Behaviour for systolic array execution backends.

A backend implements the tick execution strategy. All backends must produce identical results for the same inputs -- this is the determinism contract.

Available backends

Tick contract (BSP)

Every backend must implement the following six steps in order, every tick. Skipping or reordering breaks determinism.

1. INJECT -- push pending external input streams into matching boundary link buffers. Defer when target is full or absent.
2. READ -- drain every link buffer once into a {coord, port} => value map. Missing links yield :empty.
3. EXECUTE -- invoke PE.step/4 for every PE with the read inputs. PEs may execute in parallel iff they cannot observe each other's writes within the same tick (BSP barrier).
4. COLLECT -- gather all PE outputs into a coord => outputs map.
5. WRITE -- for each output port that has a matching link from-endpoint, write the value to that link's buffer. Drop otherwise (e.g. the conventional :result port).
6. RECORD -- if tracing is enabled, record one Trace.Event per PE per tick. Events must be recorded in deterministic order (sorted by {tick, coord}).

Helpers in ExSystolic.Backend.LinkOps implement steps 1, 2, and 5 consistently across backends; you should always use them rather than re-implementing the link bookkeeping.

Selecting a backend

# Default (interpreted)
Clock.run(array, ticks: 10)

# Explicit
Clock.run(array, ticks: 10, backend: :interpreted)
Clock.run(array, ticks: 10, backend: :partitioned, tile_rows: 4, tile_cols: 4)

# Partitioned with Poolex pool
Clock.run(array, ticks: 10, backend: :partitioned, dispatch: :pool)

Implementing a custom backend

A backend must implement run/2 which takes an ExSystolic.Array.t() and a keyword list of options, and returns the final array state.

defmodule MyBackend do
  @behaviour ExSystolic.Backend

  @impl true
  def run(array, opts) do
    ticks = Keyword.fetch!(opts, :ticks)
    # ... execute ticks following the BSP contract ...
  end
end

Run your backend through the conformance suite at ExSystolic.Backend.ConformanceTest to verify it preserves determinism.