| # Copyright (C) 2021 Arm Limited or its affiliates. All rights reserved. |
| # |
| # SPDX-License-Identifier: Apache-2.0 |
| # |
| # Licensed under the Apache License, Version 2.0 (the License); you may |
| # not use this file except in compliance with the License. |
| # You may obtain a copy of the License at |
| # |
| # www.apache.org/licenses/LICENSE-2.0 |
| # |
| # Unless required by applicable law or agreed to in writing, software |
| # distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| # WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| # See the License for the specific language governing permissions and |
| # limitations under the License. |
| # Description: |
| # Early optimisation of the TOSA based network graph, using the rewrite_graph module to do the traversal of the graph. |
| import numpy as np |
| |
| from . import rewrite_graph |
| from .api import NpuRoundingMode |
| from .data_type import DataType |
| from .debug_database import DebugDatabase |
| from .graph_optimiser_util import bypass_memory_only_ops |
| from .graph_optimiser_util import calc_explicit_padding |
| from .graph_optimiser_util import convert_depthwise_to_conv |
| from .graph_optimiser_util import move_splitsliceread_to_consumer |
| from .graph_optimiser_util import needed_total_padding |
| from .graph_optimiser_util import set_ifm_ofm_op_shapes |
| from .graph_optimiser_util import set_tensor_equivalence |
| from .operation import ExplicitScaling |
| from .operation import Op |
| from .operation_util import create_add_nop |
| from .operation_util import create_avgpool_nop |
| from .shape4d import Shape4D |
| from .tensor import create_const_tensor |
| from .tensor import create_equivalence_id |
| |
| |
| def replace_rescale_with_avg_pool(rescale_op): |
| assert rescale_op.type == Op.Rescale |
| |
| avgpool_op = create_avgpool_nop(rescale_op.name + "_avgpool") |
| rescale_op_clone = rescale_op.clone() |
| op = rescale_op |
| op.attrs = avgpool_op.attrs.copy() |
| op.type = Op.AvgPool |
| DebugDatabase.add_optimised(rescale_op_clone, op) |
| |
| return op |
| |
| |
| def calc_skirt(kernel, input_shape, explicit_padding): |
| k_w, k_h = kernel.dilated_wh() |
| s_x, s_y = kernel.stride |
| ypad = needed_total_padding(int(input_shape.height), int(s_y), int(k_h)) |
| xpad = needed_total_padding(int(input_shape.width), int(s_x), int(k_w)) |
| |
| top, left, bottom, right = explicit_padding |
| top_pad, bottom_pad = calc_explicit_padding(int(input_shape.height), int(s_y), int(k_h), int(top), int(bottom)) |
| left_pad, right_pad = calc_explicit_padding(int(input_shape.width), int(s_x), int(k_w), int(left), int(right)) |
| |
| padding = (top_pad, left_pad, bottom_pad, right_pad) |
| skirt = (top_pad, left_pad, ypad - top_pad, xpad - left_pad) |
| return padding, skirt |
| |
| |
| def add_padding_fields(op, arch, nng): |
| if op.run_on_npu: |
| if "explicit_padding" in op.attrs: |
| input_shape = op.ifm_shapes[0] |
| |
| if op.type == Op.Conv2DBackpropInputSwitchedBias: |
| # TODO not yet supported, but there will be need for separate handling |
| assert False |
| else: |
| padding, skirt = calc_skirt(op.kernel, input_shape, op.attrs.get("explicit_padding")) |
| |
| op.attrs["explicit_padding"] = padding |
| op.attrs["skirt"] = skirt |
| |
| return op |
| |
| |
| # Counts leading zeroes for a (int32) |
| def count_leading_zeros(a): |
