Function complex_sqrt

fn complex_sqrt<F: FixedPointNumber>(x: &F) -> Option<Complex<F>>
where
    F::Inner: From<u8>,

Computes the principal square root of a fixed-point number, returning a Complex result.

Unlike fixed_sqrt, this function is defined for all inputs including negative numbers. For negative inputs, the result is a purely imaginary number representing the principal square root in the complex plane.

Internally delegates to fixed_sqrt_newton for the real square root computation, which is only valid for non-negative inputs. The sign of x is handled here before dispatching.

Domain

Defined for all fixed-point values. Never returns None.

Arguments

• x - The fixed-point number to compute the complex square root of.

Returns

Input	Result
x > 0	sqrt(x) + 0i
x = 0	0 + 0i
x < 0	`0 + sqrt(

Note

On unsigned types (FixedU64, FixedU128), negative values are not representable, so the imaginary branch is never reached. Only the real and zero branches apply.

Examples

// Positive input - purely real result
let x = FixedI64::saturating_from_integer(4);
assert_eq!(complex_sqrt(&x), Some(Complex { real: FixedI64::saturating_from_integer(2), imgn: FixedI64::zero() }));

// Negative input - purely imaginary result
let x = FixedI64::saturating_from_integer(-4);
assert_eq!(complex_sqrt(&x), Some(Complex { real: FixedI64::zero(), imgn: FixedI64::saturating_from_integer(2) }));