1.Introduction :

Below two simple examples, with C-POSIX and GO languages, which show how to do parallel loops for computing $\pi$ with Monte-Carlo method :

•    pi_mc_pthread.c


•    pi_mc.go

to compile POSIX version and run it (first argument : number of processes and second : number of iterations) :

to compile GO version and run it :

Make sure at the execution that number of iterations is divisible by number of processes.

2.Benchmark :

Following histogram represents performances of POSIX (magenta palette) and GO (gray scale) codes. For this, we plot the log inverse product of precision got on $\pi$ by runtime. This interval relies itself on the number of iterations (size of loop on abscissa) and the number of processes (in the range $2^0=1$ to $2^{12}$ by step $2$).

The bash script to get runtimes is available on run_benchmark_pi, with 'posix' parameter for POSIX version and 'go' for GO version. To make the figure below, here this Matlab script : plot_benchmark_pi.m.

We already know that estimator of $\pi$ value is as more accurate as sample is big, i.e when number of iterations is high. So we want to evaluate precision gain as a function of runtime. . Horizontal rectangles represents the average performances, for each group of size loop, with both versions. We notice then that accuracy increases relatively less quick than runtime.

For POSIX version, a good compromise is done with N_iterations = 1MB and N_process = 64, whereas for GO version, we get the best performance with N_iterations = 1MB and N_process = 8.

Finally, from a hardware implementation point of view, POSIX version gives faster results with a runtime gain of 33.91% compared with GO version. This can be explained by the fact that GO version uses another system layer, unlike C language wich is the system language of Linux.