introduction to concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and multicore programming...
TRANSCRIPT
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Introduction to Concurrency and Multicore Programming
Slides adapted fromArt of Multicore Programmingby Herlihy and Shavit
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Overview
• Introduction
• Mutual Exclusion
• Linearizability
• Concurrent Data Structure – Linked-List Set
– Lock-free Stack
• Summary
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What is Concurrency?
A property of systems in which several processes or threads are executing at the same time.
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Moore’s Law
Clock speed flattening
sharply
Transistor count still
rising
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The Uniprocessor is Vanishing!
memory
cpu
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The Shared Memory Multiprocessor (SMP)
cache
Bus Bus
shared memory
cache cache
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Your New Desktop: The Multicore Processor
(CMP)
cache
Bus Bus
shared memory
cache cache All on the same chip
Sun T2000 Niagara
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Why do we care?
• Time no longer cures software bloat – The “free ride” is over
• When you double your program’s path length – You can’t just wait 6 months
– Your software must somehow exploit twice as much concurrency
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Traditional Scaling Process
User code
Traditional Uniprocessor
Speedup 1.8x
7x
3.6x
Time: Moore’s law
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Multicore Scaling Process
User code
Multicore
Speedup 1.8x
7x
3.6x
Unfortunately, not so simple…
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Real-World Scaling Process
1.8x 2x 2.9x
User code
Multicore
Speedup
Parallelization and Synchronization require great care…
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Sequential Computation
memory
object object
thread
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Concurrent Computation
memory
object object
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Asynchrony
• Sudden unpredictable delays – Cache misses (short)
– Page faults (long)
– Scheduling quantum used up (really long)
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Model Summary
• Multiple threads
• Single shared memory
• Objects live in memory
• Unpredictable asynchronous delays
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Multithread Programming
• Java, C#, Pthreads
• Windows Thread API
• OpenMP
• Intel Parallel Studio Tool Kits
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Java Thread
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Concurrency Idea
• Challenge – Print primes from 1 to 1010
• Given – Ten-processor multiprocessor
– One thread per processor
• Goal – Get ten-fold speedup (or close)
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Load Balancing
• Split the work evenly
• Each thread tests range of 109
…
… 109 1010 2·109 1
P0 P1 P9
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Procedure for Thread i
void primePrint { int i = ThreadID.get(); // IDs in {0..9} for (j = i*109+1, j<(i+1)*109; j++) { if (isPrime(j)) print(j); } }
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Issues
• Higher ranges have fewer primes
• Yet larger numbers harder to test
• Thread workloads – Uneven
– Hard to predict
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Issues
• Higher ranges have fewer primes
• Yet larger numbers harder to test
• Thread workloads – Uneven
– Hard to predict
• Need dynamic load balancing
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Shared Counter
17
18
19
each thread takes a number
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Procedure for Thread i
int counter = new Counter(1); void primePrint { long j = 0; while (j < 1010) { j = counter.getAndIncrement(); if (isPrime(j)) print(j); } }
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Procedure for Thread i
Counter counter = new Counter(1); void primePrint { long j = 0; while (j < 1010) { j = counter.getAndIncrement(); if (isPrime(j)) print(j); } }
Shared counter object
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Where Things Reside
cache
Bus Bus
cache cache
1
shared counter
shared memory
void primePrint { int i = ThreadID.get(); // IDs in {0..9} for (j = i*109+1, j<(i+1)*109; j++) { if (isPrime(j)) print(j); } }
code
Local variables
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Counter Implementation
public class Counter { private long value; public long getAndIncrement() { return value++; } }
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Counter Implementation
public class Counter { private long value; public long getAndIncrement() { return value++; } }
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What It Means
public class Counter { private long value; public long getAndIncrement() { return value++; } }
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What It Means
public class Counter { private long value; public long getAndIncrement() { return value++; } }
temp = value;
value = value + 1;
return temp;
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time
Not so good…
Value… 1
read 1
read 1
write 2
read 2
write 3
write 2
2 3 2
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Is this problem inherent?
If we could only glue reads and writes…
read
write read
write
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Challenge
public class Counter { private long value; public long getAndIncrement() { temp = value; value = temp + 1; return temp; } }
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Challenge
public class Counter { private long value; public long getAndIncrement() { temp = value; value = temp + 1; return temp; } }
Make these steps atomic (indivisible)
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Hardware Solution
public class Counter { private long value; public long getAndIncrement() { temp = value; value = temp + 1; return temp; } } ReadModifyWrite()
instruction
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An Aside: Java™
public class Counter { private long value; public long getAndIncrement() { synchronized { temp = value; value = temp + 1; } return temp; } }
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An Aside: Java™
public class Counter { private long value; public long getAndIncrement() { synchronized { temp = value; value = temp + 1; } return temp; } }
Synchronized block
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An Aside: Java™
public class Counter { private long value; public long getAndIncrement() { synchronized { temp = value; value = temp + 1; } return temp; } }
Mutual Exclusion
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Mutual Exclusion
The problem of ensuring that no two processes or threads can be in their critical section at the same time.
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time
• An event a0 of thread A is – Instantaneous
– No simultaneous events (break ties)
a0
Events
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time
• A thread A is (formally) a sequence a0, a1, ... of events – “Trace” model
– Notation: a0 a1 indicates order
a0
Threads
a1 a2 …
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• Assign to shared variable
• Assign to local variable
• Invoke method
• Return from method
• Lots of other things …
Example Thread Events
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Threads are State Machines
Events are transitions
a0
a1 a2
a3
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States
• Thread State – Program counter
– Local variables
• System state – Object fields (shared variables)
– Union of thread states
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time
• Thread A
Concurrency
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time
time
• Thread A
• Thread B
Concurrency
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time
Interleavings
• Events of two or more threads – Interleaved
– Not necessarily independent (why?)
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time
• An interval A0 =(a0,a1) is – Time between events a0 and a1
a0 a1
Intervals
A0
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time
Intervals may Overlap
a0 a1 A0
b0 b1 B0
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time
Intervals may be Disjoint
a0 a1 A0
b0 b1 B0
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time
Precedence
a0 a1 A0
b0 b1 B0
Interval A0 precedes interval B0
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Precedence
• Notation: A0 B0
• Formally, – End event of A0 before start event of B0
– Also called “happens before” or “precedes”
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Precedence Ordering
• Never true that A A
• If A B then not true that B A
• If A B & B C then A C
• Funny thing: A B & B A might both be false!
