# Copyright 2017 The TensorFlow Authors. All Rights Reserved. # # 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 # # http://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. # ====================================== """Library of TPU helper functions.""" import enum import math from typing import List, Optional, Text, Tuple import numpy as np from tensorflow.python.platform import tf_logging as logging from tensorflow.python.tpu.topology import Topology from tensorflow.python.util.tf_export import tf_export SINGLE_CORE_ASSIGNMENT = [[[0, 0, 0, 0]]] def _compute_task_and_cores_to_replicas(core_assignment, topology): """Computes a nested dict which maps task and logical core to replicas.""" task_and_cores_to_replicas = {} for replica in range(core_assignment.shape[0]): for logical_core in range(core_assignment.shape[1]): coordinates = core_assignment[replica, logical_core, :] task_id = topology.task_ordinal_at_coordinates(coordinates) if task_id not in task_and_cores_to_replicas: task_and_cores_to_replicas[task_id] = {} if logical_core not in task_and_cores_to_replicas[task_id]: task_and_cores_to_replicas[task_id][logical_core] = set() task_and_cores_to_replicas[task_id][logical_core].add(replica) task_to_sorted_replica_id = {} for task, core_to_replicas in task_and_cores_to_replicas.items(): core_to_sorted_replicas = {} for core, replicas in core_to_replicas.items(): core_to_sorted_replicas[core] = sorted(replicas) task_to_sorted_replica_id[task] = core_to_sorted_replicas return task_to_sorted_replica_id @tf_export("tpu.experimental.DeviceAssignment") class DeviceAssignment(object): """Mapping from logical cores in a computation to the physical TPU topology. Prefer to use the `DeviceAssignment.build()` helper to construct a `DeviceAssignment`; it is easier if less flexible than constructing a `DeviceAssignment` directly. """ def __init__(self, topology: Topology, core_assignment: np.ndarray): """Constructs a `DeviceAssignment` object. Args: topology: A `Topology` object that describes the physical TPU topology. core_assignment: A logical to physical core mapping, represented as a rank 3 numpy array. See the description of the `core_assignment` property for more details. Raises: ValueError: If `topology` is not `Topology` object. ValueError: If `core_assignment` is not a rank 3 numpy array. """ if not isinstance(topology, Topology): raise ValueError("topology must be a Topology object, got {}".format( type(topology))) core_assignment = np.asarray(core_assignment, dtype=np.int32) self._topology = topology if core_assignment.ndim != 3: raise ValueError("core_assignment must be a rank 3 numpy array, " f"got shape {core_assignment.shape}") self._num_replicas = core_assignment.shape[0] self._num_cores_per_replica = core_assignment.shape[1] if core_assignment.shape[-1] != topology.mesh_rank: raise ValueError( "core_assignment.shape[-1] must have size equal to topology " f"rank ({topology.mesh_rank}), got " f"core_assignment.shape={core_assignment.shape}") self._core_assignment = core_assignment self._task_and_cores_to_replicas = _compute_task_and_cores_to_replicas( self._core_assignment, topology) @property def topology(self) -> Topology: """A `Topology` that describes the TPU topology.""" return self._topology @property def num_cores_per_replica(self) -> int: """The number of cores per replica.""" return self._num_cores_per_replica @property def num_replicas(self) -> int: """The number of replicas of the computation.""" return self._num_replicas @property def core_assignment(self) -> np.ndarray: """The logical to physical core mapping. Returns: An integer numpy array of rank 3, with shape `[num_replicas, num_cores_per_replica, topology_rank]`. Maps (replica, logical core) pairs to physical topology coordinates. """ return self._core_assignment def coordinates(self, replica: int, logical_core: int) -> Tuple: # pylint:disable=g-bare-generic """Returns the physical topology coordinates of a logical core.""" return tuple(self.core_assignment[replica, logical_core, :]) def lookup_replicas(self, task_id: int, logical_core: int) -> List[int]: """Lookup replica ids by task number and logical core. Args: task_id: TensorFlow task number. logical_core: An integer, identifying a logical core. Returns: A sorted list of the replicas that are attached to that task and logical_core. Raises: ValueError: If no replica exists in the task which contains the logical core. """ try: return self._task_and_cores_to_replicas[task_id][logical_core] except KeyError: raise ValueError( "Can not find any