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Hashing and Natural Parallism Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit
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Code Please review the code for the presented data structures from Chapter 13 of the textbook Art of Multiprocessor Programming© Herlihy-Shavit 2007 2
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3 Linked Lists We looked at a number of ways to make highly-concurrent list-based Sets: –Fine-grained locks –Optimistic synchronization –Lazy synchronization –Lock-free synchronization What’s missing?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 4 Linear-Time Set Methods Problem is –add(), remove(), contains() –Take time linear in set size We want –Constant-time methods –(at least, on average)
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 5 Hashing Hash function –h: items integers Uniformly distributed –Different item most likely have different hash values Java hashCode() method
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 6 Sequential Hash Map 0 1 2 3 16 9 h(k) = k mod 4 2 Items buckets
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 7 Add an Item 0 1 2 3 16 9 7 h(k) = k mod 4 3 Items
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 8 Add Another: Collision 0 1 2 3 164 9 7 h(k) = k mod 4 4 Items
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 9 More Collisions 0 1 2 3 164 9 715 h(k) = k mod 4 5 Items
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 10 More Collisions 0 1 2 3 164 9 715 h(k) = k mod 4 5 Items Problem: buckets getting too long
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 11 Resizing 0 1 2 3 164 9 715 4 5 6 7 Grow the array 5 Items h(k) = k mod 8
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 12 5 Items Resizing 0 1 2 3 164 9 715 4 5 6 7 h(k) = k mod 8 Adjust hash function
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 13 Resizing 0 1 2 3 16 9 715 h(4) = 0 mod 8 4 5 6 7 4 h(k) = k mod 8
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 14 Resizing 0 1 2 3 16 4 9 715 4 5 6 7 h(k) = k mod 8 h(4) = 4 mod 8
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 15 Resizing 0 1 2 3 16 4 9 715 4 5 6 7 h(k) = k mod 8 h(15) = 7 mod 8
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 16 Resizing 0 1 2 3 16 4 9 4 5 6 7 h(k) = k mod 8 h(15) = 7 mod 8 157
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 17 Hash Sets Implement a Set object –Collection of items, no duplicates –add(), remove(), contains() methods –You know the drill …
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 18 Simple Hash Set public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } …
![Art of Multiprocessor Programming© Herlihy-Shavit Simple Hash Set public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } …](http://images.slideplayer.com./26/8697864/slides/slide_18.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Simple Hash Set public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } …")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 19 Fields public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Array of lock-free lists
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Array of lock-free lists](http://images.slideplayer.com./26/8697864/slides/slide_19.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Array of lock-free lists")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 20 Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initial size
![Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initial size](http://images.slideplayer.com./26/8697864/slides/slide_20.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initial size")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 21 Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Allocate memory
![Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Allocate memory](http://images.slideplayer.com./26/8697864/slides/slide_21.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Allocate memory")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 22 Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initialization
![Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initialization](http://images.slideplayer.com./26/8697864/slides/slide_22.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Constructor public class SimpleHashSet { protected LockFreeList[] table; public SimpleHashSet(int capacity) { table = new LockFreeList[capacity]; for (int i = 0; i < capacity; i++) table[i] = new LockFreeList(); } … Initialization")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 23 Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); }
![Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); }](http://images.slideplayer.com./26/8697864/slides/slide_23.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); }")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 24 Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Use object hash code to pick a bucket
![Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Use object hash code to pick a bucket](http://images.slideplayer.com./26/8697864/slides/slide_24.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Use object hash code to pick a bucket")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 25 Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Call bucket’s add() method
![Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Call bucket’s add() method](http://images.slideplayer.com./26/8697864/slides/slide_25.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Add Method public boolean add(Object key) { int hash = key.hashCode() % table.length; return table[hash].add(key); } Call bucket’s add() method")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 26 No Brainer? We just saw a –Simple –Lock-free –Concurrent hash-based set implementation What’s not to like?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 27 No Brainer? We just saw a –Simple –Lock-free –Concurrent hash-based set implementation What’s not to like? We don’t know how to resize …
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 28 Is Resizing Necessary? Constant-time method calls require –Constant-length buckets –Table size proportional to set size –As set grows, must be able to resize
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 29 Set Method Mix Typical load –90% contains() –9% add () –1% remove() Growing is important Shrinking not so much
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 30 When to Resize? Many reasonable policies. Here’s one. Pick a threshold on num of items in a bucket Global threshold –When ≥ ¼ buckets exceed this value Bucket threshold –When any bucket exceeds this value
