1527 lines
42 KiB
C++
1527 lines
42 KiB
C++
// -*- 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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#ifndef _LIBCPP_COMPLEX
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#define _LIBCPP_COMPLEX
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/*
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complex synopsis
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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());
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complex(const complex&);
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template<class X> complex(const complex<X>&);
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T real() const;
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T imag() const;
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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>&);
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template<class T> bool operator==(const complex<T>&, const T&);
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template<class T> bool operator==(const T&, const complex<T>&);
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template<class T> bool operator!=(const complex<T>&, const complex<T>&);
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template<class T> bool operator!=(const complex<T>&, const T&);
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template<class T> bool operator!=(const T&, 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>&, 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>&);
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long double real(long double);
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double real(double);
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template<Integral T> double real(T);
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float real(float);
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template<class T> T imag(const complex<T>&);
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long double imag(long double);
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double imag(double);
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template<Integral T> double imag(T);
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float imag(float);
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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 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 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
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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
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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 value_type real() const {return __re_;}
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_LIBCPP_INLINE_VISIBILITY 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 * __c;
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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 / __c;
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return *this;
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}
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};
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template<> class _LIBCPP_TYPE_VIS complex<double>;
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template<> class _LIBCPP_TYPE_VIS complex<long double>;
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template<>
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class _LIBCPP_TYPE_VIS 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 * __c;
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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 / __c;
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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 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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}
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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 * __c;
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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 / __c;
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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 complex<long double>
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{
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long double __re_;
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long double __im_;
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public:
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typedef long double value_type;
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
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: __re_(__re), __im_(__im) {}
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_LIBCPP_CONSTEXPR complex(const complex<float>& __c);
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_LIBCPP_CONSTEXPR complex(const complex<double>& __c);
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
