MD5 brute-force attack - efficient multithreaded implementation - c++

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]);
}

Related

How to enqueue as many kernels as there are threads available on version 1.2

I'm trying to do some calculations where it starts off with 10-20~ objects, but by doing calculations on these objects it creates 20-40 and so on and so forth, so slightly recursive but not forever, eventually the amount of calculations will reach zero. I have considered using a different tool but it's kind of too late for that for me. It's kind of an odd request which is probably why no results came up.
In short I'm wondering how it is possible to set global work size to as many threads as there are available. For example if the GPU can have X different processes running in parallel it will set that to global work size to X.
edit:it would also work if I can call more kernels from the GPU but that doesn't look possible on version 1.2.
There is not really a limit to global work size (only above 2^32 threads you have to use 64-bit ulong to avoid integer overflow), and the hard limit at 2^64 threads is so large that you can never possibly come even close to it.
If you need a billion threads, than set global work size to a billion threads. The GPU scheduler and hardware will handle that just fine, even if the GPU only has a few thousand physical cores. In fact, you should always launch much more threads than there are cores on the GPU; otherwise the hardware won't be fully saturated and you loose performance.
Only issue could be to run out of GPU memory.
Launching kernels from within kernels is only possible in OpenCL 2.0-2.2, on AMD or Intel GPUs.
It sounds like each iteration depends on the result of the previous one. In that case, your limiting factor is not the number of available threads. You cannot cause some work-items to "wait" for others submitted by the same kernel enqueueing API call (except to a limited extent within a work group).
If you have an OpenCL 2.0+ implementation at your disposal, you can queue subsequent iterations dynamically from within the kernel. If not, and you have established that your bottleneck is checking whether another iteration is required and the subsequent kernel submission, you could try the following:
Assuming a work-item can trivially determine how many threads are actually needed for an iteration based on the output of the previous iteration, you could speculatively enqueue multiple batches of the kernel, each of which depends on the completion event of the previous batch. Inside the kernel, you can exit early if the thread ID is greater or equal the number of threads required in that iteration.
This only works if you either have a hard upper bound or can make a reasonable guess that will yield sensible results (with acceptable perf characteristics if the guess is wrong) for:
The maximum number of iterations.
The number of work-items required on each iteration.
Submitting, say UINT32_MAX work items for each iteration will likely not make any sense in terms of performance, as the number of work-items that fail the check for whether they are needed will dominate.
You can work around incorrect guesses for the latter number by surrounding the calculation with a loop, so that work item N will calculate both item N and M+N if the number of items on an iteration exceeds M, where M is the enqueued work size for that iteration.
Incorrect guesses for the number of iterations would need to be detected on the host, and more iterations enqueued.
So it becomes a case of performing a large number of runs with different guesses and gathering statistics on how good the guesses are and what overall performance they yielded.
I can't say whether this will yield acceptable performance in general - it really depends on the calculations you are performing and whether they are a good fit for GPU-style parallelism, and whether the overhead of the early-out for a potentially large number of work items becomes a problem.

why does having more than one thread(parallel processing) in some specific cases degrade performance?

