Homework 7 Recursive Assembly Solution

Overview



In this assignment, you will be implementing several subroutines in assembly, taking advantage of the calling convention that has been outlined in class/lecitation. For each subroutine, you will be required to implement the entire calling convention. This includes the buildup and teardown on the stack.







Instructions



You have been provided three assembly les, string ops.asm, handshake.asm, and buildheap.asm. These les contain a label for each of the subroutines that you will be asked to implement. DO NOT RENAME THE LABELS! You can add more to suit your needs, but don't change the existing ones. Implement the following subroutines, use complx to debug them, and submit your les on Gradescope.







It is in your best interest to do the problems in order. The last one builds on the rst two.




2.1 Part 1: String Operations (20 points)




The rst part of this assignment is to implement a method to count the occurrences of a character in a string. This will utilize the strlen subroutine, which has been implemented for you.




2.1.1 String Length




To help you get started on the homework, we have provided you with the implementation of strlen. It includes the buildup of the stack, body of the function, and teardown of the stack. The pseudocode is provided here for your reference, but you do not have to implement this yourself. You will, however, have to call it from the next subroutine, so make sure you are familiar with how it works.




Pseudocode




int strlen(String s) {




int count = 0;




while (s.charAt(count) != "\0") {




count++;




}




}




2.1.2 Count Character




Complete the count occurrence function in the string ops.asm le. This function should count how many times a given character appears in a string. This method should call the strlen method that you implemented in the previous part.







Pseudocode




int count_occurrence(String s, char c) {




int count = 0;




for (int i = 0; i < strlen(s); i++) {




if (s.charAt(i) == c) {




count++;




}







2



}




return count;




}




2.2 Part 2: Handshaking (30 points)




The second part of this assignment is solving the handshake problem.




Background




With n people at a party, nd the maximum number of handshakes possible given that any two people can only shake each other's hand once. This problem can be easily solved using recursion and the pseudocode for this problem is in the next section!




Pseudocode




int handshake(int n) {




if (n == 0)




return 0;




else




return (n - 1) + handshake(n - 1);




}




2.3 Part 3: Build Heap (50 points)




Background




If you have taken CS 1332 (don't worry if you haven't), then you might be familiar with the data structure known as the binary heap. A binary heap (speci cally a max heap) is essentially a binary tree with the property that for every node, its children are less than or equal to it. This means that the root node of the heap is the largest element. The cool thing about binary heaps is that they can be represented as arrays, where a node at index n has its left child at index 2n + 1 and its right child at index 2n + 2. The goal of the next two problems will be to implement a function that will order an array of elements so that they form a valid heap. While it may help you to know more about binary heaps in order to understand what is going on (you can ready about them at https://www.geeksforgeeks.org/binary-heap/), you don't actually have to know anything about them since we give you the pseudocode.




2.3.1 Heapify (35 points)




The rst subroutine that we will have you implement is heapify. Heapify takes in an array, its length, and a given node i and then ensures that the heap property of a node being larger than its children is maintained for that node. If you have to swap two elements, then heapify recursively re-checks the heap property for child nodes. Once we have implemented, we will be able to call it for every node to actually convert a given array into a heap.




Your job is to implement heapify in the buildheap.asm le, starting at the heapify label.




Heapify Pseudocode




void heapify(int[] arr, int n, int i) {




// The following are all indices, not values






3

int largest = i; // Initialize largest as root int leftChild = 2*i + 1; // left = 2*i + 1 int rightChild = 2*i + 2; // right = 2*i + 2



// If left child is larger than root




if (leftChild < n && arr[leftChild] arr[largest])




largest = leftChild;




// If right child is larger than largest so far




if (rightChild < n && arr[rightChild] arr[largest])




largest = rightChild;




If largest is not root if (largest != i)



{




swap(arr[i], arr[largest]);




Recursively heapify the affected sub-tree



heapify(arr, n, largest);




}




}




2.3.2 Build Heap (15 points)




Once you've implemented heapify, buildheap is easy. All you have to do is start at the end of the array and iterate backwards over each element, calling heapify on each one.




In buildheap.asm, implement the following pseudocode, starting at the buildheap label.




Build Heap Pseudocode




void buildheap(int arr[], int n) {




for (int i = n; i = 0; i--)




heapify(arr, n, i);




}







Deliverables



Please upload the following les onto the assignment on Gradescope:




string ops.asm



handshake.asm



buildheap.asm






Be sure to check your score to see if you submitted the right les, as well as your email frequently until the due date of the assignment for any potential updates.





