I am trying to write a MIPS program that will convert a roman numeral (entered as a string of ascii characters) into its decimal value. There's an I/0 component in that the user is prompted for an input, (limited) validity checks are performed, and then the original string, along with the value is output.
To convert each roman numeral character to its decimal value, I've used a lookup table (i.e. I get the index of each char in a "roman numeral" array, and then use this index value to get the corresponding value from the "decimal values" array.
Roman numerals are read from L to R, but I cannot simply add each character (i.e. make the sum purely recursive) because it is possible to have a string like this: XIV, where X = 10, I = 1, and V= 5, and the resulting number = 14 (as opposed to 15). I have logic in place to output this result, but (unfortunately!), I am new to MIPS and to implement the sum logic, I've set up a series of nested sub-routines.
I understand that for a sub-routine that is not arrived at via a "jal" instruction to "know" its return address, you should load the return address on the stack, and pop it at the end of the sub-routine, and then jr $ra. However, some of the math logic in my code relies on branches, rather than "jal" instructions. Somewhere in all this mess, my stack pointers are incorrect, and my code terminates too soon (i.e. doesn't sum all of the digits in the string).
Any help or pointers would be appreciated. Code is below:
# This program runs in MIPS, and performs the following functions:
#
# (1) Reads input Roman Numerals as ASCII text characters
#
# (2) Calculates the equivalent decimal value
#
# (3) Writes the calculated value as Arabic numerals to the SPIM
# console, with appropriate commentary text
#
# (4) Tests by calculating the values of these Roman numerals:
# {I:1, V:5, X:10, L:50, C:100, D:500, M:1000}
#
# (5) Calculates and displays the results of the following Roman numerals:
# -> LXXIX: 79
# -> MMXVI: 2016
# -> MCMXLVIII: 1948
# -> MDCCCCVIIII: 1909
#
# NOTE: There is no check for "valid" Roman numerals (i.e., VIIII is not "valid" but will be computed as = 9)
# However, subtraction logic is used (i.e. numbers that decrease from L to R = addition; a smaller number to the left
# of a larger number represents subtraction, such that IX == VIIII == 9.
.data
# Lookup tables
#roman: .asciiz "IVXLCDMivxlcdm"
roman: .asciiz "IVXLCDM"
#values: .byte 1, 5, 10, 50, 100, 500, 1000, 1, 5, 10, 50, 100, 500, 1000
values: .byte 1, 5, 10, 50, 100, 500, 1000
# Input
input1: .word 4
input2: .asciiz "\n "
input3: .asciiz "\n "
input4: .asciiz "\n"
# Conversion
left: .word 0
sum: .word 0
counter: .word 0
temp: .word 0
# I/O and program control
convertAgain: .word 2
prompt1: .asciiz "\nPlease enter the Roman Numeral to convert in all uppercase OR all lowercase letters (i.e. VII or vii): "
outRecap: .asciiz "\nYou entered: "
outFinal: .asciiz "\nThe equivalent decimal value is: "
loopdriver: .asciiz "\nWould you like to convert another number? Enter 1 for YES and 2 for NO: "
stop: .asciiz "\n\nProgram complete.\n"
# Exception handling
error1: .asciiz "\nThe Roman numeral you have entered contains invalid character(s). Please try again.\n"
################################################################################
.text
.globl main
main:
#Prompt user to enter the Roman Numeral to convert
li $v0, 4 # print prompt1
la $a0, prompt1 # load address
syscall
# Load the word reserved for input, and read in the Roman Numeral string input by the user
la $a0, input1 # load contents of input1 (i.e. space allocated to save the input string) into $a0
la $a1, input1 # load the length allocated for input1 (i.e. 4 bytes or 32 bits) into $a1 to prevent overflow
li $v0, 8 # read string from user
syscall
# Go to sub-routines for lookup and conversion
jal init
# Display results for the user
# Load output string 1 to show the user their original input string
la $a0, outRecap # load contents of outRecap into $a0
li $v0, 4 # print string
syscall
# Load the string the user entered
la $a0, input1 # load contents of input1 into $a0
li $v0, 4 # print string
syscall
# Display the equivalent decimal value
la $a0, outFinal # load contents of outFinal (string) into $a0
li $v0, 4 # print string
syscall
# Print the sum
lw $a0, sum
li $v0,1
syscall
# Ask the user whether they want to convert another Roman Numeral (1 if YES; 2 if NO; default is NO)
la $a0, loopdriver
li $v0, 4
syscall
# Get user input from keyboard (1 = they want to convert another Roman Numeral; 2 = Exit; default = 2)
li $v0, 5 # read integer input
syscall
# Save the user's input and jump to "Exit"
sw $v0, convertAgain
lw $t0, convertAgain
bne $t0, 1, Exit # if the user enters a number != 1, go to Exit
j main # Go back to start if the user enters 1
######################################################################################################################################################
