Getting Started
Download CS201_Lab17.zip. Import it into Eclipse (File→Import…→Existing Projects into Workspace→Archive File.) You should see a project called CS201_Lab17 in the package explorer.
Estimating π
An approximation of π can be computed by generating random points in a square of some arbitrary size centered at the origin of the x/y plane. Each time one of the random points falls within a circle centered at the origin (where the circle completely fills the square), increase a counter. After some number of random points have been generated, divide the counter (how many random points were within the circle) by the total number of random points. This number will approximate the area of a circle of radius 0.5. We know that for a circle, the area a is computed by the equation
a = πr2
Letting r equal 0.5, and re-arranging to solve for π,
π = a / .25
For example, here is a picture showing 5000 random points within a 200 by 200 square centered at the origin, along with an outline of a circle within the square:
Based on these 5000 points, we estimate π to be 3.0936. This is obviously not very accurate: computing more random points would lead to a more accurate estimate.
Your Task
Your task is to use the technique described above to estimate π using 100,000,000 (one hundred million) random points.
Your program should support two computation techniques:
- purely sequential computation (using a single thread)
- parallel computation using 2 threads
Your program should measure the number of milliseconds needed to estimate π using both techniques. Is the parallel version faster? If so, how much faster?
Hints
Create instances of the PiTask class to perform the computation (or part of the computation in the parallel version). You will need to implement the run method of this class so that generates random points and counts how many fall within the circle.
In the sequential computation, create one PiTask object and have it compute all 100,000,000 random points.
In the parallel computation, create two PiTask objects and have each compute 50,000,000 points. The total number of points that fell within the circle will thus be the sum of the counts computed by each of the two tasks.
Submitting
When you are done, submit the lab to the Marmoset server using either of the methods below.
From Eclipse
If you have the Simple Marmoset Uploader Plugin installed, select the project (CS201_Lab17) in the package explorer and then press the blue up arrow button in the toolbar. Enter your Marmoset username and password when prompted.
From a web browser
Save the project (CS201_Lab17) to a zip file by right-clicking it and choosing
Export…→Archive File
Upload the saved zip file to the Marmoset server as lab17. The server URL is