replica in task: {} contains logical_core: {} ". format(task_id, logical_core)) def tpu_ordinal(self, replica: int = 0, logical_core: int = 0) -> int: """Returns the ordinal of the TPU device assigned to a logical core.""" coordinates = self.coordinates(replica, logical_core) return self._topology.tpu_device_ordinal_at_coordinates(coordinates) def host_device(self, replica: int = 0, logical_core: int = 0, job: Optional[Text] = None) -> Text: """Returns the CPU device attached to a logical core.""" coordinates = self.coordinates(replica, logical_core) return self._topology.cpu_device_name_at_coordinates(coordinates, job=job) def tpu_device(self, replica: int = 0, logical_core: int = 0, job: Optional[Text] = None) -> Text: """Returns the name of the TPU device assigned to a logical core.""" coordinates = self.coordinates(replica, logical_core) return self._topology.tpu_device_name_at_coordinates(coordinates, job=job) @staticmethod def build(topology: Topology, computation_shape: Optional[np.ndarray] = None, computation_stride: Optional[np.ndarray] = None, num_replicas: int = 1) -> "DeviceAssignment": return device_assignment(topology, computation_shape, computation_stride, num_replicas) def _open_ring_2d(x_size: int, y_size: int, z_coord: int) -> List[Tuple[int, int, int]]: """Ring-order of a X by Y mesh, with a fixed Z coordinate. For example, in a 4x4 mesh, this returns the following order. 0 -- 1 -- 2 -- 3 | | | | 15-- 6 -- 5 -- 4 | | | | 14-- 7 -- 8 -- 9 | | | | 13-- 12-- 11-- 10 Note that chip 0 is not included in the output. Args: x_size: An integer represents the mesh size in the x-dimension. Must be larger than 1. y_size: An integer represents the mesh size in the y-dimension. Must be larger than 1. z_coord: An integer represents the z-coordinate to use for the chips in the ring. Returns: A list of (x,y,z) triples in ring order. """ ret = [] for i in range(y_size // 2): for j in range(1, x_size): ret.append((j, 2 * i, z_coord)) for j in range(x_size - 1, 0, -1): ret.append((j, 2 * i + 1, z_coord)) for i in range(y_size - 1, 0, -1): ret.append((0, i, z_coord)) return ret def _ring_3d(x_size: int, y_size: int, z_size: int) -> List[Tuple[int, int, int]]: """Ring-order of a X by Y by Z mesh. Constructs the 3d ring from 2d rings that are stacked in the Z dimension and joined in one corner. z == 0: 0 -- 1 -- 2 -- 3 | | | | 15 - 6 -- 5 -- 4 | | | | 14 - 7 -- 8 -- 9 | | | | 13 - 12 - 11 - 10 z == 1: 63 - 30 - 29 - 28 | | | | 16 - 25 - 26 - 27 | | | | 17 - 24 - 23 - 22 | | | | 18 - 19 - 20 - 21 z == 2: 62 - 31 - 32 - 33 | | | | 45 - 36 - 35 - 34 | | | | 44 - 37 - 38 - 39 | | | | 43 - 42 - 41 - 40 z == 3: 61 - 60 - 59 - 58 | | | | 46 - 55 - 56 - 57 | | | | 47 - 54 - 53 - 52 | | | | 48 - 49 - 50 - 51 Args: x_size: An integer represents the mesh size in the x-dimension. Must be larger than 1. y_size: An integer represents the mesh size in the y-dimension. Must be larger than 1. z_size: An integer represents the mesh size in the z-dimension. Must be larger than 1. For example, in a 4x4x4 mesh, this returns the following order. Returns: A list of (x,y,z) triples in ring order. """ # Handle the case where 2 dimensions are size 1. if x_size == 1 and y_size == 1: return [(0, 0, i) for i in range(z_size)] if x_size == 1 and z_size == 1: return [(0, i, 0) for i in range(y_size)] if y_size == 1 and z_size == 1: return [(i, 0, 0) for i in range(x_size)] # Handle odd mesh dimensions. This never happens in practice, so we don't # bother to try building something optimal. if (x_size > 1 and x_size % 2 != 0) or (y_size > 1 and y_size % 2 != 0) or (z_size > 1 and z_size % 2 != 0): logging.warning("Odd dimension") ret = [] for z in range(z_size): for y in range(y_size): ret.extend((x, y, z) for x in range(x_size)) return ret # Always start with chip 0. ret = [(0, 0, 0)] # Handle the case where one dimension is size 1. We just build a flat, 2d # ring. if z_size == 1: ret.extend(_open_ring_2d(x_size, y_size, 0)) return ret if y_size == 1: ret = [(0, 0, 0)] ret.extend((x, y, z) for (x, z, y) in _open_ring_2d(x_size, z_size, 0)) return ret if x_size == 1: ret = [(0, 0, 0)] ret.extend((x, y, z) for (y, z, x) in _open_ring_2d(y_size, z_size, 0)) return ret # Handle the case where all dimensions have size > 1 and even. ret = [(0, 0, 0)] for i in range(0, z_size): r = _open_ring_2d(x_size, y_size, i) if i % 2 == 0: ret.extend(r) else: ret.extend(reversed(r)) for i in range(z_size - 1, 0, -1): ret.append((0, 0, i)) return ret class DeviceOrderMode(enum.IntEnum): """The way of determining device orders when computing