The parallel implementation of integration to calculate the value of pi.
- Sameer Shende 
	CIS 630.

The area under the curve f(x) = 4/(1+x*x) from 0 to 1 = pi
The interval 0 to 1 is divided into n steps and we use data partitioning 
for parallel implementation. If there are 10 intervals and 3 processors,
first and the second get 3 intervals (1,2,3 for the first, 4,5,6 for the second)
and the third processor gets 4 intervals (7,8,9,10) - so that the last thread
is at least as busy as the rest of the threads. 

The value of pi is calculated and tested repeatedly for the same parameters.
It is consistent. (For two consecutive runs, the values are same to the 14th 
decimal place). Each thread calculates the local area and then acquires a lock
and updates the global variable and releases the lock.

After all the threads terminate, the value of pi is displayed and the error 
is calculated using the system specified value. For a large number of 
intervals (> 10000), the error reaches below the 10th decimal place in terms
of percentage.

The maximum size of the problem tested was with 8 processors and 1e9 (or 
1 billion intervals). After 1 million intervals, the error is more or less
constant and fine tuning the interval does not decrease the error 
significantly. 

The test runs consist of running different intervals with a single processor
and increasing the number of intervals and the processors.