Linked Lists: Locking, Lock- Free, and Beyond. Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit

Linked Lists: Locking, Lock- Free, and Beyond Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit

Last Lecture: Spin-Locks CS. spin lock critical section Resets lock upon exit Art of Multiprocessor Programming 2

Today: Concurrent Objects Adding threads should not lower throughput Contention effects Mostly fixed by Queue locks Art of Multiprocessor Programming 3

Today: Concurrent Objects Adding threads should not lower throughput Contention effects Mostly fixed by Queue locks Should increase throughput Not possible if inherently sequential Surprising things are parallelizable Art of Multiprocessor Programming 4

Coarse-Grained Synchronization Each method locks the object Avoid contention using queue locks Art of Multiprocessor Programming 5

Coarse-Grained Synchronization Each method locks the object Avoid contention using queue locks Easy to reason about In simple cases Art of Multiprocessor Programming 6

Coarse-Grained Synchronization Each method locks the object Avoid contention using queue locks Easy to reason about In simple cases So, are we done? Art of Multiprocessor Programming 7

Coarse-Grained Synchronization Sequential bottleneck Threads stand in line Art of Multiprocessor Programming 8

Coarse-Grained Synchronization Sequential bottleneck Threads stand in line Adding more threads Does not improve throughput Struggle to keep it from getting worse Art of Multiprocessor Programming 9

Coarse-Grained Synchronization Sequential bottleneck Threads stand in line Adding more threads Does not improve throughput Struggle to keep it from getting worse So why even use a multiprocessor? Well, some apps inherently parallel Art of Multiprocessor Programming 10

This Lecture Introduce four patterns Bag of tricks Methods that work more than once Art of Multiprocessor Programming 11

This Lecture Introduce four patterns Bag of tricks Methods that work more than once For highly-concurrent objects Concurrent access More threads, more throughput Art of Multiprocessor Programming 12

First: Fine-Grained Synchronization Instead of using a single lock Split object into Independently-synchronized components Methods conflict when they access The same component At the same time Art of Multiprocessor Programming 13

Second: Optimistic Synchronization Search without locking If you find it, lock and check OK: we are done Oops: start over Evaluation Usually cheaper than locking, but Mistakes are expensive Art of Multiprocessor Programming 14

Third: Lazy Synchronization Postpone hard work Removing components is tricky Logical removal Mark component to be deleted Physical removal Do what needs to be done Art of Multiprocessor Programming 15

Fourth: Lock-Free Synchronization Don t use locks at all Use compareandset() & relatives Advantages No Scheduler Assumptions/Support Disadvantages Complex Sometimes high overhead Art of Multiprocessor Programming 16

Linked List Illustrate these patterns Using a list-based Set Common application Building block for other apps Art of Multiprocessor Programming 17

Set Interface Unordered collection of items No duplicates Methods add(x) put x in set remove(x) take x out of set contains(x) tests if x in set Art of Multiprocessor Programming 18

List-Based Sets public interface Set<T> { public boolean add(t x); public boolean remove(t x); public boolean contains(t x); } Art of Multiprocessor Programming 19

List-Based Sets public interface Set<T> { public boolean add(t x); public boolean remove(t x); public boolean contains(t x); } Add item to set Art of Multiprocessor Programming 20

List-Based Sets public interface Set<T> { public boolean add(t x); public boolean remove(t x); public boolean contains(tt x); } Remove item from set Art of Multiprocessor Programming 21

List-Based Sets public interface Set<T> { public boolean add(t x); public boolean remove(t x); public boolean contains(t x); } Is item in set? Art of Multiprocessor Programming 22

List Node public class Node { public T item; public int key; public Node next; } Art of Multiprocessor Programming 23

List Node public class Node { public T item; public int key; public Node next; } item of interest Art of Multiprocessor Programming 24

List Node public class Node { public T item; public int key; public Node next; } Usually hash code Art of Multiprocessor Programming 25

List Node public class Node { public T item; public int key; public Node next; } Reference to next node Art of Multiprocessor Programming 26

