Concurrent Queues and Stacks Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit.

Concurrent Queues and Stacks

Companion slides forThe Art of Multiprocessor

Programmingby Maurice Herlihy & Nir Shavit

Art of Multiprocessor Programming© Herlihy-Shavit

2007

2

The Five-Fold Path

• Coarse-grained locking• Fine-grained locking• Optimistic synchronization• Lazy synchronization• Lock-free synchronization


2007

3

Another Fundamental Problem

• We told you about – Sets implemented using linked lists

• Next: queues• Next: stacks


2007

4

Queues & Stacks

• Both: pool of items• Queue

– enq() & deq()– First-in-first-out (FIFO) order

• Stack– push() & pop()– Last-in-first-out (LIFO) order


2007

5

Bounded vs Unbounded

• Bounded– Fixed capacity– Good when resources an issue

• Unbounded– Holds any number of objects


2007

6

Blocking vs Non-Blocking

• Problem cases:– Removing from empty pool– Adding to full (bounded) pool

• Blocking– Caller waits until state changes

• Non-Blocking– Method throws exception


2007

7

This Lecture

• Bounded, Blocking, Lock-based Queue

• Unbounded, Non-Blocking, Lock-free Queue

• Monitors• ABA problem• Unbounded Non-Blocking Lock-free

Stack• Elimination-Backoff Stack


2007

8

Queue: Concurrency

enq(x) y=deq()

enq() and deq() work at

different ends of the object

tail head


2007

9

Concurrency

enq(x)

Challenge: what if the queue is empty or full?

y=deq()ta

ilhead


2007

10

Bounded Queue

Sentinel

head

tail


2007

11

Bounded Queue

head

tail

First actual item


2007

12

Bounded Queue

head

tail

Lock out other deq() calls

deqLock


2007

13

Bounded Queue

head

tail

Lock out other enq() calls

deqLock

enqLock


2007

14

Not Done Yet

head

tail

deqLock

enqLock

Need to tell whether queue is

full or empty


2007

15

Not Done Yet

head

tail

deqLock

enqLock

Permission to enqueue 8 items

permits

8


2007

16

Not Done Yet

head

tail

deqLock

enqLock

Incremented by deq()Decremented by enq()

permits

8


2007

17

Enqueuer

head

tail

deqLock

enqLock

permits

8

Lock enqLock


2007

18

Enqueuer

head

tail

deqLock

enqLock

permits

8

Read permits

OK


2007

19

Enqueuer

head

tail

deqLock

enqLock

permits

8

No need to lock

tail


2007

20

Enqueuer

head

tail

deqLock

enqLock

permits

8

Enqueue Node


2007

21

Enqueuer

head

tail

deqLock

enqLock

permits

87

getAndDecrement()


2007

22

Enqueuer

head

tail

deqLock

enqLock

permits

8 Release lock7


2007

23

Enqueuer

head

tail

deqLock

enqLock

permits

7

If queue was empty, notify/signal waiting

dequeuers


2007

24

Unsuccesful Enqueuer

head

tail

deqLock

enqLock

permits

0

Uh-oh

Read permits


2007

25

Dequeuer

head

tail

deqLock

enqLock

permits

8

Lock deqLock


2007

26

Dequeuer

head

tail

deqLock

enqLock

permits

7

Read sentinel’s next field

OK


2007

27

Dequeuer

head

tail

deqLock

enqLock

permits

7

Read value


2007

28

Dequeuer

head

tail

deqLock

enqLock

permits

7

Make first Node new sentinel


2007

29

Dequeuer

head

tail

deqLock

enqLock

permits

8

Increment permits


2007

30

Dequeuer

head

tail

deqLock

enqLock

permits

7Release deqLock


2007

31

Unsuccesful Dequeuer

head

tail

deqLock

enqLock

permits

8

Read sentinel’s next field

uh-oh


2007

32

Bounded Queue

public class BoundedQueue<T> { ReentrantLock enqLock, deqLock; Condition notEmptyCondition, notFullCondition; AtomicInteger permits; Node head; Node tail; int capacity; enqLock = new ReentrantLock(); notFullCondition = enqLock.newCondition(); deqLock = new ReentrantLock(); notEmptyCondition = deqLock.newCondition();}


