# Split Binary Semaphores

The Split Binary Semaphore (SBS) approach is a general technique for implementing conditional waiting. It was originally proposed by Tony Hoare and popularized by Edsger Dijkstra. A binary semaphore is a generalization of a lock. While a lock is always initialized in the released state, a binary semaphore---if so desired---can be initialized in the acquired state. SBS is an extension of a critical section that is protected by a lock. If there are $$n$$ waiting conditions, then SBS uses $$n+1$$ binary semaphores to protect the critical section. An ordinary critical section has no waiting conditions and therefore uses just one binary semaphore (because $$n = 0$$). But, for example, a bounded buffer has two waiting conditions:

1. consumers waiting for the buffer to be non-empty;

2. producers waiting for an empty slot in the buffer.

So, it will require 3 binary semaphores if the SBS technique is applied.

Think of each of these binary semaphores as a gate that a thread must go through in order to enter the critical section. A gate is either open or closed. Initially, exactly one gate, the main gate, is open. Each of the other gates, the waiting gates, is associated with a waiting condition. When a gate is open, one thread can enter the critical section, closing the gate behind it.

When leaving the critical section, the thread must open exactly one of the gates, but it does not have to be the gate that it used to enter the critical section. In particular, when a thread leaves the critical section, it should check for each waiting gate if its waiting condition holds and if there are threads trying to get through the gate. If there is such a gate, then it must select one and open that gate. If there is no such gate, then it must open the main gate.

Finally, if a thread is executing in the critical section and needs to wait for a particular condition, then it leaves the critical section and waits for the gate associated with that condition to open.

The following invariants hold:

• At any time, at most one gate is open;

• If some gate is open, then no thread is in the critical section. Equivalently, if some thread is in the critical section, then all gates are closed;

• At any time, at most one thread is in the critical section.

The main gate is implemented by a binary semaphore, initialized in the released state (signifying that the gate is open). The waiting gates each consist of a pair: a counter that counts how many threads are waiting behind the gate and a binary semaphore initialized in the acquired state (signifying that the gate is closed).

RWsbs.hny
from synch import BinSema, acquire, release

def RWlock():
result = {
.nreaders: 0, .nwriters: 0, .mutex: BinSema(False),
.r_gate: { .sema: BinSema(True), .count: 0 },
.w_gate: { .sema: BinSema(True), .count: 0 }
}

def release_one(rw):
if (rw->nwriters == 0) and (rw->r_gate.count > 0):
release(?rw->r_gate.sema)
elif ((rw->nreaders + rw->nwriters) == 0) and (rw->w_gate.count > 0):
release(?rw->w_gate.sema)
else:
release(?rw->mutex)

acquire(?rw->mutex)
if rw->nwriters > 0:
rw->r_gate.count += 1; release_one(rw)
acquire(?rw->r_gate.sema); rw->r_gate.count -= 1
release_one(rw)

def write_acquire(rw):
acquire(?rw->mutex)
if (rw->nreaders + rw->nwriters) > 0:
rw->w_gate.count += 1; release_one(rw)
acquire(?rw->w_gate.sema); rw->w_gate.count -= 1
rw->nwriters += 1
release_one(rw)

def write_release(rw):
acquire(?rw->mutex); rw->nwriters -= 1; release_one(rw)


We will illustrate the technique using the reader/writer problem. Figure 16.1 shows code. The first step is to enumerate all waiting conditions. In the case of the reader/writer problem, there are two: a thread that wants to read may have to wait for a writer to leave the critical section, while a thread that wants to write may have to wait until all readers have left the critical section or until a writer has left. The state of a reader/writer lock thus consists of the following:

• nwriters: the number of writers in the critical section (0 or 1);

• mutex: the main gate binary semaphore;

• r_gate: the waiting gate used by readers, consisting of a binary semaphore and the number of readers waiting to enter;

• w_gate: the waiting gate used by writers, similar to the readers' gate.

