Computing the value of $\pi$

• Computing the value of $\pi$.
• Based on generating random numbers in a unit length square and counting the number of points that fall within the largest circle inscribed in the square.
• Since the area of the circle ($\pi r^2$) is equal to $\pi/4$, and the area of the square is $1 \times 1$, the fraction of random points that fall in the circle should approach $\pi/4$.
• Threaded strategy:
• assigns a fixed number of points to each thread.
• Each thread generates these random points and keeps track of the number of points in the circle locally.
• After all threads finish execution, their counts are combined to compute the value of $\pi$ (by calculating the fraction over all threads and multiplying by 4).

The arg field is used to pass an integer id that is used as a seed for randomization.

• For computing the value of $\pi$,
• First read in the desired number of threads, num_threads, and the desired number of sample points, sample_points.
• These points are divided equally among the threads.
• The program uses an array, hits, for assigning an integer id to each thread (this id is used as a seed for randomizing the random number generator).
• The same array is used to keep track of the number of hits (points inside the circle) encountered by each thread upon return.

• The program creates num_threads threads, each invoking the same function compute_pi, using the pthread_create function.
• Once the respective compute_pi threads have generated assigned number of random points and computed their hit ratios, the results must be combined to determine $\pi$.
• Once all threads have joined, the value of $\pi$ is computed by multiplying the combined hit ratio by 4.0.
• The use of the function rand_r (instead of superior random number generators such as drand48).
• The reason for this is that many functions (including rand and drand48) are not reentrant.