phis = append(phis, v)
					}
					continue
				}
				for _, a := range v.Args {
					if s.values[a.ID].needSlot {
						live.add(a.ID)
					}
				}
			}

			// for each predecessor of b, expand its list of live-at-end values
			// invariant: s contains the values live at the start of b (excluding phi inputs)
			for i, e := range b.Preds {
				p := e.b
				t.clear()
				t.addAll(s.live[p.ID])

			// cannot determine the real line number.
			if f.begin > expand {
				f.begin -= expand
			} else if f.begin > 1 {
				f.begin = 1
			}
		} else {
			// Find gap from predecessor and divide between predecessor and f.
			halfGap := (f.begin - funcs[i-1].end) / 2
			if halfGap > expand {
				halfGap = expand
			}
			funcs[i-1].end += halfGap
			f.begin -= halfGap
		}
		funcs[i] = f
	}

  let summary = "Colocates each Split op with its predecessor";
  let constructor = "TFTPU::CreateTPUColocateSplitsPass()";
  let description = [{
    It is beneficial for performance to assign a `Split` op to the same device
    as its predecessor. This is because the weight of cut edges is always
    minimized when the `Split` is with its predecessor. This colocation

				}
				if m.Op == ssa.OpPhi {
					break
				}
			}
			// Find the two predecessor blocks (write barrier on and write barrier off)
			if len(m.Args) != 2 {
				lv.f.Fatalf("phi before write barrier end mark has %d args, want 2", len(m.Args))
			}
			c := b.Preds[0].Block()
			d := b.Preds[1].Block()

			// Find their common predecessor block (the one that branches based on wb on/off).

    for (Operation* op : ops_to_process) {
      if (predecessors) {
        for (Value operand : op->getOperands()) {
          // Stop at the block boundary.
          if (mlir::isa<BlockArgument>(operand)) continue;

          Operation* predecessor = operand.getDefiningOp();
          if (!operations->contains(predecessor) &&
              !ops_to_avoid.contains(predecessor)) {
            new_ops.insert(operand.getDefiningOp());

  }) {...} : () -> tensor<4xf32>
```
### `-tf-tpu-colocate-splits`

_Colocates each Split op with its predecessor_

It is beneficial for performance to assign a `Split` op to the same device
as its predecessor. This is because the weight of cut edges is always
minimized when the `Split` is with its predecessor. This colocation
constraint will be used by the placer graph optimization to assign a device
to the op.

func ValidateAllObjectFunc(ctx context.Context, obj runtime.Object) error {
	return nil
}

// ValidateObjectUpdateFunc is a function to act on a given object and its predecessor.
// An error may be returned if the hook cannot be completed. An UpdateObjectFunc
// may NOT transform the provided object.
type ValidateObjectUpdateFunc func(ctx context.Context, obj, old runtime.Object) error

// Creates a pass that propagates TPU devices to users.
std::unique_ptr<OperationPass<func::FuncOp>> CreateTPUDevicePropagationPass();

// Create a pass that colocates each `Split` with its predecessor.
std::unique_ptr<OperationPass<func::FuncOp>> CreateTPUColocateSplitsPass();

// Creates a pass that replicates the tf._TPUCompileMlir op on each host that

		// If p and p.Succs[0] are dominators it means that every path
		// from entry to b passes through p and p.Succs[0]. We care that
		// no path from entry to b passes through p.Succs[1]. If p.Succs[0]
		// has one predecessor then (apart from the degenerate case),
		// there is no path from entry that can reach b through p.Succs[1].
		// TODO: how about p->yes->b->yes, i.e. a loop in yes.

	{name: "FMA", argLength: 3}, // compute (a*b)+c without intermediate rounding

	// Data movement. Max argument length for Phi is indefinite.
	{name: "Phi", argLength: -1, zeroWidth: true}, // select an argument based on which predecessor block we came from
	{name: "Copy", argLength: 1},                  // output = arg0
	// Convert converts between pointers and integers.
	// We have a special op for this so as to not confuse GC