DPS915/CodeKirin

Calculations of Pi

Team Member

1. Tony Yu

Progress

Assignment 1

Brief Overview

Monte Carlo approach to calculating Pi involves a circle on top of a square. Dots will be randomly drawn onto the square, and by adding up all the dots that landed within the circle then dividing by 4, will get you a value close to Pi. The more dots drawn, the more accurate Pi will become.

Findings

The code used is taken from the following site http://www.cplusplus.com/forum/beginner/1149/ with some changes to the code.

This program will calculate pi to a precision based on the value entered by the user. Currently it displays to a precision of 9 decimal places.

Will attempt to figure out a way to calculate to as much decimal places as possible, which should drastically increase the time it takes to run the program. Currrent possible solution is to use the BigNumber library.

(Updated)

The code used is taken from the following site https://helloacm.com/cc-coding-exercise-finding-approximation-of-pi-using-monto-carlo-algorithm/ with some changes to it.

This program will calculate pi using the Monte Carlo approach to a precision based on the value entered by the user.

Value of 1 Million

Value of 10 Million

Value of 100 Million

Value of 1 Billion

Assignment 2 and 3

I have combined the 2nd and 3rd part of the assignment together, since I had some issues with the kernel.

The following results compares the upgraded code with the original to show a significant increase in speed.

(Note)

For some reason the code crashes my graphic driver past 8000000 (8 million) dots, and even at 8 million it crashes most of the time. The Nvidia Visual Profiler doesn't work either, it gets stuck on generating timeline, so I used clock_t in the code instead in order to calculate execution time of the kernel. Don't think this is 100% accurate though.

Value of 1 Million

Value of 5 Million

Value of 8 Million

Comparison Chart

Some Code Snippets

Sets the tid (threadIdx.x) index of the temp array in shared memory to 1, when the total <= 1.0, and sync the threads. Then sum up all the 1s in the array for that specific block and pass it out into another array.

After copying from the device to host, obtain the total sum of results from all kernels and calculates the value of pi.