Download presentation
Presentation is loading. Please wait.
1
Concurrent Objects Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit
2
Art of Multiprocessor Programming 2 Concurrent Computation memory object
3
Art of Multiprocessor Programming 3 Objectivism What is a concurrent object? –How do we describe one? –How do we implement one? –How do we tell if we’re right?
4
Art of Multiprocessor Programming 4 Objectivism What is a concurrent object? –How do we describe one? –How do we tell if we’re right?
5
Art of Multiprocessor Programming 5 FIFO Queue: Enqueue Method q.enq( )
6
Art of Multiprocessor Programming 6 FIFO Queue: Dequeue Method q.deq()/
7
Art of Multiprocessor Programming 7 Lock-Based Queue head tail 0 2 1 54 3 y x capacity = 8 7 6
8
Art of Multiprocessor Programming 8 Lock-Based Queue head tail 0 2 1 54 3 capacity = 8 7 6 Fields protected by single shared lock y x
9
class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 9 A Lock-Based Queue Fields protected by single shared lock 0 1 capacity-1 2 head tail y z
![class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 9 A Lock-Based Queue Fields protected by single shared lock 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_9.jpg "class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 9 A Lock-Based Queue Fields protected by single shared lock 0 1 capacity-1 2 head tail y z")
10
Art of Multiprocessor Programming 10 Lock-Based Queue head tail 0 2 1 54 3 Initially: head = tail 7 6
11
class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 11 A Lock-Based Queue Initially head = tail 0 1 capacity-1 2 head tail y z
![class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 11 A Lock-Based Queue Initially head = tail 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_11.jpg "class LockBasedQueue { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; } Art of Multiprocessor Programming 11 A Lock-Based Queue Initially head = tail 0 1 capacity-1 2 head tail y z")
12
Art of Multiprocessor Programming 12 Lock-Based deq() head tail 0 2 54 7 36 1 y x
13
Art of Multiprocessor Programming 13 Acquire Lock head tail 0 2 54 7 36 y x 1 Waiting to enqueue… My turn … y x
14
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 14 Implementation: deq() Acquire lock at method start 0 1 capacity-1 2 head tail y z
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 14 Implementation: deq() Acquire lock at method start 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_14.jpg "public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 14 Implementation: deq() Acquire lock at method start 0 1 capacity-1 2 head tail y z")
15
Art of Multiprocessor Programming 15 Check if Non-Empty head tail 0 2 54 7 36 1 y x Waiting to enqueue… Not equal?
16
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 16 Implementation: deq() If queue empty throw exception 0 1 capacity-1 2 head tail y z
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 16 Implementation: deq() If queue empty throw exception 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_16.jpg "public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 16 Implementation: deq() If queue empty throw exception 0 1 capacity-1 2 head tail y z")
17
Art of Multiprocessor Programming 17 Modify the Queue head tail 0 2 1 54 7 36 head Waiting to enqueue… y x
18
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 18 Implementation: deq() Queue not empty? Remove item and update head 0 1 capacity-1 2 head tail y z
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 18 Implementation: deq() Queue not empty.](http://images.slideplayer.com/18/6162299/slides/slide_18.jpg "Remove item and update head 0 1 capacity-1 2 head tail y z.")
19
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 19 Implementation: deq() Return result 0 1 capacity-1 2 head tail y z
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 19 Implementation: deq() Return result 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_19.jpg "public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 19 Implementation: deq() Return result 0 1 capacity-1 2 head tail y z")
20
Art of Multiprocessor Programming 20 Release the Lock tail 0 2 1 54 7 36 y x head Waiting…
21
Art of Multiprocessor Programming 21 Release the Lock tail 0 2 1 54 7 36 y x head My turn!
22
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 22 Implementation: deq() Release lock no matter what! 0 1 capacity-1 2 head tail y z
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 22 Implementation: deq() Release lock no matter what.](http://images.slideplayer.com/18/6162299/slides/slide_22.jpg "0 1 capacity-1 2 head tail y z.")
