Speculative N-Way Barriers

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Speculative N-Way Barriers

• Lukasz Ziarek, Suresh Jagannathan
• Purdue University
• Mathew Fluet, Umut Acar
• TTI Chicago

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Speculation

• Performance
• Tool for better utilization of multi-core
  processors
• Highly constrained
• Short lived
• Isolated
• Few side effects, if any
• Rarely formalized
• Can we safely relax these limitations?

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Programming Model

• Higher Order Concurrent Language
• References
• N-way barriers
• Synchronization point of n interacting threads
• Fork/Join execution model
• Threads operate over local heaps
• Easier to reason about speculation
• Heaps merged at join points (barriers)
• N-way barriers server as a communication medium

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Motivating Example All Pairs Shortest Path

• Utilizes a matrix representation for a DAG
• Partitions the matrix into smaller units
• Each worker thread operates on disjoint
  partitions
• All workers synchronize on an n-way barrier

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Motivating Example All Pairs Shortest Path
2nd iteration
1st iteration
T1
T2
T1 dependant on T2,T3,T4
T3
T4
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Motivating Example All Pairs Shortest Path

• Observation
• Each thread is only dependant on the work done by
  a fix number of threads in a previous iteration
• Solution 1
• Rewrite the algorithm
• Algorithmic Complexity
• Specialized Barriers and Counters
• Results in 6x more code

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Solution 2 Optimistic Concurrency

• Utilize Speculation
• Requires no change to the underlying core
  algorithm
• Allows for the extraction of additional
  concurrency
• Challenges
• Maintaining a consistent view of memory
• Interacting speculations

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Representing N-Way Barriers
match(P) gt e

• Patterns (P)
• Rd(l) read of location l
• Wr(l) write of location l
• Wr(l, v) write of v to l
• Wr?(l, v) write of v to l
• if l does not already contain v

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Representing N-Way Barriers
match(P) gt e

• Barriers (match())
• Each thread that matches a base pattern blocks
  until the entire pattern is satisfied
• Thread which creates the barrier does not block
• Guarded Expressions (e)
• e delayed until completion of pattern
• Executed in separate thread of control
• can be utilized to encode spawn
• match() gt e spawn (e)

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Speculative Execution Model

• Allow Speculation Past Barriers
• Execute guarded expression speculatively
• Participating threads proceed
• Speculate a thread local store
• Validate When Last Thread Participates in the
  Barrier
• Confirm thread local store

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Example Program
T1 match(wr(x) wr(y)) gt !x !y !z
T2 x 1 T3 z
3 y 2 y 42
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Synchronous Execution
T1
T2
T3
z3
BLOCKED
T4
y2
Satisfied
!x 1 !y 2 !z 3
y42
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Speculative Execution
T1
T2
T3
sx-gt1, y-gt2, z-gt3
z3
!x 1 !y 2 !z 3
y2
T4
Validate
y42
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Speculative Execution Requiring Rollback
T1
T2
T3
sx-gt1, y-gt2, z-gt3
z3 y2
!x 1 !y 2 !z 3
y42
T4
Validate
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Potential for Self Satisfying Code
T1
match(wr(x) wr(y))gt !xy2!z
T2
!x y 2 !z
x1
Validate
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Time Travel
T3
T1
T2
match(wr(x) wr(y))
x2
match(wr(x) wr(y))
y4
Validate
!x y 2 !z
x1
T4
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So how DO we choose a store?

• Observation 1
• Only need to estimate what we need and what has
  changed
• Observation 2
• Each thread participating in the pattern
  contributes at least 1 value
• Observation 3
• Patterns which specify a value for a location
  guide our choice
• Observation 4
• The more threads blocked on a barrier the more we
  know about the speculation context

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Formalization

• Synchronous Semantics
• Speculative Semantics
• Trace
• Allows for the bridging of the speculative and
  synchronous semantics
• Speculative Semantics composed of a committed
  trace and a speculative trace
• Validated speculative actions are committed
• Validation is done one thread at a time

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Related Work

• Compiler/Architecture Driven Speculation
• Safe Futures
• Software Transactions
• Join Calculus
• Fork/Join parallelism (Cilk)

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Conclusion

• Provided a Formal Definition of Unconstrained
  Speculation in a Multithreaded Context
• Proved Speculative Semantics Adhere to
  Synchronous Semantics

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Questions?