Recursive function in assembly in ARM Architecture - Mini Project: Build & Apply

Recursive Function in ARM Assembly

📖 Scenario: You are learning how to write a recursive function in ARM assembly language. Recursive functions call themselves to solve smaller parts of a problem. This is useful for tasks like calculating factorials.

🎯 Goal: Create a simple recursive function in ARM assembly that calculates the factorial of a number.

📋 What You'll Learn

Create a label for the factorial function

Use the stack to save and restore the return address

Implement the base case for factorial (when input is 0 or 1)

Use recursion to calculate factorial for numbers greater than 1

💡 Why This Matters

🌍 Real World

Recursive functions are used in many algorithms like sorting, searching, and mathematical computations. Understanding recursion in assembly helps in low-level programming and optimization.

💼 Career

Knowledge of recursion and stack management in assembly is valuable for embedded systems developers, firmware engineers, and anyone working close to hardware.

1

Set up the input number in register r0

Write a line of ARM assembly code to move the number 5 into register r0. This will be the input for the factorial function.

ARM Architecture

# Move the number 5 into register r0
# Your code here

Hint

Use the MOV instruction to put the number 5 into r0.

2

Create the factorial function label and base case check

Write the label factorial and add code to check if r0 is less than or equal to 1. If yes, return 1 by moving 1 into r0 and then return from the function using BX LR.

ARM Architecture

    MOV r0, #5

factorial:
    # Check if r0 <= 1
    # If yes, move 1 into r0 and return
    # Your code here

Hint

Use CMP to compare r0 with 1, then BLE to branch to base_case if less or equal.

3

Implement the recursive call with stack management

In the recurse section, push the link register LR onto the stack to save the return address. Then subtract 1 from r0, call factorial recursively, pop LR from the stack, multiply the original r0 value by the returned value in r0, and finally return using BX LR. Use register r1 to store the original r0 value before the recursive call.

ARM Architecture

    MOV r0, #5

factorial:
    CMP r0, #1
    BLE base_case

    B recurse

base_case:
    MOV r0, #1
    BX LR

recurse:
    # Save LR on stack
    # Store r0 in r1
    # Subtract 1 from r0
    # Call factorial recursively
    # Restore LR from stack
    # Multiply r1 by r0
    # Return
    # Your code here

Hint

Use PUSH {LR} and POP {LR} to save and restore the return address. Use BL factorial to call the function recursively.

4

Add the program entry point and call the factorial function

Add a label _start as the program entry point. From there, call the factorial function using BL factorial. After the call, add an infinite loop to end the program using a label end and a branch to itself.

ARM Architecture

    MOV r0, #5

factorial:
    CMP r0, #1
    BLE base_case

    B recurse

base_case:
    MOV r0, #1
    BX LR

recurse:
    PUSH {LR}
    MOV r1, r0
    SUB r0, r0, #1
    BL factorial
    POP {LR}
    MUL r0, r1, r0
    BX LR

_start:
    # Call factorial function
    # Infinite loop to end program
    # Your code here

Hint

Use BL factorial to call the function and create an infinite loop with a label and branch to itself.

Practice

1. What is the main purpose of a recursive function in ARM assembly?

easy

A. To execute instructions only once

B. To call itself to solve smaller parts of a problem

C. To avoid using the stack

D. To run faster than iterative loops

Solution

1. Step 1: Understand recursion concept

   A recursive function calls itself to break down a problem into smaller parts.

2. Step 2: Apply to ARM assembly context

   In ARM assembly, recursion is used to solve problems by repeated self-calls with updated parameters.

3. Final Answer:

   To call itself to solve smaller parts of a problem -> Option B

4. Quick Check:

   Recursion means self-calling function [OK]

Hint: Recursion means function calls itself repeatedly [OK]

Common Mistakes:

• Thinking recursion avoids stack usage
• Confusing recursion with iteration
• Assuming recursion always runs faster

2. Which ARM assembly instruction is commonly used to return from a recursive function call?

easy

A. BL

B. MOV

C. BX LR

D. PUSH

Solution

1. Step 1: Identify return instruction

   In ARM assembly, BX LR is used to branch back to the address stored in the link register, effectively returning from a function.

