[Solved] PPROG Assignment 4-MPI Programming

5/5 – (1 vote)

The purpose of this assignment is to familiarize yourself with MPI programming.

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Get the source code:

$ wget https://nycu-sslab.github.io/PP-f21/HW4/HW4.zip$ unzip HW4.zip -d HW4$ cd HW4

0. Setting Up the Environment

To make MPI work properly, you need to be able to execute jobs on remote nodes without typing a password. You will need to generate an ssh key by yourself. You may follow the instructions below or refer to this article for instruction.

You will also need to configure your ~/.ssh/config file to define host names. Use HW4/config as a template for the configuration. Notice that in the configuration template, the string follows each User should be your student ID.

ATTENTION: We will test your code based on this config.

# <login to one of the PP nodes>$ mkdir -p ~/.ssh$ ssh-keygen -t rsa # Leave all empty# <setup the config>$ cat ~/.ssh/id_rsa.pub >> ~/.ssh/authorized_keys

Wait minutes for system setup Then, login to all machines at least once to make sure the configuration works. This will save the SSH fingerprints of the machines in ~/.ssh/known_hosts.

# Log in without entering password$ ssh pp1$ ssh pp2$ ssh pp3$ ssh pp4$ ...$ ssh pp9

1. Part 1: Getting Familiar with MPI Programming

1.1 MPI Hello World, Getting Familiar with the MPI Environment

Here were going to implement our first MPI program.

Expected knowledge includes basic understanding of the MPI environment, how to compile an MPI program, how to set the number of MPI processes, and retrieve the rank of the process and number of MPI processes at runtime.

Lets learn how to launch an MPI code on NYCU-PP workstations.

There is a starter code for you. Look at hello.cc. Please finish the TODOs with the MPI_Comm_size and MPI_Comm_rank functions.

We will work on NFS (which is already set up ), so we dont need to copy and compile the code again and again on different nodes.

Lets first compile hello.cc on NFS:

$ cd ./HW4$ mpicxx ./hello.cc -o mpi_hello

Then create a file hosts, which is a text file with hosts specified, one per line. We will use the file to specify on which hosts to launch MPI processes when running mpirun. For example, we put the following two lines into the file to specify we will launch MPI processes on nodes pp1 and pp2. Notice that you should use the same hostnames as in ~/.ssh/config.

hosts:

pp1 # 1st node hostnamepp2 # 2ed node hostname

Make sure mpi_hello is located in the same directory hierarchy on the two nodes (should not be a problem under NFS) before running mpirun to start MPI processes:

$ mpirun -np 8 --hostfile hosts mpi_hello

This command will launch eight processes to run mpi_hello on the two nodes, and you should be able to get an output similar to:

Hello world from processor ec037-072, rank 0 out of 8 processorsHello world from processor ec037-072, rank 1 out of 8 processorsHello world from processor ec037-072, rank 3 out of 8 processorsHello world from processor ec037-072, rank 2 out of 8 processorsHello world from processor ec037-073, rank 4 out of 8 processorsHello world from processor ec037-073, rank 6 out of 8 processorsHello world from processor ec037-073, rank 5 out of 8 processorsHello world from processor ec037-073, rank 7 out of 8 processors

PS: There may be some No protocol specified messages in the beginning, its ok to just ignore them.

Code Implementation: (3 points)

• Complete hello.cc: the Hello World code in C.
• mpirun -np 8 --hostfile hosts mpi_hello should run correctly
• The argument of -np is expected to be any positive integer less than or equal to 16.

Q1 (3 points)

1. How do you control the number of MPI processes on each node? (1.5 points)
2. Which functions do you use for retrieving the rank of an MPI process and the total number of processes? (1.5 points)

1.2 Calculating PI with MPI

In this exercise, we are going to parallelize the calculation of Pi following a Monte Carlo method and using different communication functions and measure their performance.

Expected knowledge is MPI blocking and non-blocking communication, collective operations, and one-sided communication.

Instructions: Write different versions of MPI codes to calculate Pi. The technique we are implementing relies on random sampling to obtain numerical results. You have already implemented this in the previous assignments.

1.2.1 MPI Blocking Communication & Linear Reduction Algorithm

In our parallel implementation, we split the number of iterations of the main loop into all the processes (i.e., NUM_ITER / num_ranks). Each process will calculate an intermediate count, which is going to be used afterward to calculate the final value of Pi.

To calculate Pi, you need to send all the intermediate counts of each process to rank 0. This communication algorithm for reduction operation is called linear as the communication costs scales as the number of processes.

