ALE: Memory access is likely terrible

[adcroft]

The single-column nature of ALE code makes the pattern memory access to

• 3d data is declared (i,j,k) while ALE loops are typically do j, do i, f(k=1:nk)
  • Should we extract 2d slices of data, (k,i) or (i,k) so we are not making such large sparse strides through memory?
  • How ugly a job is it to move i loops inside the ALE code?
• Tracers are effectively declared as (i,j,k,m) and the ALE loop is currently do j, do i, do m, f(k=1:nk) in order to re-use the regridding column data.
  • As above, should we extract (k,m,i) or (i,k,m) slices?

[adcroft]

This refactor performed no differently:

  do j = G%jsc,G%jec
    h2d(G%isc:G%iec,:) = h(G%isc:G%iec,j,:)
    dx2d(G%isc:G%iec,:) = dxInterface(G%isc:G%iec,j,:)
    do m=1,ntr ! For each tracer
     q2d(G%isc:G%iec,:) = Reg%Tr(m)%t(G%isc:G%iec,j,:)
     do i = G%isc,G%iec
        if (G%mask2dT(i,j)>0.) then
          h1(:) = h2d(i,:)
          dx(:) = dx2d(i,:)
          call remapping_core(CS, nz, h1, q2d(i,:), nz, dx, u_column)
          q2d(i,:) = u_column(:)
        endif
      enddo ! i
      Reg%Tr(m)%t(G%isc:G%iec,j,:) = q2d(G%isc:G%iec,:)
    enddo ! m
  enddo ! j

relative to the original:

  do j = G%jsc,G%jec
    do i = G%isc,G%iec
      if (G%mask2dT(i,j)>0.) then
        h1(:) = h(i,j,:)
        dx(:) = dxInterface(i,j,:)
        do m=1,ntr ! For each tracer
          call remapping_core(CS, nz, h1, Reg%Tr(m)%t(i,j,:), nz, dx, u_column)
          Reg%Tr(m)%t(i,j,:) = u_column(:)
        enddo ! m
      endif
    enddo ! i
  enddo ! j

when tracers are just T, S and age, even after hand-fusing the j -loops between tracers and u, v (to re-use the h2d and dx2d variables. I also tried transposing the (i,k) of h2d and dx2d. Since the original is much easier to read, we'll keep it unless the above makes a difference for lots of tracers.