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Enable fused multiply-subtract in complex mul_add #148
Description
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.
Activity
recommended impl from rust-num#148