The List-Based Set - a b c + Sorted with Sentinel nodes (min & max possible keys) Art of Multiprocessor Programming 27

Reasoning about Concurrent Objects Invariant Property that always holds Established because True when object is created Truth preserved by each method Each step of each method Art of Multiprocessor Programming 28

Specifically Invariants preserved by add() remove() contains() Most steps are trivial Usually one step tricky Often linearization point Art of Multiprocessor Programming 29

Interference Invariants make sense only if methods considered are the only modifiers Art of Multiprocessor Programming 30

Interference Invariants make sense only if methods considered are the only modifiers Language encapsulation helps List nodes not visible outside class Art of Multiprocessor Programming 31

Interference Freedom from interference needed even for removed nodes Some algorithms traverse removed nodes Careful with malloc() & free()! Garbage collection helps here Art of Multiprocessor Programming 32

Abstract Data Types Concrete representation: a b Abstract Type: {a, b} Art of Multiprocessor Programming 33

Abstract Data Types Meaning of rep given by abstraction map S( a b ) = {a,b} Art of Multiprocessor Programming 34

Rep Invariant Which concrete values meaningful? Sorted? Duplicates? Rep invariant Characterizes legal concrete reps Preserved by methods Relied on by methods Art of Multiprocessor Programming 35

Blame Game Rep invariant is a contract Suppose add() leaves behind 2 copies of x remove() removes only 1 Which is incorrect? Art of Multiprocessor Programming 36

Blame Game Suppose add() leaves behind 2 copies of x remove() removes only 1 Which is incorrect? If rep invariant says no duplicates add() is incorrect Otherwise remove() is incorrect Art of Multiprocessor Programming 37

Rep Invariant (partly) Sentinel nodes tail reachable from head Sorted No duplicates Art of Multiprocessor Programming 38

Abstraction Map S(head) = { x there exists a such that } a reachable from head and a.item = x Art of Multiprocessor Programming 39

Sequential List Based Set Add() a c d Remove() a b c Art of Multiprocessor Programming 40

Sequential List Based Set Add() a c d Remove() b a b c Art of Multiprocessor Programming 41

Coarse-Grained Locking a b d Art of Multiprocessor Programming 42

Coarse-Grained Locking a b d c Art of Multiprocessor Programming 43

Coarse-Grained Locking a b d honk! honk! c Simple but hotspot + bottleneck Art of Multiprocessor Programming 44

Coarse-Grained Locking Easy, same as synchronized methods One lock to rule them all Art of Multiprocessor Programming 45

Coarse-Grained Locking Easy, same as synchronized methods One lock to rule them all Simple, clearly correct Deserves respect! Works poorly with contention Queue locks help But bottleneck still an issue Art of Multiprocessor Programming 46

Fine-grained Locking Requires careful thought Do not meddle in the affairs of wizards, for they are subtle and quick to anger Art of Multiprocessor Programming 47

Fine-grained Locking Requires careful thought Do not meddle in the affairs of wizards, for they are subtle and quick to anger Split object into pieces Each piece has own lock Methods that work on disjoint pieces need not exclude each other Art of Multiprocessor Programming 48

Hand-over-Hand locking a b c Art of Multiprocessor Programming 49

Hand-over-Hand locking a b c Art of Multiprocessor Programming 50

Hand-over-Hand locking a b c Art of Multiprocessor Programming 51

Hand-over-Hand locking a b c Art of Multiprocessor Programming 52

Hand-over-Hand locking a b c Art of Multiprocessor Programming 53

Removing a Node a b c d remove(b) Art of Multiprocessor Programming 54

Removing a Node a b c d remove(b) Art of Multiprocessor Programming 55

Removing a Node a b c d remove(b) Art of Multiprocessor Programming 56

Removing a Node a b c d remove(b) Art of Multiprocessor Programming 57

Removing a Node a b c d remove(b) Art of Multiprocessor Programming 58

Removing a Node a c d remove(b) Why hold 2 locks? Art of Multiprocessor Programming 59