i noticed that having more than a thread running for some code is much much slower than having one thread, and i have been really pulling my hair to know why,can anyone help?
code explanation :
i have ,sometimes, a very large array that i need to process parts of in a parallel way for optimization,each "part" of a row gets looped on and processed on in a specific thread, now i've noticed that if i only have one "part",i.e the whole array and a single worker thread that runs through it is noticeably faster than if i divide the array and process it as separate sub arrays with different threads.
bool m_generate_row_worker(ull t_row_start,ull t_row_end)
{
for(;t_row_start<t_row_end;t_row_start++)
{
m_current_row[t_row_start]=m_singularity_checker(m_previous_row[t_row_start],m_shared_random_row[t_row_start]);
}
return true;
}
...
//code
...
for(unsigned short thread_indx=0;thread_indx<noThreads-1;thread_indx++)
{
m_threads_array[thread_indx]=std::thread(
m_generate_row_worker,this,
thread_indx*(m_parts_per_thread),(thread_indx+1)*(m_parts_per_thread));
}
m_threads_array[noThreads-1]=std::thread(m_generate_row_worker,this,
(noThreads-1)*(m_parts_per_thread),std::max((noThreads)*(m_parts_per_thread),m_blocks_per_row));
//join
for(unsigned short thread_indx=0;thread_indx<noThreads;thread_indx++)
{
m_threads_array[thread_indx].join();
}
//EDIT
inline ull m_singularity_checker(ull t_to_be_ckecked_with,ull
t_to_be_ckecked)
{
return (t_to_be_ckecked & (t_to_be_ckecked_with<<1)
& (t_to_be_ckecked_with>>1) ) | (t_to_be_ckecked_with &
t_to_be_ckecked);
}
why does having more than one thread(parallel processing) in some specific cases degrade performance?
Because thread creation has overhead. If the task to be performed has only small computational cost, then the cost of creating multiple threads is more than the time saved by parallelism. This is especially the case when creating significantly more threads than there are CPU cores.
Because many algorithms do not easily divide into independent sub-tasks. Dependencies on other threads requires synchronisation, which has overhead that can in some cases be more than the time saved by parallelism.
Because in poorly designed programs, synchronization can cause all tasks to be processed sequentially even if they are in separate threads.
Because (depending on CPU architecture) sometimes otherwise correctly implemented, and seemingly independent tasks have effectual dependency because they operate on the same area of memory. More specifically, when a threads writes into a piece of memory, all threads operating on the same cache line must synchronise (the CPU does this for you automatically) to remain consistent. The cost of cache misses is often much higher than the time saved by parallelism. This problem is called "false sharing".
Because sometimes introduction of multi threading makes the program more complex, which makes it more difficult for the compiler / optimiser to make use of instruction level parallelism.
...
In conclusion: Threads are not a silver bullet that automatically multiplies the performance of your program.
Regarding your program, we cannot count out any of the above potential issues given the excerpt that you have shown.
Some tips on avoiding or finding above issues:
Don't create more threads than you have cores, discounting the number of threads that are expected to be blocking (waiting for input, disk, etc).
Only use multi-threading with problems that are computationally expensive, (or to do work while a thread is blocking, but this may be more efficiently solved using asynchronous I/O and coroutines).
Don't do (or do as little as possible) I/O from more than one thread into a single device (disk, NIC, virtual terminal, ...) unless it is specially designed to handle it.
Minimise the number of dependencies between threads. Consider all access to global things that may cause synchronisation, and avoid them. For example, avoid memory allocation. Keep in mind that things like operations on standard containers do memory allocation.
Keep the memory touched by distinct threads far from each other (not adjacent small elements of array). If processing an array, divide it in consecutive blocks, rather than striping one element every (number of threads)th element. In some extreme cases, extra copying into thread specific data structures, and then joining in the end may be efficient.
If you've done all you can, and multi threading measures slower, consider whether perhaps it is not a good solution for your problem.
Using threads do not always mean that you will get more work done. For example using 2 threads does not mean you will get a task done in half the time. There is an overhead to setting up the threads and depending on how many cores and OS etc... how much context switching is occurring between threads (saving the thread stack/regs and loading the next one - it all adds up). At some point adding more threads will start to slow your program down since there will be more time spent switching between threads/setting threads up/down then there is work being done. So you may be a victim of this.
If you have 100 very small items (like 1 instruction) of work to do, then 100 threads will be guaranteed to be slower since you now have ("many instructions" + 1) x 100 of work to do. Where the "many instructions" are the work of setting up the threads and clearing them up at the end - and switching between them.
So, you may want to start to profile this for yourself.. How much work is done processing each row and how many threads in total are you setting up?
One very crude, but quick/simple way to start to measure is to just take the time elapsed to processes one row in isolation (e.g. use std::chrono functions to measure the time at the start of processing one row and then take the time at the end to see total time spent. Then maybe do the same test over the entire table to get an idea how total time.
If you find that a individual row is taking very little time then you may not be getting so much benefit from the threads... You may be better of splitting the table into chunks of work that are equal to the number of cores your CPU has, then start changing the number of threads (+/-) to find the sweet spot. Just making threads based on number of rows is a poor choice - you really want to design it to max out each core (for example).
So if you had 4 cores, maybe start by splitting the work into 4 threads to start with. Then test it with 8 if its better try 16, if its worse try 12....etc...
Also you might get different results on different PCs...

how to design threading for many short tasks

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.

What is the best way to determine the number of threads to fire off in a machine with n cores? (C++)

