Escape Analysis for Java

Transcription

1 Escape Analysis for Java Michael Bohn Based on the paper by Jong-Deok Choi, Manish Gupta, Mauricio Serrano, Vugranam Sreedhar and Sam Midkiff

2 Escape Analysis? What is Escape Analysis and why do I need it? Consider this example: public int m() { Vector<Integer> v = new Vector<Integer>(); v.add(1); v.add(2); return v.size(); } 2

3 Escape Analysis? public int m() { Vector<Integer> v = new Vector<Integer>(); v.add(1); v.add(2); return v.size(); } In Java, all objects are allocated on the heap Allocation on heap is time expensive Object needs to be removed by the garbage collector Garbage collection is time expensive Improvements possible, if we know that an object does not escape a method 3

4 Escape Analysis? public int m() { Vector<Integer> v = new Vector<Integer>(); v.add(1); v.add(2); return v.size(); } Improvement here: Allocation on stack Without violating Java semantics! Object is recycled with stack frame for free 4

5 Escape Analysis? public int m() { Vector<Integer> v = new Vector<Integer>(); v.add(1); v.add(2); return v.size(); } Another improvement possible Vector is synchronized lock and unlock on every call to add() Pointless, because Object never accessed by more than one thread Sychronization can be removed 5

6 Outline Rest of this talk: How to automatically identify whether an object escapes or not Intraprocedural analysis Interprocedural analysis Objects are passed to other methods: public void m() { Object o = new Object(); callmethod(o); } How to track escape states between method calls 6

7 Definition Escape M Definition: Method Escape Let O be a concrete object Let M be a method invocation EscapeMethod(O, M) = true, if lifetime of O exceeds lifetime of M (plus: O is not passed to another thread) Push(O) Pop(O) O EscapeMethod(O,M) = false 7

8 Definition Escape M Definition: Method Escape Let O be a concrete object Let M be a method invocation EscapeMethod(O, M) = true, if lifetime of O exceeds lifetime of M (plus: O is not passed to another thread) Push(O) Pop(O) O EscapeMethod(O, M) = false stack-allocatable EscapeMethod(O,M) = false 8

9 Definition Escape Definition: Thread Escape Let O be a concrete object Let T be a thread EscapeThread(O, T) = true, if O is visible to another thread T' T T' O T EscapeThread(O,T) = true 9

10 Definition Escape Definition: Thread Escape Let O be a concrete object Let T be a thread EscapeThread(O, T) = true, if O is visible to another thread T' T T' O T EscapeThread(O, T) = false thread-local EscapeThread(O,T) = true 10

11 Java Example Program Two static methods caller callee program call graph (PCG) caller callee 11

12 Java Example Program public static void caller() { A a = new A(); a.fa2 = new Object(); public static A callee(a arg1) { A sac = new A(); A gec = new A(); } A r = callee(a); Example.global = r; A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } class A { public Object fa1; public Object fa2; } } return asc1; 12

13 Java Example Program public static A callee(a arg1) { S1: A sac = new A(); S2: A gec = new A(); S3: A asc1 = new A(); S4: A asc2 = new A(); if(...) { S5: arg1.fa1 = asc2; S6: A a = arg1.fa2; S7: A b = a; S8: Example.global = b; } else { S9: Example.global = gec; } S10: return asc1; } 13

14 Intraprocedural Analysis 14

15 Idea of the analysis Capture the references of objects in a connection graph (CG) CG = N o N v N f, E p E d E f N o : object nodes N v : reference nodes (globals, locals, parameters) N f : field nodes E p : p q p N r q N o E d : p D q p, q E d E f : p F q p N o q N f 15

16 Intraprocedural Analysis Iterative scheme for connection graph construction S CG output S CG input = f S S CG input r = r Pred S CG output (standard data flow equations) Four basic statements with non-trivial transfer functions: p = new τ() p = q p.f = q p = q.f 16

17 Initialized connection graph public static void caller() { //... A r = callee(a); //... } arg1 = a1 public static A callee(a arg1) { //... } 17

18 Initialized connection graph public static A callee(a arg1) { //... if(...) { //... S8: Example.global = b; } else { S9: Example.global = gec; } //... } 18