Each of the read_acquire, read_release, write_acquire, and write_release methods must maintain this state. First they have to acquire the mutex (i.e., enter the main gate). After acquiring the mutex, read_acquire and write_acquire each must check to see if the thread has to wait. If so, it increments the count associated with its respective gate, opens a gate (using method release_one), and then blocks until its waiting gate opens up.

release_one() is the function that a thread uses when leaving the critical section. It must check to see if there is a waiting gate that has threads waiting behind it and whose condition is met. If so, it selects one and opens that gate. In the given code, release_one() first checks the readers' gate and then the writers' gate, but the other way around works as well. If neither waiting gate qualifies, then release_one() has to open the main gate (i.e., release mutex).

Let us examine read_acquire more carefully. First, the method acquires mutex. Then, in the case that the thread finds that there is a writer in the critical section ($$\mathit{nwriters > 0}$$), it increments the counter associated with the readers' gate, leaves the critical section (release_one), and then tries to acquire the binary semaphore associated with the waiting gate. This causes the thread to block until some other thread opens that gate.

Now consider the case where there is a writer in the critical section and there are two readers waiting. Let us see what happens when the writer calls write_release:

1. After acquiring mutex, the writer decrements nwriters, which must be 1 at this time, and thus becomes 0.

2. It then calls release_one(). release_one() finds that there are no writers in the critical section and there are two readers waiting. It therefore releases not mutex but the readers' gate's binary semaphore.

3. One of the waiting readers can now re-enter the critical section. When it does, the reader decrements the gate's counter (from 2 to 1) and increments nreaders (from 0 to 1). The reader finally calls release_one().

4. Again, release_one() finds that there are no writers and that there are readers waiting, so again it releases the readers' semaphore.

5. The second reader can now enter the critical section. It decrements the gate's count from 1 to 0 and increments nreaders from 1 to 2.

6. Finally, the second reader calls release_one(). This time release_one() does not find any threads waiting, and so it releases mutex. There are now two reader threads that are holding the reader/writer lock.

## Exercises

16.1 Several of the calls to release_one() in Figure 16.1 can be replaced by simply releasing mutex. Which ones?

16.3 Implement a solution to the producer/consumer problem using split binary semaphores.

16.4 Using busy waiting, implement a "bound lock" that allows up to M threads to acquire it at the same time.[^3] A bound lock with M = 1 is an ordinary lock. You should define a constant M and two methods: acquire_bound_lock() and release_bound_lock(). (Bound locks are useful for situations where too many threads working at the same time might exhaust some resource such as a cache.)

16.5 Write a test program for your bound lock that checks that no more than M threads can acquire the bound lock.

16.6 Write a test program for bound locks that checks that up to M threads can acquire the bound lock at the same time.

gpu.hny
const N = 10

availGPUs = {1..N}

def gpuAlloc():
result = choose(availGPUs)
availGPUs -= { result }

def gpuRelease(gpu):
availGPUs |= { gpu }


16.7 Implement a thread-safe GPU allocator by modifying Figure 16.2. There are N GPUs identified by the numbers 1 through N. Method gpuAlloc() returns the identifier of an available GPU, blocking if there is currently no GPU available. Method gpuRelease(gpu) releases the given GPU. It never needs to block.

16.8 With reader/writer locks, concurrency can be improved if a thread downgrades its write lock to a read lock when its done writing but not done reading. Add a downgrade method to the code in Figure 16.1. (Similarly, you may want to try to implement an upgrade of a read lock to a write lock. Why is this problematic?)

16.9 Cornell’s campus features some one-lane bridges. On a one-lane bridge, cars can only go in one direction at a time. Consider northbound and southbound cars wanting to cross a one-lane bridge. The bridge allows arbitrary many cars, as long as they're going in the same direction. Implement a lock that observes this requirement using SBS. Write methods OLBlock() to create a new "one lane bridge" lock, nb_enter() that a car must invoke before going northbound on the bridge and nb_leave() that the car must invoke after leaving the bridge. Similarly write sb_enter() and sb_leave() for southbound cars.

16.10 Extend the solution to Exercise 16.9 by implementing the requirement that at most $$n$$ cars are allowed on the bridge. Add $$n$$ as an argument to OLBlock.