LLVM has a special value in its SSA value hierarchy called undef that is used to model (amongst other things) reads from uninitialized memory. Semantically, an undef value has a potentially new bit pattern of the compiler’s choosing at each use site, meaning that values like xor i32 %a, %a need not always evaluate to 0 when %a is undef (even though they’re allowed to). This lack of consistency lets LLVM get away without allocating registers to remember a specific “version” of undef.

Another way to look at this is that undef isn’t a normal SSA value, and uses of an undef value are also its defs. This leads to some interesting restrictions on data flow analysis via control flow, and, in some cases, accounting for undef inhibits optimization instead of enabling it.

For instance, consider this:

declare i1 @predicate()
declare void @use(i32)

define void @f(i32 %d, i32 %n) {
 entry:
  %division_unsafe = icmp eq i32 %d, 0
  br i1 %division_unsafe, label %leave, label %loop.ph

 loop.ph:
  br label %loop

 loop:
  %iv = phi i32 [ 0 , %loop.ph ], [ %iv.inc, %be ]
  %iv.inc = add i32 %iv, 1
  %p = call i1 @predicate()
  br i1 %p, label %divide, label %be

 divide:
  %q = udiv i32 1, %d
  call void @use(i32 %q)
  br label %be

 be:
  %be.cond = icmp ult i32 %iv, %n
  br i1 %be.cond, label %loop, label %leave

 leave:
  ret void
}

Is it legal to hoist the division %q in divide to the loop preheader? At first, it does look like it is legal, since the loop preheader is guarded on the %d not being 0. However, in the transformed program

declare i1 @predicate()
declare void @use(i32)

define void @f(i32 %d, i32 %n) {
 entry:
  %division_unsafe = icmp eq i32 %d, 0
  br i1 %division_unsafe, label %leave, label %loop.ph

 loop.ph:
  %q = udiv i32 1, %d
  br label %loop

 loop:
  %iv = phi i32 [ 0 , %loop.ph ], [ %iv.inc, %be ]
  %iv.inc = add i32 %iv, 1
  %p = call i1 @predicate()
  br i1 %p, label %divide, label %be

 divide:
  call void @use(i32 %q)
  br label %be

 be:
  %be.cond = icmp ult i32 %iv, %n
  br i1 %be.cond, label %loop, label %leave

 leave:
  ret void
}

we have a problem. If %d is undef, then %division_unsafe = icmp eq i32 undef, 0 is allowed to be false while %q = udiv i32 1, undef is allowed to have undefined behavior (by choosing 0 for undef). If @predicate always returns false then the original program is perfectly well defined for %d = undef while the transformed program isn’t, even though the transform we made looks very reasonable.

Generally, with undef in the play, control dependence in the control flow graph cannot be used to derive facts about SSA values. If the value we’re interested in happens to be undef, then it can “pretend” to satisfy the predicate the control dependence is on while “pretending” to not satisfy the predicate on later control dependent uses of the same value. In cases like the above, presence of undef in LLVM IR actually inhibits optimization.

This problem isn’t unique to branches – many kinds of correlated value or predicate analysis are problematic. Consider %expr = smax(%a + 1, %a) - smin(%a + 1, %a), with smax implemented using select and icmp. Is %expr always non-zero? In the absence of undef, %expr is either -1 or 1 (so it is tempting to say yes). However, if %a is undef, then %expr is undef as well (and thus allowed to be 0).