Hierarchical Pointer Analysis

Transcription

1 for Distributed Programs Amir Kamil and Katherine Yelick U.C. Berkeley August 23, Amir Kamil

2 Background 2 Amir Kamil

3 Hierarchical Machines Parallel machines often have hierarchical structure 4 A B D 1 2 C 3 level 1 (thread local) level 2 (node local) level 3 (cluster local) level 4 (grid world) 3 Amir Kamil

4 Partitioned Global Address Space Partitioned global address space (PGAS) languages provide the illusion of shared memory across the machine Wide pointers used to represent global addresses Contain identifying information plus the physical address Process ID: 1 Address: 0xf9a0cb48 Narrow pointers can still be used for addresses in the local physical address space Address: 0xf9a0cb48 4 Amir Kamil

5 The Problems 5 Amir Kamil

6 Three Problems What data is private to a thread? What data is local to the physical address space? What possible race conditions can occur? 6 Amir Kamil

7 Data Privacy Data is private if it cannot leak beyond its source thread Useful to know which data is private for global garbage collection, monitor optimization, and other applications 7 Amir Kamil

8 Data Locality Recall: global pointers composed identifying information and an address Process ID: 1 Address: 0xf9a0cb48 0 When dereferenced, runtime system must perform a check to determine if the data is actually in the local physical address space If local, l then access directly If not local, then perform communication Thus, global l pointers are more costly in both space and time, even if the actual data is local 8 Amir Kamil

9 Race Detection Shared memory introduces the possibility of race conditions Two threads access the same memory location The accesses can be simultaneous (no intermediate synchronization) At least one access is a write 9 Amir Kamil

10 The Solution 10 Amir Kamil

11 A pointer analysis that takes into account the machine hierarchy can answer the preceding questions For each variable, we want to know not only from which allocation sites the data could have originated, but also from which threads 11 Amir Kamil

12 Related Work Thread-aware pointer analysis has been done by others Rugina and Rinard, Zhu and Hendren, Hicks, and others None of them did it for hierarchical, distributed machines Data privacy and locality detection previously done by Liblit, Aiken, and Yelick Uses constraint propagation Does not distinguish allocation sites 12 Amir Kamil

13 The Implementation 13 Amir Kamil

14 Titanium Titanium is a single program, multiple data (SPMD) dialect of Java All threads execute the same program text Designed for distributed machines Global l address space all threads can access all memory At runtime, threads are grouped into processes A thread shares a physical address space with some other, but not all threads 14 Amir Kamil

15 Titanium Memory Hierarchy Global memory is composed of a hierarchy Program Processes Locations can be thread-local (tlocal), processlocal (plocal), or potentially in another process (global) Threads global 3 tlocal plocal 15 Amir Kamil

16 The Analysis 16 Amir Kamil

17 Approach We define a small SPMD language based on Titanium We produce a type system that accounts for the memory hierarchy The analysis can handle an arbitrary number of levels, but we use three levels in this talk We give an overview of the pointer analysis inference rules 17 Amir Kamil

18 Language Syntax Types τ ::= int ref q τ Qualifiers q ::= tlocal plocal global (tlocal l plocal l global) l) Expressions e ::= new l τ (allocation) transmite 1 from e 2 (communication) e 1 e 2 (dereferencing assignment) convert(e, n) (type conversion) 18 Amir Kamil

19 Type Rules Allocation The expression new l τ allocates space of type τ in local memory and returns a reference to the location The label l is unique for each allocation site and will be used by the pointer analysis The resulting reference is qualified with tlocal, since it references thread-local memory Thread 0 new l int tlocall Γ new l τ : ref tlocal τ 19 Amir Kamil

20 Type Rules Communication The expression transmit e 1 from e 2 evaluates e 1 on the thread given by e 2 and retrieves the result If e 1 has reference type, the result type must be widened to global Statically do not know source thread, so must assume it can be any thread Γ e 1 : τ Γ e 2 :int Thread 0 Thread 1 transmit y from 1 global y Γ transmit e 1 from e 2 : tlocal expand(τ, global) expand(ref q τ, q ) ref (q, q ) τ expand(τ, q ) τ otherwise 20 Amir Kamil

21 Type Rules Dereferencing Assignment The expression e 1 e 2 puts the value of e 2 into the location referenced by e 1 (like *e 1 = e 2 in C) Some assignments are unsound Γ e 1 : ref q τ Γ e 2 : τ robust(τ, q) Thread 0 Thread 1 Γ e 1 e 2 :ref q τ plocal y l l l z tlocal tlocal plocal robust(ref q τ, τ q ) false if q q robust(τ, q ) true otherwise 21 Amir Kamil

22 Type Rules Type Conversion The expression convert(e, q) is an assertion that e refers to data that is no further than q Titanium code often checks if data is plocal and then casts to it before operating on it for efficiency Thread 0 x global Γ e : ref q τ Γ convert(e, q) : ref q τ 22 Amir Kamil

