Szymański's algorithm
Szymański's algorithm is a is a mutual exclusion algorithm devised by computer scientist Bolesław Szymański.
The algorithm allows mutiple processes or tasks to access a serial resource without conflict, using only linear waiting times. It has application in multitasking and communications, especially if there is a need for massive parallelism with limited waiting times for access to resources by the parallel program's components.
- Task
- Implement Szymanski's algorithm utilizing parallel processes, threads, or similar coroutines.
- Your example should implement the steps shown in the Wikipedia's pseudocode at the Wikipedia reference below.
- See also
Julia
"""
Szymański's algorithm reference:
Boleslaw K. Szymanski. A simple solution to Lamport's concurrent programming problem with linear wait.
Proceedings of the 2nd International Conference on Supercomputing, 1988, Figure 2, Page 624.
https://dl.acm.org/doi/pdf/10.1145/55364.55425
https://en.wikipedia.org/wiki/Szyma%C5%84ski%27s_algorithm
"""
using ThreadSafeDicts # implement a single lock on all thread's shared values as a lockable Dict (keyed by thread id)
const dict = ThreadSafeDict()
flag(id) = get(dict, id, 0)
const criticalvalue = [1]
""" test the implementation on each thread, concurrently"""
function runSzymański(allszy)
id = Threads.threadid()
others = filter(!=(id), allszy)
dict[id] = 1 # Standing outside waiting room
while !all(t -> flag(t) < 3, others) # Wait for open door
yield()
end
dict[id] = 3 # Standing in doorway
if any(t -> flag(t) == 1, others) # Another process is waiting to enter
dict[id] = 2 # Waiting for other processes to enter
while !any(t -> flag(t) == 4, others) # Wait for a process to enter and close the door
yield()
end
end
dict[id] = 4 # The door is closed
for t in others # Wait for everyone of lower ID to finish exit
t >= id && continue
while flag(t) > 1
yield()
end
end
# critical section
criticalvalue[1] += id * 3
criticalvalue[1] ÷= 2
println("Thread ", id, " changed the critical value to $(criticalvalue[1]).")
# end critical section
# Exit protocol
for t in others # Ensure everyone in the waiting room has
t <= id && continue
while flag(t) ∉ [0, 1, 4] # realized that the door is supposed to be closed
yield()
end
end
dict[id] = 0 # Leave. Reopen door if nobody is still in the waiting room
end
function test_Szymański()
allszy = collect(1:Threads.nthreads())
@Threads.threads for _ in allszy
runSzymański(allszy)
end
end
test_Szymański()
- Output:
Thread 3 changed the critical value to 5. Thread 5 changed the critical value to 10. Thread 1 changed the critical value to 6. Thread 2 changed the critical value to 6. Thread 4 changed the critical value to 9. Thread 6 changed the critical value to 13.
Wren
Although Wren-CLI can spawn any number of fibers, the VM is single threaded and so only one fiber can run at a time. Consequently, there is never a need to lock a shared resource.
Also fibers are cooperatively scheduled and don't use OS threads so we never have to worry about context switches taking place.
The best we can do here is therefore to simulate Szymański's algorithm by randomizing the order in which the fibers start so that the output is not completely deterministic.
As Wren fibers don't have an id property, we pass one as an argument when starting the fiber.
import "random" for Random
var rand = Random.new()
var flag = {}
var allszy = (1..6).toList
var criticalValue = 1
var runSzymanski = Fn.new { |id|
var others = allszy.where { |t| t != id }.toList
flag[id] = 1 // Standing outside waiting room
while (!others.all { |t| flag[t] < 3}) { // Wait for open door
Fiber.yield()
}
flag[id] = 3 // Standing in doorway
if (others.any { |t| flag[t] == 1 }) { // Another fiber is waiting to enter
flag[id] = 2 // Waiting for other fibers to enter
while (!others.any { |t| flag[t] == 4 }) { // Wait for a fiber to enter & close door
Fiber.yield()
}
}
flag[id] = 4 // The door is closed
for (t in others) { // Wait for everyone of lower id to exit
if (t >= id) continue
while (flag[t] > 1) Fiber.yield()
}
// critical section
criticalValue = criticalValue + id * 3
criticalValue = (criticalValue/2).floor
System.print("Fiber %(id) changed the critical value to %(criticalValue).")
// end critical section
// exit protocol
for (t in others) { // Ensure everyone in the waiting room has
if (t <= id) continue // realized door is supposed to be closed
while (![0, 1, 4].contains(flag[t])) {
Fiber.yield()
}
}
flag[id] = 0 // Leave. Reopen door if nobody is still
// in the waiting room
}
var testSzymanski = Fn.new {
var fibers = List.filled(6, 0)
for (id in 1..6) {
fibers[id-1] = Fiber.new(runSzymanski)
flag[id] = 0
}
rand.shuffle(allszy)
for (id in allszy) {
fibers[id-1].call(id)
}
}
testSzymanski.call()
- Output:
Sample output:
Fiber 4 changed the critical value to 6. Fiber 3 changed the critical value to 7. Fiber 6 changed the critical value to 12. Fiber 1 changed the critical value to 7. Fiber 5 changed the critical value to 11. Fiber 2 changed the critical value to 8.