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 31 Coarse-Grained Locking Good parts –Simple –Hard to mess up Bad parts –Sequential bottleneck
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 32 Fine-grained Locking 0 1 2 3 48 9 711 17 Each lock associated with one bucket
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 33 Resize This Make sure table reference didn’t change between resize decision and lock acquisition 0 1 2 3 48 9 711 17 Acquire locks in ascending order
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 34 Resize This 0 1 2 3 48 9 711 17 0 1 2 3 4 5 6 7 Allocate new super-sized table
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 35 Resize This 0 1 2 3 9 7 48 17 0 1 2 3 4 5 6 7 8 4 9 7 11
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 36 Resize This 0 1 2 3 0 1 2 3 4 5 6 7 8 4 9 17 7 11
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 37 Resize This 0 1 2 3 0 1 2 3 4 5 6 7 8 4 9 17 7 11 Striped Locks: each lock now associated with two buckets
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 38 Observations We grow the table, but not locks –Resizing lock array is tricky … We use sequential lists –Not LockFreeList lists –If we’re locking anyway, why pay?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 39 Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} …
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} …](http://images.slideplayer.com./26/8697864/slides/slide_39.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} …")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 40 Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of locks
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of locks](http://images.slideplayer.com./26/8697864/slides/slide_40.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of locks")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 41 Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of buckets
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of buckets](http://images.slideplayer.com./26/8697864/slides/slide_41.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Array of buckets")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 42 Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Initially same number of locks and buckets
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Initially same number of locks and buckets](http://images.slideplayer.com./26/8697864/slides/slide_42.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Hash Set public class FGHashSet { protected RangeLock[] lock; protected List[] table; public FGHashSet(int capacity) { table = new List[capacity]; lock = new RangeLock[capacity]; for (int i = 0; i < capacity; i++) { lock[i] = new RangeLock(); table[i] = new LinkedList(); }} … Initially same number of locks and buckets")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 43 The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); }
![Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); }](http://images.slideplayer.com./26/8697864/slides/slide_43.jpg "Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); }")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 44 Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which lock?
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which lock](http://images.slideplayer.com./26/8697864/slides/slide_44.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which lock")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 45 The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Acquire the lock
![Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Acquire the lock](http://images.slideplayer.com./26/8697864/slides/slide_45.jpg "Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Acquire the lock")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 46 Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which bucket?
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which bucket](http://images.slideplayer.com./26/8697864/slides/slide_46.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Which bucket")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 47 The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Call that bucket’s add() method
![Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Call that bucket’s add() method](http://images.slideplayer.com./26/8697864/slides/slide_47.jpg "Art of Multiprocessor Programming© Herlihy-Shavit The add() method public boolean add(Object key) { int keyHash = key.hashCode() % lock.length; synchronized (lock[keyHash]) { int tabHash = key.hashCode() % table.length; return table[tabHash].add(key); } Call that bucket’s add() method")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 48 Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} resize() calls resize(0,this.table)
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} resize() calls resize(0,this.table)](http://images.slideplayer.com./26/8697864/slides/slide_48.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} resize() calls resize(0,this.table)")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 49 Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Acquire next lock
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Acquire next lock](http://images.slideplayer.com./26/8697864/slides/slide_49.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Acquire next lock")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 50 Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table) { int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Check that no one else has resized
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table) { int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Check that no one else has resized](http://images.slideplayer.com./26/8697864/slides/slide_50.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table) { int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Check that no one else has resized")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 51 Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Recursively acquire next lock
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Recursively acquire next lock](http://images.slideplayer.com./26/8697864/slides/slide_51.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Recursively acquire next lock")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 52 Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Locks acquired, do the work
![Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Locks acquired, do the work](http://images.slideplayer.com./26/8697864/slides/slide_52.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fine-Grained Locking private void resize(int depth, List[] oldTab) { synchronized (lock[depth]) { if (oldTab == this.table){ int next = depth + 1; if (next < lock.length) resize (next, oldTab); else sequentialResize(); }}} Locks acquired, do the work")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 53 Fine-Grained Locks We can resize the table But not the locks Debatable whether method calls are constant-time in presence of contention …
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 54 Insight The contains() method –Does not modify any fields –Why should concurrent contains() calls conflict?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 55 Read/Write Locks public interface ReadWriteLock { Lock readLock(); Lock writeLock(); }
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 56 Read/Write Locks public interface ReadWriteLock { Lock readLock(); Lock writeLock(); } Returns associated read lock
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 57 Read/Write Locks public interface ReadWriteLock { Lock readLock(); Lock writeLock(); } Returns associated read lock Returns associated write lock
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 58 Lock Safety Properties No thread may acquire the write lock –while any thread holds the write lock –or the read lock. No thread may acquire the read lock – while any thread holds the write lock. Concurrent read locks OK
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 59 Read/Write Lock Satisfies safety properties –If readers > 0 then writer == false –If writer = true then readers == 0 Liveness? –Lots of readers … –Writers locked out?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 60 FIFO R/W Lock As soon as a writer requests a lock No more readers accepted Current readers “drain” from lock Writer gets in
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 61 The Story So Far Resizing the hash table is the hard part Fine-grained locks –Striped locks cover a range (not resized) Read/Write locks –FIFO property tricky
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 62 Optimistic Synchronization If the contains() method –Scans without locking If it finds the key –OK to return true –Actually requires a proof …. What if it doesn’t find the key?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 63 Optimistic Synchronization If it doesn’t find the key –May be victim of resizing Must try again –Getting a read lock this time Makes sense if –Keys are present –Resizes are rare
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 64 Stop The World Resizing The resizing we have seen up till now stops all concurrent operations Can we design a resize operation that will be incremental Need to avoid locking the table A lock-free table with incremental resizing
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 65 Lock-Free Resizing Problem 0 1 2 3 48 9 715
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 66 Lock-Free Resizing Problem 0 1 2 3 48 9 715 12 Need to extend table
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 67 4 12 Lock-Free Resizing Problem 0 1 2 3 8 9 715 4 5 6 7 412 Need to extend table
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 68 Lock-Free Resizing Problem 0 1 2 3 8 4 9 715 4 5 6 7 12 4
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 69 Lock-Free Resizing Problem 0 1 2 3 9 715 4 5 6 7 12 to remove and then add even a single item single location CAS not enough 4 8 4 12 We need a new idea…
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 70 Don’t move the items Move the buckets instead Keep all items in a single lock-free list Buckets become “shortcut pointers” into the list 16 4 9 7 15 0 1 2 3
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 71 Recursive Split Ordering 0 0 4261537
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 72 Recursive Split Ordering 0 1/2 1 0 4261537
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 73 Recursive Split Ordering 0 1/2 1 1/43/4 2 3 0 4261537
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 74 Recursive Split Ordering 0 1/2 1 1/43/4 2 3 0 4261537 List entries sorted in order that allows recursive splitting. How?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 75 Recursive Split Ordering 0 0 4261537
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 76 Recursive Split Ordering 0 1 0 4261537 LSB 0 LSB 1 LSB = Least significant Bit
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 77 Recursive Split Ordering 0 1 2 3 0 4261537 LSB 00LSB 10LSB 01LSB 11
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 78 Split-Order If the table size is 2 i, –Bucket b contains keys k k = b (mod 2 i ) –bucket index consists of key's i LSBs
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 79 When Table Splits Some keys stay –b = k mod(2 i+1 ) Some move –b+2 i = k mod(2 i+1 ) Determined by (i+1) st bit –Counting backwards Key must be accessible from both –Keys that will move must come later
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 80 A Bit of Magic 0 4261537 Real keys:
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 81 A Bit of Magic 0 4261537 Real keys: 0 1234567 Split-order: Real key 1 is in the 4 th location
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 82 A Bit of Magic 0 4261537 Real keys: 0 1234567 Split-order: 000100010110001101011111 000001010011100101110111 Real key 1 is in 4 th location
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 83 A Bit of Magic Real keys: Split-order: 000100010110001101011111 000001010011100101110111
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 84 A Bit of Magic Real keys: Split-order: 000100010110001101011111 000001010011100101110111 Just reverse the order of the key bits
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 85 Split Ordered Hashing 0 1 2 3 0 4261537 000001010011100101110111 Order according to reversed bits
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 86 Parent Always Provides a Short Cut 0 1 2 3 0 4261537 search
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 87 Sentinel Nodes 0 1 2 3 16 4 9 715 Problem: how to remove a node pointed by 2 sources using CAS
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 88 Sentinel Nodes 0 1 2 3 16 4 9 715 3 Solution: use a Sentinel node for each bucket 0 1
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 89 Sentinel vs Regular Keys Want sentinel key for i ordered –before all keys that hash to bucket i –after all keys that hash to bucket (i-1)
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 90 Splitting a Bucket We can now split a bucket In a lock-free manner Using two CAS() calls...
