'''
Copyright 2019 The Microsoft DeepSpeed Team
'''

import torch
from torch._utils import _flatten_dense_tensors, _unflatten_dense_tensors
from torch.distributed.distributed_c10d import _get_global_rank
import torch.distributed as dist
import math
from torch._six import inf
from torch.autograd import Variable

import collections

from deepspeed.runtime.fp16.loss_scaler import LossScaler, DynamicLossScaler
from deepspeed.runtime.utils import see_memory_usage, is_model_parallel_parameter
from deepspeed.runtime.zero.config import ZERO_OPTIMIZATION_GRADIENTS

from deepspeed.utils import logger
#Toggle this to true to enable correctness test
#with gradient partitioning and without
pg_correctness_test = False

try:
    from apex_C import flatten
    from apex_C import unflatten
except ImportError:
    try:
        _ = warned_flatten
    except NameError:
        logger.warning(
            "apex was installed without --cpp_ext.  Falling back to Python flatten and unflatten."
        )
        warned_flatten = True
    from torch._utils import _flatten_dense_tensors as flatten
    from torch._utils import _unflatten_dense_tensors as unflatten


def input(msg):
    return


def split_half_float_double(tensors):
    dtypes = [
        "torch.cuda.HalfTensor",
        "torch.cuda.FloatTensor",
        "torch.cuda.DoubleTensor"
    ]
    buckets = []
    for i, dtype in enumerate(dtypes):
        bucket = [t for t in tensors if t.type() == dtype]
        if bucket:
            buckets.append(bucket)
    return buckets


def isclose(a, b, rtol=1e-09, atol=0.0):
    return abs(a - b) <= max(rtol * max(abs(a), abs(b)), atol)


def lcm(x, y):
    from fractions import gcd  # or can import gcd from `math` in Python 3
    return x * y // gcd(x, y)


# create a flat tensor aligned at the alignment boundary
def flatten_dense_tensors_aligned(tensor_list, alignment):
    num_elements = 0
    for tensor in tensor_list:
        num_elements = num_elements + tensor.numel()

    remaining = num_elements % alignment

    if remaining:
        elements_to_add = alignment - remaining
        pad_tensor = torch.zeros(elements_to_add,
                                 device=tensor_list[0].device,
                                 dtype=tensor_list[0].dtype)
        padded_tensor_list = tensor_list + [pad_tensor]

        num_elements = num_elements + elements_to_add
    else:
        padded_tensor_list = tensor_list

    return _flatten_dense_tensors(padded_tensor_list)


def get_alignment_padding(tensor_list, alignment):
    num_elements = sum([tensor.numel() for tensor in tensor_list])
    remainder = num_elements % alignment
    return (alignment - remainder) if remainder else remainder


def move_to_cpu(tensor_list):
    for tensor in tensor_list:
        tensor.data = tensor.data.cpu()


def print_rank_msg(msg):
    print(f"rank {dist.get_rank()} - {msg}")


class FP16_DeepSpeedZeroOptimizer(object):
    """
    DeepSpeedZeroOptimizer designed to reduce the memory footprint
    required for training large deep learning models.

    For more details please see ZeRO: Memory Optimization Towards Training A Trillion Parameter Models
    https://arxiv.org/abs/1910.02054

    For usage examples, refer to TODO: DeepSpeed Tutorial

    """
    def __init__(self,
                 init_optimizer,
                 timers,
                 static_loss_scale=1.0,
                 dynamic_loss_scale=False,
                 dynamic_loss_args=None,
                 verbose=True,
                 contiguous_gradients=True,
                 reduce_bucket_size=500000000,
                 allgather_bucket_size=5000000000,
                 dp_process_group=None,
                 reduce_scatter=True,
                 overlap_comm=False,
                 cpu_offload=False,
                 mpu=None,
                 clip_grad=0.0,
                 allreduce_always_fp32=False,
                 postscale_gradients=True,
                 gradient_predivide_factor=1.0,
                 gradient_accumulation_steps=1):

        if dist.get_rank() == 0:
            logger.info(f"Reduce bucket size {reduce_bucket_size}")
            logger.info(f"Allgather bucket size {allgather_bucket_size}")
            logger.info(f"CPU Offload: {cpu_offload}")
        # The fused optimizer does all the work. We need this layer for two reason:
        # 1. maintain same user API from apex.fp16_utils
        # 2. keep common stuff here in case we need to add ne552w fused optimizer later

