Student info

Name: Truc D Nguyen
UFID: 9482-7764

Instructions

The main source code is in lib/proj1.ex

The instructions for the bonus part is given at the end of this file

Configuration and Compilation

To configure the desired number of workers, modify the first line in proj1.exs

To compile:

mix compile

Run syntax

mix run proj1.exs <n> <k>

n: input N
k: input k

Output

On each line is the first number in the sequence for each solution.

Example

$ mix run proj1.exs 40 24
1
9
20
25

Assigning work unit

To calculate the sum of squares of a sequence 1..N, I use the following equation:

SUM(N) = N(N+1)(2N+1)/6

Therefore, for a sequence of k elements starting from i, the sum of squares will be:

SUM(i + k - 1) - SUM(i - 1)

That means each sequence only takes O(1).

Denoting c as the number of workers, each one will be given a work unit of (n/c) sequence(s).
In case n is not divisible by c, the first (n%c) workers will be given 1 more sequence.

Example: with n = 10, we have 10 sequences. Suppose 4 workers are spawn, each worker will be assigned 3, 3, 2, and 2 sequences, respectively.

Results

When running

$ mix run proj1.exs 1000000 4

there will be no sequences that satisfy the requirement.

Run time

I use 2 workers for the following problem

$ time mix run proj1.exs 1000000 4

real	0m0.409s
user	0m0.689s
sys     0m0.066s

CPU time is 0.689 + 0.066 = 0.755
REAL time is 0.409
Ratio CPU/REAL = 1.846

Large problems

I use 8 workers for the following problems

100 million

$ time mix run proj1.exs 100000000 20

real	0m8.794s
user	1m7.136s
sys     0m0.056s

CPU time is 67.136 + 0.056 = 67.192
REAL time is 8.794
Ratio CPU/REAL = 7.641

1 billion

$ time mix run proj1.exs 1000000000 20

real	1m36.164s
user	12m8.488s
sys     0m0.066s

CPU time is 728.488 + 0.066 = 728.554
REAL time is 96.164
Ratio CPU/REAL = 7.576

BONUS

This project can successfully run on 2 machines.

Half of the actors will run on the local machine, the other half will run on the remote machine.

Configuration

In proj1.exs, the noActors (first line) should be an even number
Uncomment lines 11-14, comment line 7
Line 11: edit name@host of the local machine (Ex: m1@192.168.50.25)
Line 13: edit name@host of the remote machine (Ex: m2@192.168.50.26)

Run

On the remote machine

Execute the following command:

iex --name <name@host> --cookie truc -S mix

name@host: define name and host of the machine (Ex: m2@192.168.50.26)

Example:

iex --name m2@192.168.50.26 --cookie truc -S mix

On the local machine

Execute the following command (the number of sequences n should be greater than noActors):

$ mix run proj1.exs 40 24

The output will be

trucndt/proj1-ufl-dist