std::norm(std::complex)

Since C++20

Header: <complex>

  1. Returns the squared magnitude of the complex number z.

# Declarations

template< class T >
T norm( const std::complex<T>& z );

(until C++20)

template< class T >
constexpr T norm( const std::complex<T>& z );

(since C++20)

Additional overloads (since C++11)

float norm( float f );
double norm( double f );
long double norm( long double f );

(until C++20)

constexpr float norm( float f );
constexpr double norm( double f );
constexpr long double norm( long double f );

(since C++20) (until C++23)

template< class FloatingPoint >
constexpr FloatingPoint norm( FloatingPoint f );

(since C++23)

template< class Integer >
double norm( Integer i );

(until C++20)

template< class Integer >
constexpr double norm( Integer i );

(since C++20)

# Parameters

# Notes

The norm calculated by this function is also known as field norm or absolute square.

The Euclidean norm of a complex number is provided by std::abs, which is more costly to compute. In some situations, it may be replaced by std::norm, for example, if abs(z1) > abs(z2) then norm(z1) > norm(z2).

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their argument num:

# Example

#include <cassert>
#include <complex>
#include <iostream>
 
int main()
{
    constexpr std::complex<double> z {3.0, 4.0};
    static_assert(std::norm(z) == (z.real() * z.real() + z.imag() * z.imag()));
    static_assert(std::norm(z) == (z * std::conj(z)));
           assert(std::norm(z) == (std::abs(z) * std::abs(z)));
    std::cout << "std::norm(" << z << ") = " << std::norm(z) << '\n';
}

# See also