std::proj(std::complex)

Since C++11

Header: <complex>

  1. Returns the projection of the complex number z onto the Riemann sphere.

# Declarations

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

(since C++11)

Additional overloads (since C++11)

std::complex<float> proj( float f );
std::complex<double> proj( double f );
std::complex<long double> proj( long double f );

(until C++23)

template< class FloatingPoint >
std::complex<FloatingPoint> proj( FloatingPoint f );

(since C++23)

template< class Integer >
std::complex<double> proj( Integer i );

# Parameters

# Notes

The proj function helps model the Riemann sphere by mapping all infinities to one (give or take the sign of the imaginary zero), and should be used just before any operation, especially comparisons, that might give spurious results for any of the other infinities.

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 <complex>
#include <iostream>
 
int main()
{
    std::complex<double> c1(1, 2);
    std::cout << "proj" << c1 << " = " << std::proj(c1) << '\n';
 
    std::complex<double> c2(INFINITY, -1);
    std::cout << "proj" << c2 << " = " << std::proj(c2) << '\n';
 
    std::complex<double> c3(0, -INFINITY);
    std::cout << "proj" << c3 << " = " << std::proj(c3) << '\n';
}

# See also