std:: proj (std::complex)

Parameters

Return value

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 :

• If num has a standard (until C++23) floating-point type T , then std :: proj ( num ) has the same effect as std :: proj ( std:: complex < T > ( num ) ) .
• Otherwise, if num has an integer type, then std :: proj ( num ) has the same effect as std :: proj ( std:: complex < double > ( 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';
}

proj(1,2) = (1,2)
proj(inf,-1) = (inf,-0)
proj(0,-inf) = (inf,-0)

See also