# Copyright 2019 Uber Technologies, Inc. All Rights Reserved.
# Modifications copyright Microsoft
# Modifications copyright (C) 2020, NVIDIA CORPORATION. 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.
# ==============================================================================

# Load all the necessary PyTorch C types.
import torch

import warnings

from horovod.common.basics import HorovodBasics as _HorovodBasics
from horovod.common.exceptions import HorovodInternalError
from horovod.common.process_sets import _setup as _setup_process_sets
from horovod.common.process_sets import ProcessSet, global_process_set, add_process_set, remove_process_set
from horovod.common.util import check_installed_version, get_average_backwards_compatibility_fun, gpu_available, num_rank_is_power_2

from horovod.torch.compression import Compression

# Check possible symbol not found error from pytorch version mismatch
try:
    from horovod.torch import mpi_lib_v2 as mpi_lib
except Exception as e:
    check_installed_version('pytorch', torch.__version__, e)
    raise e
else:
    check_installed_version('pytorch', torch.__version__)

_NULL = ""

_basics = _HorovodBasics(__file__, 'mpi_lib_v2')

# import basic methods
is_initialized = _basics.is_initialized
start_timeline = _basics.start_timeline
stop_timeline = _basics.stop_timeline
size = _basics.size
local_size = _basics.local_size
cross_size = _basics.cross_size
rank = _basics.rank
local_rank = _basics.local_rank
cross_rank = _basics.cross_rank
mpi_threads_supported = _basics.mpi_threads_supported
mpi_enabled = _basics.mpi_enabled
mpi_built = _basics.mpi_built
gloo_enabled = _basics.gloo_enabled
gloo_built = _basics.gloo_built
nccl_built = _basics.nccl_built
ddl_built = _basics.ddl_built
ccl_built = _basics.ccl_built
cuda_built = _basics.cuda_built
rocm_built = _basics.rocm_built
sycl_built = _basics.sycl_built

def shutdown(*args, **kwargs):
    mpi_lib.horovod_torch_reset()
    return _basics.shutdown(*args, **kwargs)

def init(*args, **kwargs):
    global _handle_map
    _handle_map = {}
    _basics.init(*args, **kwargs)
    # Call set up again to make sure the basics is in sync
    _setup_process_sets(_basics)

# import reduction op values
Average = _basics.Average
Sum = _basics.Sum
Adasum = _basics.Adasum
Min = _basics.Min
Max = _basics.Max
Product = _basics.Product

is_homogeneous = _basics.is_homogeneous

handle_average_backwards_compatibility = get_average_backwards_compatibility_fun(_basics)

_setup_process_sets(_basics)


# Schema: handle -> input, output
# We keep input in order to make sure it does not get garbage collected
# before the operation is finished.
_handle_map = {}


def _check_function(function_factory, tensor):
    function = function_factory(tensor)
    if not hasattr(mpi_lib, function):
        raise ValueError('Tensor type %s is not supported.' % tensor.type())
    if sycl_built():
        if not tensor.is_contiguous() and not tensor.is_contiguous(memory_format=torch.channels_last) and not tensor.is_contiguous(memory_format=torch.channels_last_3d):
            raise ValueError(
                'On xpu backend, tensor is required to be contiguous, or channel_last, or channels_last_3d')
    else:
        if not tensor.is_contiguous():
            raise ValueError('Tensor is required to be contiguous')

    return function


def _allreduce_function_factory(tensor):
    return 'horovod_torch_allreduce_async_' + tensor.type().replace('.', '_')


def _allreduce_async(tensor, output, name, op, prescale_factor, postscale_factor, process_set: ProcessSet):
    # Set the divisor for reduced gradients to average when necessary
    if op == Average:
        if rocm_built():
            # For ROCm, perform averaging at framework level
            divisor = process_set.size()
            op = Sum
        else:
            divisor = 1

    elif op == Adasum:
        if process_set != global_process_set:
            raise NotImplementedError("Adasum does not support non-global process sets yet.")
        if tensor.device.type != 'cpu' and gpu_available('torch'):
            if nccl_built():
                if not is_homogeneous():
                    raise NotImplementedError('Running GPU Adasum on heterogeneous cluster is not supported yet.')
                elif not num_rank_is_power_2(int(size() / local_size())):
                    raise NotImplementedError('Running GPU Adasum with non-power of 2 nodes is not supported yet.')
                if rocm_built():
                    # For ROCm, perform averaging at framework level
                    divisor = local_size()
                else:
                    divisor = 1
            else:
                warnings.warn('Adasum reduction does not currently support GPU reduction using MPI. Tensors are '
                              'copied to CPU memory instead. To use Adasum for GPU reduction, please compile Horovod '
                              'with HOROVOD_GPU_OPERATIONS=NCCL.')
                divisor = 1
        else:
            if not num_rank_is_power_2(size()):
                raise NotImplementedError('Running Adasum with non-power of 2 ranks is not supported yet.')
            divisor = 1
    else:
        divisor = 1