| lz = int(32) |
| if a != 0: |
| mask = 1 << (32 - 1) |
| lz = 0 |
| while (mask & a) == 0: |
| mask = mask >> 1 |
| lz = lz + 1 |
| return lz |
| |
| |
| def calc_scaling_avgpool(op, arch, nng): |
| if op.type == Op.AvgPool: |
| top, left, _, _ = op.attrs["explicit_padding"] |
| # TODO Only support for when global scaling can be used. |
| # That is when there is no padding |
| assert top == 0 and left == 0 |
| assert op.explicit_scaling is None |
| multiplier = [] |
| shift = [] |
| |
| kernel_wh = op.kernel.elements_wh() |
| k = 32 - count_leading_zeros(kernel_wh - 1) |
| numerator = np.int64(((1 << 30) + 1) << k) |
| multiplier.append(numerator // kernel_wh) |
| shift.append(30 + k) |
| |
| op.rounding_mode = NpuRoundingMode.NATURAL |
| op.explicit_scaling = ExplicitScaling(False, shift, multiplier) |
| return op |
| |
| |
| def remove_const_transpose(op, arch, nng): |
| if op.type == Op.Transpose: |
| removed = False |
| if len(op.ifm.ops) == 1: |
| prev_op = op.ifm.ops[0] |
| if prev_op.type == Op.Const: |
| # Transpose the Tensor and data and remove Transpose |
| # TODO move to Tensor? |
| reorder = op.attrs["perms"] |
| shape = op.ifm.shape.copy() |
| tens = op.ifm |
| |
| tens.shape = [shape[idx] for idx in reorder] |
| tens.bandwidth_shape = tens.shape |
| tens.storage_shape = tens.shape |
| |
| if tens.values is not None: |
| tens.values = tens.values.transpose(reorder) |
| |
| op.ofm.values = tens.values |
| # Bypass the Transpose op |
| prev_op.set_output_tensor(op.ofm) |
| DebugDatabase.add_optimised(op, prev_op) |
| removed = True |
| |
| if not removed: |
| print("Warning: Cannot remove Transpose, and handling of Transpose is not supported") |
| assert False |
| |
| return op |
| |
| |
| # TODO can we change to add for both TFLite and TOSA? |
| def insert_add_copy_op_after_tens(tens): |
| tens_cons_list_copy = tens.consumer_list.copy() |
| copy_tens = tens.clone() |
| |
| name = tens.name + "_add" |
| ifm2 = create_const_tensor( |
| name + "_zero_scalar", |
| [1], |
| copy_tens.dtype, |
| [0], |
| copy_tens.dtype.as_numpy_type(), |
| quantization=copy_tens.quantization, |
| ) |
| copy_op = create_add_nop(name) |
| copy_op.add_input_tensor(tens) |
| copy_op.add_input_tensor(ifm2) |
| copy_op.set_output_tensor(copy_tens) |
| copy_op.set_ifm_ofm_shapes() |
| copy_op.run_on_npu = True |
| |
| # Set copy_ifm consumers |
| for tens_cons in tens_cons_list_copy: |
| if tens_cons is not None: |
| for ifm_idx, cons_inp in enumerate(tens_cons.inputs): |
| if cons_inp == tens: |
| tens_cons.set_input_tensor(copy_tens, ifm_idx) |
| |
| DebugDatabase.add_optimised(tens.ops[0], copy_op) |
| |
| |
| def fix_sg_input_output_tosa(op, arch, nng): |
| if not op.run_on_npu or op.type != Op.Reshape: |
| return op |
| |
| # For the Reshape operators we want to remove, tensors are removed. |
| # But in order to to do this, they cannot be outputs of the sg, |
| # this need to be fixed prior to the removal. |
| # Solution is to add a copy op, to maintain the original tensor. |
| # This is also valid when reshape ifm/ofm is produced respectively |
| # consumed by CPU |
| |
| # Check if operator ifm/ofm are sg ifm/ofm |
| ifm_is_sg_ifm = op.ifm.ops[0].type in (Op.Placeholder, Op.SubgraphInput, Op.Const) |
| ifm_is_sg_ofm = any(ifm_cons is None for ifm_cons in op.ifm.consumer_list) |
| ofm_is_sg_ofm = any(ofm_cons is None for ofm_cons in op.ofm.consumer_list) |
