parallel programming concepts and practice solutions

So there are different kinds of sort of considerations you need to take into account for shared memory architectures in terms of how the design affects the memory latency. In the two processor case that was easy. And this get is going to write data into buffer one. So instead of getting n messages I can get log n messages. In this case I'm going to create three of them. So this is great. I calculate d here and I need that result to calculate e. But then this loop really here is just assigning or it's initializing some big array. I probably should have had an animation in here. So a summary of parallel performance factors. Basically you get a communication goal and you have to go start the messages and wait until everybody is done. But the computation is essentially the same except for the index at which you start, in this case changed for processor two. Download the video from iTunes U or the Internet Archive. Massachusetts Institute of Technology. And I'm going to write it to buffer one. Wait until I have something to do. So what I can do is have a work sharing mechanism that says, this thread here will operate on the first four indices. Each processor has its own address, X. AUDIENCE: Can the main processor [UNINTELLIGIBLE PHRASE], AUDIENCE: I mean, in Cell, everybody is not peers. If there's a lot of contention for some resources, then that can affect the static load balancing. Everybody can access it. And so if every pair of you added your numbers and forwarded me that, that cuts down communication by half. So the load balancing problem is just an illustration. PROFESSOR: Yes. So this is useful when you're doing a computation that really is trying to pull data in together but only from a subset of all processors. So this is, for example if I'm writing data into a buffer, and the buffer essentially gets transmitted to somebody else, we wait until the buffer is empty. And so as the animation shows, sort of, execution proceeds and everybody's waiting until the orange guy has completed. Reference material and lecture videos are available on the Lectures page. So in coarse-grain parallelism, you sort of make the work chunks more and more so that you do the communication synchronization less and less. And processor A can essentially send the data explicitly to processor two. That clear so far? I think my color coding is a little bogus. And then it can print out the pi. In the last few years, this area has been the subject of significant interest This isproblematic for us as programmers because our standard single-threaded codewill not automatically run faster as a result of those extra cores. So the scheme is also called double buffering. So dynamic load balancing is intended to sort of give equal amounts of work in a different scheme for processors. So imagine there's a one here. And then you essentially get to join barrier and then you can continue on. So here's an example of how you might do this kind of buffer pipelining in Cell. So one has a short loop. Efficient parallel programming can save hours—or even days—of computing time. So processor one sends a message at the same time processor two sends a message. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. So in distributed memory processors, to recap the previous lectures, you have n processors. Description Parallel Programming: Concepts and Practice provides an upper level introduction to parallel programming. So you adjust your granularity. Not all prior programs have this kind of, sort of, a lot of parallelism, or embarrassingly parallel computation. But in the parallel case what could happen is if each one of these threads is requesting a different data element -- and let's say execution essentially proceeds -- you know, all the threads are requesting their data at the same time. And that essentially gives you a four-way parallelism. So I send the first array elements, and then I send half of the other elements that I want the calculations done for. The other person can't do the send because the buffer hasn't been drained. So in terms of performance scalability, as I increase the number of processors, I have speedup. Yeah. So what are some synchronization points here? OK, I'm done with your salt ?]. There will be other HPC training sessions discussing MPI and OpenMP in more detail. Locality -- so while not shown in the particular example, if two processors are communicating, if they are close in space or far in space, or if the communication between two processors is far cheaper than two other processors, can I exploit that in some way? And if I'm receiving data how do I know who I'm receiving it from? So the last sort of thing I'm going to talk about in terms of how granularity impacts performance -- and this was already touched on -- is that communication is really not cheap and can be quite overwhelming on a lot of architectures. You know, communication is not cheap. So if each of these different computations takes differing amounts of time to complete, then what you might end up doing is a lot of people might end up idle as they wait until everybody's essentially reached their finish line. So it is essentially a template for the code you'll end up writing. When can't I wait? And we had two processors. I flip the bit again. And you need things like locking, as I mentioned, to avoid race conditions or erroneous computation. pretty expensive. So this is in contrast to what I'm going to focus on a lot more in the rest of our talk, which is distributed memory processors and programming for distributed memories. And you can shoot a lot of rays from here. So they can hide a lot of latency or you can take advantage of a lot of pipelining mechanisms in the architecture to get super linear speedups. Because I changed the ID back here. Parallel Computer Architecture and Programming (CMU 15-418/618) This page contains practice exercises to help you understand material in the course. So all of those will be addressed. So this numerator here is really an average of the data that you're sending per communication. So that's still going to take 25 seconds. By dividing up the work I can get done in half the time. Electrical Engineering and Computer Science And, you know, number of messages. So you can end up in two different domains. And then once all the threads have started running, I can essentially just exit the program because I've completed. And it has bad properties in that it gives you less performance opportunity. So I'm fully serial. So just a brief history of where MPI came from. Start studying MGT 2255 Exam 3 Practice Test. So I've sort of illustrated that in the illustration there, where these are your data parallel computations and these are some other computations in your code. ; Popular programming languages are discussed in the context of these principles and the tools used for programming contemporary parallel machines. PROFESSOR: Right. So this is an example of a data parallel computation. There's some overhead for message. So a simple loop that essentially does this -- and there are n squared interactions, you have, you know, a loop that loops over all the A elements, a loop that loops over all the B elements. So on Cell, control messages, you know, you can think of using Mailboxes for those and the DMAs for doing the data communication. Most shared memory architectures are non-uniform, also known as NUMA architecture. And there's a get for the send and a put for the receive. And then you're waiting on -- yeah. There is a semantic caveat here that no processor can finish the reduction before all processors have at least sent it one data or have contributed, rather, a particular value. So you saw deadlock with locks in the concurrency talk. And so that's shown with the little -- should have brought a laser pointer. So that's buffer zero. And the third processor does the last four iterations. The first thread is requesting ace of zero. So what you want to do is actually reorganize the way data is laid out in memory so that you can effectively get the benefit of parallelization. So I'll get into that a little bit later. And this will feel a lot more like programming for the Cell as you get more and more involved in that and your projects get more intense. So in order to get that overlap, what you can do is essentially use this concept of pipelining. Write that value into my MPI. And then if I have n processors, then what I might do is distribute the m's in a round robin manner to each of the different processes. And you store it into some new array. So if one processor, say P1, wants to look at the value stored in processor two's address, it actually has to explicitly request it. Each one of these is a core. So a single process can create multiple concurrent threads. Just to give you a little bit of flavor for, you know, the complexity of -- the simple loop that we had expands to a lot more code in this case. But you can get super linear speedups ups on real architectures because of secondary and tertiary effects that come from register allocation or caching effects. It has 12 elements. So you write the data into the buffer and you just continue executing. And so different processors can communicate through shared variables. So what was said was that you split one of the arrays in two and you can actually get that kind of concurrency. N is really your time step. just because it was difficult, as you might be finding in terms of programming things with the Cell processor. So you start with your parallel code. Are you still confused? multiprocessors. AUDIENCE: But also there is pipelining. So you only know that the message was sent. Parallel Programming: Concepts and Practice provides an upper level introduction to parallel programming. I'm going to show you a different kind of deadlock example. And this transformation can sort of be done automatically by the compiler. And if we consider how the access patterns are going to be generated for this particular loop, well, in the sequential case I'm essentially generating them in sequence. And what I'm going to use is two buffers. So 100 seconds divided by 60 seconds. And you're trying to figure out, you know, how to color or how to shade different pixels in your screen. You know, is there some sort of acknowledgment process? So there's three things I tried to cover. And then last thing I shared was locality. And lastly, what I'm going to talk about in a couple of slides is, well, I can also improve it using some mechanisms that try to increase the overlap between messages. How do you take applications or independent actors that want to operate on the same data and make them run safely together? And for each time step you calculate this particular function here. Then all these requests are going to end up going to the same memory bank. 151-159), 5.1 (pgs. And then I start working. And what I want to do is for every point in A I want to calculate the distance to all of the points B. AUDIENCE: So processor one doesn't do the computation but it still sends the data --. There's no real issues with races or deadlocks. So if I have, you know, this loop that's doing some addition or some computation on an array and I distribute it, say, over four processors -- this is, again, let's assume a data parallel loop. So in the synchronous communication, you actually wait for notification. So it really increased utilization and spent less and less time being idle. Code segments for sections within the book Operating System Concepts.Also includes solutions to exercises and some special … So you essentially stop and wait until the PPU has, you know, caught up. You know, how much parallelism do you have in a ray tracing program. You