        # differences from apex.fp16_utils:
        # - assume all model params in fp16
        # - assume all params requires grad
        # - flat by groups, not keeping state. TODO: remove state explicitly?
        # - master gard and unflat master weight never exist. TODO: a way to save out unflat master?
        if not torch.cuda.is_available:
            raise SystemError("Cannot use fp16 without CUDA.")
        self.optimizer = init_optimizer

        self.timers = timers

        self.reduce_scatter = reduce_scatter

        self.overlap_comm = overlap_comm

        self.cpu_offload = cpu_offload

        self.deepspeed_adam_offload = (cpu_offload
                                       and type(init_optimizer) == DeepSpeedCPUAdam)

        self.device = torch.cuda.current_device() if not self.cpu_offload else 'cpu'

        self.dp_process_group = dp_process_group

        self.partition_count = dist.get_world_size(group=self.dp_process_group)

        if mpu is None:
            self.model_parallel_group = None
            self.model_parallel_rank = 0
        else:
            self.model_parallel_group = mpu.get_model_parallel_group()
            self.model_parallel_rank = mpu.get_model_parallel_rank()

        self.overflow = False
        self.clip_grad = clip_grad
        self.allreduce_always_fp32 = allreduce_always_fp32
        self.gradient_predivide_factor = gradient_predivide_factor
        self.postscale_gradients = postscale_gradients
        self.gradient_accumulation_steps = gradient_accumulation_steps
        self.micro_step_id = 0

        if self.reduce_scatter:
            assert not self.allreduce_always_fp32, "allreduce_always_fp32 is not yet supported with ZeRO-2 with reduce scatter enabled"
            assert self.gradient_predivide_factor == 1.0, "gradient_predivide_factor != 1.0 is not yet supported with ZeRO-2 with reduce scatter enabled"
            assert self.postscale_gradients, "pre-scale gradients is not yet supported with ZeRO-2 with reduce scatter enabled"

        # param flattened by groups
        self.fp16_groups = []
        self.fp16_groups_flat = []

        #param partitioned by data parallel degree
        #this will contain a list of equal sized tensors
        #each of which will be updated by a different process
        self.parallel_partitioned_fp16_groups = []

        #a single 32-bit partition of the parallel partitioned parameters
        #that this process will update
        self.single_partition_of_fp32_groups = []

        #param partition info

        #These are the parameters in each group that will not be updated by this process directly
        self.params_not_in_partition = []

        #These are the parameters that will be updated by this process directly
        self.params_in_partition = []

        #Offset from the first paramter in the the self.params_in_partition
        #the parameter boundaries may not align with partition boundaries
        #so we need to keep track of the offset
        self.first_offset = []

        #number of elements per partition in each group
        self.partition_size = []

        partition_id = dist.get_rank(group=self.dp_process_group)

        self.all_reduce_print = False

        # padding on each partition for alignment purposes
        self.groups_padding = []
        # loop to deal with groups
        for i, param_group in enumerate(self.optimizer.param_groups):
            # push this group to list before modify
            self.fp16_groups.append(param_group['params'])
            # Record padding required to align group to world size
            if partition_id == dist.get_world_size(group=self.dp_process_group) - 1:
                padding = get_alignment_padding(self.fp16_groups[i],
                                                self.partition_count)
            else:
                padding = 0
            self.groups_padding.append(padding)

