return failure();
    }

    // Compute multiplier = scale / sqrt(variance + epsilon)
    Value multiplier = rewriter.create<mhlo::AddOp>(
        bn_op.getLoc(), bn_op.getVariance(), epsilon);
    multiplier = rewriter.create<mhlo::RsqrtOp>(bn_op.getLoc(), multiplier);
    multiplier = rewriter.create<mhlo::MulOp>(bn_op.getLoc(), multiplier,
                                              bn_op.getScale());

      absl::StrCat("device: ", DEVICE_TPU_SYSTEM, " device"));
  devices->push_back(std::make_unique<VirtualDevice>(options.env, attrs));
  VLOG(1) << "Created TPU_SYSTEM device. This host has " << device_count
          << " TPUs";

  return absl::OkStatus();
}

}  // namespace

void RegisterTpuDeviceToDeviceCopy() {
  static auto* const register_tpu_tpu_copy = new CopyTensor::Registration(

    if (tpu_replicated_input.getIsMirroredVariable()) {
      mirrored_variable_indices.push_back(pos_and_input.index());
    }
  }

  // Create replicate op.
  auto result_types = GetClusterResultTypes(cluster, partitioned_outputs);
  auto replicate_op = builder.create<mlir::tf_device::ReplicateOp>(
      cluster.getLoc(), num_replicas,
      llvm::SmallDenseMap<llvm::StringRef,

// function, which might not exist in case of multi-signature graphs. In that
// case, this pass will create a new main function, which calls signature
// functions.
//
// An already existing @main function will be renamed by attaching a numeric
// suffix like `@main_0` to avoid conflict with the newly created main function.
class InsertMainFunctionPass
    : public PassWrapper<InsertMainFunctionPass, OperationPass<ModuleOp>> {

// Test to ensure that a registered graph optimization pass is only executed
// once (i.e., on the main function side) in running distributed functions.
// This test creates a cluster with two workers, create a variable on the
// second worker, and run a distributed function (VariableAddFunction) whose ops
// span the local and remote workers. If the graph optimization pass is executed

    llvm::SmallVector<Value, 2> new_operands;
    FilterOutBlockArgControlDep(op->getOperands().drop_front(), new_operands);

    auto source_op = builder.create<tf_executor::NextIterationSourceOp>(
        op->getLoc(), op->getOperand(0).getType());
    builder.create<tf_executor::NextIterationSinkOp>(
        op->getLoc(), source_op.getToken(), /*input=*/op->getOperand(0),
        /*controlInputs=*/new_operands);

// control flow op into an i1 value.
static Value LowerCondition(Location loc, Value value, OpBuilder* builder) {
  Value zero_d = builder->create<ToBoolOp>(loc, value);
  Value scalar = builder->create<tensor::ExtractOp>(loc, zero_d);
  return scalar;
}

// Calls the function `fn` with arguments provided by the given function and

    indices[i] = dimension_numbers.start_index_map()[i];
  }

  // Fill elements from start_indices with start_index_map
  Value scattered_start_indices = builder.create<TF::TensorScatterUpdateOp>(
      loc, empty_start_indices,
      /*indices=*/
      builder.create<TF::ReshapeOp>(
          loc, RankedTensorType::get({index_map_size, 1}, builder.getI64Type()),
          Create1DConstValue<int64_t>(builder, loc, indices),

  Type resultType = RankedTensorType::get(shape, element_type);
  auto constant_attr = DenseElementsAttr::get(shape_spec_type, shape);
  auto shape_tensor =
      rewriter.create<TF::ConstOp>(loc, shape_spec_type, constant_attr);
  return rewriter.create<TF::ReshapeOp>(loc, resultType, /*tensor=*/value,
                                        /*shape=*/shape_tensor);
}

template <typename BatchMatMulOpType>

  func->setAttr(kTFImplements, attr);
  OpBuilder builder(func.getBody());
  std::string empty_option_buffer;
  auto op = builder.create<CustomOp>(
      func.getLoc(), func.getFunctionType().getResults(), func.getArguments(),
      api, CustomOption(&builder, empty_option_buffer));
  builder.create<func::ReturnOp>(func.getLoc(), op.getResults());
  return success();
}

LogicalResult VerifyNgrams(func::FuncOp func) {