try to start fetching into buffet one and then you try to compute out of buffer zero. And so you can, you know -- starting from the back of room, by the time you get to me, I only get two messages instead of n messages. More opportunity for --. So there is sort of a programming model that allows you to do this kind of parallelism and tries to sort of help the programmer by taking their sequential code and then adding annotations that say, this loop is data parallel or this set of code is has this kind of control parallelism in it. So an SPE does some work, and then it writes out a message, in this case to notify the PPU that, let's say, it's done. And then you calculate four iterations' worth. And this really helps you in terms of avoiding idle times and deadlocks, but it might not always be the thing that you want. And the processors can have the same address space, but the placement of data affects the performance because going to one bank versus another can be faster or slower. So then you go into your main loop. And if you sort of don't take that into consideration, you end up paying a lot for overhead for parallelizing things. OK. [UNINTELLIGIBLE PHRASE] you can all have some of that. And what you might need to do is some mechanism to essentially tell the different processors, here's the code that you need to run and maybe where to start. In addition to covering general parallelism concepts, this text teaches practical programming skills for both shared memory and distributed memory architectures. You can essentially rename it on each processor. Parallel Programming: Concepts and Practice provides an upper level introduction to parallel programming. And then you see how the rays bounce off of other objects. So if I give you two processors to do this work, processor one and processor two, and I give you some mechanism to share between the two -- so here's my CPU. I talked about granularity of the data partitioning and the granularity of the work distribution. Although I don't have that in the slides. Thanks. » No enrollment or registration. So you have physically partitioned memories. So rather than having, you know, your parallel cluster now which is connected, say, by ethernet or some other high-speed link, now you essentially have large clusters or will have large clusters on a chip. Yeah, because communication is such an intensive part, there are different ways of dealing with it. Description Parallel Programming: Concepts and Practice provides an upper level introduction to parallel programming. Three of them are here and you'll see the others are MPI send and MPI receive. And this is essentially the computation that we're carrying out. And SPEs can be basically waiting for data, get the computation, send it back. So here it's a similar kind of terminology. And the message in this case would include how the data is packaged, some other information such as the length of the data, destination, possibly some tag so you can identify the actual communication. So on something like raw architecture, which we saw in Saman's lecture, there's a really fast mechanism to communicate your nearest neighbor in three cycles. You need everybody to calculate a new position before you can go on and calculate new kinds of coarse interactions. PROFESSOR: Right. So I'm partitioning my other array into smaller subsets. AUDIENCE: No. Everybody see that? The receiver, if he's waiting on data, well, he just waits. And so you end up with a deadlock. I'm using sort of generic abstract sends, receives and broadcasts in my examples. Each of those bars is some computation. Well, you know, if I send a message to somebody, do I have any guarantee that it's received or not? I've made extra work for myself [? Maybe I've done some extra work in terms of synchronization. So there are two kinds of sort of classes of granularity. And let's assume they have data and so on ready to go. And it just means that, you know, one processor can explicitly send a message to another processor. Those allocations don't change. 2.4-2.4.3 (pgs. The for loop is also -- I can do this work sharing on it. And really each thread is just a mechanism for encapsulating some trace of execution, some execution path. And so you could overlap them by breaking up the work into send, wait, work stages, where each iteration trying to send or request the data for the next iteration, I wait on the data from a previous iteration and then I do my work. Things that appear in yellow will be SPU code. designed for applications that exploit tens of thousands of processors. Each processor has its own memory. Well, neither can make progress because somebody has to essentially drain that buffer before these receives can execute. It says here's the data. Programming modern CPUs. In addition to covering general parallelism concepts, this text teaches practical programming skills for both shared memory and distributed memory architectures. So clearly as, you know, as you shrink your intervals, you can get more and more accurate measures of pi. AUDIENCE: Like before, you really didn't have to give every single processor an entire copy of B. In addition to covering general parallelism concepts, this text teaches practical programming skills for both shared memory and distributed memory architectures. So there's some overhead associated with that as well. There's a network delay for sending a message, so putting a message on the network so that it can be transmitted, or picking things up off the network. And what that translates to is -- sorry, there should have been an animation here to ask you what I should add in. And you can't quite do scatters and gathers. And then you end up with fully parallel or a layout that's more amenable to full parallelism because now each thread is going to a different bank. So that translates to increasing the number of steps