Mips: function trouble - function

Question

Trying to create a function that so that f(0) = 8, and f(n) = 4f(n-1) - n + 5 if n > 0 recursively, but unable to get it to function correctly
# $a0 = inpyt
# $v0 = return value
f: bnez $a0, greaterthan0
li $v0, 8
jr $ra
greaterthan0: addi $sp,$sp,-8
sw $ra, 0($sp)
sw $a0,4($sp)
sub $t3,$a0,1 # n-1=n
jal f
lw $ra, ($sp)
lw $a0, 4($sp)
addi $sp,$sp,8
sll $t0,$t3,2 # mul n-1 by 4
sub $t1,$t0,$t3
addi $t2,$t1,5 # add 5 to n
jr $ra

Answer 1

There are a few problems here.
The first problem here is that you are not following the convention that you have set out by passing the input in $a0 and returning the value in $v0.
To fix this, change sub $t3,$a0,1 # n-1=n to sub $a0,$a0,1 # n-1=n
and addi $t2,$t1,5 # add 5 to n to addi $v0,$t1,5 # add 5 to n.
Next there are some math errors in which variables you picked to evaluate f(n-1) - n + 5.
First, the comment mul n-1 by 4 is fundamentally wrong as we in fact want to multiple f(n-1) by 4. After the recursive call returns, the value of f(n-1) is of course stored in $v0.
Below is my fix:
# $a0 = inpyt
# $v0 = return value
f: bnez $a0, greaterthan0
li $v0, 8
jr $ra
greaterthan0: addi $sp,$sp,-8
sw $ra, 0($sp)
sw $a0,4($sp)
sub $a0,$a0,1 # n=n-1
jal f
lw $ra, 0($sp)
lw $a0, 4($sp)
addi $sp,$sp,8
sll $t0,$v0,2 # mul f(n-1) by 4
sub $t1,$t0,$a0
addi $v0,$t1,5 # add 5 to n
jr $ra