Assignment 8 Solution

Description

Submit responses to all tasks which don’t specify a le name to Canvas in a le called assign-ment8.txt, docx, pdf, rtf, odt (choose one of the formats). Also, all plots should be submitted in Canvas. All source les should be submitted in the HW08 subdirectory on the master branch of your homework git repo with no subdirectories.

All commands or code must work on Euler without loading additional modules unless speci ed otherwise. They may behave di erently on your computer, so be sure to test on Euler before you submit. Note that this assignment is relevant to OpenMP and not related to GPU computing, so the following changes need to be made to your slurm script:

#SBATCH –gres=gpu:1 should be removed since GPU is not required in this assignment.

#SBATCH –nodes=1 –cpus-per-task=20 (or -N 1 -c 20 for short) should be added, which requests one node with 20 cores (note the slight misnomer). The maximum number of threads required in this assignment is 20, so you should not ask for more than 20 cores.

Please submit clean code. Consider using a formatter like clang-format.

• Before you begin, copy the provided les from HW08 of the ME759-2020 repo.

• 1. In HW02 task3, you have implemented several di erent ways to carry out matrix multipli-cation in sequential computing. In this task, you will take the mmul function in HW02 that yields the best performance and parallelize it with OpenMP.

• 1. 1. Implement in a le called matmul.cpp the parallel version of the best-performing mmul function in HW02 task3 with the prototype de ned as in matmul.h.

• 1. 2. Write a program task1.cpp that will accomplish the following:

Create and ll with float type numbers the square matrices A and B (stored as 1D arrays in the order required by the best-performed mmul method, more details can be found in the description of HW02 task3). The dimension of A and B should be n n where n is the rst command line argument, see below.

Compute the matrix multiplication C = AB using your parallel implementation with t threads where t is the second command line argument, see below.

Print the rst element of the resulting C array. Print the last element of the resulting C array.

Print the time taken to run the mmul function in milliseconds.

Compile: g++ task1.cpp matmul.cpp -Wall -O3 -o task1 -fopenmp

Run (where n is a positive integer, t is an integer in the range [1, 20] ):

./task1 n t

Example expected output: 1.0

1376.5

3.21

• 1. 3. On an Euler compute node:

Run task1 for value n = 1024, and value t = 1; 2; ; 20. Generate a plot called task1.pdf which plots time taken by your mmul function vs. t in linear-linear scale.

2. In HW02 task2, you’ve implemented the 2D convolution for sequential execution. In this task, you will use OpenMP to parallelize your previous implementation.

2. 1. Implement in a le called convolution.cpp the parallel version of Convolve function with the prototype speci ed in convolution.h.

2. 2. Write a program task2.cpp that will accomplish the following:

Create and ll with float-type numbers an n n square matrix image (stored as a 1D array in row-major order), where n is the rst command line argument, see below.

Create a 3 3 mask matrix (stored in 1D in row-major order) of whatever mask values you like.

Apply the mask matrix to the image using your Convolve function with t threads where t is the second command line argument, see below.

Print the rst element of the resulting output array. Print the last element of the resulting output array.

Print the time taken to run the Convolve function in milliseconds.

Compile: g++ task2.cpp convolution.cpp -Wall -O3 -o task2 -fopenmp

Run (where n is a positive integer, t is an integer in the range [1, 20] ):

./task2 n t

Example expected output: 2.0

137.5

3.21

2. 3. On an Euler compute node:

Run task2 for n = 1024, and t = 1; 2; ; 20. Generate a gure called task2.pdf which plots the time taken by your Convolve function vs. t in linear-linear scale.

Discuss your observations from the plot. Explain to what extent the increase in the number of threads improves the performance, and why the run time does not show signi cant decrease after reaching a certain number of threads.

2. 4. (Optional, Extra credits, 10 pts) There are ways to further improve the performance when using more threads (i.e. t > 10). For instance, the data a nity topic covered in class would be a good starting point to look into this.

Submit in a le task2 op.cpp that includes all necessary changes for improved scalability (there should be no need to change your Convolve function). Explain (if any) changes to the environment variables along with your discussions in c).

On an Euler compute node, run task2 op for value n = 1024, and value t = 1; 2; ; 20. Overlay this plot on the pattern you achieved in c) and save in a le task2 op.pdf.

Discuss your observations from the plot.

3. Implement a parallel merge sort¹ using OpenMP tasks.

3. 1. Implement in a le called msort.cpp the parallel merge sort algorithm with the proto-type speci ed in msort.h. You may add other functions in your msort.cpp program, but you should not change the msort.h le. Your msort function should take an array of integers and return the sorted results in place in ascending order. For instance, after calling msort function, the original arr = [3, 7, 10, 2, 1, 3] would become arr = [1, 2, 3, 3, 7, 10].

3. 2. Write a program task3.cpp that will accomplish the following:

Create and ll however you like with int type numbers an array arr with length n, where n is the rst command line argument, see below.

Apply your msort function to the arr. Set number of threads to t, which is the second command line argument, see below.

Print the rst element of the resulting arr array. Print the last element of the resulting arr array.

Print the time taken to run the msort function in milliseconds.

Compile: g++ task3.cpp msort.cpp -Wall -O3 -o task3 -fopenmp

Run (where n is a positive integer, t is an integer in the range [1, 20], ts is the threshold as the lower limit to make recursive calls in order to avoid the overhead of recursion/task scheduling when the input array has small size; under this limit, a serial sorting algorithm without recursion calls will be used):

./task3 n t ts

Example expected output: 1 513

3.21

3. 3. On an Euler compute node:

Run task3 for value n = 10⁶, value t = 8, and value ts = 2¹; 2²; ; 2¹⁰. Generate a plot called task3 ts.pdf which plots the time taken by your msort function vs. ts in linear-linear scale.

Run task3 for value n = 10⁶, value t = 1; 2; ; 20, and ts equals to the value that yields the best performance as you found in the plot of time vs. ts. Generate a plot called task3 t.pdf which plots time taken by your msort function vs. t in linear-linear scale.

• See the Parallel merge sort section in this link as a reference of the pseudo code.

3