Add MulAdd

[benruijl]

MulAdd provides a way to reduce rounding errors when adding and multiplying.

Here is the related Julia code:

muladd(z::Complex, w::Complex, x::Complex) =
    Complex(muladd(real(z), real(w), real(x)) - imag(z)*imag(w), # TODO: use mulsub given #15985
            muladd(real(z), imag(w), muladd(imag(z), real(w), imag(x))))

[cuviper]

I expected your link would be to num-traits' trait MulAdd, and there is also MulAddAssign. I would welcome implementations of these traits for Complex<T>, e.g. where T: MulAdd.

[Schultzer]

@cuviper I would like to impl this but I think we should make the trait work on no_std first #102

[cuviper]

These are independent concerns. The traits do exist in no_std, so you can write a generic implementation here regardless of the specific underlying types.

[Schultzer]

I'm kinda stuck on the impl

I get this error

error[E0369]: binary operation `-` cannot be applied to type `<T as traits::MulAdd>::Output`

I'm not really sure what I'm doing wrong because I expect that MulAdd will return T but it returns <T as traits::MulAdd>::Output.

impl<T: Clone + Num + MulAdd> MulAdd<Complex<T>> for Complex<T> {
    type Output = Complex<T>;

    #[inline]
    fn mul_add(self, other: Complex<T>, x: Complex<T>) -> Complex<T> {
        let re = self.re.clone().mul_add(other.re.clone(), x.re.clone()) - self.im.clone() * other.im.clone(); // FIXME: use mulsub when available in rust
        let im = self.re.mul_add(other.im, self.im.mul_add(other.re, x.im));
        Complex::new(re, im)
    }
}

[cuviper]

Use T: MulAdd<Output = T>, otherwise the output is unconstrained.