Rewrite forces computation in Cython or Cpp

[entropyqueen]

We currently have an enormous drop of fps when computing the forces between each object, the algorithm in itself may not be easy to optimize, however, switching to C++ or cython would greatly improve the speed of the simulation.

[Chelsea486MHz]

Parallelization of numerical integration when solving the N-body problem is only useful in the context of large simulation systems (n>>1)

For small systems such as those simulated here, simply optimizing the force computation by rewriting the numerical integration code in C++ should be enough.

I'll get to work on a PR and provide benchmarks for various implementations.

[entropyqueen]

See branch https://github.com/entropyqueen/StarSystemSimulation/tree/cpp_force_implem for current implementation.
It's not working yet, the positions seems to be updated too much for the given dt, also it's far from optimized (we need to remove the conversion from and to the cpp interface to speed things up)

[Chelsea486MHz]

I did some profiling runs using cProfile to figure out what is causing the performance issues on the python side of things.

Python code: 22-23 FPS

11130607 function calls (11064793 primitive calls) in 11.243 seconds

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
7150    0.076    0.000    3.515    0.000 universe.py:112(calculate_acceleration)
715    0.028    0.000    3.988    0.006 universe.py:121(update_position)
65    0.001    0.000    4.038    0.062 universe.py:53(update)
5060    0.025    0.000    1.477    0.000 object_display.py:136(update)
20240    0.032    0.000    1.148    0.000 object_display.py:76(convert_distances)
5060    0.011    0.000    1.037    0.000 object_display.py:84(compute_display_pos)
5060    0.015    0.000    1.019    0.000 object_display.py:86(<listcomp>)
460    0.004    0.000    5.579    0.012 panda3d_display.py:95(update)

The simulator spends 36% of its time doing the simulation maths. It seems optimization is required more on the display side of things than on the numerical integration and force computation.

There is a module error when trying to run your new branch, I wasn't able to profile it. Should we profile it as well, it'll provide us with additional insight regarding the actual impact of the C++ rewrite on overall simulation performance.