# Convert Roman Numeral string to integer decimal value
init:
sw $ra, 4($sp)
sw $a1, 0($sp)
addi $sp, $sp, -8 # move stack pointer
la $t2, input1 #load the address of the string (see by looking at starting index of each the length of each string
la $t3, roman
la $t4, values
# Loop through each char of the input string
loop1:
lb $a0, ($t2) # This gets the next byte of the string (from L to R); change the offset to get others (i.e. lb $a0, 3($t0) = I
beqz $a0, return # If the byte == 0, we have reached the end of the input string; jump to "return"
li $v0, 11 # print byte to console
syscall
# While string[i] != null:
jal index
addi $t2, $t2, 1 # Move to next character in input string
jal loop1 # iterate through loop1 again
# Find the index (i.e. offset) of the selected char in the "roman" lookup table
index:
lb $t5, ($t3) # load the first byte of romans
beqz $t5, invalid # if we reach the end of romans and the char isn't found, it's not a valid Roman numeral
sw $ra, 8($sp)
addi $sp, $sp, -4 # move stack pointer
beq $a0, $t5, getVal # once we find the index we want, where the romans value matches our char, need to look it up in values
jal iter # if we haven't found a match, jump to where we can increment $t3 and iterate through the loop again
# addi $t3, $t3, 1 # if we haven't found a match, increment $t3 and iterate through the loop again
# jal index # loop
# Use the index value to look up the char in the "values" array and get the decimal value
getVal:
la $t6, roman # Get the address of the array containing Roman numeral characters
la $t7, values
sub $t8, $t3, $t6 # Get the index value of the element that matches the byte we are working with [1:7]
add $t7, $t7, $t8
lb $t9, ($t7) # $t9 is the decimal value that corresponds to the letter
#added new
sw $t9, 12($sp)
addi $sp, $sp, -4 # move stack pointer
jal setup
addi $sp, $sp, 4 # reset the stack pointer
lw $ra, 8($sp) # fetch return address
jr $ra # go back to main so that results can be displayed
# This is the last part of the index loop
iter:
addi $t3, $t3, 1 # if we haven't found a match, increment $t3 and iterate through the loop again
jal index # loop
setup:
# Base case is that the string length == 1, and thus sum = the decimal equivalent of the only Roman numeral character
lw $s0, sum
beqz $s0, base # if sum == 0, this is our first pass through the loop, and we just want to add the first char's decimal value to sum and return to get the next char
jal calcSum
# Base case is our first pass through the loop, where sum == 0. We just want to add the value of the first number in the string to sum, and return to loop1 to get next char.
base: #lw $s0, sum
add $s0, $s0, $t9
sw $s0, sum
la $t3, roman
addi $sp, $sp, 4 # reset the stack pointer
lw $ra, 16($sp) # fetch return address
jr $ra # go back
#j return
# Here, we want to pop the previous letter's decimal value off the stack, compare it to current, process sum accordingly, and pop the current char onto the stack for the next iteration
calcSum: addi $sp, $sp, 8 #reset the stack pointer
lw $ra, 16($sp)
lw $t1, 12($sp) # pop the decimal value of the Roman numeral to the left of the current value in the original string
la $t3, roman
bge $t1, $t9, plus # If the decimal value of the previous char in the string is >= the current char, then we can add the current char to the sum
blt $t1, $t9, minus # if the decimal value of the previous char in the string is < the current char, we should add: current - (2*previous) to the sum
plus: lw $s0, sum
add $s0, $s0, $t9
la $t3, roman
addi $sp, $sp, 4 # reset the stack pointer
lw $ra, 16($sp) # fetch return address
jr $ra # go back
minus: lw $s0, sum
mul $t1, $t1, 2
sub $t9, $t9, $1
add $s0, $s0, $t9
la $t3, roman
addi $sp, $sp, 4 # reset the stack pointer
lw $ra, 16($sp) # fetch return address
jr $ra # go back to
# Go back to main
return:
addi $sp, $sp, 8 # reset the stack pointer
lw $a0, 0($sp) #
lw $ra, 4($sp) # fetch return address
jr $ra # go back to main so that results can be displayed
#Exception handling: User input string contains invalid character(s)
invalid:
li $v0, 4 # print string
la $a0, error1 # load address for error1 (a string)
syscall
j main
###############################################################################
#System Exit
Exit:
# Display exit message
li $v0, 4 # print string
la $a0, stop # load address for stop (a string)
syscall
li $v0, 10
syscall
################################################################################
Edit: after a lot of debugging, I managed to get this working. Code is below, in case anyone else has a similar problem, or can give feedback/pointers on how to improve this. Some things I learned: jal instructions need stack pointers above and below the sub-routine call. Bytes weren't a great choice for storing my decimal values, since 500 and 1000 are out of range (both signed and unsigned), and I had to deal with them as special cases.
