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Standard library header <complex>

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This header is part of the numeric library.

Contents

[edit] Classes

a complex number type
(class template)
a complex number type
(class template specialization)

[edit] Functions

Operations
applies unary operators to complex numbers
(function template) [edit]
performs complex number arithmetics on two complex values or a complex and a scalar
(function template) [edit]
compares two complex numbers or a complex and a scalar
(function template) [edit]
serializes and deserializes a complex number
(function template) [edit]
returns the real component
(function template) [edit]
returns the imaginary component
(function template) [edit]
returns the magnitude of a complex number
(function template) [edit]
returns the phase angle
(function template) [edit]
returns the squared magnitude
(function template) [edit]
returns the complex conjugate
(function template) [edit]
(C++11)
returns the projection onto the Riemann sphere
(function template) [edit]
constructs a complex number from magnitude and phase angle
(function template) [edit]
Exponential functions
complex base e exponential
(function template) [edit]
complex natural logarithm with the branch cuts along the negative real axis
(function template) [edit]
complex common logarithm with the branch cuts along the negative real axis
(function template) [edit]
Power functions
complex power, one or both arguments may be a complex number
(function template) [edit]
complex square root in the range of the right half-plane
(function template) [edit]
Trigonometric functions
computes sine of a complex number (sin(z))
(function template) [edit]
computes cosine of a complex number (cos(z))
(function template) [edit]
computes tangent of a complex number (tan(z))
(function template) [edit]
computes arc sine of a complex number (arcsin(z))
(function template) [edit]
computes arc cosine of a complex number (arccos(z))
(function template) [edit]
computes arc tangent of a complex number (arctan(z))
(function template) [edit]
Hyperbolic functions
computes hyperbolic sine of a complex number (sh(z))
(function template) [edit]
computes hyperbolic cosine of a complex number (ch(z))
(function template) [edit]
computes hyperbolic tangent of a complex number
(function template) [edit]
computes area hyperbolic sine of a complex number
(function template) [edit]
computes area hyperbolic cosine of a complex number
(function template) [edit]
computes area hyperbolic tangent of a complex number
(function template) [edit]


[edit] Synopsis

namespace std {
 
    template<class T> class complex;
 
    template<> class complex<float>;
    template<> class complex<double>;
    template<> class complex<long double>;
 
    // operators:
    template<class T>
    complex<T> operator+(const complex<T>&, const complex<T>&);
    template<class T> complex<T> operator+(const complex<T>&, const T&);
    template<class T> complex<T> operator+(const T&, const complex<T>&);
 
    template<class T> complex<T> operator-(
        const complex<T>&, const complex<T>&);
    template<class T> complex<T> operator-(const complex<T>&, const T&);
    template<class T> complex<T> operator-(const T&, const complex<T>&);
 
    template<class T> complex<T> operator*(
        const complex<T>&, const complex<T>&);
    template<class T> complex<T> operator*(const complex<T>&, const T&);
    template<class T> complex<T> operator*(const T&, const complex<T>&);
 
    template<class T> complex<T> operator/(
        const complex<T>&, const complex<T>&);
    template<class T> complex<T> operator/(const complex<T>&, const T&);
    template<class T> complex<T> operator/(const T&, const complex<T>&);
 
    template<class T> complex<T> operator+(const complex<T>&);
    template<class T> complex<T> operator-(const complex<T>&);
 
    template<class T> bool operator==(
        const complex<T>&, const complex<T>&);
    template<class T> bool operator==(const complex<T>&, const T&);
    template<class T> bool operator==(const T&, const complex<T>&);
 
    template<class T> bool operator!=(const complex<T>&, const complex<T>&);
    template<class T> bool operator!=(const complex<T>&, const T&);
    template<class T> bool operator!=(const T&, const complex<T>&);
 
    template<class T, class charT, class traits>
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>&, complex<T>&);
 
    template<class T, class charT, class traits>
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>&, const complex<T>&);
 
    // values:
    template<class T> T real(const complex<T>&);
    template<class T> T imag(const complex<T>&);
 
    template<class T> T abs(const complex<T>&);
    template<class T> T arg(const complex<T>&);
    template<class T> T norm(const complex<T>&);
 
    template<class T> complex<T> conj(const complex<T>&);
    template <class T> complex<T> proj(const complex<T>&);
    template<class T> complex<T> polar(const T&, const T& = 0);
 