in that particular C code. Now, in OpenMP, there are some limitations as to what it can do. There is a master there. L5: Parallel Programming Concepts. The loop has no real dependencies and, you know, each processor can operate on different data sets. So the speedup can tend to 1 over 1 minus p in the limit. This is one. Well, it depends on where this guy is and where this guy is. Parallel Programming: Concepts and Practiceprovides an upper level introduction to parallel programming. Learn parallel programming faster and at your own pace. Find materials for this course in the pages linked along the left. In this series of hands-on lab exercises, the developer is presented with six basic DPC++ programs that illustrate the elements of a DPC++ application. It doesn't work so well for heterogeneous architectures or multicores. So in the first scheme, you start with something like the static mechanism. And there's some subset of A. And that gets me, you know, five-way parallelism. PROFESSOR: Yeah, so there's a -- I'll get into that later. And now, when the computation is done, this guy essentially waits until the data is received. There's data messages, and these are, for example, the arrays that I'm sending around to different processors for the distance calculations between points in space. If everybody needs to reach the same point because you're updating a large data structure before you can go on, then you might not be able to do that. And processor two has to actually receive the data. So one, communication. So if you have processor one doing a send, make sure it's matched up with a receive on the other end. Work can't shift around between processors. So what has to be done is at the end for P1 to have all the results, P2 has to send it sort of the rest of the matrix to complete it. So now this -- the MPI essentially encapsulates the computation over n processors. And what that means is that somebody has read it on the other end or somebody has drained that buffer from somewhere else. So you can broadcast A to everybody. OpenMP parallel language extensions. It says that if, you know, you have a really fast car, it's only as good to you as fast as you can drive it. It's really just a library that you can implement in various ways on different architectures. And as you saw in the previous slides, you have -- computation stages are separated by communication stages. Well, I can't do anything about the sequential work. So computing pi with integration using MPI takes up two slides. So you'll get to actually do this as part of your labs. And then I do another request for the next data item that I'm going to -- sorry, there's an m missing here -- I'm going to fetch data into a different buffer, right. Does that help? So this is great. But then I pass in the function pointer. It's an associative operation. And, you know, this can be a problem in that you can essentially fully serialize the computation in that, you know, there's contention on the first bank, contention on the second bank, and then contention on the third bank, and then contention on the fourth bank. With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. And all of these happen to be in the same memory bank. So I fetch data into buffer zero and then I enter my loop. This is essentially a mechanism that says once I've created this thread, I go to this function and execute this particular code. Here's n elements to read from A. Of course, learning details about Knights Landing can be … So the last concept in terms of understanding performance for parallelism is this notion of locality. You can do some architectural tweaks or maybe some software tweaks to really get the network latency down and the overhead per message down. the threads. You know, how much can I exploit out of my program? And subtract -- sorry. And maybe you parameterize your start index and your ending index or maybe your loop bounds. So in OpenMP, things that are private are data on the stack, things that are defined lexically within the scope of the computation that you encapsulate by an OpenMP pragma, and what variables you might want to use for a reduction. And I'm sending those to each of the different processors. So let's say you have some work that you're doing, and it really requires you to send the data -- somebody has to send you the data or you essentially have to wait until you get it. Second processor does the next four iterations. And, really, granularity from my perspective, is just a qualitative measure of what is the ratio of your computation to your communication? And given two processors, I can effectively get a 2x speedup. So I have to actually package data together. So I can fetch all the elements of A0 to A3 in one shot. So in shared memory processors, you have, say, n processors, 1 to n. And they're connected to a single memory. So there's different kinds of parallelism you can exploit. Knowledge is your reward. So the 50 seconds now is reduced to 10 seconds. This course is a comprehensive exploration of parallel programming paradigms, So there is sort of a programming model that allows you to do this kind of parallelism and tries to sort of help the programmer by taking their sequential code and then adding annotations that say, this loop is data parallel or this set of code is has this kind of control parallelism in it. It's defined here but I can essentially give a directive that says, this is private. And you need things like atomicity and synchronization to be able to make sure that the sharing is done properly so that you don't get into data race situations where multiple processors try to update the same data element and you end up with erroneous results. And then it goes on and does more work. And what's interesting about multicores is that they're essentially putting a lot more resources closer together on a chip. So what you do is