |
| 653 |
|
| 654 |
template<class _Tp> |
| 655 |
inline _LIBCPP_INLINE_VISIBILITY |
| 656 |
complex<_Tp> |
| 657 |
operator*(const _Tp& __x, const complex<_Tp>& __y) |
| 658 |
{
|
| 659 |
complex<_Tp> __t(__y); |
| 660 |
__t *= __x; |
| 661 |
return __t; |
| 662 |
} |
| 663 |
|
| 664 |
template<class _Tp> |
| 665 |
complex<_Tp> |
| 666 |
operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) |
| 667 |
{
|
| 668 |
int __ilogbw = 0; |
| 669 |
_Tp __a = __z.real(); |
| 670 |
_Tp __b = __z.imag(); |
| 671 |
_Tp __c = __w.real(); |
| 672 |
_Tp __d = __w.imag(); |
| 673 |
_Tp __logbw = logb(fmax(fabs(__c), fabs(__d))); |
| 674 |
if (isfinite(__logbw)) |
| 675 |
{
|
| 676 |
__ilogbw = static_cast<int>(__logbw); |
| 677 |
__c = scalbn(__c, -__ilogbw); |
| 678 |
__d = scalbn(__d, -__ilogbw); |
| 679 |
} |
| 680 |
_Tp __denom = __c * __c + __d * __d; |
| 681 |
_Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw); |
| 682 |
_Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw); |
| 683 |
if (isnan(__x) && isnan(__y)) |
| 684 |
{
|
| 685 |
if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b))) |
| 686 |
{
|
| 687 |
__x = copysign(_Tp(INFINITY), __c) * __a; |
| 688 |
__y = copysign(_Tp(INFINITY), __c) * __b; |
| 689 |
} |
| 690 |
else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d)) |
| 691 |
{
|
| 692 |
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a); |
| 693 |
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b); |
| 694 |
__x = _Tp(INFINITY) * (__a * __c + __b * __d); |
| 695 |
__y = _Tp(INFINITY) * (__b * __c - __a * __d); |
| 696 |
} |
| 697 |
else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b)) |
| 698 |
{
|
| 699 |
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c); |
| 700 |
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d); |
| 701 |
__x = _Tp(0) * (__a * __c + __b * __d); |
| 702 |
__y = _Tp(0) * (__b * __c - __a * __d); |
| 703 |
} |
| 704 |
} |
| 705 |
return complex<_Tp>(__x, __y); |
| 706 |
} |
| 707 |
|
| 708 |
template<class _Tp> |
| 709 |
inline _LIBCPP_INLINE_VISIBILITY |
| 710 |
complex<_Tp> |
| 711 |
operator/(const complex<_Tp>& __x, const _Tp& __y) |
| 712 |
{
|
| 713 |
return complex<_Tp>(__x.real() / __y, __x.imag() / __y); |
| 714 |
} |
| 715 |
|
| 716 |
template<class _Tp> |
| 717 |
inline _LIBCPP_INLINE_VISIBILITY |
| 718 |
complex<_Tp> |
| 719 |
operator/(const _Tp& __x, const complex<_Tp>& __y) |
| 720 |
{
|
| 721 |
complex<_Tp> __t(__x); |
| 722 |
__t /= __y; |
| 723 |
return __t; |
| 724 |
} |
| 725 |
|
| 726 |
template<class _Tp> |
| 727 |
inline _LIBCPP_INLINE_VISIBILITY |
| 728 |
complex<_Tp> |
| 729 |
operator+(const complex<_Tp>& __x) |
| 730 |
{
|
| 731 |
return __x; |
| 732 |
} |
| 733 |
|
| 734 |
template<class _Tp> |
| 735 |
inline _LIBCPP_INLINE_VISIBILITY |
| 736 |
complex<_Tp> |
| 737 |
operator-(const complex<_Tp>& __x) |
| 738 |
{
|
| 739 |
return complex<_Tp>(-__x.real(), -__x.imag()); |
| 740 |
} |
| 741 |
|
| 742 |
template<class _Tp> |
| 743 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 744 |
bool |
| 745 |
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| 746 |
{
|
| 747 |
return __x.real() == __y.real() && __x.imag() == __y.imag(); |
| 748 |
} |
| 749 |
|
| 750 |
template<class _Tp> |
| 751 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 752 |
bool |
| 753 |
operator==(const complex<_Tp>& __x, const _Tp& __y) |
| 754 |
{
|
| 755 |
return __x.real() == __y && __x.imag() == 0; |
