artdag: cost-based scheduling — critical path + makespan + speedup + 13 tests

cost.sx: injected cost-fn keeps media costs opaque. critical-path = longest
weighted path (= unlimited-worker makespan); makespan sums each batch's slowest
node (full plan == critical path, serial == total-work); speedup = work/makespan.
cost 13/13, total 115/115.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lib/artdag/cost.sx

@@ -0,0 +1,66 @@
+; lib/artdag/cost.sx — cost model for the scheduler: per-node weights, critical
+; path (min makespan with unlimited parallelism), plan makespan under batching/cap,
+; total serial work, and the resulting speedup. Costs come from an injected
+; cost-fn (op params) -> number so media-op costs stay opaque. Depends on dag.sx.
+
+(define artdag/const-cost (fn (op params) 1))
+
+(define
+  artdag/op-cost
+  (fn
+    (table)
+    (fn (op params) (if (has-key? table op) (get table op) 1))))
+
+(define
+  artdag/-node-cost
+  (fn
+    (dag cost-fn id)
+    (let
+      ((n (artdag/dag-get dag id)))
+      (cost-fn (artdag/node-op n) (artdag/node-params n)))))
+
+(define
+  artdag/-max
+  (fn (xs) (reduce (fn (mx x) (if (> x mx) x mx)) 0 xs)))
+
+; longest weighted path through the dag = makespan with unlimited workers.
+(define
+  artdag/critical-path
+  (fn
+    (dag cost-fn)
+    (let
+      ((ft (reduce (fn (m id) (let ((maxdep (artdag/-max (map (fn (d) (get m d)) (artdag/node-inputs (artdag/dag-get dag id)))))) (assoc m id (+ (artdag/-node-cost dag cost-fn id) maxdep)))) {} (artdag/dag-order dag))))
+      (artdag/-max (map (fn (id) (get ft id)) (keys ft))))))
+
+; estimated wall-clock for a plan: each batch runs in parallel (costs its
+; slowest node), batches run in sequence.
+(define
+  artdag/makespan
+  (fn
+    (dag plan cost-fn)
+    (reduce
+      (fn
+        (total batch)
+        (+
+          total
+          (artdag/-max
+            (map (fn (id) (artdag/-node-cost dag cost-fn id)) batch))))
+      0
+      plan)))
+
+; total serial work = sum of all node costs.
+(define
+  artdag/total-work
+  (fn
+    (dag cost-fn)
+    (reduce
+      (fn (s id) (+ s (artdag/-node-cost dag cost-fn id)))
+      0
+      (keys (artdag/dag-nodes dag)))))
+
+; speedup of a plan vs running everything serially.
+(define
+  artdag/speedup
+  (fn
+    (dag plan cost-fn)
+    (/ (artdag/total-work dag cost-fn) (artdag/makespan dag plan cost-fn))))