MIPS hermite stack example use

Question

I'm stuck on a stack. I have to call to a function in mips-32 assembly code, in which I have to evaluate a Hermite polynomial just by giving the n and the x as parameters. It must be done using recursion.

I've tried to set 2 base cases H0 and H1, using them both at the same time, but I can't identify the sequence and the pile draw that makes the code clear.

Follows the code:

li $t2,2

recursive_hermite: #H(n,x,___,___)      
        bge     $a0,$t5,more_than_2         
        ####    base
        ####    case

         jr $ra ##<--- this takes us to the operation of the value
    more_than_2:

        ## here you are supposed to store the values on stack 
        ##     (such as return address and n values)

      addi $a0,$a0,-1         ##you must decrease n (or increase I'm not sure)
      jal recursive_hermite   ##once they are stored, you just recall  

    ### operations of value



    ## $f12 must contain the whole value
    jr $ra         ####this one returns to the main

Does anyone know how to solve this problem?

Answer 1

I see you are in trouble. Judging the way you wrote the question it seems like your assigment is due tomorrow, so we have to work things fast.

You remind me of myself 20 years back, good old times when c++ was just being born and assembly was all the rage. I have heard of those cringy MIPS emulators like QTspim, you should avoid them and work like a real man with some real handy hardware.

Here is my tip: you have to store the partial results of the polinomials tested in every recursion. To do that you have to control time and space, which have to be perfectly balanced like all things should be.

If I was you I would start working in your step by step execution of the program so you can check what the register values are.

It is dangerous to go alone, take this:

    .data

  #COMPUTER PRINCIPLES UNIVERSITY OF MACANDCHESTER
  #PRACTIC 5: HERMITE POLINOMYALS CALCULUS
  #JACK ROBERTS II


  userInput:    .space  700
  empty:   .asciiz "Input is empty."
   long:    .asciiz "Input is too long."
  invalid: .asciiz "Invalid base-33 number."

.text

ErrorLong:
#prints message for input that is too long
  la $a0, long
  li $v0, 4
  syscall
  j end

ErrorInvalid:
#prints message for invalid input
  la $a0, invalid
  li $v0, 4
  syscall
  j end

ErrorEmpty:
#prints message for empty string
  la $a0, empty
  li $v0, 4
  syscall
  j end

.globl main

main:
  li $v0, 8
  la $a0, userInput
  li $a1, 200
  syscall

Rid:
#takes care of leading spaces
li $t9, 32 # space
lb $t8, 0($a0)
beq $t9, $t8, Character
move $t8, $a0
j length

Character:
addi $a0, $a0, 1
j Rid

#takes care of length
length:
addi $t0, $t0, 0
addi $t1, $t1, 10
add $t2, $t2, $a0

#itertates through the array
traverse:
lb $s2, 0($a0)
beqz $s2, discovered
beq $s2, $t1, discovered
addi $a0, $a0, 1
addi $t0, $t0, 1
j traverse

#busted empty space or input that violates limit
discovered:
#if it's empty go to case for empty which outputs 
beqz $t0, ErrorEmpty
slti $t4, $t0, 5
#if it's too long, go to case for too long and print 
beqz $t4, ErrorLong
move $a0, $t2
#go to next verification process
j verify

#Comenzamos a calcular H0
verify:
lb $s3, 0($a0)  #loads address here
beqz $s3, initial
beq $s3, $t1, initial
slti $t3, $s3, 48                 #invalid for anything below 0
bne $t3, $zero, ErrorInvalid
slti $t3, $s3, 58                 #legal input for everything less than or equal to 9
bne $t3, $zero, Move
slti $t3, $s3, 65                 #legal input for everything less than or equal to 65,  'a'
bne $t3, $zero, Move
slti $t3, $s3, 88                 #legal input for anything less than or equal to 88
bne $t3, $zero, Move
slti $t3, $s3, 97                 # invalid input, not numerical nor alphabetical
bne $t3, $zero, ErrorInvalid
slti $t3, $s3, 120                #legal input for lower case characters
bne $t3, $zero, Move
bgt $s3, 119, ErrorInvalid   # illegal input, out of range

#now I iterate again, this time to check for invalid input
Move:
addi $a0, $a0, 1 #iterates
j verify #goes to verification point

#first step of conversion, does the prerequisite work for translation 
initial:
move $a0, $t2  #moves content
addi $t5, $t5, 0  #$t5 has 0 now
add $s0, $s0, $t0  
addi $s0, $s0, -1 #decrement    
#aqui empieza lo bueno

Must:
addi $sp, $sp, -16
sw $ra, 0($sp)
sw $ra, 4($sp)
sw $ra, 8($sp)
sw $ra, 12($sp)
jal Must

ExitMust:

lw  $ra,16($sp)
lw $s4, 3($sp) 
lw $s5, 2($sp)
lw  $s6, 1($sp)
lw $s1, 0($sp)

jr $ra   #return

#li $s4, 3  #each digit
#li $s5, 2
#li $s6, 1
#li $s1, 0

translate:
lb $s7, 0($a0)   #loads digits
beqz $s7, final  #final conversion step
beq $s7, $t1, final #if branch statement is true, move to final conversion statement
slti $t3, $s7, 58  #checks for less than or equal to 58
bne $t3, $zero, Base  #OK to move forward if $t3 is not null
slti $t3, $s7, 88  #max for upper
bne $t3, $zero, Mari  #OK to go to conversion of upper characters if $t3 is not null
slti $t3, $s7, 120     #max for lower
bne $t3, $zero, Mici #OK to go to conversion of lower characters if $t3 is not null

Base:
addi $s7, $s7, -48  #conversion for regular numbers
j row

Mari:
addi $s7, $s7, -55  #conversion for upper case
j row

Mici:
addi $s7, $s7, -87  #conversion for lower case

row:  #determines which digit needs to be converted
beq $s0, $s4, one  
beq $s0, $s5, two
beq $s0, $s6, three
beq $s0, $s1, last

#first character
one:
li $t6, 35937   #values to multiply by for the power of 3
mult $s7, $t6
mflo $t7
add $t5, $t5, $t7
addi $s0, $s0, -1
addi $a0, $a0, 1
j translate

#second character
two:
li $t6, 1089   #values to multiply by for the power of 2
mult $s7, $t6
mflo $t7
add $t5, $t5, $t7
addi $s0, $s0, -1
addi $a0, $a0, 1
j translate

#third character
three:
li $t6, 33   #values to multiply by for the power of 1
mult $s7, $t6
mflo $t7
add $t5, $t5, $t7
addi $s0, $s0, -1
addi $a0, $a0, 1
j translate

#fourth character
last:
li $t6, 1    #values to multiply by for the power of 0
mult $s7, $t6
mflo $t7
add $t5, $t5, $t7
#no more need to go back to translation step


final:                  #final step
li $v0, 1
move $a0, $t5  #moves content to $a0 so it can be printed
syscall

#last system call of the program will end program
end:   #prints result
 li $v0, 10

Hope it helps, if you need, ask for further explanation here, its been directly taken out of my Final grade Work, and in my Masters.

PD: It is licensed under the GPL, so be careful on what you do with it, FBI might be looking for you. Love :)