| # Check if ifm/ofm is produced repectivly consumed by CPU |
| ifm_is_cpu_produced = any(ifm_prod is not None and not ifm_prod.run_on_npu for ifm_prod in op.ifm.ops) |
| ofm_is_cpu_consumed = any(ofm_cons is not None and not ofm_cons.run_on_npu for ofm_cons in op.ofm.consumer_list) |
| |
| if (ifm_is_sg_ofm or ifm_is_sg_ifm or ifm_is_cpu_produced) and (ofm_is_sg_ofm or ofm_is_cpu_consumed): |
| # Both ifm and ofm need to persist, but only ifm need a copy, in order to remove the Reshape |
| insert_add_copy_op_after_tens(op.ifm) |
| |
| return op |
| |
| |
| def create_add_for_concat(concat_op, name, ifm, ifm_shape: Shape4D, write_offset: Shape4D): |
| """Creates an add op for the given concat op/input feature map""" |
| ofm = concat_op.ofm |
| ifm2 = create_const_tensor( |
| name + "_zero_scalar", [1], ofm.dtype, [0], ofm.dtype.as_numpy_type(), quantization=ofm.quantization |
| ) |
| add_op = create_add_nop(name) |
| |
| add_op.inputs = [ifm, ifm2] |
| add_op.outputs = [ofm] |
| add_op.write_offset = write_offset |
| add_op.write_shape = ifm_shape |
| ofm.ops.append(add_op) |
| DebugDatabase.add_optimised(concat_op, add_op) |
| add_op.ifm_shapes.append(ifm_shape) |
| add_op.ifm_shapes.append(Shape4D(ifm2.shape)) |
| add_op.ofm_shapes.append(concat_op.ofm_shapes[0]) |
| add_op.memory_function = Op.ConcatSliceWrite |
| return add_op |
| |
| |
| # TODO Could be further optimized checking the type of the consumer, |
| # rather than just mimic the TFLite behaviour depending on type. |
| # TOSA bool_t not considered yet |
| def remove_splitsliceread(op, arch): |
| |
| if op.type == Op.SplitSliceRead: |
| # Check if it is possible to put the SplitSliceRead on the tensor consumer, or if an avgpool need to be inserted |
| if ( |
| len(op.ofm.consumer_list) == 1 |
| and op.ofm.consumer_list[0] is not None |
| and op.ofm.consumer_list[0].run_on_npu |
| and op.ofm.consumer_list[0].type != Op.Reshape |
| and op.ofm_shapes[0] == Shape4D.from_list(op.ofm.shape) |
| and op.ofm.dtype in (DataType.uint8, DataType.int8, DataType.int16) |
| ): |
| # SplitSliceRead can be performed by tensor consumer |
| cons_op = op.ofm.consumer_list[0] |
| move_splitsliceread_to_consumer(op, cons_op) |
| else: |
| name = op.name + "_add" |
| ofm = op.ofm |
| ifm2 = create_const_tensor( |
| name + "_zero_scalar", [1], ofm.dtype, [0], ofm.dtype.as_numpy_type(), quantization=ofm.quantization |
| ) |
| add_op = create_add_nop(name) |
| add_op.inputs = [op.ifm, ifm2] |
| add_op.outputs = [ofm] |
| op.ofm.ops.remove(op) |
| op.ofm.ops.append(add_op) |
| add_op.ifm_shapes.append(op.ifm_shapes[0]) |
| add_op.ifm_shapes.append(Shape4D(ifm2.shape)) |
| add_op.ofm_shapes.append(op.ofm_shapes[0]) |
| add_op.read_offsets[0] = op.read_offsets[0] |
| add_op.read_shapes[0] = op.read_shapes[0] |
| |
| op.ifm.consumer_list.remove(op) |
| DebugDatabase.add_optimised(op, add_op) |
| |
| |
| def rewrite_concat_ops(op, arch): |
| if not op.run_on_npu or not op.type == Op.Concat: |
| return |
| |
| axis_4D = 0 |
| ofm = op.ofm |
| ofm.ops = [] |
| offset = 0 |
| |
| inputs = op.inputs |
| axis = op.attrs["axis"] |
| |
| for idx, inp in enumerate(inputs): |
| op.ifm_shapes[idx] = Shape4D(inp.shape) |
| if axis >= 0: |
| axis_4D = axis + (4 - len(inp.shape)) |
| else: |
| axis_4D = axis |
| write_offset = [0, 0, 0, 0] |
| write_offset[axis_4D] = offset |
