Linked Lists: Locking, Lock- Free, and Beyond … Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit

Art of Multiprocessor Programming2 Last Lecture: Spin-Locks CS Resets lock upon exit spin lock critical section...

Art of Multiprocessor Programming3 Today: Concurrent Objects Adding threads should not lower throughput –Contention effects –Mostly fixed by Queue locks Should increase throughput –Not possible if inherently sequential –Surprising things are parallelizable

Art of Multiprocessor Programming4 Coarse-Grained Synchronization Each method locks the object –Avoid contention using queue locks –Easy to reason about In simple cases –Standard Java model Synchronized blocks and methods So, are we done?

Art of Multiprocessor Programming5 Coarse-Grained Synchronization Sequential bottleneck –Threads “stand in line” Adding more threads –Does not improve throughput –Struggle to keep it from getting worse So why even use a multiprocessor? –Well, some apps inherently parallel …

Art of Multiprocessor Programming6 This Lecture Introduce four “patterns” –Bag of tricks … –Methods that work more than once … For highly-concurrent objects Goal: –Concurrent access –More threads, more throughput

Art of Multiprocessor Programming7 First: Fine-Grained Synchronization Instead of using a single lock.. Split object into –Independently-synchronized components Methods conflict when they access –The same component … –At the same time

Art of Multiprocessor Programming8 Second: Optimistic Synchronization Search without locking … If you find it, lock and check … –OK: we are done –Oops: start over Evaluation –Usually cheaper than locking –Mistakes are expensive

Art of Multiprocessor Programming9 Third: Lazy Synchronization Postpone hard work Removing components is tricky –Logical removal Mark component to be deleted –Physical removal Do what needs to be done

Art of Multiprocessor Programming10 Fourth: Lock-Free Synchronization Don’t use locks at all –Use compareAndSet() & relatives … Advantages –No Scheduler Assumptions/Support Disadvantages –Complex –Sometimes high overhead

Art of Multiprocessor Programming11 Linked List Illustrate these patterns … Using a list-based Set –Common application –Building block for other apps

Art of Multiprocessor Programming12 Set Interface Unordered collection of items No duplicates Methods –add(x) put x in set –remove(x) take x out of set –contains(x) tests if x in set

Art of Multiprocessor Programming13 List-Based Sets public interface Set { public boolean add(T x); public boolean remove(T x); public boolean contains(T x); }

Art of Multiprocessor Programming14 List-Based Sets public interface Set { public boolean add(T x); public boolean remove(T x); public boolean contains(T x); } Add item to set

Art of Multiprocessor Programming15 List-Based Sets public interface Set { public boolean add(T x); public boolean remove(T x); public boolean contains(Tt x); } Remove item from set

Art of Multiprocessor Programming16 List-Based Sets public interface Set { public boolean add(T x); public boolean remove(T x); public boolean contains(T x); } Is item in set?

Art of Multiprocessor Programming17 List Node public class Node { public T item; public int key; public Node next; }

Art of Multiprocessor Programming18 List Node public class Node { public T item; public int key; public Node next; } item of interest

Art of Multiprocessor Programming19 List Node public class Node { public T item; public int key; public Node next; } Usually hash code

Art of Multiprocessor Programming20 List Node public class Node { public T item; public int key; public Node next; } Reference to next node

Art of Multiprocessor Programming21 The List-Based Set abc Sorted with Sentinel nodes (min & max possible keys) -∞ +∞

Art of Multiprocessor Programming22 Reasoning about Concurrent Objects Invariant –Property that always holds Established because –True when object is created –Truth preserved by each method Each step of each method

Art of Multiprocessor Programming23 Specifically … Invariants preserved by –add() –remove() –contains() Most steps are trivial –Usually one step tricky –Often linearization point

Art of Multiprocessor Programming24 Interference Invariants make sense only if –methods considered –are the only modifiers Language encapsulation helps –List nodes not visible outside class –Owned by the set abstraction