An example of linear reduction with eight processes is as follows:

Rank 0 is going to receive the intermediate count calculated by each process and accumulate them to its own count value. (Rank 0 also needs to calculate a count, and this stands for the following sections in Part One.) Finally, after rank 0 has received and accumulated all the intermediate counts, it will calculate Pi and show the result, as in the original code.

Implement this code using blocking communication and test its performance.

Hint 1. Change the main loop to include the number of iterations per process, and not NUM_ITER (which is the total number of iterations).

Hint 2. Do not forget to multiply the seed of srand() with the rank of each process (e.g., rank * SEED) to ensure the RNGs of processes generate different random numbers. There is a starter code pi_block_linear.cc for you.

$ mpicxx pi_block_linear.cc -o pi_block_linear; mpirun -np 4 --hostfile hosts pi_block_linear 1000000000

Code Implementation: (7 points)

• Complete pi_block_linear.cc: the MPI block communication for PI.
• Implement the code using a linear algorithm with MPI_Send/MPI_Recv.
• Do not modify the output messages.
• $ mpicxx pi_block_linear.cc -o pi_block_linear; mpirun -np 4 --hostfile hosts pi_block_linear 1000000000 should run correctly.
• The argument of -np is expected to be any positive integer less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_block_linear 1000000000 should run almost as fast as TAs reference version (refer to /HW4/ref). The difference (in execution time) should be within 15%.

You may use up to five nodes (and up to four processors in each node) for Part 1, so you may want to try different configurations in the hostfile. Q2 (2 points)

1. Why MPI_Send and MPI_Recv are called blocking communication? (1 points)
2. Measure the performance (execution time) of the code for 2, 4, 8, 12, 16 MPI processes and plot it. (1 points)

1.2.2 MPI Blocking Communication & Binary Tree Reduction Communication Algorithm

Implement the binary tree communication algorithm for performing the reduction on rank 0 using blocking communication (e.g., MPI_Send/MPI_Recv).

The communication pattern for a reduction with a binary tree with eight processes is as follows:

In you implementation, you can assume that we use a power-of-two number of processes.

There is a starter code pi_block_tree.cc for you.

$ mpicxx pi_block_tree.cc -o pi_block_tree; mpirun -np 4 --hostfile hosts pi_block_tree 1000000000

Code Implementation: (7 points)

• Complete pi_block_tree.cc: the MPI block communication for PI.
• Implement the code using a binary tree reduction algorithm with MPI_Send/MPI_Recv.
• Do not modify the output messages.
• $ mpicxx pi_block_tree.cc -o pi_block_tree; mpirun -np 4 --hostfile hosts pi_block_tree 1000000000 should run correctly.
• The argument of -np is expected to be any power-of-two number less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_block_tree 1000000000 should run almost as fast as TAs reference version. The difference (in execution time) should be within 15%.

Q3 (6 points)

1. Measure the performance (execution time) of the code for 2, 4, 8, 16 MPI processes and plot it. (1 points)
2. How does the performance of binary tree reduction compare to the performance of linear reduction? (2 points)
3. Increasing the number of processes, which approach (linear/tree) is going to perform better? Why? Think about the number of messages and their costs. (3 points)

1.2.3 MPI Non-Blocking Communication & Linear Reduction Algorithm

Use non-blocking communication for the linear reduction operation (in Section 1.2.1).

Hint: Use a non-blocking MPI_Irecv() (MPI Receive with Immediate return). The basic idea is that rank 0 is going to issue all the receive operations and then wait for them to finish. You can either use MPI_Wait() individually to wait for each request to finish or MPI_Waitall(). Regardless of your decision, keep in mind that we want you to perform the receive operations in parallel. Thus, do not call MPI_Irecv() and immediately MPI_Wait()! In addition, we recommend you allocate an array of MPI_Request and also an array of counts (i.e., one for each receive needed). There is a starter code pi_nonblock_linear.cc for you.

$ mpicxx pi_nonblock_linear.cc -o pi_nonblock_linear; mpirun -np 4 --hostfile hosts pi_nonblock_linear 1000000000

Code Implementation: (7 points)

• Complete pi_nonblock_linear.cc: the MPI non-blocking communication for PI.
• Implement the code using a non-blocking algorithm with MPI_Send/MPI_IRecv/MPI_Wait/MPI_Waitall.
• Do not modify the output messages.
• $ mpicxx pi_nonblock_linear.cc -o pi_nonblock_linear; mpirun -np 4 --hostfile hosts pi_nonblock_linear 1000000000 should run correctly.
• The argument of -np is expected to be any positive integer less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_nonblock_linear 1000000000 should run almost as fast as TAs reference version. The difference (in execution time) should be within 15%.

