Standard library header <complex>

 

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Technical Specifications

 

Standard Library header files

Language Support
<cstddef> <limits> <climits> <cfloat> <cstdint> <new> <typeinfo> <exception> <ciso646>	<initializer_list> <csignal> <csetjmp> <cstdalign> <cstdarg> <cstdbool> <cstdlib> <ctime>
Diagnostics
<stdexcept> <cassert>	<cerrno> <system_error>
General utilities
<utility> <tuple> <bitset> <memory> <cstdlib> <cstring> <functional>	<type_traits> <ratio> <chrono> <ctime> <scoped_allocator> <typeindex>
Strings
<string> <cctype> <cwctype> <cstring>	<cwchar> <cstdlib> <cuchar>
Localization
<locale> <codecvt> <clocale>

Containers
<array> <deque> <forward_list> <list> <vector>	<map> <set> <unordered_map> <unordered_set> <queue> <stack>
Iterators
<iterator>
Algorithms
<algorithm>	<cstdlib>
Numerics
<cfenv> <complex> <random> <valarray>	<numeric> <cmath> <ctgmath> <cstdlib>
Input/Output
<iosfwd> <iostream> <ios> <streambuf> <istream> <ostream>	<iomanip> <sstream> <fstream> <cstdio> <cinttypes>
Regular expressions
<regex>
Thread support
<thread> <mutex> <atomic>	<shared_mutex> <condition_variable> <future>

 

This header is part of the numeric library.

Classes

complex	a complex number type (class template)
complex<float>complex<double>complex<long double>	a complex number type (class template specialization)

Functions

Operations
operator+operator-	applies unary operators to complex numbers (function template)
operator+operator-operator*operator/	performs complex number arithmetics on two complex values or a complex and a scalar (function template)
operator==operator!=	compares two complex numbers or a complex and a scalar (function template)
operator<<operator>>	serializes and deserializes a complex number (function template)
real	returns the real component (function template)
imag	returns the imaginary component (function template)
abs(std::complex)	returns the magnitude of a complex number (function template)
arg	returns the phase angle (function template)
norm	returns the squared magnitude (function template)
conj	returns the complex conjugate (function template)
proj (C++11)	returns the projection onto the Riemann sphere (function template)
polar	constructs a complex number from magnitude and phase angle (function template)
Exponential functions
exp(std::complex)	complex base e exponential (function template)
log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
log10(std::complex)	complex common logarithm with the branch cuts along the negative real axis (function template)
Power functions
pow(std::complex)	complex power, one or both arguments may be a complex number (function template)
sqrt(std::complex)	complex square root in the range of the right half-plane (function template)
Trigonometric functions
sin(std::complex)	computes sine of a complex number (sin(z)) (function template)
cos(std::complex)	computes cosine of a complex number (cos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (tan(z)) (function template)
asin(std::complex) (C++11)	computes arc sine of a complex number (arcsin(z)) (function template)
acos(std::complex) (C++11)	computes arc cosine of a complex number (arccos(z)) (function template)
atan(std::complex) (C++11)	computes arc tangent of a complex number (arctan(z)) (function template)
Hyperbolic functions
sinh(std::complex)	computes hyperbolic sine of a complex number (sh(z)) (function template)
cosh(std::complex)	computes hyperbolic cosine of a complex number (ch(z)) (function template)
tanh(std::complex)	computes hyperbolic tangent of a complex number (function template)
asinh(std::complex) (C++11)	computes area hyperbolic sine of a complex number (function template)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (function template)
atanh(std::complex) (C++11)	computes area hyperbolic tangent of a complex number (function template)

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>&);
 
 
}

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>&);   
 
};

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>&);
 
};