#of variables in SSA

Question

Consider the following code segment:

c=b+a

e=c-a

f=c*e

h=c+a

i=h+f

The minimum number of  $\color{blue} {total}$ and $\color{blue} {temporary }$ variable required to convert the above code segment to static single assignment form are  ________

Comments

yeah, you are right the code is itself in SSA form, as there are no variable with multiple assignment.

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although given code is already in SSA but still the results are stored in temprory variable hence 4 or 5 temprory variable must be required.. according to me unless given we should not apply optimization while converting to SSA because its an intermediate representation which is done before optimization so 5 variable are required

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draw dag and count nodes =7

but two things are cosidered through dag in ssa form

1. dead code elimination if some node is used to make final node => don't count it as shown in figure 2

2. if more expressions to evaluate at child level as shown in figure 3

Answer 1

p3 = p1 + p2

p4 = p3 - p2

p5 = p3 * p4

p6 = p3 + p2

p7 = p6 + p5

Therefore, total 7 temporary variables are needed.

Answer 2

I guess answer would be 0, because the above code is already in Static single assignment form.

Refer to this links.

https://www.cs.cmu.edu/~fp/courses/15411-f08/lectures/09-ssa.pdf

https://www.geeksforgeeks.org/gate-gate-cs-2016-set-1-question-29/

Answer 3

4 should be ans

Comments

Why are people saying that answer is 0 in the above comments ? I am getting answer as 4.

 In the below mentioned GATE 2016 question, the answer is 10 including the temporary variables. My doubt is if the number of temporary variables had to be considered as 0 then the answer should have been 5 right and not 10 considering the fact that we have to convert this code segment in to SSA form. 

Consider the following code segment.

x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y; 

The minimum number of total variables required to convert the above code segment to static single assignment form is ?

Somebody please provide a clear understanding on this. 

Answer 4

Answer should be 7.

1. 5 For LHS of assignment statements and,
2. 2 for (a,b) as they are not generated and directly been used.