Improve spectralnorm

[TeXitoi]

The fn A() is not autovectorized, and then simd are not used anywhere (as it can be seen in the generated ASM). I think writing something like fn Ax2(i: u64x2, j: u64x2) -> f64x2 and use it where we use A() should do the trick.

[llogiq]

Could we use the simd crate? It's not tested on stable AFAIK, but it might work on beta, at least.

[TeXitoi]

The simd crate is used on the rust repo. You can contribute here, but it'll be merged here when stable will support simd (or a couple of days before).

This issue is about writing the code such that llvm optimizes with simd without using the simd crate.

[llogiq]

Ah, I see. Do you mean something like the following?

#[allow(non_camel_case_types)]
#[derive(Debug)]
struct u64x2(u64, u64);
impl std::ops::Add for u64x2 {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        u64x2(self.0 + rhs.0, self.1 + rhs.1)
    }
}
impl std::ops::Div for u64x2 {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        u64x2(self.0 / rhs.0, self.1 / rhs.1)
    }
}

fn Ax2(i: u64x2, j: u64x2) -> f64x2 {
    f64x2(((i.0 + j.0) * (i.0 + j.0 + 1) / 2 + i.0 + 1) as f64,
           ((i.1 + j.1) * (i.1 + j.1 + 1) / 2 + i.1 + 1) as f64)
}

I don't see any advantage to that in a minimal test setup (look at the assembly output). Maybe within a loop?

[llogiq]

Also if I try to keep the operations within x2 representations, the assembly stays the same: http://is.gd/65q7NN

[TeXitoi]

It seems different in release mode.

[TeXitoi]

And yes, I was thinking of

fn ax2(i: u64x2, j: u64x2) -> f64x2 {
    ((i + j) * (i + j + u64x2(1, 1)) / u64x2(2, 2) + i + u64x2(1, 1)).into()

[llogiq]

Yeah, I just diffed the assembly versions. They are different, although I'm not sure if the vectorized version is actually faster. Guess there's only one way to find out... 😄