2007

33

Bounded Queue


Enq & deq locks


2007

34

Digression: Monitor Locks

• Java Synchronized objects and Java ReentrantLocks are monitors

• Allow blocking on a condition rather than spinning

• Threads: – acquire and release lock– wait on a condition


2007

35

public interface Lock { void lock(); void lockInterruptibly() throws InterruptedException; boolean tryLock(); boolean tryLock(long time, TimeUnit unit); Condition newCondition(); void unlock;}

The Java Lock Interface

Acquire lock


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36



Release lock


2007

37



Try for lock, but not too hard


2007

38



Create condition to wait on


2007

39



Guess what this method does?


2007

40

Lock Conditions

public interface Condition { void await(); boolean await(long time, TimeUnit unit); … void signal(); void signalAll(); }


2007

41


Lock Conditions

Release lock and wait on condition


2007

42


Lock Conditions

Wake up one waiting thread


2007

43


Lock Conditions

Wake up all waiting threads


2007

44

Await

• Releases lock associated with q• Sleeps (gives up processor)• Awakens (resumes running)• Reacquires lock & returns

q.await()


2007

45

Signal

• Awakens one waiting thread– Which will reacquire lock

q.signal();


2007

46

Signal All

• Awakens all waiting threads– Which will each reacquire lock

q.signalAll();


2007

47

A Monitor Lock

Cri

tical S

ecti

on

waiting roomlock()

unLock()


2007

48

Unsuccessful Deq

Cri

tical S

ecti

on

waiting roomlock(

)

await()

deq()

Oh no, empty!


2007

49

Another One

Cri

tical S

ecti

on

waiting roomlock(

)

await()

deq()

Oh no, empty!


2007

50

Enqueuer to the Rescue

Cri

tical S

ecti

on

waiting roomlock()

signalAll()

enq( )

unLock()

Yawn!Yawn!


2007

51

Yawn!

Monitor Signalling

Cri

tical S

ecti

on

waiting room

Yawn!

Awakened thread might still lose lock to outside contender…


2007

52

Dequeurs Signalled

Cri

tical S

ecti

on

waiting room

Found it

Yawn!


2007

53

Yawn!

Dequeurs Signalled

Cri

tical S

ecti

on

waiting room

Still empty!


2007

54

Dollar Short + Day Late

Cri

tical S

ecti

on

waiting room


2007 55

Lost Wake-Up

Cri

tical S

ecti

on

waiting roomlock()

signal ()enq( )

unLock()

Yawn!


2007

56

Lost Wake-Up

Cri

tical S

ecti

on

waiting roomlock()

enq( )

unLock()

Yawn!


2007

57

Lost Wake-Up

Cri

tical S

ecti

on

waiting room

Yawn!


2007

58

Lost Wake-Up

Cri

tical S

ecti

on

waiting room

Found it


2007

59

What’s Wrong Here?

Cri

tical S

ecti

on

waiting room

zzzz….!

Solution to Lost Wakeup

• Always use signalAll and notifyAll • Not signal and notify


2007

60


2007

61

public class Queue<T> {

int head = 0, tail = 0; T[QSIZE] items;

public synchronized T deq() { while (tail – head == 0) this.wait(); T result = items[head % QSIZE]; head++; this.notifyAll(); return result; } …}}

Java Synchronized Methods


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62





Each object has an implicit lock with an

implicit condition


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63





Lock on entry, unlock on

return


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64





Wait on implicit condition


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65





Signal all threads waiting on condition


2007

66

(Pop!) The Bounded Queue



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67

Bounded Queue Fields


Enq & deq locks


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68



Enq lock’s associated condition


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69



Num permits: 0 to capacity


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70



Head and Tail


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71

Enq Method Part Onepublic void enq(T x) { boolean mustWakeDequeuers = false; enqLock.lock(); try { while (permits.get() == 0) notFullCondition.await(); Node e = new Node(x); tail.next = e; tail = e; if (permits.getAndDecrement() == capacity) mustWakeDequeuers = true; } finally { enqLock.unlock(); } …}


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72

public void enq(T x) { boolean mustWakeDequeuers = false; enqLock.lock(); try { while (permits.get() == 0) notFullCondition.await(); Node e = new Node(x); tail.next = e; tail = e; if (permits.getAndDecrement() == capacity) mustWakeDequeuers = true; } finally { enqLock.unlock(); } …}

Enq Method Part One

Lock and unlock enq

lock


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73


Enq Method Part One

If queue is full, patiently await further

instructions …


2007

74


Be Afraid

How do we know the permits field won’t

change?


