std::sqrt(std::complex)
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Defined in header
<complex>
template< class T >
std::complex <T> sqrt( const std::complex <T>& z );
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.
Contents
[edit] Parameters
z
-
complex number to take the square root of
[edit] 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).
[edit] 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)
[edit] Notes
The semantics of this function are intended to be consistent with the C function csqrt.
[edit] Example
Run this code
#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)
[edit] 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 |
[edit] See also
C documentation for csqrt