| 756 |
} |
| 757 |
|
| 758 |
template<class _Tp> |
| 759 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 760 |
bool |
| 761 |
operator==(const _Tp& __x, const complex<_Tp>& __y) |
| 762 |
{
|
| 763 |
return __x == __y.real() && 0 == __y.imag(); |
| 764 |
} |
| 765 |
|
| 766 |
template<class _Tp> |
| 767 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 768 |
bool |
| 769 |
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| 770 |
{
|
| 771 |
return !(__x == __y); |
| 772 |
} |
| 773 |
|
| 774 |
template<class _Tp> |
| 775 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 776 |
bool |
| 777 |
operator!=(const complex<_Tp>& __x, const _Tp& __y) |
| 778 |
{
|
| 779 |
return !(__x == __y); |
| 780 |
} |
| 781 |
|
| 782 |
template<class _Tp> |
| 783 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 784 |
bool |
| 785 |
operator!=(const _Tp& __x, const complex<_Tp>& __y) |
| 786 |
{
|
| 787 |
return !(__x == __y); |
| 788 |
} |
| 789 |
|
| 790 |
// 26.3.7 values: |
| 791 |
|
| 792 |
// real |
| 793 |
|
| 794 |
template<class _Tp> |
| 795 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 796 |
_Tp |
| 797 |
real(const complex<_Tp>& __c) |
| 798 |
{
|
| 799 |
return __c.real(); |
| 800 |
} |
| 801 |
|
| 802 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 803 |
long double |
| 804 |
real(long double __re) |
| 805 |
{
|
| 806 |
return __re; |
| 807 |
} |
| 808 |
|
| 809 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 810 |
double |
| 811 |
real(double __re) |
| 812 |
{
|
| 813 |
return __re; |
| 814 |
} |
| 815 |
|
| 816 |
template<class _Tp> |
| 817 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 818 |
typename enable_if |
| 819 |
< |
| 820 |
is_integral<_Tp>::value, |
| 821 |
double |
| 822 |
>::type |
| 823 |
real(_Tp __re) |
| 824 |
{
|
| 825 |
return __re; |
| 826 |
} |
| 827 |
|
| 828 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 829 |
float |
| 830 |
real(float __re) |
| 831 |
{
|
| 832 |
return __re; |
| 833 |
} |
| 834 |
|
| 835 |
// imag |
| 836 |
|
| 837 |
template<class _Tp> |
| 838 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 839 |
_Tp |
| 840 |
imag(const complex<_Tp>& __c) |
| 841 |
{
|
| 842 |
return __c.imag(); |
| 843 |
} |
| 844 |
|
| 845 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 846 |
long double |
| 847 |
imag(long double __re) |
| 848 |
{
|
| 849 |
return 0; |
| 850 |
} |
| 851 |
|
| 852 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 853 |
double |
| 854 |
imag(double __re) |
| 855 |
{
|
| 856 |
return 0; |
| 857 |
} |
| 858 |
|
| 859 |
template<class _Tp> |
| 860 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 861 |
typename enable_if |
| 862 |
< |
| 863 |
is_integral<_Tp>::value, |
| 864 |
double |
| 865 |
>::type |
| 866 |
imag(_Tp __re) |
| 867 |
{
|
| 868 |
return 0; |
| 869 |
} |
| 870 |
|
| 871 |
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
| 872 |
float |
| 873 |
imag(float __re) |
| 874 |
{
|
| 875 |
return 0; |
| 876 |
} |
| 877 |
|
| 878 |
// abs |
| 879 |
|
| 880 |
template<class _Tp> |
| 881 |
inline _LIBCPP_INLINE_VISIBILITY |
| 882 |
_Tp |
| 883 |
abs(const complex<_Tp>& __c) |
| 884 |
{
|
| 885 |
return hypot(__c.real(), __c.imag()); |
| 886 |
} |
| 887 |
|
| 888 |
// arg |
| 889 |
|
| 890 |
template<class _Tp> |
| 891 |
inline _LIBCPP_INLINE_VISIBILITY |
| 892 |
_Tp |
| 893 |
arg(const complex<_Tp>& __c) |
| 894 |
{
|
| 895 |
return atan2(__c.imag(), __c.real()); |