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_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
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_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
|
|
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
|
|
|
|
_LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
|
|
{__re_ = __re; __im_ = value_type(); return *this;}
|
|
_LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
|
|
_LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
|
|
_LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
|
|
_LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
|
|
|
|
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
|
|
{
|
|
__re_ = __c.real();
|
|
__im_ = __c.imag();
|
|
return *this;
|
|
}
|
|
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
|
|
{
|
|
__re_ += __c.real();
|
|
__im_ += __c.imag();
|
|
return *this;
|
|
}
|
|
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
|
|
{
|
|
__re_ -= __c.real();
|
|
__im_ -= __c.imag();
|
|
return *this;
|
|
}
|
|
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
|
|
{
|
|
*this = *this * __c;
|
|
return *this;
|
|
}
|
|
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
|
|
{
|
|
*this = *this / __c;
|
|
return *this;
|
|
}
|
|
};
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR
|
|
complex<float>::complex(const complex<double>& __c)
|
|
: __re_(__c.real()), __im_(__c.imag()) {}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR
|
|
complex<float>::complex(const complex<long double>& __c)
|
|
: __re_(__c.real()), __im_(__c.imag()) {}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR
|
|
complex<double>::complex(const complex<float>& __c)
|
|
: __re_(__c.real()), __im_(__c.imag()) {}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR
|
|
complex<double>::complex(const complex<long double>& __c)
|
|
: __re_(__c.real()), __im_(__c.imag()) {}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR
|
|
complex<long double>::complex(const complex<float>& __c)
|
|
: __re_(__c.real()), __im_(__c.imag()) {}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_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
|
|
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
|
|
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
|
|
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
|
|
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
|
|
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
|
|
complex<_Tp>
|
|
operator-(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __t(-__y);
|
|
__t += __x;
|
|
return __t;
|
|
}
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
|
|
{
|
|
_Tp __a = __z.real();
|
|
_Tp __b = __z.imag();
|
|
_Tp __c = __w.real();
|
|
_Tp __d = __w.imag();
|
|
_Tp __ac = __a * __c;
|
|
_Tp __bd = __b * __d;
|
|
_Tp __ad = __a * __d;
|
|
_Tp __bc = __b * __c;
|
|
_Tp __x = __ac - __bd;
|
|
_Tp __y = __ad + __bc;
|
|
if (isnan(__x) && isnan(__y))
|
|
{
|
|
bool __recalc = false;
|
|
if (isinf(__a) || isinf(__b))
|
|
{
|
|
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
|
|
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
|
|
if (isnan(__c))
|
|
__c = copysign(_Tp(0), __c);
|
|
if (isnan(__d))
|
|
__d = copysign(_Tp(0), __d);
|
|
__recalc = true;
|
|
}
|
|
if (isinf(__c) || isinf(__d))
|
|
{
|
|
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
|
|
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
|
|
if (isnan(__a))
|
|
__a = copysign(_Tp(0), __a);
|
|
if (isnan(__b))
|
|
__b = copysign(_Tp(0), __b);
|
|
__recalc = true;
|
|
}
|
|
if (!__recalc && (isinf(__ac) || isinf(__bd) ||
|
|
isinf(__ad) || isinf(__bc)))
|
|
{
|
|
if (isnan(__a))
|
|
__a = copysign(_Tp(0), __a);
|
|
if (isnan(__b))
|
|
__b = copysign(_Tp(0), __b);
|
|
if (isnan(__c))
|
|
__c = copysign(_Tp(0), __c);
|
|
if (isnan(__d))
|
|
__d = 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
|
|
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
|
|
complex<_Tp>
|
|
operator*(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __t(__y);
|
|
__t *= __x;
|
|
return __t;
|
|
}
|
|
|
|
template<class _Tp>
|
|
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 = logb(fmax(fabs(__c), fabs(__d)));
|
|
if (isfinite(__logbw))
|
|
{
|
|
__ilogbw = static_cast<int>(__logbw);
|
|
__c = scalbn(__c, -__ilogbw);
|
|
__d = scalbn(__d, -__ilogbw);
|
|
}
|
|
_Tp __denom = __c * __c + __d * __d;
|
|
_Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
|
|
_Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
|
|
if (isnan(__x) && isnan(__y))
|
|
{
|
|
if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
|
|
{
|
|
__x = copysign(_Tp(INFINITY), __c) * __a;
|
|
__y = copysign(_Tp(INFINITY), __c) * __b;
|
|
}
|
|
else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
|
|
{
|
|
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
|
|
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
|
|
__x = _Tp(INFINITY) * (__a * __c + __b * __d);
|
|
__y = _Tp(INFINITY) * (__b * __c - __a * __d);
|
|
}
|
|
else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
|
|
{
|
|
