Consider the following C code segment: for (i = 0; i < n; i++) { for (j = 0; j…

Overview of the Code

• Two nested loops: each runs n times → total iterations = n²

• Condition: if (i % 2)
  → executes only when i is odd

• Inner computations:

  • x += (4*j + 5*i)

  • y += (7 + 4*j)

Analysis of Compiler Optimizations

(A) Loop Invariant Code Motion (LICM)

An expression is loop-invariant if it does not change within a loop.

• 5*i → invariant w.r.t inner loop (j loop)

• 7 → constant (fully invariant)

These can be moved outside the inner loop

LICM is applicable

(B) Common Subexpression Elimination (CSE)

Common subexpressions:

• 4*j appears in both:

  • x += (4*j + 5*i)

  • y += (7 + 4*j)

Can be computed once:

t = 4*j;
x += (t + 5*i);
y += (7 + t);

CSE is applicable

(C) Strength Reduction

Strength reduction replaces expensive operations with cheaper ones.

• 4*j → can be replaced using incremental addition:
  

  • Instead of multiplication, use:

    t = t + 4

Strength reduction is applicable

(D) Dead Code Elimination

Dead code refers to computations whose results are never used.

• x and y are being updated (accumulated)

• Their values are assumed to be used later in the program

No statement is redundant or unused

Dead Code Elimination is NOT applicable

Summary Table

Answer:

Dead Code Elimination is NOT applicable (False statement)