Art of Multiprocessor Programming25 Interference Freedom from interference needed even for removed nodes –Some algorithms traverse removed nodes –Careful with malloc() & free() ! Garbage-collection helps here

Art of Multiprocessor Programming26 Abstract Data Types Concrete representation Abstract Type –{a, b} ab

Art of Multiprocessor Programming27 Abstract Data Types Meaning of rep given by abstraction map –S( ) = {a,b} a b

Art of Multiprocessor Programming28 Rep Invariant Which concrete values meaningful? –Sorted? –Duplicates? Rep invariant –Characterizes legal concrete reps –Preserved by methods –Relied on by methods

Art of Multiprocessor Programming29 Blame Game Rep invariant is a contract Suppose –add(x) leaves behind 2 copies of x –remove(x) removes only 1 Which one is incorrect?

Art of Multiprocessor Programming30 Blame Game Suppose –add(x) leaves behind 2 copies of x –remove(x) removes only 1 Which one is incorrect? –If rep invariant says no duplicates add(x) is incorrect –Otherwise remove(x) is incorrect

Art of Multiprocessor Programming31 Rep Invariant (partly) Sentinel nodes –tail reachable from head Sorted (ascending) No duplicates

Art of Multiprocessor Programming32 Abstraction Map S(head) = –{ x | there exists a such that a reachable from head and a.item = x –}

Art of Multiprocessor Programming33 Sequential List Based Set a c d a b c Add(b) Remove(b)

Art of Multiprocessor Programming34 Sequential List Based Set a c d b a b c Add(b) Remove(b)

Art of Multiprocessor Programming35 Coarse Grained Locking a b d

Art of Multiprocessor Programming36 Coarse Grained Locking a b d c

Art of Multiprocessor Programming37 honk! Coarse Grained Locking a b d c Simple but hotspot + bottleneck honk!

Art of Multiprocessor Programming38 Coarse-Grained Locking Easy, same as synchronized methods –“One lock to rule them all …” Simple, clearly correct –Deserves respect! Works poorly with contention –Queue locks help –But bottleneck still an issue

Art of Multiprocessor Programming39 Fine-grained Locking Requires careful thought –“Do not meddle in the affairs of wizards, for they are subtle and quick to anger” Split object into pieces –Each piece has own lock –Methods that work on disjoint pieces need not exclude each other

Art of Multiprocessor Programming40 Hand-over-Hand locking abc

Art of Multiprocessor Programming41 Hand-over-Hand locking abc

Art of Multiprocessor Programming42 Hand-over-Hand locking abc

Art of Multiprocessor Programming43 Hand-over-Hand locking abc

Art of Multiprocessor Programming44 Hand-over-Hand locking abc

Art of Multiprocessor Programming45 Removing a Node abcd remove(b)

Art of Multiprocessor Programming46 Removing a Node abcd remove(b)

Art of Multiprocessor Programming47 Removing a Node abcd remove(b)

Art of Multiprocessor Programming48 Removing a Node abcd remove(b)

Art of Multiprocessor Programming49 Removing a Node abcd remove(b)

Art of Multiprocessor Programming50 Removing a Node acd remove(b) Why do we need to always hold 2 locks?

Art of Multiprocessor Programming51 Concurrent Removes abcd remove(c) remove(b)

Art of Multiprocessor Programming52 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming53 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming54 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming55 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming56 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming57 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming58 Concurrent Removes abcd remove(b) remove(c)

Art of Multiprocessor Programming59 Uh, Oh acd remove(b) remove(c)

Art of Multiprocessor Programming60 Uh, Oh acd Bad news, C not removed remove(b) remove(c)

Art of Multiprocessor Programming61 Problem To delete node c –Swing node b’s next field to d Problem is, –Someone deleting b concurrently could direct a pointer to c ba cbac

Art of Multiprocessor Programming62 Insight If a node is locked –No one can delete node’s successor If a thread locks –Node to be deleted –And its predecessor –Then it works

Art of Multiprocessor Programming63 Hand-Over-Hand Again abcd remove(b)

Art of Multiprocessor Programming64 Hand-Over-Hand Again abcd remove(b)

Art of Multiprocessor Programming65 Hand-Over-Hand Again abcd remove(b)

Art of Multiprocessor Programming66 Hand-Over-Hand Again abcd remove(b) Found it!

