CS2110 Homework 6 -Subroutines and Calling Conventions Solution

1 Overview
1.1 Purpose
Now that you’ve been introduced to assembly, think back to some high level languages you know such as Python or Java. When writing code in Python or Java, you typically use functions or methods. Functions and methods are called subroutines in assembly language.
In assembly language, how do we handle jumping around to different parts of memory to execute code from functions or methods? How do we remember where in memory the current function was called from (where to return to)? How do we pass arguments to the subroutine, and then pass the return value back to the caller?
The goal of this assignment is to introduce you to the Stack and the Calling Convention in LC-3 Assembly. This will be accomplished by writing your own subroutines, calling subroutines, and even creating subroutines that call themselves (recursion). By the end of this assignment, you should have a strong understanding of the LC-3 Calling Convention and the Stack Frame, and how subroutines are implemented in assembly language.
1.2 Task
You will implement each of the four subroutines (functions) listed below in LC-3 assembly language. Please see the detailed instructions for each subroutine on the following pages. We have provided pseudocode for each of the subroutines, and suggest that you follow these algorithms when writing your assembly code. Your subroutines must adhere to the LC-3 calling convention.
1. collatz.asm
2. sort.asm
3. llsum.asm
More information on the LC-3 Calling Convention can be found on Canvas in the Lab Guides and in Lecture Slides L12 and L13. More detailed information on each LC-3 instruction can be found in the Patt/Patel book Appendix A (also on Canvas under LC3 Resources). Please check the rest of this document for some advice on debugging your assembly code, as well some general tips for successfully writing assembly code.
1.3 Criteria
Your assignment will be graded based on your ability to correctly translate the given pseudocode for subroutines (functions) into LC-3 assembly code, following the LC-3 calling convention. Please use the LC-3 instruction set when writing these programs. Check the deliverables section for deadlines and other related information.
You must obtain the correct values for each function. In addition, registers R0-R5 and R7 must be restored from the perspective of the caller, so they contain the same values after the caller’s JSR subroutine call. Your subroutine must return to the correct point in the caller’s code, and the caller must find the return value on the stack where it is expected to be. If you follow the LC-3 calling convention correctly, each of these things will happen automatically.
While we will give partial credit where we can, your code must assemble with no warnings or errors. (Complx will tell you if there are any.) If your code does not assemble, we will not be able to grade that file and you will not receive any points. Each function is in a separate file, so you will not lose all points if one function does not assemble. Good luck and have fun!
2 Detailed Instructions
2.1 Part 1
2.1.1 Collatz Conjecture
The Collatz conjecture states that the hailstone sequence, defined below, for any positive integer n will eventually reach 1.

For example, n = 5 results in the sequence 5 → 16 → 8 → 4 → 2 → 1, taking a total of 5 steps. Another example, n = 3, takes 7 steps with the sequence 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1.
For this part of the assignment, you will be recursively computing the number of steps a number in the hailstone sequence takes to reach 1. The collatz subroutine takes in a single parameter that is the starting number of the hailstone sequence and returns the total number of steps it takes for the sequence to reach 1.
A divide by 2 subroutine is also provided to help calculate n/2 when n is even.
If you would like additional reading on the hailstone sequence and Collatz conjecture, see https://plus.
maths.org/content/mathematical-mysteries-hailstone-sequences.
2.1.2 Pseudocode
The pseudocode is as follows:
collatz(int n, function div2) { if (n == 1) { return 0;
}
if (n % 2 == 0) {
return collatz(n/2) + 1;
} else { return collatz(3 * n + 1) + 1;
}
}
2.2 Part 2
2.2.1 Selection Sort
For this part of this assignment, you will be implementing selection sort on an array of integers. The parameters for the sort subroutine are the memory address of the first element in the array, an integer value representing the number of elements in the array, and the memory address of the subroutine used to compare elements. Following execution of this subroutine, the specified array will be sorted according to the provided comparison function.
To compare two elements a and b with the comparison function, pass a and b as arguments to the subroutine. compare(a, b) returns a positive number if the value of a is considered to be greater than the value of b. That is, a should appear after b in the sorted array.
If you are unfamiliar with selection sort and would like more information about it, see https://www. geeksforgeeks.org/selection-sort/.
Note: Unlike previous questions, you can’t use JSR to jump to the provided function. JSR takes in the PC-relative location of a subroutine as one of its operands, but some of the provided functions are located too far away for JSR to reach. What function similar to JSR can be used instead?
2.2.2 Pseudocode
The pseudocode for this function is as follows.
sort(array, len, function compare) { i = 0; while (i < len - 1) { j = i; k = i + 1;
while (k < len) {
// update j if ARRAY[j] > ARRAY[k] if (compare(ARRAY[j], ARRAY[k]) > 0) { j = k;
} k++;
} temp = ARRAY[i]; ARRAY[i] = ARRAY[j]; ARRAY[j] = temp; i++;
}
}
2.3 Part 3
2.3.1 Linked List Sum
For this part of the assignment, you will write a recursive subroutine to calculate the sum of all the nodes in a linked list. The parameter of the function is a node representing the head node of the linked list and the return value is the sum of all the data in the list.
2.3.2 Linked List Data Structure
The below figure depicts how each node in our linked list is laid out. Each node will have two attributes: the next node, and a value for that node.
Memory Memory Memory Memory Head Node x4000 x4001 x4008 x4009
x4000 x4008 x0000
Address of Address of Data Address Data next node next node of next
node (null)
See https://www.geeksforgeeks.org/data-structures/linked-list/#singlyLinkedList for more information regarding linked lists.
2.3.3 Pseudocode
Here is the pseudocode for this subroutine:
llsum(Node head) {
// note that a NULL address is the same thing as the value 0 if (head == NULL) { return 0;
}
Node next = head.next; sum = head.data + llsum(next); return sum;
}
3 Autograder
To run the autograder locally, follow the steps below depending upon your operating system:
• Mac/Linux Users:
1. Navigate to the directory your homework is in (in your terminal on your host machine, not in the Docker container via your browser)
2. Run the command sudo chmod +x grade.sh
3. Now run ./grade.sh
• Windows Users:
1. In Git Bash (or Docker Quickstart Terminal for legacy Docker installations), navigate to the directory your homework is in
2. Run chmod +x grade.sh
3. Run ./grade.sh
4 Deliverables
Turn in the following files to Gradescope:
1. collatz.asm
2. sort.asm
3. llsum.asm
Note: Please do not wait until the last minute to run/test your homework. Last minute turn-ins will result in long queue times for grading on Gradescope. You have been warned.
5 Appendix
5.1 Appendix A: LC-3 Instruction Set Architecture

