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Incrementalized Pointer and Escape Analysis

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1 Incrementalized Pointer and Escape Analysis
Frédéric Vivien ICPS/LSIIT Université Louis Pasteur Strasbourg, France Martin Rinard Laboratory for Computer Science Massachusetts Institute of Technology Cambridge, MA, USA

2 Start with a program void main(i,j) ——————— void compute(d,e) ————
void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) ——————

3 Lots of allocation sites
void main(i,j) ——————— void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) ——————

4 Stack Allocation Optimization
void main(i,j) ——————— void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) ——————

5 Stack Allocation Optimization
void main(i,j) ——————— Precise Whole-Program Pointer and Escape Analysis void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) ——————

6 Drawbacks to Whole-Program Analysis
Resource Intensive Large analysis times Large memory consumption Unsuitable for partial programs

7 Key Observation Number One:
void main(i,j) ——————— Most optimizations require only the analysis of a small part of program surrounding the object allocation site void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) ——————

8 99% of objects allocated at these two sites
Key Observation Number Two: void main(i,j) ——————— Most of the optimization benefit comes from a small percentage of the allocation sites void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) —————— 99% of objects allocated at these two sites

9 99% of objects allocated at these two sites
Intuition for Better Analysis void main(i,j) ——————— Locate important allocation sites Use demand-driven approach to analyze region surrounding site Somehow avoid sinking analysis resources into sites that can’t be optimized void compute(d,e) ———— void evaluate(i,j) —————— void multiplyAdd(a,b,c) ————————— void abs(r) ———— void scale(n,m) —————— void multiply(m) ———— void add(u,v) —————— 99% of objects allocated at these two sites

10 How we turned this intuition into an algorithm that usually
What This Talk is About How we turned this intuition into an algorithm that usually obtains almost all the benefit of the whole program analysis 2) analyzes a small fraction of program 3) consumes a small fraction of whole program analysis time

11 Structure of Talk Motivating Example
Base whole program analysis (Whaley and Rinard, OOPSLA 99) Incrementalized analysis Analysis policy Experimental results Conclusion

12 Motivating Example

13 Employee Database Example
Read in database of employee records Extract statistics like max salary

14 Employee Database Example
Read in database of employee records Extract statistics like max salary John Doe $45,000 Ben Bit $30,000 Jane Roe $55,000 Vector Name Salary

15 Computing Max Salary Traverse Records to Find Max Salary Vector Name
John Doe Ben Bit Jane Roe Salary $45,000 $30,000 $55,000 max = $0

16 Computing Max Salary Traverse Records to Find Max Salary Vector Name
John Doe Ben Bit Jane Roe Salary $45,000 $30,000 $55,000 max = $45,000 who = John Doe

17 Computing Max Salary Traverse Records to Find Max Salary Vector Name
John Doe Ben Bit Jane Roe Salary $45,000 $30,000 $55,000 max = $45,000 who = John Doe

18 Computing Max Salary Traverse Records to Find Max Salary Vector Name
John Doe Ben Bit Jane Roe Salary $45,000 $30,000 $55,000 max = $55,000 who = Jane Roe

19 Computing Max Salary Traverse Records to Find Max Salary Vector Name
John Doe Ben Bit Jane Roe Salary $45,000 $30,000 $55,000 max salary = $55,000 highest paid = Jane Roe

20 Coding Max Computation (in Java)
class EmployeeDatabase { Vector database = new Vector(); Employee highestPaid; void computeMax() { int max = 0; Enumeration enum = database.elements(); while (enum.hasMoreElements()) { Employee e = enum.nextElement(); if (max < e.salary()) { max = e.salary(); highestPaid = e; }

21 Coding Max Computation (in Java)
class EmployeeDatabase { Vector database = new Vector(); Employee highestPaid; void computeMax() { int max = 0; Enumeration enum = database.elements(); while (enum.hasMoreElements()) { Employee e = enum.nextElement(); if (max < e.salary()) { max = e.salary(); highestPaid = e; }

22 Issues In Implementation
Enumeration object allocated on heap Increases heap memory usage Increases garbage collection frequency Heap allocation is unnecessary Enumeration object allocated inside max Not accessible outside max Should be able to use stack allocation

23 Basic Idea Use pointer and escape analysis to recognize captured objects Transform program to allocate captured objects on stack

24 Base Analysis

25 Base Analysis Basic Abstraction: Points-to Escape Graph
Intraprocedural Analysis Flow sensitive abstract interpretation Produces points-to escape graph at each program point Interprocedural Analysis Bottom Up and Compositional Analyzes each method once to obtain a single parameterized analysis result Result is specialized for use at each call site

26 Points-to Escape Graph in Example
void computeMax() { int max = 0; Enumeration enum = database.elements(); while (enum.hasMoreElements()) { Employee e = enum.nextElement(); if (max < e.salary()) { max = e.salary(); highestPaid = e; } } [ ] vector elementData enum database highestPaid this e