| 896 |
} |
| 897 |
|
| 898 |
inline _LIBCPP_INLINE_VISIBILITY |
| 899 |
long double |
| 900 |
arg(long double __re) |
| 901 |
{
|
| 902 |
return atan2l(0.L, __re); |
| 903 |
} |
| 904 |
|
| 905 |
inline _LIBCPP_INLINE_VISIBILITY |
| 906 |
double |
| 907 |
arg(double __re) |
| 908 |
{
|
| 909 |
return atan2(0., __re); |
| 910 |
} |
| 911 |
|
| 912 |
template<class _Tp> |
| 913 |
inline _LIBCPP_INLINE_VISIBILITY |
| 914 |
typename enable_if |
| 915 |
< |
| 916 |
is_integral<_Tp>::value, |
| 917 |
double |
| 918 |
>::type |
| 919 |
arg(_Tp __re) |
| 920 |
{
|
| 921 |
return atan2(0., __re); |
| 922 |
} |
| 923 |
|
| 924 |
inline _LIBCPP_INLINE_VISIBILITY |
| 925 |
float |
| 926 |
arg(float __re) |
| 927 |
{
|
| 928 |
return atan2f(0.F, __re); |
| 929 |
} |
| 930 |
|
| 931 |
// norm |
| 932 |
|
| 933 |
template<class _Tp> |
| 934 |
inline _LIBCPP_INLINE_VISIBILITY |
| 935 |
_Tp |
| 936 |
norm(const complex<_Tp>& __c) |
| 937 |
{
|
| 938 |
if (isinf(__c.real())) |
| 939 |
return abs(__c.real()); |
| 940 |
if (isinf(__c.imag())) |
| 941 |
return abs(__c.imag()); |
| 942 |
return __c.real() * __c.real() + __c.imag() * __c.imag(); |
| 943 |
} |
| 944 |
|
| 945 |
inline _LIBCPP_INLINE_VISIBILITY |
| 946 |
long double |
| 947 |
norm(long double __re) |
| 948 |
{
|
| 949 |
return __re * __re; |
| 950 |
} |
| 951 |
|
| 952 |
inline _LIBCPP_INLINE_VISIBILITY |
| 953 |
double |
| 954 |
norm(double __re) |
| 955 |
{
|
| 956 |
return __re * __re; |
| 957 |
} |
| 958 |
|
| 959 |
template<class _Tp> |
| 960 |
inline _LIBCPP_INLINE_VISIBILITY |
| 961 |
typename enable_if |
| 962 |
< |
| 963 |
is_integral<_Tp>::value, |
| 964 |
double |
| 965 |
>::type |
| 966 |
norm(_Tp __re) |
| 967 |
{
|
| 968 |
return (double)__re * __re; |
| 969 |
} |
| 970 |
|
| 971 |
inline _LIBCPP_INLINE_VISIBILITY |
| 972 |
float |
| 973 |
norm(float __re) |
| 974 |
{
|
| 975 |
return __re * __re; |
| 976 |
} |
| 977 |
|
| 978 |
// conj |
| 979 |
|
| 980 |
template<class _Tp> |
| 981 |
inline _LIBCPP_INLINE_VISIBILITY |
| 982 |
complex<_Tp> |
| 983 |
conj(const complex<_Tp>& __c) |
| 984 |
{
|
| 985 |
return complex<_Tp>(__c.real(), -__c.imag()); |
| 986 |
} |
| 987 |
|
| 988 |
inline _LIBCPP_INLINE_VISIBILITY |
| 989 |
complex<long double> |
| 990 |
conj(long double __re) |
| 991 |
{
|
| 992 |
return complex<long double>(__re); |
| 993 |
} |
| 994 |
|
| 995 |
inline _LIBCPP_INLINE_VISIBILITY |
| 996 |
complex<double> |
| 997 |
conj(double __re) |
| 998 |
{
|
| 999 |
return complex<double>(__re); |
| 1000 |
} |
| 1001 |
|
| 1002 |
template<class _Tp> |
| 1003 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1004 |
typename enable_if |
| 1005 |
< |
| 1006 |
is_integral<_Tp>::value, |
| 1007 |
complex<double> |
| 1008 |
>::type |
| 1009 |
conj(_Tp __re) |
| 1010 |
{
|
| 1011 |
return complex<double>(__re); |
| 1012 |
} |
| 1013 |
|
| 1014 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1015 |
complex<float> |
| 1016 |
conj(float __re) |
| 1017 |
{
|
| 1018 |
return complex<float>(__re); |
| 1019 |
} |
| 1020 |
|
| 1021 |
// proj |
| 1022 |
|
| 1023 |
template<class _Tp> |
| 1024 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1025 |
complex<_Tp> |
| 1026 |
proj(const complex<_Tp>& __c) |
| 1027 |
{
|
| 1028 |
std::complex<_Tp> __r = __c; |
| 1029 |
if (isinf(__c.real()) || isinf(__c.imag())) |
| 1030 |
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag())); |
| 1031 |
return __r; |
| 1032 |
} |
| 1033 |
