Strength reduction in Compiler Design - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to replace multiplication by 2 with a faster operation.

Compiler Design

result = x [1] 1

Drag options to blanks, or click blank then click option'

A*

B+

C<<

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '*' does not apply strength reduction.

Using '+' or '-' changes the value incorrectly.

Using the left shift operator (<<) by 1 is equivalent to multiplying by 2, which is faster in many processors.

2fill in blank

medium

Complete the code to replace division by 4 with a faster operation.

Compiler Design

result = x [1] 2

Drag options to blanks, or click blank then click option'

A*

B/

C<<

D>>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '/' does not optimize the operation.

Using '<<' multiplies instead of dividing.

Right shifting by 2 bits (>>) divides the number by 4 efficiently.

3fill in blank

hard

Fix the error in the strength reduction code replacing multiplication by 8.

Compiler Design

result = x [1] 3

Drag options to blanks, or click blank then click option'

A<<

B>>

C+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using '*' does not apply strength reduction.

Using '>>' shifts right, which divides.

Multiplying by 8 is equivalent to left shifting by 3 bits.

4fill in blank

hard

Fill both blanks to replace multiplication and division by powers of two with shifts.

Compiler Design

mul_result = x [1] 2
div_result = y [2] 1

Drag options to blanks, or click blank then click option'

A<<

B>>

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '*' or '/' does not optimize the operations.

Multiplying by 4 is left shift by 2 bits, dividing by 2 is right shift by 1 bit. Here, the code uses shifts for both operations.

5fill in blank

hard

Fill all three blanks to apply strength reduction for multiplication and division by powers of two.

Compiler Design

a = b [1] 2
c = d [2] 3
e = f [3] 4

Drag options to blanks, or click blank then click option'

A<<

B>>

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '/' for division is slower than shifts.

Using '<<' for division is incorrect.

Multiplying by 2 is left shift by 1 bit, dividing by 8 and 16 uses right shift '>>' by 3 and 4 bits respectively. This shows strength reduction for both multiplication and division.

Practice

1. What is the main goal of strength reduction in compiler design?

easy

A. Remove all loops from the program

B. Increase the number of operations to improve accuracy

C. Replace expensive operations with cheaper ones to speed up code

D. Convert all variables to constants

Solution

1. Step 1: Understand the purpose of strength reduction

   Strength reduction aims to replace slow operations like multiplication with faster ones like addition.

2. Step 2: Identify the effect on code speed

   This replacement makes the program run faster without changing its output.

3. Final Answer:

   Replace expensive operations with cheaper ones to speed up code -> Option C

4. Quick Check:

   Strength reduction = Replace slow ops with fast ops [OK]

Hint: Think: slow operation replaced by faster one [OK]

Common Mistakes:

• Confusing strength reduction with loop unrolling
• Thinking it removes loops entirely
• Believing it changes program output

2. Which of the following code snippets correctly applies strength reduction to replace multiplication inside a loop?

easy

A. x = 0
for i in range(n): x = x + 5

B. for i in range(n): x = 5 ** i

C. for i in range(n): x = x * 5

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

Solution

1. Step 1: Identify multiplication inside the loop

   for i in range(n): x = i * 5 multiplies i by 5 each iteration, which is expensive.

2. Step 2: Check for addition replacing multiplication

   x = 0 for i in range(n): x = x + 5 uses addition (x = x + 5) to replace repeated multiplication, which is strength reduction.

3. Final Answer:

   x = 0 for i in range(n): x = x + 5 -> Option A

4. Quick Check:

   Multiplication replaced by addition = x = 0 for i in range(n): x = x + 5 [OK]

Hint: Look for addition replacing multiplication in loops [OK]

Common Mistakes:

• Choosing code that still multiplies inside the loop
• Confusing exponentiation with multiplication
• Ignoring initialization of variables

3. Consider the following code snippet:

sum = 0
for i in range(4):
    sum += i * 3
print(sum)

After applying strength reduction, what will be the output?

medium

A. 9

B. 24

C. 12

D. 18

Solution

1. Step 1: Calculate original sum with multiplication

   Values: 0*3=0, 1*3=3, 2*3=6, 3*3=9; sum = 0+3+6+9 = 18.

2. Step 2: Apply strength reduction by replacing multiplication with addition

   Instead of i*3, add 3 each time: sum = 0 + 0 + 3 + 6 + 9 = 18 (same result).

3. Final Answer:

   18 -> Option D

4. Quick Check:

   Sum of multiples of 3 from 0 to 9 = 18 [OK]

Hint: Sum multiples manually to verify output [OK]

Common Mistakes:

• Adding 3 only once instead of multiple times
• Miscounting loop iterations
• Confusing multiplication with addition results

4. Identify the error in this code snippet that attempts strength reduction:

total = 0
for i in range(5):
    total = total * 4
print(total)

medium

A. Variable 'total' should be initialized to 1

B. Multiplication should be replaced with addition inside the loop

C. The loop range is incorrect

D. The print statement is missing parentheses

Solution

1. Step 1: Analyze the loop operation

   The code multiplies total by 4 each iteration, but total starts at 0, so total stays 0.

2. Step 2: Identify strength reduction mistake

   Strength reduction replaces multiplication with addition, but here multiplication remains, so it's not optimized.

3. Final Answer:

   Multiplication should be replaced with addition inside the loop -> Option B

4. Quick Check:

   Strength reduction needs multiplication replaced by addition [OK]

Hint: Check if multiplication is replaced by addition in loops [OK]

Common Mistakes:

• Thinking initialization to 1 fixes the problem
• Ignoring the need to replace multiplication
• Confusing syntax errors with logic errors

5. You have a loop that calculates y = x * 8 for increasing values of x. Using strength reduction, which of the following is the best way to optimize this calculation inside the loop?

hard

A. Replace multiplication by shifting x left by 3 bits

B. Replace multiplication by adding x eight times each iteration

C. Replace multiplication by dividing x by 8

D. Replace multiplication by subtracting x eight times

Solution

1. Step 1: Understand multiplication by 8

   Multiplying by 8 is the same as shifting left by 3 bits in binary, which is faster.

2. Step 2: Identify the best strength reduction method

   Using bit shift (x << 3) is faster and more efficient than repeated addition or subtraction.

3. Final Answer:

   Replace multiplication by shifting x left by 3 bits -> Option A

4. Quick Check:

   Multiply by 8 = shift left 3 bits [OK]

Hint: Use bit shifts for multiplication by powers of two [OK]

Common Mistakes:

• Using repeated addition instead of bit shifts
• Dividing instead of multiplying
• Using subtraction which is incorrect