Recursive function in assembly in ARM Architecture

Introduction

Recursion lets a function call itself to solve smaller parts of a problem. In assembly, it helps break down complex tasks step-by-step.

Calculating factorial of a number where the problem breaks down into smaller factorials

Traversing tree-like data structures where each node leads to smaller subtrees

Solving problems like Fibonacci numbers where each result depends on previous results

Implementing algorithms like quicksort or mergesort that divide data into smaller parts

When a problem naturally fits a divide-and-conquer approach requiring repeated function calls

Core Concept

ARM Architecture

/* ARM Assembly Recursive Function Template */

.global recursive_function
recursive_function:
    push {lr}              /* Save return address */

    /* Base case check */
    cmp r0, #0             /* Compare input parameter in r0 with 0 */
    beq base_case          /* If zero, jump to base case */

    /* Recursive case */
    sub r0, r0, #1         /* Decrement parameter */
    bl recursive_function  /* Recursive call */

    /* Process after recursive call */
    /* ... your code ... */

    pop {pc}               /* Return from function */

base_case:
    /* Base case code here */
    mov r0, #1             /* Example: return 1 */
    pop {pc}               /* Return from function */

The function uses push {lr} to save the return address before calling itself.

The base case stops the recursion to avoid infinite calls.

Key Points

This example shows a factorial function using recursion. It saves the return address, checks the base case, calls itself with n-1, then multiplies the result.

ARM Architecture

/* Example: Factorial function in ARM assembly */

.global factorial
factorial:
    push {lr}              /* Save return address */
    cmp r0, #0             /* Check if n == 0 */
    beq factorial_base     /* If yes, base case */

    sub r0, r0, #1         /* n = n - 1 */
    bl factorial           /* Recursive call factorial(n-1) */

    mul r0, r0, r1         /* Multiply result by n (stored in r1) */
    pop {pc}               /* Return */

factorial_base:
    mov r0, #1             /* factorial(0) = 1 */
    pop {pc}               /* Return */

This shows handling the edge case where the input is zero, immediately returning a value without further recursion.

ARM Architecture

/* Edge case: Recursive call with parameter 0 */

.global test_zero

test_zero:
    push {lr}
    cmp r0, #0
    beq base_case
    /* Recursive call if not zero */
    sub r0, r0, #1
    bl test_zero
    pop {pc}

base_case:
    mov r0, #42  /* Return a fixed value for base case */
    pop {pc}

This example handles the case when the input is 1, stopping recursion and returning a value.

ARM Architecture

/* Edge case: Recursive call with parameter 1 (single element) */

.global test_one

test_one:
    push {lr}
    cmp r0, #1
    beq base_case
    sub r0, r0, #1
    bl test_one
    pop {pc}

base_case:
    mov r0, #100  /* Return a fixed value for base case */
    pop {pc}

This example shows recursion stopping at both the start (0) and end (10) of a sequence.

ARM Architecture

/* Edge case: Recursive call at the beginning and end of a sequence */

.global recursive_sequence

recursive_sequence:
    push {lr}
    cmp r0, #0
    beq base_case
    cmp r0, #10
    beq end_case

    sub r0, r0, #1
    bl recursive_sequence
    pop {pc}

base_case:
    mov r0, #0
    pop {pc}

end_case:
    mov r0, #10
    pop {pc}

Detailed Explanation

This program calculates factorial of 5 using recursion. It saves the return address, checks the base case (0), calls itself with n-1, then multiplies the result by n. The final result 120 is stored in register r0.

ARM Architecture

/* Complete ARM Assembly Program: Recursive Factorial Function */

.global main

/* factorial function: calculates factorial of r0 */
factorial:
    push {lr}              /* Save return address */
    cmp r0, #0             /* Check if n == 0 */
    beq factorial_base     /* Base case: factorial(0) = 1 */

    /* Save current n in r1 before recursive call */
    mov r1, r0
    sub r0, r0, #1         /* n = n - 1 */
    bl factorial           /* Recursive call factorial(n-1) */

    mul r0, r0, r1         /* Multiply result by n */
    pop {pc}               /* Return */

factorial_base:
    mov r0, #1             /* Return 1 for factorial(0) */
    pop {pc}

/* main function to test factorial */
main:
    mov r0, #5             /* Calculate factorial(5) */
    bl factorial           /* Call factorial */

    /* Result in r0 now contains 120 */
    /* Normally, here you would return or use the result */

    /* Infinite loop to end program (for embedded) */
end:
    b end

Important Notes

Time complexity of recursive factorial is O(n) because it calls itself n times.

Space complexity is O(n) due to call stack growth with each recursive call.

Common mistake: forgetting to save and restore the return address (lr) causes crashes.

Use recursion when problems naturally break down into smaller similar problems; otherwise, iteration may be simpler and more efficient.

Summary

Recursive functions call themselves to solve smaller parts of a problem.

In ARM assembly, save the return address with push {lr} before recursion and restore it with pop {pc} to return.

Always include a base case to stop recursion and avoid infinite loops.