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Partial Orders (you may know this already)
• Irreflexive: – Never true that A A
• Antisymmetric: – If A B then not true that B A
• Transitive: – If A B & B C then A C
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Total Orders (you may know this already)
• Also – Irreflexive
– Antisymmetric
– Transitive
• Except that for every distinct A, B, – Either A B or B A
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Implementing a Counter
public class Counter { private long value; public long getAndIncrement() { temp = value; value = temp + 1; return temp; } }
Make these steps indivisible using
locks
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Locks (Mutual Exclusion)
public interface Lock { public void lock(); public void unlock(); }
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Locks (Mutual Exclusion)
public interface Lock {
public void lock(); public void unlock(); }
acquire lock
![Page 59: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/59.jpg)
Locks (Mutual Exclusion)
public interface Lock { public void lock(); public void unlock(); }
release lock
acquire lock
![Page 60: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/60.jpg)
Using Locks
public class Counter { private long value; private Lock lock; public long getAndIncrement() { lock.lock(); try { int temp = value; value = value + 1; } finally { lock.unlock(); } return temp;
}}
![Page 61: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/61.jpg)
Using Locks
public class Counter { private long value; private Lock lock; public long getAndIncrement() { lock.lock(); try { int temp = value; value = value + 1; } finally { lock.unlock(); } return temp; }}
acquire Lock
![Page 62: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/62.jpg)
Using Locks
public class Counter { private long value; private Lock lock; public long getAndIncrement() { lock.lock(); try { int temp = value; value = value + 1; } finally { lock.unlock(); } return temp;
}}
Release lock (no matter what)
![Page 63: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/63.jpg)
Using Locks
public class Counter { private long value; private Lock lock; public long getAndIncrement() { lock.lock(); try { int temp = value; value = value + 1; } finally { lock.unlock(); } return temp;
}}
Critical section
![Page 64: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/64.jpg)
Mutual Exclusion
• Let CSik be thread i’s k-th critical
section execution
![Page 65: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/65.jpg)
Mutual Exclusion
• Let CSik be thread i’s k-th critical
section execution
• And CSjm be thread j’s m-th critical
section execution
![Page 66: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/66.jpg)
Mutual Exclusion
• Let CSik be thread i’s k-th critical
section execution
• And CSjm be j’s m-th execution
• Then either – or
![Page 67: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/67.jpg)
Mutual Exclusion
• Let CSik be thread i’s k-th critical
section execution
• And CSjm be j’s m-th execution
• Then either – or
CSik CSj
m
![Page 68: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/68.jpg)
Mutual Exclusion
• Let CSik be thread i’s k-th critical
section execution
• And CSjm be j’s m-th execution
• Then either – or
CSik CSj
m
CSjm CSi
k
![Page 69: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/69.jpg)
Deadlock-Free
• If some thread calls lock() – And never returns
– Then other threads must complete lock() and unlock() calls infinitely often
• System as a whole makes progress – Even if individuals starve
![Page 70: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/70.jpg)
Starvation-Free
• If some thread calls lock() – It will eventually return
• Individual threads make progress
![Page 71: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/71.jpg)
class … implements Lock { … // thread-local index, 0 or 1 public void lock() { int i = ThreadID.get(); int j = 1 - i; …
} }
Two-Thread Conventions
![Page 72: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/72.jpg)
class … implements Lock { … // thread-local index, 0 or 1 public void lock() { int i = ThreadID.get(); int j = 1 - i; …
} }
Two-Thread Conventions
Henceforth: i is current thread, j is other thread
![Page 73: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/73.jpg)
LockOne
class LockOne implements Lock { private boolean[] flag = new boolean[2]; public void lock() { flag[i] = true; while (flag[j]) {} }
![Page 74: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/74.jpg)
LockOne
class LockOne implements Lock { private boolean[] flag = new boolean[2]; public void lock() { flag[i] = true; while (flag[j]) {} }
Set my flag
![Page 75: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/75.jpg)
class LockOne implements Lock { private boolean[] flag = new boolean[2]; public void lock() { flag[i] = true; while (flag[j]) {} }
LockOne
Wait for other flag to go false
Set my flag
![Page 76: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/76.jpg)
• Assume CSAj overlaps CSB
k
• Consider each thread's last (j-th and k-th) read and write in the lock() method before entering
• Derive a contradiction
LockOne Satisfies Mutual Exclusion
![Page 77: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/77.jpg)
• writeA(flag[A]=true) readA(flag[B]==false) CSA
• writeB(flag[B]=true) readB(flag[A]==false) CSB
From the Code
class LockOne implements Lock { … public void lock() { flag[i] = true; while (flag[j]) {} }
![Page 78: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/78.jpg)
• readA(flag[B]==false) writeB(flag[B]=true)
• readB(flag[A]==false) writeA(flag[B]=true)
From the Assumption
![Page 79: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/79.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 80: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/80.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 81: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/81.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 82: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/82.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 83: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/83.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 84: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/84.jpg)
• Assumptions: – readA(flag[B]==false) writeB(flag[B]=true)
– readB(flag[A]==false) writeA(flag[A]=true)
• From the code – writeA(flag[A]=true) readA(flag[B]==false)
– writeB(flag[B]=true) readB(flag[A]==false)
Combining
![Page 85: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/85.jpg)
Cycle!