|
| 1034 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1035 |
complex<long double> |
| 1036 |
proj(long double __re) |
| 1037 |
{
|
| 1038 |
if (isinf(__re)) |
| 1039 |
__re = abs(__re); |
| 1040 |
return complex<long double>(__re); |
| 1041 |
} |
| 1042 |
|
| 1043 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1044 |
complex<double> |
| 1045 |
proj(double __re) |
| 1046 |
{
|
| 1047 |
if (isinf(__re)) |
| 1048 |
__re = abs(__re); |
| 1049 |
return complex<double>(__re); |
| 1050 |
} |
| 1051 |
|
| 1052 |
template<class _Tp> |
| 1053 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1054 |
typename enable_if |
| 1055 |
< |
| 1056 |
is_integral<_Tp>::value, |
| 1057 |
complex<double> |
| 1058 |
>::type |
| 1059 |
proj(_Tp __re) |
| 1060 |
{
|
| 1061 |
return complex<double>(__re); |
| 1062 |
} |
| 1063 |
|
| 1064 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1065 |
complex<float> |
| 1066 |
proj(float __re) |
| 1067 |
{
|
| 1068 |
if (isinf(__re)) |
| 1069 |
__re = abs(__re); |
| 1070 |
return complex<float>(__re); |
| 1071 |
} |
| 1072 |
|
| 1073 |
// polar |
| 1074 |
|
| 1075 |
template<class _Tp> |
| 1076 |
complex<_Tp> |
| 1077 |
polar(const _Tp& __rho, const _Tp& __theta = _Tp(0)) |
| 1078 |
{
|
| 1079 |
if (isnan(__rho) || signbit(__rho)) |
| 1080 |
return complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
| 1081 |
if (isnan(__theta)) |
| 1082 |
{
|
| 1083 |
if (isinf(__rho)) |
| 1084 |
return complex<_Tp>(__rho, __theta); |
| 1085 |
return complex<_Tp>(__theta, __theta); |
| 1086 |
} |
| 1087 |
if (isinf(__theta)) |
| 1088 |
{
|
| 1089 |
if (isinf(__rho)) |
| 1090 |
return complex<_Tp>(__rho, _Tp(NAN)); |
| 1091 |
return complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
| 1092 |
} |
| 1093 |
_Tp __x = __rho * cos(__theta); |
| 1094 |
if (isnan(__x)) |
| 1095 |
__x = 0; |
| 1096 |
_Tp __y = __rho * sin(__theta); |
| 1097 |
if (isnan(__y)) |
| 1098 |
__y = 0; |
| 1099 |
return complex<_Tp>(__x, __y); |
| 1100 |
} |
| 1101 |
|
| 1102 |
// log |
| 1103 |
|
| 1104 |
template<class _Tp> |
| 1105 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1106 |
complex<_Tp> |
| 1107 |
log(const complex<_Tp>& __x) |
| 1108 |
{
|
| 1109 |
return complex<_Tp>(log(abs(__x)), arg(__x)); |
| 1110 |
} |
| 1111 |
|
| 1112 |
// log10 |
| 1113 |
|
| 1114 |
template<class _Tp> |
| 1115 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1116 |
complex<_Tp> |
| 1117 |
log10(const complex<_Tp>& __x) |
| 1118 |
{
|
| 1119 |
return log(__x) / log(_Tp(10)); |
| 1120 |
} |
| 1121 |
|
| 1122 |
// sqrt |
| 1123 |
|
| 1124 |
template<class _Tp> |
| 1125 |
complex<_Tp> |
| 1126 |
sqrt(const complex<_Tp>& __x) |
| 1127 |
{
|
| 1128 |
if (isinf(__x.imag())) |
| 1129 |
return complex<_Tp>(_Tp(INFINITY), __x.imag()); |
| 1130 |
if (isinf(__x.real())) |
| 1131 |
{
|
| 1132 |
if (__x.real() > _Tp(0)) |
| 1133 |
return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag())); |
| 1134 |
return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag())); |
| 1135 |
} |
| 1136 |
return polar(sqrt(abs(__x)), arg(__x) / _Tp(2)); |
| 1137 |
} |
| 1138 |
|
| 1139 |
// exp |
| 1140 |
|
| 1141 |
template<class _Tp> |
| 1142 |
complex<_Tp> |
| 1143 |
exp(const complex<_Tp>& __x) |
| 1144 |
{
|
| 1145 |
_Tp __i = __x.imag(); |
| 1146 |
if (isinf(__x.real())) |
| 1147 |
{
|
| 1148 |
if (__x.real() < _Tp(0)) |
| 1149 |
{
|
| 1150 |
if (!isfinite(__i)) |
| 1151 |
__i = _Tp(1); |
| 1152 |
