Homework 2 (Part 2):

Parallelizing a Particle Simulation

Overview

This assignment is an introduction to parallel programming using a distributed memory model. Most of this page will be similar to the HW 2-1 page.

In this assignment, we will be parallelizing a toy particle simulation (similar simulations are used in mechanics, biology, and astronomy). In our simulation, particles interact by repelling one another. A run of our simulation is shown here:

The particles repel one another, but only when closer than a cutoff distance highlighted around one particle in grey.

Asymptotic Complexity

Serial Solution Time Complexity

If we were to naively compute the forces on the particles by iterating through every pair of particles, then we would expect the asymptotic complexity of our simulation to be O(n^2).

However, in our simulation, we have chosen a density of particles sufficiently low so that with n particles, we expect only O(n) interactions. An efficient implementation can reach this time complexity.

Parallel Speedup

Suppose we have a code that runs in time T = O(n) on a single processor. Then we'd hope to run close to time T/p when using p processors. After implementing an efficient serial O(n) solution, you will attempt to reach this speedup using MPI.

For Remote Students

Dear remote students, we are thrilled to be a part of your parallel computing learning experience and to share these resources with you! To avoid confusion, please note that the assignment instructions, deadlines, and other assignment details posted here were designed for the local students. You should check with your local instruction team about submission, deadlines, job-running details, etc. and utilize Moodle for questions. With that in mind, the problem statement, source code, and references should still help you get started (just beware of institution-specific instructions). Best of luck and we hope you enjoy the assignment!

Due Date: Thursday March 4th, 2021 (11:59 PM PST)

Instructions

Teams

You must use the same groups as with HW2-1. If this is a problem, please privately contact the GSIs.

Getting Set Up

The starter code is available on Bitbucket at https://bitbucket.org/Berkeley-CS267/hw2-2.git and should work out of the box. To get started, we recommend you log in to Cori and download the first part of the assignment. This will look something like the following:

student@local:~> ssh demmel@cori.nersc.gov

student@cori04:~> git clone https://bitbucket.org/Berkeley-CS267/hw2-2.git

student@cori04:~> cd hw2-2

student@cori04:~/hw2-2> ls

CMakeLists.txt common.h job-mpi main.cpp mpi.cpp

There are five files in the base repository. Their purposes are as follows:

CMakeLists.txt

The build system that manages compiling your code.

main.cpp

A driver program that runs your code.

common.h

A header file with shared declarations

job-mpi

A sample job script to run the MPI executable

mpi.cpp - - - You may modify this file.

A skeleton file where you will implement your mpi simulation algorithm. It is your job to write an algorithm within the simulate_one_step and gather_for_save functions.

Please do not modify any of the files besides mpi.cpp.

Building our Code

First, we need to make sure that the CMake module is loaded and that the GNU compiler is selected.

student@cori04:~/hw2-2> module load cmake

student@cori04:~/hw2-2> module swap PrgEnv-intel PrgEnv-gnu

You should put these commands in your ~/.bash_profile.ext file to avoid typing them every time you log in.

Next, let's build the code. CMake prefers out of tree builds, so we start by creating a build directory.

student@cori04:~/hw2-2> mkdir build

student@cori04:~/hw2-2> cd build

student@cori04:~/hw2-2/build>

Next, we have to configure our build. We can either build our code in Debug mode or Release mode. In debug mode, optimizations are disabled and debug symbols are embedded in the binary for easier debugging with GDB. In release mode, optimizations are enabled, and debug symbols are omitted. For example:

student@cori04:~/hw2-2/build> cmake -DCMAKE_BUILD_TYPE=Release ..

-- The C compiler identification is GNU 8.3.0

...

-- Configuring done

-- Generating done

-- Build files have been written to: /global/homes/s/student/hw2-2/build

Once our build is configured, we may actually execute the build:

student@cori04:~/hw2-2/build> make

Scanning dependencies of target mpi

[ 33%] Building CXX object CMakeFiles/mpi.dir/main.cpp.o

[ 66%] Building CXX object CMakeFiles/mpi.dir/mpi.cpp.o

[100%] Linking CXX executable mpi

[100%] Built target mpi

student@cori04:~/hw2-2/build> ls

CMakeCache.txt CMakeFiles cmake_install.cmake Makefile mpi job-mpi

We now have a binary (mpi) and a job script (job-mpi).