    // transcendentals:
    template<class T> complex<T> acos(const complex<T>&);
    template<class T> complex<T> asin(const complex<T>&);
    template<class T> complex<T> atan(const complex<T>&);
 
    template<class T> complex<T> acosh(const complex<T>&);
    template<class T> complex<T> asinh(const complex<T>&);
    template<class T> complex<T> atanh(const complex<T>&);
 
    template<class T> complex<T> cos  (const complex<T>&);
    template<class T> complex<T> cosh (const complex<T>&);
    template<class T> complex<T> exp  (const complex<T>&);
    template<class T> complex<T> log  (const complex<T>&);
    template<class T> complex<T> log10(const complex<T>&);
 
    template<class T> complex<T> pow(const complex<T>&, const T&);
    template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
    template<class T> complex<T> pow(const T&, const complex<T>&);
 
    template<class T> complex<T> sin    (const complex<T>&);
    template<class T> complex<T> sinh   (const complex<T>&);
    template<class T> complex<T> sqrt   (const complex<T>&);
    template<class T> complex<T> tan    (const complex<T>&);
    template<class T> complex<T> tanh   (const complex<T>&);
 
 
}


[edit] Class std::complex

template<class T>
class complex {
public:
    typedef T value_type;
    complex(const T& re = T(), const T& im = T());
    complex(const complex&);
    template<class X> complex(const complex<X>&);
 
    T real() const;
    void real(T);
    T imag() const;
    void imag(T);
 
    complex<T>& operator= (const T&);
    complex<T>& operator+=(const T&);
    complex<T>& operator-=(const T&);
    complex<T>& operator*=(const T&);
    complex<T>& operator/=(const T&);
 
    complex& operator=(const complex&);     
    template<class X> complex<T>& operator= (const complex<X>&);   
    template<class X> complex<T>& operator+=(const complex<X>&);   
    template<class X> complex<T>& operator-=(const complex<X>&);   
    template<class X> complex<T>& operator*=(const complex<X>&);   
    template<class X> complex<T>& operator/=(const complex<X>&);   
 
};

[edit] std::complex specializations

template<> class complex<float> {
public:
    typedef float value_type;
 
    constexpr complex(float re = 0.0f, float im = 0.0f);
    explicit constexpr complex(const complex<double>&);
    explicit constexpr complex(const complex<long double>&);
 
    constexpr float real();
    void real(float);
    constexpr float imag();
    void imag(float);
 
    complex<float>& operator= (float);
    complex<float>& operator+=(float);
    complex<float>& operator-=(float);
    complex<float>& operator*=(float);
    complex<float>& operator/=(float);
 
    complex<float>& operator=(const complex<float>&);
    template<class X> complex<float>& operator= (const complex<X>&);
    template<class X> complex<float>& operator+=(const complex<X>&);
    template<class X> complex<float>& operator-=(const complex<X>&);
    template<class X> complex<float>& operator*=(const complex<X>&);
    template<class X> complex<float>& operator/=(const complex<X>&);
};
 
template<> class complex<double> {
public:
    typedef double value_type;
 
    constexpr complex(double re = 0.0, double im = 0.0);
    constexpr complex(const complex<float>&);
    explicit constexpr complex(const complex<long double>&);
 
    constexpr double real();
    void real(double);
    constexpr double imag();
    void imag(double);
 
    complex<double>& operator= (double);
    complex<double>& operator+=(double);
    complex<double>& operator-=(double);
    complex<double>& operator*=(double);
    complex<double>& operator/=(double);
 
    complex<double>& operator=(const complex<double>&);
    template<class X> complex<double>& operator= (const complex<X>&);
    template<class X> complex<double>& operator+=(const complex<X>&);
    template<class X> complex<double>& operator-=(const complex<X>&);
    template<class X> complex<double>& operator*=(const complex<X>&);
    template<class X> complex<double>& operator/=(const complex<X>&);
};
 
template<> class complex<long double> {
public:
    typedef long double value_type;
 
    constexpr complex(long double re = 0.0L, long double im = 0.0L);
    constexpr complex(const complex<float>&);
    constexpr complex(const complex<double>&);
 
    constexpr long double real();
    void real(long double);
    constexpr long double imag();
    void imag(long double);
 
    complex<long double>& operator=(const complex<long double>&);
    complex<long double>& operator= (long double);
    complex<long double>& operator+=(long double);
    complex<long double>& operator-=(long double);
    complex<long double>& operator*=(long double);
    complex<long double>& operator/=(long double);
 
    template<class X> complex<long double>& operator= (const complex<X>&);
    template<class X> complex<long double>& operator+=(const complex<X>&);
    template<class X> complex<long double>& operator-=(const complex<X>&);
    template<class X> complex<long double>& operator*=(const complex<X>&);
    template<class X> complex<long double>& operator/=(const complex<X>&);
 
};