} |
| 1153 |
else if (__i == 0 || !isfinite(__i)) |
| 1154 |
{
|
| 1155 |
if (isinf(__i)) |
| 1156 |
__i = _Tp(NAN); |
| 1157 |
return complex<_Tp>(__x.real(), __i); |
| 1158 |
} |
| 1159 |
} |
| 1160 |
else if (isnan(__x.real()) && __x.imag() == 0) |
| 1161 |
return __x; |
| 1162 |
_Tp __e = exp(__x.real()); |
| 1163 |
return complex<_Tp>(__e * cos(__i), __e * sin(__i)); |
| 1164 |
} |
| 1165 |
|
| 1166 |
// pow |
| 1167 |
|
| 1168 |
template<class _Tp> |
| 1169 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1170 |
complex<_Tp> |
| 1171 |
pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
| 1172 |
{
|
| 1173 |
return exp(__y * log(__x)); |
| 1174 |
} |
| 1175 |
|
| 1176 |
template<class _Tp, class _Up> |
| 1177 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1178 |
complex<typename __promote<_Tp, _Up>::type> |
| 1179 |
pow(const complex<_Tp>& __x, const complex<_Up>& __y) |
| 1180 |
{
|
| 1181 |
typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| 1182 |
return _VSTD::pow(result_type(__x), result_type(__y)); |
| 1183 |
} |
| 1184 |
|
| 1185 |
template<class _Tp, class _Up> |
| 1186 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1187 |
typename enable_if |
| 1188 |
< |
| 1189 |
is_arithmetic<_Up>::value, |
| 1190 |
complex<typename __promote<_Tp, _Up>::type> |
| 1191 |
>::type |
| 1192 |
pow(const complex<_Tp>& __x, const _Up& __y) |
| 1193 |
{
|
| 1194 |
typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| 1195 |
return _VSTD::pow(result_type(__x), result_type(__y)); |
| 1196 |
} |
| 1197 |
|
| 1198 |
template<class _Tp, class _Up> |
| 1199 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1200 |
typename enable_if |
| 1201 |
< |
| 1202 |
is_arithmetic<_Tp>::value, |
| 1203 |
complex<typename __promote<_Tp, _Up>::type> |
| 1204 |
>::type |
| 1205 |
pow(const _Tp& __x, const complex<_Up>& __y) |
| 1206 |
{
|
| 1207 |
typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
| 1208 |
return _VSTD::pow(result_type(__x), result_type(__y)); |
| 1209 |
} |
| 1210 |
|
| 1211 |
// asinh |
| 1212 |
|
| 1213 |
template<class _Tp> |
| 1214 |
complex<_Tp> |
| 1215 |
asinh(const complex<_Tp>& __x) |
| 1216 |
{
|
| 1217 |
const _Tp __pi(atan2(+0., -0.)); |
| 1218 |
if (isinf(__x.real())) |
| 1219 |
{
|
| 1220 |
if (isnan(__x.imag())) |
| 1221 |
return __x; |
| 1222 |
if (isinf(__x.imag())) |
| 1223 |
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag())); |
| 1224 |
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
| 1225 |
} |
| 1226 |
if (isnan(__x.real())) |
| 1227 |
{
|
| 1228 |
if (isinf(__x.imag())) |
| 1229 |
return complex<_Tp>(__x.imag(), __x.real()); |
| 1230 |
if (__x.imag() == 0) |
| 1231 |
return __x; |
| 1232 |
return complex<_Tp>(__x.real(), __x.real()); |
| 1233 |
} |
| 1234 |
if (isinf(__x.imag())) |
| 1235 |
return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
| 1236 |
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1))); |
| 1237 |
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag())); |
| 1238 |
} |
| 1239 |
|
| 1240 |
// acosh |
| 1241 |
|
| 1242 |
template<class _Tp> |
| 1243 |
complex<_Tp> |
| 1244 |
acosh(const complex<_Tp>& __x) |
| 1245 |
{
|
| 1246 |
const _Tp __pi(atan2(+0., -0.)); |
| 1247 |
if (isinf(__x.real())) |
| 1248 |
{
|
| 1249 |
if (isnan(__x.imag())) |
| 1250 |
return complex<_Tp>(abs(__x.real()), __x.imag()); |
| 1251 |
if (isinf(__x.imag())) |
| 1252 |
{
|
| 1253 |
if (__x.real() > 0) |
| 1254 |