23
public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 23 Implementation: deq() Should be correct because modifications are mutually exclusive… Should be correct because modifications are mutually exclusive…
![public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 23 Implementation: deq() Should be correct because modifications are mutually exclusive… Should be correct because modifications are mutually exclusive…](http://images.slideplayer.com/18/6162299/slides/slide_23.jpg "public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Art of Multiprocessor Programming 23 Implementation: deq() Should be correct because modifications are mutually exclusive… Should be correct because modifications are mutually exclusive…")
24
Art of Multiprocessor Programming 24 Now consider the following implementation The same thing without mutual exclusion For simplicity, only two threads –One thread enq only –The other deq only
25
Art of Multiprocessor Programming 25 Wait-free 2-Thread Queue head tail 0 2 1 54 7 36 y x capacity = 8
26
Art of Multiprocessor Programming 26 Wait-free 2-Thread Queue tail 0 2 54 7 36 y x 1 enq(z) deq() z head
27
Art of Multiprocessor Programming 27 Wait-free 2-Thread Queue head tail 0 2 54 7 36 y 1 queue[tail] = z result = x z x
![Art of Multiprocessor Programming 27 Wait-free 2-Thread Queue head tail y 1 queue[tail] = z result = x z x](http://images.slideplayer.com/18/6162299/slides/slide_27.jpg "Art of Multiprocessor Programming 27 Wait-free 2-Thread Queue head tail y 1 queue[tail] = z result = x z x")
28
Art of Multiprocessor Programming 28 Wait-free 2-Thread Queue tail 0 2 54 7 36 y 1 tail-- head++ z head x
29
public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} Art of Multiprocessor Programming 29 Wait-free 2-Thread Queue No lock needed ! 0 1 capacity-1 2 head tail y z
![public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} Art of Multiprocessor Programming 29 Wait-free 2-Thread Queue No lock needed .](http://images.slideplayer.com/18/6162299/slides/slide_29.jpg "0 1 capacity-1 2 head tail y z.")
30
Wait-free 2-Thread Queue Art of Multiprocessor Programming 30 public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } How do we define “correct” when modifications are not mutually exclusive?
![Wait-free 2-Thread Queue Art of Multiprocessor Programming 30 public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } How do we define correct when modifications are not mutually exclusive](http://images.slideplayer.com/18/6162299/slides/slide_30.jpg "Wait-free 2-Thread Queue Art of Multiprocessor Programming 30 public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } How do we define correct when modifications are not mutually exclusive")
31
Art of Multiprocessor Programming 31 What is a Concurrent Queue? Need a way to specify a concurrent queue object Need a way to prove that an algorithm implements the object’s specification Lets talk about object specifications …
32
Correctness and Progress In a concurrent setting, we need to specify both the safety and the liveness properties of an object Need a way to define –when an implementation is correct –the conditions under which it guarantees progress Art of Multiprocessor Programming 32 Lets begin with correctness
33
Art of Multiprocessor Programming 33 Sequential Objects Each object has a state –Usually given by a set of fields –Queue example: sequence of items Each object has a set of methods –Only way to manipulate state –Queue example: enq and deq methods
34
Art of Multiprocessor Programming 34 Sequential Specifications If (precondition) –the object is in such-and-such a state –before you call the method, Then (postcondition) –the method will return a particular value –or throw a particular exception. and (postcondition, con’t) –the object will be in some other state –when the method returns,
35
Art of Multiprocessor Programming 35 Pre and PostConditions for Dequeue Precondition: –Queue is non-empty Postcondition: –Returns first item in queue Postcondition: –Removes first item in queue
36
Art of Multiprocessor Programming 36 Pre and PostConditions for Dequeue Precondition: –Queue is empty Postcondition: –Throws Empty exception Postcondition: –Queue state unchanged
37
Art of Multiprocessor Programming 37 Why Sequential Specifications Totally Rock Interactions among methods captured by side- effects on object state –State meaningful between method calls Documentation size linear in number of methods –Each method described in isolation Can add new methods –Without changing descriptions of old methods
38
Art of Multiprocessor Programming 38 What About Concurrent Specifications ? Methods? Documentation? Adding new methods?
39
Art of Multiprocessor Programming 39 Methods Take Time time
40
Art of Multiprocessor Programming 40 Methods Take Time time invocation 12:00 q.enq(... ) time
41
Art of Multiprocessor Programming 41 Methods Take Time time Method call invocation 12:00 time q.enq(... )
42
Art of Multiprocessor Programming 42 Methods Take Time time Method call invocation 12:00 time q.enq(... )
43
Art of Multiprocessor Programming 43 Methods Take Time time Method call invocation 12:00 time void response 12:01 q.enq(... )
44
Art of Multiprocessor Programming 44 Sequential vs Concurrent Sequential –Methods take time? Who knew? Concurrent –Method call is not an event –Method call is an interval.