.data
# Lookup tables
roman: .asciiz "IVXLCDM"
values: .byte 1, 5, 10, 50, 100, 500, 1000
# Input
input1: .word 4
input2: .asciiz "\n "
input3: .asciiz "\n "
input4: .asciiz "\n"
# Conversion
left: .word 0
sum: .word 0
# I/O and program control
convertAgain: .word 2
prompt1: .asciiz "\nPlease enter the Roman Numeral to convert in all uppercase letters (i.e. VII): "
outRecap: .asciiz "\nYou entered: "
outFinal: .asciiz "\nThe equivalent decimal value is: "
loopdriver: .asciiz "\nWould you like to convert another number? Enter 1 for YES and 2 for NO: "
stop: .asciiz "\n\nProgram complete.\n"
# Exception handling
error1: .asciiz "\nThe Roman numeral you have entered contains invalid character(s). Please try again.\n"
######################################################################################################################################################
.text
.globl main
main:
#Prompt user to enter the Roman Numeral to convert
li $v0, 4 # Print prompt1
la $a0, prompt1 # Load address
syscall
# Load the word reserved for input, and read in the Roman Numeral string input by the user
la $a0, input1 # Load contents of input1 (i.e. space allocated to save the input string) into $a0
la $a1, input1 # Load the length allocated for input1 (i.e. 4 bytes or 32 bits) into $a1 to prevent overflow
li $v0, 8 # Read string from user
syscall
sw $ra, 0($sp) # Push return address onto the stack
addi $sp, $sp, -4 # Move stack pointer
# Go to sub-routines for lookup and conversion
jal init
lw $ra, 0($sp) # Pop return address off the stack
addi $sp, $sp, 4 # Move stack pointer
# Display results for the user
display:
# Load output string 1 to show the user their original input string
la $a0, outRecap # load contents of outRecap into $a0
li $v0, 4 # print string
syscall
# Load the string the user entered
la $a0, input1 # load contents of input1 into $a0
li $v0, 4 # print string
syscall
# Display the equivalent decimal value
la $a0, outFinal # load contents of outFinal (string) into $a0
li $v0, 4 # print string
syscall
# Print the sum
lw $a0, sum # Load contents of sum into $a0
li $v0,1 # Print integer
syscall
# Ask the user whether they want to convert another Roman Numeral (1 if YES; 2 if NO; default is NO)
la $a0, loopdriver # Load contents of loopdriver (string) into $a0
li $v0, 4 # Print string
syscall
# Get user input from keyboard (1 = they want to convert another Roman Numeral; 2 = Exit; default = 2)
li $v0, 5 # Read integer input
syscall
# Save the user's input and jump to "Exit"
sw $v0, convertAgain
lw $t0, convertAgain
bne $t0, 1, Exit # if the user enters a number != 1, go to Exit
move $s0, $zero # Reinitialize
sw $zero, sum # Reinitialize
sw $zero, left # Reinitialize
j main # Go back to start if the user enters 1
######################################################################################################################################################
# Convert Roman Numeral string to integer decimal value
init:
#sw $ra, 4($sp)
sw $a1, 4($sp)
addi $sp, $sp, -4 # move stack pointer
la $t2, input1 #Load the address of the string (see by looking at starting index of each the length of each string
la $t3, roman # Load the address of the roman lookup table into $t3
la $t4, values # Load the address of the decimal lookup table into $t4
# Loop through each char of the input string
loop1:
lb $a0, ($t2) # This gets the next byte of the string (from L to R); change the offset to get others (i.e. lb $a0, 3($t0) = I
beq $a0, 10, return # If the ascii char == 0, we have reached the end of the input string; jump to "return"
beq $a0, 1, return # If the ascii char == 1, we've reached the "start of heading" (i.e. end of line; max = 12 char)
#li $v0, 11 # print byte to console
#syscall
sw $ra, 8($sp) # Push return address onto the stack
addi $sp, $sp, -4 # Move stack pointer
# While string[i] != null:
jal index
lw $ra, 8($sp) # Pop return address off stack
addi $sp, $sp, 4 # Move stack pointer
addi $t2, $t2, 1 # Move to next character in input string
sw $ra, 8($sp) # Push return address onto the stack
addi $sp, $sp, -4 # Move stack pointer
jal loop1 # iterate through loop1 again
lw $ra, 8($sp) # Pop return address off the stack
addi $sp, $sp, 4 # Move stack pointer
# Find the index (i.e. offset) of the selected char in the "roman" lookup table
index:
lb $t5, ($t3) # Load the first byte of romans
beqz $t5, invalid # If we reach the end of romans && char !found, INVALID char
beq $a0, $t5, getVal # When char == element in romans table, branch to getVal to look it up in decimal table
sw $ra, 12($sp) # Push return address onto the stack
addi $sp, $sp, -4 # Move stack pointer
