How to build the application

• To build the application, simply execute bash make.sh. This will create three executable files nbody, nbody-gui and nbody-test.
• To run the command line simulation, execute ./nbody <iterations> <dt> (-b <bodies> | -f <filename>) <number of threads>. Note that <number of threads> is an optional argument. If it isn't provided, the number of threads defaults to 1.
• To run the GUI simulation, execute ./nbody-gui <resolution_width> <resolution_height> <iterations> <dt> (-b <bodies> | -f <filename>) <scale> <number of threads>. Note that I have implemented a scaling feature whereby a scaling value of 1 makes the data fit the bounds of the display perfectly. Also note that <number of threads> is an optional argument. If it isn't provided, the number of threads defaults to 1.
• To run the suite of test cases outlined in nbody_test.c, execute ./nbody-test.

Benchmark

• To run the benchmark script, first build the application by executing bash make.sh, then execute benchmark.sh. This runs the nbody command line simulation using a different number of threads and compares their execution times.

Errors Encountered

• During the development of the project, I encountered an issue where my energy calculations were fluctuating significantly between iterations. The root cause was in my kinetic energy function where I was incorrectly using positional values to compute velocity^2.
• I also encountered an issue where my multi-threaded program was updating the position of bodies using velocity(t+1) rather than velocity(t). To counteract this issue, I synchronized the threads using a barrier. The barrier makes sure that the correct velocity values are used when each of the threads are updating the positions of their assigned bodies.
• The last issue I encountered was that some of my calculations were returning -nan, i.e. not a number. This was due to the fact that my distance function was in some cases returning zero, and thus other functions were attempting to divide values by zero. To fix this, I changed my distance function so that it returns 1e-10 instead of zero, in the case that the actual distance between the two bodies is zero.

Step Function

• My step function spawns N threads, each of which computes and updates the velocities/positions of N/(number of bodies) bodies in the system.
• Before any thread can update the positions of the bodies, they all have to finish calculating and storing velocity(t+1). To enforce this restriction, my step function initialises a barrier which is passed to and used by the thread_step worker function.