Lecture 18: Sequential Consistency

COSC 273: Parallel and Distributed Computing

Spring 2023

Announcements

1. Lab 03 Due Friday MONDAY!!
   • Mandelbrot computations using Vector operations

   • Make sure your machine supports Vector ops today:

       > javac --add-modules jdk.incubator.vector SomeFile.java
       > java --add-modules jdk.incubator.vector SomeFile
     

     on HPC cluster, first run

     > module load amh-java/19.0.1 
     

Last Time

Concurrent Objects!

• concurrent linked lists:
  1. lock the whole list to insert
  2. lock affected nodes to insert

Option 1 is easy to reason about, but offers no benefit from parallelism

Option 2 may offer some performance benefit from parallelism, but reasoning about correctness is subtle

A Subtle Issue

Concurrent Queues

Question

What is a queue?

From Data Structures

An abstract data type (ADT) specifies:

1. allowed operations
2. effects of operations
   • return values
   • updates to internal state of object

Example. Queue ADT?

What Does an ADT Give Us?

For any sequence of operations $op_1, op_2, op_3, \ldots, op_n$ an ADT specifies the results of these operations.

• this is a sequential specification of an object

Question. Why is a sequential specification insufficient for concurrent objects?

The Challenges of Concurrency

What if two or more operations are performed concurrently?

• What is the “correct” behavior?
• How can an implementation guarantee that the correct behavior occurs?
  • in general, each operation consists of several elemenatry steps
  • must guarantee correct behavior for all interleavings of elementary operations

Concurrent Queue Example

Thread 1:

1. enq(x)
2. deq()

Thread 2:

1. enq(y)

Question. What are “acceptable” results of deq()?

Concurrent Queue Timelines

• call to deq() could return either x or y
  • both reasonable!
• any other response seems “un-queue-ish”

Sequential Consistency

A Sensible Feature

Consider all operations performed by all threads

• Each operation has some effect

Behavior of execution should be consistent with some sequential execution of those method calls.

Example.

1. Thread 1 calls enq(1), enq(2), deq(), enq(3)
2. Thread 2 calls enq(4) deq() enq(5) deq()

Is This Enough?

Behavior of execution should be consistent with some sequential execution of the method calls.

1. Thread 1 calls enq(1), enq(2), deq(), enq(3)
2. Thread 2 calls enq(4) deq() enq(5) deq()

Another Sensible Feature

Method calls should appear to take effect in program order

• if a single thread calls op1() before op2(), then op1() should take effect before op2() in sequential execution.

Sequential Consistency

An execution is sequentially consistent if all method calls can be ordered such that:

1. they are consistent with program order
2. they meet object’s sequential specification

An implementation of an object is sequentially consistent if

1. it guarantees every execution is sequentially consistent

Sequentially Consistent Outcomes?

Example: A Sequentially Consistent Queue

An Array-Based Queue

public class LockedQueue<T> {
    int head, tail;
    T[] contents;
    Lock lock;
}

Enqueuing

    public void enq(T x) {
        lock.lock();
        try {
            items[tail] = x;
            tail++;
        } finally {
            lock.unlock();
        }
    }

Dequeueing

    public T deq() {
        lock.lock();
        try {
            T x = items[head];
            head++;
            return x;
        } finally {
            lock.unlock();
        }
    }

What Happens?

What Happens with Locks?

Equivalent Sequential Execution

Why is Queue Sequentially Consistent?

Questions

1. Can we achieve sequential consistency without resorting to locks?
   • again, this technique is essentially sequential
2. Is sequential consistency enough?

What are “Acceptable” Outcomes?

Next Time

Linearizability: A stronger notion of correctness for concurrent objects

• considers “wall clock” time in addition ot program order