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std::sqrt(std::complex)(3) | C++ Standard Libary | std::sqrt(std::complex)(3) |
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.
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)
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 erroneous requirement
imaginary parts removed
See also¶
pow(std::complex) complex power, one or both arguments may be a
complex number
(function template)
sqrt computes square root (\(\small{\sqrt{x} }\)
sqrtf √
sqrtl x)
(C++11) (function)
(C++11)
sqrt(std::valarray) applies the function std::sqrt to each element of
valarray
(function template)
2022.07.31 | http://cppreference.com |