# Assignment 3 - Tiled Matrix Multiplication

## Overview

The objective of this assignment is to implement a tiled matrix multiplication kernel that can support arbitrary sized matrices.

## Tiled Matrix Multiplication

1. For this lab, we will be using Github Classroom.
Please join the classroom by clicking the following link: https://classroom.github.com/a/j4J9Ecei Once you join the classroom, a private github repository will automatically be created with the starter code.
Simply `git clone` to copy the starter code to Bender.

2. Edit the source files `kernel.cu` and `main.cu` to complete the functionality of the matrix multiplication on the device. The two matrices could be any size, but we will not test your code with an output matrix size exceeding 65,536 elements (for example, 256 x 256 input matrices). This is purely a limitation for testing your code in a timely manner. Your code should still be able to run for significantly larger matrices.

3. There are three modes of operation for the application. Check `main()` for a description of the modes (repeated below). You will support each of these modes using a Tiled matrix multiplication implementation.

• No arguments: The application will create two randomly initialized matrices to multiply size (1000x1000). After the device multiplication is invoked, it will compute the correct solution matrix using the CPU, and compare that solution with the device-computed solution. If it matches (within a certain tolerance), if will print out "Test PASSED" to the screen before exiting.
• One argument: The application will use the random initialization to create the input matrices (size mxm, where m is the argument. Start your testing with small matrices.
• Three arguments m, k, and n: The application will initialize the two input matrices with random values. A matrix will be of size m x k while the B matrix will be of size k x n, producing a C matrix of size m x n
• Note that if you wish, you may add a mode to accept input matrices from files, or to dump input and output matrices to files to facilitate testing. The first three modes must remain untouched.
4. Commit and push your completed tiled matrix multiplication code to the private repository.

1. On Bender, compare the execution time of a 256 x 256 square matrix multiplication compared to a 1024 x 64 and 64 x 1024 rectangular matrix multiply. All input matricies have 65k entries. What do you observe? Which is faster? Can you explain the observed behavior? Tip: You may want to comment out the `verify()` function in `main.cu` when timing this question.
1. Commit and push your completed tiled matrix multiplication code to the github repository. (You only need to modify `kernel.cu` and `main.cu`.)
2. Answer the previous questions by including a report document in the repository in either PDF, Plain text, or Markdown format only. Please name your report `FirstName-LastName.pdf` or `FirstName-LastName.txt` or `FirstName-LastName.md`, etc.