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 91 Initialization of Buckets 0 1 16 4 9 715 0 1
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 92 Initialization of Buckets 0 1 2 3 16 4 9 715 0 1 3 Need to initialize bucket 3 to split bucket 1 3 in list but not connected to bucket yet Now 3 points to sentinel – bucket has been split
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 93 Adding 10 0 1 2 3 16 4 9 37 0 1 2 10 = 2 mod 4 2 Must initialize bucket 2 Then can add 10
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 94 Recursive Initialization 0 1 2 3 8 12 0 7 = 3 mod 4 To add 7 to the list 3 Must initialize bucket 3Must initialize bucket 1 = 1 mod 2 1 Could be log n depth But EXPECTED depth is constant
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 95 Lock-Free List int makeRegularKey(int key) { return reverse(key | 0x80000000); } int makeSentinelKey(int key) { return reverse(key); }
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 96 Lock-Free List int makeRegularKey(int key) { return reverse(key | 0x80000000); } int makeSentinelKey(int key) { return reverse(key); } Regular key: set high-order bit to 1 and reverse
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 97 Lock-Free List int makeRegularKey(int key) { return reverse(key | 0x80000000); } int makeSentinelKey(int key) { return reverse(key); } Sentinel key: simply reverse (high-order bit is 0)
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 98 Main List Lock-Free List from earlier class With some minor variations
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 99 Lock-Free List public class LockFreeList { public boolean add(Object object, int key) {...} public boolean remove(int k) {...} public boolean contains(int k) {...} public LockFreeList(LockFreeList parent, int key) {...}; }
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 100 Lock-Free List public class LockFreeList { public boolean add(Object object, int key) {...} public boolean remove(int k) {...} public boolean contains(int k) {...} public LockFreeList(LockFreeList parent, int key) {...}; } Change: add takes key argument
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 101 Lock-Free List public class LockFreeList { public boolean add(Object object, int key) {...} public boolean remove(int k) {...} public boolean contains(int k) {...} public LockFreeList(LockFreeList parent, int key) {...}; } Inserts sentinel with key if not already present …
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 102 Lock-Free List public class LockFreeList { public boolean add(Object object, int key) {...} public boolean remove(int k) {...} public boolean contains(int k) {...} public LockFreeList(LockFreeList parent, int key) {...}; } … returns new list starting with sentinel (shares with parent)
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 103 Split-Ordered Set: Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); }
![Art of Multiprocessor Programming© Herlihy-Shavit Split-Ordered Set: Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); }](http://images.slideplayer.com./26/8697864/slides/slide_103.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Split-Ordered Set: Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); }")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 104 Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } For simplicity treat table as big array …
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } For simplicity treat table as big array …](http://images.slideplayer.com./26/8697864/slides/slide_104.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } For simplicity treat table as big array …")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 105 Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } In practice, want something that grows dynamically
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } In practice, want something that grows dynamically](http://images.slideplayer.com./26/8697864/slides/slide_105.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } In practice, want something that grows dynamically")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 106 Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } How much of table array are we actually using?
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } How much of table array are we actually using](http://images.slideplayer.com./26/8697864/slides/slide_106.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } How much of table array are we actually using")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 107 Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } Track set size so we know when to resize
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } Track set size so we know when to resize](http://images.slideplayer.com./26/8697864/slides/slide_107.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(2); setSize = new AtomicInteger(0); } Track set size so we know when to resize")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 108 Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(1); setSize = new AtomicInteger(0); } Initially use 1 bucket and size is zero
![Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(1); setSize = new AtomicInteger(0); } Initially use 1 bucket and size is zero](http://images.slideplayer.com./26/8697864/slides/slide_108.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Fields public class SOSet { protected LockFreeList[] table; protected AtomicInteger tableSize; protected AtomicInteger setSize; public SOSet(int capacity) { table = new LockFreeList[capacity]; table[0] = new LockFreeList(); tableSize = new AtomicInteger(1); setSize = new AtomicInteger(0); } Initially use 1 bucket and size is zero")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 109 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; }
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 110 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } Pick a bucket
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 111 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } Non-Sentinel split-ordered key
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 112 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } Get pointer to bucket’s sentinel, initializing if necessary
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 113 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } Call bucket’s add() method with reversed key
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 114 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } No change? We’re done.