    function = _check_function(_allreduce_function_factory, tensor)
    try:
        handle = getattr(mpi_lib, function)(tensor, output, divisor,
                                            name.encode() if name is not None else _NULL, op,
                                            prescale_factor, postscale_factor, process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tensor, output)
    return handle


def allreduce_async(tensor, average=None, name=None, op=None,
                    prescale_factor=1.0, postscale_factor=1.0,
                    process_set=global_process_set):
    """
    A function that performs asynchronous averaging or summation of the input tensor
    over all the Horovod processes. The input tensor is not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A name of the reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the allreduce operation that can be used with `poll()` or
        `synchronize()`.
    """
    op = handle_average_backwards_compatibility(op, average)
    output = tensor.new(tensor.shape)
    return _allreduce_async(tensor, output, name, op, prescale_factor, postscale_factor, process_set)


class HorovodAllreduce(torch.autograd.Function):
    """An autograd function that performs allreduce on a tensor."""

    @staticmethod
    def forward(ctx, tensor, average, name, op, prescale_factor, postscale_factor, process_set):
        ctx.average = average
        ctx.op = op
        ctx.prescale_factor = prescale_factor
        ctx.postscale_factor = postscale_factor
        ctx.process_set = process_set
        handle = allreduce_async(tensor, average, name, op, prescale_factor, postscale_factor, process_set)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, grad_output):
        return allreduce(grad_output, average=ctx.average, op=ctx.op,
                         prescale_factor=ctx.prescale_factor,
                         postscale_factor=ctx.postscale_factor,
                         process_set=ctx.process_set), None, None, None, None, None, None


def allreduce(tensor, average=None, name=None, compression=Compression.none, op=None,
              prescale_factor=1.0, postscale_factor=1.0, process_set=global_process_set):
    """
    A function that performs averaging or summation of the input tensor over all the
    Horovod processes. The input tensor is not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    This acts as a thin wrapper around an autograd function.  If your input
    tensor requires gradients, then callings this function will allow gradients
    to be computed and backpropagated.

    Arguments:
        tensor: A tensor to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A name of the reduction operation.
        compression: Compression algorithm used during allreduce to reduce the amount
                     of data sent during the each parameter update step.  Defaults to
                     not using compression.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A tensor of the same shape and type as `tensor`, averaged or summed across all
        processes.
    """
    tensor_compressed, ctx = compression.compress(tensor)
    summed_tensor_compressed = HorovodAllreduce.apply(tensor_compressed, average, name, op,
                                                      prescale_factor, postscale_factor,
                                                      process_set)
    return compression.decompress(summed_tensor_compressed, ctx)


def allreduce_async_(tensor, average=None, name=None, op=None,
                     prescale_factor=1.0, postscale_factor=1.0,
                     process_set=global_process_set):
    """
    A function that performs asynchronous in-place averaging or summation of the input
    tensor over all the Horovod processes.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A name of the reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the allreduce operation that can be used with `poll()` or
        `synchronize()`.
    """
    op = handle_average_backwards_compatibility(op, average)
    return _allreduce_async(tensor, tensor, name, op, prescale_factor, postscale_factor, process_set)


def allreduce_(tensor, average=None, name=None, op=None,
               prescale_factor=1.0, postscale_factor=1.0,
               process_set=global_process_set):
    """
    A function that performs in-place averaging or summation of the input tensor over
    all the Horovod processes.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A name of the reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A tensor of the same shape and type as `tensor`, averaged or summed across all
        processes.
    """
    handle = allreduce_async_(tensor, average, name, op, prescale_factor, postscale_factor, process_set)
    return synchronize(handle)


def _grouped_allreduce_function_factory(tensor):
    return 'horovod_torch_grouped_allreduce_async_' + tensor.type().replace('.', '_')


def _grouped_allreduce_async(tensors, outputs, name, op, prescale_factor, postscale_factor, process_set: ProcessSet):
    # Set the divisor for reduced gradients to average when necessary
    if op == Average:
        if rocm_built():
            # For ROCm, perform averaging at framework level
            divisor = process_set.size()
            op = Sum
        else:
            divisor = 1
    elif op == Adasum:
        if process_set != global_process_set:
            raise NotImplementedError("Adasum does not support non-global process sets yet.")
        if tensors[0].device.type != 'cpu' and gpu_available('torch'):
            if nccl_built():
                if not is_homogeneous():
                    raise NotImplementedError('Running GPU Adasum on heterogeneous cluster is not supported yet.')
                elif not num_rank_is_power_2(int(size() / local_size())):
                    raise NotImplementedError('Running GPU Adasum with non-power of 2 nodes is not supported yet.')
                if rocm_built():
                    # For ROCm, perform averaging at framework level
                    divisor = local_size()
                else:
                    divisor = 1
            else:
                warnings.warn('Adasum reduction does not currently support GPU reduction using MPI. Tensors are '
                              'copied to CPU memory instead. To use Adasum for GPU reduction, please compile Horovod '
                              'with HOROVOD_GPU_OPERATIONS=NCCL.')
                divisor = 1
        else:
            if not num_rank_is_power_2(size()):
                raise NotImplementedError('Running Adasum with non-power of 2 ranks is not supported yet.')
            divisor = 1
    else:
        divisor = 1

    function = _check_function(_grouped_allreduce_function_factory, tensors[0])
    try:
        handle = getattr(mpi_lib, function)(tensors, outputs, divisor,
                                            name.encode() if name is not None else _NULL, op,
                                            prescale_factor, postscale_factor, process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tuple(tensors), tuple(outputs))
    return handle


def grouped_allreduce_async(tensors, average=None, name=None, op=None,
                            prescale_factor=1.0, postscale_factor=1.0,
                            process_set=global_process_set):
    """
    A function that performs asynchronous averaging or summation of the input tensor
    list over all the Horovod processes. The input tensors are not modified.

