// generalizing to multiple TPU clusters.
  Region* region = (*forward_pass_ops.begin())->getParentRegion();
  StringAttr replication_attr = GetReplicationAttr(*forward_pass_ops.begin());
  llvm::SmallVector<Operation*> checkset(forward_pass_ops.getArrayRef());
  checkset.append(backward_pass_ops.begin(), backward_pass_ops.end());
  for (Operation* op : checkset) {
    if (op->getParentRegion() != region) {

 public:
  QuantizeContext(func::FuncOp func, const DeviceTarget &spec);

  // Returns all the quant region ops.
  std::vector<quantfork::QuantizeRegionOp> GetAllOps();

  // For each quant region op, propagates its quantization parameters according
  // to the kernel specification and also returns the adjacent quant region ops
  // which get the new quantization parameters propagated.
  LogicalResult Handle(quantfork::QuantizeRegionOp op,

    if (auto cast = dyn_cast<TF::CastOp>(op)) {
      this->join(results[0], *operands[0]);
    } else if (auto while_op = dyn_cast<TF::WhileRegionOp>(op)) {
      for (auto &region : while_op->getRegions()) {
        for (auto [arg, value] :
             llvm::zip(region.getArguments(), while_op->getOperands())) {
          this->join(getLatticeElement(arg), *getLatticeElement(value));
        }
      }

	// Virtual Memory Map of process 53799 (gopls)
	// Output report format:  2.4  -64-bit process
	// VM page size:  16384 bytes
	//
	// ==== Non-writable regions for process 53799
	// REGION TYPE                    START END         [ VSIZE  RSDNT  DIRTY   SWAP] PRT/MAX SHRMOD PURGE    REGION DETAIL
	// __TEXT                      1029a0000-1033bc000    [ 10.1M  7360K     0K     0K] r-x/rwx SM=COW          /Users/USER/*/gopls

                       bool wouldBeCloned) const final {
    return true;
  }
  // Returns true if the given region 'src' can be inlined into the region
  // 'dest' that is attached to an operation registered to the current dialect.
  bool isLegalToInline(Region *dest, Region *src, bool wouldBeCloned,
                       IRMapping &) const final {
    return true;
  }

}

// -----

// Check that an empty graph is invalid (it needs a region).
func.func @empty_graph() {
 "tf_executor.graph" () ({
// expected-error@-1 {{'tf_executor.graph' op region #0 ('body') failed to verify constraint: region with 1 blocks}}
  }) : () -> ()
  func.return
}

// -----

// Check that an empty graph is invalid (it needs a region).
func.func @empty_graph() {
 "tf_executor.graph" () ({

mlir::LogicalResult PropagateValuesConstraints(
    mlir::Region &region, const ClusteringPolicySet &policies,
    ValuesConstraintSet &constraints, bool resolve, bool emit_remarks) {
  // Propagate constraints for all operations in the region.
  llvm::SmallVector<Operation *> worklist;
  region.walk([&](Operation *op) { worklist.emplace_back(op); });

  // Propagate constraints only through operations inside the `region`.

// set of unique IDs representing the possible resources it could alias.
//
// Note that this is not an inter-procedural or inter-regional analysis, i.e.,
// each function and region are handled separately and cross-function or cross-
// region aliasing cannot be checked by this analysis.
class ResourceAliasAnalysis : public detail::PerFunctionAggregateAnalysis<
                                  detail::ResourceAliasAnalysisInfo> {

// first-fit approach.
//
// Each entry in the radix tree is a summary that describes three properties of
// a particular region of the address space: the number of contiguous free pages
// at the start and end of the region it represents, and the maximum number of
// contiguous free pages found anywhere in that region.
//
// Each level of the radix tree is stored as one contiguous array, which represents

</ul>

<h2>User-defined tasks and regions</h2>
<p>
  The trace API allows a target program to annotate a <a
  href='https://pkg.go.dev/runtime/trace#Region'>region</a> of code
  within a goroutine, such as a key function, so that its performance
  can be analyzed.

  <a href='https://pkg.go.dev/runtime/trace#Log'>Log events</a> may be
  associated with a region to record progress and relevant values.