std::sqrt(std::complex) - cppreference.com

From cppreference.com


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

Computes the square root of the complex number z with a branch cut along the negative real axis.

Parameters

complex number to take the square root of

Return value

If no errors occur, returns the square root of z, in the range of the right half-plane, including the imaginary axis ([0; +∞) along the real axis and (−∞; +∞) along the imaginary axis).

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

The function is continuous onto the branch cut taking into account the sign of imaginary part
std::sqrt(std::conj(z)) == std::conj(std::sqrt(z))
If z is (±0,+0), the result is (+0,+0)
If z is (x,+∞), the result is (+∞,+∞) even if x is NaN
If z is (x,NaN), the result is (NaN,NaN) (unless x is ±∞) and FE_INVALID may be raised
If z is (-∞,y), the result is (+0,+∞) for finite positive y
If z is (+∞,y), the result is (+∞,+0) for finite positive y
If z is (-∞,NaN), the result is (NaN,∞) (sign of imaginary part unspecified)
If z is (+∞,NaN), the result is (+∞,NaN)
If z is (NaN,y), the result is (NaN,NaN) and FE_INVALID may be raised
If z is (NaN,NaN), the result is (NaN,NaN)

Notes

The semantics of this function are intended to be consistent with the C function csqrt.

Example

#include <complex>
#include <iostream>

int main()
{
    std::cout << "Square root of -4 is "
              << std::sqrt(std::complex<double>(-4.0, 0.0)) << '\n'
              << "Square root of (-4,-0) is "
              << std::sqrt(std::complex<double>(-4.0, -0.0))
              << " (the other side of the cut)\n";
}

Output:

Square root of -4 is (0,2)
Square root of (-4,-0) is (0,-2) (the other side of the cut)

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.