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 60

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 61

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 62

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 63

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 64

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 65

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 66

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 67

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 68

Concurrent Removes a b c d remove(b) remove(c) Art of Multiprocessor Programming 69

Uh, Oh a c d remove(b) remove(c) Art of Multiprocessor Programming 70

Uh, Oh Bad news, c not removed a c d remove(b) remove(c) Art of Multiprocessor Programming 71

Problem To delete node c Swing node b s next field to d a b c Problem is, Someone deleting b concurrently could direct a pointer a b c to c Art of Multiprocessor Programming 72

Insight If a node is locked No one can delete node s successor If a thread locks Node to be deleted And its predecessor Then it works Art of Multiprocessor Programming 73

Hand-Over-Hand Again a b c d remove(b) Art of Multiprocessor Programming 74

Hand-Over-Hand Again a b c d remove(b) Art of Multiprocessor Programming 75

Hand-Over-Hand Again a b c d remove(b) Art of Multiprocessor Programming 76

Hand-Over-Hand Again a b c d remove(b) Found it! Art of Multiprocessor Programming 77

Hand-Over-Hand Again a b c d remove(b) Found it! Art of Multiprocessor Programming 78

Hand-Over-Hand Again a c d remove(b) Art of Multiprocessor Programming 79

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 80

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 81

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 82

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 83

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 84

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 85

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 86

Removing a Node a b c d remove(b) remove(c) Art of Multiprocessor Programming 87

Removing a Node a b c d Must acquire Lock for b remove(c) Art of Multiprocessor Programming 88

Removing a Node a b c d Cannot acquire lock for b remove(c) Art of Multiprocessor Programming 89

Removing a Node a b c d Wait! remove(c) Art of Multiprocessor Programming 90

Removing a Node a b d Proceed to remove (b) Art of Multiprocessor Programming 91

Removing a Node a b d remove(b) Art of Multiprocessor Programming 92

Removing a Node a b d remove(b) Art of Multiprocessor Programming 93

Removing a Node a d remove(b) Art of Multiprocessor Programming 94

Removing a Node a d Art of Multiprocessor Programming 95

Remove method public boolean remove(item item) { int key = item.hashcode(); Node pred, curr; try { } finally { curr.unlock(); pred.unlock(); }} Art of Multiprocessor Programming 96

Remove method public boolean remove(item item) { int key = item.hashcode(); Node pred, curr; try { } finally { curr.unlock(); pred.unlock(); }} Key used to order node Art of Multiprocessor Programming 97

Remove method public boolean remove(item item) { int key = item.hashcode(); Node pred, curr; try { } finally { currnode.unlock(); prednode.unlock(); }} Predecessor and current nodes Art of Multiprocessor Programming 98

Remove method public boolean remove(item item) { int key = item.hashcode(); Node pred, curr; try { } finally { curr.unlock(); pred.unlock(); }} Make sure locks released Art of Multiprocessor Programming 99

Remove method public boolean remove(item item) { int key = item.hashcode(); Node pred, curr; try { } finally { curr.unlock(); pred.unlock(); }} Everything else Art of Multiprocessor Programming 100

Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); } finally { } Art of Multiprocessor Programming 101

Remove method lock pred == head try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); } finally { } Art of Multiprocessor Programming 102

Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); } finally { } Lock current Art of Multiprocessor Programming 103

Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); } finally { } Traversing list Art of Multiprocessor Programming 104

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 105

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } Search key range pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 106

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; At start of each loop: curr and pred locked Art of Multiprocessor Programming 107

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; If item found, remove node Art of Multiprocessor Programming 108

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; If node found, remove it Art of Multiprocessor Programming 109

Remove: searching Unlock predecessor while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 110

Remove: searching Only one node locked! while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 111

Remove: searching while (curr.key <= key) { demote current if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 112

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = currnode; curr = curr.next; curr.lock(); } return false; Find and lock new current Art of Multiprocessor Programming 113

Remove: searching while (curr.key <= key) { Lock if (item invariant == curr.item) restored { pred.next = curr.next; return true; } pred.unlock(); pred = currnode; curr = curr.next; curr.lock(); } return false; Art of Multiprocessor Programming 114

Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Otherwise, not present Art of Multiprocessor Programming 115

Why does this work? To remove node e Must lock e Must lock e s predecessor Therefore, if you lock a node It can t be removed And neither can its successor Art of Multiprocessor Programming 116

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; pred reachable from head curr is pred.next So curr.item is in the set Art of Multiprocessor Programming 117

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Linearization point if item is present Art of Multiprocessor Programming 118

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Node locked, so no other thread can remove it. Art of Multiprocessor Programming 119

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Item not present Art of Multiprocessor Programming 120

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; pred reachable from head curr.lock(); curr is pred.next } pred.key < key return false; key < curr.key Art of Multiprocessor Programming 121

Why remove() is linearizable while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Linearization point Art of Multiprocessor Programming 122

Adding Nodes To add node e Must lock predecessor Must lock successor Neither can be deleted (Is successor lock actually required?) Art of Multiprocessor Programming 123

Same Abstraction Map S(head) = { x there exists a such that } a reachable from head and a.item = x Art of Multiprocessor Programming 124

Rep Invariant Easy to check that tail always reachable from head Nodes sorted, no duplicates Art of Multiprocessor Programming 125

Drawbacks Better than coarse-grained lock Threads can traverse in parallel Still not ideal Long chain of acquire/release Inefficient Art of Multiprocessor Programming 126

Optimistic Synchronization Find nodes without locking Lock nodes Check that everything is OK Art of Multiprocessor Programming 127

Optimistic: Traverse without Locking a b d e add(c) Aha! Art of Multiprocessor Programming 128

Optimistic: Lock and Load a b d e add(c) Art of Multiprocessor Programming 129

Optimistic: Lock and Load c a b d e add(c) Art of Multiprocessor Programming 130

What could go wrong? a b d e add(c) Aha! Art of Multiprocessor Programming 131

What could go wrong? a b d e add(c) Art of Multiprocessor Programming 132

What could go wrong? a b d e remove(b) Art of Multiprocessor Programming 133

What could go wrong? a b d e remove(b) Art of Multiprocessor Programming 134

What could go wrong? a b d e add(c) Art of Multiprocessor Programming 135

What could go wrong? c a b d e add(c) Art of Multiprocessor Programming 136

What could go wrong? a d e add(c) Uh-oh Art of Multiprocessor Programming 137

Validate Part 1 a b d e add(c) Yes, b still reachable from head Art of Multiprocessor Programming 138

What Else Could Go Wrong? a b d e add(c) Aha! Art of Multiprocessor Programming 139

What Else Coould Go Wrong? a b d e add(c) add(b ) Art of Multiprocessor Programming 140

What Else Coould Go Wrong? a b d e add(c) b add(b ) Art of Multiprocessor Programming 141

What Else Could Go Wrong? a b d e add(c) b Art of Multiprocessor Programming 142

What Else Could Go Wrong? c a b d e add(c) Art of Multiprocessor Programming 143

Validate Part 2 (while holding locks) a b d e add(c) Yes, b still points to d Art of Multiprocessor Programming 144

Optimistic: Linearization Point a b d e add(c) c Art of Multiprocessor Programming 145

Same Abstraction Map S(head) = { x there exists a such that } a reachable from head and a.item = x Art of Multiprocessor Programming 146

Invariants Careful: we may traverse deleted nodes But we establish properties by Validation After we lock target nodes Art of Multiprocessor Programming 147

Correctness If Nodes b and c both locked Node b still accessible Node c still successor to b Then Neither will be deleted OK to delete and return true Art of Multiprocessor Programming 148

Unsuccessful Remove a b d e remove(c) Aha! Art of Multiprocessor Programming 149

Validate (1) a b d e remove(c) Yes, b still reachable from head Art of Multiprocessor Programming 150

Validate (2) a b d e remove(c) Yes, b still points to d Art of Multiprocessor Programming 151