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag())); |
| 1255 |
else |
| 1256 |
return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag())); |
| 1257 |
} |
| 1258 |
if (__x.real() < 0) |
| 1259 |
return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag())); |
| 1260 |
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
| 1261 |
} |
| 1262 |
if (isnan(__x.real())) |
| 1263 |
{
|
| 1264 |
if (isinf(__x.imag())) |
| 1265 |
return complex<_Tp>(abs(__x.imag()), __x.real()); |
| 1266 |
return complex<_Tp>(__x.real(), __x.real()); |
| 1267 |
} |
| 1268 |
if (isinf(__x.imag())) |
| 1269 |
return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag())); |
| 1270 |
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); |
| 1271 |
return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag())); |
| 1272 |
} |
| 1273 |
|
| 1274 |
// atanh |
| 1275 |
|
| 1276 |
template<class _Tp> |
| 1277 |
complex<_Tp> |
| 1278 |
atanh(const complex<_Tp>& __x) |
| 1279 |
{
|
| 1280 |
const _Tp __pi(atan2(+0., -0.)); |
| 1281 |
if (isinf(__x.imag())) |
| 1282 |
{
|
| 1283 |
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
| 1284 |
} |
| 1285 |
if (isnan(__x.imag())) |
| 1286 |
{
|
| 1287 |
if (isinf(__x.real()) || __x.real() == 0) |
| 1288 |
return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag()); |
| 1289 |
return complex<_Tp>(__x.imag(), __x.imag()); |
| 1290 |
} |
| 1291 |
if (isnan(__x.real())) |
| 1292 |
{
|
| 1293 |
return complex<_Tp>(__x.real(), __x.real()); |
| 1294 |
} |
| 1295 |
if (isinf(__x.real())) |
| 1296 |
{
|
| 1297 |
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
| 1298 |
} |
| 1299 |
if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) |
| 1300 |
{
|
| 1301 |
return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag())); |
| 1302 |
} |
| 1303 |
complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2); |
| 1304 |
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag())); |
| 1305 |
} |
| 1306 |
|
| 1307 |
// sinh |
| 1308 |
|
| 1309 |
template<class _Tp> |
| 1310 |
complex<_Tp> |
| 1311 |
sinh(const complex<_Tp>& __x) |
| 1312 |
{
|
| 1313 |
if (isinf(__x.real()) && !isfinite(__x.imag())) |
| 1314 |
return complex<_Tp>(__x.real(), _Tp(NAN)); |
| 1315 |
if (__x.real() == 0 && !isfinite(__x.imag())) |
| 1316 |
return complex<_Tp>(__x.real(), _Tp(NAN)); |
| 1317 |
if (__x.imag() == 0 && !isfinite(__x.real())) |
| 1318 |
return __x; |
| 1319 |
return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag())); |
| 1320 |
} |
| 1321 |
|
| 1322 |
// cosh |
| 1323 |
|
| 1324 |
template<class _Tp> |
| 1325 |
complex<_Tp> |
| 1326 |
cosh(const complex<_Tp>& __x) |
| 1327 |
{
|
| 1328 |
if (isinf(__x.real()) && !isfinite(__x.imag())) |
| 1329 |
return complex<_Tp>(abs(__x.real()), _Tp(NAN)); |
| 1330 |
if (__x.real() == 0 && !isfinite(__x.imag())) |
| 1331 |
return complex<_Tp>(_Tp(NAN), __x.real()); |
| 1332 |
if (__x.real() == 0 && __x.imag() == 0) |
| 1333 |
return complex<_Tp>(_Tp(1), __x.imag()); |
| 1334 |
if (__x.imag() == 0 && !isfinite(__x.real())) |
| 1335 |
return complex<_Tp>(abs(__x.real()), __x.imag()); |
| 1336 |
return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag())); |
| 1337 |
} |
| 1338 |
|
| 1339 |
// tanh |
| 1340 |
|
| 1341 |
template<class _Tp> |
| 1342 |
complex<_Tp> |
| 1343 |
tanh(const complex<_Tp>& __x) |
| 1344 |
{
|
| 1345 |
if (isinf(__x.real())) |
| 1346 |
{
|
| 1347 |
if (!isfinite(__x.imag())) |
| 1348 |
