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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>
118 lines
2.5 KiB
Plaintext
118 lines
2.5 KiB
Plaintext
; cost model: critical path, makespan under cap, total work, speedup.
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(define
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cost-CHAIN
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(artdag/build
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(list
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(list "a" "in" (list) {})
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(list "b" "f" (list "a") {})
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(list "c" "f" (list "b") {})
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(list "d" "f" (list "c") {}))))
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(define
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cost-DIA
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(artdag/build
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(list
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(list "a" "in" (list) {})
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(list "b" "f" (list "a") {})
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(list "c" "g" (list "a") {})
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(list "d" "add" (list "b" "c") {} true))))
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(define cost-W (artdag/op-cost {:f 2 :add 5}))
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; ---- unit cost ----
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(artdag-test
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"critical path: chain is its length"
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(artdag/critical-path cost-CHAIN artdag/const-cost)
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4)
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(artdag-test
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"critical path: diamond longest path"
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(artdag/critical-path cost-DIA artdag/const-cost)
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3)
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(artdag-test
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"total work: unit cost equals node count"
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(artdag/total-work cost-DIA artdag/const-cost)
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4)
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(artdag-test
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"single node critical path is its cost"
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(artdag/critical-path
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(artdag/build (list (list "a" "in" (list) {})))
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artdag/const-cost)
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1)
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; ---- makespan vs cap ----
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(artdag-test
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"full plan makespan equals critical path"
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(artdag/makespan
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cost-DIA
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(artdag/plan cost-DIA 0)
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artdag/const-cost)
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(artdag/critical-path cost-DIA artdag/const-cost))
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(artdag-test
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"serial plan makespan equals total work"
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(artdag/makespan
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cost-DIA
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(artdag/plan cost-DIA 1)
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artdag/const-cost)
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(artdag/total-work cost-DIA artdag/const-cost))
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(artdag-test
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"capped makespan is never below the critical path"
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(>=
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(artdag/makespan
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cost-DIA
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(artdag/plan cost-DIA 1)
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artdag/const-cost)
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(artdag/critical-path cost-DIA artdag/const-cost))
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true)
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; ---- weighted costs ----
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(artdag-test
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"weighted critical path follows heavy ops"
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(artdag/critical-path cost-DIA cost-W)
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8)
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(artdag-test
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"weighted total work sums all node costs"
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(artdag/total-work cost-DIA cost-W)
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9)
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(artdag-test
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"op-cost defaults unknown ops to 1"
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(artdag/total-work
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(artdag/build (list (list "a" "in" (list) {})))
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cost-W)
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1)
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(artdag-test
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"weighted full-plan makespan equals critical path"
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(artdag/makespan cost-DIA (artdag/plan cost-DIA 0) cost-W)
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(artdag/critical-path cost-DIA cost-W))
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; ---- speedup ----
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(artdag-test
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"serial plan has no speedup"
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(artdag/speedup
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cost-DIA
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(artdag/plan cost-DIA 1)
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artdag/const-cost)
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1)
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(artdag-test
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"parallel plan beats serial"
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(>
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(artdag/speedup
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cost-DIA
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(artdag/plan cost-DIA 0)
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artdag/const-cost)
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1)
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true)
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