std::sqrt(std::complex) (3) - Linux Man Pages

std::sqrt(std::complex): std::sqrt(std::complex)

NAME

std::sqrt(std::complex) - std::sqrt(std::complex)

Synopsis


Defined in header <complex>
template< class T >
complex<T> sqrt( const complex<T>& z );


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

Parameters


z - 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.


Defect reports


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


DR Applied to Behavior as published Correct behavior
LWG_2597 C++98 specification mishandles signed zero imaginary parts erroneous requirement removed

Example


// Run this code


  #include <iostream>
  #include <complex>


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

Output:


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

See also


                    complex power, one or both arguments may be a complex number
pow(std::complex) (function template)


sqrt
sqrtf computes square root (
sqrtl √
                    x)
                    (function)
(C++11)
(C++11)
                    applies the function std::sqrt to each element of valarray
sqrt(std::valarray) (function template)