OK Computer a b d e remove(c) return false Art of Multiprocessor Programming 152

Correctness If Nodes b and d both locked Node b still accessible Node d still successor to b Then Neither will be deleted No thread can add c after b OK to return false Art of Multiprocessor Programming 153

Validation private boolean validate(node pred, Node curry) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Art of Multiprocessor Programming 154

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } Predecessor & return false; current nodes } Art of Multiprocessor Programming 155

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Begin at the beginning Art of Multiprocessor Programming 156

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Search range of keys Art of Multiprocessor Programming 157

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Predecessor reachable Art of Multiprocessor Programming 158

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Is current node next? Art of Multiprocessor Programming 159

Validation private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Otherwise move on Art of Multiprocessor Programming 160

Validation Predecessor not reachable private boolean validate(node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Art of Multiprocessor Programming 161

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Art of Multiprocessor Programming 162

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Search key Art of Multiprocessor Programming 163

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Retry on synchronization conflict Art of Multiprocessor Programming 164

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Examine predecessor and current nodes Art of Multiprocessor Programming 165

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; Search by key } Art of Multiprocessor Programming 166

Remove: searching public boolean remove(item item) { int key = item.hashcode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Stop if we find item Art of Multiprocessor Programming 167

Remove: searching public boolean remove(item item) { int key Move = item.hashcode(); along retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } Art of Multiprocessor Programming 168

On Exit from Loop If item is present curr holds item pred just before curr If item is absent curr has first higher key pred just before curr Assuming no synchronization problems Art of Multiprocessor Programming 169

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Art of Multiprocessor Programming 170

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Always unlock Art of Multiprocessor Programming 171

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Lock both nodes Art of Multiprocessor Programming 172

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Check for synchronization conflicts Art of Multiprocessor Programming 173

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} target found, remove node Art of Multiprocessor Programming 174

Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} target not found Art of Multiprocessor Programming 175

Optimistic List Limited hot-spots Targets of add(), remove(), contains() No contention on traversals Moreover Traversals are wait-free Food for thought Art of Multiprocessor Programming 176

So Far, So Good Much less lock acquisition/release Performance Concurrency Problems Need to traverse list twice contains() method acquires locks Art of Multiprocessor Programming 177

Evaluation Optimistic is effective if cost of scanning twice without locks is less than cost of scanning once with locks Drawback contains() acquires locks 90% of calls in many apps Art of Multiprocessor Programming 178

Lazy List Like optimistic, except Scan once contains(x) never locks Key insight Removing nodes causes trouble Do it lazily Art of Multiprocessor Programming 179

Lazy List remove() Scans list (as before) Locks predecessor & current (as before) Logical delete Marks current node as removed (new!) Physical delete Redirects predecessor s next (as before) Art of Multiprocessor Programming 180

Lazy Removal a b c d Art of Multiprocessor Programming 181

Lazy Removal a b c d Present in list Art of Multiprocessor Programming 182

Lazy Removal a b c d Logically deleted Art of Multiprocessor Programming 183

Lazy Removal a b c d Physically deleted Art of Multiprocessor Programming 184

Lazy Removal a b d Physically deleted Art of Multiprocessor Programming 185

Lazy List All Methods Scan through locked and marked nodes Removing a node doesn t slow down other method calls Must still lock pred and curr nodes. Art of Multiprocessor Programming 186

Validation No need to rescan list! Check that pred is not marked Check that curr is not marked Check that pred points to curr Art of Multiprocessor Programming 187

Business as Usual a b c Art of Multiprocessor Programming 188

Business as Usual a b c Art of Multiprocessor Programming 189

Business as Usual a b c Art of Multiprocessor Programming 190

Business as Usual a b c remove(b) Art of Multiprocessor Programming 191

Business as Usual a b c a not marked Art of Multiprocessor Programming 192

Business as Usual a b c a still points to b Art of Multiprocessor Programming 193

Business as Usual a b c Logical delete Art of Multiprocessor Programming 194

Business as Usual a b c physical delete Art of Multiprocessor Programming 195

Business as Usual a b c Art of Multiprocessor Programming 196

New Abstraction Map S(head) = { x there exists node a such that } a reachable from head and a.item = x and a is unmarked Art of Multiprocessor Programming 197

