I have a computational algebra task I need to code up. The problem is broken into well-defined individuals tasks that naturally form a tree - the task is combinatorial in nature, so there's a main task which requires a small number of sub-calculations to get its results. Those sub-calculations have sub-sub-calculations and so on. Each calculation only depends on the calculations below it in the tree (assuming the root node is the top). No data sharing needs to happen between branches. At lower levels the number of subtasks may be extremely large.
I had previously coded this up in a functional fashion, calling the functions as needed and storing everything in RAM. This was a terrible approach, but I was more concerned about the theory then.
I'm planning to rewrite the code in C++ for a variety of reasons. I have a few requirements:
Checkpointing: The calculation takes a long time, so I need to be able to stop at any point and resume later.
Separate individual tasks as objects: This helps me keep a good handle of where I am in the computations, and offers a clean way to do checkpointing via serialization.
Multi-threading: The task is clearly embarrassingly parallel, so it'd be neat to exploit that. I'd probably want to use Boost threads for this.
I would like suggestions on how to actually implement such a system. Ways I've thought of doing it:
Implement tasks as a simple stack. When you hit a task that needs subcalculations done, it checks if it has all the subcalculations it requires. If not, it creates the subtasks and throws them onto the stack. If it does, then it calculates its result and pops itself from the stack.
Store the tasks as a tree and do something like a depth-first visitor pattern. This would create all the tasks at the start and then computation would just traverse the tree.
These don't seem quite right because of the problems of the lower levels requiring a vast number of subtasks. I could approach it in a iterator fashion at this level, I guess.
I feel like I'm over-thinking it and there's already a simple, well-established way to do something like this. Is there one?
Technical details in case they matter:
The task tree has 5 levels.
Branching factor of the tree is really small (say, between 2 and 5) for all levels except the lowest which is on the order of a few million.
Each individual task would only need to store a result tens of bytes large. I don't mind using the disk as much as possible, so long as it doesn't kill performance.
For debugging, I'd have to be able to recall/recalculate any individual task.
All the calculations are discrete mathematics: calculations with integers, polynomials, and groups. No floating point at all.
there's a main task which requires a small number of sub-calculations to get its results. Those sub-calculations have sub-sub-calculations and so on. Each calculation only depends on the calculations below it in the tree (assuming the root node is the top). No data sharing needs to happen between branches. At lower levels the number of subtasks may be extremely large... blah blah resuming, multi-threading, etc.
Correct me if I'm wrong, but it seems to me that you are exactly describing a map-reduce algorithm.
Just read what wikipedia says about map-reduce :
"Map" step: The master node takes the input, partitions it up into smaller sub-problems, and distributes those to worker nodes. A worker node may do this again in turn, leading to a multi-level tree structure. The worker node processes that smaller problem, and passes the answer back to its master node.
"Reduce" step: The master node then takes the answers to all the sub-problems and combines them in some way to get the output – the answer to the problem it was originally trying to solve.
Using an existing mapreduce framework could save you a huge amount of time.
I just google "map reduce C++" and I start to get results, notably one in boost http://www.craighenderson.co.uk/mapreduce/
These don't seem quite right because of the problems of the lower levels requiring a vast number of subtasks. I could approach it in a iterator fashion at this level, I guess.
You definitely do not want millions of CPU-bound threads. You want at most N CPU-bound threads, where N is the product of the number of CPUs and the number of cores per CPU on your machine. Exceed N by a little bit and you are slowing things down a bit. Exceed N by a lot and you are slowing things down a whole lot. The machine will spend almost all its time swapping threads in and out of context, spending very little time executing the threads themselves. Exceed N by a whole lot and you will most likely crash your machine (or hit some limit on threads). If you want to farm lots and lots (and lots and lots) of parallel tasks out at once, you either need to use multiple machines or use your graphics card.
Related
I am currently building a Monte Carlo application in C++ and I have a question regarding parallelization with MPI.
The process I want to parallelize is the MC generation of data. To have good precision in my final results, I specify the goal number of data points. Each data point is generated independently, but might require vastly differing amounts of time.
How do I organize the parallelization and workload distribution of the data generation most efficiently?
What I have done so far
So far I have come up with three possible ways of organizing the MPI part of the code:
The simplest way, but most likely inefficient way: I divide the desired sample size by the number of workers and let every worker generate that amount of data in isolation. However, when the slowest worker finishes, all other workers have been idling for a potentially long time. They could have been "supporting" the slowest worker by sharing its workload.