19 Intraprocedural Analysis Statement type: p = new τ() 1. New object node O for new allocation site (1-limited scheme) 2. Apply ByPass(p) 3. Add p O Precisely, transform first: A sac = null; sac = new A(); 19

20 ByPass? ByPass(p) Formally: Let R={r r D p}(incoming deferred edges) Let S ={s p P s}(outgoing points-to edges) Let T ={t p D t}(outgoing deferred edges) ByPass p removes the edges in set {r D p} {p P s} {p D t} from the CG and adds edges {r P s r R s S } {r D s r R t T } to the CG 20

21 Intraprocedural Analysis Statement type: p = new τ() 1. New object node O for new allocation site (1-limited scheme) 2. Apply ByPass(p) 3. Add p O 21

22 Intraprocedural Analysis Statement type: p = new τ() 1. New object node O for new allocation site 2. Apply ByPass(p) 3. Add p O 22

23 Intraprocedural Analysis Statement type: p = new τ() 1. New object node O for new allocation site 2. Apply ByPass(p) 3. Add p O 23

24 Intraprocedural Analysis Statement type: p = new τ() 1. New object node O for new allocation site 2. Apply ByPass(p) 3. Add p O 24

25 Intraprocedural Analysis Identity transfer function (condition without side-effects) 25

26 Intraprocedural Analysis Control flow branch We take left branch first 26

27 Intraprocedural Analysis Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object 27

28 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5 and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object 28

29 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5 and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object 29

30 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5 and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object Lazily add field node fa1 30

31 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5 and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object Lazily add field node fa1 31

32 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object Lazily add field node fa1 Add fa1 D asc2 to CG 32

33 Intraprocedural Analysis Objects arg1 points to= add phantom object node S5and arg1 S5 to CG Statement type: p.f = q 1. Get objects p possibly points to 2. Lazily add field node f to objects 3. Add f D q to CG for each object Lazily add field node fa1 Add fa1 D asc2 to CG 33

34 Intraprocedural Analysis Statement type: p = q.f Get objects q possibly points to Lazily add field node f to objects ByPass(p) Add object p D f to CG for each 34

35 Intraprocedural Analysis Objects arg1 points to={s5} Statement type: p = q.f 1. Get objects q possibly points to 2. Lazily add field node f to objects 3. ByPass(p) 4. Add f to CG for p D each object 35

36 Intraprocedural Analysis Objects arg1 points to={s5} Lazily add field node fa2 Statement type: p = q.f 1. Get objects q possibly points to 2. Lazily add field node f to objects 3. ByPass(p) 4. Add f to CG for p D each object 36

37 Intraprocedural Analysis Objects arg1 points to={s5} Lazily add field node fa2 Statement type: p = q.f 1. Get objects q possibly points to 2. Lazily add field node f to objects 3. ByPass(p) 4. Add f to CG for p D each object 37

38 Intraprocedural Analysis Objects arg1 points to={s5} Lazily add field node fa2 Statement type: p = q.f 1. Get objects q possibly points to 2. Lazily add field node f to objects 3. ByPass(p) 4. Add f to CG for p D each object ByPass a Add a D fa2 to CG 38

39 Intraprocedural Analysis Objects arg1 points to={s5} Lazily add field node fa2 Statement type: p = q.f 1. Get objects q possibly points to 2. Lazily add field node f to objects 3. ByPass(p) 4. Add f to CG for p D each object ByPass a Add a D fa2 to CG 39

40 Intraprocedural Analysis Statement type: p = q Apply ByPass p Add edge p D q to CG 40

41 Intraprocedural Analysis Apply ByPass p Add edge p D q to CG ByPass b Add edge b D a 41

42 Intraprocedural Analysis Apply ByPass p Add edge p D q to CG ByPass b Add edge b D a 42

43 Intraprocedural Analysis Statement type again: p.f = q But here: global variable Similar transfer function 43

44 Intraprocedural Analysis 44

45 Intraprocedural Analysis 45

46 Intraprocedural Analysis We now take the right branch Extend CG at exit of if-node (conceptually) 46

47 Intraprocedural Analysis Again assignment to global variable 47

48 Intraprocedural Analysis 48

49 Intraprocedural Analysis 49

50 Intraprocedural Analysis Control flow merge: Meet-Operation = graph merge 50

51 Intraprocedural Analysis Left branch result Right branch result Merged 51

52 Intraprocedural Analysis Return statement: Modeled as an assignment to phantom variable return (return = asc1) Statement type: p = q Apply ByPass p Add edge p D q to CG 52