I have a vector<int> with 10,000,000 (10 million) elements, and that my workstation has four cores. There is a function, called ThrFunc, that operates on an integer. Assume that the runtime for ThrFunc for each integer in the vector<int> is roughly the same.
How should I determine the optimal number of threads to fire off? Is the answer as simple as the number of elements divided by the number of cores? Or is there a more subtle computation?
Editing to provide extra information
No need for blocking; each function invocation needs only read-only
access
The optimal number of threads is likely to be either the number of cores in your machine or the number of cores times two.
In more abstract terms, you want the highest possible throughput. Getting the highest throughput requires the fewest contention points between the threads (since the original problem is trivially parallelizable). The number of contention points is likely to be the number of threads sharing a core or twice that, since a core can either run one or two logical threads (two with hyperthreading).
If your workload makes use of a resource of which you have fewer than four available (ALUs on Bulldozer? Hard disk access?) then the number of threads you should create will be limited by that.
The best way to find out the correct answer is, with all hardware questions, to test and find out.
Borealid's answer includes test and find out, which is impossible to beat as advice goes.
But there's perhaps more to testing this than you might think: you want your threads to avoid contention for data wherever possible. If the data is entirely read-only, then you might see best performance if your threads are accessing "similar" data -- making sure to walk through the data in small blocks at a time, so each thread is accessing data from the same pages over and over again. If the data is completely read-only, then there is no problem if each core gets its own copy of the cache lines. (Though this might not make the most use of each core's cache.)
If the data is in any way modified, then you will see significant performance enhancements if you keep the threads away from each other, by a lot. Most caches store data along cache lines, and you desperately want to keep each cache line from bouncing among CPUs for good performance. In that case, you might want to keep the different threads running on data that is actually far apart to avoid ever running into each other.
So: if you're updating the data while working on it, I'd recommend having N or 2*N threads of execution (for N cores), starting them with SIZE/N*M as their starting point, for threads 0 through M. (0, 1000, 2000, 3000, for four threads and 4000 data objects.) This will give you the best chance of feeding different cache lines to each core and allowing updates to proceed without cache line bouncing:
+--------------+---------------+--------------+---------------+--- ...
| first thread | second thread | third thread | fourth thread | first ...
+--------------+---------------+--------------+---------------+--- ...
If you're not updating the data while working on it, you might wish to start N or 2*N threads of execution (for N cores), starting them with 0, 1, 2, 3, etc.. and moving each one forward by N or 2*N elements with each iteration. This will allow the cache system to fetch each page from memory once, populate the CPU caches with nearly identical data, and hopefully keep each core populated with fresh data.
+-----------------------------------------------------+
| 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 ... |
+-----------------------------------------------------+
I also recommend using sched_setaffinity(2) directly in your code to force the different threads to their own processors. In my experience, Linux aims to keep each thread on its original processor so much it will not migrate tasks to other cores that are otherwise idle.
Assuming ThrFunc is CPU-bound then you want probably one thread per core, and divide the elements between them.
If there's an I/O element to the function then the answer is more complicated, because you can have one or more threads per core waiting for I/O while another is executing. Do some tests and see what happens.
I agree with the previous comments. You should run tests to determine what number yields the best performance. However, this will only yield the best performance for the particular system you're optimizing for. In most scenarios, your program will be run on other people's machines, on the architecture of which you should not make too many assumptions.
A good way to numerically determine the number of threads to start would be to use
std::thread::hardware_concurrency()
This is part of the C++11 and should yield the number of logical cores in the current system. Logical cores means either the physical number of cores - in case the processor does not support hardware threads (ie HyperThreading) - or the number of hardware threads.
There's also a Boost-function that does the same, see Programmatically find the number of cores on a machine.
The optimal number of threads should equal the number of cores, in which situation the computation capacity of each core will be fully utilized, if the computation on each element is independently.
The optimal number of cores (threads) will probably be determined by when you achieve saturation of the memory system (caches and RAM). Another factor that could come into play is that of inter-core locking (locking a memory area that other cores might want to access, updating it and then unlocking it) and how efficient it is (how long the lock is in place and how often it is locked/unlocked).
A single core running a generic software whose code and data are not optmized for multi-core will come close to saturating memory all by itself. Adding more cores will, in such a scenario, result in a slower application.
So unless your code economizes heavily on memory accesses I'd guess the answer to your question is one (1).
I've found a real world example I'll put here for the ones who want a less technical / more intuitional answer:
Having multiple threads per core is like having two queues in an airport for each scanner(which people on both queues eventually have to pass through).
Two people at a time can put their baggage on the conveyer belt, but only one at a time can pass through the scanner. Now at this point, obviously there's a contention point at the entrance of the scanner, but what happens in reality is most of the times both queues function very well.
In this example, the queues represent threads and the scanner is the main functions of a core. As a general rule of thumb, the impact of each thread is 1.25th a core, i.e., it's not like having an entire new core. So if the task is CPU-bound slightly over the number of available processors is probably best.
But notice that if the task is IO-Bound, where threads will be spending most of their time waiting for external resources such as database connections, file systems, or other external sources of data, then you can assign (many) more threads than the number of available processors.
Source1, Source2

Organizing a task-based scientific computation

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.