Use a master: A master communicates with the workers who work continuously until the master process registers that we have enough data and tells everybody to stop what they are doing. The disadvantage I see is that the master process might not be necessary and could be generating data instead (especially when I don't have a lot of workers).
A "ring communication" algorithm I came up with myself: A message is continuously sent and updated in a circle (1->2, 2->3, ... , N ->1). This message contains the global number of generated data point. Once the desired goal is met, the message is tagged, circles one more time and thereby tells everybody to stop working. Important here is I use non-blocking communication (with MPI_Iprobe before receiving via MPI_Recv, and sending via MPI_Isend). This way, everybody works, and no one ever idles.
No matter, which solution is chosen, in the end I reduce all data sets to one big set and continue to process the data.
The concrete questions:
Is there an "optimal" way of parallelizing such a fairly simple process? Would you prefer any of the proposed solutions for some reason?
What do you think of this "ring communication" solution?
I'm sure I'm not the first one to come up with e.g. the ring communication algorithm. I have tried to google this problem, but it seems to me that I do not know the right terminology in this context. I'm sure there must be a lot of material and literature on such simple algorithms, but I never had a formal course on MPI/parallelization. What are the "keywords" to look for?
Any advice and tips are much appreciated.
I want to implement a multithreaded MD5 brute-force attack algorithm (in C++). I know about Rainbow tables and dictionaries, but I'm not going to implement the most efficient MD5 cracker, just interested in brute-force algorithm
The problem is how to distribute all password variations of all available lengths between threads. For example, to restore a password containing only lower-case characters from 4 to 6 symbols we should look over N=26^4+26^5+26^6=321254128 combinations (according to variation with repetitions formula, Vnk = n^k)
So that distribute all permutations in equial parts between, for example 8 threads, we should know every (N/8)*t variation, where t=(1..7). And take notice, these variationa have different length (4,5,6), and variations of 4-5 symbols could be pushed to the same thread with some number of 6-symbols variations
Does anybody know, how that algorithm is implemented in "real-world" brute-force applications? Maybe some kind of thread-pool?
The approach I find quite flexible is to spawn threads running the following code:
void thread_fn() {
PASSWORD_BLOCK block;
while (get_next_password_block(&block) {
for (PASSWORD password in block) {
if (verify_password(password)) set_password_found(password);
}
}
}
Typically, if code is well optimised, you will spawn as many threads as active cores; however in some cases launching more threads than cores can provide some performance gain (this points to sub-optimal code optimisation).
get_next_password_block() is where all locking and synchronisation is done. This function is responsible for keeping track of password list/range, incrementing password, etc.
Why use PASSWORD_BLOCK and not just a single password? Well, MD5 is a very fast algorithm, so if we will call get_next_password_block() for each password then overhead of locking/incrementing will be extreme. Besides, SIMD instructions allow us to perform bulk MD5 computations (4 passwords at a time), so we want a fast and efficient way to get a sizeable chunk of passwords to reduce overhead.
Particular size of the block depends on CPU speed and algorithm complexity; for MD5 I would expect it to be on the order of millions passwords.
The "correct" way of doing this would be to have a pool of workers (equal to the number of CPU cores, either not counting hyperthread cores, or counting all of them as "one") and a lockfree FIFO queue to which you submit groups of a hundred thousand or so tasks. This gives an acceptable balance between synchronization overhead and load balancing.
The trick is to divide work into relatively small groups, so the time when only one thread remains doing the last group is not too long (no parallelism there!), but at the same time not make the groups too small so you are bound by synchronization / bus contention. MD5 is pretty fast, so a few ten thousand to hundred thousand work items should be fine.
However, given the concrete problem, that's actually overkill. Way too complicated.
There are 26 times more 5-letter passwords than there are 4- letter passwords, and 26 times more 6-letter passwords than there are 5-letter ones, and so on. In other words, the longest password length has by far the biggest share in the total number of combinations. All 4,5,6 digit combinations together only make up about 3.9% of the combinations of all 7-digit combinations. In other words, they are totally insiginificant. 96% of the total runtime is within the 7 digit combinations, no matter what you do with the rest. It is even more extreme if you consider letters and digits or capitalization.
Thus, you can simply fire up as many threads as you have CPU cores, and run all 4-digit combinations in one thread, all 5-digit combinations in another one, and so on. That's not great, but it is good enough since nobody will notice a difference anyway.
