### 15.4 Loop-closed SSA form

Throughout the loop optimizations on tree level, one extra condition is enforced on the SSA form: No SSA name is used outside of the loop in that it is defined. The SSA form satisfying this condition is called “loop-closed SSA form” – LCSSA. To enforce LCSSA, PHI nodes must be created at the exits of the loops for the SSA names that are used outside of them. Only the real operands (not virtual SSA names) are held in LCSSA, in order to save memory.

There are various benefits of LCSSA:

- Many optimizations (value range analysis, final value replacement) are interested in the values that are defined in the loop and used outside of it, i.e., exactly those for that we create new PHI nodes.
- In induction variable analysis, it is not necessary to specify the loop in that the analysis should be performed – the scalar evolution analysis always returns the results with respect to the loop in that the SSA name is defined.
- It makes updating of SSA form during loop transformations simpler. Without LCSSA, operations like loop unrolling may force creation of PHI nodes arbitrarily far from the loop, while in LCSSA, the SSA form can be updated locally. However, since we only keep real operands in LCSSA, we cannot use this advantage (we could have local updating of real operands, but it is not much more efficient than to use generic SSA form updating for it as well; the amount of changes to SSA is the same).

However, it also means LCSSA must be updated. This is usually straightforward, unless you create a new value in loop and use it outside, or unless you manipulate loop exit edges (functions are provided to make these manipulations simple). `rewrite_into_loop_closed_ssa` is used to rewrite SSA form to LCSSA, and `verify_loop_closed_ssa` to check that the invariant of LCSSA is preserved.