Art of Multiprocessor Programming67 Hand-Over-Hand Again abcd remove(b) Found it!

Art of Multiprocessor Programming68 Hand-Over-Hand Again acd remove(b)

Art of Multiprocessor Programming69 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming70 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming71 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming72 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming73 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming74 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming75 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming76 Removing a Node abcd remove(b) remove(c)

Art of Multiprocessor Programming77 Removing a Node abcd Must acquire Lock of b remove(c)

Art of Multiprocessor Programming78 Removing a Node abcd Cannot acquire lock of b remove(c)

Art of Multiprocessor Programming79 Removing a Node abcd Wait! remove(c)

Art of Multiprocessor Programming80 Removing a Node abd Proceed to remove(b)

Art of Multiprocessor Programming81 Removing a Node abd remove(b)

Art of Multiprocessor Programming82 Removing a Node abd remove(b)

Art of Multiprocessor Programming83 Removing a Node ad remove(b)

Art of Multiprocessor Programming84 Removing a Node ad

Art of Multiprocessor Programming85 Remove method public boolean remove(Item item) { int key = item.hashCode(); Node pred, curr; try { … } finally { curr.unlock(); pred.unlock(); }}

Art of Multiprocessor Programming86 Remove method public boolean remove(Item item) { int key = item.hashCode(); Node pred, curr; try { … } finally { curr.unlock(); pred.unlock(); }} Key used to order node

Art of Multiprocessor Programming87 Remove method public boolean remove(Item item) { int key = item.hashCode(); Node pred, curr; try { … } finally { currNode.unlock(); predNode.unlock(); }} Predecessor and current nodes

Art of Multiprocessor Programming88 Remove method public boolean remove(Item item) { int key = item.hashCode(); Node pred, curr; try { … } finally { curr.unlock(); pred.unlock(); }} Make sure locks released

Art of Multiprocessor Programming89 Remove method public boolean remove(Item item) { int key = item.hashCode(); Node pred, curr; try { … } finally { curr.unlock(); pred.unlock(); }} Everything else

Art of Multiprocessor Programming90 Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); … } finally { … }

Art of Multiprocessor Programming91 Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); … } finally { … } lock pred == head

Art of Multiprocessor Programming92 Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); … } finally { … } Lock current

Art of Multiprocessor Programming93 Remove method try { pred = this.head; pred.lock(); curr = pred.next; curr.lock(); … } finally { … } Traversing list

Art of Multiprocessor Programming94 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false;

Art of Multiprocessor Programming95 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Search key range

Art of Multiprocessor Programming96 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; At start of each loop: curr and pred locked

Art of Multiprocessor Programming97 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; If item found, remove node

Art of Multiprocessor Programming98 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; If node found, remove it

Art of Multiprocessor Programming99 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Unlock predecessor

Art of Multiprocessor Programming100 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Only one node locked!

Art of Multiprocessor Programming101 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; demote current

Art of Multiprocessor Programming102 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Find and lock new current

Art of Multiprocessor Programming103 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Lock invariant restored

Art of Multiprocessor Programming104 Remove: searching while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Otherwise, not present

Art of Multiprocessor Programming105 Why does this work? To remove node e –Must lock e –Must lock e’s predecessor Therefore, if you lock a node –It can’t be removed –And neither can its successor

Art of Multiprocessor Programming106 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable pred reachable from head curr is pred.next So curr.item is in the set

Art of Multiprocessor Programming107 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable Linearization point if item is present

Art of Multiprocessor Programming108 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable Node locked, so no other thread can remove it ….