| concat_end = offset + op.ifm_shapes[idx][axis_4D] |
| create_add_for_concat(op, op.name + str(idx) + "_add", inp, op.ifm_shapes[idx], Shape4D.from_list(write_offset)) |
| offset = concat_end |
| assert ofm.shape[axis] == offset |
| |
| return op |
| |
| |
| def remove_reshapes(op, arch): |
| if op.run_on_npu and op.type == Op.Reshape: |
| bypass_memory_only_ops(op) |
| |
| |
| def rewrite_activation(op, arch, nng): |
| if op.type not in (Op.ReluN, Op.Clamp): |
| return op |
| |
| ifm = op.ifm |
| zp = ifm.quantization.zero_point if ifm.quantization.zero_point else 0 |
| if op.ofm.quantization.zero_point is None: |
| op.ofm.quantization.zero_point = zp |
| |
| if op.type == Op.Clamp: |
| op.attrs["min"] = op.attrs["min_int"] - zp |
| op.attrs["max"] = op.attrs["max_int"] - zp |
| elif op.type == Op.ReluN: |
| op.attrs["max"] = op.attrs["max_int"] - zp |
| |
| return op |
| |
| |
| def rewrite_rescale(op, arch, nng): |
| if op.type == Op.Rescale: |
| ifm = op.ifm |
| ofm = op.ofm |
| |
| # some error checking |
| assert len(ifm.ops) == 1 |
| prev_op = ifm.ops[0] |
| |
| # TODO currently not supported |
| assert len(ifm.consumer_list) == 1 |
| |
| input_zp = op.attrs["input_zp"] |
| output_zp = op.attrs["output_zp"] |
| multiplier = op.attrs["multiplier"] |
| shift = op.attrs["shift"] |
| scale32 = op.attrs["scale32"] |
| double_round = op.attrs["double_round"] |
| per_channel = op.attrs["per_channel"] |
| |
| assert ifm.dtype in (DataType.uint8, DataType.int8, DataType.int32) |
| assert ifm.dtype in (DataType.uint8, DataType.int8) or input_zp == 0 |
| assert ofm.dtype in (DataType.uint8, DataType.int8) or output_zp == 0 |
| assert (scale32 and ifm.dtype != DataType.int48) or (not scale32 and not double_round) |
| |
| # Check that input tensor has the same zp or no zp |
| ifm_zp = ifm.quantization.zero_point |
| if ifm_zp is not None and ifm_zp != input_zp: |
| print("Error (fuse_rescale): zp of tensors producer/consumer differs unexpectedidly ") |
| assert False |
| ifm.quantization.zero_point = input_zp |
| ofm.quantization.zero_point = output_zp |
| for s, m in zip(shift, multiplier): |
| # TODO these are the TOSA limitations |
| assert m >= 0 |
| assert 2 <= s <= 62 |
| # TODO these are the HW limitations |
| assert 0 <= s < (1 << 6) |
| explicit_scaling = ExplicitScaling(per_channel, shift, multiplier) |
| |
| if double_round and scale32: |
| rounding_mode = NpuRoundingMode.TFL |
| else: |
| rounding_mode = NpuRoundingMode.NATURAL |
| |
| if prev_op.type.is_depthwise_conv2d_op() or prev_op.type.is_conv2d_op() or prev_op.type == Op.FullyConnected: |
| assert len(multiplier) == len(shift) == len(prev_op.bias.values) |
| |
| if ifm.dtype == DataType.int32 and per_channel: |
| prev_op.explicit_scaling = explicit_scaling |
| prev_op.rounding_mode = rounding_mode |
| |
| # Bypass op |
| prev_op.set_output_tensor(ofm) |
| DebugDatabase.add_optimised(op, prev_op) |
| return op |
| else: |
| print("Warning, unsupported fusing of TOSA Rescale previous operator is of type:", prev_op.type) |
| assert False |
| # TODO which are the cases we need to and can do standalone Rescale? |
| # TODO should we try to identify a conversion uint8<->int8 accomplished by 2 RESCALE ops? |
| # origin might be TFLite op QUANTIZE, should we look to see if they can be translated to QUANTIZE? |
| # limited to these at the moment: |
| elif ( |
