Assignment-10 Solution

Description

Submit responses to all tasks which don’t specify a le name to Canvas in a le called assign-ment10.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 HW10 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. The executables may behave di erently on your computer, so be sure to test on Euler before you submit. For the ILP task; i.e. Task 1, you will not need to use multiple cores, thus, asking for 1 node and 1 core (-N 1 -c 1) would be su cient. For the hybrid OpenMP+MPI task, i.e. Task 2, the following speci cations need to be included in your slurm script:

#SBATCH –nodes=2 –cpus-per-task=20 –ntasks-per-node=1.

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

• Before you begin, copy the provided les from HW10 of the ME759-2020 repo.

• 1. In this task, you will explore the optimizations using ILP (instruction level parallelism) based on the code examples given in Lecture 26 slides 5-35. Some macros and utils functions are de ned in the provided le optimize.h with the same naming fashion as the code examples in the lecture slides. You will need to accomplish the following:

• 1. 1. Write ve optimization functions that each (either represents the baseline, or) uses a di erent technique to achieve ILP as the following:

optimize1 will be the same as combine4 function in slide 9.

optimize2 will be the same as unroll2a combine function in slide 20. optimize3 will be the same as unroll2aa combine function in slide 22. optimize4 will be the same as unroll2a combine function in slide 25.

optimize5 will be similar to optimize4, but with K = 3 and L = 3, where K and L are the parameters de ned in slide 28 and 29.

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

Create and ll with data t type numbers however you like a vec v of length n where n is the rst command line argument, see below.

Call your optimizeX functions to get the results of OP operations and save it in dest.

Print the result of dest.

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

Compile: g++ task1.cpp optimize.cpp -Wall -O3 -o task1 -fno-tree-vectorize

Run (where n is a positive integer):

./task1 n

Example expected output: 3125 //from optimize1 0.706 //from optimize1 3125 //from optimize2 0.710 //from optimize2 3125 //from optimize3 0.353 //from optimize3 3125 //from optimize4 0.354 //from optimize4 3125 //from optimize5 0.236 //from optimize5

• 1. 3. On an Euler compute node:

Table 1: Setting of macros for each le.

data t OP IDENT

task11.pdf	int	+	0
task12.pdf	int	*	1
task13.pdf	float	+	0.f
task14.pdf	float	*	1.f

Run task1 for value n = 10⁶, with the settings of data t, OP, and IDENT, and the naming of pdf les referring to Table 1. Each pdf should plot the time taken by all ve of your optimizeX functions and one additional data point from SIMD version of optimize1¹ vs. X in linear-linear scale, where X = 1,…,6. Run the optimizeX function for 10 times and use the average time for plotting.

Note for optimize.h le: You can change the de nition of macros in optimize.h le to run tests for plotting, but your code should not depend on any changes in the provided optimize.h le in order to compile and run.

• data point X=6 should come from the result of optimize1 when compiled with command: g++ task1.cpp optimize.cpp -Wall -O3 -o task1 -march=native -fopt-info-vec

2. In this task, you will implement a parallel reduction (summation of an array) using hybrid OpenMP+MPI. You will use OpenMP to speed up the reduction, and use two MPI processes that each run on one node to execute the reduce function to add further parallelism. Figure 1 demonstrates the expected work ow of your program.

Figure 1: Schematic for the execution of reduction program.

a) Implement in a le called reduce.cpp with the prototype speci ed in reduce.h the function that uses OpenMP to speed up the reduction as much as possible (i.e., use simd directive).

b) Your program task2.cpp should accomplish the following:

Create and ll with float-type numbers however you like an array arr of length n, where n is the rst command line argument, see below. Note that n is half of the length of the array that we are doing reduction on.

Initialize necessary variables for MPI environment.

Set the number of OpenMP threads as t, where t is the second command line argument, see below.

Call the reduce function and save the result in each MPI process’s local res as indicated in Figure 1.

Use MPI Reduce to combine the local results and get the global res.

Print the global res from one process.

Print the time taken for the entire reduction process (including the call to reduce function and MPI Reduce) in milliseconds¹.

Compile²: mpicxx task2.cpp reduce.cpp -Wall -O3 -o task2 -fopenmp -fno-tree-vectorize -march=native -fopt-info-vec

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

mpirun -np 2 –bind-to none ./task2 n t

Example expected output:

3562.7

0.352

c) On an Euler compute node:

Run task2 for n = 10⁶, and t = 1; 2; ; 20. Generate a plot called task2.pdf that includes the run time of your program (the second output of your program) vs. t in linear-linear scale.

(Optional, extra credit 10 points) Compare the timing you received from two MPI processes running on two nodes with pure OpenMP implementation that runs

¹This time is the \absolute” time. You will start timing when the rst process calls the reduce function (you may add MPI Barrier before timing starts to make sure that the two processes approximately start from the same time) and end timing when MPI Reduce is nished. Do not time each process separately like in HW09.

• Use module load mpi/openmpi. Some notes about optional inspection into the execution if you are interested in understanding the performance better: You can compile with gcc/9.2.0 (module load gcc/9.2.0), and add export OMP DISPLAY AFFINITY=true to check the mapping between OpenMP threads and the physical cores.

on one node. Make a plot of run time vs. t in linear-linear scale with these two patterns in task2 op.pdf. Submit your code for timing the pure OpenMP implementation as task2 op.cpp that should take the input arguments in the same way as task2.cpp. Note that here n should be 2 10⁶ to compare with previous results. Discuss the di erences between the two and the optimal choice of achieving parallelism/reducing run time for arrays of di erent sizes.

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