jal iter # If we haven't found a match, jump to where we can increment $t3 and iterate through the loop again
lw $ra, 12($sp) # Pop return address off the stack
addi $sp, $sp, 4 # Move stack pointer
getVal:
la $t6, roman # Get the address of the array containing Roman numeral characters
la $t7, values
sub $t8, $t3, $t6 # Get the index value of the element that matches the byte we are working with [1:7]
add $t7, $t7, $t8
lbu $t9, ($t7) # $t9 is the decimal value that corresponds to the letter
bgeu $t9, 232, adjust1
j afterGV
adjust1:
seq $a2, $t5, 68 # If the character in question == D, set $a2 to 1; else, 0
mul $t9, $t9, $zero
beq $a2, 1, adjustD
addi $t9, $t9, 1000 # Char == M; decimal value = 1000
j afterGV
adjustD: addi $t9, $t9, 500
j afterGV
afterGV: sw $ra, 16($sp)
addi $sp, $sp, -4 # move stack pointer
jal setup
addi $sp, $sp, 4 # reset the stack pointer
lw $ra, 16($sp) # Pop return address off stack
# lw $t9, 12($sp) # fetch $t9
jr $ra # go back
# This is the last part of the index loop
iter:
addi $t3, $t3, 1 # if we haven't found a match, increment $t3 and iterate through the loop again
jal index # loop
# Prepare to compare current char w/previous char (i.e. if string is XI, compare I to X)
setup:
# Base case is that the string length == 1, and thus sum = the decimal equivalent of the only Roman numeral character
lw $s0, sum # Load sum into $s0
beqz $s0, base # If sum == 0, this is our first pass through the loop, and we just want to add the first char's decimal value to sum and return to get the next char
sw $ra, 20($sp) # Push return address onto stack
addi $sp, $sp, -4 # Move stack pointer
jal calcSum # Jump to subroutine that calculates the sum
addi $sp, $sp, 4 # Reset the stack pointer
lw $ra, 20($sp) # Pop return address off stack
jr $ra # Go back to return address
# Base case is our first pass through the loop, where sum == 0.
# We just want to add the value of the first number in the string to sum, and return to loop1 to get next char.
base: add $s0, $s0, $t9 # Add value of first char + 0 and store in $s0
sw $s0, sum # Store contents of $s0 in sum
sw $t9, left # Store contents of $t9 (i.e. current char) as "left" for use in next iteration
la $t3, roman # Load address of roman array into $t3 (reset pointer)
addi $t2, $t2, 1 # Add 1 to $t2, so that we can select next char in input string
jal loop1 # Jump back to beginning of loop
# Compare current char to previous, and calculate sum accordingly, per rules of Roman Numerals
calcSum: addi $sp, $sp, 8 # Reset the stack pointer
lw $t1, left # Pop the decimal value of the Roman numeral to the left of the current value in the original string
sw $t9, left # Reset left pointer so it points to current char ("left" of *next* char)
la $t3, roman # Load address of roman array into $t3 (reset pointer)
bge $t1, $t9, plus # If value of the previous char >= current char, then add the current char's value to the sum
blt $t1, $t9, minus # If the previous char in the string is < the current char, add: current - (2*previous) to the sum
plus: lw $s0, sum # Load sum into $s0
add $s0, $s0, $t9 # Add current char's decimal value to sum
sw $s0, sum # Store the result in sum
la $t3, roman # Load address of roman array into $t3 (reset pointer)
addi $t2, $t2, 1 # Add 1 to $t2, so that we can select next char in input string
jal loop1 # Jump back to beginning of loop
minus: lw $s0, sum # Load sum into $s0
mul $t1, $t1, 2 # Multiply $1 by 2 (need to subtract twice, to get a net impact of -1 * $t1)
sub $t9, $t9, $t1 # Subtract (previous char - (2* current char)) (i.e. if XIV, do 11 + (5-(2*1)) = 14)
add $s0, $s0, $t9 # Add this result to the existing sum
sw $s0, sum # Store the result in sum
la $t3, roman # Load address of roman array into $t3 (reset pointer)
addi $t2, $t2, 1 # Add 1 to $t2, so that we can select next char in input string
jal loop1 # Jump back to beginning of loop
# Go back to main
return:
sw $s0, sum # Store sum
j display # Jump to display to print output for the user
#Exception handling: User input string contains invalid character(s)
invalid:
li $v0, 4 # Print string
la $a0, error1 # Load address for error1 (a string)
syscall
j main
######################################################################################################################################################
#System Exit
Exit:
# Display exit message
li $v0, 4 # Print string
la $a0, stop # Load address for stop (a string)
syscall
li $v0, 10 # System exit
syscall
######################################################################################################################################################