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Correctness-Preserving Derivation of Concurrent Garbage Collection Algorithms Martin T. Vechev Eran Yahav David F. Bacon University of Cambridge IBM T.J.

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Presentation on theme: "Correctness-Preserving Derivation of Concurrent Garbage Collection Algorithms Martin T. Vechev Eran Yahav David F. Bacon University of Cambridge IBM T.J."— Presentation transcript:

1 Correctness-Preserving Derivation of Concurrent Garbage Collection Algorithms Martin T. Vechev Eran Yahav David F. Bacon University of Cambridge IBM T.J. Watson Research Center PLDI – June 2006

2 Why Concurrent Garbage Collection ? Java and C#  Garbage-collected languages are prevalent Multicore  Concurrency is becoming prevalent Cheap RAM  Large heaps are becoming prevalent Real-Time Systems  More widely used

3 Memory Model Thread Model Concurrency Primitives CPU primitives Tracing/reference counting moving Allocate White / Black Dijkstra / Steele / Yuasa Barrier Atomic / Incremental Stack Snapshot Write Barrier Atomic / Non-atomic Color toggle, stacklets etc etc etc Implementation Existing Way to Create a Concurrent GC ENVIRONMENT REQUIREMENTS TECHNIQUES ?? Hard to verify/test Often buggy Did the monkey choose well?? Throughput Memory Consumption Pause Time

4 Ben-Ari Base ‘84 Dijkstra(C) ‘78 Doligez(C) ‘93 Azatchi ‘03 Domani ‘03 Yuasa ‘90 Pixley ‘88 Ben-Ari Base ‘84 Doligez ‘94 Ben-Ari Extended ‘84 Steele(C) ‘75 Boehm ‘91 Barabash ‘03 ‘03 ALGORITHMS PROOFS Concurrent GC algorithms and proofs are hard Incorrect Correct (C) Corrected FAMILY THEOREM PROVING

5 Optimal Correct Implementation Our Research Vision Memory Model Thread Model Concurrency Primitives CPU primitives ENVIRONMENT (Declarative Specification) Formally Defined Techniques Automated System Throughput Memory Consumption Pause Time REQUIREMENTS

6 In This Work Memory Model Thread Model Concurrency Primitives CPU primitives FIXED ENVIRONMENT Formally Defined Techniques for Tracing Non- Moving GC Automated System REQUIREMENTS Throughput Pause Time Memory Consumption Algorithm 1 Algorithm 2 Algorithm 3 Algorithm N <<< …

7 Problem : Interference A C B Traced Not Traced 1. GC traced B SYSTEM = MUTATOR || GC

8 Problem : Interference A C B A C B Traced Not Traced 1. GC traced B2. Mutator links C to B SYSTEM = MUTATOR || GC

9 Problem : Interference A C B A C B A C B X Traced Not Traced 1. GC traced B2. Mutator links C to B 3. Mutator unlinks C from A SYSTEM = MUTATOR || GC

10 Problem : Interference A C B A C B A C B A C B Traced Not Traced C LOST 1. GC traced B2. Mutator links C to B 3. Mutator unlinks C from A 4. GC traced A SYSTEM = MUTATOR || GC

11 The 3 Families of Concurrent GC Algorithms A C B 1. Marks C when C is linked to B (DIJKSTRA) A C B 2. Marks C when link to C is removed (YUASA) X A C B 3. Rescan B when C is linked to B (STEELE) Solutions are applied uniformly for all objects C C B

12 Contributions Systematic Exploration  A new parametric model of concurrent GC  Better understanding  New algorithms – potentially useful Formal Relationship between algorithms  Space - Relative precision between algorithms Sharing Proof Burden  Correctness-preserving “transformations”

13 A Parametric Concurrent GC Skeleton Intuition : Common out as much as possible Record interaction history between collector and mutator during tracing Collector exposes “hidden objects” based on entire interaction history

14 mark … reclaim Complete Garbage Collection Expose(L,D) Change Heap COLLECTOR MUTATOR markExpose(L,D) Change Heap A Parametric Concurrent GC Skeleton

15 Dimensions: an intuition The effect of each Mutator/GC action is controlled by a dimension Collector Scans PointerWavefront Granularity Mutator Allocates ObjectAllocation Color AB Mutator Creates Pointer Counting Mutator Overwrites Pointer Snapshot X C

16 Implementation Choice: Wavefront Per-Field Wavefront Exact information One bit per field More expensive More synchronization More garbage collected Per-Object Wavefront Approximate Information One bit per object Less expensive Less synchronization Less garbage collected

17 Choice: Record on Link or Unlink Record on Link More synchronization More garbage collected Record on Unlink Less synchronization Less garbage collected X

18 Combined Choices Record on LinkRecord on Unlink Per-Field WF Per-Object WF AB X X AB AB AB

19 Combined Choices Per Object Rec. Link A Rec. Link B Rec. Link A Unlink B Per-Field A Per-Field B Rec. Unlink A Rec. Link B Rec. Unlink A Rec. Unlink B Per-Field A Per-Obj B Per-Obj A Per-Field B Per-Obj A Per-Obj B X X X X X X X X A B

20 Correctness Transformations = Proof Steps APEX (U, U, U, U, {}) APEX (U, U, U, U, {}) STEELE DIJKSTRA (stacks,U,{},U,{}) STEELE-D STEELE-YC STEELE-D-YC DIJKSTRA-OLD DIJKSTRA-YC STEELE-BC HYBRID-YC (stacks,A,{},{},{}) HYBRID-YC (stacks,A,{},{},{}) STEELE-D-BC DIJKSTRA-BC YUASA (stacks, A, {}, {}, U) START WITH A CORRECT ALGORITHM RETAIN LESS GARBAGE RETAIN MORE GARBAGE

21 Intuition: an algorithm is more precise than another if it collects more garbage An algorithm that is less precise (more conservative) than a correct algorithm is guaranteed to be correct Should be a reference point for practical comparisons  no ad-hoc methods Hard to do manually: need a tool to provide insights  Finding the “right” definition was harder than proving safety, yet simpler than “relative concurrency” Relative Precision

22 Precision APEX (U, U, U, U, {}) APEX (U, U, U, U, {}) STEELE DIJKSTRA (stacks,U,{},U,{}) STEELE-D STEELE-YC STEELE-D-YC DIJKSTRA-OLD DIJKSTRA-YC STEELE-BC HYBRID-YC (stacks,A,{},{},{}) HYBRID-YC (stacks,A,{},{},{}) STEELE-D-BC DIJKSTRA-BC YUASA (stacks, A, {}, {}, U) MORE PRECISE LESS PRECISE

23 Conclusions Systematic exploration of an algorithm space  Useful new algorithms Formal definition of Relative precision between algorithms A first step towards automatic derivation of concurrent garbage collectors

24

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