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Information-Flow Models for Shared Memory Allon Adir Hagit Attiya Gil Shurek

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Final state: R2=2 ? Prog 1 Prog 2 load(X, R1)load(Y, R3) R2 := R1R3 := R3 + 1 R1 := 1 store(R1, Y)store(R3, X) Initial state: All=0 Program Example

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Prog 1 Prog 2 load(X, R1)load(Y, R3) R2 := R1R3 := R3 + 1 R1 := 1 store(R1, Y)store(R3, X) Initial state: All=0 Final state: Y=R1=1, X=R2=R3=2 Program Example

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Final state: Y=R1=1, X=R2=R3=2 Prog 1 Prog 2 load(X, R1)load(Y, R3) R2 := R1R3 := R3 + 1 R1 := 1 store(R1, Y)store(R3, X) Initial state: All=0 PowerPC Consistency

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Shared-Memory Semantics Capturing intricate shared-memory behaviors: Speculation Out-of-Order Execution Synchronization Granularity of Memory Accesses Without revealing micro-architecture details

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Outline What is an Architecture? What is a Computation Model? The Framework Sequential Consistency PowerPC Consistency

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What is an "Architecture"?

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Elements of an Architecture Resources Granules States Instructions Formats Operands Source/Target Addressing-Mode State Transformation

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Elements of an Architecture Program order

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Computation Model Can we reach final state s 2 by running a program Prog from initial state s 1 ? Written as Is s 1, s 2, Prog possible?

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Prog 1 Prog 2 store(R2, X) R1:=1 R2:=2 store(R1, X)store(R2, X) Initial state: R1=R2=X=0 Final state: R1=1, R2=2, X=0 X=1 X=2 Example: Sequential Consistency

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load store mul xor load Text Order nand branch cmp Instruction instances + Text order Flow-of-Information Is the flow-of-information allowed by the model? The Framework

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Resource X,R Assignment resource-value pair (X,5) Operation in-out pair ({(X,5)},{(R,5)}) Instruction ({(X,0)},{(R,0)}), ({(X,1)},{(R,1)}),... Program sequence of commands C 1,...,C m Commandan instruction B and a function next: B [1..m] { } The Elements

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Program Order: Example C 1 : load(X,R1) C 2 : R3 := R1+R2 next(C 1 )=2 next(C 2 )= op 1 : ({(X,1)},{(R1,1)}) op 2 : ({(R1,1),(R2,1)}, {(R3,2)}) s 1 : {(X,1), (R1,1), (R2,1), (R3,1)} s 2 : {(X,1), (R1,1), (R2,1), (R3,2)} Prog Instantiating Prog Program order: s 1 op 1 op 2 s 2

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Reads-From Mapping s 1 : All=1 load(X,R1) R3 := R1+R2 s 2 : R3=2, others=1 R1 R2

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Reads-From Mapping s 1 : All=1 load(X,R1) R3 := R1+R2 s 2 : R3=2, others=1 R1 R2 R1 R2, X R3

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store(R2,X) store(R1,Y) s 1 : All=0 s 2 : All=1 load(X,R1) load(Y,R2) The Reads-From Mapping is not Cyclic

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View orders Order the operations in Prog One for each Prog i Obey architecture-specific rules relating program-order reads-from mapping

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I(X) s1s1 op 3 s2s2 op 4 op 2 op 1 op 5 < < < < (x) O(X) Sequential Execution Information can not be read from the hidden past

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s1s1 op 3 s2s2 op 4 op 2 op 1 < < < < Sequential Execution Information can not be read from the future op 5 Relative to which order?

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Sequential Consistency S 1,S 2,Prog is sequentially consistent if Prog can be instantiated with a set of operations A and program order A single view order linear extends the program order Information flow satisfies the sequential execution conditions relative to view order

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PowerPC Consistency Information flow satisfies the sequential execution conditions Relative to program order Relative to view orders

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View orders enforce that Memory is coherent, except for local stores. Shared resource dependencies are preserved. sync orders operations around it. sync is transitive (sort of…). Branch dependencies are preserved. PowerPC Consistency: View Orders

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PowerPC Consistency: View Orders I

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PowerPC Consistency: View Orders II

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Speculation is Visible to Programs Final state: X=Y=1 R1=1,R2=0 R3=1,R4=0 Initial state: All=0 Prog 1 Prog 2 Prog 3 Prog 4 load(X,R1)load(Y,R3)store(1,X)store(1,Y) sync load(Y,R2)load(X,R4)

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