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 115 Add() Method public boolean add(Object object) { int hash = object.hashCode(); int bucket = hash % tableSize.get(); int key = makeRegularKey(hash); LockFreeList list = getBucketList(bucket); if (!list.add(object, key)) return false; resizeCheck(); return true; } Time to resize?
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 116 Resize Divide set size by total number of buckets If quotient exceeds threshold –Double tableSize field –Up to fixed limit
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 117 Initialize Buckets Buckets originally null If you find one, initialize it Go to bucket’s parent –Earlier nearby bucket –Recursively initialize if necessary Constant expected work
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 118 Recall: Recursive Initialization 0 1 2 3 8 12 0 7 = 3 mod 4 To add 7 to the list 3 Must initialize bucket 3Must initialize bucket 1 = 1 mod 2 1 Could be log n depth But EXPECTED depth is constant
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 119 Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); }
![Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); }](http://images.slideplayer.com./26/8697864/slides/slide_119.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); }")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 120 Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Find parent, recursively initialize if needed
![Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Find parent, recursively initialize if needed](http://images.slideplayer.com./26/8697864/slides/slide_120.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Find parent, recursively initialize if needed")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 121 Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Prepare key for new sentinel
![Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Prepare key for new sentinel](http://images.slideplayer.com./26/8697864/slides/slide_121.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Prepare key for new sentinel")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 122 Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Insert sentinel if not present, and get back reference to rest of list
![Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Insert sentinel if not present, and get back reference to rest of list](http://images.slideplayer.com./26/8697864/slides/slide_122.jpg "Art of Multiprocessor Programming© Herlihy-Shavit Initialize Bucket void initializeBucket(int bucket) { int parent = getParent(bucket); if (table[parent] == null) initializeBucket(parent); int key = makeSentinelKey(bucket); LockFreeList list = new LockFreeList(table[parent], key); } Insert sentinel if not present, and get back reference to rest of list")
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 123 Correctness Linearizable concurrent set implementation Theorem: O(1) expected time –No more than O(1) items expected between two dummy nodes on average –Lazy initialization causes at most O(1) expected recursion depth in initializeBucket()
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 124 Empirical Evaluation On a 30-processor Sun Enterprise 3000 Lock-Free vs. fine-grained (Lea) optimistic In a non-multiprogrammed environment 10 6 operations: 88% contains(), 10% add(), 2% remove()
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 125 Work = 0 ops/time threads (2) locking lock-free
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 126 Work = 500 ops/time threads (2) locking lock-free
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 127 Expected Bucket Length ops/time Load factor (2) locking lock-free 64 threads
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 128 Varying The Mix ops/time (2) locking lock-free 64 threads More reads More updates
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 129 Summary Concurrent resizing is tricky Lock-based –Fine-grained –Read/write locks –Optimistic Lock-free –Builds on lock-free list
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 130 Additional Performance The effects of the choice of locking granularity The effects of bucket size
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 131 Number of Fine-Grain Locks
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 132 Lock-free vs Locks
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 133 Hash Table Load Factor (load factor = nodes per bucket)
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 134 Varying Operations
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Art of Multiprocessor Programming© Herlihy-Shavit 2007 135 This work is licensed under a Creative Commons Attribution- ShareAlike 2.5 License.Creative Commons Attribution- ShareAlike 2.5 License You are free: –to Share — to copy, distribute and transmit the work –to Remix — to adapt the work Under the following conditions: –Attribution. You must attribute the work to “The Art of Multiprocessor Programming” (but not in any way that suggests that the authors endorse you or your use of the work). –Share Alike. If you alter, transform, or build upon this work, you may distribute the resulting work only under the same, similar or a compatible license. For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to –http://creativecommons.org/licenses/by-sa/3.0/. Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this license impairs or restricts the author's moral rights.
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