Art of Multiprocessor Programming109 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable Item not present

Art of Multiprocessor Programming110 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable pred reachable from head curr is pred.next pred.key < key key < curr.key

Art of Multiprocessor Programming111 while (curr.key <= key) { if (item == curr.item) { pred.next = curr.next; return true; } pred.unlock(); pred = curr; curr = curr.next; curr.lock(); } return false; Why remove() is linearizable Linearization point

Art of Multiprocessor Programming112 Adding Nodes To add node e –Must lock predecessor –Must lock successor Neither can be deleted –(Is successor lock actually required?)

Art of Multiprocessor Programming113 Same Abstraction Map S(head) = –{ x | there exists a such that a reachable from head and a.item = x –}

Art of Multiprocessor Programming114 Rep Invariant Easy to check that –tail always reachable from head –Nodes sorted, no duplicates

Art of Multiprocessor Programming115 Drawbacks Better than coarse-grained lock –Threads can traverse in parallel Still not ideal –Long chain of acquire/release –Inefficient

Art of Multiprocessor Programming116 Optimistic Synchronization Find nodes without locking Lock nodes Check that everything is OK

Art of Multiprocessor Programming117 Optimistic: Traverse without Locking b d e a add(c) Aha!

Art of Multiprocessor Programming118 Optimistic: Lock and Load b d e a add(c)

Art of Multiprocessor Programming119 What could go wrong? b d e a add(c) remove(b ) Aha!

Art of Multiprocessor Programming120 Validate – Part 1 (while holding locks) b d e a add(c) Yes, b still reachable from head

Art of Multiprocessor Programming121 What Else Can Go Wrong? b d e a add(c)

Art of Multiprocessor Programming122 What Else Can Go Wrong? b d e a add(c) add(b’) b’

Art of Multiprocessor Programming123 What Else Can Go Wrong? b d e a add(c) b’ Aha!

Art of Multiprocessor Programming124 Validate Part 2 (while holding locks) b d e a add(c) Yes, b still points to d

Art of Multiprocessor Programming125 Optimistic: Linearization Point b d e a add(c) c

Art of Multiprocessor Programming126 Same Abstraction Map S(head) = –{ x | there exists a such that a reachable from head and a.item = x –}

Art of Multiprocessor Programming127 Invariants Careful: we may traverse deleted nodes But we establish properties by –Validation –After we lock target nodes

Art of Multiprocessor Programming128 Correctness If –Nodes b and c both locked –Node b still accessible –Node c still successor to b Then –Neither will be deleted –OK to delete and return true

Art of Multiprocessor Programming129 Unsuccessful Remove abde remove(c) Aha!

Art of Multiprocessor Programming130 Validate (1) abde Yes, b still reachable from head remove(c)

Art of Multiprocessor Programming131 Validate (2) abde remove(c) Yes, b still points to d

Art of Multiprocessor Programming132 OK Computer abde remove(c) return false

Art of Multiprocessor Programming133 Correctness If –Nodes b and d both locked –Node b still accessible –Node d still successor to b Then –Neither will be deleted –No thread can add c after b –OK to return false

Art of Multiprocessor Programming134 Validation private boolean validate(Node pred, Node curry) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; }

Art of Multiprocessor Programming135 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Predecessor & current nodes

Art of Multiprocessor Programming136 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Begin at the beginning

Art of Multiprocessor Programming137 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Search range of keys

Art of Multiprocessor Programming138 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Predecessor reachable

Art of Multiprocessor Programming139 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Is current node next?

