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Near Optimal Work-Stealing Tree for Highly Irregular Data-Parallel Workloads Aleksandar Prokopec Martin Odersky 1

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Near Optimal Work-Stealing Tree for Highly Irregular Data-Parallel Workloads Aleksandar Prokopec Martin Odersky Irregular Data-Parallel 2

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Uniform workload (0 until 10000000) reduce (+) 3

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Uniform workload (0 until 10000000) reduce (+) sum = sum + x 4

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Uniform workload (0 until 10000000) reduce (+) sum = sum + x … N cycles 5

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Baseline workload for (0 until 10000000) {} … N cycles 6

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Irregular workload 7

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N cycles 8

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Irregular workload for { x <- 0 until width y <- 0 until height } image(x, y) = compute(x, y) N cycles 9

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Irregular workload for { x <- 0 until width y <- 0 until height } image(x, y) = compute(x, y) image(x, y) = compute(x, y) N cycles 10

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Workload function workload(n) – work spent on element n after the data-parallel operation completed 11

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Workload function Could be… Runtime value dependent for { x <- 0 until width y <- 0 until height } img(x, y) = compute(x, y) workload(n) – work spent on element n after the data-parallel operation completed 12

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Workload function Could be… Execution-schedule dependent for (n <- nodes) n.neighbours += new Node workload(n) – work spent on element n after the data-parallel operation completed 13

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Workload function Could be… Totally random for ((x, y) <- img.indices) img(x, y) = sample( x + random(), y + random() ) workload(n) – work spent on element n after the data-parallel operation completed 14

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Data-parallel scheduler Assign loop elements to workers without knowledge about the workload function. 15

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Data-parallel scheduler 1. Linear speedup for the baseline workload Assign loop elements to workers without knowledge about the workload function. 16

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Data-parallel scheduler 1. Linear speedup for the baseline workload 2. Optimal speedup for irregular workloads Assign loop elements to workers without knowledge about the workload function. 17

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Static batching Decides on the worker-element assignment before the data-parallel operation begins. N cycles 18

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Static batching Decides on the worker-element assignment before the data-parallel operation begins. No knowledge → divide uniformly. Not optimal for even mildly irregular workloads. N cycles 19

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Fixed-size batching Workload-driven – decides during execution. N cycles progress 20

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Fixed-size batching Workload-driven – decides during execution. N cycles 0 21

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Fixed-size batching Workload-driven – decides during execution. N cycles 2 T0: CAS T0 22

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Fixed-size batching Workload-driven – decides during execution. N cycles 4 T1: CAS T0T1 23

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Fixed-size batching Workload-driven – decides during execution. N cycles 6 T0: CAS T0T1 24

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Fixed-size batching Workload-driven – decides during execution. N cycles 8 T0: CAS T0T1 25

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Fixed-size batching Workload-driven – decides during execution. N cycles 10 T0: CAS T0T1 26

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Fixed-size batching Workload-driven – decides during execution. N cycles 12 T0: CAS T0T1 27

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Fixed-size batching Workload-driven – decides during execution. N cycles progress Pros: lightweight Cons: minimum batch size, contention 28

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Fixed-size batching - contention 29

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Factoring, GSS, TS Batch size varies. N cycles progress Pros: lightweight Cons: contention 30

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Task-based work-stealing N cycles 0..2 2..44..8 8..16 31

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Task-based work-stealing N cycles 0..2 2..44..8 8..16 2..4 4..8 8..16 T0 T1 0..2 32

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Task-based work-stealing N cycles 0..2 2..44..8 8..16 2..4 4..8 8..16 T0 T1 0..2 steal – a rare event 33

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Task-based work-stealing N cycles 0..2 2..44..8 8..16 2..4 4..8 8..16 T0 T1 10..12 12..16 8..100..2 34

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Task-based work-stealing Pros: can be adaptive - uses stealing information Cons: heavyweight - minimum batch size much larger N cycles 0..2 2..44..8 8..16 2..4 4..8 8..16 T0 T1 10..12 12..16 0..28..10 35

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Task-based work-stealing N cycles 0..2 2..44..8 8..16 Cannot be stolen after T0 starts processing it 36

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Work-stealing tree 00T0N owned 37

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Work-stealing tree 00T0N050T0N owned T0: CAS 38

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Work-stealing tree 00T0N050T0N0N N … owned completed T0: CAS What about stealing? 39

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Work-stealing tree 00T0N050T0N0N N … owned completed 0-51T0N T0: CAS T1: CAS stolen T0: CAS 40

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Work-stealing tree 050T0N0N N … ownedcompleted 0-51T0N T0: CAS stolen T0: CAS 00T0N owned T1: CAS 41

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Work-stealing tree 050T0N0N N … ownedcompleted 0-51T0N T0: CAS stolen 0-51T0N expanded 50 T0M MMT1N T0: CAS 00T0N owned M = (50 + N) / 2 42

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Work-stealing tree 050T0N0N N … ownedcompleted 0-51T0N T0: CAS stolen 0-51T0N expanded 50 T0M MMT1N T0: CAS 00T0N owned M = (50 + N) / 2 T0 or T1: CAS 43

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Work-stealing tree 050T0N0N N … ownedcompleted 0-51T0N T0: CAS stolen 0-51T0N expanded 50 T0M MMT1N T0 or T1: CAS T0: CAS 00T0N owned M = (50 + N) / 2 44

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Work-stealing tree - contention 45

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 0-51T0100 50 T0100 75 T1100 46

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 2)if not found, terminate 0100T0100 47

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 2)if not found, terminate 3)if not owned, steal and/or expand, and descend 0-51T0N T1: CAS stolen 0-51T0N expanded 50 T0M MMT1N T1: CAS 48

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 2)if not found, terminate 3)if not owned, steal and/or expand, and descend 4)advance until node is completed or stolen 00T0N050T0N0N N … owned completed T0: CAS 49

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 2)if not found, terminate 3)if not owned, steal and/or expand, and descend 4)advance until node is completed or stolen 5)go to 1) 50

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Work-stealing tree scheduling 1)find either a non-expanded, non-completed node 2)if not found, terminate 3)if not owned, steal and/or expand, and descend 4)advance until node is completed or stolen 5)go to 1) 1)find either a non-expanded, non-completed node 51

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Choosing the node to steal Find first, in-order traversal 29 5 3 52

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Choosing the node to steal Find first, in-order traversal 29 5 3 Catastrophic – a lot of stealing, huge trees 53

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Choosing the node to steal Find first, in-order traversalFind first, random order traversal 29 5 3 29 5 3 Catastrophic – a lot of stealing, huge trees 54

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Choosing the node to steal Find first, in-order traversalFind first, random order traversal 29 5 3 29 5 3 Catastrophic – a lot of stealing, huge trees Works reasonably well. 55

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Choosing the node to steal Find first, in-order traversalFind first, random order traversalFind most elements 29 5 3 29 5 3 29 5 3 Catastrophic – a lot of stealing, huge trees Works reasonably well. Generates least nodes. Seems to be best. 56

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Comparison with fixed-size batching 57

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Comparison with fixed-size batching 58

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Comparison with task work-stealing 59

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Thank you! Questions? 60

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Finding work 61

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Other workloads 62

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