MIPS Assembly - how to calculate the square of n recursively

Question

I want to write a program that calculates the square of n using recursion based on the equation n^2 = (n - 1)^2 + 2(n - 1) + 1 But I don't know how to write the nonbasecase: part. Can anyone help?

A python program would be

def square(n) {
    if (n==0):
        return 0
    else:
        return square(n-1) + 2*(n-1) + 1 
}

Here is what I got so far.

start:      
        li  $a0, 0x0003     #$a0 contains the number to be squared              
        jal square          # recursive call
        
square:     
        subi $sp, $sp, 8    # decrement the stack pointer $sp
        sw  $ra, 4($sp)     # push the return address register $ra
        sw  $a0, 0($sp)     # push argument register $a0
        li  $t0, 0x0001     # load $t0 with 1 as part of test for base case
        bne $a0, $t0, nonbasecase   # branch if not the base case
        li $v0, 0x0001      # return base result in $v0
        addi $sp, $sp 8     # recover stack space 
        jr $ra          # jump to return address in $ra

nonbasecase:    
       #not sure how to write when it is not the base case


        jr $ra          # jump to contents of return address register $ra

Answer 1

Write the function so that it inputs n2 and n and returns n2+2*n+1 and n+1.