53 Intraprocedural Analysis Apply ByPass p Add edge p D q to CG 53

54 Intraprocedural Analysis Apply ByPass p Add edge p D q to CG 54

55 Intraprocedural Analysis Graph Compacting Apply ByPass(p) to each non-terminal node p Terminal node = node without outgoing edges Makes subsequent calculations more efficient Works, because we are only interested in the objects 55

56 Intraprocedural Analysis - Graph Compacting Apply ByPass(p) to each non-terminal node p Terminal node = node without outgoing edges Makes subsequent calculations more efficient Works, because we are only interested in the objects 56

57 Intraprocedural Analysis - Graph Compacting Apply ByPass(p) to each non-terminal node p Terminal node = node without outgoing edges Makes subsequent calculations more efficient Works, because we are only interested in the objects 57

58 Intraprocedural Analysis - Graph Compacting Special handling of terminal nodes 58

59 Intraprocedural Analysis - Graph Compacting Special handling of terminal nodes 59

60 Intraprocedural Analysis - Graph Compacting Special handling of terminal nodes 60

61 Intraprocedural Analysis Three escape states: Global, Arg, No Global = stack-allocatable thread-local Arg = stack-allocatable thread-local No = stack-allocatable thread-local 61

62 Intraprocedural Analyis The escape states form a lattice With es EscapeSet : NoEscape < < ArgEscape GlobalEscape es es = es es NoEscape = es es GlobalEscape = GlobalEscape 62

63 Intraprocedural Analysis Initial marking of nodes Global = all static fields (red) 63

64 Intraprocedural Analysis Initial marking of nodes Global = all static fields (red) Arg = phantom argument nodes and return phantom node (yellow) 64

65 Intraprocedural Analysis Initial marking of nodes Global = all static fields (red) Arg = phantom argument nodes and return phantom node (yellow) No = all other nodes 65

66 Intraprocedural Analysis Reachability analysis Subgraph of nodes that are reachable from global-escape-node 66

67 Intraprocedural Analysis Reachability analysis Subgraph of nodes that are reachable from arg-escape-nodes, but not from global-escape-nodes 67

68 Intraprocedural Analysis Reachability analysis Subgraph of nodes that are not reachable from global-escapenodes or arg-escape-node (remain marked no-escape) 68

69 Intraprocedural Analysis No-escape-nodes Do not escape method call and can be marked stack-allocatable 69

70 Intraprocedural Analysis public static A callee(a arg1) { S1: A sac = new A(); S2: A gec = new A(); S3: A asc1 = new A(); S4: A asc2 = new A(); if(...) { S5: arg1.fa1 = asc2; S6: A a = arg1.fa2; S7: A b = a; S8: Example.global = b; } else { S9: Example.global = gec; } S10: return asc1; } 70

71 Intraprocedural Analysis public static A callee(a arg1) { S1: A sac = new A(); S2: A gec = new A(); S3: A asc1 = new A(); S4: A asc2 = new A(); if(...) { S5: arg1.fa1 = asc2; S6: A a = arg1.fa2; S7: A b = a; S8: Example.global = b; } else { S9: Example.global = gec; } S10: return asc1; } We keep the red and yellow subgraphs for interprocedural analysis 71

72 Interprocedural analysis 72

73 Idea of interprocedural analysis Use callee CG to update caller CG Connect object nodes in caller with object nodes in callee program call graph (PCG) caller callee Traversal in inverse topologicial order (if there are no cycles in the PCG) 73

74 General traversal 74

75 The Java example public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 75

76 Interprocedural Analysis public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Before call: connect caller CG constructed so far with callee CG 76

77 Interprocedural Analysis public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } After call: Apply effect of method call to caller CG 77

78 Interprocedural Analysis Construct CG up to method call public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 78

79 Interprocedural Analysis Construct CG up to method call public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 79

80 Interprocedural Analysis Construct CG up to method call public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Modelling parameter passing Assignment of parameter to phantom node Return value: new phantom object node 80

81 Interprocedural Analysis Parameter passing to method public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Modelling parameter passing Assignment of parameter to phantom node 81

