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Enable fused multiply-subtract in complex mul_add #148

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@fre-hu

Fused multiply-add was added for complex numbers in #37, based on the Julia implementation:

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))))

The Julia code was later changed in JuliaLang/julia#36140 to:

muladd(z::Complex, w::Complex, x::Complex) =
    Complex(muladd(real(z), real(w), -muladd(imag(z), imag(w), -real(x))),
            muladd(real(z), imag(w),  muladd(imag(z), real(w),  imag(x))))

The reason was that LLVM could optimize the negation to use fused multiply-subtract.

I tested this in Rust with the function:

fn mul_add_new<T: Clone + Num + MulAdd<Output = T> + Neg<Output = T>>(
    this: Complex<T>,
    other: Complex<T>,
    add: Complex<T>,
) -> Complex<T> {
    let re = this.re.clone().mul_add(
        other.re.clone(),
        -this.im.clone().mul_add(other.im.clone(), -add.re),
    );
    let im = this.re.mul_add(other.im, this.im.mul_add(other.re, add.im));
    Complex::new(re, im)
}

When compiling with fma enabled in release mode, it is optimized in the same way to use fused multiply-subtract.

A potential drawback is that it requires an additional Neg bound. It is not possible to change the negation to subtraction from zero, since the optimization no longer works.

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