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
|
|
__d = copysign(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
|
|
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
|
|
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
|
|
complex<_Tp>
|
|
operator+(const complex<_Tp>& __x)
|
|
{
|
|
return __x;
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<_Tp>
|
|
operator-(const complex<_Tp>& __x)
|
|
{
|
|
return complex<_Tp>(-__x.real(), -__x.imag());
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
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
|
|
bool
|
|
operator==(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
return __x.real() == __y && __x.imag() == 0;
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
bool
|
|
operator==(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
return __x == __y.real() && 0 == __y.imag();
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
bool
|
|
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
return !(__x == __y);
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
bool
|
|
operator!=(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
return !(__x == __y);
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
bool
|
|
operator!=(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
return !(__x == __y);
|
|
}
|
|
|
|
// 26.3.7 values:
|
|
|
|
// real
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
real(const complex<_Tp>& __c)
|
|
{
|
|
return __c.real();
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
long double
|
|
real(long double __re)
|
|
{
|
|
return __re;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
double
|
|
real(double __re)
|
|
{
|
|
return __re;
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
double
|
|
>::type
|
|
real(_Tp __re)
|
|
{
|
|
return __re;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
float
|
|
real(float __re)
|
|
{
|
|
return __re;
|
|
}
|
|
|
|
// imag
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
imag(const complex<_Tp>& __c)
|
|
{
|
|
return __c.imag();
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
long double
|
|
imag(long double __re)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
double
|
|
imag(double __re)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
double
|
|
>::type
|
|
imag(_Tp __re)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
float
|
|
imag(float __re)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
// abs
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
abs(const complex<_Tp>& __c)
|
|
{
|
|
return hypot(__c.real(), __c.imag());
|
|
}
|
|
|
|
// arg
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
arg(const complex<_Tp>& __c)
|
|
{
|
|
return atan2(__c.imag(), __c.real());
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
long double
|
|
arg(long double __re)
|
|
{
|
|
return atan2l(0.L, __re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
double
|
|
arg(double __re)
|
|
{
|
|
return atan2(0., __re);
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
double
|
|
>::type
|
|
arg(_Tp __re)
|
|
{
|
|
return atan2(0., __re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
float
|
|
arg(float __re)
|
|
{
|
|
return atan2f(0.F, __re);
|
|
}
|
|
|
|
// norm
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
_Tp
|
|
norm(const complex<_Tp>& __c)
|
|
{
|
|
if (isinf(__c.real()))
|
|
return abs(__c.real());
|
|
if (isinf(__c.imag()))
|
|
return abs(__c.imag());
|
|
return __c.real() * __c.real() + __c.imag() * __c.imag();
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
long double
|
|
norm(long double __re)
|
|
{
|
|
return __re * __re;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
double
|
|
norm(double __re)
|
|
{
|
|
return __re * __re;
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
double
|
|
>::type
|
|
norm(_Tp __re)
|
|
{
|
|
return (double)__re * __re;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
float
|
|
norm(float __re)
|
|
{
|
|
return __re * __re;
|
|
}
|
|
|
|
// conj
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<_Tp>
|
|
conj(const complex<_Tp>& __c)
|
|
{
|
|
return complex<_Tp>(__c.real(), -__c.imag());
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<long double>
|
|
conj(long double __re)
|
|
{
|
|
return complex<long double>(__re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<double>
|
|
conj(double __re)
|
|
{
|
|
return complex<double>(__re);
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
complex<double>
|
|
>::type
|
|
conj(_Tp __re)
|
|
{
|
|
return complex<double>(__re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<float>
|
|
conj(float __re)
|
|
{
|
|
return complex<float>(__re);
|
|
}
|
|
|
|
// proj
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<_Tp>
|
|
proj(const complex<_Tp>& __c)
|
|
{
|
|
std::complex<_Tp> __r = __c;
|
|
if (isinf(__c.real()) || isinf(__c.imag()))
|
|
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
|
|
return __r;
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<long double>
|
|
proj(long double __re)
|
|
{
|
|
if (isinf(__re))
|
|
__re = abs(__re);
|
|