2. Step 2: Confirm usage in recursion

   Recursive functions use BX LR to return after completing each call.

3. Final Answer:

   BX LR -> Option C

4. Quick Check:

   Return uses BX LR instruction [OK]

Hint: Return from function with BX LR instruction [OK]

Common Mistakes:

• Using BL to return instead of call
• Confusing PUSH with return
• Using MOV incorrectly for return

3. Consider this ARM assembly snippet for a recursive factorial function:

factorial:
    CMP R0, #1
    BLE end_factorial
    PUSH {LR}
    SUB R0, R0, #1
    BL factorial
    POP {LR}
    MUL R0, R0, R1
end_factorial:
    MOV R1, R0
    BX LR

What will be the value in R1 after calling factorial with R0 = 3?

medium

A. 0

B. 3

C. 1

D. 6

Solution

1. Step 1: Trace the recursive factorial

   The function saves LR, decrements R0, calls factorial recursively, restores LR, then multiplies R0 by R1.

2. Step 2: Calculate factorial for R0=3

   Call factorial(3): R0=3, not base case, PUSH LR, SUB R0=2, BL factorial(2). factorial(2): PUSH LR, SUB R0=1, BL factorial(1). factorial(1): base case, sets R1=1, returns. factorial(2): POP LR, MUL R0=1 * R1=1 =1, MOV R1=1, return. factorial(3): POP LR, MUL R0=2 * R1=1=2, MOV R1=2, return.

3. Step 3: Correction

   However, the MUL uses R0 and R1, but R0 was decremented before recursive call, so the multiplication is (n-1) * fact(n-1), which is incorrect for factorial.

4. Step 4: Final value

   Tracing carefully, the final R1 will be 2, which is incorrect factorial of 3 (should be 6). But the code as given will produce 2.

5. Final Answer:

   2 -> Option D

Hint: SUB decrements R0 before call; MUL uses decremented R0 causing incorrect factorial [Check carefully]

Common Mistakes:

• Assuming correct factorial computation (expecting 6)
• Confusing R0 and R1 values
• Missing base case return value

4. Identify the error in this recursive ARM assembly function snippet:

factorial:
    CMP R0, #1
    BLE end_factorial
    SUB R0, R0, #1
    BL factorial
    MUL R0, R0, R1
end_factorial:
    MOV R1, R0
    BX LR

What is the main problem?

medium

A. Missing PUSH and POP of LR causing return address loss

B. Incorrect base case comparison

C. Wrong multiplication order

D. Using MOV instead of MOVS

Solution

1. Step 1: Check stack usage for recursion

   Recursive calls must save LR on stack before calling to preserve return address.

2. Step 2: Identify missing PUSH/POP

   This code lacks PUSH {LR} before BL and POP {LR} after, risking corrupted return address.

3. Final Answer:

   Missing PUSH and POP of LR causing return address loss -> Option A

4. Quick Check:

   Save LR on stack in recursion [OK]

Hint: Always save LR on stack before recursive call [OK]

Common Mistakes:

• Ignoring stack save for LR
• Assuming base case is wrong
• Confusing MOV with MOVS

5. You want to write a recursive ARM assembly function to compute the nth Fibonacci number. Which of these is essential to correctly implement recursion here?

hard

A. Handle base cases to stop recursion and save LR on stack before recursive calls

B. Use only registers without stack to speed up recursion

C. Avoid base cases to allow infinite recursion for all n

D. Use unconditional jumps instead of BL for recursive calls

Solution

1. Step 1: Importance of base cases

   Base cases stop recursion to prevent infinite loops, essential for Fibonacci calculation.

2. Step 2: Save LR on stack before recursive calls

   Saving LR preserves return addresses during multiple recursive calls, avoiding crashes.

3. Final Answer:

   Handle base cases to stop recursion and save LR on stack before recursive calls -> Option A

4. Quick Check:

   Base cases + LR save = correct recursion [OK]

Hint: Always include base cases and save LR in recursion [OK]

Common Mistakes:

• Skipping base cases causing infinite recursion
• Not saving LR causing return errors
• Using jumps instead of BL for calls