45
Art of Multiprocessor Programming 45 time Concurrent Methods Take Overlapping Time time
46
Art of Multiprocessor Programming 46 time Concurrent Methods Take Overlapping Time time Method call
47
Art of Multiprocessor Programming 47 time Concurrent Methods Take Overlapping Time time Method call
48
Art of Multiprocessor Programming 48 time Concurrent Methods Take Overlapping Time time Method call
49
Art of Multiprocessor Programming 49 Sequential vs Concurrent Sequential: –Object needs meaningful state only between method calls Concurrent –Because method calls overlap, object might never be between method calls
50
Art of Multiprocessor Programming 50 Sequential vs Concurrent Sequential: –Each method described in isolation Concurrent –Must characterize all possible interactions with concurrent calls What if two enq() calls overlap? Two deq() calls? enq() and deq() ? …
51
Art of Multiprocessor Programming 51 Sequential vs Concurrent Sequential: –Can add new methods without affecting older methods Concurrent: –Everything can potentially interact with everything else
52
Art of Multiprocessor Programming 52 Sequential vs Concurrent Sequential: –Can add new methods without affecting older methods Concurrent: –Everything can potentially interact with everything else Panic!
53
Art of Multiprocessor Programming 53 The Big Question What does it mean for a concurrent object to be correct? –What is a concurrent FIFO queue? –FIFO means strict temporal order –Concurrent means ambiguous temporal order
54
Art of Multiprocessor Programming 54 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); }
![Art of Multiprocessor Programming 54 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); }](http://images.slideplayer.com/18/6162299/slides/slide_54.jpg "Art of Multiprocessor Programming 54 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); }")
55
Art of Multiprocessor Programming 55 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } All queue modifications are mutually exclusive
![Art of Multiprocessor Programming 55 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } All queue modifications are mutually exclusive](http://images.slideplayer.com/18/6162299/slides/slide_55.jpg "Art of Multiprocessor Programming 55 Intuitively… public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } All queue modifications are mutually exclusive")
56
Art of Multiprocessor Programming 56 time Intuitively q.deq q.enq enq deq lock() unlock() lock() unlock() Behavior is “Sequential” enq deq Lets capture the idea of describing the concurrent via the sequential
57
Art of Multiprocessor Programming 57 Linearizability Each method should –“take effect” –Instantaneously –Between invocation and response events Object is correct if this “sequential” behavior is correct Any such concurrent object is –Linearizable™
58
Art of Multiprocessor Programming 58 Is it really about the object? Each method should –“take effect” –Instantaneously –Between invocation and response events Sounds like a property of an execution… A linearizable object: one all of whose possible executions are linearizable
59
Art of Multiprocessor Programming 59 Example time
60
Art of Multiprocessor Programming 60 Example time q.enq(x) time
61
Art of Multiprocessor Programming 61 Example time q.enq(x) q.enq(y) time
62
Art of Multiprocessor Programming 62 Example time q.enq(x) q.enq(y)q.deq(x) time
63
Art of Multiprocessor Programming 63 Example time q.enq(x) q.enq(y)q.deq(x) q.deq(y) time
64
Art of Multiprocessor Programming 64 Example time q.enq(x) q.enq(y)q.deq(x) q.deq(y) linearizable q.enq(x) q.enq(y)q.deq(x) q.deq(y) time
65
Art of Multiprocessor Programming 65 Example time q.enq(x) q.enq(y)q.deq(x) q.deq(y) Valid? q.enq(x) q.enq(y)q.deq(x) q.deq(y) time
66
Art of Multiprocessor Programming 66 Example time
67
Art of Multiprocessor Programming 67 Example time q.enq(x)
68
Art of Multiprocessor Programming 68 Example time q.enq(x)q.deq(y)
69
Art of Multiprocessor Programming 69 Example time q.enq(x) q.enq(y) q.deq(y)
70
Art of Multiprocessor Programming 70 Example time q.enq(x) q.enq(y) q.deq(y) q.enq(x) q.enq(y)
71
Art of Multiprocessor Programming 71 Example time q.enq(x) q.enq(y) q.deq(y) q.enq(x) q.enq(y) not linearizable
72
Art of Multiprocessor Programming 72 Example time
73
Art of Multiprocessor Programming 73 Example time q.enq(x) time
74
Art of Multiprocessor Programming 74 Example time q.enq(x) q.deq(x) time
75
Art of Multiprocessor Programming 75 Example time q.enq(x) q.deq(x) q.enq(x) q.deq(x) time
76
Art of Multiprocessor Programming 76 Example time q.enq(x) q.deq(x) q.enq(x) q.deq(x) linearizable time
77
Art of Multiprocessor Programming 77 Example time q.enq(x) time
78
Art of Multiprocessor Programming 78 Example time q.enq(x) q.enq(y) time
79
Art of Multiprocessor Programming 79 Example time q.enq(x) q.enq(y) q.deq(y) time
80
Art of Multiprocessor Programming 80 Example time q.enq(x) q.enq(y) q.deq(y) q.deq(x) time
81
Art of Multiprocessor Programming 81 q.enq(x) q.enq(y) q.deq(y) q.deq(x) Comme ci Example time Comme ça multiple orders OK linearizable
