In this HW, we cover using the Xeon Phi accelerators on the cluster. If you have any questions, don't hesitate to post on Piazza or come to OH!
Submission: A tarball/git-link of the provided directory
The Julia Set is a famous mathematical object that you may have seen before. It is one of the canonical fractals common in mathematical art and dynamical systems. The mathematical definition of fractals and the dynamical systems giving rise to fractal behavior is out-of-scope for this course, so if you are curious, please refer to outside resources for more information. We found this link to be particularly easy to understand.
To be a bit less precise, let's say that one has a 2 dimensional array of pixels. If we color each pixel based on a recursive formula involving that pixel's previous color (with a some base case dependent upon that pixel's location) , we will often obtain very interesting mathematical behavior. The Julia Set arises from a specific recursive formula with mathematical behavior known as fractal. Fractal behavior often results in very pretty pictures! If you don't know what the Julia set looks like, run the code and find out!
We have given you julia.c, the makefile, submission script and a visualizer written in Python. You run julia.c as follows:
./julia 100
Where 100 is the desired width and length of your image. julia will then spit out a text file containing pixel information and metadata. We then use
python visualizer.py julia.txt
To generate the image. If you don't feel like using any input arguments, we have set the default image size to 500 pixels by 500 pixels and the default output name to julia.txt. Your job is thus to parallelize and offload the marked portion in julia.c to the Xeon Phis.
julia.c and visualize.py both contain parameters for you to play around with, in order to get your very own "custom Julia Set". Please do take a look at which parameters you can modify! We are looking forward to seeing a variety of different images.
As with many accelerator programming models, you need to explicitly copy data between the host and the device (the CPU and Xeon Phi in this case). OpenMP is once again the language you will be using. For instructions, please check the class slides for a quick tutorial and these slides for an alternative.
We have included a specific makefile recipe for offloading named julia-xeonphi which contains the compiler flags necessary for offloading.
If you are generating a large image using visualize.py, please use your personal computer so you don't slow down the login node for everyone else. You can still submit job files, but don't run visualize.py afterwards on the login node; simply copy julia.txt to your personal computer.
On another note, we will be working with other accelerators (GPUs) for the next Programming Project in case you were hoping to get some hands-on experience with GPUs.
All you need to do is use the Xeon Phis to work on the array julia_counts by declaring it as something to be offloaded. Then, you may parallelize the outer for loop in the same way you did for the previous HW.
If you are feeling especially motivated, try vectorizing the computational kernel julia_loop. It's current form is rather inefficient, as it works on individual pixels rather than sets of pixels!