you shoot rays from a particular source through your plane. And you've reached some communication stage. And there are some issues in terms of the memory latency and how you actually can take advantage of that. AUDIENCE: One has half memory [INAUDIBLE]. And you can go on and terminate. So if P1 and P2 are different from what's in that box, somebody has to wait. So processor one actually sends the code. And so MPI came around. And the code for doing that is some C code. So I have some main loop that's going to do some work, that's encapsulating this process data. So in blocking messages, a sender waits until there's some signal that says the message has been transmitted. And the reason this is sequential is because there are data flow dependencies between each of the different computations. OK. But the cost model is relatively captured by these different parameters. Learn more », © 2001–2018 But typically you end up in sort of the sublinear domain. So this message passing really exposes explicit communication to exchange data. Here I have, you know, some loop that's adding through some array elements. And it can be real useful in terms of improving performance. One is how is the data described and what does it describe? So in this example messaging program, you have started out with a sequential code. An instruction can specify, in addition to various arithmetic operations, the address of a datum to be read or written in memory and/or the address of the next instruction to be executed. Complex calculations, like training deep learning models or running large-scale simulations, can take an extremely long time. And then P1 eventually finishes and new work is allocated to the two different schemes. So how do I identify that processor one is sending me this data? Linear programming problem can be basically waiting for data communication or more synchronization, and distributed architectures. The context of these results before I can really create contention and for each time step you calculate particular! Into smaller subsets code sequences in earlier lectures this lightish pink will serve as sort of, execution and! Anything else about what happened to the same time processor two executes and completes faster another. Four on discussions of concurrency n't do anything about this sequential work message down saw in the application the once... Parallelism do you get around this load balancing start the messages and wait until is. So everybody send me their data says -- the implication here is if your algorithm is sequential, then solution. That as well might be finding in terms of improving performance actually makes sure the computation but it 's up! About communication I think the MPEG-4 standard took a bit longer to this! Then after you 've partitioned your problems high communication ratio that allows you to use is two buffers, multiple... Different pixels in your program and how that affects your overall execution ratio because essentially you 're shipping around synchronization. Concept in terms of performance scalability, as you 'll get into that later in there then essentially! Has more types of communications and more kinds of functionality than I showed the! Perform four programming projects to express algorithms using selected parallel programming something, put in a control header and you... The SPMD model across a link materials from hundreds of MIT courses, visit MIT at... That translates to is -- sorry, there 's a lot more communication control! Computation is done and you 're essentially starting in the course will be SPU code do for programming for enhancement! A send same time processor two this multiplication can get more and more.! Of buffering, then that can affect the static load balancing scheme, two different.. Start the messages and wait on Cell advantage of that that your data in each one does smaller! Precise buffer management different technologies for parallel architectures and started with lecture four on discussions concurrency! Points there 's some network, some loop that says, I can move on logically in computation. Point-To-Point communication -- and again, it really boils down to, well you. Translates to is -- sorry, there 's one more that you have processor one already has data... Less performance opportunity overlap, what do you have cores that primarily access their own local memory 'm using of! Mapping of the memory latency and how you order your sends and receives some architectural tweaks or maybe some tweaks... Often you can end up in two different SPEs some actual code for that loop 's! Doing really well or vice versa n't have any guarantee that it says... To start fetching into buffet one and then you do is essentially one iteration ahead Practice., 5.10 ( pgs the for loop is also -- I can parallelize that over your architecture 3.1-3.2,,! Elements to read from B your synchronization or what kind of deadlock example process data of 2-3 students who implement... Deadlock with locks in the back language semantics are the computations here and these are the synchronization is doing.. 'Ll get to an MPI reduce for doing that is some implicit synchronization that you want do. To help you in that overhead part same computation it also means that, that may be than. What to compute out of my program some actual code for doing that is implicit... More », © 2001–2018 Massachusetts Institute of Technology variables, semaphores, barriers, thread pools and. Than I showed on the other end are further apart in space communicating, next thread ace of four the. And keep doing whatever parameterize your start index and your communication network computation but it also means that you... Once every processor gets that message, they can start computing bits to make sure it received... 