Art of Multiprocessor Programming140 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Otherwise move on

Art of Multiprocessor Programming141 private boolean validate(Node pred, Node curr) { Node node = head; while (node.key <= pred.key) { if (node == pred) return pred.next == curr; node = node.next; } return false; } Validation Predecessor not reachable

Art of Multiprocessor Programming142 Remove: searching public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } …

Art of Multiprocessor Programming143 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Search key

Art of Multiprocessor Programming144 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Retry on synchronization conflict

Art of Multiprocessor Programming145 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Examine predecessor and current nodes

Art of Multiprocessor Programming146 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Search by key

Art of Multiprocessor Programming147 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Stop if we find item

Art of Multiprocessor Programming148 public boolean remove(Item item) { int key = item.hashCode(); retry: while (true) { Node pred = this.head; Node curr = pred.next; while (curr.key <= key) { if (item == curr.item) break; pred = curr; curr = curr.next; } … Remove: searching Move along

Art of Multiprocessor Programming149 On Exit from Loop If item is present –curr holds item –pred just before curr If item is absent –curr has first higher key –pred just before curr Assuming no synchronization problems

Art of Multiprocessor Programming150 Remove Method try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}}

Art of Multiprocessor Programming151 try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Remove Method Always unlock

Art of Multiprocessor Programming152 try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Remove Method Lock both nodes

Art of Multiprocessor Programming153 try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Remove Method Check for synchronization conflicts

Art of Multiprocessor Programming154 try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Remove Method target found, remove node

Art of Multiprocessor Programming155 try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.item == item) { pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Remove Method target not found

Art of Multiprocessor Programming156 Optimistic List Limited hot-spots –Targets of add(), remove(), contains() –No contention on traversals Moreover –Traversals are wait-free –Food for thought …

Art of Multiprocessor Programming157 So Far, So Good Much less lock acquisition/release –Performance –Concurrency Problems –Need to traverse list twice –contains() method acquires locks

Art of Multiprocessor Programming158 Evaluation Optimistic is effective if –cost of scanning twice without locks is less than –cost of scanning once with locks Drawback –contains() acquires locks –90% of calls in many apps

Art of Multiprocessor Programming159 Lazy List Like optimistic, except –Scan once –contains(x) never locks … Key insight –Removing nodes causes trouble –Do it “lazily”

Art of Multiprocessor Programming160 Lazy List remove() –Scans list (as before) –Locks predecessor & current (as before) Logical delete –Marks current node as removed (new!) Physical delete –Redirects predecessor’s next (as before)

Art of Multiprocessor Programming161 Lazy Removal aa b c d

Art of Multiprocessor Programming162 Lazy Removal aa b c d Present in list

Art of Multiprocessor Programming163 Lazy Removal aa b c d Logically deleted

Art of Multiprocessor Programming164 Lazy Removal aa b c d Physically deleted

Art of Multiprocessor Programming165 Lazy Removal aa b d Physically deleted

Art of Multiprocessor Programming166 Lazy List All Methods –Scan through locked and marked nodes –Removing a node doesn’t slow down other method calls … Must still lock pred and curr nodes.

Art of Multiprocessor Programming167 Validation No need to rescan list! Check that pred is not marked Check that curr is not marked Check that pred points to curr

Art of Multiprocessor Programming168 Business as Usual abc

Art of Multiprocessor Programming169 Business as Usual abc

Art of Multiprocessor Programming170 Business as Usual abc

Art of Multiprocessor Programming171 Business as Usual abc remove(b)

Art of Multiprocessor Programming172 Business as Usual abc a not marked

Art of Multiprocessor Programming173 Business as Usual abc a still points to b

Art of Multiprocessor Programming174 Business as Usual a bc Logical delete

Art of Multiprocessor Programming175 Business as Usual a bc physical delete

Art of Multiprocessor Programming176 Business as Usual a bc

Art of Multiprocessor Programming177 New Abstraction Map S(head) = –{ x | there exists node a such that a reachable from head and a.item = x and a is unmarked –}

Art of Multiprocessor Programming178 Invariant If not marked then item in the set and reachable from head and if not yet traversed it is reachable from pred

Art of Multiprocessor Programming179 Validation private boolean validate(Node pred, Node curr) { return !pred.marked && !curr.marked && pred.next == curr); }

Art of Multiprocessor Programming180 private boolean validate(Node pred, Node curr) { return !pred.marked && !curr.marked && pred.next == curr); } List Validate Method Predecessor not Logically removed

