Part $2.$ The Stack

In this part of the assignment, you are given the file stack.asm, containing simple procedures to compare the digit sum of two integers. The details of the algorithm in the procedures are irrelevant to the assignment, but you are free to investigate and understand the algorithm used.

Your task is to save and retrieve any necessary registers on the stack. Note that the procedure PROC$\_$GREATER$\_$DIGIT$\_$SUM calls the procedure PROC$\_$ADD$\_$DIGITS. Thus, it is necessary to save any caller$-$saved registers used in the caller before calling a procedure, and restore the saved registers after the call to the procedure.

Specification

Your solution must follow the following specification:

$1.$ You are only allowed to use following instructions: addi, lw$,$ sw$.$

$2.$ You are only allowed to write assembly code within the block delimited by comments containing the words START EDITING HERE and END EDITING HERE. There are $4$ such blocks in the file stack.asm.

$3.$ Do not modify any other line in the file. Do not modify the lines containing START EDITING HERE and END EDITING HERE. Failure to follow the instructions will result in a grade penalty.

$.$data

$.$text

$.$globl PROC$\_$GREATER$\_$DIGIT$\_$SUM

$.$globl PROC$\_$ADD$\_$DIGITS

# $-----------------------------------------------------------------------------$

# Given two positive integers, return the integer with the greater digit sum.

# The digit sum of an integer is the sum of its digits, ie$.$

# digit$\_$sum$(432)==9$

# If they have equal digit sums, return $-1$

#

# Pre:

# $-$ $a$0$ contains the first positive integer

# $-$ $a$1$ contains the second positive integer

# Post:

# $-$ $a$0$ contains the integer with the greater digit sum

# $-----------------------------------------------------------------------------$

PROC$\_$GREATER$\_$DIGIT$\_$SUM:$$

# $--$ START EDITING HERE $--$

# $--$ END EDITING HERE $--$

addi s$0,$ a$0,0$ # Save the first integer

addi s$1,$ a$1,0$ # Save the second integer

# Sum digits of first integer and save to t$0$

addi a$0,$ s$0,0$

jal ra$,$ PROC$\_$ADD$\_$DIGITS

addi t$0,$ a$0,0$

# $--$ START EDITING HERE $--$

# $--$ END EDITING HERE $--$

# Sum digits of second integer and save to t$1$

addi a$0,$ s$1,0$

jal ra$,$ PROC$\_$ADD$\_$DIGITS

addi t$1,$ a$0,0$

# $--$ START EDITING HERE $--$

# $--$ END EDITING HERE $--$

# Assume the first integer has the greater digit sum

addi a$0,$ s$0,0$

# Check our assumption

beq t$0,$ t$1,$ PROC$\_$GDS$\_$EQUAL

blt t$0,$ t$1,$ PROC$\_$GDS$\_$SECOND$\_$INTEGER$\_$GREATER

j PROC$\_$GDS$\_$EXIT

PROC$\_$GDS$\_$EQUAL:

li a$0,-1$

j PROC$\_$GDS$\_$EXIT

PROC$\_$GDS$\_$SECOND$\_$INTEGER$\_$GREATER:

addi a$0,$ s$1,0$

PROC$\_$GDS$\_$EXIT:

# $--$ START EDITING HERE $--$

# $--$ END EDITING HERE $--$

jr ra$,0$

# $-----------------------------------------------------------------------------$

# Given a positive integer, return the sum of its digits.

#

# Pre:

# $-$ $a$0$ contains the positive integer

# Post:

# $-$ $a$0$ contains the integer's digit sum

# $-----------------------------------------------------------------------------$

PROC$\_$ADD$\_$DIGITS:

li t$0,0$ # Accumulator

li t$1,10$ # Constant $10$ for divrem

li t$2,0$ # Temporary to store rem result

PROC$\_$AD$\_$LOOP:

rem t$2,$ a$0,$ t$1$

add t$0,$ t$0,$ t$2$

ble a$0,$ t$1,$ PROC$\_$AD$\_$EXIT

div a$0,$ a$0,$ t$1$

j PROC$\_$AD$\_$LOOP

PROC$\_$AD$\_$EXIT:

addi a$0,$ t$0,0$

jr ra$,0$