82
Art of Multiprocessor Programming 82 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(0)
83
Art of Multiprocessor Programming 83 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(0) write(1) already happened
84
Art of Multiprocessor Programming 84 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(0) write(1) write(1) already happened
85
Art of Multiprocessor Programming 85 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(0) write(1) write(1) already happened not linearizable
86
Art of Multiprocessor Programming 86 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(1) write(1) already happened
87
Art of Multiprocessor Programming 87 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(1) write(1)write(2) write(1) already happened
88
Art of Multiprocessor Programming 88 Read/Write Register Example time read(1)write(0) write(1) write(2) time read(1) write(1)write(2) not linearizable write(1) already happened
89
Art of Multiprocessor Programming 89 Read/Write Register Example time write(0) write(1) write(2) time read(1)
90
Art of Multiprocessor Programming 90 Read/Write Register Example time write(0) write(1) write(2) time read(1) write(1) write(2)
91
Art of Multiprocessor Programming 91 Read/Write Register Example time write(0) write(1) write(2) time read(1) write(1) write(2) linearizable
92
Art of Multiprocessor Programming 92 Talking About Executions Why? –Can’t we specify the linearization point of each operation without describing an execution? Not Always –In some cases, linearization point depends on the execution
93
Art of Multiprocessor Programming 93 Formal Model of Executions Define precisely what we mean –Ambiguity is bad when intuition is weak Allow reasoning –Formal –But mostly informal In the long run, actually more important Ask me why!
94
Art of Multiprocessor Programming 94 Split Method Calls into Two Events Invocation –method name & args –q.enq(x) Response –result or exception –q.enq(x) returns void –q.deq() returns x –q.deq() throws empty
95
Art of Multiprocessor Programming 95 Invocation Notation A q.enq(x)
96
Art of Multiprocessor Programming 96 Invocation Notation A q.enq(x) thread
97
Art of Multiprocessor Programming 97 Invocation Notation A q.enq(x) thread method
98
Art of Multiprocessor Programming 98 Invocation Notation A q.enq(x) thread object method
99
Art of Multiprocessor Programming 99 Invocation Notation A q.enq(x) thread object method arguments
100
Art of Multiprocessor Programming 100 Response Notation A q: void
101
Art of Multiprocessor Programming 101 Response Notation A q: void thread
102
Art of Multiprocessor Programming 102 Response Notation A q: void thread result
103
Art of Multiprocessor Programming 103 Response Notation A q: void thread object result
104
Art of Multiprocessor Programming 104 Response Notation A q: void thread object result Method is implicit
105
Art of Multiprocessor Programming 105 Response Notation A q: empty() thread object Method is implicit exception
106
Art of Multiprocessor Programming 106 History - Describing an Execution A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 Sequence of invocations and responses H =
107
Art of Multiprocessor Programming 107 Definition Invocation & response match if A q.enq(3) A q:void Thread names agree Object names agree Method call
108
Art of Multiprocessor Programming 108 Object Projections A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 H =
109
Art of Multiprocessor Programming 109 Object Projections A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 H|q =
110
Art of Multiprocessor Programming 110 Thread Projections A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 H =
111
Art of Multiprocessor Programming 111 Thread Projections A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 H|B =
112
Art of Multiprocessor Programming 112 Complete Subhistory A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 An invocation is pending if it has no matching respnse H =
113
Art of Multiprocessor Programming 113 Complete Subhistory A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 May or may not have taken effect H =
114
Art of Multiprocessor Programming 114 Complete Subhistory A q.enq(3) A q:void A q.enq(5) B p.enq(4) B p:void B q.deq() B q:3 discard pending invocations H =
115
Art of Multiprocessor Programming 115 Complete Subhistory A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 Complete(H) =
116
Art of Multiprocessor Programming 116 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5)
117
Art of Multiprocessor Programming 117 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match
118
Art of Multiprocessor Programming 118 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match
119
Art of Multiprocessor Programming 119 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match
120
Art of Multiprocessor Programming 120 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match Final pending invocation OK
121
Art of Multiprocessor Programming 121 Sequential Histories A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 A q:enq(5) match Final pending invocation OK Method calls of different threads do not interleave