    The reduction operations are keyed by the base name. If a base name is not
    provided, an incremented auto-generated base name is used. Reductions are
    performed across tensors in the same list position. The tensor type and
    shape must be the same on all Horovod processes for tensors sharing
    positions in the input tensor list. The reduction will not start until all
    processes are ready to send and receive the tensors.

    Arguments:
        tensors: A list of tensors to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A base name to use for the group reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the group allreduce operation that can be used with `poll()` or
        `synchronize()`.
    """
    op = handle_average_backwards_compatibility(op, average)
    outputs = [t.new(t.shape) for t in tensors]
    return _grouped_allreduce_async(tensors, outputs, name, op, prescale_factor, postscale_factor, process_set)


class HorovodGroupedAllreduce(torch.autograd.Function):
    """An autograd function that performs allreduce on a list of tensors."""

    @staticmethod
    def forward(ctx, average, name, op, prescale_factor, postscale_factor, process_set: ProcessSet, *tensors):
        ctx.average = average
        ctx.op = op
        ctx.prescale_factor = prescale_factor
        ctx.postscale_factor = postscale_factor
        ctx.process_set = process_set
        handle = grouped_allreduce_async(list(tensors), average, name, op, prescale_factor, postscale_factor,
                                         process_set)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, *grad_output):
        grad_reduced = grouped_allreduce(list(grad_output), average=ctx.average, op=ctx.op,
                                         prescale_factor=ctx.prescale_factor,
                                         postscale_factor=ctx.postscale_factor,
                                         process_set=ctx.process_set)
        return (None, None, None, None, None, None, *grad_reduced)


def grouped_allreduce(tensors, average=None, name=None, compression=Compression.none, op=None,
                      prescale_factor=1.0, postscale_factor=1.0, process_set=global_process_set):
    """
    A function that performs averaging or summation of the input tensor
    list over all the Horovod processes. The input tensors are not modified.

    The reduction operations are keyed by the base name. If a base name is not
    provided, an incremented auto-generated base name is used. Reductions are
    performed across tensors in the same list position. The tensor type and
    shape must be the same on all Horovod processes for tensors sharing
    positions in the input tensor list. The reduction will not start until all
    processes are ready to send and receive the tensors.

    This acts as a thin wrapper around an autograd function.  If your input
    tensors require gradients, then calling this function will allow gradients
    to be computed and backpropagated.

    Arguments:
        tensors: A list of tensors to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A base name to use for the group reduction operation.
        compression: Compression algorithm used during allreduce to reduce the amount
                     of data sent during the each parameter update step.  Defaults to
                     not using compression.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A list containing tensors of the same shape and type as in `tensors`,
        averaged or summed across all processes.
    """
    tensors_compressed, ctxs = zip(*[compression.compress(t) for t in tensors])
    summed_tensors_compressed = HorovodGroupedAllreduce.apply(average, name, op,
                                                              prescale_factor, postscale_factor,
                                                              process_set, *tensors_compressed)
    return [compression.decompress(t, ctx) for t, ctx in zip(summed_tensors_compressed, ctxs)]


def grouped_allreduce_async_(tensors, average=None, name=None, op=None,
                             prescale_factor=1.0, postscale_factor=1.0,
                             process_set=global_process_set):
    """
    A function that performs asynchronous in-place averaging or summation of the input
    tensors over all the Horovod processes.

    The reduction operations are keyed by the base name. If a base name is not
    provided, an incremented auto-generated base name is used. Reductions are
    performed across tensors in the same list position. The tensor type and
    shape must be the same on all Horovod processes for tensors sharing
    positions in the input tensor list. The reduction will not start until all
    processes are ready to send and receive the tensors.

    Arguments:
        tensors: A list of tensors to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A base name to use for the group reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the group allreduce operation that can be used with `poll()` or
        `synchronize()`.
    """
    op = handle_average_backwards_compatibility(op, average)
    return _grouped_allreduce_async(tensors, tensors, name, op, prescale_factor, postscale_factor, process_set)


def grouped_allreduce_(tensors, average=None, name=None, op=None,
                       prescale_factor=1.0, postscale_factor=1.0,
                       process_set=global_process_set):
    """
    A function that performs in-place averaging or summation of the input tensors over
    all the Horovod processes.

    The reduction operations are keyed by the base name. If a base name is not
    provided, an incremented auto-generated base name is used. Reductions are
    performed across tensors in the same list position. The tensor type and
    shape must be the same on all Horovod processes for tensors sharing
    positions in the input tensor list. The reduction will not start until all
    processes are ready to send and receive the tensors.