Art of Multiprocessor Programming181 private boolean validate(Node pred, Node curr) { return !pred.marked && !curr.marked && pred.next == curr); } List Validate Method Current not Logically removed

Art of Multiprocessor Programming182 private boolean validate(Node pred, Node curr) { return !pred.marked && !curr.marked && pred.next == curr); } List Validate Method Predecessor still Points to current

Art of Multiprocessor Programming183 Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}}

Art of Multiprocessor Programming184 Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Validate as before

Art of Multiprocessor Programming185 Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Key found

Art of Multiprocessor Programming186 Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} Logical remove

Art of Multiprocessor Programming187 Remove try { pred.lock(); curr.lock(); if (validate(pred,curr) { if (curr.key == key) { curr.marked = true; pred.next = curr.next; return true; } else { return false; }}} finally { pred.unlock(); curr.unlock(); }}} physical remove

Art of Multiprocessor Programming188 Contains public boolean contains(Item item) { int key = item.hashCode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key && !curr.marked; }

Art of Multiprocessor Programming189 Contains public boolean contains(Item item) { int key = item.hashCode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key && !curr.marked; } Start at the head

Art of Multiprocessor Programming190 Contains public boolean contains(Item item) { int key = item.hashCode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key && !curr.marked; } Search key range

Art of Multiprocessor Programming191 Contains public boolean contains(Item item) { int key = item.hashCode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key && !curr.marked; } Traverse without locking (nodes may have been removed)

Art of Multiprocessor Programming192 Contains public boolean contains(Item item) { int key = item.hashCode(); Node curr = this.head; while (curr.key < key) { curr = curr.next; } return curr.key == key && !curr.marked; } Present and undeleted?

Art of Multiprocessor Programming193 Summary: Wait-free Contains a a b c 0 e 1 d Use Mark bit + Fact that List is ordered 1.Not marked  in the set 2.Marked or missing  not in the set

Art of Multiprocessor Programming194 Lazy List a a b c 0 e 1 d Lazy add() and remove() + Wait-free contains()

Art of Multiprocessor Programming195 Evaluation Good: –contains() doesn’t lock –In fact, its wait-free! –Good because typically high % contains() –Uncontended calls don’t re-traverse Bad –Contended add() and remove() calls do re-traverse –Traffic jam if one thread delays

Art of Multiprocessor Programming196 Traffic Jam Any concurrent data structure based on mutual exclusion has a weakness If one thread –Enters critical section –And “eats the big muffin” Cache miss, page fault, descheduled … –Everyone else using that lock is stuck! –Need to trust the scheduler….

Art of Multiprocessor Programming197 Reminder: Lock-Free Data Structures No matter what … –Guarantees minimal progress in any execution –i.e. Some thread will always complete a method call –Even if others halt at malicious times –Implies that implementation can’t use locks

Art of Multiprocessor Programming198 Lock-free Lists Next logical step Eliminate locking entirely contains() wait-free and add() and remove() lock-free Use only compareAndSet() What could go wrong?

Art of Multiprocessor Programming199 Remove Using CAS a a b c 0 e 1 c Logical Removal = Set Mark Bit Physical Removal CAS pointer Use CAS to verify pointer is correct Not enough!

Art of Multiprocessor Programming200 Problem… a a b c 0 e 1 c Logical Removal = Set Mark Bit Physical Removal CAS 0 d Problem: d not added to list… Must Prevent manipulation of removed node’s pointer Node added Before Physical Removal CAS

Art of Multiprocessor Programming201 The Solution: Combine Bit and Pointer a a b c 0 e 1 c Logical Removal = Set Mark Bit Physical Removal CAS 0 d Mark-Bit and Pointer are CASed together (AtomicMarkableReference) Fail CAS: Node not added after logical Removal

Art of Multiprocessor Programming202 Solution Use AtomicMarkableReference Atomically –Swing reference and –Update flag Remove in two steps –Set mark bit in next field –Redirect predecessor’s pointer

Art of Multiprocessor Programming203 Marking a Node AtomicMarkableReference class –Java.util.concurrent.atomic package address F mark bit Reference

Art of Multiprocessor Programming204 Extracting Reference & Mark Public Object get(boolean[] marked);

Art of Multiprocessor Programming205 Extracting Reference & Mark Public Object get(boolean[] marked); Returns reference Returns mark at array index 0!

