My application that I selected is a PI approximation method. PI can be approximated in a number of ways however I chose to use the dartboard algorithm. Although not the fastest, the algorithm is very feasible to parallelize. The main idea behind it can be compared to a dartboard – you throw a random number (n) of darts at the board and note down the darts that have landed within it and those that have not. The image below demonstrates this concept:

[[File:dart.gif]]

The ratio of the randomly thrown dart is: (hits within dartboard) vs. (hits within square) is equal to the ratio between the two areas i.e. PI/4. The more darts we throw, the better we can approximate PI.

During the execution, the program takes the number of iterations through the command line. It generates two random decimal numbers between 0 and 1 and determines if the randomly generated coordinates are inside in the circle. Then it calculates the size of PI. As we increase the number of iteration we are getting a more realistic value of PI.

I created a screenshot from the first execution, the rest of the execution is summarized on the table and the chart below.

As we can see the hotspot of the program is the pi () function, which takes 100% of the execution time. This function is containing a single for loop, which is calculating the size of the PI. This can be executed independently, because it has no data dependency, therefor it is possible to parallelize with CUDA to speed up the processing time.