    Arguments:
        tensors: A list of tensors to reduce.
        average:
            .. warning:: .. deprecated:: 0.19.0

                Use `op` instead. Will be removed in v1.0.

        name: A base name to use for the group reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Supported op values are Sum, Average, Min, Max, and Product. Defaults
            to Average if None is given.
        prescale_factor: Multiplicative factor to scale tensor before allreduce.
        postscale_factor: Multiplicative factor to scale tensor after allreduce.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A list containing tensors of the same shape and type as in `tensors`,
        averaged or summed across all processes.
    """
    handle = grouped_allreduce_async_(tensors, average, name, op, prescale_factor, postscale_factor, process_set)
    return synchronize(handle)


def sparse_allreduce_async(tensor, name, op, process_set=global_process_set):
    # Allgather aggregates along the first dimension, so we need to transpose the
    # indices to enforce correct concatenation behavior, then transpose back prior to
    # constructing the new aggregated sparse gradient
    t = tensor
    indices_handle = allgather_async(t._indices().transpose(0, 1).contiguous(), name=f'{name}.indices',
                                     process_set=process_set)
    values_handle = allgather_async(t._values(), name=f'{name}.values', process_set=process_set)

    def handle():
        # We need to sync values handle firstly for torch nightly >= 10.0
        # Issue: https://github.com/horovod/horovod/issues/2961
        values = synchronize(values_handle)
        indices = synchronize(indices_handle)

        values = (values / process_set.size()) if op == Average else values

        if indices.dim() == 0 or values.dim() == 0:
            return t.new().resize_as_(t)
        return t.new(indices.transpose(0, 1), values, t.size())

    return handle


def _allgather_function_factory(tensor):
    return 'horovod_torch_allgather_async_' + tensor.type().replace('.', '_')


def _allgather_async(tensor, output, name, process_set: ProcessSet):
    function = _check_function(_allgather_function_factory, tensor)
    try:
        handle = getattr(mpi_lib, function)(
            tensor, output, name.encode() if name is not None else _NULL,
            process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tensor, output)
    return handle


def allgather_async(tensor, name=None, process_set=global_process_set):
    """
    A function that asynchronously concatenates the input tensor with the same input
    tensor on all other Horovod processes. The input tensor is not modified.

    The concatenation is done on the first dimension, so the input tensors on the
    different processes must have the same rank and shape, except for the first
    dimension, which is allowed to be different.

    Arguments:
        tensor: A tensor to allgather.
        name: A name of the allgather operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the allgather operation that can be used with `poll()` or
        `synchronize()`.
    """
    output = tensor.new()
    return _allgather_async(tensor, output, name, process_set)


class HorovodAllgather(torch.autograd.Function):
    """An autograd function that performs allgather on a tensor."""

    @staticmethod
    def forward(ctx, tensor, name, process_set: ProcessSet):
        ctx.dim = tensor.shape[0]
        ctx.process_set = process_set
        handle = allgather_async(tensor, name, process_set)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, grad_output):
        grad_reduced = allreduce(grad_output, average=True, process_set=ctx.process_set)

        dim_t = torch.IntTensor([ctx.dim])
        dim = allgather(dim_t, process_set=ctx.process_set).view(ctx.process_set.size())

        r = ctx.process_set.rank()
        offset = torch.sum(dim.narrow(0, 0, r)).item() if r != 0 else 0
        return grad_reduced.narrow(0, offset, ctx.dim), None, None


def allgather(tensor, name=None, process_set=global_process_set):
    """
    A function that concatenates the input tensor with the same input tensor on
    all other Horovod processes. The input tensor is not modified.

    The concatenation is done on the first dimension, so the corresponding
    input tensors on the different processes must have the same rank and
    shape, except for the first dimension, which is allowed to be different.

    This acts as a thin wrapper around an autograd function.  If your input
    tensor requires gradients, then callings this function will allow gradients
    to be computed and backpropagated.

    Arguments:
        tensor: A tensor to allgather.
        name: A name of the allgather operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A tensor of the same type as `tensor`, concatenated on dimension zero
        across all processes. The shape is identical to the input shape, except for
        the first dimension, which may be greater and is the sum of all first
        dimensions of the tensors in different Horovod processes.
    """
    return HorovodAllgather.apply(tensor, name, process_set)


def _grouped_allgather_function_factory(tensor):
    return 'horovod_torch_grouped_allgather_async_' + tensor.type().replace('.', '_')


def _grouped_allgather_async(tensors, outputs, name, process_set: ProcessSet):
    function = _check_function(_grouped_allgather_function_factory, tensors[0])
    try:
        handle = getattr(mpi_lib, function)(
            tensors, outputs, name.encode() if name is not None else _NULL,
            process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tuple(tensors), tuple(outputs))
    return handle


def grouped_allgather_async(tensors, name=None, process_set=global_process_set):
    """
    A function that asynchronously concatenates each input tensor with the corresponding
    input tensor on all other Horovod processes for a list of input tensors. The input
    tensors are not modified.