23 Pointer Analysis Since language is SPMD, analysis is only done for a single thread We use thread 0 in our examples Each expression has a points-to set of abstract locations that it can reference Abstract locations also have points-to sets 23 Amir Kamil

24 Abstract Locations Abstract locations consist of label and qualifier A-loc (l, q) can refer to any concrete location allocated at label l that is at most distance q from thread 0 (l, tlocal) Thread 0 Thread 1 new l int new l int (l, plocal) l) tlocal tlocal 24 Amir Kamil

25 Pointer Analysis Allocation and Communication The inference rules for allocation and communication are similar to the type rules An allocation new l τ produces a new abstract location (l, tlocal) The result of the expression transmit e 1 from e 2 is the set of a-locs resulting from e 1 but with global qualifiers e 1 {(l 1, tlocal), (l 2, plocal), (l 3, global)} transmit e 1 from e 2 {(l 1, global), (l 2, global), (l 3, global)} 25 Amir Kamil

26 Pointer Analysis Dereferencing Assignment For assignment, must take into account actions of other threads x Thread 0 Thread 1 Thread 2 (l 1, tlocal) x (l 1, plocal) x (l 1, plocal) (l 2, tlocal) (l 2, plocal) (l 2, plocal) y y y x {(l 1, tlocal)}, l)} y {(l 2, plocal)} x y : (l 1, tlocal) (l 2, plocal), (l 1, plocal) (l 2, plocal), (l 1, global) lbl) (l 2, global) lbl) 26 Amir Kamil

27 Pointer Analysis Type Conversion Inthetypeconversionconvert(e type convert(e, q), the program is illegal if e evaluates to a location further than q Thus, the result of the expression convert(e, q) is the set of a-locs resulting from e with the qualifiers reduced to at most q e {(l 1, tlocal), (l 2, plocal), (l 3, global)} convert(e, plocal) l) {(l 1, tlocal), l) (l 2, plocal), l) (l 3, plocal)} l)} 27 Amir Kamil

28 Evaluation 28 Amir Kamil

29 Benchmarks Five application benchmarks used to evaluate the pointer analysis Benchmark Line Count Description amr 7581 Adaptive mesh refinement suite gas 8841 Hyperbolic solver for a gas dynamics problem ft 1192 NAS Fourier transform benchmark cg 1595 NAS conjugate gradient benchmark mg 1952 NAS multigrid benchmark 29 Amir Kamil

30 Running Time Determine actual cost of introducing multiple levels into the pointer analysis Tests run on 2.4GHz Pentium 4 with 512MB RAM Three analysis variants compared Name PA1 PA2 PA3 Description Single-level pointer analysis Two-level pointer analysis (thread-local and global) Three-level pointer analysis 30 Amir Kamil

31 Running Time Results 4 Pointer Analysis Running Time PA1 PA2 PA3 3.5 Analysis s Time (sec conds) Good amr gas ft cg mg Benchmark 31 Amir Kamil

32 Data Privacy Detection In pointer analysis, an allocation site is private if only thread-local references to it are used Thus, only two levels, thread-local and global, needed in the pointer analysis Two types of analysis compared Name SQI PA2 Description Constraint-based analysis by Liblit, Aiken, and Yelick; does not distinguish allocation sites Two-level pointer analysis (thread-local and global) 32 Amir Kamil

33 Perc cent Determ mined to be Thread-P Private Data Privacy Detection Results Data Privacy Detection SQI PA2 amr gas ft cg mg Benchmark Good 33 Amir Kamil

34 Data Locality Detection Goal: statically determine which pointers must be process-local Three analyses compared Name LQI PA2 PA3 Description Constraint-based analysis by Liblit and Aiken; does not distinguish allocation sites Two-level pointer analysis (thread-local and global) Three-level pointer analysis 34 Amir Kamil

35 Perc cent Determ mined to be Process- -Local Data Locality Detection Results Data Locality Detection LQI PA2 PA3 Good 0 amr gas ft cg mg Benchmark 35 Amir Kamil

36 Race Detection Pointer analysis used with an existing concurrency analysis to detect potential races at compile-time Three analyses compared Name concur concur+pa1 concur+pa3 Description Concurrency analysis plus constraint-based data sharing analysis and type-based alias analysis Concurrency analysis plus single-level level pointer analysis Concurrency analysis plus three-level pointer analysis 36 Amir Kamil

37 Race Detection Results Static Races Detected concur concur+pa1 concur+pa3 Races (Lo ogarithmic Scale) Good 10 amr gas ft cg mg Benchmark 37 Amir Kamil

38 Conclusion 38 Amir Kamil

39 Conclusion We developed a pointer analysis for hierarchical, distributed machines The cost of introducing the memory hierarchy into the analysis is small On the other hand, the payoff is large 39 Amir Kamil

40 Future Work Scientific programs tend to use a lot of arraybased data structures Need array index analysis to properly analyze them Implement a dynamic race detector Use static results to minimize the program locations that need to be tracked 40 Amir Kamil

41 Questions 41 Amir Kamil