![Page 86: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/86.jpg)
Deadlock Freedom
• LockOne Fails deadlock-freedom – Concurrent execution can deadlock
– Sequential executions OK
flag[i] = true; flag[j] = true; while (flag[j]){} while (flag[i]){}
![Page 87: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/87.jpg)
LockTwo public class LockTwo implements Lock { private int victim; public void lock() { victim = i; while (victim == i) {}; } public void unlock() {} }
![Page 88: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/88.jpg)
LockTwo public class LockTwo implements Lock { private int victim; public void lock() { victim = i; while (victim == i) {}; } public void unlock() {} }
Let other go first
![Page 89: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/89.jpg)
LockTwo public class LockTwo implements Lock { private int victim; public void lock() { victim = i; while (victim == i) {}; } public void unlock() {} }
Wait for permission
![Page 90: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/90.jpg)
LockTwo public class Lock2 implements Lock { private int victim; public void lock() { victim = i; while (victim == i) {}; } public void unlock() {} }
Nothing to do
![Page 91: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/91.jpg)
public void LockTwo() { victim = i; while (victim == i) {}; }
LockTwo Claims
• Satisfies mutual exclusion – If thread i in CS
– Then victim == j
– Cannot be both 0 and 1
• Not deadlock free – Sequential execution deadlocks
– Concurrent execution does not
![Page 92: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/92.jpg)
Peterson’s Algorithm
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
![Page 93: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/93.jpg)
Peterson’s Algorithm
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
Announce I’m interested
![Page 94: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/94.jpg)
Peterson’s Algorithm
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
Announce I’m interested
Defer to other
![Page 95: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/95.jpg)
Peterson’s Algorithm
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
Announce I’m interested
Defer to other
Wait while other interested & I’m
the victim
![Page 96: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/96.jpg)
Peterson’s Algorithm
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
Announce I’m interested
Defer to other
Wait while other interested & I’m
the victim No longer interested
![Page 97: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/97.jpg)
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {};
Mutual Exclusion
• If thread 1 in critical section, – flag[1]=true,
– victim = 0
• If thread 0 in critical section, – flag[0]=true,
– victim = 1
Cannot both be true
![Page 98: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/98.jpg)
Deadlock Free
• Thread blocked – only at while loop
– only if it is the victim
• One or the other must not be the victim
public void lock() { … while (flag[j] && victim == i) {};
![Page 99: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/99.jpg)
Starvation Free
• Thread i blocked only if j repeatedly re-enters so that
flag[j] == true and victim == i
• When j re-enters – it sets victim to j. – So i gets in
public void lock() { flag[i] = true; victim = i; while (flag[j] && victim == i) {}; } public void unlock() { flag[i] = false; }
![Page 100: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/100.jpg)
Other Lock Algorithms
• The Filter Algorithm for n Threads
• Bakery Algorithm
Theorem: At least N MRSW (multi-reader/single-writer) registers are needed to solve deadlock-free mutual exclusion.
N registers like Flag[]…
![Page 101: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/101.jpg)
FIFO Queue: Enqueue Method
q.enq( )
![Page 102: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/102.jpg)
FIFO Queue: Dequeue Method
q.deq()/
![Page 103: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/103.jpg)
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]; }
![Page 104: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/104.jpg)
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]; }
0 1
capacity-1 2
head tail
y z
Queue fields protected by single shared lock
![Page 105: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/105.jpg)
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]; }
0 1
capacity-1 2
head tail
y z
Initially head = tail
![Page 106: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/106.jpg)
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(); } }
0 1
capacity-1 2
head tail
y z
![Page 107: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/107.jpg)
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
0 1
capacity-1 2
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 empty throw exception
0 1
capacity-1 2
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
0 1
capacity-1 2
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
0 1
capacity-1 2
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!
0 1
capacity-1 2
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(); } }
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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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Art of Multiprocessor Programming
114
Wait-free 2-Thread Queue public 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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Wait-free 2-Thread Queue 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 1
capacity-1 2
head tail
y z
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Lock-free 2-Thread Queue 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 1
capacity-1 2
head tail
y z
Queue is updated without a lock!
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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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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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What About Concurrent Specifications ?
• Methods?
• Documentation?
• Adding new methods?
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Methods Take Time
time time
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Methods Take Time
time
invocation 12:00
q.enq(...)
time
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Art of Multiprocessor Programming
125
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
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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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Is it really about the object?
• Each method should – “take effect”
– Instantaneously
– Between invocation and response events
• Object is correct if this “sequential” behavior is correct
• A linearizable object: one all of whose possible executions are linearizable
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Example
time time
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Example
time
q.enq(x)
time
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Example
time
q.enq(x)
q.enq(y)
time
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
time
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
time
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
q.deq(y) q.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
time
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Example
time
q.enq(x)
q.enq(y) q.deq(x)
q.deq(y) q.enq(x)
q.enq(y) q.deq(x)
q.deq(y)
time
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Example
time
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Example
time
q.enq(x)
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Example
time
q.enq(x) q.deq(y)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y) q.enq(x)
q.enq(y)
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Example
time
q.enq(x)
q.enq(y)
q.deq(y) q.enq(x)
q.enq(y)
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Example
time time
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Example
time
q.enq(x)
time
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Example
time
q.enq(x)
q.deq(x)
time
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Example
time
q.enq(x)
q.deq(x)
q.enq(x)
q.deq(x)
time
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Example
time
q.enq(x)
q.deq(x)
q.enq(x)
q.deq(x)
time
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Example
time
q.enq(x)
time
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Example
time
q.enq(x)
q.enq(y)
time
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
time
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Example
time
q.enq(x)
q.enq(y)
q.deq(y)
q.deq(x)
time
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q.enq(x)
q.enq(y)
q.deq(y)
q.deq(x)
Comme ci Example
time
Comme ça
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(0)
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(0)
write(1) already happened
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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
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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
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1)
write(1) already happened
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1) write(1)
write(2)
write(1) already happened
![Page 170: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/170.jpg)
Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1) write(1)
write(2)
write(1) already happened
![Page 171: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/171.jpg)
Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1)
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Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1) write(1)
write(2)
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Read/Write Register Example
time
write(0)
write(1)
write(2)
time
read(1) write(1)
write(2)
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1)
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Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1) write(1)
![Page 176: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/176.jpg)
Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(1) write(1)
write(2)
![Page 177: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/177.jpg)
Read/Write Register Example
time
read(1) write(0)
write(1)
write(2)
time
read(2) write(1)
write(2)
![Page 178: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/178.jpg)
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
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Formal Model of Executions
• Define precisely what we mean – Ambiguity is bad when intuition is weak
• Allow reasoning – Formal
– But mostly informal
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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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Invocation Notation
A q.enq(x)