    The concatenation is done on the first dimension, so the input tensors on the
    different processes must have the same rank and shape, except for the first
    dimension, which is allowed to be different.

    Arguments:
        tensors: A list of tensors to allgather.
        name: A base name to use for the group allgather operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the group allgather operation that can be used with `poll()` or
        `synchronize()`.
    """
    outputs = [t.new() for t in tensors]
    return _grouped_allgather_async(tensors, outputs, name, process_set)


class HorovodGroupedAllgather(torch.autograd.Function):
    """An autograd function that performs allgather on a list of tensors."""

    @staticmethod
    def forward(ctx, name, process_set: ProcessSet, *tensors):
        ctx.dims = [t.shape[0] for t in tensors]
        ctx.process_set = process_set
        handle = grouped_allgather_async(list(tensors), name, process_set)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, *grad_output):
        grad_reduced = grouped_allreduce(list(grad_output), average=True, process_set=ctx.process_set)

        dim_ts = [torch.IntTensor([dim]) for dim in ctx.dims]
        dims = [dt.view(ctx.process_set.size())
                for dt in grouped_allgather(dim_ts, process_set=ctx.process_set)]

        r = ctx.process_set.rank()
        offsets = [torch.sum(dim.narrow(0, 0, r)).item() if r != 0 else 0
                   for dim in dims]
        result = [gr.narrow(0, offset, dim)
                  for gr, offset, dim in zip(grad_reduced, offsets, ctx.dims)]
        return (None, None, *result)


def grouped_allgather(tensors, name=None, process_set=global_process_set):
    """
    A function that concatenates each input tensor with the corresponding
    input tensor on all other Horovod processes for a list of input tensors.
    The input tensors are not modified.

    The concatenation is done on the first dimension, so the corresponding input
    tensors on the different processes must have the same rank and shape, except
    for the first dimension, which is allowed to be different.

    Arguments:
        tensors: A list of tensors to allgather.
        name: A base name to use for the group allgather operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A list containing tensors of the same type as in `tensors`. Each tensor
        is concatenated on dimension zero across all processes. Its shape is
        identical to the corresponding input shape, expect for the first
        dimension, which may be greater and is the sum of all first dimensions
        of the corresponding tensor in different Horovod processes.
    """
    return HorovodGroupedAllgather.apply(name, process_set, *tensors)


def _broadcast_function_factory(tensor):
    return 'horovod_torch_broadcast_async_' + tensor.type().replace('.', '_')


def _broadcast_async(tensor, output, root_rank, name, process_set: ProcessSet):
    function = _check_function(_broadcast_function_factory, tensor)
    try:
        handle = getattr(mpi_lib, function)(
            tensor, output, root_rank, name.encode() if name is not None else _NULL,
            process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tensor, output)
    return handle


def broadcast_async(tensor, root_rank, name=None, process_set=global_process_set):
    """
    A function that asynchronously broadcasts the input tensor on root rank to the same
    input tensor on all other Horovod processes. The input tensor is not modified.

    The broadcast operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The broadcast will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to broadcast.
        root_rank: The rank to broadcast the value from.
        name: A name of the broadcast operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the broadcast operation that can be used with `poll()` or
        `synchronize()`.
    """
    output = tensor.new(tensor.shape)
    return _broadcast_async(tensor, output, root_rank, name, process_set)


class HorovodBroadcast(torch.autograd.Function):
    """An autograd function that broadcasts a tensor."""

    @staticmethod
    def forward(ctx, tensor, root_rank, name, process_set: ProcessSet):
        ctx.root_rank = root_rank
        ctx.process_set = process_set
        handle = broadcast_async(tensor, root_rank, name, process_set)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, grad_output):
        grad_reduced = allreduce(grad_output, average=True, process_set=ctx.process_set)
        if rank() != ctx.root_rank:
            grad_reduced *= 0
        return grad_reduced, None, None, None


def broadcast(tensor, root_rank, name=None, process_set=global_process_set):
    """
    A function that broadcasts the input tensor on root rank to the same input tensor
    on all other Horovod processes. The input tensor is not modified.

    The broadcast operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The broadcast will not start until all processes
    are ready to send and receive the tensor.

    This acts as a thin wrapper around an autograd function.  If your input
    tensor requires gradients, then callings this function will allow gradients
    to be computed and backpropagated.

    Arguments:
        tensor: A tensor to broadcast.
        root_rank: The rank to broadcast the value from.
        name: A name of the broadcast operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A tensor of the same shape and type as `tensor`, with the value broadcasted
        from root rank.
    """
    return HorovodBroadcast.apply(tensor, root_rank, name, process_set)


def broadcast_async_(tensor, root_rank, name=None, process_set=global_process_set):
    """
    A function that asynchronously broadcasts the input tensor on root rank to the same
    input tensor on all other Horovod processes. The operation is performed in-place.

    The broadcast operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The broadcast will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to broadcast.
        root_rank: The rank to broadcast the value from.
        name: A name of the broadcast operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A handle to the broadcast operation that can be used with `poll()` or
        `synchronize()`.
    """
    return _broadcast_async(tensor, tensor, root_rank, name, process_set)


def broadcast_(tensor, root_rank, name=None, process_set=global_process_set):
    """
    A function that broadcasts the input tensor on root rank to the same input tensor
    on all other Horovod processes. The operation is performed in-place.