27 Edge Types Inside Edges: created in currently analyzed part of program
Outside Edges: created outside currently analyzed part of program [ ] vector elementData enum database highestPaid dashed = outside this solid = inside e

28 Node Types Inside Nodes:
Represent objects created in currently analyzed part of program Outside Nodes: Parameter nodes – represent parameters Load nodes - represent objects accessed via pointers created outside analyzed part [ ] vector elementData enum database highestPaid dashed = outside this solid = inside e

29 Escaped Nodes Escaped nodes parameter nodes thread nodes
returned nodes nodes reachable from other escaped nodes Captured is the opposite of escaped [ ] vector elementData enum database highestPaid green = escaped this white = captured e

30 Stack Allocation Optimization
Examine graph from end of method If a node is captured in this graph Allocate corresponding objects on stack (may need to inline methods to apply optimization) Can allocate enum object on stack [ ] vector elementData enum database highestPaid green = escaped this white = captured e

31 Interprocedural Analysis
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); }

32 Start with graph before call site
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e

33 Retrieve graph from end of callee
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e elementData [ ] database this highestPaid Enum object is not present because it was captured in the callee

34 Map formals to actuals graph before call site
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e database elementData [ ] this highestPaid

35 Match corresponding inside and outside edges to complete mapping
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e database elementData [ ] this highestPaid

36 Match corresponding inside and outside edges to complete mapping
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e database elementData [ ] this highestPaid

37 Match corresponding inside and outside edges to complete mapping
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e database elementData [ ] this highestPaid

38 Match corresponding inside and outside edges to complete mapping
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e database elementData [ ] this highestPaid

39 Combine graphs to obtain new graph after call site
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e elementData [ ] database this highestPaid [ ] graph after call site elementData e highestPaid

40 Continue analysis after call site
void printStatistics(BufferedReader r) { EmployeeDatabase e = new EmployeeDatabase(r); e.computeMax(); System.out.println(“max salary = “ + e.highestPaid); } [ ] graph before call site database elementData e [ ] graph after call site elementData e highestPaid

41 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

42 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

43 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

44 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

45 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

46 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

47 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

48 Whole Program Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

49 Incrementalized Analysis

50 Incrementalized Analysis Requirements
Must be able to Analyze method independently of callers Base analysis is compositional Already does this Skip analysis of invoked methods But later incrementally integrate analysis results if desirable to do so

51 First Extension to Base Analysis
Skip the analysis of invoked methods Parameters are marked as escaping into skipped call site Assume analysis skips enum.nextElement() 1 vector enum database highestPaid Node 1 escapes into enum.nextElement() this e

52 First Extension Almost Works
Can skip analysis of invoked methods If allocation site is captured, great! If not, escape information tells you what methods you should have analyzed… Should have analyzed enum.nextElement() 1 vector enum database highestPaid Node 1 escapes into enum.nextElement() this e

53 Second Extension to Base Algorithm
Record enough information to undo skip and incorporate analysis into existing result Parameter mapping at call site Ordering information for call sites

54 Graphs from Whole Program Analysis
void compute() { —————— foo(x,y); ——————— } Graph before call site Generated during analysis Graph after call site Used to apply stack allocation optimization Graph at end of method

55 Graphs from Incrementalized Analysis
void compute() { —————— foo(x,y); ——————— } Graph before call site Generated during analysis Graph after skipped call site Used to apply stack allocation optimization Graph at end of method

56 Incorporating Result from Skipped Call Site
Naive approach: use mapping algorithm directly on graph from end of caller method After incorporating result from skipped call site Before incorporating result from skipped call site

57 Incorporating Result from Skipped Call Site
Naive approach: use mapping algorithm directly on graph from end of caller method After incorporating result from skipped call site Graph from whole program analysis

58 Basic Problem and Solution
Problem: additional edges in graph from end of method make result less precise Solution: augment abstraction For each call skipped call site, record Edges which were present in the graph before the call site Edges which were present after call site Use this information when incorporating results from skipped call sites

59 After Augmenting Abstraction
After incorporating result from skipped call site Graph from whole program analysis

60 Incrementalized Analysis
void printStatistics() ——————— void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

61 Incrementalized Analysis
void printStatistics() ——————— Attempt to stack allocate Enumeration object from elements void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

62 Incrementalized Analysis
void printStatistics() ——————— Analyze elements (intraprocedurally) void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

63 Incrementalized Analysis
void printStatistics() ——————— Analyze elements (intraprocedurally) void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

64 Incrementalized Analysis
void printStatistics() ——————— Analyze elements (intraprocedurally) Escapes only into the caller void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

65 Incrementalized Analysis
void printStatistics() ——————— Analyze computeMax (intraprocedurally) void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

66 Incrementalized Analysis
void printStatistics() ——————— Analyze computeMax (intraprocedurally) void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

67 Incrementalized Analysis
void printStatistics() ——————— Analyze computeMax (intraprocedurally) void computeMax() ———— Escapes to hasMoreElements nextElement Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