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Invocation Notation
A q.enq(x)
thread
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Invocation Notation
A q.enq(x)
thread method
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Invocation Notation
A q.enq(x)
thread
object
method
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Invocation Notation
A q.enq(x)
thread
object
method
arguments
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Response Notation
A q: void
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Response Notation
A q: void
thread
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Response Notation
A q: void
thread result
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Response Notation
A q: void
thread
object
result
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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 =
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Definition
• Invocation & response match if
A q.enq(3)
A q:void
Thread names agree
Object names agree
Method call
![Page 192: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/192.jpg)
Object Projections
A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3
H =
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Object Projections
A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3
H|q =
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Thread Projections
A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3
H =
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Thread Projections
A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3
H|B =
![Page 196: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/196.jpg)
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 =
![Page 197: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/197.jpg)
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 =
![Page 198: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/198.jpg)
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 =
![Page 199: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/199.jpg)
Complete Subhistory
A q.enq(3) A q:void B p.enq(4) B p:void B q.deq() B q:3
Complete(H) =
![Page 200: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/200.jpg)
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)
![Page 201: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/201.jpg)
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
![Page 202: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/202.jpg)
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
match
![Page 203: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/203.jpg)
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
match
match
![Page 204: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/204.jpg)
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
match
match
Final pending invocation OK
![Page 205: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/205.jpg)
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
match
match
Final pending invocation OK
![Page 206: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/206.jpg)
Well-Formed Histories
H=
A q.enq(3) B p.enq(4) B p:void B q.deq() A q:void B q:3
![Page 207: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/207.jpg)
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
![Page 208: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/208.jpg)
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
![Page 209: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/209.jpg)
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
![Page 210: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/210.jpg)
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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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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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 Method call
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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
Method call
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Notation
• Given – History H – method executions m0 and m1 in H
• We say m0 H m1, if
– m0 precedes m1
• Relation m0 H m1 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 S
c G
G = {ac,bc}
S = {ab,ac,bc}
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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: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)
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Art of Multiprocessor Programming
219
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)
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Example
Complete this pending invocation
time
B.q.enq(4) B.q.deq(4) B. q.enq(6)
A.q.enq(3)
A q.enq(3) B q.enq(4) B q:void B q.deq() B q:4 B q:enq(6) A q:void
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Example
time
B.q.enq(4) B.q.deq(4) B. q.enq(6)
A.q.enq(3)
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
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Art of Multiprocessor Programming
222
Example
time
B.q.enq(4) B.q.deq(4)
A.q.enq(3)
A q.enq(3) B q.enq(4) B q:void B 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:void B q.deq() B q:4 A q:void
Example
time
B.q.enq(4) B.q.deq(4)
A.q.enq(3)
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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)
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B.q.enq(4) B.q.deq(4)
A.q.enq(3)
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
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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
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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
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228
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
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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; }}
More Reasoning: Wait-free
0 1 capacity-1
2
head tail
y z Linearization order is order head and tail
fields modified
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Linearizability: Summary
• Powerful specification tool for shared objects
• Allows us to capture the notion of objects being “atomic”
• Don’t leave home without it
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Ordered linked list implementation of a set
a b c -∞ +∞
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a b c
Sorted with Sentinel nodes (min & max possible keys)
-∞
+∞
Defining the linked list
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Defining concurrent methods properties
• Invariant: – Property that always holds.
– Established because
– True when object is created.
– Truth preserved by each method • Each step of each method.
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Defining concurrent methods properties
• Rep-Invariant: – The invariant on our concrete
Representation = on the list.
– Preserved by methods.
– Relied on by methods.
– Allows us to reason about each method in isolation without considering how they interact.
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Defining concurrent methods properties
• Our Rep-invariant: – Sentinel nodes
• tail reachable from head.
– Sorted
– No duplicates
• Depends on the implementation.
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Defining concurrent methods properties
• Abstraction Map:
• S(List) = – { x | there exists a such that
• a reachable from head and
• a.item = x
– }
• Depends on the implementation.
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Abstract Data Types
• Example:
– S( ) = {a,b} a b
a b
• Concrete representation:
• Abstract Type: – {a, b}
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Defining concurrent methods properties
• Wait-free: Every call to the function finishes in a finite number of steps.
Supposing the Scheduler is fair:
• Starvation-free: every thread calling the method eventually returns.
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Algorithms
• Next: going throw each algorithm. • 1. Describing the algorithm.
• 2. Explaining why every step of the algorithm is needed.
• 3. Code review.
• 4. Analyzing each method properties.
• 5. Advantages / Disadvantages.
• 6. Presenting running times for the implementation of the algorithm.
• + Example of proving correctness for Remove(x) in FineGrained.
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240
0.Sequential List Based Set
a c d
a b c
Add()
Remove()
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a c d
b
a b c
Add()
Remove()
0.Sequential List Based Set
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1.Course Grained
a b d
1. Describing the algorithm:
• Most common implementation
today.
• Add(x) / Remove(x) / Contains(x): - Lock the entire list then perform the operation.
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1.Course Grained
a b d
c
• Most common implementation today
1. Describing the algorithm:
• All methods perform operations on the list while holding the lock, so the execution is essentially sequential.
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3. Code review:
Add:
public boolean add(T item) {
Node pred, curr;
int key = item.hashCode();
lock.lock();
try {
pred = head;
curr = pred.next;
while (curr.key < key) {
pred = curr;
curr = curr.next;
}
if (key == curr.key) {
return false;
} else {
Node node = new Node(item);
node.next = curr;
pred.next = node;
return true;
}
} finally {
lock.unlock();
}
}
Finding the place to add the item
Adding the item if it wasn’t already in the list
1.Course Grained
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Art of Multiprocessor Programming 245
3. Code review:
Remove:
public boolean remove(T item) {
Node pred, curr;
int key = item.hashCode();
lock.lock();
try {
pred = this.head;
curr = pred.next;
while (curr.key < key) {
pred = curr;
curr = curr.next;
}
if (key == curr.key) {
pred.next = curr.next;
return true;
} else {
return false;
}
} finally {
lock.unlock();
}
}
Finding the item
Removing the item
1.Course Grained
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246
3. Code review:
Contains:
public boolean contains(T item) {
Node pred, curr;
int key = item.hashCode();
lock.lock();
try {
pred = head;
curr = pred.next;
while (curr.key < key) {
pred = curr;
curr = curr.next;
}
return (key == curr.key);
} finally {lock.unlock();
}
}
Finding the item
Returning true if found
1.Course Grained
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4. Methods properties:
• The implementation inherits its progress
conditions from those of the Lock, and so assuming fair Scheduler:
- If the Lock implementation is Starvation free
Every thread will eventually get the lock and eventually the call to the function will return.
• So our implementation of Insert, Remove and Contains is Starvation-free
1.Course Grained
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5. Advantages / Disadvantages:
Advantages:
- Simple.
