std::sqrt(std::complex)
From cppreference.com
| Defined in header <complex>
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| template< class T > std::complex<T> sqrt( const std::complex<T>& z ); |
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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.
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)
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 |
See also
| complex power, one or both arguments may be a complex number (function template) | |
| (C++11)(C++11) |
computes square root (√x) (function) |
| applies the function std::sqrt to each element of valarray (function template) | |
| C documentation for csqrt
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