| (ifm.dtype == DataType.int8 and ofm.dtype == DataType.int8) |
| or (ifm.dtype == DataType.uint8 and ofm.dtype == DataType.int8) |
| or (ifm.dtype == DataType.int8 and ofm.dtype == DataType.uint8) |
| ): |
| # Create NOP performing the RESCALE |
| avgpool_op = replace_rescale_with_avg_pool(op) |
| avgpool_op.rounding_mode = rounding_mode |
| |
| if per_channel: |
| # TODO |
| avgpool_op.explicit_scaling = explicit_scaling |
| print("Warning, unsupported TOSA Rescale") |
| assert False |
| else: |
| avgpool_op.explicit_scaling = explicit_scaling |
| else: |
| print("Warning, unsupported fusing of TOSA Rescale previous operator is of type:", prev_op.type) |
| assert False |
| return op |
| |
| |
| # TODO modified copy of TFLite, solution for TOSA PAD will change so reuse has not been considered |
| def convert_pad(op, arch, nng): |
| """ |
| Rewrites PAD operator to an add that copies the IFM to the OFM |
| + up to 4 add operators that fill the OFM with zeros at the borders. |
| """ |
| |
| if op.type != Op.Pad: |
| return op |
| |
| # TODO assuming rank <= 4 and N = 1 for rank ==4 |
| # This is checked in tosa_supported_operators |
| ifm = op.ifm |
| assert ifm is not None |
| ifm_shape = Shape4D(ifm.shape) |
| ofm = op.ofm |
| assert ofm is not None |
| ofm.ops = [] |
| ofm_shape = op.ofm_shapes[0] |
| |
| rank = len(ifm.shape) |
| padding = op.inputs[1].values |
| pad_depth = padding[-1] |
| if not (pad_depth == 0).all(): |
| print("Warning: For PAD, padding in depth not supported yet") |
| assert False |
| |
| top, bottom = 0, 0 |
| left, right = 0, 0 |
| if rank > 1: |
| left, right = padding[-2][0], padding[-2][1] |
| if rank > 2: |
| top, bottom = padding[-3][0], padding[-3][1] |
| if rank == 4 and not (padding[-4] == 0).all(): |
| print("Warning: For PAD, padding not supported in first dimension when rank == 4 yet") |
| assert False |
| |
| # Add op that copies IFM to the right place inside the OFM |
| shp0 = Shape4D(0, 0, 0, 0) |
| shp_top = shp0.with_height(top) |
| add_op = create_add_for_concat(op, op.name + "_main", ifm, ifm_shape, shp_top.with_width(left)) |
| add_op.activation = op.activation |
| |
| quant = ofm.quantization |
| pad_value = ifm.quantization.zero_point |
| # Add operations that fill the borders of the OFM |
| if top > 0: |
| shape = Shape4D(1, top, ofm_shape.width, ofm_shape.depth) |
| zero_tens = create_const_tensor( |
| op.name + "_top", |
| shape.as_list(), |
| ofm.dtype, |
| shape.elements() * [pad_value], |
| np.uint8, |
| quantization=quant, # TODO |
| ) |
| # If top/bottom or left/right are equal, the const tensors can be allocated to the same address |
| zero_tens.equivalence_id = create_equivalence_id(tuple(zero_tens.values)) |
| create_add_for_concat(op, op.name + "_top", zero_tens, shape, shp0) |
| if bottom > 0: |
| shape = Shape4D(1, bottom, ofm_shape.width, ofm_shape.depth) |
| zero_tens = create_const_tensor( |
| op.name + "_bottom", |
| shape.as_list(), |
| ofm.dtype, |
| shape.elements() * [pad_value], |
| np.uint8, |
| quantization=quant, |
| ) |
| zero_tens.equivalence_id = create_equivalence_id(tuple(zero_tens.values)) |
| create_add_for_concat(op, op.name + "_bottom", zero_tens, shape, shp0.with_height(ofm_shape.height - bottom)) |
| if left > 0: |
| shape = Shape4D(1, ifm_shape.height, left, ofm_shape.depth) |
| zero_tens = create_const_tensor( |
