Monte Carlo PI

Monte Carlo PI explores and implements a randomized solution to the calculation of the mathematical constant π. It uses the Pthreads library and the GNU Multiple Precision Arithmetic Library (GMP) for dealing with as precise as possible floating-point numbers.

Prerequisites

1. UNIX-like operating system supporting the Pthreads library
2. A system-wide installation of GMP
3. GNU Make

Running instructions

Supposing all the prerequisites are set up, in order to run Monte Carlo PI simply have

make run

To run the test suite, invoke instead

make testrun

Credits

Monte Carlo PI was inspired by the book Operating System Concepts, 9th edition by A. Silberschatz et al., pages 193-194.

Problem statement

An interesting way of calculating π is to use a technique known as Monte Carlo, which involves randomization. This technique works as follows:
Suppose you have a circle inscribed within a square, as shown in Figure 4.18. (Assume that the radius of this circle is 1.) First, generate a series of random points as simple (x, y) coordinates. These points must fall within the Cartesian coordinates that bound the square. Of the total number of random points that are generated, some will occur within the circle. Next, estimate π by performing the following calculation:

π = 4 X (number of points in circle) / (total number of points)

Write a multithreaded version of this algorithm that creates a separate thread to generate a number of random points. The thread will count the number of points that occur within the circle and store that result in a global variable.
When this thread has exited, the parent thread will calculate and output the estimated value of π. It is worth experimenting with the number of random points generated. As a general rule, the greater the number of points, the closer the approximation to π. In the source-code download for this text, we provide a sample program that provides a technique for generating random numbers, as well as determining if the random (x, y) point occurs within the circle. Readers interested in the details of the Monte Carlo method for estimating π should consult the bibliography at the end of this chapter. In Chapter 6, we modify this exercise using relevant material from that chapter.