Q4 (5 points)

1. Measure the performance (execution time) of the code for 2, 4, 8, 12, 16 MPI processes and plot it. (1 points)
2. What are the MPI functions for non-blocking communication? (1 points)
3. How the performance of non-blocking communication compares to the performance of blocking communication? (3 points)

1.2.4 MPI Collective: MPI_Gather

Use the collective MPI_Gather() operation, instead of point-to-point communication.

Hint: You can keep rank 0 as the root of the communication and still make this process aggregate manually the intermediate counts. Remember that the goal of MPI_Gather() is to provide the root with an array of all the intermediate values. Reuse the array of counts as the output for the gather operation.

There is a starter code pi_gather.cc for you.

$ mpicxx pi_gather.cc -o pi_gather; mpirun -np 4 --hostfile hosts pi_gather 1000000000

Code Implementation: (7 points)

• Complete pi_gather.cc: the MPI gather communication for PI.
• Implement the code using MPI_Gather.
• Do not modify the output messages.
• $ mpicxx pi_gather.cc -o pi_gather; mpirun -np 4 --hostfile hosts pi_gather 1000000000 should run correctly.
• The argument of -np is expected to be any positive integer less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_gather 1000000000 should run almost as fast as TAs reference version. The difference (in execution time) should be within 15%.

Q5 (1 points)

1. Measure the performance (execution time) of the code for 2, 4, 8, 12, 16 MPI processes and plot it. (1 points)

1.2.5 MPI Collective: MPI_Reduce

Use the collective MPI_Reduce() operation.

Hint 1: Remember that the goal of MPI_Reduce() is to perform a collective computation. Use the MPI_SUM operator to aggregate all the intermediate count values into rank 0, But, watch out: rank 0 has to provide its own count as well, alongside the one from the other processes.

Hint 2: The send buffer of MPI_Reduce() must not match the receive buffer. In other words, use a different variable on rank 0 to store the result. There is a starter code pi_reduce.cc for you.

$ mpicxx pi_reduce.cc -o pi_reduce; mpirun -np 4 --hostfile hosts pi_reduce 1000000000

Code Implementation: (7 points)

• Complete pi_reduce.cc: the MPI reduce communication for PI.
• Implement the code using MPI_Reduce.
• Do not modify the output messages.
• $ mpicxx pi_reduce.cc -o pi_reduce; mpirun -np 4 --hostfile hosts pi_reduce 1000000000 should run correctly.
• The argument of -np is expected to be any positive integer less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_reduce 1000000000 should run almost as fast as TAs reference version. The difference (in execution time) should be within 15%.

Q6 (1 points)

1. Measure the performance (execution time) of the code for 2, 4, 8, 12, 16 MPI processes and plot it. (1 points)

1.2.6 MPI Windows and One-Sided Communication & Linear Reduction Algorithm

Use MPI Windows and MPI one-sided communication, which we didnt cover this in class. You can choose the functions youd like to use but remember that there is a reduction on the same MPI window from many processes! You may refer to one_side_example.c to get familiar with it.

There is a starter code pi_one_side.cc for you.

$ mpicxx pi_one_side.cc -o pi_one_side; mpirun -np 4 --hostfile hosts pi_one_side 1000000000

Code Implementation: (7 points)

• Complete pi_one_side.cc: the MPI one sided communication for PI.
• Implement the code using MPI_Widows_* (or MPI_Put, MPI_Get, and MPI_Accumulate). You only need to implement the first one, and the remainings are optional.
• Do not modify the output messages.
• $ mpicxx pi_one_side.cc -o pi_one_side; mpirun -np 4 --hostfile hosts pi_one_side 1000000000 should run correctly.
• The argument of -np is expected to be any positive integer less than or equal to 16.
• mpirun -np 4 --hostfile hosts pi_one_side 1000000000 should run almost as fast as TAs reference version. The difference (in execution time) should be within 15%.

Q7 (5 points)

1. Measure the performance (execution time) of the code for 2, 4, 8, 12, 16 MPI processes and plot it. (1 points)
2. Which approach gives the best performance among the 1.2.11.2.6 cases? What is the reason for that? (4 points)

1.3 Measuring Bandwidth and Latency on NYCU-PP workstations with Ping-Pong

Expected knowledge is concepts of bandwidth and latency and performance model for parallel communication.