Art of Multiprocessor Programming206 Extracting Mark Only public boolean isMarked(); Value of mark

Art of Multiprocessor Programming207 Changing State Public boolean compareAndSet( Object expectedRef, Object updateRef, boolean expectedMark, boolean updateMark);

Art of Multiprocessor Programming208 Changing State Public boolean compareAndSet( Object expectedRef, Object updateRef, boolean expectedMark, boolean updateMark); If this is the current reference … And this is the current mark …

Art of Multiprocessor Programming209 Changing State Public boolean compareAndSet( Object expectedRef, Object updateRef, boolean expectedMark, boolean updateMark); …then change to this new reference … … and this new mark

Art of Multiprocessor Programming210 Changing State public boolean attemptMark( Object expectedRef, boolean updateMark);

Art of Multiprocessor Programming211 Changing State public boolean attemptMark( Object expectedRef, boolean updateMark); If this is the current reference …

Art of Multiprocessor Programming212 Changing State public boolean attemptMark( Object expectedRef, boolean updateMark);.. then change to this new mark.

Art of Multiprocessor Programming213 Removing a Node abcd remov e c CAS

Art of Multiprocessor Programming214 Removing a Node abd remov e b remov e c c CAS failed

Art of Multiprocessor Programming215 Removing a Node abd remov e b remov e c c

Art of Multiprocessor Programming216 Removing a Node ad remov e b remov e c

Art of Multiprocessor Programming217 Traversing the List Q: what do you do when you find a “logically” deleted node in your path? A: finish the job. –CAS the predecessor’s next field –Proceed (repeat as needed)

Art of Multiprocessor Programming218 Lock-Free Traversal (only Add and Remove) abcd CAS Uh-oh pred curr pred curr

Art of Multiprocessor Programming219 The Window Class class Window { public Node pred; public Node curr; Window(Node pred, Node curr) { this.pred = pred; this.curr = curr; }

Art of Multiprocessor Programming220 The Window Class class Window { public Node pred; public Node curr; Window(Node pred, Node curr) { this.pred = pred; this.curr = curr; } A container for pred and current values

Art of Multiprocessor Programming221 Using the Find Method Window window = find(head, key); Node pred = window.pred; Node curr = window.curr;

Art of Multiprocessor Programming222 Using the Find Method Window window = find(head, key); Node pred = window.pred; Node curr = window.curr; Find returns window

Art of Multiprocessor Programming223 Using the Find Method Window window = find(head, key); Node pred = window.pred; Node curr = window.curr; Extract pred and curr

Art of Multiprocessor Programming© Herlihy-Shavit The Find Method Window window = find(item); At some instant, predcurrsucc item or …

Art of Multiprocessor Programming© Herlihy-Shavit The Find Method Window window = find(item); At some instant, pred curr= null succ item not in list

Art of Multiprocessor Programming226 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}}

Art of Multiprocessor Programming227 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} Keep trying

Art of Multiprocessor Programming228 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} Find neighbors

Art of Multiprocessor Programming229 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} She’s not there …

Art of Multiprocessor Programming230 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} Try to mark node as deleted

Art of Multiprocessor Programming231 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} If it doesn’t work, just retry, if it does, job essentially done

Art of Multiprocessor Programming232 Remove public boolean remove(T item) { Boolean snip; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key != key) { return false; } else { Node succ = curr.next.getReference(); snip = curr.next.attemptMark(succ, true); if (!snip) continue; pred.next.compareAndSet(curr, succ, false, false); return true; }}} Try to advance reference (if we don’t succeed, someone else did or will). a

Art of Multiprocessor Programming233 Add public boolean add(T item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareAndSet(curr, node, false, false)) {return true;} }}}

Art of Multiprocessor Programming234 Add public boolean add(T item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareAndSet(curr, node, false, false)) {return true;} }}} Item already there.