122
Art of Multiprocessor Programming 122 Well-Formed Histories H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3
123
Art of Multiprocessor Programming 123 Well-Formed Histories H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 H|B= B p.enq(4) B p:void B q.deq() B q:3 Per-thread projections sequential
124
Art of Multiprocessor Programming 124 Well-Formed Histories H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 H|B= B p.enq(4) B p:void B q.deq() B q:3 A q.enq(3) A q:void H|A= Per-thread projections sequential
125
Art of Multiprocessor Programming 125 Equivalent Histories H= A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3 Threads see the same thing in both A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3 G= H|A = G|A H|B = G|B
126
Art of Multiprocessor Programming 126 Sequential Specifications A sequential specification is some way of telling whether a –Single-thread, single-object history –Is legal For example: –Pre and post-conditions –But plenty of other techniques exist …
127
Art of Multiprocessor Programming 127 Legal Histories A sequential (multi-object) history H is legal if –For every object x –H|x is in the sequential spec for x
128
Art of Multiprocessor Programming 128 Precedence A q.enq(3) B p.enq(4) B p.void A q:void B q.deq() B q:3 A method call precedes another if response event precedes invocation event Method call
129
Art of Multiprocessor Programming 129 Non-Precedence A q.enq(3) B p.enq(4) B p.void B q.deq() A q:void B q:3 Some method calls overlap one another Method call
130
Art of Multiprocessor Programming 130 Notation Given –History H –method executions m 0 and m 1 in H We say m 0 H m 1, if –m 0 precedes m 1 Relation m 0 H m 1 is a –Partial order –Total order if H is sequential m0m0 m1m1
131
Art of Multiprocessor Programming 131 Linearizability History H is linearizable if it can be extended to G by –Appending zero or more responses to pending invocations –Discarding other pending invocations So that G is equivalent to –Legal sequential history S –where G S
132
Art of Multiprocessor Programming 132 Remarks Some pending invocations –Took effect, so keep them –Discard the rest Condition G S –Means that S respects “real-time order” of G
133
Art of Multiprocessor Programming 133 Ensuring G S time a b GG SS c GG G = {a c,b c} S = {a b,a c,b c} A limitation on the Choice of S!
134
Art of Multiprocessor Programming 134 A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) Example time B q.enq(4 ) A q.enq(3) B q.deq(4 ) B q.enq(6)
135
Art of Multiprocessor Programming 135 Example Complete this pending invocation time B q.enq(4 ) B q.deq(3 ) B q.enq(6) A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q.enq(3)
136
Art of Multiprocessor Programming 136 Example Complete this pending invocation time B q.enq(4 ) B q.deq(4 ) B q.enq(6) A q.enq(3 ) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q:void
137
Art of Multiprocessor Programming 137 Example time B q.enq(4 ) B q.deq(4 ) B q.enq(6) A q.enq(3 ) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q:void discard this one
138
Art of Multiprocessor Programming 138 Example time B q.enq(4 ) B q.deq(4 ) A q.enq(3 ) B q.enq(4) B q:void B q.deq() B q:4 A q:void discard this one
139
Art of Multiprocessor Programming 139 A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void Example time B q.enq(4 ) B q.deq(4 ) A q.enq(3 )
140
Art of Multiprocessor Programming 140 A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 A q:void Example time B q.enq(4) B q:void A q.enq(3) A q:void B q.deq() B q:4 B q.enq(4 ) B q.deq(4 ) A q.enq(3 )
141
Art of Multiprocessor Programming 141 B q.enq(4 ) B q.deq(4 ) A q.enq(3 ) B q.enq(4) B q:void B q.deq() B q:4 A q:void Example time B q.enq(4) B q:void A q.enq(3) A q:void B q.deq() B q:4 Equivalent sequential history
142
Art of Multiprocessor Programming 142 Concurrency How much concurrency does linearizability allow? When must a method invocation block?
143
Art of Multiprocessor Programming 143 Concurrency Focus on total methods –Defined in every state Example: –deq() that throws Empty exception –Versus deq() that waits … Why? –Otherwise, blocking unrelated to synchronization
144
Art of Multiprocessor Programming 144 Concurrency Question: When does linearizability require a method invocation to block? Answer: never. Linearizability is non-blocking
145
Art of Multiprocessor Programming 145 Non-Blocking Theorem If method invocation A q.inv( … ) is pending in history H, then there exists a response A q:res( … ) such that H + A q:res( … ) is linearizable
146
Art of Multiprocessor Programming 146 Proof Pick linearization S of H If S already contains –Invocation A q.inv( … ) and response, –Then we are done. Otherwise, pick a response such that –S + A q.inv( … ) + A q:res( … ) –Possible because object is total.
147
Art of Multiprocessor Programming 147 Composability Theorem History H is linearizable if and only if –For every object x –H|x is linearizable We care about objects only! –(Materialism?)
