I am having problem understanding the complete step and incomplete step in greedy scheduling in Multi-threaded programing in cilk.
Here is the power-point presentation for reference.
Cilk ++ Multi-threaded Programming
The problem I have understanding is in from slide # 32 - 37.
Can someone please explain especially the how is
Complete step>=P threads ready to run
incomplete steps < p threads ready
Thanks for your time and help
First, note that "threads" mentioned in the slides are not like OS threads as one may think. Their definition of a thread is given at slide 10: "a maximal sequence of instructions not containing parallel control (spawn, sync, return)". To avoid further confusion, let me call it a task instead.
On slides 32-35, a circle represents a task ("thread"), and edges represent dependencies between tasks. And the sentences you ask about are in fact definitions: when P or more tasks are ready to run (and so all P processors can be busy doing some work) the situation is called a complete step, while if less than P tasks are ready, the situation is called an incomplete step. To simplify the analysis, it is (implicitly) assumed that all tasks contain equal work (of size 1).
Then the theorem on the slide 35 provides an upper bound of time required for a greedy scheduler to run a program. Since all the execution is a sequence of complete and incomplete steps, the execution time is the sum of all steps. Since each complete step performs exactly P work, the number of complete steps cannot be bigger than T1 (total work) divided by P. Then, each incomplete step must execute a task belonging to the critical path (because at every step at least one critical path task must be ready, and incomplete steps execute all ready tasks); so the overall number of incomplete steps does not exceed the span T_inf (critical path length). Thus the sum of T1/P and T_inf gives an upper bound on execution time.
The rest of slides in the "Scheduling Theory" section are rather straightforward.
Related
I want to see the intrinsic difference between a thread and a long-running go block in Clojure. In particular, I want to figure out which one I should use in my context.
I understand if one creates a go-block, then it is managed to run in a so-called thread-pool, the default size is 8. But thread will create a new thread.
In my case, there is an input stream that takes values from somewhere and the value is taken as an input. Some calculations are performed and the result is inserted into a result channel. In short, we have input and out put channel, and the calculation is done in the loop. So as to achieve concurrency, I have two choices, either use a go-block or use thread.
I wonder what is the intrinsic difference between these two. (We may assume there is no I/O during the calculations.) The sample code looks like the following:
(go-loop []
(when-let [input (<! input-stream)]
... ; calculations here
(>! result-chan result))
(recur))
(thread
(loop []
(when-let [input (<!! input-stream)]
... ; calculations here
(put! result-chan result))
(recur)))
I realize the number of threads that can be run simultaneously is exactly the number of CPU cores. Then in this case, is go-block and thread showing no differences if I am creating more than 8 thread or go-blocks?
I might want to simulate the differences in performance in my own laptop, but the production environment is quite different from the simulated one. I could draw no conclusions.
By the way, the calculation is not so heavy. If the inputs are not so large, 8,000 loops can be run in 1 second.
Another consideration is whether go-block vs thread will have an impact on GC performance.
There's a few things to note here.
Firstly, the thread pool that threads are created on via clojure.core.async/thread is what is known as a cached thread pool, meaning although it will re-use recently used threads inside that pool, it's essentially unbounded. Which of course means it could potentially hog a lot of system resources if left unchecked.
But given that what you're doing inside each asynchronous process is very lightweight, threads to me seem a little overkill. Of course, it's also important to take into account the quantity of items you expect to hit the input stream, if this number is large you could potentially overwhelm core.async's thread pool for go macros, potentially to the point where we're waiting for a thread to become available.
You also didn't mention preciously where you're getting the input values from, are the inputs some fixed data-set that remains constant at the start of the program, or are inputs continuously feed into the input stream from some source over time?
If it's the former then I would suggest you lean more towards transducers and I would argue that a CSP model isn't a good fit for your problem since you aren't modelling communication between separate components in your program, rather you're just processing data in parallel.
If it's the latter then I presume you have some other process that's listening to the result channel and doing something important with those results, in which case I would say your usage of go-blocks is perfectly acceptable.
I want to approximate the Worst Case Execution Time (WCET) for a set of tasks on linux. Most professional tools are either expensive (1000s $), or don't support my processor architecture.
Since, I don't need a tight bound, my line of thought is that I :
disable frequency scaling
disbale unnecesary background services and tasks
set the program affinity to run on a specified core
run the program for 50,000 times with various inputs
Profiling it and storing the total number of cycles it had completed to
execute.
Given the largest clock cycle count and knowing the core frequency, I can get an estimate
Is this is a sound Practical approach?
Secondly, to account for interference from other tasks, I will run the whole task set (40) tasks in parallel with each randomly assigned a core and do the same thing for 50,000 times.