return complex<long double>(__re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<double>
|
|
proj(double __re)
|
|
{
|
|
if (isinf(__re))
|
|
__re = abs(__re);
|
|
return complex<double>(__re);
|
|
}
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
typename enable_if
|
|
<
|
|
is_integral<_Tp>::value,
|
|
complex<double>
|
|
>::type
|
|
proj(_Tp __re)
|
|
{
|
|
return complex<double>(__re);
|
|
}
|
|
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<float>
|
|
proj(float __re)
|
|
{
|
|
if (isinf(__re))
|
|
__re = abs(__re);
|
|
return complex<float>(__re);
|
|
}
|
|
|
|
// polar
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
|
|
{
|
|
if (isnan(__rho) || signbit(__rho))
|
|
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
|
|
if (isnan(__theta))
|
|
{
|
|
if (isinf(__rho))
|
|
return complex<_Tp>(__rho, __theta);
|
|
return complex<_Tp>(__theta, __theta);
|
|
}
|
|
if (isinf(__theta))
|
|
{
|
|
if (isinf(__rho))
|
|
return complex<_Tp>(__rho, _Tp(NAN));
|
|
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
|
|
}
|
|
_Tp __x = __rho * cos(__theta);
|
|
if (isnan(__x))
|
|
__x = 0;
|
|
_Tp __y = __rho * sin(__theta);
|
|
if (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>(log(abs(__x)), arg(__x));
|
|
}
|
|
|
|
// log10
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<_Tp>
|
|
log10(const complex<_Tp>& __x)
|
|
{
|
|
return log(__x) / log(_Tp(10));
|
|
}
|
|
|
|
// sqrt
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
sqrt(const complex<_Tp>& __x)
|
|
{
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(_Tp(INFINITY), __x.imag());
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (__x.real() > _Tp(0))
|
|
return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
|
|
return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
|
|
}
|
|
return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
|
|
}
|
|
|
|
// exp
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
exp(const complex<_Tp>& __x)
|
|
{
|
|
_Tp __i = __x.imag();
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (__x.real() < _Tp(0))
|
|
{
|
|
if (!isfinite(__i))
|
|
__i = _Tp(1);
|
|
}
|
|
else if (__i == 0 || !isfinite(__i))
|
|
{
|
|
if (isinf(__i))
|
|
__i = _Tp(NAN);
|
|
return complex<_Tp>(__x.real(), __i);
|
|
}
|
|
}
|
|
else if (isnan(__x.real()) && __x.imag() == 0)
|
|
return __x;
|
|
_Tp __e = exp(__x.real());
|
|
return complex<_Tp>(__e * cos(__i), __e * sin(__i));
|
|
}
|
|
|
|
// pow
|
|
|
|
template<class _Tp>
|
|
inline _LIBCPP_INLINE_VISIBILITY
|
|
complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
return exp(__y * 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));
|
|
}
|
|
|
|
// asinh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
asinh(const complex<_Tp>& __x)
|
|
{
|
|
const _Tp __pi(atan2(+0., -0.));
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (isnan(__x.imag()))
|
|
return __x;
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
|
|
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
|
|
}
|
|
if (isnan(__x.real()))
|
|
{
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(__x.imag(), __x.real());
|
|
if (__x.imag() == 0)
|
|
return __x;
|
|
return complex<_Tp>(__x.real(), __x.real());
|
|
}
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
|
|
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
|
|
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
|
|
}
|
|
|
|
// acosh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
acosh(const complex<_Tp>& __x)
|
|
{
|
|
const _Tp __pi(atan2(+0., -0.));
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (isnan(__x.imag()))
|
|
return complex<_Tp>(abs(__x.real()), __x.imag());
|
|
if (isinf(__x.imag()))
|
|
{
|
|
if (__x.real() > 0)
|
|
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
|
|
else
|
|
return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
|
|
}
|
|
if (__x.real() < 0)
|
|
return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
|
|
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
|
|
}
|
|
if (isnan(__x.real()))
|
|
{
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(abs(__x.imag()), __x.real());
|
|
return complex<_Tp>(__x.real(), __x.real());
|
|
}
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
|
|
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
|
|
return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
|
|
}
|
|
|
|
// atanh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
atanh(const complex<_Tp>& __x)
|
|
{
|
|
const _Tp __pi(atan2(+0., -0.));
|
|
if (isinf(__x.imag()))
|
|
{
|
|
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
|
|
}
|
|
if (isnan(__x.imag()))
|
|
{
|
|
if (isinf(__x.real()) || __x.real() == 0)
|
|
return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
|
|
return complex<_Tp>(__x.imag(), __x.imag());
|
|
}
|
|
if (isnan(__x.real()))
|
|
{
|
|
return complex<_Tp>(__x.real(), __x.real());
|
|
}
|
|
if (isinf(__x.real()))
|
|
{
|
|
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
|
|
}
|
|
if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
|
|
{
|
|
return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
|
|
}
|
