Return value in R0 in ARM Architecture - Time & Space Complexity

Time Complexity: Return value in R0

O(1)

Understanding Time Complexity

We want to understand how the time taken by ARM code changes when it returns a value in register R0.

Specifically, how does the return operation affect execution time as input changes?

Scenario Under Consideration

Analyze the time complexity of the following ARM code snippet.

    MOV R0, #5      ; Load immediate value 5 into R0
    BX LR           ; Return from function
    

This code sets the return value to 5 in R0 and then returns from the function.

Identify Repeating Operations

Look for any repeated steps or loops in the code.

• Primary operation: Single move instruction and return instruction
• How many times: Each runs once per function call

How Execution Grows With Input

The instructions run the same number of times regardless of input size.

Input Size (n)	Approx. Operations
10	2 instructions
100	2 instructions
1000	2 instructions

Pattern observation: Execution time stays constant no matter the input size.

Final Time Complexity

Time Complexity: O(1)

This means the time to return a value in R0 does not grow with input size; it takes a fixed amount of time.

Common Mistake

[X] Wrong: "Returning a value in R0 takes longer if the value is bigger or the input is larger."

[OK] Correct: The instructions to move a value into R0 and return run once and take the same time regardless of the value size or input.

Interview Connect

Understanding that returning values in registers is a constant-time operation helps you reason about function call costs in low-level programming.

Self-Check

"What if the function returned a value stored in memory instead of R0? How would the time complexity change?"

Practice

1. In ARM assembly, which register is used to hold the return value of a function?

easy

A. LR

B. R1

C. R0

D. SP

Solution

1. Step 1: Understand ARM calling convention

   In ARM, the first register R0 is used to pass the return value from a function to the caller.

2. Step 2: Identify the return value register

   Since R0 holds the return value, the caller reads the result from R0 after the function returns.

3. Final Answer:

   R0 -> Option C

4. Quick Check:

   Return value register = R0 [OK]

Hint: Return values are always in R0 register in ARM [OK]

Common Mistakes:

• Confusing LR with return value
• Using SP as return value
• Thinking R1 holds return value

2. Which ARM assembly instruction is commonly used to return from a function after setting R0?

easy

A. MOV R0, #0

B. ADD R0, R0, #1

C. STR R0, [SP]

D. BX LR

Solution

1. Step 1: Identify return instruction in ARM

   The instruction BX LR branches to the address stored in the link register (LR), effectively returning from the function.

2. Step 2: Confirm usage after setting R0

   After placing the return value in R0, BX LR is used to return control to the caller.

3. Final Answer:

   BX LR -> Option D

4. Quick Check:

   Return instruction = BX LR [OK]

Hint: Return with BX LR after setting R0 [OK]

Common Mistakes:

• Using MOV instead of BX LR to return
• Storing R0 to stack before return
• Using ADD as return instruction

3. Consider this ARM assembly snippet:

MOV R0, #5
BX LR

What value will the caller receive after this function returns?

medium

A. 5

B. 0

C. LR value

D. Undefined

Solution

1. Step 1: Analyze MOV instruction

   The instruction MOV R0, #5 sets the R0 register to 5, which is the return value.

2. Step 2: Analyze return instruction

   BX LR returns control to the caller, with R0 holding the return value 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   R0 value after return = 5 [OK]

Hint: Value in R0 before BX LR is the return value [OK]

Common Mistakes:

• Thinking LR value is returned
• Assuming R0 resets to 0
• Ignoring MOV sets return value

4. Identify the error in this ARM function that intends to return 10:

ADD R0, R0, #10
BX LR

medium

A. R0 is not initialized before ADD

B. BX LR should be MOV PC, LR

C. ADD instruction syntax is incorrect

D. Function should use R1 for return value

Solution

1. Step 1: Check initial value of R0

   The instruction ADD R0, R0, #10 adds 10 to R0, but R0 is not initialized, so the result is unpredictable.

2. Step 2: Confirm correct return method

   BX LR is correct to return; the problem is the uninitialized R0.

3. Final Answer:

   R0 is not initialized before ADD -> Option A

4. Quick Check:

   Uninitialized R0 causes wrong return value [OK]

Hint: Initialize R0 before adding to it [OK]

Common Mistakes:

• Assuming R0 starts at zero
• Confusing BX LR with MOV PC, LR
• Using wrong register for return value

5. You want to write an ARM function that returns the sum of two input values passed in R0 and R1. Which code correctly sets the return value in R0 before returning?

hard

A. MOV R0, R1
BX LR

B. ADD R0, R0, R1
BX LR

C. ADD R1, R0, R1
BX LR

D. SUB R0, R0, R1
BX LR

Solution

1. Step 1: Understand input and output registers

   Inputs are in R0 and R1; the sum should be stored in R0 as the return value.

2. Step 2: Check each option

   ADD R0, R0, R1 BX LR adds R0 and R1, stores result in R0, then returns with BX LR, which is correct.

3. Final Answer:

   ADD R0, R0, R1 BX LR -> Option B

4. Quick Check:

   Sum in R0 before BX LR returns correct value [OK]

Hint: Sum inputs into R0, then BX LR to return [OK]

Common Mistakes:

• Storing sum in R1 instead of R0
• Using SUB instead of ADD
• Not returning with BX LR