| op.name + "_left", shape.as_list(), ofm.dtype, shape.elements() * [pad_value], np.uint8, quantization=quant |
| ) |
| zero_tens.equivalence_id = create_equivalence_id(tuple(zero_tens.values)) |
| create_add_for_concat(op, op.name + "_left", zero_tens, shape, shp_top) |
| if right > 0: |
| shape = Shape4D(1, ifm_shape.height, right, ofm_shape.depth) |
| zero_tens = create_const_tensor( |
| op.name + "_right", shape.as_list(), ofm.dtype, shape.elements() * [pad_value], np.uint8, quantization=quant |
| ) |
| zero_tens.equivalence_id = create_equivalence_id(tuple(zero_tens.values)) |
| create_add_for_concat(op, op.name + "_right", zero_tens, shape, shp_top.with_width(ofm_shape.width - right)) |
| |
| op.type = Op.ConcatTFLite |
| return add_op |
| |
| |
| def fixup_quantization(op, arch, nng): |
| if op.ifm and op.ifm.quantization.zero_point is None: |
| op.ifm.quantization.zero_point = 0 |
| if op.ifm2 and op.ifm2.quantization.zero_point is None: |
| op.ifm.quantization.zero_point = 0 |
| if op.ofm and op.ofm.quantization.zero_point is None: |
| op.ofm.quantization.zero_point = 0 |
| return op |
| |
| |
| def supported_operator_check(op, arch, nng): |
| op.run_on_npu = arch.tosa_supported_operators.is_operator_supported(op) |
| assert op.run_on_npu or op.type in (Op.Placeholder, Op.SubgraphInput, Op.Const) |
| return op |
| |
| |
| def tosa_optimise_graph(nng, arch): |
| # Pre-processing step |
| pre_process_list = [ |
| supported_operator_check, |
| set_ifm_ofm_op_shapes, |
| ] |
| |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], pre_process_list, rewrite_unsupported=False, |
| ) |
| |
| # Removal of Transpose |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], [remove_const_transpose], rewrite_unsupported=False, |
| ) |
| |
| # Handle sg input output |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], [fix_sg_input_output_tosa], rewrite_unsupported=False, |
| ) |
| |
| # Rewrite concat ops |
| for idx, sg in enumerate(nng.subgraphs): |
| rewrite_graph.visit_graph_post_order(sg.output_tensors, arch, [], [rewrite_concat_ops]) |
| sg.refresh_after_modification() |
| |
| # Removal of reshapes |
| for sg in nng.subgraphs: |
| rewrite_graph.visit_graph_post_order(sg.output_tensors, arch, [], [remove_reshapes]) |
| sg.refresh_after_modification() |
| |
| # TODO, when and where to best handle calc_scaling_avgpool |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], [calc_scaling_avgpool], rewrite_unsupported=False, |
| ) |
| |
| # Rewite Operators step |
| op_rewrite_list = [set_tensor_equivalence, rewrite_rescale, convert_depthwise_to_conv] |
| |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], op_rewrite_list, rewrite_unsupported=False, |
| ) |
| |
| # Post-processing step 1 |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order( |
| nng, sg, arch, [], [rewrite_activation, convert_pad, add_padding_fields], |
| ) |
| |
| # Removal of Slice, need to be done after optimisation has been performed, |
| # since ifm/ofm_shapes are of importance to this function |
| for sg in nng.subgraphs: |
| rewrite_graph.visit_graph_post_order(sg.output_tensors, arch, [], [remove_splitsliceread]) |
| sg.refresh_after_modification() |
| |
| # Post-processing step 2 |
| for idx, sg in enumerate(nng.subgraphs): |
| nng.subgraphs[idx] = rewrite_graph.rewrite_graph_pre_order(nng, sg, arch, [], [fixup_quantization],) |
| |
| return nng |