148
Art of Multiprocessor Programming 148 Why Does Composability Matter? Modularity Can prove linearizability of objects in isolation Can compose independently-implemented objects
149
Art of Multiprocessor Programming 149 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } 0 1 capacity-1 2 head tail y z
![Art of Multiprocessor Programming 149 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_149.jpg "Art of Multiprocessor Programming 149 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } 0 1 capacity-1 2 head tail y z")
150
Art of Multiprocessor Programming 150 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Linearization points are when locks are released 0 1 capacity-1 2 head tail y z
![Art of Multiprocessor Programming 150 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Linearization points are when locks are released 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_150.jpg "Art of Multiprocessor Programming 150 Reasoning About Linearizability: Locking public T deq() throws EmptyException { lock.lock(); try { if (tail == head) throw new EmptyException(); T x = items[head % items.length]; head++; return x; } finally { lock.unlock(); } Linearization points are when locks are released 0 1 capacity-1 2 head tail y z")
151
Art of Multiprocessor Programming 151 More Reasoning: Wait-free 0 1 capacity-1 2 head tail y z public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} 0 1 capacity-1 2 head tail y z
![Art of Multiprocessor Programming 151 More Reasoning: Wait-free 0 1 capacity-1 2 head tail y z public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} 0 1 capacity-1 2 head tail y z](http://images.slideplayer.com/18/6162299/slides/slide_151.jpg "Art of Multiprocessor Programming 151 More Reasoning: Wait-free 0 1 capacity-1 2 head tail y z public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} 0 1 capacity-1 2 head tail y z")
152
public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} Art of Multiprocessor Programming 152 More Reasoning: Wait-free Linearization order is order head and tail fields modified Remember that there Is only one enqueuer and only one dequeuer Remember that there Is only one enqueuer and only one dequeuer
![public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} Art of Multiprocessor Programming 152 More Reasoning: Wait-free Linearization order is order head and tail fields modified Remember that there Is only one enqueuer and only one dequeuer Remember that there Is only one enqueuer and only one dequeuer](http://images.slideplayer.com/18/6162299/slides/slide_152.jpg "public class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity]; public void enq(Item x) { if (tail-head == capacity) throw new FullException(); items[tail % capacity] = x; tail++; } public Item deq() { if (tail == head) throw new EmptyException(); Item item = items[head % capacity]; head++; return item; }} Art of Multiprocessor Programming 152 More Reasoning: Wait-free Linearization order is order head and tail fields modified Remember that there Is only one enqueuer and only one dequeuer Remember that there Is only one enqueuer and only one dequeuer")
153
Art of Multiprocessor Programming 153 Strategy Identify one atomic step where method “happens” –Critical section –Machine instruction Doesn’t always work –Might need to define several different steps for a given method
154
Art of Multiprocessor Programming 154 Linearizability: Summary Powerful specification tool for shared objects Allows us to capture the notion of objects being “atomic” Don’t leave home without it
155
Art of Multiprocessor Programming 155 Alternative: Sequential Consistency History H is Sequentially Consistent if it can be extended to G by –Appending zero or more responses to pending invocations –Discarding other pending invocations So that G is equivalent to a –Legal sequential history S – Where G S Differs from linearizability
156
Art of Multiprocessor Programming 156 Sequential Consistency No need to preserve real-time order –Cannot re-order operations done by the same thread –Can re-order non-overlapping operations done by different threads Often used to describe multiprocessor memory architectures
157
Art of Multiprocessor Programming 157 Example time
158
Art of Multiprocessor Programming 158 Example time q.enq(x)
159