- Obviously correct.
Disadvantages:
- High Contention.
- Bottleneck!
1.Course Grained
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6. Running times:
1.Course Grained
• The tests were run on Aries – Supports 32 running threads. UltraSPARC T1 - Sun Fire T2000.
• Total of 200000 operations.
• 10% adds, 2% removes, 88% contains – normal work load percentages on a set.
• Each time the list was initialized with 100 elements.
• One run with a max of 20000 items in the list. Another with only 2000.
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6. Running times:
1.Course Grained
Speed up
0
5
10
15
20
25
30
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s 2000 maxitems in list
20000 maxitems in list
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2.Fine Grained
1. Describing the algorithm:
• Split object into pieces – Each piece has own lock.
– Methods that work on disjoint pieces need not exclude each other.
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2.Fine Grained
• Add(x) / Remove(x) / Contains(x):
– Go throw the list, lock each node and release only after the lock of the next element has been acquired.
– Once you have reached the right point of the list perform the Add / Remove / Contains operation.
1. Describing the algorithm:
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a b c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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a b c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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a b c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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a b c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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a b c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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a c d
remove(b)
2.Fine Grained
1. Describing the algorithm: illustrated Remove.
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Why do we need to always hold 2 locks?
2.Fine Grained
2. Explaining why every step is needed.
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a b c d
remove(c) remove(b)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
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a b c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
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a b c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
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a b c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
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a b c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
![Page 265: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/265.jpg)
a b c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
![Page 266: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/266.jpg)
Concurrent Removes
a b c d
remove(b) remove(c)
2. Explaining why every step is needed.
![Page 267: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/267.jpg)
Concurrent Removes
a b c d
remove(b) remove(c)
2. Explaining why every step is needed.
![Page 268: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/268.jpg)
a c d
remove(b) remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
![Page 269: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/269.jpg)
a c d
Bad news, C not removed remove(b)
remove(c)
2.Fine Grained
Concurrent removes
2. Explaining why every step is needed.
![Page 270: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/270.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 271: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/271.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 272: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/272.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 273: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/273.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 274: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/274.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 275: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/275.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 276: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/276.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 277: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/277.jpg)
a b c d
remove(b) remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 278: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/278.jpg)
a b c d
Must acquire
Lock of b
remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 279: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/279.jpg)
a b c d
Cannot acquire
lock of b
remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 280: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/280.jpg)
a b c d
Wait! remove(c)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 281: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/281.jpg)
a b d
Proceed to
remove(b)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 282: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/282.jpg)
a b d
remove(b)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 283: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/283.jpg)
a b d
remove(b)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 284: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/284.jpg)
a d
remove(b)
Concurrent removes
Now with 2 locks.
2.Fine Grained
2. Explaining why every step is needed.
![Page 285: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/285.jpg)
2.Fine Grained
• Conclusion:
• Now that we hold 2 locks for Remove / Add / Contains. If a node is locked : – It can’t be removed and so does the next node in the
list.
– No new node can be added before it and after it.
2. Explaining why every step is needed.
![Page 286: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/286.jpg)
3. Code review:
Add:
public boolean add(T item) {
int key = item.hashCode();
head.lock();
Node pred = head;
try {
Node curr = pred.next;
curr.lock();
try {
while (curr.key < key) {
pred.unlock();
pred = curr;
curr = curr.next;
curr.lock();
}
Finding the place to add the item:
2.Fine Grained
if (curr.key == key) {
return false;
}
Node newNode = new Node(item);
newNode.next = curr;
pred.next = newNode;
return true;
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
Adding the item:
Continued:
![Page 287: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/287.jpg)
3. Code review:
Remove:
Node pred = null, curr = null;
int key = item.hashCode();
head.lock();
try {
pred = head;
curr = pred.next;
curr.lock();
try {
while (curr.key < key) {
pred.unlock();
pred = curr;
curr = curr.next;
curr.lock();
}
2.Fine Grained
if (curr.key == key) {
pred.next = curr.next;
return true;
}
return false;
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
Removing the item:
Continued:
Finding the place to add the item:
![Page 288: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/288.jpg)
3. Code review:
Contains:
public boolean contains(T item) {
Node pred = null, curr = null;
int key = item.hashCode();
head.lock();
try {
pred = head;
curr = pred.next;
curr.lock();
try {
while (curr.key < key) {
pred.unlock();
pred = curr;
curr = curr.next;
curr.lock();
}
2.Fine Grained
return (curr.key == key);
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
Return true iff found
Continued:
Finding the place to add the item:
![Page 289: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/289.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
• So how do we prove correctness of a method in a concurrent environment?
1. Decide on a Rep-Invariant. Done!
2. Decide on an Abstraction map. Done!
3. Defining the operations: Remove(x): If x in the set => x won’t be in the set and return
true.
If x isn’t in the set => don’t change the set and return false. Done!
![Page 290: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/290.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
4. Proving that each function keeps the Rep-Invariant:
1. Tail reachable from head.
2. Sorted.
3. No duplicates.
1. The newly created empty list obviously keeps the Rep-invariant.
2. Easy to see from the code that for each function if the Rep-invariant was kept before the call it will still hold after it. Done!
![Page 291: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/291.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
5. Split the function to all possible run time outcomes.
In our case:
1. Successful remove. (x was in the list)
2. Failed remove. (x wasn’t in the list)
Done!
6. Proving for each possibility.
We will start with a successful remove. (failed remove is not much different)
![Page 292: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/292.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
6. Deciding on a linearization point for a successful remove. Reminder: Linearization point – a point in time that we
can say the function has happened in a running execution.
We will set the Linearization point to after the second lock was acquired. Done!
successful remove.
![Page 293: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/293.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
Node pred = null, curr = null;
int key = item.hashCode();
head.lock();
try {
pred = head;
curr = pred.next;
curr.lock();
try {
while (curr.key < key) {
pred.unlock();
pred = curr;
curr = curr.next;
curr.lock();
}
if (curr.key == key) {
pred.next = curr.next;
return true;
}
return false;
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
In the code its:
Here!
Remove:
Continued:
successful remove.
![Page 294: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/294.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
y z x w
And in the list, for example: if the Set is {y,z,x,w} and we call Remove(x). After this lock is the linearization point:
successful remove.