    The broadcast operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The broadcast will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to broadcast.
        root_rank: The rank to broadcast the value from.
        name: A name of the broadcast operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        A tensor of the same shape and type as `tensor`, with the value broadcasted
        from root rank.
    """
    handle = broadcast_async_(tensor, root_rank, name, process_set)
    return synchronize(handle)

def _alltoall_function_factory(tensor):
    return 'horovod_torch_alltoall_async_' + tensor.type().replace('.', '_')

def _alltoall_async(tensor, splits, output, output_received_splits, name, process_set: ProcessSet):
    if splits is None:
        # If splits not provided, create empty tensor as placeholder
        splits = torch.tensor([], dtype=torch.int32, device='cpu')
    elif not isinstance(splits, torch.Tensor):
        splits = torch.tensor(splits, dtype=torch.int32, device='cpu')
    function = _check_function(_alltoall_function_factory, tensor)
    try:
        handle = getattr(mpi_lib, function)(
            tensor, splits, output, output_received_splits, name.encode() if name is not None else _NULL,
            process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tensor, splits, (output, output_received_splits))
    return handle


def alltoall_async(tensor, splits=None, name=None, process_set=global_process_set):
    """
    A function that scatters slices of the input tensor to all other Horovod processes
    and returns a tensor of gathered slices from all other Horovod processes. The input
    tensor is not modified.

    The slicing is done on the first dimension, so the input tensors on
    the different processes must have the same rank and shape, except for the
    first dimension, which is allowed to be different.

    Arguments:
        tensor: A tensor to distribute with alltoall.
        splits: A tensor of integers in rank order describing how many
                elements in `tensor` to send to each worker.  Splitting is
                applied along the first dimension of `tensor`. If `splits` is
                not provided, the first dimension is split equally by the
                number of Horovod processes.
        name: A name of the alltoall operation.
        process_set: Process set object to limit this operation to a subset of
                Horovod processes. Default is the global process set.

    Returns:
        A handle to the alltoall operation that can be used with `poll()` or
        `synchronize()`.
    """
    output = tensor.new()
    if isinstance(splits, torch.Tensor):
        output_received_splits = splits.new()
    else:
        output_received_splits = torch.empty(size(), dtype=torch.int32, device='cpu')
    return _alltoall_async(tensor, splits, output, output_received_splits, name, process_set)


class HorovodAlltoall(torch.autograd.Function):
    """An autograd function that performs alltoall on a tensor."""

    @staticmethod
    def forward(ctx, tensor, splits, name, process_set: ProcessSet):
        handle = alltoall_async(tensor, splits, name, process_set)
        output, received_splits = synchronize(handle)

        ctx.process_set = process_set
        ctx.recvsplits = received_splits
        if splits is None:
            return output
        else:
            ctx.mark_non_differentiable(received_splits)
            return output, received_splits

    @staticmethod
    def backward(ctx, grad_output, *dead_gradients):
        grad_wrt_tensor, _ = alltoall(grad_output, splits=ctx.recvsplits,
                                      process_set=ctx.process_set)
        return grad_wrt_tensor, None, None, None


def alltoall(tensor, splits=None, name=None, process_set=global_process_set):
    """
    A function that scatters slices of the input tensor to all other Horovod processes
    and returns a tensor of gathered slices from all other Horovod processes. The input
    tensor is not modified.

    The slicing is done on the first dimension, so the input tensors on
    the different processes must have the same rank and shape, except for the
    first dimension, which is allowed to be different.

    This acts as a thin wrapper around an autograd function.  If your input
    tensor requires gradients, then callings this function will allow gradients
    to be computed and backpropagated.

    Arguments:
        tensor: A tensor to distribute with alltoall.
        splits: A tensor of integers in rank order describing how many
                elements in `tensor` to send to each worker.  Splitting is
                applied along the first dimension of `tensor`. If `splits` is
                not provided, the first dimension is split equally by the
                number of Horovod processes.
        name: A name of the alltoall operation.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.

    Returns:
        1) A tensor containing the gathered tensor data from all workers.
        2) If `splits` has been provided: A tensor of integers in rank order
           describing how many elements in the output tensor have been received
           from each worker.
     """
    return HorovodAlltoall.apply(tensor, splits, name, process_set)


def _reducescatter_function_factory(tensor):
    return 'horovod_torch_reducescatter_async_' + tensor.type().replace('.', '_')


def _reducescatter_async(tensor, output, name, op, process_set: ProcessSet,
                         prescale_factor, postscale_factor):
    function = _check_function(_reducescatter_function_factory, tensor)
    try:
        handle = getattr(mpi_lib, function)(tensor, output,
                                            name.encode() if name is not None else _NULL,
                                            op, process_set.process_set_id,
                                            prescale_factor, postscale_factor)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tensor, output)
    return handle


def reducescatter_async(tensor, name=None, op=Average, process_set=global_process_set,
                        prescale_factor=1.0, postscale_factor=1.0):
    """
    A function that performs asynchronous reduction of the input tensor over all the
    Horovod processes, then scatters the results across all Horovod processes. The
    input tensor is not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    The input tensors on the different processes must have the same rank and shape. The
    output tensor will be the same rank on all processes, but the first dimension may
    be different.

