concurrent objects mit 6.05s by maurice herlihy & nir shavit
TRANSCRIPT
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Concurrent Objects
MIT 6.05sby Maurice Herlihy & Nir
Shavit
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Art of Multiprocessor Programming
2
Concurrent Computaton
memory
object object
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Art of Multiprocessor Programming
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Objectivism
• What is a concurrent object?– How do we describe one?– How do we implement one?– How do we tell if we’re right?
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Art of Multiprocessor Programming
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Objectivism
• What is a concurrent object?– How do we describe one?
– How do we tell if we’re right?
(later)
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FIFO Queue: Enqueue Method
q.enq( )
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Art of Multiprocessor Programming
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FIFO Queue: Dequeue Method
q.deq()/
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A Lock-Based Queue
class LockBasedQueue<T> { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; }
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A Lock-Based Queue
class LockBasedQueue<T> { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; }
Queue fields protected by single shared lock
head tail
y z
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A Lock-Based Queue
class LockBasedQueue<T> { int head, tail; T[] items; Lock lock; public LockBasedQueue(int capacity) { head = 0; tail = 0; lock = new ReentrantLock(); items = (T[]) new Object[capacity]; }
Initially head = tail
head tail
y z
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Implementation: Deq
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(); } }
head tail
y z
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Implementation: Deq
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(); } }
Method calls mutually exclusive
head tail
y z
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Implementation: Deq
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(); } }
If queue emptythrow exception
head tail
y z
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Implementation: Deq
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(); } }
Queue not empty:remove item and
update head
head tail
y z
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Implementation: Deq
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(); } }
Return result
head tail
y z
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Implementation: Deq
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(); } } Release lock no matter
what!
head tail
y z
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Implementation: Deq
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(); } }
Should be correct because
modifications are mutually
exclusive…
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Now consider the following implementation
• The same thing without mutual exclusion
• For simplicity, only two threads – One thread enq only– The other deq only
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Lock-free 2-Thread Queuepublic class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity];
public void enq(Item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; }
public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item;}}
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Lock-free 2-Thread Queuepublic class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity];
public void enq(Item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; }
public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item;}}
head tail
y z
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Lock-free 2-Thread Queuepublic class WaitFreeQueue { int head = 0, tail = 0; items = (T[]) new Object[capacity];
public void enq(Item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; }
public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item;}}
Queue is updated without a lock!
head tail
y z
How do we define
“correct” when
modifications are not
mutually exclusive?
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Defining concurrent queue implementations
• 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 …
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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
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Lets begin with correctness
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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
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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,
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Pre and PostConditions for Dequeue
• Precondition:– Queue is non-empty
• Postcondition:– Returns first item in queue
• Postcondition:– Removes first item in queue
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Pre and PostConditions for Dequeue
• Precondition:– Queue is empty
• Postcondition:– Throws Empty exception
• Postcondition:– Queue state unchanged
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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
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What About Concurrent Specifications?
• Methods? • Documentation?• Adding new methods?
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Methods Take Time
timetime
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Methods Take Time
time
invocation 12:00
q.enq(...
)
time
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Methods Take Time
time
Method call
invocation 12:00
q.enq(...
)
time
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Methods Take Time
time
Method call
invocation 12:00
q.enq(...
)
time
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Methods Take Time
time
Method call
invocation 12:00
q.enq(...
)
time
void
response 12:01
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Sequential vs Concurrent
• Sequential– Methods take time? Who knew?
• Concurrent– Method call is not an event– Method call is an interval.
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time
Concurrent Methods Take Overlapping Time
time
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time
Concurrent Methods Take Overlapping Time
time
Method call
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time
Concurrent Methods Take Overlapping Time
time
Method call
Method call
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time
Concurrent Methods Take Overlapping Time
time
Method call Method call
Method call
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Sequential vs Concurrent
• Sequential:– Object needs meaningful state only
between method calls
• Concurrent– Because method calls overlap, object
might never be between method calls
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Sequential vs Concurrent
• Sequential:– Each method described in isolation
• Concurrent– Must characterize all possible
interactions with concurrent calls • What if two enqs overlap?• Two deqs? enq and deq? …
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Sequential vs Concurrent
• Sequential:– Can add new methods without
affecting older methods
• Concurrent:– Everything can potentially interact
with everything else
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Sequential vs Concurrent
• Sequential:– Can add new methods without
affecting older methods
• Concurrent:– Everything can potentially interact
with everything else Panic!
