Standard library header <complex>
This header is part of the numeric library.
Classes
| a complex number type (class template) |
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| a complex number type (class template specialization) |
Functions
Operations |
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| applies unary operators to complex numbers (function template) |
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| performs complex number arithmetics on two complex values or a complex and a scalar (function template) |
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| compares two complex numbers or a complex and a scalar (function template) |
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| serializes and deserializes a complex number (function template) |
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| returns the real component (function template) |
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| returns the imaginary component (function template) |
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| returns the magnitude of a complex number (function template) |
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| returns the phase angle (function template) |
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| returns the squared magnitude (function template) |
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| returns the complex conjugate (function template) |
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(C++11) | returns the projection onto the Riemann sphere (function template) |
| constructs a complex number from magnitude and phase angle (function template) |
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Exponential functions |
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| complex base e exponential (function template) |
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| complex natural logarithm with the branch cuts along the negative real axis (function template) |
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| complex common logarithm with the branch cuts along the negative real axis (function template) |
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Power functions |
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| complex power, one or both arguments may be a complex number (function template) |
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| complex square root in the range of the right half-plane (function template) |
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Trigonometric functions |
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| computes sine of a complex number (sin(z)) (function template) |
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| computes cosine of a complex number (cos(z)) (function template) |
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| computes tangent of a complex number (tan(z)) (function template) |
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(C++11) | computes arc sine of a complex number (arcsin(z)) (function template) |
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(C++11) | computes arc cosine of a complex number (arccos(z)) (function template) |
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(C++11) | computes arc tangent of a complex number (arctan(z)) (function template) |
Hyperbolic functions |
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| computes hyperbolic sine of a complex number (sh(z)) (function template) |
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| computes hyperbolic cosine of a complex number (ch(z)) (function template) |
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| computes hyperbolic tangent of a complex number (function template) |
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(C++11) | computes area hyperbolic sine of a complex number (function template) |
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(C++11) | computes area hyperbolic cosine of a complex number (function template) |
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(C++11) | computes area hyperbolic tangent of a complex number (function template) |
Literals |
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(C++14) | A std::complex literal representing pure imaginary number (function) |
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> constexpr complex<T> operator+(
const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator+(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator+(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator-(
const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator-(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator-(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator*(
const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator*(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator*(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator/(
const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator/(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator/(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator+(const complex<T>&);
template<class T> constexpr complex<T> operator-(const complex<T>&);
template<class T> constexpr bool operator==(
const complex<T>&, const complex<T>&);
template<class T> constexpr bool operator==(const complex<T>&, const T&);
template<class T> constexpr bool operator==(const T&, const complex<T>&);
template<class T> constexpr bool operator!=(const complex<T>&, const complex<T>&);
template<class T> constexpr bool operator!=(const complex<T>&, const T&);
template<class T> constexpr 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> constexpr T real(const complex<T>&);
template<class T> constexpr T imag(const complex<T>&);
template<class T> T abs(const complex<T>&);
template<class T> T arg(const complex<T>&);
template<class T> constexpr T norm(const complex<T>&);
template<class T> constexpr 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>&);
// complex literals:
inline namespace literals {
inline namespace complex_literals {
constexpr complex<long double> operator""il(long double);
constexpr complex<long double> operator""il(unsigned long long);
constexpr complex<double> operator""i(long double);
constexpr complex<double> operator""i(unsigned long long);
constexpr complex<float> operator""if(long double);
constexpr complex<float> operator""if(unsigned long long);
}
}
}Class std::complex
template<class T>
class complex {
public:
typedef T value_type;
constexpr complex(const T& re = T(), const T& im = T());
constexpr complex(const complex&);
template<class X> constexpr complex(const complex<X>&);
constexpr T real() const;
constexpr void real(T);
constexpr T imag() const;
constexpr void imag(T);
constexpr complex<T>& operator= (const T&);
constexpr complex<T>& operator+=(const T&);
constexpr complex<T>& operator-=(const T&);
constexpr complex<T>& operator*=(const T&);
constexpr complex<T>& operator/=(const T&);
constexpr complex& operator=(const complex&);
template<class X> constexpr complex<T>& operator= (const complex<X>&);
template<class X> constexpr complex<T>& operator+=(const complex<X>&);
template<class X> constexpr complex<T>& operator-=(const complex<X>&);
template<class X> constexpr complex<T>& operator*=(const complex<X>&);
template<class X> constexpr complex<T>& operator/=(const complex<X>&);
};
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() const;
constexpr void real(float);
constexpr float imag() const;
constexpr void imag(float);
constexpr complex<float>& operator= (float);
constexpr complex<float>& operator+=(float);
constexpr complex<float>& operator-=(float);
constexpr complex<float>& operator*=(float);
constexpr complex<float>& operator/=(float);
constexpr complex<float>& operator=(const complex<float>&);
template<class X> constexpr complex<float>& operator= (const complex<X>&);
template<class X> constexpr complex<float>& operator+=(const complex<X>&);
template<class X> constexpr complex<float>& operator-=(const complex<X>&);
template<class X> constexpr complex<float>& operator*=(const complex<X>&);
template<class X> constexpr 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() const;
constexpr void real(double);
constexpr double imag() const;
constexpr void imag(double);
constexpr complex<double>& operator= (double);
constexpr complex<double>& operator+=(double);
constexpr complex<double>& operator-=(double);
constexpr complex<double>& operator*=(double);
constexpr complex<double>& operator/=(double);
constexpr complex<double>& operator=(const complex<double>&);
template<class X> constexpr complex<double>& operator= (const complex<X>&);
template<class X> constexpr complex<double>& operator+=(const complex<X>&);
template<class X> constexpr complex<double>& operator-=(const complex<X>&);
template<class X> constexpr complex<double>& operator*=(const complex<X>&);
template<class X> constexpr 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() const;
constexpr void real(long double);
constexpr long double imag() const;
constexpr void imag(long double);
constexpr complex<long double>& operator=(const complex<long double>&);
constexpr complex<long double>& operator= (long double);
constexpr complex<long double>& operator+=(long double);
constexpr complex<long double>& operator-=(long double);
constexpr complex<long double>& operator*=(long double);
constexpr complex<long double>& operator/=(long double);
template<class X> constexpr complex<long double>& operator= (const complex<X>&);
template<class X> constexpr complex<long double>& operator+=(const complex<X>&);
template<class X> constexpr complex<long double>& operator-=(const complex<X>&);
template<class X> constexpr complex<long double>& operator*=(const complex<X>&);
template<class X> constexpr complex<long double>& operator/=(const complex<X>&);
};
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