    Arguments:
        tensor: A tensor to average and sum.
        name: A name of the reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Defaults to Average.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.
        prescale_factor: Multiplicative factor to scale tensor before reducescatter.
        postscale_factor: Multiplicative factor to scale tensor after reducescatter.

    Returns:
        A handle to the reducescatter operation that can be used with `poll()` or
        `synchronize()`.
    """
    output = tensor.new()
    return _reducescatter_async(tensor, output, name, op, process_set,
                                prescale_factor, postscale_factor)


class HorovodReducescatter(torch.autograd.Function):
    """An autograd function that performs reducescatter on a tensor."""

    @staticmethod
    def forward(ctx, tensor, name, op, process_set, prescale_factor, postscale_factor):
        ctx.op = op
        ctx.process_set = process_set
        ctx.prescale_factor = prescale_factor
        ctx.postscale_factor = postscale_factor
        handle = reducescatter_async(tensor, name, op, process_set, prescale_factor, postscale_factor)
        return synchronize(handle)

    @staticmethod
    def backward(ctx, grad_output):
        if ctx.op == Sum:
            grad_output *= ctx.process_set.size()
        if ctx.prescale_factor != 1.0:
            grad_output *= ctx.prescale_factor
        if ctx.postscale_factor != 1.0:
            grad_output *= ctx.postscale_factor

        return allgather(grad_output, process_set=ctx.process_set), None, None, None, None, None


def reducescatter(tensor, name=None, compression=Compression.none, op=Average,
                  process_set=global_process_set, prescale_factor=1.0, postscale_factor=1.0):
    """
    A function that performs reduction of the input tensor over all the Horovod
    processes, then scatters the results across all Horovod processes. The input tensor
    is not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensor: A tensor to average/sum and scatter.
        name: A name of the reduction operation.
        compression: Compression algorithm used during reducescatter to reduce the amount
                     of data sent during the each parameter update step.  Defaults to
                     not using compression.
        op: The reduction operation to combine tensors across different ranks.
            Defaults to Average.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.
        prescale_factor: Multiplicative factor to scale tensor before reducescatter.
        postscale_factor: Multiplicative factor to scale tensor after reducescatter.

    Returns:
        A tensor of the same rank and type as `tensor` across all processes. The shape
        is identical to the input shape, except for the first dimension, which will be
        divided across the different Horovod processes.
    """
    tensor_compressed, ctx = compression.compress(tensor)
    reduced_tensor_compressed = HorovodReducescatter.apply(tensor_compressed, name, op, process_set,
                                                           prescale_factor, postscale_factor)
    return compression.decompress(reduced_tensor_compressed, ctx)


def _grouped_reducescatter_function_factory(tensor):
    return 'horovod_torch_grouped_reducescatter_async_' + tensor.type().replace('.', '_')


def _grouped_reducescatter_async(tensors, outputs, name, op, process_set: ProcessSet,
                                 prescale_factor, postscale_factor):
    function = _check_function(_grouped_reducescatter_function_factory, tensors[0])
    try:
        handle = getattr(mpi_lib, function)(tensors, outputs,
                                            name.encode() if name is not None else _NULL,
                                            op, process_set.process_set_id,
                                            prescale_factor, postscale_factor)
    except RuntimeError as e:
        raise HorovodInternalError(e)
    _handle_map[handle] = (tuple(tensors), tuple(outputs))
    return handle


def grouped_reducescatter_async(tensors, name=None, op=Average, process_set=global_process_set,
                                prescale_factor=1.0, postscale_factor=1.0):
    """
    A function that performs asynchronous reduction of a list of input tensors over all the
    Horovod processes, then scatters the results across all Horovod processes. The
    input tensors are not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. For each of the input tensors, the type and shape must
    be the same on all Horovod processes for a given name. The reduction will not start
    until all processes are ready to send and receive the tensors.

    The input tensor at some place in the list tensor must have the same rank and shape
    on the different processes. The corresponding output tensor will be the same rank on
    all processes, but the first dimension may be different.

    Arguments:
        tensors: A list of tensors to average and sum.
        name: A base name to use for the group reduction operation.
        op: The reduction operation to combine tensors across different ranks.
            Defaults to Average.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.
        prescale_factor: Multiplicative factor to scale tensors before reducescatter.
        postscale_factor: Multiplicative factor to scale tensors after reducescatter.

    Returns:
        A handle to the group reducescatter operation that can be used with `poll()` or
        `synchronize()`.
    """
    outputs = [t.new() for t in tensors]
    return _grouped_reducescatter_async(tensors, outputs, name, op, process_set,
                                        prescale_factor, postscale_factor)


class HorovodGroupedReducescatter(torch.autograd.Function):
    """An autograd function that performs reducescatter on a list of tensors."""

