Loop optimization (invariant code motion) in Compiler Design - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is loop invariant code motion?

Loop invariant code motion is a compiler optimization technique that moves calculations or expressions that do not change inside a loop to outside the loop. This reduces repeated work and improves performance.

beginner

Why is moving invariant code outside a loop beneficial?

Moving invariant code outside a loop avoids repeating the same calculation multiple times, which saves processing time and makes the program run faster.

beginner

Give an example of a loop invariant expression.

An example is calculating a constant value like 'x = 5 * 3' inside a loop. Since 5 * 3 is always 15, it can be moved outside the loop to avoid repeated calculation.

intermediate

What conditions must be met for code to be considered loop invariant?

The code must not change during the loop iterations, meaning it does not depend on variables modified inside the loop and produces the same result every time.

intermediate

Can loop invariant code motion affect program correctness?

If done correctly, it does not affect correctness. However, if the code depends on variables that change inside the loop, moving it outside can cause wrong results.

Which of the following is an example of loop invariant code?

A A constant value calculation

B An assignment to a loop counter

C A function call that changes global state

D A calculation using a variable updated inside the loop

A constant value calculation does not change during the loop and is loop invariant.

What is the main goal of loop invariant code motion?

A To reduce repeated calculations inside the loop

B To move code inside the loop for clarity

C To increase the number of loop iterations

D To change the loop's output

The goal is to reduce repeated calculations by moving invariant code outside the loop.

Which condition disqualifies code from being loop invariant?

A Code uses only constants

B Code depends on variables updated inside the loop

C Code is a simple arithmetic operation

D Code is outside the loop

If code depends on variables updated inside the loop, it is not invariant.

What could happen if loop invariant code motion is applied incorrectly?

A Program runs faster without issues

B Loop becomes infinite

C Loop runs fewer times

D Program output may become incorrect

Incorrectly moving code that depends on loop variables can cause wrong results.

Which of these is a benefit of loop invariant code motion?

A Makes code harder to read

B Increases memory usage

C Reduces CPU cycles spent in the loop

D Increases loop complexity

Moving invariant code outside the loop reduces CPU cycles spent repeating calculations.

Explain what loop invariant code motion is and why it is useful.

Think about what code inside a loop does not change and how moving it helps.

Describe the conditions that must be met for code to be safely moved outside a loop.

Consider what makes code 'invariant' in the context of a loop.

Practice

1. What is the main goal of loop optimization (invariant code motion) in compiler design?

easy

A. To move calculations that do not change outside the loop to improve efficiency

B. To increase the number of loops in the program

C. To add more calculations inside the loop for accuracy

D. To remove all loops from the program

Solution

1. Step 1: Understand loop invariant code

   Loop invariant code means calculations inside a loop that produce the same result every time.

2. Step 2: Purpose of moving invariant code

   Moving such code outside the loop avoids repeating the same calculation, saving time.

3. Final Answer:

   To move calculations that do not change outside the loop to improve efficiency -> Option A

4. Quick Check:

   Invariant code motion = move unchanging code outside loop [OK]

Hint: Move unchanging calculations outside loops to speed up code [OK]

Common Mistakes:

• Thinking loop optimization adds more loops
• Believing invariant code should stay inside loops
• Confusing optimization with removing loops

2. Which of the following code snippets correctly applies invariant code motion?

easy

A. for i in range(n):
x = 5 * 3
print(i + x)

B. for i in range(n):
x = i * 3
print(x)

C. for i in range(n):
print(i + 5 * 3)

D. x = 5 * 3
for i in range(n):
print(i + x)

Solution

1. Step 1: Identify invariant calculation

   The calculation 5 * 3 does not depend on the loop variable i, so it is invariant.

2. Step 2: Check code placement

   x = 5 * 3 for i in range(n): print(i + x) moves 5 * 3 outside the loop, calculating it once before looping.

3. Final Answer:

   x = 5 * 3 for i in range(n): print(i + x) -> Option D

4. Quick Check:

   Invariant code outside loop = x = 5 * 3 for i in range(n): print(i + x) [OK]

Hint: Put constant calculations before the loop starts [OK]

Common Mistakes:

• Calculating invariant code inside the loop repeatedly
• Moving variable-dependent code outside the loop
• Ignoring the loop variable dependency

3. Consider the following code snippet:

sum = 0
for i in range(1, 5):
    x = 10 * 2
    sum += i + x
print(sum)

What will be the output after applying invariant code motion optimization?

medium

A. 50

B. 70

C. 90

D. 110

Solution

1. Step 1: Move invariant calculation outside loop

   Calculate x = 10 * 2 = 20 once before the loop.

2. Step 2: Calculate sum with optimized code

   sum = 0; loop i=1 to 4: sum += i + 20
   Sum = (1+20)+(2+20)+(3+20)+(4+20) = 21+22+23+24 = 90

3. Final Answer:

   90 -> Option C

4. Quick Check:

   Sum of (i+20) for i=1 to 4 = 90 [OK]

Hint: Calculate constants once, then sum loop values [OK]

Common Mistakes:

• Adding 10*2 inside loop each time
• Miscounting loop iterations
• Forgetting to add i in sum

4. Identify the error in the following code related to invariant code motion:

for i in range(3):
    y = i * 2
    x = 4 + 5
    print(x + y)

What is the problem if we move x = 4 + 5 inside the loop?

medium

A. Moving x inside loop causes repeated calculation, reducing efficiency

B. x depends on i, so moving it outside causes error

C. No problem, code is optimized correctly

D. x is undefined inside the loop

Solution

1. Step 1: Analyze variable dependency

   x = 4 + 5 is invariant; it does not depend on i.

2. Step 2: Effect of moving x inside loop

   Moving x inside loop causes repeated calculation each iteration, wasting resources.

3. Final Answer:

   Moving x inside loop causes repeated calculation, reducing efficiency -> Option A

4. Quick Check:

   Invariant code inside loop = inefficient [OK]

Hint: Keep invariant code outside loop to avoid repeats [OK]

Common Mistakes:

• Thinking invariant code depends on loop variable
• Believing repeated calculation improves speed
• Confusing variable scope with optimization

5. Given the nested loop below, which is the best way to apply invariant code motion to optimize it?

for i in range(3):
    for j in range(4):
        x = 2 * 3
        y = i + j
        print(x + y)

hard

A. Move both x and y outside all loops

B. Move x outside both loops, keep y inside inner loop

C. Keep both x and y inside inner loop

D. Move y outside inner loop, keep x inside inner loop

Solution

1. Step 1: Identify invariant expressions

   x = 2 * 3 is invariant (does not depend on i or j). y = i + j depends on both loop variables.

2. Step 2: Apply invariant code motion

   Move x outside both loops to calculate once. y must stay inside inner loop as it changes each iteration.

3. Final Answer:

   Move x outside both loops, keep y inside inner loop -> Option B

4. Quick Check:

   Invariant x outside loops, variable y inside loop [OK]

Hint: Only move calculations independent of all loops outside [OK]

Common Mistakes:

• Moving variable-dependent code outside loops
• Keeping invariant code inside loops unnecessarily
• Confusing which variables depend on loop indices