operator+,-,*,/ (std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex
C++
Numerics library
std::complex
(1)
template < class T >

std::complex <T> operator+ ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator+ ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(2)
template < class T >

std::complex <T> operator+ ( const std::complex <T> & lhs,

const T& rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator+ ( const std::complex <T> & lhs,

const T& rhs ) ;
(since C++20)
(3)
template < class T >

std::complex <T> operator+ ( const T& lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator+ ( const T& lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(4)
template < class T >

std::complex <T> operator- ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator- ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(5)
template < class T >

std::complex <T> operator- ( const std::complex <T> & lhs,

const T& rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator- ( const std::complex <T> & lhs,

const T& rhs ) ;
(since C++20)
(6)
template < class T >

std::complex <T> operator- ( const T& lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator- ( const T& lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(7)
template < class T >

std::complex <T> operator* ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator* ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(8)
template < class T >

std::complex <T> operator* ( const std::complex <T> & lhs,

const T& rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator* ( const std::complex <T> & lhs,

const T& rhs ) ;
(since C++20)
(9)
template < class T >

std::complex <T> operator* ( const T& lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator* ( const T& lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(10)
template < class T >

std::complex <T> operator/ ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator/ ( const std::complex <T> & lhs,

const std::complex <T> & rhs ) ;
(since C++20)
(11)
template < class T >

std::complex <T> operator/ ( const std::complex <T> & lhs,

const T& rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator/ ( const std::complex <T> & lhs,

const T& rhs ) ;
(since C++20)
(12)
template < class T >

std::complex <T> operator/ ( const T& lhs,

const std::complex <T> & rhs ) ;
(until C++20)
template < class T >

constexpr std::complex <T> operator/ ( const T& lhs,

const std::complex <T> & rhs ) ;
(since C++20)

Implements the binary operators for complex arithmetic and for mixed complex/scalar arithmetic. Scalar arguments are treated as complex numbers with the real part equal to the argument and the imaginary part set to zero.

1-3) Returns the sum of its arguments.
4-6) Returns the result of subtracting rhs from lhs.
7-9) Multiplies its arguments.
10-12) Divides lhs by rhs.

Parameters

lhs, rhs - the arguments: either both complex numbers or one complex and one scalar of matching type (float, double, long double

Return value

1-3) std::complex <T> (lhs) + =
4-6) std::complex <T> (lhs) - =
7-9) std::complex <T> (lhs) * =
10-12) std::complex <T> (lhs) / =

Notes

Because template argument deduction

The GCC flag "-fcx-limited-range" (included by "-ffast-math") changes the behavior of complex multiply/division by removing checks for floating point edge cases. This impacts loop vectorization.

Example

Run this code
#include <complex>
#include <iostream>
 
int main()
{
    std::complex<double> c2(2.0, 0.0);
    std::complex<double> ci(0.0, 1.0);
 
    std::cout << ci << " + " << c2 << " = " << ci + c2 << '\n'
              << ci << " * " << ci << " = " << ci * ci << '\n'
              << ci << " + " << c2 << " / " << ci << " = " << ci + c2 / ci << '\n'
              << 1  << " / " << ci << " = " << 1.0 / ci << '\n';
 
//    std::cout << 1.0f / ci; // compile error
//    std::cout << 1 / ci; // compile error
}

Output: 

(0,1) + (2,0) = (2,1)
(0,1) * (0,1) = (-1,0)
(0,1) + (2,0) / (0,1) = (0,-1)
1 / (0,1) = (0,-1)

See also

 compound assignment of two complex numbers or a complex and a scalar
(public member function)
applies unary operators to complex numbers
(function template)
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