# Compiler Design | Detection of a Loop in Three Address Code

• Difficulty Level : Easy
• Last Updated : 10 Nov, 2021

Prerequisite – Three address code in Compiler
Loop optimization is the phase after the Intermediate Code Generation. The main intention of this phase is to reduce the number of lines in a program. In any program majority of the time is spent by any program is actually inside the loop for an iterative program. In the case of the recursive program a block will be there and the majority of the time will present inside the block.

Loop Optimization –

1. To apply loop optimization we must first detect loops.
2. For detecting loops we use Control Flow Analysis(CFA) using Program Flow Graph(PFG).
3. To find program flow graph we need to find Basic Block

Basic Block – A basic block is a sequence of three address statements where control enters at the beginning and leaves only at the end without any jumps or halts.

Finding the Basic Block –
In order to find the basic blocks, we need to find the leaders in the program. Then a basic block will start from one leader to the next leader but not include the next leader. This means if you find out that line no 1 is a leader and line no 15 is the next leader, then the line from 1 to 14 is a basic block, but not including line no 15.

Identifying leader in a Basic Block –

1. First statement is always a leader
2. Statement that is target of conditional or un-conditional statement is a leader
3. Statement that follows immediately a conditional or un-conditional statement is a leader

 `fact(x) ` `{ ` `    ``int` `f = 1; ` `    ``for` `(i = 2; i <= x; i++) ` `        ``f = f * i; ` `    ``return` `f; ` `} `

Three Address Code of the above C code:

1. f = 1;
2. i = 2;
3. if (i > x) goto 9
4. t1 = f * i;
5. f = t1;
6. t2 = i + 1;
7. i = t2;
8. goto(3)
9. goto calling program

Leader and Basic Block –

Control Flow Analysis –

If the control enter B1 there is no other option after B1, it has to enter B2. Now, if control enters B2, then depending on the condition control will flow, if the condition is true we are going to line no 9, which means 9 is nothing but B4. But if the condition is false control goes to the next block B3. After B3, there is no condition at all we are direct goes to 3rd statement B2. Above control flow graph have a cycle between B2 and B3 which is nothing but a loop.

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