In my last article, I posted a function for calculating one partition of a larger matrix. THe function looked like this

void partial(k, i, g, M, f){ 
        for (m=0; m < n; m++){ 
            j = m * k;
            g[i] = g[i] + M[i][j] * f[i];
        }
}

This is actually wrong. Lets look where I messed up. It was all the way back in the equation.

The equation I had looked something like this (not going to use inkscape to do the math this time)

g[i] = sum m=1..n of A[i,j]f[j]
     

When I divided it up, I fell victim to the 1-based array that I had and simply calculated j by multiplying m*k. This is wrong. If we think of it as a base 4 number, we want k to be the 4’s column (and larger) and m to be the ones column. In function form:

j=k*4+m

However, this implies that m goes from 0 to (n-1)/4.

Thus the partial function should look like this:

void partial(k, i, g, M, f){ 
        for (m=0; m < n; m++){ 
            j = k * n + m;
            g[i] = g[i] + M[i][j] * f[i];
        }
}

With that corrected, we can try to implement it in ARM64 assembly.