device assignment.""" # By default the mode is set to AUTO, the library will choose to form rings # when that is possible. AUTO = 0 # Form rings for replicas and model-parallel cores. RING = 1 # Form meshes for replicas and/or model-parallel cores. MESH = 2 def device_assignment( topology: Topology, computation_shape: Optional[np.ndarray] = None, computation_stride: Optional[np.ndarray] = None, num_replicas: int = 1, device_order_mode: DeviceOrderMode = DeviceOrderMode.AUTO ) -> DeviceAssignment: """Computes a device_assignment of a computation across a TPU topology. Attempts to choose a compact grid of cores for locality. Returns a `DeviceAssignment` that describes the cores in the topology assigned to each core of each replica. `computation_shape` and `computation_stride` values should be powers of 2 for optimal packing. Args: topology: A `Topology` object that describes the TPU cluster topology. To obtain a TPU topology, evaluate the `Tensor` returned by `initialize_system` using `Session.run`. Either a serialized `TopologyProto` or a `Topology` object may be passed. Note: you must evaluate the `Tensor` first; you cannot pass an unevaluated `Tensor` here. computation_shape: A rank 1 int32 numpy array with size equal to the topology rank, describing the shape of the computation's block of cores. If None, the `computation_shape` is `[1] * topology_rank`. computation_stride: A rank 1 int32 numpy array of size `topology_rank`, describing the inter-core spacing of the `computation_shape` cores in the TPU topology. If None, the `computation_stride` is `[1] * topology_rank`. num_replicas: The number of computation replicas to run. The replicas will be packed into the free spaces of the topology. device_order_mode: An enum of `DeviceOrderMode` class which indicates whether to assign devices to form rings or meshes, or let the library to choose. Returns: A DeviceAssignment object, which describes the mapping between the logical cores in each computation replica and the physical cores in the TPU topology. Raises: ValueError: If `topology` is not a valid `Topology` object. ValueError: If `computation_shape` or `computation_stride` are not 1D int32 numpy arrays with shape [3] where all values are positive. ValueError: If computation's replicas cannot fit into the TPU topology. """ # Deserialize the Topology proto, if it is a string. if isinstance(topology, bytes): topology = Topology(serialized=topology) if not isinstance(topology, Topology): raise ValueError( f"`topology` is not a Topology object; got {type(topology)}") topology_rank = len(topology.mesh_shape) mesh_shape = topology.mesh_shape if computation_shape is None: computation_shape = np.array([1] * topology_rank, dtype=np.int32) else: computation_shape = np.asarray(computation_shape, dtype=np.int32) if computation_stride is None: computation_stride = np.array([1] * topology_rank, dtype=np.int32) else: computation_stride = np.asarray(computation_stride, dtype=np.int32) if computation_shape.shape != (topology_rank,): raise ValueError( f"computation_shape must have shape [{topology_rank}]; " f"got {computation_shape.shape}" ) if computation_stride.shape != (topology_rank,): raise ValueError( f"computation_stride must have shape [{topology_rank}]; " f"got {computation_stride.shape}" ) if any(computation_shape < 1): raise ValueError( "computation_shape must be positive; got computation_shape={}".format( computation_shape)) if any(computation_stride < 1): raise ValueError( "computation_stride must be positive; got computation_stride={}".format( computation_stride)) # Computes the physical size of one computation instance. computation_footprint = computation_shape * computation_stride if any(computation_footprint > mesh_shape): raise ValueError( "computation footprint {} does not fit in TPU topology shape {}".format( computation_footprint, mesh_shape)) # Computes how many copies of the computation footprint fit in the mesh. block_counts = mesh_shape // computation_footprint replica_counts = block_counts * computation_stride max_replicas = np.prod(replica_counts) if num_replicas > max_replicas: raise ValueError( "requested {} replicas but only {} replicas with shape {} and " "computation_stride {} fit in a TPU mesh of shape {}".format( num_replicas, max_replicas, computation_shape, computation_stride, mesh_shape)) def ceil_of_ratio(n, m): return (n + m - 1) // m if topology.missing_devices.size == 0: replica_shape = [0] * topology_rank if num_replicas > 0: remaining_replicas = num_replicas remaining_dims = topology_rank # Choose