Then simply partition the possible 7-digit combinations into num_thread equal-sized ranges, and have each thread that is finished with its initial range continue with that one.
Work will not always be perfectly balanced, but it will be during 96% of the runtime. And, it works with the absolute minimum of task management (none) and synchronization (merely need to set a global flag to exit when a match was found).
Since you cannot expect perfect load balancing even if you do perfect, correct task scheduling (since thread scheduling is in the hands of the operating system, not yours), this should be very close to the "perfect" approach.
Alternatively, you could consider firing up one extra thread which does the entire all-but-longest range of combinations (the "insignificant 3%") and partition the rest equally. This will cause a few extra context switches during startup, but on the other hand makes the program logic even simpler.
Manual partitioning of a task to worker threads is not efficient from both view: the effort spent and the resulting load balance. Modern processors and OSes add to the imbalance even of what initially looks like very balanced workload due to:
cache misses: one thread can hit cache, another can suffer from the cache miss spending up to thousands cycles per memory load operation where the same load can be performed in a few cycles.
Turbo-boost, power-management, core-parking features. Both processor itself and OS can manage frequency and availability of computing units contributing to the imbalance.
Thread preemption: there are other processes running in modern multitasking operation systems which can temporarily interrupting execution flow of a thread.
Modern work-stealing scheduling algorithms are quite efficient in mapping and load-balancing of even imbalanced work to worker threads: you just describe where you have the potential parallelism and task scheduler assigns it to the available resources. Work-stealing is a distributed approach which does not involve one shared state (e.g. iterator) and thus has no bottlenecks.
Check out cilk, tbb, or ppl for more information about implementations of such scheduling algorithms.
Moreover, they are friendly to nested and recursive parallel constructs like:
void check_from(std::string pass) {
check_password(pass);
if(pass.size() < MAX_SIZE)
cilk_for(int i = 0; i < syms; i++)
check_from(pass+sym[i]);
}
I want to use multi-threads to accelerate my program, but not sure which way is optimal.
Say we have 10000 small tasks, it takes maybe only 0.1s to finish one of them. Now I have a CPU with 12 cores and I want to use 12 threads to make it faster.
So far as I know, there are two ways:
1.Tasks Pool
There are always 12 threads running, each of them get one new task from the tasks pool after it finished its current work.
2.Separate Tasks
By separating the 10000 tasks into 12 parts and each thread works on one part.
The problem is, if I use tasks pool it is a waste of time for lock/unlock when multiple threads try to access the tasks pool. But the 2nd way is not ideal because some of the threads finish early, the total time depends on the slowest thread.
I am wondering how you deal with this kind of work and any other best way to do it? Thank you.
EDIT: Please note that the number 10000 is just for example, in practice, it may be 1e8 or more tasks and 0.1 per task is also an average time.
EDIT2: Thanks for all your answers :] It is good to know kinds of options.
So one midway between the two approaches is to break into say 100 batches of 100 tasks each and let the a core pick a batch of 100 tasks at a time from the task pool.
Perhaps if you model the randomness in execution time in a single core for a single task, and get an estimate of mutex locking time, you might be able to find an optimal batch size.
But without too much work we at least have the following lemma :
The slowest thread can only take at max 100*.1 = 10s more than others.
Task pool is always the best solution here. It's not just optimum time, it's also comprehensibility of code. You should never force your tasks to conform to the completely unrelated criteria of having the same number of subtasks as cores - your tasks have nothing to do with that (in general), and such a separation doesn't scale when you change machines, etc. It requires overhead to collaborate on combining results in subtasks for the final task, and just generally makes an easy task hard.
But you should not be worrying about the use of locks for taskpools. There are lockfree queues available if you ever determined them necessary. But determine that first. If time is your concern, use the appropriate methods of speeding up your task, and put your effort where you will get the most benefit. Profile your code. Why do your tasks take 0.1 s? Do they use an inefficient algorithm? Can loop unrolling help? If you find the hotspots in your code through profiling, you may find that locks are the least of your worries. And if you find everything is running as fast as possible, and you want that extra second from removing locks, search the internet with your favorite search engine for "lockfree queue" and "waitfree queue". Compare and swap makes atomic lists easy.
Both ways suggested in the question will perform well and similarly to each another (in simple cases with predictable and relatively long duration of the tasks). If the target system type is known and available (and if performance is really a top concern), the approach should be chosen based on prototyping and measurements.
