Problem 2: Compute the Value of Pi

Write a parallel program to calculate using the Monte Carlo method. The process is as follws:

randomly located points are generated within a 22 square which has a circle inscribed within it.

The algorithm generates a large number of points and checks to see if the coordinates, x and y, of

each point are inside the circle- x2+y21. The ratio, P, of points inside the circle to the total number

of points tried is calculated. Using this ratio, the approximation of can be computed by assuming

that P approaches the value of ratio of the area of the circle to the area of the square when the

number of points, niter, is large. Thus we can say: P= (r)/4r = /4 and solve for . To do this, P

is multiplied by 4 and the result is an approximation of .

Use a total number of iterations N=10000000. In your program, the iterations are divided among

the available processes such that each process will run a subset of these iterations in parallel. Each

process will compute the number of points that it has found inside the circle and report the results

back to the master. The master will aggregate the results to compute the approximate value of pi.

Hint:

To generate a random number in the range [0,1] in C:

//First set the seed for the random number generator (Each

process should have a different seed)

srand(rank+1);

//Next generate a random number in the range [0,1]

Double x=((double)rand())/RAND_MAX;