2007

75


Enq Method Part One

Add new node


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76


Enq Method Part One

If queue was empty, wake frustrated dequeuers


2007

77

Enq Method Part Deux

public void enq(T x) { … if (mustWakeDequeuers) { deqLock.lock(); try { notEmptyCondition.signalAll(); } finally { deqLock.unlock(); } } }


2007

78


public void enq(T x) { … if (mustWakeDequeuers) { deqLock.lock(); try { notEmptyCondition.signalAll(); } finally { deqLock.unlock(); } } }Are there dequeuers to be signaled?


2007

79



Lock and unlock deq

lock


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80



Signal dequeuers that queue no longer

empty


2007

81

The Enq() & Deq() Methods

• Share no locks– That’s good

• But do share an atomic counter– Accessed on every method call– That’s not so good

• Can we alleviate this bottleneck?


2007

82

Split the Counter

• The enq() method– Decrements only– Cares only if value is zero

• The deq() method– Increments only– Cares only if value is capacity


2007

83

Split Counter

• Enqueuer decrements enqSidePermits• Dequeuer increments deqSidePermits• When enqueuer runs out

– Locks deqLock– Transfers permits

• Intermittent synchronization– Not with each method call– Need both locks! (careful …)


2007

84

A Lock-Free Queue

Sentinel

head

tail


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85

Compare and Set

CAS


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86

Enqueue

head

tail

Enq( )


2007

87

Enqueue

head

tail


2007

88

Logical Enqueue

head

tail

CAS


2007

89

Physical Enqueue

head

tail

Enqueue Node

CAS


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90

Enqueue

• These two steps are not atomic• The tail field refers to either

– Actual last Node (good)– Penultimate Node (not so good)

• Be prepared!


200791

Enqueue

• What do you do if you find– A trailing tail?

• Stop and help fix it– If tail node has non-null next field– CAS the queue’s tail field to tail.next

• As in the universal construction


2007

92

When CASs Fail

• During logical enqueue– Abandon hope, restart– Still lock-free (why?)

• During physical enqueue– Ignore it (why?)


2007

93

Dequeuer

head

tail

Read value


2007

94

Dequeuer

head

tail

Make first Node new sentinel

CAS


2007

95

Memory Reuse?

• What do we do with nodes after we dequeue them?

• Java: let garbage collector deal?• Suppose there is no GC, or we

prefer not to use it?


2007

96

Dequeuer

head

tail

CAS

Can recycle


2007

97

Simple Solution

• Each thread has a free list of unused queue nodes

• Allocate node: pop from list• Free node: push onto list• Deal with underflow somehow …


2007

98

Why Recycling is Hard

Free pool

head tail

Want to redirect

tailfrom

grey to red

zzz…


2007

99

Both Nodes Reclaimed

Free pool

zzz

head tail


2007

100

One Node Recycled

Free pool

Yawn!

head tail


2007

101

Why Recycling is Hard

Free pool

CAShead tail

OK, here I go!


2007

102

Final State

Free pool

zOMG what went wrong?

head tail

Bad news


2007

103

The Dreaded ABA Problem

Head pointer has value AThread reads value A

head tail


2007

104

Dreaded ABA continued

zzz Head pointer has value BNode A freed

head tail


2007

105


Yawn! Head pointer has value A againNode A recycled & reinitialized

head tail


2007

106


CAS succeeds because pointer matcheseven though pointer’s meaning has changed

CAShead tail


2007

107

The Dreaded ABA Problem

• Is a result of CAS() semantics– I blame Sun, Intel, AMD, …

• Not with Load-Locked/Store-Conditional– Good for IBM?


2007

108

Dreaded ABA – A Solution

• Tag each pointer with a counter• Unique over lifetime of node• Pointer size vs word size issues• Overflow?

– Don’t worry be happy?– Bounded tags?