|
complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
|
|
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
|
|
}
|
|
|
|
// sinh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
sinh(const complex<_Tp>& __x)
|
|
{
|
|
if (isinf(__x.real()) && !isfinite(__x.imag()))
|
|
return complex<_Tp>(__x.real(), _Tp(NAN));
|
|
if (__x.real() == 0 && !isfinite(__x.imag()))
|
|
return complex<_Tp>(__x.real(), _Tp(NAN));
|
|
if (__x.imag() == 0 && !isfinite(__x.real()))
|
|
return __x;
|
|
return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
|
|
}
|
|
|
|
// cosh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
cosh(const complex<_Tp>& __x)
|
|
{
|
|
if (isinf(__x.real()) && !isfinite(__x.imag()))
|
|
return complex<_Tp>(abs(__x.real()), _Tp(NAN));
|
|
if (__x.real() == 0 && !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 && !isfinite(__x.real()))
|
|
return complex<_Tp>(abs(__x.real()), __x.imag());
|
|
return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
|
|
}
|
|
|
|
// tanh
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
tanh(const complex<_Tp>& __x)
|
|
{
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (!isfinite(__x.imag()))
|
|
return complex<_Tp>(_Tp(1), _Tp(0));
|
|
return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
|
|
}
|
|
if (isnan(__x.real()) && __x.imag() == 0)
|
|
return __x;
|
|
_Tp __2r(_Tp(2) * __x.real());
|
|
_Tp __2i(_Tp(2) * __x.imag());
|
|
_Tp __d(cosh(__2r) + cos(__2i));
|
|
_Tp __2rsh(sinh(__2r));
|
|
if (isinf(__2rsh) && isinf(__d))
|
|
return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
|
|
__2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
|
|
return complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
|
|
}
|
|
|
|
// asin
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
asin(const complex<_Tp>& __x)
|
|
{
|
|
complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
|
|
return complex<_Tp>(__z.imag(), -__z.real());
|
|
}
|
|
|
|
// acos
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
acos(const complex<_Tp>& __x)
|
|
{
|
|
const _Tp __pi(atan2(+0., -0.));
|
|
if (isinf(__x.real()))
|
|
{
|
|
if (isnan(__x.imag()))
|
|
return complex<_Tp>(__x.imag(), __x.real());
|
|
if (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, signbit(__x.imag()) ? -__x.real() : __x.real());
|
|
return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
|
|
}
|
|
if (isnan(__x.real()))
|
|
{
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(__x.real(), -__x.imag());
|
|
return complex<_Tp>(__x.real(), __x.real());
|
|
}
|
|
if (isinf(__x.imag()))
|
|
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
|
|
if (__x.real() == 0)
|
|
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
|
|
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
|
|
if (signbit(__x.imag()))
|
|
return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
|
|
return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
|
|
}
|
|
|
|
// atan
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
atan(const complex<_Tp>& __x)
|
|
{
|
|
complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
|
|
return complex<_Tp>(__z.imag(), -__z.real());
|
|
}
|
|
|
|
// sin
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
sin(const complex<_Tp>& __x)
|
|
{
|
|
complex<_Tp> __z = 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 cosh(complex<_Tp>(-__x.imag(), __x.real()));
|
|
}
|
|
|
|
// tan
|
|
|
|
template<class _Tp>
|
|
complex<_Tp>
|
|
tan(const complex<_Tp>& __x)
|
|
{
|
|
complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
|
|
return complex<_Tp>(__z.imag(), -__z.real());
|
|
}
|
|
|
|
template<class _Tp, class _CharT, class _Traits>
|
|
basic_istream<_CharT, _Traits>&
|
|
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
|
|
{
|
|
if (__is.good())
|
|
{
|
|
ws(__is);
|
|
if (__is.peek() == _CharT('('))
|
|
{
|
|
__is.get();
|
|
_Tp __r;
|
|
__is >> __r;
|
|
if (!__is.fail())
|
|
{
|
|
ws(__is);
|
|
_CharT __c = __is.peek();
|
|
if (__c == _CharT(','))
|
|
{
|
|
__is.get();
|
|
_Tp __i;
|
|
__is >> __i;
|
|
if (!__is.fail())
|
|
{
|
|
ws(__is);
|
|
__c = __is.peek();
|
|
if (__c == _CharT(')'))
|
|
{
|
|
__is.get();
|
|
__x = complex<_Tp>(__r, __i);
|
|
}
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
else if (__c == _CharT(')'))
|
|
{
|
|
__is.get();
|
|
__x = complex<_Tp>(__r, _Tp(0));
|
|
}
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
else
|
|
{
|
|
_Tp __r;
|
|
__is >> __r;
|
|
if (!__is.fail())
|
|
__x = complex<_Tp>(__r, _Tp(0));
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
}
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
return __is;
|
|
}
|
|
|
|
template<class _Tp, class _CharT, class _Traits>
|
|
basic_ostream<_CharT, _Traits>&
|
|
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
|
|
{
|
|
basic_ostringstream<_CharT, _Traits> __s;
|
|
__s.flags(__os.flags());
|
|
__s.imbue(__os.getloc());
|
|
__s.precision(__os.precision());
|
|
__s << '(' << __x.real() << ',' << __x.imag() << ')';
|
|
return __os << __s.str();
|
|
}
|
|
|
|
_LIBCPP_END_NAMESPACE_STD
|
|
|
|
#endif // _LIBCPP_COMPLEX
|