Art of Multiprocessor Programming 159 Example time q.enq(x)q.deq(y)
160
Art of Multiprocessor Programming 160 Example time q.enq(x) q.enq(y) q.deq(y)
161
Art of Multiprocessor Programming 161 Example time q.enq(x) q.enq(y) q.deq(y) q.enq(x) q.enq(y)
162
Art of Multiprocessor Programming 162 Example time q.enq(x) q.enq(y) q.deq(y) q.enq(x) q.enq(y) not linearizable
163
Art of Multiprocessor Programming 163 Example time q.enq(x) q.enq(y) q.deq(y) q.enq(x) q.enq(y) Yet Sequentially Consistent
164
Art of Multiprocessor Programming 164 Theorem Sequential Consistency is not composable
165
Art of Multiprocessor Programming 165 FIFO Queue Example time p.enq(x)p.deq(y)q.enq(x) time
166
Art of Multiprocessor Programming 166 FIFO Queue Example time p.enq(x)p.deq(y)q.enq(x) q.enq(y)q.deq(x)p.enq(y) time
167
Art of Multiprocessor Programming 167 FIFO Queue Example time p.enq(x)p.deq(y)q.enq(x) q.enq(y)q.deq(x)p.enq(y) History H time
168
Art of Multiprocessor Programming 168 H|p Sequentially Consistent time p.enq(x)p.deq(y) p.enq(y) q.enq(x) q.enq(y)q.deq(x) time
169
Art of Multiprocessor Programming 169 H|q Sequentially Consistent time p.enq(x)p.deq(y)q.enq(x) q.enq(y)q.deq(x)p.enq(y) time
170
Art of Multiprocessor Programming 170 Ordering imposed by p time p.enq(x)p.deq(y)q.enq(x) q.enq(y)q.deq(x)p.enq(y) time
171
Art of Multiprocessor Programming 171 Ordering imposed by q time p.enq(x)p.deq(y)q.enq(x) q.enq(y)q.deq(x)p.enq(y) time
172
Art of Multiprocessor Programming 172 p.enq(x) Ordering imposed by both time q.enq(x) q.enq(y)q.deq(x) time p.deq(y) p.enq(y)
173
Art of Multiprocessor Programming 173 p.enq(x) Combining orders time q.enq(x) q.enq(y)q.deq(x) time p.deq(y) p.enq(y)
174
Art of Multiprocessor Programming 174 Fact Most hardware architectures don’t support sequential consistency Because they think it’s too strong Here’s another story …
175
Art of Multiprocessor Programming 175 The Flag Example time x.write(1) y.read(0) y.write(1) x.read(0) time
176
Art of Multiprocessor Programming 176 The Flag Example time x.write(1) y.read(0) y.write(1) x.read(0) Each thread’s view is sequentially consistent –It went first
177
Art of Multiprocessor Programming 177 The Flag Example time x.write(1) y.read(0) y.write(1) x.read(0) Entire history isn’t sequentially consistent –Can’t both go first
178
Art of Multiprocessor Programming 178 The Flag Example time x.write(1) y.read(0) y.write(1) x.read(0) Is this behavior really so wrong? –We can argue either way …
179
Art of Multiprocessor Programming 179 Opinion: It’s Wrong This pattern –Write mine, read yours Is exactly the flag principle –Beloved of Alice and Bob –Heart of mutual exclusion Peterson Bakery, etc. It’s non-negotiable!
180
Art of Multiprocessor Programming 180 Peterson's Algorithm public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
![Art of Multiprocessor Programming 180 Peterson s Algorithm public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }](http://images.slideplayer.com/18/6162299/slides/slide_180.jpg "Art of Multiprocessor Programming 180 Peterson s Algorithm public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }")
181
Art of Multiprocessor Programming 181 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim)
![Art of Multiprocessor Programming 181 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim)](http://images.slideplayer.com/18/6162299/slides/slide_181.jpg "Art of Multiprocessor Programming 181 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim)")
182
Art of Multiprocessor Programming 182 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim) Observation: proof relied on fact that if a location is stored, a later load by some thread will return this or a later stored value.
![Art of Multiprocessor Programming 182 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim) Observation: proof relied on fact that if a location is stored, a later load by some thread will return this or a later stored value.](http://images.slideplayer.com/18/6162299/slides/slide_182.jpg "Art of Multiprocessor Programming 182 Crux of Peterson Proof (1) write B (flag[B]=true) write B (victim=B) (3) write B (victim=B) write A (victim=A) (2) write A (victim=A) read A (flag[B]) read A (victim) Observation: proof relied on fact that if a location is stored, a later load by some thread will return this or a later stored value.")