• AtomicStampedReference class


2007

109

Atomic Stamped Reference

• AtomicStampedReference class– Java.util.concurrent.atomic package

address S

Stamp

Reference

Can get reference and stamp atomically


2007

110

Concurrent Stack

• Methods– push(x) – pop()

• Last-in, First-out (LIFO) order• Lock-Free!


2007

111

Empty Stack

Top


2007

112

Push

Top


2007

113

Push

TopCAS


2007

114

Push

Top


2007

115

Push

Top


2007

116

Push

Top


2007

117

Push

TopCAS


2007

118

Push

Top


2007

119

Pop

Top


2007

120

Pop

TopCAS


2007

121

Pop

TopCAS

mine!


2007

122

Pop

TopCAS


2007

123

Pop

Top


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124

public class LockFreeStack { private AtomicReference top = new AtomicReference(null); public boolean tryPush(Node node){ Node oldTop = top.get(); node.next = oldTop; return(top.compareAndSet(oldTop, node)) } public void push(T value) { Node node = new Node(value); while (true) { if (tryPush(node)) { return; } else backoff.backoff(); }}

Lock-free Stack


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125

public class LockFreeStack { private AtomicReference top = new AtomicReference(null); public Boolean tryPush(Node node){ Node oldTop = top.get(); node.next = oldTop; return(top.compareAndSet(oldTop, node)) }public void push(T value) { Node node = new Node(value); while (true) { if (tryPush(node)) { return; } else backoff.backoff()}}

Lock-free Stack

tryPush attempts to push a node


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126

public class LockFreeStack { private AtomicReference top = new AtomicReference(null); public boolean tryPush(Node node){ Node oldTop = top.get(); node.next = oldTop; return(top.compareAndSet(oldTop, node)) } public void push(T value) { Node node = new Node(value); while (true) { if (tryPush(node)) { return; } else backoff.backoff()}}

Lock-free Stack

Read top value


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127


Lock-free Stack

current top will be new node’s successor


2007

128


Lock-free Stack

Try to swing top, return success or failure


2007

129


Lock-free Stack

Push calls tryPush


2007

130


Lock-free Stack

Create new node


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131


Lock-free Stack

If tryPush() fails,back off before retrying

Makes scheduling benevolent so Method is effectively wait-free


2007

132

Lock-free Stack

• Good– No locking

• Bad– Without GC, fear ABA– Without backoff, huge contention at

top – In any case, no parallelism


2007

133

Big Question

• Are stacks inherently sequential?• Reasons why

– Every pop() call fights for top item

• Reasons why not– Stay tuned …


2007

134

Elimination-Backoff Stack

• How to– “turn contention into parallelism”

• Replace familiar– exponential backoff

• With alternative– elimination-backoff


2007

135

Observation

Push( )

Pop()

linearizable stack

After an equal number of pushes and pops, stack stays the same

Yes!


2007

136

Idea: Elimination Array

Push( )

Pop()

stack

Pick at random

Pick at random

Elimination Array


2007

137

Push Collides With Pop

Push( )

Pop()

stack

continue

continue

No need to access stack

Yes!


2007

138

No Collision

Push( )

Pop()

stack

If no collision, access stack

If pushes collide or pops collide access stack


2007

139


• Lock-free stack + elimination array• Access Lock-free stack,

– If uncontended, apply operation – if contended, back off to elimination

array and attempt elimination


2007

140


Push( )

Pop()TopCAS

If CAS fails, back off


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141

Dynamic Range and Delay

Push( )

Pick random range and max time to wait for collision based on level ofcontention encountered


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142

Linearizability

• Un-eliminated calls– linearized as before

• Eliminated calls:– linearize pop() immediately after

matching push()

• Combination is a linearizable stack


2007

143

Un-Eliminated Linearizability

push(v1)

timetime

linearizable

push(v1)

pop(v1)pop(v1)


2007

144

Eliminated Linearizability

pop(v2)push(v1)

push(v2)

timetime

push(v2)

linearizable

pop(v2)push(v1)

pop(v1)pop(v1)