Invariant If not marked then item in the set and reachable from head and if not yet traversed it is reachable from pred Art of Multiprocessor Programming 198

Validation private boolean validate(node pred, Node curr) { return!pred.marked &&!curr.marked && pred.next == curr); } Art of Multiprocessor Programming 199

List Validate Method private boolean validate(node pred, Node curr) { return!pred.marked &&!curr.marked && pred.next == curr); } Predecessor not Logically removed Art of Multiprocessor Programming 200

List Validate Method private boolean validate(node pred, Node curr) { return!pred.marked &&!curr.marked && pred.next == curr); } Current not Logically removed Art of Multiprocessor Programming 201

List Validate Method private boolean validate(node pred, Node curr) { return!pred.marked &&!curr.marked && pred.next == curr); } Predecessor still Points to current Art of Multiprocessor Programming 202

Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Art of Multiprocessor Programming 203

Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Validate as before Art of Multiprocessor Programming 204

Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Key found Art of Multiprocessor Programming 205

Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Logical remove Art of Multiprocessor Programming 206

Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} physical remove Art of Multiprocessor Programming 207

Contains public boolean contains(item item) { int key = item.hashcode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key &&!curr.marked; } Art of Multiprocessor Programming 208

Contains public boolean contains(item item) { int key = item.hashcode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key &&!curr.marked; } Start at the head Art of Multiprocessor Programming 209

Contains public boolean contains(item item) { int key = item.hashcode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key &&!curr.marked; } Search key range Art of Multiprocessor Programming 210

Contains public boolean contains(item item) { int key = item.hashcode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key &&!curr.marked; } Traverse without locking (nodes may have been removed) Art of Multiprocessor Programming 211

Contains public boolean contains(item item) { int key = item.hashcode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key &&!curr.marked; } Present and undeleted? Art of Multiprocessor Programming 212

Summary: Wait-free Contains a 0 b 0 d c 10 e 0 Use Mark bit + list ordering 1. Not marked à in the set 2. Marked or missing à not in the set Art of Multiprocessor Programming 213

Lazy List a 0 b 0 d c 10 e 0 Lazy add() and remove() + Wait-free contains() Art of Multiprocessor Programming 214

Evaluation Good: contains() doesn t lock In fact, its wait-free! Good because typically high % contains() Uncontended calls don t re-traverse Bad Contended add() and remove() calls do re-traverse Traffic jam if one thread delays Art of Multiprocessor Programming 215

Traffic Jam Any concurrent data structure based on mutual exclusion has a weakness If one thread Enters critical section And eats the big muffin Cache miss, page fault, descheduled Everyone else using that lock is stuck! Need to trust the scheduler. Art of Multiprocessor Programming 216

Reminder: Lock-Free Data No matter what Structures Guarantees minimal progress in any execution i.e. Some thread will always complete a method call Even if others halt at malicious times Implies that implementation can t use locks Art of Multiprocessor Programming 217

Lock-free Lists Next logical step Wait-free contains() lock-free add() and remove() Use only compareandset() What could go wrong? Art of Multiprocessor Programming 218

Lock-free Lists Logical Removal a 0 b 0 c 10 e 0 Use CAS to verify pointer is correct Physical Removal Not enough! Art of Multiprocessor Programming 219

Problem Logical Removal a 0 b 0 c 10 e 0 Physical Removal d 0 Node added Art of Multiprocessor Programming 220

The Solution: Combine Bit and Pointer Logical Removal = Set Mark Bit a 0 b 0 c 10 e 0 Physical Removal CAS Mark-Bit and Pointer are CASed together (AtomicMarkableReference) d 0 Fail CAS: Node not added after logical Removal Art of Multiprocessor Programming 221

Solution Use AtomicMarkableReference Atomically Swing reference and Update flag Remove in two steps Set mark bit in next field Redirect predecessor s pointer Art of Multiprocessor Programming 222

Marking a Node class package Reference address F mark bit Art of Multiprocessor Programming 223