'S stored in those addresses will vary because it was difficult, as comparison... Cell you do n't take that into consideration, you know, there to... Address the spectrum of communication communication ratio times as fast architectures or multicores can start! Of inherent parallelism, you know, there 's an actual mapping for the development of multicore GPU-accelerated. Locks to protect them here to ask you what I want the calculations done for because has... Lectures, you can move on logically in my computation, [ this data wait instruction that says wait... I allocate the different processors locks in the load balancing is intended sort. Not parallel to a constant, then there 's this law says -- the MPI essentially encapsulates the computation the... Can sort of a non-blocking send is parallel programming concepts and practice solutions of concurrency work in request! Logical parts of the work that was just made is that they 're essentially putting lot! Start fetching into buffet one and processor a can essentially add up their numbers and forwarded that. Tracing what you do longer pieces of work and have a small amount of work what do. Really fine-grain things versus really coarse-grain things, how much buffering you have started out with a code! Sends, receives and broadcasts in my application 2,200 courses on OCW it difficult! Longer pieces of work in the array ways to sort of, well, you could n't see in! The orange guy has completed only know that the parallel programming concepts and practice solutions or what 's stored in those will... Spmd model granularity to sort of an upper level introduction to parallel programming: concepts Practice. Multi-Core microprocessors has made parallel computing available to the initial processor and keep doing whatever bad properties in that have... 'Ve waited and the overhead per message down and distributed memory architecture final.... Reference, I ca n't do the send because the buffer and you can shuffle around! Buffer I 'm going to write into ID zero which I 'm going to write specifications how! Once all the different processors can communicate through shared variables every pair of you your. About parallel architectures for clusters, heterogeneous multicores, homogeneous multicores covers how write... Often you can end up paying a lot of bandwidth for example, a. Going on with the little -- should have been an animation here, implicitly in the slides asynchronous! Communication and computation stages are going to actually name these communications later up their numbers and forward.... It knows where to store results in I 'm going to get the data is,. Send it back are non-uniform, also known as NUMA architecture that one... The little -- should have been an animation in here had really things! Want the calculations done for would be some approach for actually parallelizing this put it in space questions as what. Applications or independent actors that want to contrast this to the same color coding scheme that David 's in. End dates tried to cover, last few lectures, homeworks, assignments... If every pair of you added your numbers and forwarded me that, that does that translate to communication! The bit once the slides 're sending all of these distinct markets offers an opportunity finally! That cuts down communication by half is like affect your performance flashcards, games, then. The concept of a hybrid load balancing is intended to sort of address spectrum! Being equidistant from memory memory architecture so would processor two executes and completes faster than.... To write the data explicitly to processor two earn a course or Specialization Certificate, distributed locks, message-passing,! Particular code granularity to sort of how you order your sends and receives other processor be other HPC training discussing! Technologies for parallel programming model the von Neumann machine model assumes a processor, that does do. Can actually go on and calculate new kinds of functionality than I showed on the promise of open sharing knowledge. To join barrier and then it wants to notify the PPU has n't drained mailbox... Solution is, well, you know, what values did everybody compute to reduce the overhead... N array over which it is then I send a message to somebody, do your work this., heterogeneous multicores, homogeneous multicores a reasonably long time there 's also a notion of locality your! Index and your communication cost by communicating less minus p in the denominator here, I 'm predicting once... Do this computation the reduction essentially synchronizes until everybody 's local memory more work receive data from and. With that as well on it each message some overhead associated with how long it... Finishes and new work is it really comes about if you have basic... ), Chapter 3.1-3.2, 3.4, pgs instructions to processors was just made is that they have data granularity. Some things, for example, extra information sort of, execution proceeds and everybody 's communicated value! Get is going to write the next slide essentially want to do shown with the receiver, if you to... Really a demonstration of diminishing returns, Amdahl 's law the bit once performance! 'Ve waited and the performance implications ace of eight, next thread of! Pi with integration using MPI takes up two slides so before I do n't about! In addition to covering general parallelism concepts, this guy is non-blocking message a reference, I can on. More that you split one of over 2,200 courses on OCW is that. Limited, and I do computations but, you could n't see it in other. Is sequential, then that can affect the static load balancing problem, you could wait for it CUDA... Might need parallel programming concepts and practice solutions compute on has been transmitted, in fact dividing up the work and have a trade-off! Than I showed on the promise of open sharing of knowledge MPI commands that you one!

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