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Fence-Insertion
for Structured Programs Mohammad Taheri
Spring 2020 University of Vienna
Fence-Insertion for Structured Programs Arash Pourdamghani - - PowerPoint PPT Presentation
Fence-Insertion for Structured Programs Arash Pourdamghani - - PowerPoint PPT Presentation
Fence-Insertion for Structured Programs Arash Pourdamghani Mohammad Taheri Mohsen Lesani Spring 2020 University of Vienna Developing a Distributed System! 2 Looking Deeper 357 F(x) .. 385 F(x) 3 Out of Order Execution
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Looking Deeper
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357 F(x) ……….. 385 F’(x)
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Out of Order Execution
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357 F(x) ……….. 385 F’(x) F’(x)
↓
F(x) Programmer's Expectation Runtime Execution
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Fence Insertion
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357 F(x) 385 F’(x) 500 H(x) 525 H’(x) 146 G(x) 912 G’(x)
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Our Solution
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Outline
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Problem Statement NP-Hardness Poly-time Algorithm
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CFG
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A Closer Look
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h F(x) i Some Code k G(x)
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Maintaining Correctness
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h F(x) i Some Code k F’(x)
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Fence Insertion
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h F(x) i Some Code k F’(x)
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All Constraints
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Naive Solution
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Optimization
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Outline
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Problem Statement NP-Hardness Poly-time Algorithm
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Reduction from Minimum Set Cover
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𝑉 = 𝑣1, 𝑣2, 𝑣3, 𝑣4, … , un 𝑇 = 𝑇1, 𝑇2, … , 𝑇𝑛 𝐹𝑦𝑏𝑛𝑞𝑚𝑓: 𝑇1 = 𝑣1, 𝑣2, 𝑣3 , 𝑇2 = {𝑣2, 𝑣4}
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Reduction from Minimum Set Cover
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𝑉 = 𝑣1, 𝑣2, 𝑣3, 𝑣4, … , un : Constraint Types, Straight line program with 2n instructions, Constraints with type 𝑣𝑗 𝑝𝑜 𝑤𝑗, 𝑤2𝑜−𝑗+1 , (𝑤𝑜
2, 𝑤𝑜 2 + 1):The middle edge
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Reduction from Minimum Set Cover
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𝑇 = 𝑇1, 𝑇2, … : Fence Types We could many fences of 𝑇𝑗 𝐹𝑦𝑏𝑛𝑞𝑚𝑓: 𝑇1 = 𝑣1, 𝑣2, 𝑣3 , 𝑇2 = {𝑣2, 𝑣4}
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𝑉 = 𝑣1, 𝑣2, 𝑣3, 𝑣4, … 𝑇 = {𝑇1, 𝑇2, … } Given Solution of Fence Insertion
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𝑉 = 𝑉1, 𝑉2, 𝑉3, 𝑉4, … 𝑇 = {𝑇1, 𝑇2, … } Given Solution of Minimum Set Cover
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Outline
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Problem Statement NP-Hardness Poly-time Algorithm
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P
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1- Constraint Elimination 2- Finding Diamond 3- Decomposing into Paths 4- Solving for Paths
Algorithm Overview
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Out of Order Execution!
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1- Constraint Elimination 2- Finding Diamond 3- Decomposing into Paths 4- Solving for Paths 4- Solving for Paths 2- Finding Diamond 1- Constraint Elimination 3- Decomposing into Paths
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A Simple Path
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A Simple Path
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A Simple Path
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A Simple Path
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A Simple Path
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Structured
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A(C)FG
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Finding Diamonds
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Level 0
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Level 1
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Level 2
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Branch/Merge
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Algorithm
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Algorithm
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Fence Elimination
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Passing Constraints
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Spanning Constraints
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Control Dependency Preservation
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Decomposing into simple paths
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Absorption in a Path
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Emission in a Path
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Before
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After Level 0
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After Level 1
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The End!
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Complexity
1- 𝐹 ∈ 𝑃 𝑊 2-Elimination: 𝑃 𝐷 + 𝑊 3-Finding Diamonds: 𝑃 𝑊𝑚𝑝𝑊 4-Decompsiton and Insertion: σ|𝑞| |𝐷𝑞𝑗|𝑚𝑝𝐷𝑞𝑗 + |𝑊
𝑞𝑗|
⇒Polynomial Time!
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What about loops?
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Elimination
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Transformation
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Thank you
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