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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
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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(); } }
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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 modifications of queue are done mutually exclusive
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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
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Linearizability
• Each method should– “Take effect”– Instantaneously– Between invocation and response
events
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Example
timetime
(6)
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Example
time
q.enq(x)
time
(6)
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Example
time
q.enq(x)
q.enq(y)
time
(6)
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
time
(6)
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
time
(6)
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
linearizableq.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
time
(6)
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Example
time
(5)
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Example
time
q.enq(x)
(5)
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Example
time
q.enq(x) q.deq(y)
(5)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
(5)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)q.enq(x)
q.enq(y)
(5)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)q.enq(x)
q.enq(y)
(5)
not
linearizable
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Example
timetime
(4)
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Example
time
q.enq(x)
time
(4)
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Example
time
q.enq(x)
q.deq(x)
time
(4)
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Example
time
q.enq(x)
q.deq(x)
q.enq(x)
q.deq(x)
time
(4)
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Art of Multiprocessor Programming
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Example
time
q.enq(x)
q.deq(x)
q.enq(x)
q.deq(x)
linearizable
time
(4)
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Example
time
q.enq(x)
time
(8)
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Art of Multiprocessor Programming
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Example
time
q.enq(x)
q.enq(y)
time
(8)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
time
(8)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
q.deq(x)
time
(8)
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Art of Multiprocessor Programming
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q.enq(x)
q.enq(y)
q.deq(y)
q.deq(x)
Comme ci Example
time
Comme ça multiple orders
OKlinearizable
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(0)
(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(0)write(1) already
happened(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(0)write(1)write(1) already
happened(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(0)write(1)write(1) already
happened(4)
not
linearizable
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)write(1) already
happened(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)write(1)
write(2)
(4)
write(1) already
happened
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)write(1)
write(2)
not
linearizable
(4)
write(1) already
happened
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Art of Multiprocessor Programming
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Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1)
(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1)write(1)
write(2)
(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1)write(1)
write(2)
linearizable
(4)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)
(2)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)write(1)
(2)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(1)write(1)
write(2)
(2)
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Art of Multiprocessor Programming
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Read/Write Register Example
time
read(1)write(0)
write(1)
write(2)
time
read(2)write(1)
write(2)
Not
linearizable
(2)
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Art of Multiprocessor Programming
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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
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Art of Multiprocessor Programming
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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
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Art of Multiprocessor Programming
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Invocation Notation
A q.enq(x)
(4)
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Art of Multiprocessor Programming
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Invocation Notation
A q.enq(x)
thread
(4)
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Art of Multiprocessor Programming
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Invocation Notation
A q.enq(x)
thread method
(4)
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Art of Multiprocessor Programming
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Invocation Notation
A q.enq(x)
thread
object(4)
method
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Invocation Notation
A q.enq(x)
thread
object
method
arguments(4)
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Art of Multiprocessor Programming
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Response Notation
A q: void
(2)
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Art of Multiprocessor Programming
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Response Notation
A q: void
thread
(2)
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Art of Multiprocessor Programming
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Response Notation
A q: void
thread result
(2)
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Art of Multiprocessor Programming
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Response Notation
A q: void
thread
object
result
(2)
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Art of Multiprocessor Programming
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Response Notation
A q: void
thread
object
result
(2)
Met
hod
is
impl
icit
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Art of Multiprocessor Programming
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Response Notation
A q: empty()
thread
object(2)
Met
hod
is
impl
icit
exception
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Art of Multiprocessor Programming
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History - Describing an Execution
A q.enq(3)A q:voidA q.enq(5)B p.enq(4)B p:voidB q.deq()B q:3
Sequence of invocations and
responses
H =
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Art of Multiprocessor Programming
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Definition
• Invocation & response match if
A q.enq(3)
A q:void
Thread names agree
Object names agree
Method call
(1)
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Art of Multiprocessor Programming
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Object Projections
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3
H =
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Art of Multiprocessor Programming