82 Interprocedural Analysis Parameter passing to method public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Formally: Let u 1. foo u 2,...,u n be a method call, with u 2,..., u n actual arguments to foo Model the call as follows: a 1 =u 1, a 2 =u 2, where a i is a phantom reference node 82

83 Update of caller CG Two steps Update nodes Update edges Node update via MapsTo-Relation 83

84 MapsTo-Relation Initially caller callee MapsTo: a 1 a 1 return r 84

85 MapsTo-Relation Recursive update caller callee MapsTo: a 1 a 1 return r S5 T1 85

86 MapsTo-Relation Recursive update caller callee MapsTo: a 1 a 1 return r S5 T1 pfa2 T2 86

87 MapsTo-Relation Recursive update caller callee MapsTo: a 1 a 1 return r S5 T1 pfa2 T2 S4 T0 87

88 MapsTo-Relation Recursive update caller callee MapsTo: a 1 a 1 return r S5 T1 pfa2 T2 S4 T0 S3 T3 88

89 MapsTo-Relation Update Escape state caller callee Nodes in MapsTo(n) are marked global escape, if escape state of n is global escape MapsTo: a 1 a 1 S5 T1 S3 T3 S4 T01 pfa2 T2 89

90 MapsTo-Relation Update Escape state caller callee Nodes in MapsTo(n) are marked global escape, if escape state of n is global escape MapsTo: a 1 a 1 S5 T1 S3 T3 S4 T01 pfa2 T2 90

91 Update of caller CG Node update Finds objects in caller that possibly could be the objects in callee Next: Edge update Updates the connection effects of calling a method 91

92 MapsTo-Relation Edge update MapsTo: a 1 a 1 S5 T1 S3 T3 S4 T01 pfa2 T2 92

93 MapsTo-Relation Edge update MapsTo: a 1 a 1 S5 T1 S3 T3 S4 T01 pfa2 T2 93

94 Update of caller CG Edge update Let p, q be object nodes of the callee graph such that: p F f p P q For each p MapsTo p q MapsTo q : establish p F f p P q for fid f p = fid f p 94

95 Interprocedural Analysis CG after method call public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Only remaining statement: assignment to global variable 95

96 Interprocedural Analysis CG after method call public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Only remaining statement: assignment to global variable 96

97 Interprocedural Analysis Again propagation of escape states: public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 97

98 Interprocedural Analysis Again propagation of escape states: public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 98

99 Interprocedural Analysis Again propagation of escape states: public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } Problem: Object T3 marked as global escape in caller, but not in callee 99

100 Interprocedural Analysis Solution For each object marked global escape in caller: find corresponding nodes in (all) callees (via inverse MapsTo- Relation) 100

101 Interprocedural Analysis Solution For each object marked global escape in caller: find corresponding nodes in (all) callees (via inverse MapsTo- Relation) 101

102 Interprocedural Analysis Checking the result public static A callee(a arg1) { S1: A sac = new A(); S2: A gec = new A(); S3: A asc1 = new A(); S4: A asc2 = new A(); if(...) { S5: arg1.fa1 = asc2; S6: A a = arg1.fa2; S7: A b = a; S8: Example.global = b; } else { S9: Example.global = gec; } S10: return asc1; } 102

103 Interprocedural Analysis Checking the result public static void caller() { T1: A a = new A(); T2: a.fa2 = new Object(); T3: A r = callee(a); T4: Example.global = r; } 103

104 Special cases Loops Iterate until solution converges Maximum of 10 iterations If maximum exceeded Mark all objects in method as global escape Recursive method calls No inverse topological sort possible Iterate until solution converges (again max. 10 iterations) 104

105 Special cases Objects of classes that implement Runnable interface Threads Objects that could be used as threads Marked as global escape Virtual methods Apply effects of all possible methods to caller Objects with non-trivial finalizers Mark all objects with overwritten finalizer-method as global escape 105

106 Special cases Exceptions Inside try-catch block: Kill only references to variables that are local to the block Objects that are thrown are marked as global escape Native or non-analyzable methods Mark all objects passed to or returned from such methods as global escape 106

107 Conclusion Static program analysis that finds out whether an object can be allocated on stack synchronization can be omitted Approach Construct a graph that captures all possible references to objects Combine graphs in interprocedural analysis The question if an object escapes is transformed to a graph reachability problem 107

