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

Notes

Because template argument deduction does not consider implicit conversions, these operators cannot be used for mixed integer/complex arithmetic. In all cases, the scalar must have the same type as the underlying type of the complex number.

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

#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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