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16 votes
16 votes

The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can have atmost two source operands and one destination operand. Assume that all variables are dead after this code segment.

c = a + b; 
d = c * a; 
e = c + a; 
x = c * c; 
if (x > a) { 
 y = a * a; 
} 
else { 
 d = d * d; 
 e = e * e; 
}

What is the minimum number of registers needed in the instruction set architecture of the processor to compile this code segment without any spill to memory? Do not apply any optimization other than optimizing register allocation.

  1. 3
  2. 4
  3. 5
  4. 6

3 Answers

Best answer
24 votes
24 votes

Here, we are told not to do code motion. So, we start with 3 registers

c = a + b; //a, c in register
d = c * a; //a, c, d in register
e = c + a; //a, c, e in register, d spilled. 

So, now we try with 4 registers

c = a + b; //a, c in register
d = c * a; //a, c, d in register
e = c + a; //a, c, d, e in register
x = c * c; //a, x, d, e in register
if (x > a) { 
 y = a * a; 
} 
else { 
 d = d * d; 
 e = e * e; 
} 

No spilling. So, 4 is the minimum number of registers needed for avoiding spilling. (If code motion was allowed, we need only 3 registers for avoiding spilling).

selected by
6 votes
6 votes

BOLD lines describe Live variable just before entering the next statement 


{ a,b }
c = a + b;
{ a,c }
d = c * a;
{ a,c,d }
e = c + a;
{ a,c,d,e }
x = c * c;
{ a,d,x,e }
if (x > a)
Either IF condition passes
{ a }
{ y = a * a; }
or when IF condition fails
{ d,e }
else 
{d = d * d;
e = e * e; }

So as we can see that at max only 4 variables are live, therefore we need 4 registers to avoid register spilling.

@ sir, is this method correct?

Because everyone draws a graph and then finds its chromatic number, i don’t understand why do we need a graph?

For example, https://gateoverflow.in/78311/how-to-draw-register-allocation-interference-graph

edited by
Answer:

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