Once I get the estimate, a 10% safe margin will be added to account for unforseeble interference and untested path. This 10% margin has been suggested in the paper "Approximation of Worst Case Execution time in Preepmtive Multitasking Systems" by Corti, Brega and Gross
Some comments:
1) Even attempting to compute worst case bounds in this way means making assumptions that there aren't uncommon inputs that cause tasks to take much more or even much less time. An extreme example would be a bug that causes one of the tasks to go into an infinite loop, or that causes the whole thing to deadlock. You need something like a code review to establish that the time taken will always be pretty much the same, regardless of input.
2) It is possible that the input data does influence the time taken to some extent. Even if this isn't apparent to you, it could happen because of the details of the implementation of some library function that you call. So you need to run your tests on a representative selection of real life data.
3) When you have got your 50K test results, I would draw some sort of probability plot - see e.g. http://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm and links off it. I would be looking for isolated points that show that in a few cases some runs were suspiciously slow or suspiciously fast, because the code review from (1) said there shouldn't be runs like this. I would also want to check that adding 10% to the maximum seen takes me a good distance away from the points I have plotted. You could also plot time taken against different parameters from the input data to check that there wasn't any pattern there.
4) If you want to try a very sophisticated approach, you could try fitting a statistical distribution to the values you have found - see e.g. https://en.wikipedia.org/wiki/Generalized_Pareto_distribution. But plotting the data and looking at it is probably the most important thing to do.
I'm trying to learn about synchornization and understand there are 3 conditions that need to be met for things to work properly
1)mutual exclusion - no data is being corrupted
2)bounded waiting - a thread won't do nothing forever
3)progress being made - system as a whole is doing work e.g. not just passing around who's turn it is
I don't fully understand why the code bellow doesn't work. According to my notes it has mutual exclusion but doesn't satisfy making progress or bounded waiting. Why? Each thread can do something and as long as now thread crashes everythread will get a turn.
The following are shared variables
int turn; // initially turn = 0
turn == i: Pi can enter its critical section
The code is
do {
while (turn != i){}//wait
critical section
turn = j;//j signifies process Pj in contrast to Pi
remainder section
} while (true);
It's basically slide 10 of these notes.
I think the important bit is that according to slide 6 of your notes the 3 rules apply to the critical section of the algorithm and are exactly as follows:
Progress: If no one is in the critical section and someone wants in,
then those processes not in their remainder section must
be able to decide in a finite time who should go in.
Bounded Wait: All requesters must eventually be let into the critical
section.
How to break it:
Pi executes and its remainder section runs indefinitely (no restriction for this)
Pj runs in its entirety, setting turn:= i so it's now Pi's turn to run the critical section.
Pi is still running its remainder which runs indefinitely.
Pj is back to it's critical section but never gets to run it since Pi never gets back to the point where it can give the turn to Pj.
That breaks the progress rule. No one is in the critical section, Pj wants in but cannot decide in a finite time if it can go in.
That breaks the bounded wait rule. Pj will never be let back in into the critical section.
As Malvavisco correctly points out, if a process never releases a resource no other process will have access to it. This is an uninteresting case and typically it's considered trivial. (In practice, it turns out not to be -- which is why there's a lot of emphasis on being able to manage processes from outside, e.g. forcibly terminate a process with minimal ill effects.)
The slides are actually a little imprecise in their definitions. I find that this Wikipedia page on Peterson's algorithm (Algorithm #3 on slide 12) is more exact. Specifically:
Bounded waiting means that "there exists a bound or limit on the number of times that other processes are allowed to enter their critical sections after a process has made a request to enter its critical section and before that request is granted"
Some thought experimentation makes it pretty clear that Algorithm #1 (slide 10) fails this. There is no bound on the number of times the critical section could be entered by either process if the process switching timing was unfortunate. Suppose process 1 executes, enters the critical section, and from there on process 2 only is switched to while process 1 is in its critical section. Process 1 will never account for this. Peterson's algorithm will as process 1 will forfeit its ability to enter the critical section if process 2 is waiting (and vice versa).
I have a Large-Scale Gradient Descent optimization problem that I am running using Matlab. The code has got two parts:
A Sequential update part that fires every iteration that updates the parameter vector.
A validation error computation part that fires every 10 iterations or so using the parameter value at the end of the corresponding iteration in which its fired.
The way that I am running this now is to do (1) and (2) sequentially. But (2) takes a lot of time and its not the core part of my routine - I made it just to check the progress and plot the error of my model. Is it possible in Matlab to run (2) in a parallel manner to (1) ? Please note that (1) cannot be run in parallel since it performs sequential update. So a simple 'parfor' usage is not a solution, unless there is a really smart way of doing that.
I don't think Matlab has any way of multi-threading outside of the (rather restricted) parallel computing toolbox. There is a work over which may help you though:
Open 2 sessions of Matlab, sessions A and B (or instances, or workspaces, however you call it)
Matlab session A:
Calculate the 10 iterations of your sequential process (1)
Saves the result in a file (adequately and uniquely named)
Goes on to calculate the next 10 iterations (back to the top of this loop basically)
In parralel:
Matlab session B:
Check periodically for the existence of the file written by process A (define a timer that will do that at the time interval which make sense for your process, a few seconds or a few minutes ...)