183
Art of Multiprocessor Programming 183 Opinion: But It Feels So Right … Many hardware architects think that sequential consistency is too strong Too expensive to implement in modern hardware OK if flag principle –violated by default –Honored by explicit request
184
Hardware Consistancy mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store mov b, %ebx ;Load mov 1, b ;Store mov a, %eax ;Load mov 1, b ;Store mov a, %eax ;Load Initially, a = b = 0. Processor 0Processor 1 What are the final possible values of %eax and %ebx after both processors have executed? Sequential consistency implies that no execution ends with %eax= %ebx = 0 Slide used with permission of Charles E. Leiserson
185
Hardware Consistency ∙ No modern-day processor implements sequential consistency. ∙ Hardware actively reorders instructions. ∙ Compilers may reorder instructions, too. ∙ Why? ∙ Because most of performance is derived from a single thread’s unsynchronized execution of code. Art of Multiprocessor Programming
186
Instruction Reordering Q.Why might the hardware or compiler decide to reorder these instructions? A.To obtain higher performance by covering load latency — instruction-level parallelism. mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store Program OrderExecution Order Slide used with permission of Charles E. Leiserson
187
Instruction Reordering Q.When is it safe for the hardware or compiler to perform this reordering? A.When a ≠ b. A′.And there’s no concurrency. mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store mov b, %ebx ;Load mov 1, a ;Store Program OrderExecution Order Slide used with permission of Charles E. Leiserson
188
Hardware Reordering ∙ Processor can issue stores faster than the network can handle them ⇒ store buffer. ∙ Loads take priority, bypassing the store buffer. ∙ Except if a load address matches an address in the store buffer, the store buffer returns the result. Memory System Load Bypass ProcessorNetwork Store Buffer Slide used with permission of Charles E. Leiserson
189
X86: Memory Consistency 1.Loads are not reordered with loads. 2.Stores are not reordered with stores. 3.Stores are not reordered with prior loads. 4.A load may be reordered with a prior store to a different location but not with a prior store to the same location. 5.Stores to the same location respect a global total order. Store1 Store2 Load1 Store3 Store4 Load3 Load2 Load4 Load5 Thread’s Code Art of Multiprocessor Programming
190
1.Loads are not reordered with loads. 2.Stores are not reordered with stores. 3.Stores are not reordered with prior loads. 4.A load may be reordered with a prior store to a different location but not with a prior store to the same location. 5.Stores to the same location respect a global total order. X86: Memory Consistency Store1 Store2 Load1 Store3 Store4 Load3 Load2 Load4 Load5 Thread’s Code Total Store Ordering (TSO)…weaker than sequential consistency LOADSLOADS LOADSLOADS OK! Art of Multiprocessor Programming
191
Memory Barriers (Fences) ∙ A memory barrier (or memory fence) is a hardware action that enforces an ordering constraint between the instructions before and after the fence. ∙ A memory barrier can be issued explicitly as an instruction (x86: mfence) ∙ The typical cost of a memory fence is comparable to that of an L2-cache access. Art of Multiprocessor Programming
192
1.Loads are not reordered with loads. 2.Stores are not reordered with stores. 3.Stores are not reordered with prior loads. 4.A load may be reordered with a prior store to a different location but not with a prior store to the same location. 5.Stores to the same location respect a global total order. X86: Memory Consistency Store1 Store2 Load1 Store3 Store4 Load3 Load2 Load4 Load5 Thread’s Code Total Store Ordering + properly placed memory barriers = sequential consistency Barrier
193
Art of Multiprocessor Programming 193 Memory Barriers Explicit Synchronization Memory barrier will –Flush write buffer –Bring caches up to date Compilers often do this for you –Entering and leaving critical sections
194
Art of Multiprocessor Programming 194 Volatile Variables In Java, can ask compiler to keep a variable up-to-date by declaring it volatile Adds a memory barrier after each store Inhibits reordering, removing from loops, & other “compiler optimizations” Will talk about it in detail in later lectures
195
Art of Multiprocessor Programming 195 Summary: Real-World Hardware weaker than sequential consistency Can get sequential consistency at a price Linearizability better fit for high-level software
196
Art of Multiprocessor Programming 196 Linearizability –Operation takes effect instantaneously between invocation and response –Uses sequential specification, locality implies composablity
197
Art of Multiprocessor Programming 197 Summary: Correctness Sequential Consistency –Not composable –Harder to work with –Good way to think about hardware models We will use linearizability as our consistency condition in the remainder of this course unless stated otherwise
198
Progress We saw an implementation whose methods were lock-based (deadlock-free) We saw an implementation whose methods did not use locks (lock-free) How do they relate? Art of Multiprocessor Programming 198
199
Progress Conditions Deadlock-free: some thread trying to acquire the lock eventually succeeds. Starvation-free: every thread trying to acquire the lock eventually succeeds. Lock-free: some thread calling a method eventually returns. Wait-free: every thread calling a method eventually returns. Art of Multiprocessor Programming 199
200
Progress Conditions Art of Multiprocessor Programming 200 Wait-free Lock-free Starvation-free Deadlock-free Everyone makes progress Non-Blocking Blocking Someone makes progress
201
Art of Multiprocessor Programming 201 Summary We will look at linearizable blocking and non-blocking implementations of objects.
202
Art of Multiprocessor Programming 202 This work is licensed under a Creative Commons Attribution- ShareAlike 2.5 License.Creative Commons Attribution- ShareAlike 2.5 License You are free: –to Share — to copy, distribute and transmit the work –to Remix — to adapt the work Under the following conditions: –Attribution. You must attribute the work to “The Art of Multiprocessor Programming” (but not in any way that suggests that the authors endorse you or your use of the work). –Share Alike. If you alter, transform, or build upon this work, you may distribute the resulting work only under the same, similar or a compatible license. For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to –http://creativecommons.org/licenses/by-sa/3.0/. Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this license impairs or restricts the author's moral rights.
Similar presentations