108 Almost last slide... Questions? 108

109 References Jong-Deok Choi, Manish Gupta, Mauricio Serrano, Vugranam C. Sreedhar, Sam Midkiff Escape Analysis for Java, 1999 Jong-Deok Choi, Manish Gupta, Mauricio Serrano, Vugranam C. Sreedhar, Sam Midkiff Stack Allocation and Synchronization Optimizations for Java Using Escape Analysis, 2003 Gary A. Kildall A Unified Approach to Global Program Optimization,

110 Backup-Slides 110

111 Thread-local vs. Stack-allocatable Stack-allocatable => Thread-local If object does not escape method, it does not escape thread If object is not passed to another thread Thread-local > Stack-allocatable e.g. if object is returned from method, but not accessed from another thread Global escape = Stack-allocatable Thread-local 111

112 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); } if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } return asc1; class A { public Object fa1; public Object fa2; } 112

113 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } does not escape stack-allocatable (locally decidable) } return asc1; 113

114 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } global escapes } return asc1; 114

115 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } object returned definitely not stack-allocatable thread-locality depends on (any) caller } return asc1; 115

116 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } object returned (via argument) definitely not stack-allocatable thread-locality depends on caller } return asc1; 116

117 Java Example Program public static A callee(a arg1) { A sac = new A(); A gec = new A(); A asc1 = new A(); A asc2 = new A(); if(...) { arg1.fa1 = asc2; A a = arg1.fa2; A b = a; Example.global = b; } else { Example.global = gec; } object passed in whether stack-allocatable in caller depends on this method } return asc1; 117

118 Java Example Program public static void caller() { A a = new A(); a.fa2 = new Object(); } A r = callee(a); Example.global = r; 118

119 Java Example Program public static void caller() { A a = new A(); a.fa2 = new Object(); escape state depends on callee } A r = callee(a); Example.global = r; 119

120 Java Example Program public static void caller() { A a = new A(); a.fa2 = new Object(); } A r = callee(a); Example.global = r; return value escapes 120

121 Intraprocedural Analysis Statement type: p.f = q Let U =PointsTo p If U = create phantom node O ph and add points-to edge from p to O ph Let V ={v u F v u U fid v = f } For each u U if corresponding field reference node v does not exists, add it to V Add edges in{v D q v V } to CG 121

122 PointsTo? PointsTo(p) = {O1, O2} PointsTo(p) Traverse each outgoing path terminated by a points-to edge Set of all object that can be reached from p = PointsTo-Set 122

123 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node 123

124 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node 124

125 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node V = add field node fa1 to every object U 125

126 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node V = add field node fa1 to every object U 126

127 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node V = add field node fa1 to every object U Add deferred edges from fa1 to asc2 for every v V 127

128 Intraprocedural Analysis U = add phantom node and points-to edge from arg1 to phantom node V = add field node fa1 to every object U Add deferred edges from fa1 to asc2 for every v V 128

129 Intraprocedural Analysis Statement type: p = q.f Let U =PointsTo q If U = create phantom node O ph and add points-to edge from p to O ph Let V ={v u F v u U fid v = f } For each u U if corresponding field reference node v does not exists, add it to V Apply ByPass p Add edges in {v D q v V } to CG Precisely, transform first: A a = null; a = arg1.fa2; 129

130 Intraprocedural Analysis Statement type: p = q.f Get objects q possibly points to Lazily add field node f to objects ByPass(p) Add object p D f to CG for each Precisely, transform first: A a = null; a = arg1.fa2; 130

131 Intraprocedural Analysis U ={S5} V = add field node fa2 to every object U 131

132 Intraprocedural Analysis U ={S5} V = add field node fa2to every object U 132

133 Intraprocedural Analysis U ={S5} V = add field node fa2 to every object U Apply ByPass a Add deferred edges from a to fa2 for every v V 133

134 Intraprocedural Analysis U ={S5} V = add field node fa2 to every object U Apply ByPass a Add deferred edges from a to fa2 for every v V 134

135 MapsTo-Relation Formally 1 a i a i 2 O p PointsTo p O q PointsTo q, if p=a i q= a i, or p=o.f q= O. g O O fid f = fid g 135

136 Interprocedural Analysis Conservative solution Consider all arg-escape nodes in callee as not thread-local (i.e. accessed by more than one thread) 136