dimensions as close to an equal cube as possible, # in order of increasing dimension size. By visiting dimensions # in increasing size, we assign the most constrained dimension # first, so we won't make infeasible choices. # # As a secondary sort order, visit the last dimension (core index) first, # then the other dimensions in increasing order. This means we try to use # both cores on the same chip in preference to two cores on different # chips. We visit the x dimension first, and the z dimension last, so # that we prefer to arrange adjacent replicas on the same machine when # possible. # # For example, if num_replicas == 4, we prefer to use a replica_shape of # (2,1,1,2) over (1,1,2,2). for x, ni in sorted(((x, ((i + 1) % topology_rank)) for (i, x) in enumerate(replica_counts))): i = (ni + topology_rank - 1) % topology_rank target_size = int(math.ceil(remaining_replicas**(1.0 / remaining_dims))) replica_shape[i] = min(target_size, x) remaining_replicas = ceil_of_ratio(remaining_replicas, replica_shape[i]) remaining_dims -= 1 assert remaining_replicas == 1 and remaining_dims == 0 # Assigns an offset to each replica such that no two replicas overlap. replica_offsets = np.full([num_replicas, topology_rank], -1, dtype=np.int32) enable_3d_tiling = ( topology_rank == 4 and computation_shape[-1] == mesh_shape[-1] # Only handle 3D case. and np.prod(computation_stride) == 1 # Ensure no stride. and num_replicas == max_replicas) # Full replication. if device_order_mode != DeviceOrderMode.AUTO: if device_order_mode == DeviceOrderMode.RING and not enable_3d_tiling: raise ValueError( "device_order_mode=DeviceOrderMode.RING is not compatible with the " "3D tiling current topology. Try setting " "device_order_mode=DeviceOrderMode.AUTO" ) enable_3d_tiling = device_order_mode == DeviceOrderMode.RING if enable_3d_tiling: assignment = [] inner_ring = _ring_3d(computation_shape[0], computation_shape[1], computation_shape[2]) outer_ring = _ring_3d(replica_shape[0], replica_shape[1], replica_shape[2]) for replica in range(num_replicas): outer_x, outer_y, outer_z = outer_ring[replica] per_replica_assignment = [] for index in range(np.prod(computation_shape)): inner_x, inner_y, inner_z = inner_ring[index // mesh_shape[-1]] px = outer_x * computation_shape[0] + inner_x py = outer_y * computation_shape[1] + inner_y pz = outer_z * computation_shape[2] + inner_z pi = index % mesh_shape[-1] per_replica_assignment.append([px, py, pz, pi]) assignment.append(per_replica_assignment) else: for replica in range(num_replicas): # Chooses a replica number in each axis. t = replica pos = [] # Visit the core number first. for dim in np.concatenate([[replica_shape[-1]], replica_shape[:-1]]): pos.append(t % dim) t //= dim replica_pos = np.concatenate([pos[1:], [pos[0]]]) # Determines where that replica starts in each axis. outer = replica_pos // computation_stride inner = replica_pos % computation_stride replica_offsets[replica, :] = outer * computation_footprint + inner # Computes a logical core -> physical core mapping for each replica. indices = [ np.arange(0, computation_shape[i] * computation_stride[i], computation_stride[i]) for i in range(topology_rank) ] indices = np.concatenate( [i[..., np.newaxis] for i in np.meshgrid(*indices, indexing="ij")], axis=-1) indices = indices.reshape((-1, topology_rank)) assignment = indices + replica_offsets[:, np.newaxis, :] else: # We have a slice with missing chips. We define a simple assignment by # ignoring computation stride. This assignment should enable a consistent # and correct device assignment on degraded slices. It is optimal when # weights are not sharded. But this device assignment may be sub-optimal for # other model parallelism scenarios. assert np.prod(computation_stride) == 1 # Next, we check if we have sufficient devices. assert num_replicas * np.prod( computation_shape) <= topology.num_tasks * topology.num_tpus_per_task # Map replicas to physical devices in task order. device_coordinates = topology.device_coordinates assignment = [] devices_per_replica = np.prod(computation_shape) for rindex in range(num_replicas): replica_assignment = [] for index in range(devices_per_replica): logical_id = rindex * devices_per_replica + index # Pick logical cores in task order task = logical_id // topology.num_tpus_per_task device = logical_id % topology.num_tpus_per_task # Append physical cores to the replica assignment replica_assignment.append(device_coordinates[task, device, :]) assignment.append(replica_assignment) return DeviceAssignment(topology, core_assignment=assignment)