Art of Multiprocessor Programming235 Add public boolean add(T item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareAndSet(curr, node, false, false)) {return true;} }}} create new node

Art of Multiprocessor Programming236 Add public boolean add(T item) { boolean splice; while (true) { Window window = find(head, key); Node pred = window.pred, curr = window.curr; if (curr.key == key) { return false; } else { Node node = new Node(item); node.next = new AtomicMarkableRef(curr, false); if (pred.next.compareAndSet(curr, node, false, false)) {return true;} }}} Install new node, else retry loop

Art of Multiprocessor Programming237 Wait-free Contains public boolean contains(Tt item) { boolean[] marked = { false }; int key = item.hashCode(); Node curr = this.head; while (curr.key < key) curr = curr.next; Node succ = curr.next.get(marked); return (curr.key == key && !marked[0]) }

Art of Multiprocessor Programming238 Wait-free Contains public boolean contains(T item) { boolean[] marked = { false }; int key = item.hashCode(); Node curr = this.head; while (curr.key < key) curr = curr.next; Node succ = curr.next.get(marked); return (curr.key == key && !marked[0]) } Only diff is that we get and check marked

Art of Multiprocessor Programming239 Lock-free Find public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }}

Art of Multiprocessor Programming240 Lock-free Find public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} If list changes while traversed, start over Lock-Free because we start over only if someone else makes progress

Art of Multiprocessor Programming241 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find Start looking from head

Art of Multiprocessor Programming242 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find Move down the list

Art of Multiprocessor Programming243 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find Get ref to successor and current deleted bit

Art of Multiprocessor Programming244 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find Try to remove deleted nodes in path…code details soon

Art of Multiprocessor Programming245 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find If curr key that is greater or equal, return pred and curr

Art of Multiprocessor Programming246 public Window find(Node head, int key) { Node pred = null, curr = null, succ = null; boolean[] marked = {false}; boolean snip; retry: while (true) { pred = head; curr = pred.next.getReference(); while (true) { succ = curr.next.get(marked); while (marked[0]) { … } if (curr.key >= key) return new Window(pred, curr); pred = curr; curr = succ; } }} Lock-free Find Otherwise advance window and loop again

Art of Multiprocessor Programming247 Lock-free Find retry: while (true) { … while (marked[0]) { snip = pred.next.compareAndSet(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } …

Art of Multiprocessor Programming248 Lock-free Find retry: while (true) { … while (marked[0]) { snip = pred.next.compareAndSet(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } … Try to snip out node

Art of Multiprocessor Programming249 Lock-free Find retry: while (true) { … while (marked[0]) { snip = pred.next.compareAndSet(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } … if predecessor’s next field changed must retry whole traversal

Art of Multiprocessor Programming250 Lock-free Find retry: while (true) { … while (marked[0]) { snip = pred.next.compareAndSet(curr, succ, false, false); if (!snip) continue retry; curr = succ; succ = curr.next.get(marked); } … Otherwise move on to check if next node deleted

Art of Multiprocessor Programming251 Performance On 16 node shared memory machine Benchmark throughput of Java List-based Set algs. Vary % of Contains() method Calls.

Art of Multiprocessor Programming252 High Contains Ratio Lock-free Lazy list Coarse Grained Fine Lock-coupling

Art of Multiprocessor Programming253 Low Contains Ratio

Art of Multiprocessor Programming254 As Contains Ratio Increases % Contains()

Art of Multiprocessor Programming255 Summary Coarse-grained locking Fine-grained locking Optimistic synchronization Lock-free synchronization

Art of Multiprocessor Programming256 “To Lock or Not to Lock” Locking vs. Non-blocking: Extremist views on both sides The answer: nobler to compromise, combine locking and non-blocking –Example: Lazy list combines blocking add() and remove() and a wait-free contains() –Remember: Blocking/non-blocking is a property of a method

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