Extracting Reference & Mark Public Object get(boolean[] marked); Art of Multiprocessor Programming 224

Extracting Reference & Mark Public Object get(boolean[] marked); Returns reference Returns mark at array index 0! Art of Multiprocessor Programming 225

Extracting Reference Only public boolean ismarked(); Value of mark Art of Multiprocessor Programming 226

Changing State Public boolean compareandset( Object expectedref, Object updateref, boolean expectedmark, boolean updatemark); Art of Multiprocessor Programming 227

Changing State If this is the current reference Public boolean compareandset( Object expectedref, Object updateref, boolean expectedmark, boolean updatemark); And this is the current mark Art of Multiprocessor Programming 228

Changing State then change to this new reference Public boolean compareandset( Object expectedref, Object updateref, boolean expectedmark, boolean updatemark); and this new mark Art of Multiprocessor Programming 229

Changing State public boolean attemptmark( Object expectedref, boolean updatemark); Art of Multiprocessor Programming 230

Changing State public boolean attemptmark( Object expectedref, boolean updatemark); If this is the current reference Art of Multiprocessor Programming 231

Changing State public boolean attemptmark( Object expectedref, boolean updatemark);.. then change to this new mark. Art of Multiprocessor Programming 232

Removing a Node a b CAS c d remove c Art of Multiprocessor Programming 233

Removing a Node failed a CAS b CAS c d remove b remove c Art of Multiprocessor Programming 234

Removing a Node a b c d remove b remove c Art of Multiprocessor Programming 235

Removing a Node a d remove b remove c Art of Multiprocessor Programming 236

Traversing the List Q: what do you do when you find a logically deleted node in your path? A: finish the job. CAS the predecessor s next field Proceed (repeat as needed) Art of Multiprocessor Programming 237

Lock-Free Traversal (only Add and Remove) pred curr pred curr CAS a b c d Uh-oh Art of Multiprocessor Programming 238

The Window Class class Window { public Node pred; public Node curr; Window(Node pred, Node curr) { this.pred = pred; this.curr = curr; } } Art of Multiprocessor Programming 239

The Window Class class Window { public Node pred; public Node curr; Window(Node pred, Node curr) { this.pred = pred; this.curr = curr; } } A container for pred and current values Art of Multiprocessor Programming 240

Using the Find Method Window window = find(head, key); Node pred = window.pred; curr = window.curr; Art of Multiprocessor Programming 241

Using the Find Method Window window = find(head, key); Node pred = window.pred; curr = window.curr; Find returns window Art of Multiprocessor Programming 242

Using the Find Method Window window = find(head, key); Node pred = window.pred; curr = window.curr; Extract pred and curr Art of Multiprocessor Programming 243

The Find Method Window window = find(item); At some instant, item or pred curr succ Art of Multiprocessor Programming Herlihy-Shavit 2007 244

The Find Method Window window = find(item); At some instant, item not in list pred curr= null succ Art of Multiprocessor Programming Herlihy-Shavit 2007 245

Remove public boolean remove(t item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset(succ, succ, false true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; }}} Art of Multiprocessor Programming 246

Remove public boolean remove(t item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset (succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); Keep trying return true; Art of Multiprocessor Programming 247 }}}

Remove public boolean remove(t item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset (succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; Find neighbors Art of Multiprocessor Programming 248 }}}

Remove public boolean remove(t item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset(succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; She s not there }}} Art of Multiprocessor Programming 249

Remove public boolean remove(t item) { Boolean Try snip; to mark node as deleted while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset(succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; }}} Art of Multiprocessor Programming 250

Remove public boolean remove(t item) { Boolean If it snip; doesn t work, while (true) just retry, { Window window = find(head, key); Node if it pred does, = window.pred, job curr = window.curr; essentially if (curr.key done!= key) { return false; } else { Node succ = curr.next.getreference(); snip = curr.next.compareandset(succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; }}} Art of Multiprocessor Programming 251

