Computer Science 335
Parallel Processing and High Performance Computing

Fall 2024, Siena College

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In this programming project, you will work with more of MPI's collective communication functionality.

You may work alone or with a partner on this programming project.

There is a significant amount of work to be done here. It will be difficult if not impossible to complete the assignment if you wait until the last minute. A slow and steady approach will be much more effective.

Learning goals:

1. To learn about more efficient communication patterns.
2. To gain experience using MPI collective communication functionality.

Getting Set Up

In Canvas, you will find a link to follow to set up your GitHub repository, which will be named coll2-proj-yourgitname, for this programming project. Only one member of the group should follow the link to set up the repository on GitHub, then others should request a link to be granted write access.

You may choose to answer the lab questions in the README.md file in the top-level directory of your repository, or upload a document with your responses to your repository, or add a link to a shared document containing your responses to the README.md file.

Improving RDS

Section 3.4.1 of Pacheco shows how we can improve the gathering of values from the processes at all ranks back to the rank 0 process for operations such as a global sum. Such a mechanism can be used to improve the speed of the communication at end of the RDS program from the earlier lab.

For the questions below, assume you are running your original or improved programs with 512 processes. You don't need to run it, just base your answers on your code.

Of course you have been doing the readings and keeping up with your lab work, so you have realized that this communication can be done with one of MPI's higher-level collective communication routines: an MPI_Reduce.

A Monte Carlo Method to Compute pi

There is a class of algorithms knows as Monte Carlo methods that use random numbers to help compute some result.

We will write a parallel program that uses a Monte Carlo method to estimate the value of pi.

The algorithm is fairly straightforward. We repeatedly choose (x,y) coordinate pairs, where the x and y values are in the range 0-1 (i.e.the square with corners at (0,0) and (1,1). For each pair, we determine if its distance from (0,0) is less than or equal to 1. If it is, it means that point lies within the first quardant of a unit circle. Otherwise, it lies outside. If we have a truly random sample of points, there should be an equal probability that they have been chosen at any location in our square domain. The space within the circle occupies (pi)/(4) of the square of area 1.

So we can approximate pi by taking the number of random points found to be within the unit circle, dividing that by the total number of points and multiplying it by 4!

A sequential Java program that uses this method to approximate pi is included for your reference in the pi directory of your repository.

• Your program should take a single command-line parameter, which is the number of random points to generate on each process. Store this in a long so you can generate large numbers of points to get good approximations. Convert this to a long only on the rank 0 process (with good error checking) and use MPI to broadcast the value to all other processes. If the rank 0 process finds an error condition when parsing the command-line parameter, it should call MPI_Abort to terminate the computation.
• Use the drand48 function to generate your random numbers. Each process needs to seed the random number generator with a different value so they all will compute a different pseudorandom sequence. You might make the seed a function of the current time, the rank, and maybe the number of processes.
• No process other than the rank 0 process should produce output.
• After each process has generated its random points and counted the number that lie within the unit circle, gather all of those counts back to the rank 0 process so it can print out information and compute the approximation of pi.

Here is a sample run of my program, on 4 processes with 100,000,000 points per process. Your program should output the same information in a similar format. Of course, we are choosing random numbers, so your answers will vary.

Will use 100000000 points per process
[0] 78540219 in circle, pi approx = 3.141609
[1] 78538052 in circle, pi approx = 3.141522
[2] 78541818 in circle, pi approx = 3.141673
[3] 78543977 in circle, pi approx = 3.141759
in circle values range from 78538052 to 78543977
Final approximation of pi: 3.141641

Submission

Commit and push! Make sure your answers to lab questions are provided using one of the mechanisms mentioned in the "Getting Set Up" part of the lab.

Grading

This assignment will be graded out of 50 points.