![Page 295: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/295.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
7. Now that the linearization point is set we need to prove that:
7.1. Before the linearization point the set contained x.
7.2. After it the set won’t contain x.
successful remove.
![Page 296: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/296.jpg)
296
Proving correctness for Remove(x) function:
2.Fine Grained
7.1. Before the linearization point the set contained x.
1. Since we proved the Rep-Invariant holds then pred=z is accessible from the head.
2. Since z,x are locked. No other concurrent call can remove them.
3. Since curr=x is pointed to by pred then x is also accessible from the head.
y z x w
successful remove.
![Page 297: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/297.jpg)
297
Proving correctness for Remove(x) function:
2.Fine Grained
– S( ) = {a,b}
y z x w
7.1. Before the linearization point the set contained x. Now by the Abstraction map definition:
since x is reachable from the head => x is in the set! Done!
a b
successful remove.
![Page 298: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/298.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
7.1. After it the set won’t contain x.
1. after the linearization point: pred.next = curr.next;
Curr=x won’t be pointed to by pred=z and so won’t be accessible from head.
y z x w
successful remove.
![Page 299: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/299.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
7.1. After it the set won’t contain x.
2. Now by the Abstraction map definition:
since x is not reachable from the head => x is not in the set! Done!
y z x w
successful remove.
![Page 300: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/300.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
300
• Now quicker for an unsuccessful remove: – Linearization point again will be after the second lock
was acquired at: return false;
– Before x wasn’t in the list since pred is reachable from head & pred.key < key & curr.key > key. (x = key) and the rep-invariant property of an ordered list holds.
– After the linearization point since it just returns false nothing changed in the Rep-Invariant and so nothing changed in the Abstraction-Map and the Set.
300
y z w v
Done!
![Page 301: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/301.jpg)
Proving correctness for Remove(x) function:
2.Fine Grained
• In conclusion:
– For every possible run time execution for Remove(x) we found a linearization point that holds the remove function specification in the set using the Abstraction map while holding the Rep-Invariant.
Done!
![Page 302: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/302.jpg)
4. Methods properties:
2.Fine Grained
• Assuming fair scheduler. If the Lock implementation is Starvation free:
Every thread will eventually get the lock and since all methods move in the same direction in the list there won’t be deadlock and eventually the call to the function will return.
• So our implementation of Insert, Remove and Contains is Starvation-free.
![Page 303: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/303.jpg)
5. Advantages / Disadvantages:
Advantages:
- Better than coarse-grained lock
Threads can traverse in parallel.
Disadvantages:
- Long chain of acquire/release.
- Inefficient.
2.Fine Grained
![Page 304: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/304.jpg)
6. Running times:
Speed up
0
10
20
30
40
50
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s 2000 maxitems in list
20000 maxitems in list
2.Fine Grained
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6. Running times:
Speed up
max of 2000 items
02468
1012
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s Fine List
CoarseGrained
2.Fine Grained
![Page 306: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/306.jpg)
6. Running times:
Speed up
max of 20000 items
0
10
20
30
40
50
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s Fine List
CoarseGrained
2.Fine Grained
![Page 307: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/307.jpg)
3. Optimistic
1. Describing the algorithm:
Add(x) / Remove (x) / Contains(x):
1. Find nodes without locking
2. Lock nodes
3. Check that everything is OK = Validation.
3.1 Check that pred is still reachable from head.
3.2 Check that pred still points to curr.
4. If validation passed => do the operation.
![Page 308: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/308.jpg)
b d e a
add(c) Aha!
3. Optimistic
1. Describing the algorithm:
• Example of add(c):
Finding without locking
![Page 309: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/309.jpg)
b d e a
add(c)
1. Describing the algorithm:
Locking • Example of add(c):
3. Optimistic
![Page 310: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/310.jpg)
b d e a
add(c)
1. Describing the algorithm:
Validation 1 • Example of add(c):
3. Optimistic
![Page 311: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/311.jpg)
b d e a
add(c)
1. Describing the algorithm:
Validation 1 • Example of add(c):
3. Optimistic
![Page 312: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/312.jpg)
b d e a
add(c)
1. Describing the algorithm:
Validation 2 • Example of add(c):
Yes. b is still reachable from head.
3. Optimistic
![Page 313: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/313.jpg)
b d e a
add(c)
1. Describing the algorithm:
Validation 2 • Example of add(c):
Yes. b still points to d.
3. Optimistic
![Page 314: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/314.jpg)
b d e a
add(c)
c
3. Optimistic
1. Describing the algorithm:
Add c. • Example of add(c):
![Page 315: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/315.jpg)
Why do we need to Validate?
3. Optimistic
2. Explaining why every step is needed.
![Page 316: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/316.jpg)
3. Optimistic
• First: Why do we need to validate that pred is accessible from head?
• Thread A Adds(c).
• After thread A found b, before A locks. Another thread removes b.
2. Explaining why every step is needed.
b d e a
![Page 317: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/317.jpg)
b d e a
add(c) Aha!
3. Optimistic
• Adds(c). Finding without locking
2. Explaining why every step is needed.
![Page 318: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/318.jpg)
d e a
add(c)
3. Optimistic
b
Another thread removed b
• Adds(c).
2. Explaining why every step is needed.
![Page 319: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/319.jpg)
d e a
add(c)
3. Optimistic
b
Now A locks b and d
• Adds(c).
2. Explaining why every step is needed.
![Page 320: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/320.jpg)
d e a
add(c)
3. Optimistic
b
And adds c
c
• Adds(c).
2. Explaining why every step is needed.
![Page 321: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/321.jpg)
d e a
3. Optimistic
b
Now frees the locks.
But c isn’t added!
c
• Adds(c).
2. Explaining why every step is needed.
![Page 322: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/322.jpg)
3. Optimistic
• Second: Why do we need to validate that pred Still points to curr?
• Thread A removes(d).
• then thread A found b, before A locks. Another thread adds(c).
2. Explaining why every step is needed.
b d e a
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b d e a
add(c) Aha!
3. Optimistic
• Removes(d) Finding without locking
2. Explaining why every step is needed.
![Page 324: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/324.jpg)
d e a
add(c)
3. Optimistic
b
Another thread Adds(c)
c
• Removes(d)
2. Explaining why every step is needed.
![Page 325: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/325.jpg)
d e a
add(c)
3. Optimistic
b
Now A locks.
c
• Removes(d)
2. Explaining why every step is needed.
![Page 326: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/326.jpg)
d e a
add(c)
3. Optimistic
b
pred.next = curr.next;
• Removes(d)
c
2. Explaining why every step is needed.
![Page 327: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/327.jpg)
3. Optimistic
Instead c and d were deleted!