Remove public boolean remove(t item) { Boolean snip; while (true) { a Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key!= key) { return false; Try to advance reference } else { Node (if we succ don t = curr.next.getreference(); succeed, someone else did or will). snip = curr.next.compareandset(succ, succ, false, true); if (!snip) continue; pred.next.compareandset(curr, succ, false, false); return true; }}} Art of Multiprocessor Programming 252

Add public boolean add(t item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareandset(curr, node, false, false)) {return true;} }}} Art of Multiprocessor Programming 253

Add public boolean add(t item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareandset(curr, node, false, false)) {return true;} }}} Item already there. Art of Multiprocessor Programming 254

Add public boolean add(t item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareandset(curr, node, false, false)) {return true;} }}} create new node Art of Multiprocessor Programming 255

Add public boolean add(t item) { boolean splice; Install new node, while (true) { else retry loop Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareandset(curr, node, false, false)) {return true;} }}} Art of Multiprocessor Programming 256

Wait-free Contains public boolean contains(t item) { boolean marked; int key = item.hashcode(); Node curr = this.head; while (curr.key < key) curr = curr.next; Node succ = curr.next.get(marked); return (curr.key == key &&!marked[0]) } Art of Multiprocessor Programming 257

Wait-free Contains public boolean contains(t item) { boolean marked; Only diff is that we int key = item.hashcode(); get and check Node curr = this.head; marked while (curr.key < key) curr = curr.next; Node succ = curr.next.get(marked); return (curr.key == key &&!marked[0]) } Art of Multiprocessor Programming 258

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Art of Multiprocessor Programming 259

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); }} while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } If list changes while traversed, start over Art of Multiprocessor Programming 260

Lock-free Find public Window find(node head, int key) { Node pred = null, Start curr looking = null, succ from = head null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Art of Multiprocessor Programming 261

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { Move down the list pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Art of Multiprocessor Programming 262

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); }} } pred = curr; curr = succ; Get ref to successor and current deleted bit Art of Multiprocessor Programming 263

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} path code details soon Try to remove deleted nodes in Art of Multiprocessor Programming 264

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); If while curr (true) key that { is greater or equal, succ = return curr.next.get(marked); pred and curr while (marked[0]) { } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Art of Multiprocessor Programming 265

Lock-free Find public Window find(node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getreference(); while (true) { succ = curr.next.get(marked); Otherwise while (marked[0]) advance { window and loop again } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Art of Multiprocessor Programming 266

Lock-free Find retry: while (true) { while (marked[0]) { snip = pred.next.compareandset(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } Art of Multiprocessor Programming 267

Lock-free Find Try to snip out node retry: while (true) { while (marked[0]) { snip = pred.next.compareandset(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } Art of Multiprocessor Programming 268

Lock-free Find if predecessor s next field changed must retry whole traversal retry: while (true) { while (marked[0]) { snip = pred.next.compareandset(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } Art of Multiprocessor Programming 269

Lock-free Find Otherwise move on to check if next node deleted retry: while (true) { while (marked[0]) { snip = pred.next.compareandset(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } Art of Multiprocessor Programming 270

Performance On 16 node shared memory machine Benchmark throughput of Java List-based Set algs. Vary % of Contains() method Calls. Art of Multiprocessor Programming 271

High Contains Ratio Lock-free Lazy list Coarse Grained Fine Lock-coupling Art of Multiprocessor Programming 272

Low Contains Ratio Lock-free Lazy list Coarse Grained Fine Lock-coupling Art of Multiprocessor Programming 273

As Contains Ratio Increases Lock-free Lazy list Coarse Grained Fine Lock-coupling % Contains() Art of Multiprocessor Programming 274

Summary Coarse-grained locking Fine-grained locking Optimistic synchronization Lock-free synchronization Art of Multiprocessor Programming 275

To Lock or Not to Lock Locking vs. Non-blocking: Extremist views on both sides The answer: nobler to compromise, combine locking and non-blocking Example: Lazy list combines blocking add() and remove() and a wait-free contains() Remember: Blocking/non-blocking is a property of a method Art of Multiprocessor Programming 276

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