6 Debugging LC-3 Assembly
1. First off, we can get these replay strings in two places: the local grader, or off of Gradescope. When you run the autograder, you should see an output like this:

Side Note: If you do not have Docker installed, you can still use the tester strings to debug your assembly code. In your Gradescope error output, you will see a tester string. When copying, make sure you copy from the first letter to the final backslash and again, don’t copy the quotations.

2. Secondly, navigate to the clipboard in your Docker image and paste in the string.

3. Next, go to the Test Tab and click Setup Replay String

4. Now, paste your tester string in the box!

5. Now, Complx is set up with the test that you failed! The nicest part of Complx is the ability to step through each instruction and see how they change register values. To do so, click the step button. To change the number representation of the registers, double click inside the register box.

6. If you are interested in looking how your code changes different portions of memory, click the view tab and indicate ’New View’

7. Now in your new view, go to the area of memory where your data is stored by CTRL+G and insert the address

8. One final tip: to automatically shrink your view down to only those parts of memory that you care about (instructions and data), you can use View Tab → Hide Addresses → Show Only Code/Data.

6.1 Appendix C: LC-3 Assembly Programming Requirements and Tips
1. Your code must assemble with NO WARNINGS OR ERRORS. To assemble your program, open the file with Complx. It will complain if there are any issues. If your code does not assemble you WILL get a zero for that file.
2. Comment your code! This is especially important in assembly, because it’s much harder to interpret what is happening later, and you’ll be glad you left yourself notes on what certain instructions are contributing to the code. Comment things like what registers are being used for and what less intuitive lines of code are actually doing. To comment code in LC-3 assembly just type a semicolon (;), and the rest of that line will be a comment.
3. Avoid stating the obvious in your comments, it doesn’t help in understanding what the code is doing.
Good Comment
ADD R3, R3, -1 ; counter--
BRp LOOP
Bad Comment ; if counter == 0 don’t loop again
ADD R3, R3, -1 ; Decrement R3
BRp LOOP ; Branch to LOOP if positive
4. DO NOT assume that ANYTHING in the LC-3 is already zero. Treat the machine as if your program was loaded into a machine with random values stored in the memory and register file.
5. Following from 3. You can randomize the memory and load your program by doing File - Randomize and Load.
6. Use the LC-3 calling convention. This means that all local variables, frame pointer, etc... must be pushed onto the stack. Our autograder will be checking for correct stack setup.
7. Start the stack at xF000. The stack pointer always points to the last used stack location. This means you will allocate space first, then store onto the stack pointer.
8. Do NOT execute any data as if it were an instruction (meaning you should put .fills after HALT or RET).
9. Do not add any comments beginning with @plugin or change any comments of this kind.
10. Test your assembly. Don’t just assume it works and turn it in.
7 Appendix D: Rules and Regulations
7.1 General Rules
2. If you find any problems with the assignment it would be greatly appreciated if you reported them to the author (which can be found at the top of the assignment). Announcements will be posted if the assignment changes.
7.2 Submission Conventions
1. Do not submit links to files. The autograder does not understand it, and we will not manually grade assignments submitted this way as it is easy to change the files after the submission period ends. You must submit all files listed in the Deliverables section individually to Gradescope as separate files.
7.3 Submission Guidelines
2. You are also responsible for ensuring that what you turned in is what you meant to turn in. After submitting you should be sure to download your submission into a brand new folder and test if it works. No excuses if you submit the wrong files, what you turn in is what we grade. In addition, your assignment must be turned in via Canvas/Gradescope. Under no circumstances whatsoever we will accept any email submission of an assignment. Note: if you were granted an extension you will still turn in the assignment over Canvas/Gradescope.
7.4 Syllabus Excerpt on Academic Misconduct
Academic misconduct is taken very seriously in this class. Quizzes, timed labs and the final examination are individual work.
Homework assignments are collaborative, In addition many if not all homework assignments will be evaluated via demo or code review. During this evaluation, you will be expected to be able to explain every aspect of your submission. Homework assignments will also be examined using computer programs to find evidence of unauthorized collaboration.
You are expressly forbidden to supply a copy of your homework to another student via electronic means. This includes simply e-mailing it to them so they can look at it. If you supply an electronic copy of your homework to another student and they are charged with copying, you will also be charged. This includes storing your code on any site which would allow other parties to obtain your code such as but not limited to public repositories (Github), pastebin, etc. If you would like to use version control, use github.gatech.edu
7.5 Is collaboration allowed?