• Removes(d)
d e a b
c
Now frees the locks.
2. Explaining why every step is needed.
![Page 328: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/328.jpg)
3. Optimistic
• Do notice that threads might traverse deleted nodes. May cause problems to our Rep-Invariant.
• Careful not to recycle to the lists nodes that were deleted while threads are in a middle of an operation.
• With a garbage collection language like java – ok.
• For C – you need to solve this manually.
Important comment.
![Page 329: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/329.jpg)
3. Code review:
Add:
public boolean add(T item) {
int key = item.hashCode();
while (true) {
Entry pred = this.head;
Entry curr = pred.next;
while (curr.key <= key) {
pred = curr; curr = curr.next;
}
pred.lock(); curr.lock();
Search the list from the beginning each
time, until validation succeeds
try {
if (validate(pred, curr)) {
if (curr.key == key) {
return false;
} else {
Entry entry = new Entry(item);
entry.next = curr;
pred.next = entry;
return true;
}
}
} finally {
pred.unlock(); curr.unlock();
}
}
}
If validation succeeds Attempt Add
Continued:
3. Optimistic
![Page 330: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/330.jpg)
3. Code review:
Remove:
public boolean add(T item) {
int key = item.hashCode();
while (true) {
Entry pred = this.head;
Entry curr = pred.next;
while (curr.key <= key) {
pred = curr; curr = curr.next;
}
pred.lock(); curr.lock();
Search the list from the beginning each
time, until validation succeeds
try {
if (validate(pred, curr)) {
if (curr.key == key) {
pred.next = curr.next;
return true;
} else {
return false;
}
}
} finally {
pred.unlock(); curr.unlock();
}
}
}
If validation succeeds Attempt remove
Continued:
3. Optimistic
![Page 331: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/331.jpg)
3. Code review:
Contains:
public boolean contains(T item) {
int key = item.hashCode();
while (true) {
Entry pred = this.head;
Entry curr = pred.next;
while (curr.key < key) {
pred = curr; curr = curr.next;
}
try {
pred.lock(); curr.lock();
if (validate(pred, curr)) {
return (curr.key == key);
}
} finally {
pred.unlock(); curr.unlock();
}
}
}
Search the list from the beginning each
time, until validation succeeds
If validation succeeds Return the result
3. Optimistic
![Page 332: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/332.jpg)
4. Methods properties:
• Assuming fair scheduler. Even if all the lock
implementations are Starvation free. We will show a scenario in which the methods Remove / Add / Contains do not return.
• And so our implementation won’t be starvation free.
3. Optimistic
![Page 333: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/333.jpg)
4. Methods properties:
• Assuming Thread A operation is Remove(d) /
Add(c) / Contains(c).
• If the following sequence of operations will happen:
3. Optimistic
d e a b
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4. Methods properties:
The sequence:
• 1. Thread A will find b.
• 2. Thread B will remove b.
• 3. The validation of thread A will fail.
3. Optimistic
The thread call to the function won’t return!
d e a b
• 4. Thread C will add b.
now go to 1.
![Page 335: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/335.jpg)
5. Advantages / Disadvantages:
Advantages:
- Limited hot-spots
• Targets of add(), remove(), contains().
• No contention on traversals.
- Much less lock acquisition/releases.
– Better concurrency.
Disadvantages:
- Need to traverse list twice!
- Contains() method acquires locks.
3.Optimistic
![Page 336: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/336.jpg)
5. Advantages / Disadvantages:
3.Optimistic
• Optimistic is effective if:
– The cost of scanning twice without locks is less than the cost of scanning once with locks
• Drawback:
– Contains() acquires locks. Normally, about 90% of the calls are contains.
![Page 337: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/337.jpg)
6. Running times:
Speed up
0
5
10
15
20
25
30
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s 2000 maxitems in list
20000 maxitems in list
3. Optimistic
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6. Running times:
Speed up
max of 2000 items
0
5
10
15
20
25
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s Fine List
CoarseGrained
Optimistic
3. Optimistic
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6. Running times:
Speed up
max of 20000 items
0
10
20
30
40
50
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s Fine List
CoarseGrained
Optimistic
3. Optimistic
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4. Lazy
1. Describing the algorithm:
Validate:
– Pred is not marked as deleted.
– Curr is not marked as deleted.
– Pred points to curr.
![Page 341: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/341.jpg)
4. Lazy
1. Describing the algorithm:
Remove(x):
• Find the node to remove.
• Lock pred and curr.
• Validate. (New validation!)
• Logical delete
– Marks current node as removed (new!).
• Physical delete
– Redirects predecessor’s next.
![Page 342: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/342.jpg)
4. Lazy
1. Describing the algorithm:
Add(x):
• Find the node to remove.
• Lock pred and curr.
• Validate. (New validation!)
• Physical add
– The same as Optimistic.
![Page 343: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/343.jpg)
4. Lazy
1. Describing the algorithm:
Contains(x):
• Find the node to remove without locking!
• Return true if found the node and it isn’t marked as deleted.
• No locks!
![Page 344: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/344.jpg)
a a b c d
4. Lazy
1. Describing the algorithm:
• Remove(c):
![Page 345: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/345.jpg)
c a a b d
Present in list
4. Lazy
1. Describing the algorithm:
• Remove(c):
1. Find the node
![Page 346: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/346.jpg)
c a a b d
Present in list
4. Lazy
1. Describing the algorithm:
• Remove(c):
2. lock
![Page 347: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/347.jpg)
c a a b d
Present in list
4. Lazy
1. Describing the algorithm:
• Remove(c):
3. Validate
![Page 348: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/348.jpg)
c a a b d
Set as marked
4. Lazy
1. Describing the algorithm:
• Remove(c):
4. Logically delete
![Page 349: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/349.jpg)
a a b c d
Pred.next = curr.next
4. Lazy
1. Describing the algorithm:
• Remove(c):
5. Physically delete
![Page 350: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/350.jpg)
a a b d
Cleaned
4. Lazy
1. Describing the algorithm:
• Remove(c):
5. Physically delete
![Page 351: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/351.jpg)
4. Lazy
1. Describing the algorithm:
Given the Lazy Synchronization algorithm.
