--negotiate: PathFinder rounds on the empty board before routing

Every connection is routed N times on the empty board, where routes may
share cells at a price that doubles each round for every other net on a
cell, and a cell that stays shared gains history. The real routing then
pays that history on free cells, so the first routes stop taking the space
later routes (a fine-pitch part's escapes) have no way round. Off by
default.

The old history term never steered: it only accrued at rip-up fights,
after the first routes had claimed the contested space, and routed
connections are never revisited in later passes.

src/freeroute/route/grid_router.py

@@ -180,6 +180,7 @@ class GridRouter:
         seed: int | None = None,
         route_first: frozenset | None = None,
         access_cost: float = 0.0,
+        negotiate: int = 0,
         rollback: bool = True,
         net_widths: dict[int, int] | None = None,
         via_drill: int | None = None,
@@ -191,6 +192,15 @@ class GridRouter:
         # and the clearance around both) cost other nets this much extra, so
         # they route round a fine-pitch pin's way out instead of sealing it.
         self.access_cost = max(float(access_cost), 0.0)
+        # Negotiated congestion (PathFinder): before the real routing, every
+        # connection is routed this many times on the empty board, where routes
+        # may overlap at a price that grows where they compete. The cells that
+        # stay contested keep a history cost the real routing pays, so the first
+        # routes leave room around the places later routes have no way round.
+        self.negotiate = max(int(negotiate), 0)
+        self._history: dict[Node, float] = {}
+        self._present: dict[Node, dict[int, int]] | None = None
+        self._present_cost = 0.0
         self._doorways: dict[Node, list[tuple[int, int]]] = {}
         self._pending: dict[int, int] = {}
         # Rip-up as a transaction: the connections a rip-up route crosses are
@@ -767,6 +777,8 @@ class GridRouter:
                         continue
                     if self._doorways:
                         enter += self._access(nxt, net_no)
+                    if self._history or self._present is not None:
+                        enter += self._congestion(nxt, net_no)
                 step = 1.0 if dx == 0 or dy == 0 else math.sqrt(2)
                 self._relax(
                     current, nxt, base + step + enter, goal_cell, g_score, came_from, open_heap
@@ -779,9 +791,12 @@ class GridRouter:
                     if layer == cl:
                         continue
                     nxt = (cx, cy, layer)
-                    if g_via < g_score.get(nxt, math.inf):
+                    g_layer = g_via
+                    if self._history or self._present is not None:
+                        g_layer += self._congestion(nxt, net_no)
+                    if g_layer < g_score.get(nxt, math.inf):
                         heapq.heappush(
-                            open_heap, (g_via + self._h(nxt, goal_cell), nxt, g_via, current)
+                            open_heap, (g_layer + self._h(nxt, goal_cell), nxt, g_layer, current)
                         )
         return None
 
@@ -1359,6 +1374,74 @@ class GridRouter:
                 return self.access_cost
         return 0.0
 
+    # --- negotiated congestion --------------------------------------------
+
+    def _congestion(self, node: Node, net_no: int) -> float:
+        """History of a contested cell, plus while negotiating the price of
+        sharing it with the other nets on it now."""
+        cost = self._history.get(node, 0.0)
+        if self._present is not None:
+            users = self._present.get(node)
+            if users:
+                others = len(users) - (1 if net_no in users else 0)
+                cost += self._present_cost * others
+        return cost
+
+    def _footprint(self, path: list[Node]) -> set[Node]:
+        """The nodes a route claims: its cells and their clearance halo on
+        its layer, and every via's footprint on all layers."""
+        wire_segs, via_cells = _split_path(path)
+        halo = [(0, 0), *self._halo_offsets]
+        nodes: set[Node] = set()
+        for layer, cells in wire_segs:
+            for cx, cy in cells:
+                for dx, dy in halo:
+                    nodes.add((cx + dx, cy + dy, layer))
+        for cell in via_cells:
+            for c in self._via_cells(cell):
+                for layer in self.layers:
+                    nodes.add((*c, layer))
+        return nodes
+
+    def _negotiate(self, order: list[_Connection], conns: list[_Connection]) -> None:
+        """Route every connection on the empty board ``self.negotiate`` times,
+        letting routes share cells at a price: the number of other nets on a
+        cell times a factor that doubles every round, plus the cell's history,
+        which grows by one for every extra net each round it stays shared.
+        Only the history is kept; the board is left empty."""
+        present: dict[Node, dict[int, int]] = {}
+        claimed: dict[int, set[Node]] = {}
+        ends = [(c, c.a_end, c.b_end) for c in conns]
+        self._present, self._present_cost = present, 0.5
+        try:
+            for _ in range(self.negotiate):
+                for conn in order:
+                    for node in claimed.pop(conn.index, ()):
+                        users = present[node]
+                        users[conn.net_no] -= 1
+                        if not users[conn.net_no]:
+                            del users[conn.net_no]
+                    path = self._search(conn, allow_ripup=False, conns=conns)
+                    if path is None:
+                        continue
+                    nodes = self._footprint(path)
+                    claimed[conn.index] = nodes
+                    for node in nodes:
+                        users = present.setdefault(node, {})
+                        users[conn.net_no] = users.get(conn.net_no, 0) + 1
+                shared = 0
+                for node, users in present.items():
+                    if len(users) > 1:
+                        shared += 1
+                        self._history[node] = self._history.get(node, 0.0) + len(users) - 1
+                if not shared:
+                    break
+                self._present_cost *= 2
+        finally:
+            self._present = None
+            for conn, a_end, b_end in ends:  # the search picks ends; undo that
+                conn.a_end, conn.b_end = a_end, b_end
+
     # --- passes -------------------------------------------------------------
 
     def route(self) -> RouteResult:
@@ -1382,6 +1465,8 @@ class GridRouter:
         if self.route_first:
             # stable: the promoted keep their order among themselves, as do the rest
             order.sort(key=lambda c: (c.net_no, *_ends_of(c)) not in self.route_first)
+        if self.negotiate:
+            self._negotiate(order, conns)
         for _ in range(passes):
             changed = False
             for conn in order:
@@ -1778,6 +1863,7 @@ def route_board(
     seed: int | None = None,
     route_first: frozenset | None = None,
     access_cost: float = 0.0,
+    negotiate: int = 0,
     rollback: bool = True,
     net_widths: dict[int, int] | None = None,
     via_drill: int | None = None,
@@ -1800,6 +1886,7 @@ def route_board(
         seed=seed,
         route_first=route_first,
         access_cost=access_cost,
+        negotiate=negotiate,
         rollback=rollback,
         net_widths=net_widths,
         via_drill=via_drill,