Partitions a systolic array into rectangular tiles.

The default strategy divides the grid into approximately equal-sized rectangular tiles. Tile size is configurable via the tile_rows: and tile_cols: options.

Why tiles?

Tiles balance granularity and locality:

• Too fine (1 PE per tile) -- excessive coordination overhead
• Too coarse (1 tile for the whole array) -- no parallelism
• Just right -- good data locality, parallel across tiles

Partitioning algorithm

Given a grid of rows x cols and tile size tr x tc:

• The grid is divided into ceil(rows/tr) x ceil(cols/tc) tiles
• Edge tiles may be smaller than tr x tc
• Each tile owns the PEs and internal links within its bounds
• A link is internal to a tile when both its from and to endpoints are coordinates within that tile
• Links crossing tile boundaries (where one endpoint is in a different tile) are not assigned to any tile; they are managed globally by the partitioned backend's BSP read/write cycle

Examples

iex> alias ExSystolic.{Array, TilePartitioner, PE.MAC}
iex> array = Array.new(rows: 4, cols: 4) |> Array.fill(MAC) |> Array.connect(:west_to_east) |> Array.connect(:north_to_south)
iex> tiles = TilePartitioner.partition(array, tile_rows: 2, tile_cols: 2)
iex> length(tiles)
4
iex> hd(tiles).id
{0, 0}