return complex<_Tp>(_Tp(1), _Tp(0)); |
| 1349 |
return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag()))); |
| 1350 |
} |
| 1351 |
if (isnan(__x.real()) && __x.imag() == 0) |
| 1352 |
return __x; |
| 1353 |
_Tp __2r(_Tp(2) * __x.real()); |
| 1354 |
_Tp __2i(_Tp(2) * __x.imag()); |
| 1355 |
_Tp __d(cosh(__2r) + cos(__2i)); |
| 1356 |
_Tp __2rsh(sinh(__2r)); |
| 1357 |
if (isinf(__2rsh) && isinf(__d)) |
| 1358 |
return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), |
| 1359 |
__2i > _Tp(0) ? _Tp(0) : _Tp(-0.)); |
| 1360 |
return complex<_Tp>(__2rsh/__d, sin(__2i)/__d); |
| 1361 |
} |
| 1362 |
|
| 1363 |
// asin |
| 1364 |
|
| 1365 |
template<class _Tp> |
| 1366 |
complex<_Tp> |
| 1367 |
asin(const complex<_Tp>& __x) |
| 1368 |
{
|
| 1369 |
complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real())); |
| 1370 |
return complex<_Tp>(__z.imag(), -__z.real()); |
| 1371 |
} |
| 1372 |
|
| 1373 |
// acos |
| 1374 |
|
| 1375 |
template<class _Tp> |
| 1376 |
complex<_Tp> |
| 1377 |
acos(const complex<_Tp>& __x) |
| 1378 |
{
|
| 1379 |
const _Tp __pi(atan2(+0., -0.)); |
| 1380 |
if (isinf(__x.real())) |
| 1381 |
{
|
| 1382 |
if (isnan(__x.imag())) |
| 1383 |
return complex<_Tp>(__x.imag(), __x.real()); |
| 1384 |
if (isinf(__x.imag())) |
| 1385 |
{
|
| 1386 |
if (__x.real() < _Tp(0)) |
| 1387 |
return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag()); |
| 1388 |
return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag()); |
| 1389 |
} |
| 1390 |
if (__x.real() < _Tp(0)) |
| 1391 |
return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real()); |
| 1392 |
return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real()); |
| 1393 |
} |
| 1394 |
if (isnan(__x.real())) |
| 1395 |
{
|
| 1396 |
if (isinf(__x.imag())) |
| 1397 |
return complex<_Tp>(__x.real(), -__x.imag()); |
| 1398 |
return complex<_Tp>(__x.real(), __x.real()); |
| 1399 |
} |
| 1400 |
if (isinf(__x.imag())) |
| 1401 |
return complex<_Tp>(__pi/_Tp(2), -__x.imag()); |
| 1402 |
if (__x.real() == 0) |
| 1403 |
return complex<_Tp>(__pi/_Tp(2), -__x.imag()); |
| 1404 |
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); |
| 1405 |
if (signbit(__x.imag())) |
| 1406 |
return complex<_Tp>(abs(__z.imag()), abs(__z.real())); |
| 1407 |
return complex<_Tp>(abs(__z.imag()), -abs(__z.real())); |
| 1408 |
} |
| 1409 |
|
| 1410 |
// atan |
| 1411 |
|
| 1412 |
template<class _Tp> |
| 1413 |
complex<_Tp> |
| 1414 |
atan(const complex<_Tp>& __x) |
| 1415 |
{
|
| 1416 |
complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real())); |
| 1417 |
return complex<_Tp>(__z.imag(), -__z.real()); |
| 1418 |
} |
| 1419 |
|
| 1420 |
// sin |
| 1421 |
|
| 1422 |
template<class _Tp> |
| 1423 |
complex<_Tp> |
| 1424 |
sin(const complex<_Tp>& __x) |
| 1425 |
{
|
| 1426 |
complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real())); |
| 1427 |
return complex<_Tp>(__z.imag(), -__z.real()); |
| 1428 |
} |
| 1429 |
|
| 1430 |
// cos |
| 1431 |
|
| 1432 |
template<class _Tp> |
| 1433 |
inline _LIBCPP_INLINE_VISIBILITY |
| 1434 |
complex<_Tp> |
| 1435 |
cos(const complex<_Tp>& __x) |
| 1436 |
{
|
| 1437 |
return cosh(complex<_Tp>(-__x.imag(), __x.real())); |
| 1438 |
} |
| 1439 |
|
| 1440 |
// tan |
| 1441 |
|
| 1442 |
template<class _Tp> |
| 1443 |
complex<_Tp> |
| 1444 |
tan(const complex<_Tp>& __x) |
| 1445 |
{
|
| 1446 |
complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real())); |
| 1447 |