Do not necessarily prejudice yourself as to the optimal number of threads matching the number of the cores. If this is a regular server or desktop system, there will be various system processes kicking in here and then and you may see your 12 threads variously floating between processors which hurts memory caching.
There are also crucial non-measurement factors you should check: do those small tasks require any resources to execute? Do these resources impose additional potential delays (blocking) or competition? Are there additional apps competing for the CPU power? Will the application need to be grow to accommodate different execution environments, task types, or user interaction models?
If the answer to all is negative, here are some additional approaches that you can measure and consider.
Use only 10 or 11 threads. You will observe a small slowdown, or even
a small speedup (the additional core will serve OS processes, so that
thread affinity of the rest will become more stable compared to 12
threads). Any concurrent interactive activity on the system will see
a big boost in responsiveness.
Create exactly 12 threads but explicitly set a different processor
affinity mask to each, to impose a 1-1 mapping between threads and processors.
This is good in the simplest near-academical case
where there are no resources other than CPU and shared memory
involved; you will see no chronic migration of threads across
processes. The drawback is an
algorithm closely coupled to a particular machine; on another machine
it could behave so poorly as to finish never at all (because of an
unrelated real time task that
blocks one of your threads forever).
Create 12 threads and split the tasks evenly. Have each thread
downgrade its own priority once it is past 40% and again once it is
past 80% of its load. This will improve load balancing inside your
process, but it will behave poorly if your application is competing
with other CPU-bound processes.
100ms/task - pile 'em on as they are - pool overhead will be insignificant.
OTOH..
1E8 tasks # 0.1s/task = 10,000,000 seconds
= 2777.7r hours
= 115.7 days
That's much more than the interval between patch Tuesday reboots.
Even if you run this on Linux, you should batch up the output and flush it to disk in such a manner that the job is restartable.
Is there a database involved? If so, you should have told us!
Each working thread may have its own small task queue with the capacity of no more than one or two memory pages. When the queue size becomes low (a half of capacity) it should send a signal to some manager thread to populate it with more tasks. If queue is organized in batches then working threads do not need to enter critical sections as long as current batch is not empty. Avoiding critical sections will give you extra cycles for actual job. Two batches per queue are enough, and in this case one batch can take one memory page, and so queue takes two.
The point of memory pages is that thread does not have to jump all over the memory to fetch data. If all data are in one place (one memory page) you avoid cache misses.
Problem Description:
there is n tasks, and in these tasks, one might be dependent on the others, which means if A is dependent on B, then B must be finished before A gets finished.
1.find a way to finish these tasks as quickly as possible?
2.if take parallelism into account, how to design the program to finish these tasks?
Question:
Apparently, the answer to the first question is, topological-sort these tasks, then finish them in that order.
But how to do the job if parallelism taken into consideration?
My answer was,first topological-sort these tasks, then pick those tasks which are independent and finish them first, then pick and finish those independent ones in the rest...
Am I right?
Topological sort algorithms may give you various different result orders, so you cannot just take the first few elements and assume them to be the independent ones.
Instead of topological sorting I'd suggest to sort your tasks by the number of incoming dependency edges. So, for example if your graph has A --> B, A --> C, B --> C, D-->C you would sort it as A[0], D[0], B[1], C[3] where [i] is the number of incoming edges.
With topological sorting, you could also have gotting A,B,D,C. In that case, it wouldn't be easy to find out that you can execute A and D in parallel.
Note that after a task was completely processed you then have to update the remaining tasks, in particular, the ones that were dependent on the finished task. However, if the number of dependencies going into a task is limited to a relatively small number (say a few hundreds), you can easily rely on something like radix/bucket-sort and keep the sort structure updated in constant time.
With this approach, you can also easily start new tasks, once a single parallel task has finished. Simply update the dependency counts, and start all tasks that now have 0 incoming dependencies.
Note that this approach assumes you have enough processing power to process all tasks that have no dependencies at the same time. If you have limited resources and care for an optimal solution in terms of processing time, then you'd have to invest more effort, as the problem becomes NP-hard (as arne already mentioned).
So to answer your original question: Yes, you are basically right, however, you lacked to explain how to determine those independent tasks efficiently (see my example above).
I would try sorting them in a directed forest structure with task execution time as edge weigths. Order the arborescences from heaviest to lightest and start with the heaviest. Using this approach you can, at the same time, check for circular dependencies.