The ping-pong is a benchmark code to measure the bandwidth and latency of a supercomputer. In this benchmark, two MPI processes use MPI_Send and MPI_Recv to continually bounce messages off of each other until a final limit.

The ping-pong benchmark provides as output the average time for the ping-pong for different messages sizes.

If we plot the results of the ping-pong with size on the x-axis and ping-pong time on the y-axis, we will roughly obtain points distributed along a line. If we do a linear best fit of the obtained points, we will get the intercept and the slope of the line. The inverse of the line slope is the bandwidth while the intercept is the latency of the system.

We will use ping_pong.c to measure the ping-pong time for different message sizes.

Instructions. For completing this exercise, you may refer to this video: Performance Modeling & Ping-Pong

Run the ping-pong code and calculate the bandwidth and latency for:

• case 1: intra-node communication (two processes on the same node), and
• case 2: inter-node communication (two processes on different nodes). You should consider more different nodes in this case.

Q8 (9 points)

1. Plot ping-pong time in function of the message size for cases 1 and 2, respectively. (4 points)
2. Calculate the bandwidth and latency for cases 1 and 2, respectively. (5 points)

2. Part 2: Matrix Multiplication with MPI

Write a MPI program which reads an $n times m$ matrix $A$ and an $m times l$ matrix $B$, and prints their product, which is stored in an $n times l$ matrix $C$. An element of matrix $C$ is obtained by the following formula:

$$c{ij} = sum{k=1}^m a{ik}b{kj}$$

where $a{ij}$, $b{ij}$ and $c_{ij}$ are elements of $A$, $B$, and $C$, respectively.

Your mission is to calculate the matrix multiplication as fast as possible. You may try many methods (Ex: tiling or some algorithms. Note that SIMD isnt allowed here!) to achieve a higher performance. You are allowed to use any code on the Internet, but you need to re-write the code yourself, which means copying and pasting is not allowed. In addition, you are not allowed to use any third-party library; that is, you have to write your MPI program from scratch. Furthermore, each node is allowed to run a single-threaded process, so using OpenMP, Pthread, fork, GPU, etc. are not allowed.

If you are not sure about the rule, ask on our Facebook group! Input

In the first line, three integers $n$, $m$ and $l$ are given separated by space characters.

In the following lines, the $n times m$ matrix $A$ and the $m times l$ matrix $B$ are given. All the numbers are integers.

Output

Print elements of the $n times l$ matrix $C$ ($c_{ij}$). Print a single space character after each element!

Constraints

1. $1 n, m, l 10000$
2. $0 a{ij}, b{ij} 100$

Sample Input

3 2 31 20 34 51 2 10 3 2

Sample Output

1 8 5 0 9 6 4 23 14 

Note: There is
at the end of each line!

Data Sets

There are two data sets. The table shows the credit, the range of $n$, $m$, and $l$, and the hosts used for each data set.

Set	Credit	n, m, l	Hosts
1	10 points	300-500	Any of four from pp1pp9
2	10 points	1000-2000	pp1pp9

You may have different implementations for the two data sets.

Notice that only one process per node is allowed.

Here is an example hostfile:

pp1 slots=1pp3 slots=1pp5 slots=1pp7 slots=1

Q9 (5 points)

1. Describe what approach(es) were used in your MPI matrix multiplication for each data set.

3. Requirements

3.1 Requirements for Part One

• Code implementation (following the instructions in Sections 1.2.11.2.6
  • hello.cc
  • pi_block_linear.cc
  • pi_block_tree.cc
  • pi_gather.cc
  • pi_nonblock_linear.cc
  • pi_one_side.cc
  • pi_reduce.cc
• Answer the questions (marked with Q1-Q8) in a REPORT using HackMD. (Notice that in this assignment a higher standard will be applied when grading the quality of your report.)

3.2 Requirements for Part Two

• Code implementation
  • You should write a program that fits the input/output criteria as described in Section 2.
  • You should write a Makefile that aims to generate an executable called matmul. In addition, main.cc, which contains the main() function, must be a part of matmul and cannot be modified.
  • Your program will be evaluated with command $ make; mpirun -np %N% --hostfile %hosts% matmul < %data_file%, where N is 2-8, hosts is our hostfile, and data_file is the input.
  • There are some data in the /HW4/data folder for testing. The data are available at /HW4/data.zip if youd like to test them in your own machine(s). The testing script provided uses the data to verify your program. You dont expect to pass only the testing data.
• Answer the questions (marked with Q9) in a REPORT using HackMD. (Notice that in this assignment a higher standard will be applied when grading the quality of your report.)