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

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

Contents

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 Defect reports
• 7 See also

[edit] Parameters

[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

#include #include   int main() { std::cout << "Square root of -4 is " << std::sqrt(std::complex(-4.0, 0.0)) << '\n' << "Square root of (-4,-0) is " << std::sqrt(std::complex(-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.

[edit] See also