Using parallelism, you get the bin problem, which is NP-hard. Try looking up approximative solutions for that problem.
Have a look at the Critical Path Method, taken from the are of project management. It basically do what you need: given tasks with dependecies and durations, it produces how much time it will take, and when to activate each task.
(*)Note that this technique is assuming infinite number of resources for optimal solution. For limited resources there are heuristics for greedy algorithms such as: GPRW [current+following tasks time] or MSLK [minimum total slack time].
(*)Also note, it requires knowing [or at least estimating] how long will each task take.
How to predict C++ program running time, if program executes different functions (working with database, reading files, parsing xml and others)? How installers do it?
They do not predict the time. They calculate the number of operations to be done on a total of operations.
You can predict the time by using measurement and estimation. Of course the quality of the predictions will differ. And BTW: The word "predict" is correct.
You split the workload into small tasks, and create an estimation rule for each task, e.g.: if copying files one to ten took 10s, then the remaining 90 files may take another 90s. Measure the time that these tasks take at runtime, and update your estimations.
Each new measurement will make the prediction a bit more precise.
There really is no way to do this in any sort of reliable way, since it depends on thousands of factors.
Progress bars typically measure this in one of two ways:
Overall progress - I have n number of bytes/files/whatever to transfer, and so far I have done m.
Overall work divided by current speed - I have n bytes to transfer, and so far I have done m and it took t seconds, so if things continue at this rate it will take u seconds to complete.
Short answer:
No you can't. For progress bars and such, most applications simply increase the bar length with a percentage based on the overall tasks done. Some psuedo-code:
for(int i=0; i<num_files_to_load; ++i){
files.push_back(File(filepath[i]));
SetProgressBarLength((float)i/((float)num_files_to_load) - 1.0f);
}
This is a very simplified example. Making a for-loop like this would surely block the window system's event/message queue. You would probably add a timed event or something similar instead.
Longer answer:
Given N known parameters, the problem finding whether a program completes at all is undecidable. This is called the Halting problem. You can however, find the time it takes to execute a single instruction. Some very old games actually depended on exact cycle timings, and failed to execute correctly on newer computers due to race conditions that occur because of subtle differences in runtime. Also, on architectures with data and instruction caches, the cycles the instructions consume is not constant anymore. So cache makes cycle-counting unpredictable.
Raymond Chen discussed this issue in his blog.
Why does the copy dialog give such
horrible estimates?
Because the copy dialog is just
guessing. It can't predict the future,
but it is forced to try. And at the
very beginning of the copy, when there
is very little history to go by, the
prediction can be really bad.
In general it is impossible to predict the running time of a program. It is even impossible to predict whether a program will even halt at all. This is undecidable.
http://en.wikipedia.org/wiki/Halting_problem
As others have said, you can't predict the time. Approaches suggested by Partial and rmn are valid solutions.
What you can do more is assign weights to certain operations (for instance, if you know a db call takes roughly twice as long as some processing step, you can adjust accordingly).
A cool installer compiler would execute a faux install, time each op, then save this to disk for the future.
I used such a technique for a 3D application once, which had a pretty dead-on progress bar for loading and mashing data, after you've run it a few times. It wasn't that hard, and it made development much nicer. (Since we had to see that bar 10-15 times/day, startup was 10-20 secs)
You can't predict it entirely.
What you can do is wait until a fraction of the work is done, say 1%, and estimate the remaining time by that - just time how long it takes for 1% and multiply by 100, for example. That is easily done if you can enumerate all that you have to do in advance, or have some kind of a loop going on..
As I mentioned in a previous answer, it is impossible in general to predict the running time.
However, empirically it may be possible to predict with good accuracy.
Typically all of these programs are approximatelyh linear in some input.
But if you wanted a more sophisticated approach, you could define a large number of features (database size, file size, OS, etc. etc.) and input those feature values + running time into a neural network. If you had millions of examples (obviously you would have an automated method for gathering data, e.g. some discovery programs) you might come up with a very flexible and intelligent prediction algorithm.
Of course this would only be worth doing for fun, as I'm sure the value to your company over some crude guessing algorithm will probably be nil :)
You should make estimation of time needed for different phases of the program. For example: reading files - 50, working with database - 30, working with network - 20. In ideal it would be good if you make some progress callback during all of those phases, but it requires coding the progress calculation into the iterations of algorithm.