What else should we change?
![Page 352: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/352.jpg)
4. Lazy
1. Describing the algorithm:
• New Abstraction map!
• S(head) =
– { x | there exists node a such that
• a reachable from head and
• a.item = x and
• a is unmarked
– }
![Page 353: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/353.jpg)
Why do we need to Validate?
2. Explaining why every step is needed.
4. Lazy
![Page 354: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/354.jpg)
• First: Why do we need to validate that pred Still points to curr?
• The same as in Optimistic:
• Thread A removes(d).
• Then thread A found b, before A locks. Another thread adds(c). – c and d will be removed instead of just d.
2. Explaining why every step is needed.
4. Lazy
b d e a
![Page 355: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/355.jpg)
• Second: Why do we need to validate that pred and curr aren’t marked logically removed?
• To make sure a thread hasn’t removed them between our find and our lock.
• The same scenario we showed for validating that pred is still accessible from head holds here: – After thread A found b, before A locks. Another
thread removes b. (our operation won’t take place).
2. Explaining why every step is needed.
4. Lazy
d e b a
![Page 356: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/356.jpg)
3. Code review:
Add:
public boolean add(T item) {
int key = item.hashCode();
while (true) {
Node pred = this.head;
Node curr = head.next;
while (curr.key < key) {
pred = curr; curr = curr.next;
}
pred.lock();
try {
curr.lock();
Search the list from the beginning each
time, until validation succeeds
try {
if (validate(pred, curr)) {
if (curr.key == key) {
return false;
} else {
Node Node = new Node(item);
Node.next = curr;
pred.next = Node;
return true;
}
}
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
}
If validation succeeds Attempt Add
Continued:
4. Lazy
![Page 357: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/357.jpg)
3. Code review:
Remove:
public boolean remove(T item) {
int key = item.hashCode();
while (true) {
Node pred = this.head;
Node curr = head.next;
while (curr.key < key) {
pred = curr; curr = curr.next;
}
pred.lock();
try {
curr.lock();
try {
Search the list from the beginning each
time, until validation succeeds
try{
if (validate(pred, curr)) {
if (curr.key != key) {
return false;
} else {
curr.marked = true;
pred.next = curr.next;
return true;
}
}
} finally {
curr.unlock();
}
} finally {
pred.unlock();
}
}
}
Validation
Continued:
4. Lazy
Logically remove
Physically remove
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3. Code review:
Contains:
public boolean contains(T item) {
int key = item.hashCode();
Node curr = this.head;
while (curr.key < key)
curr = curr.next;
return curr.key == key && !curr.marked;
}
Check if its there and not marked
4. Lazy
No Lock!
![Page 359: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/359.jpg)
4. Methods properties:
Remove and Add:
• Assuming fair scheduler. Even if all the lock implementations are Starvation free. The same scenario we showed for optimistic holds here.
• (only here the validation will fail because the node will be marked and not because it can’t be reached from head)
• And so our implementation won’t be starvation free.
4. Lazy
![Page 360: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/360.jpg)
4. Methods properties:
But… Contains:
• Contains does not lock!
• In fact it isn’t dependent on other threads to work.
• And so… Contains is Wait-free.
• Do notice that other threads can’t increase the list forever while the thread is in contains because we have a maximum size to the list (<tail).
4. Lazy
![Page 361: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/361.jpg)
5. Advantages / Disadvantages:
• Advantages:
– Contains is Wait-free. Usually 90% of the calls!
– Validation doesn’t rescan the list.
• Drawbacks:
– Failure to validate restarts the function call.
– Add and Remove use locks.
Lock-free implementation
4. Lazy
![Page 362: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/362.jpg)
6. Running times:
Speed up
0
2
4
6
8
10
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s 2000 maxitems in list
20000 maxitems in list
4. Lazy
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6. Running times:
Speed up
max of 2000 items
0
5
10
15
20
25
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s
Fine List
CoarseGrained
Optimistic
Lazy
4. Lazy
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6. Running times:
Speed up
max of 20000 items
0
10
20
30
40
50
4 8 12 16 20 24 28 32
No. Threads
Seco
nd
s
Fine List
CoarseGrained
Optimistic
Lazy
4. Lazy
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Optimistic lock-free Concurrency
Pessimistic Optimistic
lock x;
x++;
unlock x;
int t;
do {
t = x;
} while (!CAS(&x, t, t+1))
CAS(&x,a,b) = if *x = a then *x = b return true else return false
![Page 366: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/366.jpg)
An Optimistic Lock-free Stack
pop( ){
1 local done, next, t;
2 done = false;
3 while (!done) {
4 t = Top;
5 if (t==null) return null;
6 next = t.Next;
7 done = CAS(&Top, t, next);
8 }
9 return t;
push(x){
10 local done, t;
11 done = false;
12 while(!done) {
13 t = Top;
14 x.Next = t;
15 done = CAS(&Top, t, x);
16 }
17 return true; Bug#1: t might be a dangling pointer
Bug#2: ABA problem leads to corrupted stacks
… n Nex
t n Next
Top
![Page 367: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/367.jpg)
ABA Problem Threads T1 and T2 are interleaved as follows:
A
C
B
Top
t
next
B
C next (removed)
Top
A
B
t
Top
C next (removed)
Timeline
T1:
pop()
{
t = Top
next = t.Next
interrupted
resumes
CAS(&Top,t,next)
succeeds
stack corrupted
T2:
a = pop();
c = pop();
push(a);
![Page 368: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/368.jpg)
Summary
Our winner: Optimistic Lock-free.
Second best: Lazy.
Third: Optimistic.
Fourth: Fine-Grained.
Last: Coarse-Grained.
?
![Page 369: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/369.jpg)
Summary
Answer: No.
Choose your implementation carefully based on your requirements.
![Page 370: Introduction to Concurrencystaff.ustc.edu.cn/.../concurrency-intro.pdf · and Multicore Programming . Slides adapted from Art of Multicore Programming by Herlihy and Shavit . Overview](https://reader035.vdocument.in/reader035/viewer/2022081522/5fc640e126b68f457d635667/html5/thumbnails/370.jpg)
Summary
• Concurrent programming is hard.
• Concurrency is error-prone.
• Formal method is necessary.