Collision Point

Red calls are eliminated


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145

Backoff Has Dual Effect

• Elimination introduces parallelism• Backoff onto array cuts contention

on lock-free stack• Elimination in array cuts down

total number of threads ever accessing lock-free stack


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146

public class EliminationArray { private static final int duration = ...; private static final int timeUnit = ...; Exchanger<T>[] exchanger; public EliminationArray(int capacity) { exchanger = new Exchanger[capacity]; for (int i = 0; i < capacity; i++) exchanger[i] = new Exchanger<T>(); … } …}

Elimination Array


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147

public class EliminationArray { private static final int duration = ...; private static final int timeUnit = ...; Exchanger<T>[] exchanger; public EliminationArray(int capacity) { exchanger = new Exchanger[capacity]; for (int i = 0; i < capacity; i++) exchanger[i] = new Exchanger<T>(); … } …}

Elimination Array

An array of exchangers


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148

Lock-free Exchanger

EMPTY


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149

EMPTY

Lock-free Exchanger

CAS


2007

150

WAITING

Lock-free Exchanger


2007

151

Lock-free ExchangerIn search of partner …

WAITING


2007

152

WAITING

Lock-free Exchanger

Slot

Still waiting …

Try to exchange

item and set state to BUSY

CAS


2007

153

BUSY

Lock-free Exchanger

Slot

Partner showed up, take item and reset to

EMPTY

item stamp/state


2007

154

EMPTYBUSY

Lock-free Exchanger

Slot

item stamp/state

Partner showed up, take item and reset to

EMPTY


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155

public class Exchanger<T> { AtomicStampedReference<T> slot = new AtomicStampedReference<T>(null, 0);

A Lock-Free Exchanger


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156

public class Exchanger<T> { AtomicStampedReference<T> slot = new AtomicStampedReference<T>(null, 0);

A Lock-Free Exchanger

Atomically modifiable reference + time stamp


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157

Atomic Stamped Reference

• AtomicStampedReference class– Java.util.concurrent.atomic package

• In C or C++:

address S

Stamp

Reference


2007

158

Extracting Reference & Stamp

Public T get(int[] stampHolder);


2007

159

Extracting Reference & Stamp

Public T get(int[] stampHolder);

Returns reference to object of type T

Returns stamp at array index

0!


2007

160

Exchanger Status

enum Status {EMPTY, WAITING, BUSY};


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161

Exchanger Status


Nothing yet


2007

162

Exchange Status


Nothing yet

One thread is waiting for

rendez-vous


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163

Exchange Status


Nothing yet

One thread is waiting for

rendez-vous Other threads busy with rendez-

vous


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164

public T Exchange(T myItem, long nanos) throws TimeoutException { long timeBound = System.nanoTime() + nanos; int[] stampHolder = {EMPTY}; while (true) { if (System.nanoTime() > timeBound) throw new TimeoutException(); T herItem = slot.get(stampHolder); int stamp = stampHolder[0]; switch(stamp) { case EMPTY: … // slot is free case WAITING: … // someone waiting for me case BUSY: … // others exchanging } }

The Exchange


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165


The Exchange

Item & timeout


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166


The Exchange

Array to hold timestamp


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167

public T Exchange(T myItem, long nanos) throws TimeoutException { long timeBound = System.nanoTime() + nanos; int[] stampHolder = {0}; while (true) { if (System.nanoTime() > timeBound) throw new TimeoutException(); T herItem = slot.get(stampHolder); int stamp = stampHolder[0]; switch(stamp) { case EMPTY: // slot is free case WAITING: // someone waiting for me case BUSY: // others exchanging } }}

The Exchange

Loop until timeout


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public T Exchange(T myItem, long nanos) throws TimeoutException { long timeBound = System.nanoTime() + nanos; int[] stampHolder = {0}; while (true) { if (System.nanoTime() > timeBound) throw new TimeoutException(); T herItem = slot.get(stampHolder); int stamp = stampHolder[0]; switch(stamp) { case EMPTY: // slot is free case WAITING: // someone waiting for me case BUSY: // others exchanging } }}

The Exchange

Get other’s item and timestamp


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169

public T Exchange(T myItem, long nanos) throws TimeoutException { long timeBound = System.nanoTime() + nanos; int[] stampHolder = {0}; while (true) { if (System.nanoTime() > timeBound) throw new TimeoutException(); T herItem = slot.get(stampHolder); int stamp = stampHolder[0]; switch(stamp) { case EMPTY: … // slot is free case WAITING: … // someone waiting for me case BUSY: … // others exchanging } }}