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Object Projections
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3
H|q =
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Art of Multiprocessor Programming
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Thread Projections
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3
H =
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Art of Multiprocessor Programming
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Thread Projections
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3
H|B =
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Art of Multiprocessor Programming
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Complete Subhistory
A q.enq(3)A q:voidA q.enq(5)B p.enq(4)B p:voidB q.deq()B q:3
An invocation is pending if it has
no matching respnse
H =
![Page 104: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/104.jpg)
Art of Multiprocessor Programming
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Complete Subhistory
A q.enq(3)A q:voidA q.enq(5)B p.enq(4)B p:voidB q.deq()B q:3
May or may not have taken effect
H =
![Page 105: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/105.jpg)
Art of Multiprocessor Programming
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Complete Subhistory
A q.enq(3)A q:voidA q.enq(5)B p.enq(4)B p:voidB q.deq()B q:3
discard pending invocations
H =
![Page 106: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/106.jpg)
Art of Multiprocessor Programming
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Complete Subhistory
A q.enq(3)A q:void B p.enq(4)B p:voidB q.deq()B q:3
Complete(H) =
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Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
(4)
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Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
match
(4)
![Page 109: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/109.jpg)
Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
match
match
(4)
![Page 110: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/110.jpg)
Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
match
match
match
(4)
![Page 111: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/111.jpg)
Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
match
match
match
Final pending invocation OK
(4)
![Page 112: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/112.jpg)
Art of Multiprocessor Programming
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Sequential Histories
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3A q:enq(5)
match
match
match
Final pending invocation OK
(4)
Method calls of
different threads
do not interleave
![Page 113: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/113.jpg)
Art of Multiprocessor Programming
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Well-Formed Histories
H=
A q.enq(3)B p.enq(4)B p:voidB q.deq()A q:voidB q:3
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Art of Multiprocessor Programming
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Well-Formed Histories
H=
A q.enq(3)B p.enq(4)B p:voidB q.deq()A q:voidB q:3
H|B=B p.enq(4)B p:voidB q.deq()B q:3
Per-thread projections sequential
![Page 115: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/115.jpg)
Art of Multiprocessor Programming
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Well-Formed Histories
H=
A q.enq(3)B p.enq(4)B p:voidB q.deq()A q:voidB q:3
H|B=B p.enq(4)B p:voidB q.deq()B q:3
A q.enq(3)A q:void
H|A=
Per-thread projections sequential
![Page 116: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/116.jpg)
Art of Multiprocessor Programming
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Equivalent Histories
H=
A q.enq(3)B p.enq(4)B p:voidB q.deq()A q:voidB q:3
Threads see the same thing in both
A q.enq(3)A q:voidB p.enq(4)B p:voidB q.deq()B q:3
G=
H|A = G|AH|B = G|B
![Page 117: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/117.jpg)
Art of Multiprocessor Programming
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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
…
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Art of Multiprocessor Programming
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Legal Histories
• A sequential (multi-object) history H is legal if– For every object x– H|x is in the sequential spec for x
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Art of Multiprocessor Programming
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Precedence
A q.enq(3)B p.enq(4)B p.voidA q:voidB q.deq()B q:3
A method call precedes another if
response event precedes invocation
event
Method call Method call
(1)
![Page 120: Concurrent Objects MIT 6.05s by Maurice Herlihy & Nir Shavit](https://reader035.vdocuments.site/reader035/viewer/2022062400/5697bfc51a28abf838ca6e32/html5/thumbnails/120.jpg)
Art of Multiprocessor Programming
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Non-Precedence
A q.enq(3)B p.enq(4)B p.voidB q.deq()A q:voidB q:3
Some method calls overlap one
anotherMethod call
Method call
(1)
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Notation
• Given – History H– method executions m0 and m1 in H
• We say m0 Hm1, if– m0 precedes m1
• Relation m0 Hm1 is a– Partial order – Total order if H is sequential
m0 m1
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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
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What is G S
time
a
b
time
(8)
G
S
cG
G = {ac,bc}
S = {ab,ac,bc}
A limita
tion on th
e
Choice of S
!
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Remarks
• Some pending invocations– Took effect, so keep them– Discard the rest
• Condition G S
– Means that S respects “real-time order” of G
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A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4B q:enq(6)
Example
time
B.q.enq(4)
A. q.enq(3)
B.q.deq(4) B. q.enq(6)
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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:voidB q.deq()B q:4B q:enq(6)
A. q.enq(3)
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Example
Complete this pending
invocation
time
B.q.enq(4) B.q.deq(4) B. q.enq(6)
B.q.enq(3)
A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4B q:enq(6)A q:void
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Example
time
B.q.enq(4) B.q.deq(4) B. q.enq(6)
B.q.enq(3)
A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4B q:enq(6)A q:void
discard this one
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Example
time
B.q.enq(4) B.q.deq(4)
B.q.enq(3)
A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4
A q:void
discard this one
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A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4A q:void
Example
time
B.q.enq(4) B.q.deq(4)
B.q.enq(3)
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A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4A q:void
Example
time
B q.enq(4)B q:voidA q.enq(3)A q:voidB q.deq()B q:4
B.q.enq(4) B.q.deq(4)
B.q.enq(3)
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B.q.enq(4) B.q.deq(4)
B.q.enq(3)
A q.enq(3)B q.enq(4)B q:voidB q.deq()B q:4A q:void
Example
time
B q.enq(4)B q:voidA q.enq(3)A q:voidB q.deq()B q:4
Equivalent sequential history
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Linearization Points
• Identify one atomic step where method “happens”– Critical section?– Machine instruction?