    @staticmethod
    def forward(ctx, name, op, process_set, prescale_factor, postscale_factor, *tensors):
        ctx.op = op
        ctx.process_set = process_set
        ctx.prescale_factor = prescale_factor
        ctx.postscale_factor = postscale_factor
        handle = grouped_reducescatter_async(list(tensors), name, op, process_set,
                                             prescale_factor, postscale_factor, )
        return synchronize(handle)

    @staticmethod
    def backward(ctx, *grad_output):
        if ctx.op == Sum:
            grad_output = [g * ctx.process_set.size() for g in grad_output]
        if ctx.prescale_factor != 1.0:
            grad_output = [ctx.prescale_factor * g for g in grad_output]
        if ctx.postscale_factor != 1.0:
            grad_output = [ctx.postscale_factor * g for g in grad_output]

        return (None, None, None, None, None,
                *grouped_allgather(grad_output, process_set=ctx.process_set))


def grouped_reducescatter(tensors, name=None, compression=Compression.none, op=Average,
                          process_set=global_process_set, prescale_factor=1.0, postscale_factor=1.0):
    """
    A function that performs reduction of a list of input tensors over all the
    Horovod processes, then scatters the results across all Horovod processes. The
    input tensors are not modified.

    The reduction operation is keyed by the name. If name is not provided, an incremented
    auto-generated name is used. The tensor type and shape must be the same on all
    Horovod processes for a given name. The reduction will not start until all processes
    are ready to send and receive the tensor.

    Arguments:
        tensors: A list of tensors to average and sum.
        name: A base name to use for the group reduction operation.
        compression: Compression algorithm used during reducescatter to reduce the amount
                     of data sent during the each parameter update step.  Defaults to
                     not using compression.
        op: The reduction operation to combine tensors across different ranks.
            Defaults to Average.
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.
        prescale_factor: Multiplicative factor to scale tensors before reducescatter.
        postscale_factor: Multiplicative factor to scale tensors after reducescatter.


    Returns:
        A list containing tensors of the same rank and type as in `tensors`. For each
        tensor the shape is identical to the input shape, except for the first dimension,
        which will be divided across the different Horovod processes.
    """
    tensors_compressed = []
    ctxs = []
    for tensor in tensors:
        tensor_compressed, ctx = compression.compress(tensor)
        tensors_compressed.append(tensor_compressed)
        ctxs.append(ctx)
    reduced_tensors_compressed = HorovodGroupedReducescatter.apply(name, op, process_set,
                                                                   prescale_factor, postscale_factor,
                                                                   *tensors_compressed)
    return [compression.decompress(reduced_tensor_compressed, ctx)
            for reduced_tensor_compressed, ctx in zip(reduced_tensors_compressed, ctxs)]


def poll(handle):
    """
    Polls an allreduce, allgather, alltoall, broadcast, or reducescatter handle to determine whether
    underlying asynchronous operation has completed. After `poll()` returns `True`,
    `synchronize()` will return without blocking.

    Arguments:
        handle: A handle returned by an allreduce, allgather, alltoall, broadcast, or reducescatter
                asynchronous operation.

    Returns:
        A flag indicating whether the operation has completed.
    """
    return mpi_lib.horovod_torch_poll(handle) != 0


def synchronize(handle):
    """
    Synchronizes an asynchronous allreduce, allgather, alltoall, broadcast, or reducescatter operation
    until  it's completed. Returns the result of the operation.

    Arguments:
        handle: A handle returned by an allreduce, allgather, alltoall, broadcast, or reducescatter
                asynchronous operation.

    Returns:
        A single output tensor of the operation or a tuple of multiple output tensors.
    """
    if handle not in _handle_map:
        return

    try:
        mpi_lib.horovod_torch_wait_and_clear(handle)
        output = _handle_map.pop(handle)[-1]
        return output
    except RuntimeError as e:
        _handle_map.pop(handle, None)
        raise HorovodInternalError(e)


def join(device=-1) -> int:
    """A function that indicates that the rank finished processing data.

    All ranks that did not call join() continue to process allreduce operations.
    This function blocks Python thread until all ranks join.

    Arguments:
        device: An id of the device to create temprorary zero tensors (default -1, CPU)

    Returns:
        Id of the rank that joined last.
    """
    output = torch.tensor(-1, dtype=torch.int, device=torch.device("cpu"))
    try:
        handle = mpi_lib.horovod_torch_join(output, device)
    except RuntimeError as e:
        raise HorovodInternalError(e)

    _handle_map[handle] = (None, output)

    return synchronize(handle).item()

def barrier(process_set=global_process_set):
    """
    A function that acts as a simple sychronization point for ranks specified
    in the given process group(default to global group). Ranks that reach
    this function call will stall until all other ranks have reached.

    Arguments:
        process_set: Process set object to limit this operation to a subset of
                     Horovod processes. Default is the global process set.
    """

    try:
        handle = mpi_lib.horovod_torch_barrier(process_set.process_set_id)
    except RuntimeError as e:
        raise HorovodInternalError(e)

    _handle_map[handle] = (None, None)

    synchronize(handle)