If the file exist => load it then do the validation computation (your process (2)) and display/report the results.
note: This only works if process (1) doesn't need the result of process (2) to run its iterations, but if it is the case I don't know how you could parallelise anyway.
If you have multiple cores on your machine that should run smoothly, if you have a single core then the 2 sessions will have to share and you will see a performance impact.
I'm looking for a design pattern that would fit my application design.
My application processes large amounts of data and produces some graphs.
Data processing (fetching from files, CPU intensive calculations) and graph operations (drawing, updating) are done in seperate threads.
Graph can be scrolled - in this case new data portions need to be processed.
Because there can be several series on a graph, multiple threads can be spawned (two threads per serie, one for dataset update and one for graph update).
I don't want to create multiple progress bars. Instead, I'd like to have single progress bar that inform about global progress. At the moment I can think of MVC and Observer/Observable, but it's a little bit blurry :) Maybe somebody could point me in a right direction, thanks.
I once spent the best part of a week trying to make a smooth, non-hiccupy progress bar over a very complex algorithm.
The algorithm had 6 different steps. Each step had timing characteristics that were seriously dependent on A) the underlying data being processed, not just the "amount" of data but also the "type" of data and B) 2 of the steps scaled extremely well with increasing number of cpus, 2 steps ran in 2 threads and 2 steps were effectively single-threaded.
The mix of data effectively had a much larger impact on execution time of each step than number of cores.
The solution that finally cracked it was really quite simple. I made 6 functions that analyzed the data set and tried to predict the actual run-time of each analysis step. The heuristic in each function analyzed both the data sets under analysis and the number of cpus. Based on run-time data from my own 4 core machine, each function basically returned the number of milliseconds it was expected to take, on my machine.
f1(..) + f2(..) + f3(..) + f4(..) + f5(..) + f6(..) = total runtime in milliseconds
Now given this information, you can effectively know what percentage of the total execution time each step is supposed to take. Now if you say step1 is supposed to take 40% of the execution time, you basically need to find out how to emit 40 1% events from that algorithm. Say the for-loop is processing 100,000 items, you could probably do:
for (int i = 0; i < numItems; i++){
if (i % (numItems / percentageOfTotalForThisStep) == 0) emitProgressEvent();
.. do the actual processing ..
}
This algorithm gave us a silky smooth progress bar that performed flawlessly. Your implementation technology can have different forms of scaling and features available in the progress bar, but the basic way of thinking about the problem is the same.
And yes, it did not really matter that the heuristic reference numbers were worked out on my machine - the only real problem is if you want to change the numbers when running on a different machine. But you still know the ratio (which is the only really important thing here), so you can see how your local hardware runs differently from the one I had.
Now the average SO reader may wonder why on earth someone would spend a week making a smooth progress bar. The feature was requested by the head salesman, and I believe he used it in sales meetings to get contracts. Money talks ;)
In situations with threads or asynchronous processes/tasks like this, I find it helpful to have an abstract type or object in the main thread that represents (and ideally encapsulates) each process. So, for each worker thread, there will presumably be an object (let's call it Operation) in the main thread to manage that worker, and obviously there will be some kind of list-like data structure to hold these Operations.
Where applicable, each Operation provides the start/stop methods for its worker, and in some cases - such as yours - numeric properties representing the progress and expected total time or work of that particular Operation's task. The units don't necessarily need to be time-based, if you know you'll be performing 6,230 calculations, you can just think of these properties as calculation counts. Furthermore, each task will need to have some way of updating its owning Operation of its current progress in whatever mechanism is appropriate (callbacks, closures, event dispatching, or whatever mechanism your programming language/threading framework provides).
So while your actual work is being performed off in separate threads, a corresponding Operation object in the "main" thread is continually being updated/notified of its worker's progress. The progress bar can update itself accordingly, mapping the total of the Operations' "expected" times to its total, and the total of the Operations' "progress" times to its current progress, in whatever way makes sense for your progress bar framework.
Obviously there's a ton of other considerations/work that needs be done in actually implementing this, but I hope this gives you the gist of it.
Multiple progress bars aren't such a bad idea, mind you. Or maybe a complex progress bar that shows several threads running (like download manager programs sometimes have). As long as the UI is intuitive, your users will appreciate the extra data.
When I try to answer such design questions I first try to look at similar or analogous problems in other application, and how they're solved. So I would suggest you do some research by considering other applications that display complex progress (like the download manager example) and try to adapt an existing solution to your application.
Sorry I can't offer more specific design, this is just general advice. :)
Stick with Observer/Observable for this kind of thing. Some object observes the various series processing threads and reports status by updating the summary bar.