• Usually straightforward• Sometimes not
– E.g., Successful vs unsuccessful search …
– Stay tuned …
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Linearization Points : 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(); } }
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Linearization Points: 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 pointsare when locks are
released
0 1capacity-1
2
head tail
y z
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Linearization Points : Lock-free
public class LockFreeQueue {
int head = 0, tail = 0; items = (T[]) new Object[capacity];
public void enq(Item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item;}}
0 1capacity-1
2
head tail
y z
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public class LockFreeQueue {
int head = 0, tail = 0; items = (T[]) new Object[capacity];
public void enq(Item x) { while (tail-head == capacity); // busy-wait items[tail % capacity] = x; tail++; } public Item deq() { while (tail == head); // busy-wait Item item = items[head % capacity]; head++; return item;}}
Linearization order is order head and tail fields modified
Remem
ber that t
here
is only
one e
nqueuer
and only
one d
equeuer
Linearization Points : Lock-free
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Concurrency
• How much concurrency does linearizability allow?
• When must a method invocation block?
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Technicality
• Focus on total methods– Defined for every state
• Example:– deq() that throws EmptyException– Versus deq() that waits …
• Why?– Otherwise, blocking unrelated to
synchronization
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Concurrency
• Question:– When does linearizability require a
method invocation to block?
• Answer:– never.– Linearizability is non-blocking
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Radical, Dude!
• Linearizability permits lock-free implementations …
• Where no thread is ever blocked waiting for another …
• How to do so is another story!
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Composability
• A system is linearizable if and only if each individual object is linearizable.
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Modular, Dude!
• You can contract out pieces of your system.
• If each contractor individually guarantees that module’s linearizability …
• Then your entire system is linearizable.• Do not take this property for granted!
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Linearizability
• Each method should– “Take effect”– Instantaneously– Between invocation and response
events
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Sequential Consistency
• Each method should– “Take effect”– Instantaneously– In program order.
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Sequential Consistency
• No need to preserve real-time order– Cannot re-order same-thread operations– Can re-order different-thread operations
all you want
• Often used to describe multiprocessor memory architectures
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Composability
• Sequential consistency is not composable.
• Composing sequentially-consistent modules does not guarantee a sequentially consistent system.
• Sequential consistency is useful, but maybe not for software.
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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
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H|p Sequentially Consistent
time
p.enq(x) p.deq(y)
p.enq(y)
q.enq(x)
q.enq(y) q.deq(x)
time
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H|q Sequentially Consistent
time
p.enq(x) p.deq(y)q.enq(x)
q.enq(y) q.deq(x)p.enq(y)
time
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Ordering imposed by p
time
p.enq(x) p.deq(y)q.enq(x)
q.enq(y) q.deq(x)p.enq(y)
time
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Ordering imposed by q
time
p.enq(x) p.deq(y)q.enq(x)
q.enq(y) q.deq(x)p.enq(y)
time
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p.enq(x)
Ordering imposed by both
time
q.enq(x)
q.enq(y) q.deq(x)
time
p.deq(y)
p.enq(y)
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p.enq(x)
Combining orders
time
q.enq(x)
q.enq(y) q.deq(x)
time
p.deq(y)
p.enq(y)
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Fact
• Most hardware architectures don’t support sequential consistency
• Because they think it’s too strong• Here’s another story …
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The Flag Example
time
x.write(1) y.read(0)
y.write(1) x.read(0)
time
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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
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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
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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 …
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Opinion1: 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!
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Opinion2: 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
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Memory Hierarchy
• On modern multiprocessors, processors do not read and write directly to memory.
• Memory accesses are very slow compared to processor speeds,
• Instead, each processor reads and writes directly to a cache
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Memory Operations
• To read a memory location,– load data into cache.
• To write a memory location– update cached copy,– Lazily write cached data back to
memory
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While Writing to Memory
• A processor can execute hundreds, or even thousands of instructions
• Why delay on every memory write?
• Instead, write back in parallel with rest of the program.
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Revisionist History
• Flag violation history is actually OK– processors delay writing to memory– Until after reads have been issued.
• Otherwise unacceptable delay between read and write instructions.
• Who knew you wanted to synchronize?
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Memory Hierarchy
• Writing to memory = mailing a letter
• Most of the time,– No need to wait at the post office
• If you want to synchronize– Announce it explicitly– Pay for it only when you need it
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Explicit Synchronization
• Memory barrier instruction– Flush unwritten caches– Bring caches up to date
• Compilers often do this for you– Entering and leaving critical sections
• Expensive
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Volatile
• In Java, can ask compiler to keep a variable up-to-date with volatile keyword
• Also inhibits reordering, removing from loops, & other “optimizations”
• Stay tuned …
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Sequential Consistency
• Not composable• Harder to work with• Good way to think about hardware
models
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Summary
• Linearizability is the gold standard for software object correctness– Non-blocking– Composable
• Not always what you want– But it’s the condition you’re not
satisfying …
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