Parallel approximation of PI in C

Here is a parallel C code that approximates PI using riemann integration. We do that calculating an aproximation for the integral of f(x) = sqrt(1 - x^2), with x in [0, 1], which corresponds to one quarter of a unitary circle's area. As we know this value can also be calculated as (pi * radius^2) / 4, which, in this case, is pi / 4. So to get a PI approximation we just have to multiply the value of the integration by 4.

The goal is not to have the best PI approximation strategy, but to show a simple and annotated pthread code for those who are learning parallel programming in C with pthreads.

To compile

You must have gcc and make installed. Than, run:

    $ make

(tested on linux only)

To run

    $ time ./pi <num_threads> <integration_divisions>

Where num_threads is the desired number of threads to be used and integration_divisions is the number of partitions to be made for the riemann integration.

Tip:

Run with a high value of integration_divisions (say, 1.e9), and compare the time when you change num_threads from 1 to 4 (or 8, depending on your CPU).

You can then calculate the speedup with n threads, which is the result of sequential_time / time_with_n_threads. This value will show the effectiveness of the parallel version against the sequential and the higher it is, the better.