The Exchange

Exchanger slot has three states


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170

case EMPTY: // slot is free if (slot.compareAndSet(herItem, myItem, EMPTY, WAITING)) { while (System.nanoTime() < timeBound){ herItem = slot.get(stampHolder); if (stampHolder[0] == BUSY) { slot.set(null, EMPTY); return herItem; }} if (slot.compareAndSet(myItem, null, WAITING, EMPTY)){throw new TimeoutException(); } else { herItem = slot.get(stampHolder); slot.set(null, EMPTY); return herItem; }} break;

Exchanger State EMPTY


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171



Slot is free, try to insert myItem and change state to WAITING


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172



Loop while still time left to attempt exchange


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173

case EMPTY: // slot is free if (slot.compareAndSet(herItem, myItem, WAITING, BUSY)) { while (System.nanoTime() < timeBound){ herItem = slot.get(stampHolder); if (stampHolder[0] == BUSY) { slot.set(null, EMPTY); return herItem; }} if (slot.compareAndSet(myItem, null, WAITING, EMPTY)){throw new TimeoutException(); } else { herItem = slot.get(stampHolder); slot.set(null, EMPTY); return herItem; }} break;


Get item and stamp in slot and check if state changed to BUSY


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174



If successful reset slot state to EMPTY


2007

175



and return item found in slot


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176



Otherwise we ran out of time, try to reset state to EMPTY, if successful time out


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177



If reset failed, someone showed up after all, take that item


2007

178



Set slot to EMPTY with new timestamp and return item found


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179



If initial CAS failed then someone else changed state from EMPTY to WAITING so retry from start


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180

case WAITING: // someone waiting for me if (slot.CAS(herItem, myItem, WAITING, BUSY)) return herItem; break;case BUSY: // others in middle of exchanging break;default: // impossible break;}

States WAITING and BUSY


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Someone is waiting for an exchange, so try to CAS in my item in & change state to BUSY


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182



If successful, return that item. Otherwise another thread got it.


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183



Other threads using slot, so start over.


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184

The Exchanger Slot

• Exchanger is lock-free• Because the only way an exchange

can fail is if others repeatedly succeeded or no-one showed up

• The slot we need does not require symmetric exchange


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185

public class EliminationArray {…public T visit(T value, int Range) throws TimeoutException { int slot = random.nextInt(Range); int nanodur = convertToNanos(duration, timeUnit)); return (exchanger[slot].exchange(value, nanodur) }}

Elimination Array


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Elimination Array

Visit elimination array with value and range


2007

187


Elimination Array

Pick a random array entry


2007

188


Elimination Array

Exchange value or time out


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189

public void push(T value) {... while (true) { if (tryPush(node)) { return; } else try { T otherValue = eliminationArray.visit(value,policy.Range); if (otherValue == null) { return; }}

Elimination Stack Push


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190



First try to push


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191



If failed back-off to try to eliminate


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192



Value being pushed and range to try


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Only a pop inserts null value so elimination was successful


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194



Else retry push on lock-free stack


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195

public T pop() { ... while (true) { if (tryPop()) { return returnNode.value; } else try { T otherValue = eliminationArray.visit(null,policy.Range; if otherValue != null) { return otherValue; } }}}

Elimination Stack Pop


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public T pop() { ... while (true) { if (tryPop()) { return returnNode.value; } else try { T otherValue = eliminationArray.visit(null,policy.Range; if ( otherValue != null) { return otherValue; } }}}

Elimination Stack Pop

Like push, non-null value pushed by other thread, so elimination

succeeds


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197

Summary• We saw both lock-based and lock-

free implementations of queues and stacks

• Not every data structure that looks sequential is sequential.– Linearizable stack not inherently

sequential • ABA is a real problem, fear it.


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Concurrent Queues and Stacks Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit.

Documents

deq tail head slide

exception slide

getanddecrement slide

ok slide

bounded queue head tail

deq calls deqlock slide

enqueue node slide

lifo order slide