68 Analyze hasMoreElements
Incrementalized Analysis void printStatistics() ——————— Analyze hasMoreElements void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

69 Analyze hasMoreElements
Incrementalized Analysis void printStatistics() ——————— Analyze hasMoreElements void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

70 Incrementalized Analysis
void printStatistics() ——————— Analyze hasMoreElements Combine results void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

71 Incrementalized Analysis
void printStatistics() ——————— Analyze hasMoreElements Combine results Still escaping to nextElement void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

72 Incrementalized Analysis
void printStatistics() ——————— Analyze nextElement void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

73 Incrementalized Analysis
void printStatistics() ——————— Analyze nextElement void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

74 Incrementalized Analysis
void printStatistics() ——————— Analyze nextElement Combine results void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

75 Incrementalized Analysis
void printStatistics() ——————— Analyze nextElement Combine results void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

76 Incrementalized Analysis
void printStatistics() ——————— Enumeration object Captured in computeMax void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

77 Incrementalized Analysis
void printStatistics() ——————— Enumeration object Captured in computeMax Inline elements Stack allocate enumeration object void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

78 Incrementalized Analysis
void printStatistics() ——————— We skipped the analysis of some methods void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

79 Incrementalized Analysis
void printStatistics() ——————— We skipped the analysis of some methods We ignored some other methods void computeMax() ———— Enumeration elements() ——— boolean hasMoreElements() —————— Employee nextElement() —————— int salary() —————— Vector elementData() ————

80 Result We can incrementally analyze Only what is needed
For whatever allocation site we want And even temporarily suspend analysis part of the way through!

81 New Issue We can incrementally analyze Only what is needed
For whatever allocation site we want And even temporarily suspend analysis part of the way through! But… Lots of analysis opportunities Not all opportunities are profitable Where to invest analysis resources? How much resources to invest?

82 Analysis Policy Formulate policy as solution to an investment problem
Goal Maximize optimization payoff from invested analysis resources

83 Analysis Policy Implementation
For each allocation site, estimate marginal return on invested analysis resources Loop Invest a unit of analysis resources (time) in site that offers best return Expand analyzed region surrounding site When unit expires, recompute marginal returns (best site may change)

84 Marginal Return Estimate
N · P(d) C · T N = Number of objects allocated at the site P(d) = Probability of capturing the site, knowing we explored a region of call depth d C = Number of skipped call sites the allocation site escapes through T = Average time needed to analyze a call site

85 Marginal Return Estimate
N · P(d) C · T As invest analysis resources explore larger regions around allocation sites get more information about sites marginal return estimates improve analysis makes better investment decisions!

86 Usage Scenarios Ahead of time compiler
Give algorithm an analysis budget Algorithm spends budget Takes whatever optimizations it uncovered Dynamic compiler Algorithm acquires analysis budget as a percentage of run time Periodically spends budget, delivers additional optimizations Longer program runs, more optimizations

87 Experimental Results

88 Methodology Implemented analysis in MIT Flex System
Obtained several benchmarks Scientific computations: barnes, water Our lexical analyzer: jlex Spec benchmarks: db, raytrace, compress

89 Analysis Times 223 645 jdk 1.2

90 Allocation Sites Analyzed

91 Analysis Time Payoff barnes water jlex db raytrace compress
% of Objects Analysis Time (seconds) Analysis Time (seconds) Analysis Time (seconds) db raytrace compress % of Objects Analysis Time (seconds) Analysis Time (seconds) Analysis Time (seconds) Stack allocated by incrementalized analysis Decided Stack allocated by whole-program analysis

92 Stack Allocation

93 Normalized Execution Times
Reference: execution time without optimization

94 Experimental Summary Key Application Properties
Most objects allocated at very few allocation sites Can capture objects with an incremental analysis of region surrounding allocation sites Consequence Most of the benefits of whole-program analysis Fraction of the cost of whole-program analysis

95 Demand-driven Analyses
Related Work Demand-driven Analyses Horwitz, Reps, Sagiv (FSE 1995) Duesterwald, Soffa, Gupta (TOPLAS 1997) Heintze, Tardieu (PLDI 2001) Key differences Integration of escape information enables incrementalized algorithms to suspend partially completed analyses Maintain accurate marginal payoff estimates Avoid overly costly analyses

96 Previous Escape Analyses
Related Work Previous Escape Analyses Blanchet (OOPSLA 1999) Bogda, Hoelzle (OOPSLA 1999) Choi, Gupta, Serrano, Sreedhar, Midkiff (OOPSLA 1999) Whaley, Rinard (OOPSLA 1999) Ruf (PLDI 2000) Key Differences Previous algorithms analyze whole program But could incrementalize other analyses Get a range of algorithms with varying analysis time/precision tradeoffs

97 Conclusion Properties Results Incrementalized Whole-Program Analysis
Uses escape information to incrementally analyze relevant regions of program Analysis policy driven by estimates of optimization benefits and costs Results Most of benefits of whole program analysis Fraction of the cost

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