return complex<_Tp>(__z.imag(), -__z.real()); |
| 1448 |
} |
| 1449 |
|
| 1450 |
template<class _Tp, class _CharT, class _Traits> |
| 1451 |
basic_istream<_CharT, _Traits>& |
| 1452 |
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) |
| 1453 |
{
|
| 1454 |
if (__is.good()) |
| 1455 |
{
|
| 1456 |
ws(__is); |
| 1457 |
if (__is.peek() == _CharT('('))
|
| 1458 |
{
|
| 1459 |
__is.get(); |
| 1460 |
_Tp __r; |
| 1461 |
__is >> __r; |
| 1462 |
if (!__is.fail()) |
| 1463 |
{
|
| 1464 |
ws(__is); |
| 1465 |
_CharT __c = __is.peek(); |
| 1466 |
if (__c == _CharT(','))
|
| 1467 |
{
|
| 1468 |
__is.get(); |
| 1469 |
_Tp __i; |
| 1470 |
__is >> __i; |
| 1471 |
if (!__is.fail()) |
| 1472 |
{
|
| 1473 |
ws(__is); |
| 1474 |
__c = __is.peek(); |
| 1475 |
if (__c == _CharT(')'))
|
| 1476 |
{
|
| 1477 |
__is.get(); |
| 1478 |
__x = complex<_Tp>(__r, __i); |
| 1479 |
} |
| 1480 |
else |
| 1481 |
__is.setstate(ios_base::failbit); |
| 1482 |
} |
| 1483 |
else |
| 1484 |
__is.setstate(ios_base::failbit); |
| 1485 |
} |
| 1486 |
else if (__c == _CharT(')'))
|
| 1487 |
{
|
| 1488 |
__is.get(); |
| 1489 |
__x = complex<_Tp>(__r, _Tp(0)); |
| 1490 |
} |
| 1491 |
else |
| 1492 |
__is.setstate(ios_base::failbit); |
| 1493 |
} |
| 1494 |
else |
| 1495 |
__is.setstate(ios_base::failbit); |
| 1496 |
} |
| 1497 |
else |
| 1498 |
{
|
| 1499 |
_Tp __r; |
| 1500 |
__is >> __r; |
| 1501 |
if (!__is.fail()) |
| 1502 |
__x = complex<_Tp>(__r, _Tp(0)); |
| 1503 |
else |
| 1504 |
__is.setstate(ios_base::failbit); |
| 1505 |
} |
| 1506 |
} |
| 1507 |
else |
| 1508 |
__is.setstate(ios_base::failbit); |
| 1509 |
return __is; |
| 1510 |
} |
| 1511 |
|
| 1512 |
template<class _Tp, class _CharT, class _Traits> |
| 1513 |
basic_ostream<_CharT, _Traits>& |
| 1514 |
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) |
| 1515 |
{
|
| 1516 |
basic_ostringstream<_CharT, _Traits> __s; |
| 1517 |
__s.flags(__os.flags()); |
| 1518 |
__s.imbue(__os.getloc()); |
| 1519 |
__s.precision(__os.precision()); |
| 1520 |
__s << '(' << __x.real() << ',' << __x.imag() << ')';
|
| 1521 |
return __os << __s.str(); |
| 1522 |
} |
| 1523 |
|
| 1524 |
#if _LIBCPP_STD_VER > 11 |
| 1525 |
// Literal suffix for complex number literals [complex.literals] |
| 1526 |
inline namespace literals |
| 1527 |
{
|
| 1528 |
inline namespace complex_literals |
| 1529 |
{
|
| 1530 |
constexpr complex<long double> operator""il(long double __im) |
| 1531 |
{
|
| 1532 |
return { 0.0l, __im };
|
| 1533 |
} |
| 1534 |
|
| 1535 |
constexpr complex<long double> operator""il(unsigned long long __im) |
| 1536 |
{
|
| 1537 |
return { 0.0l, static_cast<long double>(__im) };
|
| 1538 |
} |
| 1539 |
|
| 1540 |
|
| 1541 |
constexpr complex<double> operator""i(long double __im) |
| 1542 |
{
|
| 1543 |
return { 0.0, static_cast<double>(__im) };
|
| 1544 |
} |
| 1545 |
|
| 1546 |
constexpr complex<double> operator""i(unsigned long long __im) |
| 1547 |
{
|
| 1548 |
return { 0.0, static_cast<double>(__im) };
|
| 1549 |
} |
| 1550 |
|
| 1551 |
|
| 1552 |
constexpr complex<float> operator""if(long double __im) |
| 1553 |
{
|
| 1554 |
return { 0.0f, static_cast<float>(__im) };
|
| 1555 |
} |
| 1556 |
|
| 1557 |
constexpr complex<float> operator""if(unsigned long long __im) |
| 1558 |
{
|
| 1559 |
return { 0.0f, static_cast<float>(__im) };
|
| 1560 |
} |
| 1561 |
} |
| 1562 |
} |
| 1563 |
#endif |
| 1564 |
|
| 1565 |
_LIBCPP_END_NAMESPACE_STD |
| 1566 |
|
| 1567 |
#endif // _LIBCPP_COMPLEX |