LC-3 Assembly Programming Requirements



4.1 Overview




Your code must assemble with NO WARNINGS OR ERRORS. To assemble your program, open the le with Complx. It will complain if there are any issues. If your code does not assemble you WILL get a zero for that le.



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.



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 ; if counter == 0 don't loop again




Bad Comment




ADD R3, R3, -1 ; Decrement R3




BRp LOOP ; Branch to LOOP if positive




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 le.



Following from 3. You can randomize the memory and load your program by doing File - Randomize and Load.



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.



Start the stack at xF000. The stack pointer always points to the last used stack location. This means you will allocate space rst, then store onto the stack pointer.



Do NOT execute any data as if it were an instruction (meaning you should put . lls after HALT or RET).



Do not add any comments beginning with @plugin or change any comments of this kind.



Test your assembly. Don't just assume it works and turn it in.



4.2 LC-3 Calling Convention Guide




A handy assembly guide written by Kyle Murray (RIP) follows on the next page:


Rules and Regulations



5.1 General Rules




Starting with the assembly homeworks, any code you write must be meaningfully commented. You should comment your code in terms of the algorithm you are implementing; we all know what each line of code does.



Although you may ask TAs for clari cation, you are ultimately responsible for what you submit. This means that (in the case of demos) you should come prepared to explain to the TA how any piece of code you submitted works, even if you copied it from the book or read about it on the internet.



Please read the assignment in its entirety before asking questions.



Please start assignments early, and ask for help early. Do not email us the night the assignment is due with questions.



If you nd 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.



5.2 Submission Conventions




All les you submit for assignments in this course should have your name at the top of the le as a comment for any source code le, and somewhere in the le, near the top, for other les unless otherwise noted.



When preparing your submission you may either submit the les individually to Canvas/Gradescope or you may submit an archive (zip or tar.gz only please) of the les. You can create an archive by right clicking on les and selecting the appropriate compress option on your system. Both ways (uploading raw les or an archive) are exactly equivalent, so choose whichever is most convenient for you.



Do not submit compiled les, that is .class les for Java code and .o les for C code. Only submit the les we ask for in the assignment.



Do not submit links to les. The autograder does not understand it, and we will not manually grade assignments submitted this way as it is easy to change the les after the submission period ends.



5.3 Submission Guidelines




You are responsible for turning in assignments on time. This includes allowing for unforeseen circum-stances. If you have an emergency let us know IN ADVANCE of the due time supplying documenta-tion (i.e. note from the dean, doctor's note, etc). Extensions will only be granted to those who contact us in advance of the deadline and no extensions will be made after the due date.



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 les, 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.



There is a 6-hour grace period added to all assignments. You may submit your assignment without penalty up until 11:55PM, or with 25% penalty up until 5:55AM. So what you should take from this is not to start assignments on the last day and plan to submit right at 11:54AM. You alone are responsible for submitting your homework before the grace period begins or ends; neither Canvas/Gradescope, nor
your aky internet are to blame if you are unable to submit because you banked on your computer working up until 11:54PM. The penalty for submitting during the grace period (25%) or after (no credit) is non-negotiable.




5.4 Syllabus Excerpt on Academic Misconduct




Academic misconduct is taken very seriously in this class. Quizzes, timed labs and the nal 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 nd evidence of unauthorized collaboration.




What is unauthorized collaboration? Each individual programming assignment should be coded by you. You may work with others, but each student should be turning in their own version of the assignment. Submissions that are essentially identical will receive a zero and will be sent to the Dean of Students' O ce of Academic Integrity. Submissions that are copies that have been super cially modi ed to conceal that they are copies are also considered unauthorized collaboration.




You are expressly forbidden to supply a copy of your homework to another student via elec-tronic 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




5.5 Is collaboration allowed?




Collaboration is allowed on a high level, meaning that you may discuss design points and concepts relevant to the homework with your peers, share algorithms and pseudo-code, as well as help each other debug code. What you shouldn't be doing, however, is pair programming where you collaborate with each other on a single instance of the code. Furthermore, sending an electronic copy of your homework to another student for them to look at and gure out what is wrong with their code is not an acceptable way to help them, because it is frequently the case that the recipient will simply modify the code and submit it as their own. Consider instead using a screen-sharing collaboration app, such as http://webex.gatech.edu/, to help someone with debugging if you're not in the same room.