For info on running jobs and editing the code, refer to the HW1 page.

Important notes for Performance:

There will be two types of scaling that are tested for your parallel codes:

In strong scaling we keep the problem size constant but increase the number of processors
In weak scaling we increase the problem size proportionally to the number of processors so the work/processor stays the same (Note that for the purposes of this assignment we will assume a linear scaling between work and processors)

While the scripts we are providing have small numbers of particles 1000 to allow for the O(n²) algorithm to finish execution, the final codes should be tested with values much larger to better see their performance. Test up to 2 nodes and 1,500,000 particles.

Grading

We will grade your assignment by reviewing your assignment write-up, measuring the scaling of the implementation, and benchmarking your code's raw performance. To benchmark your code, we will compile it with the exact process detailed above, with the GNU compiler. We will run your submissions on Cori's KNL processors.

Submission Details

Supposing your custom group name is XYZ, follow these steps to create an appropriate submission archive:

Ensure that your write-up is located in your source directory, next to serial.cpp. It should be named cs267XYZ_hw2_2.pdf
From your build directory, run:

student@cori04:~/hw2-2/build> cmake -DGROUP_NAME=XYZ ..

student@cori04:~/hw2-2/build> make package

This second command will fail if the PDF is not present.

Confirm that it worked using the following command. You should see output like:

student@cori04:~/hw2-2/build> tar tfz cs267XYZ_hw2_2.tar.gz

cs267XYZ_hw2_2/cs267XYZ_hw2_2.pdf

cs267XYZ_hw2_2/mpi.cpp

Submit your .tar.gz through bCourses.

Write-up Details

Your write-up should contain:
- The names of the people in your group and each member's contribution.
- A plot in log-log scale that shows that your parallel codes performance and a description of the data structures that you used to achieve it.
- A description of the communication you used in the distributed memory implementation.
- A description of the design choices that you tried and how did they affect the performance.
- Speedup plots that show how closely your MPI code approaches the idealized p-times speedup and a discussion on whether it is possible to do better. Both strong and weak scaling. Test up to 2 nodes and 1,500,000 particles.
- Where does the time go? Consider breaking down the runtime into computation time, synchronization time and/or communication time. How do they scale with p?

Notes:

Your grade will mostly depend on three factors:
- Scaling sustained by your codes on the Cori supercomputer (varying n).
- Performance sustained by your codes on the Cori supercomputer.
- Explanations of your methodologies and the performance features you observed (including what didn't work).
You must use the GNU C Compiler for this assignment. If your code does not compile and run with GCC, it will not be graded.
If your code produces incorrect results, it will not be graded.
You must target Cori's KNL processors for this assignment, not Haswell, like HW1.

For info on running the rendering output, refer to the HW2-1 page.

For info on checking output correctness, refer to the HW2-1 page.

Resources

Programming in shared and distributed memory models are introduced in Lectures.
Shared memory implementations may require using locks that are available as omp_lock_t in OpenMP (requires omp.h)
You may consider using atomic operations such as __sync_lock_test_and_set with the GNU compiler.
Other useful resources: pthreads tutorial, OpenMP tutorial, OpenMP specifications and MPI specifications.
Hints on getting O(n) serial and Shared memory and MPI implementations (pdf)
It can be very useful to use a performance measuring tool in this homework. Parallel profiling is a complicated business but there are a couple of tools that can help.
TAU (Tuning and Analysis Utilities) is a source code instrumentation system to gather profiling information. You need to "module load tau" to access these capabilities. This system can profile MPI, OpenMP and PThread code, and mixtures, but it has a learning curve.
HPCToolkit Is a sampling profiler for parallel programs. You need to "module load hpctoolkit". You can install the hpcviewer on your own computer for offline analysis, or use the one on NERSC by using the NX client to get X windows displayed back to your own machine.
If you are using TAU or HPCToolkit you should run in your $SCRATCH directory which has faster disk access to the compute nodes (profilers can generate big profile files).