            #not sure why apex was cloning the weights before flattening
            #removing cloning here

            see_memory_usage(f"Before moving param group {i} to CPU")
            #move all the parameters to cpu to free up GPU space for creating flat buffer
            move_to_cpu(self.fp16_groups[i])
            see_memory_usage(f"After moving param group {i} to CPU")

            #create flat buffer in CPU and move to GPU
            self.fp16_groups_flat.append(
                flatten_dense_tensors_aligned(
                    self.fp16_groups[i],
                    dist.get_world_size(group=self.dp_process_group)).cuda(
                        torch.cuda.current_device()))
            see_memory_usage(f"After flattening and moving param group {i} to GPU")

            if dist.get_rank(group=self.dp_process_group) == 0:
                see_memory_usage(
                    f"After Flattening and after emptying param group {i} cache")

            # set model fp16 weight to slices of flattened buffer
            updated_params = _unflatten_dense_tensors(self.fp16_groups_flat[i],
                                                      self.fp16_groups[i])
            for p, q in zip(self.fp16_groups[i], updated_params):
                p.data = q.data

            #divide the flat weights into near equal partition equal to the data parallel degree
            #each process will compute on a different part of the partition
            data_parallel_partitions = self.get_data_parallel_partitions(
                self.fp16_groups_flat[i])
            self.parallel_partitioned_fp16_groups.append(data_parallel_partitions)

            # a partition of the fp32 master weights that will be updated by this process
            self.single_partition_of_fp32_groups.append(
                self.parallel_partitioned_fp16_groups[i][partition_id].to(
                    self.device).clone().float().detach())

            # modify optimizer of have flat master weight
            self.single_partition_of_fp32_groups[
                i].requires_grad = True  # keep this in case internal optimizer uses it
            param_group['params'] = [self.single_partition_of_fp32_groups[i]]

            partition_size = len(self.fp16_groups_flat[i]) / dist.get_world_size(
                group=self.dp_process_group)
            params_in_partition, params_not_in_partition, first_offset = self.get_partition_info(self.fp16_groups[i], partition_size, partition_id)

            self.partition_size.append(partition_size)
            self.params_in_partition.append(params_in_partition)
            self.params_not_in_partition.append(params_not_in_partition)
            self.first_offset.append(first_offset)

        self.reduce_bucket_size = int(reduce_bucket_size)
        self.allgather_bucket_size = int(allgather_bucket_size)

        self.reduction_event = torch.cuda.Event(enable_timing=False, blocking=False)
        self.reduction_stream = torch.cuda.Stream()
        self.cpu_computation_stream = torch.cuda.Stream()
        self.migration_stream = torch.cuda.Stream()
        self.callback_queued = False

        self.param_dict = {}

        #map between param_id and bool to specify if a param is in this partition
        self.is_param_in_current_partition = {}

        # CPU-Offload requires contiguous gradients
        self.contiguous_gradients = contiguous_gradients or cpu_offload
        self.grads_in_ipg_bucket = []
        self.params_in_ipg_bucket = []
        self.elements_in_ipg_bucket = 0
        self.params_already_reduced = []
        self._release_ipg_buffers()
        self.previous_reduced_grads = None

        #simplified param id
        self.param_id = {}

        largest_param_numel = 0
        count = 0
        for i, params_group in enumerate(self.fp16_groups):
            for param in params_group:
                unique_id = id(param)
                self.param_id[unique_id] = count
                self.param_dict[count] = param
                self.params_already_reduced.append(False)
                if param.numel() > largest_param_numel:
                    largest_param_numel = param.numel()
                count = count + 1

        for param_group in self.params_in_partition:
            for param in param_group:
                self.is_param_in_current_partition[self.get_param_id(param)] = True

        for param_group in self.params_not_in_partition:
            for param in param_group:
                self.is_param_in_current_partition[self.get_param_id(param)] = False

        if self.cpu_offload:
            self.accumulated_grads_in_cpu = {}
            self.norm_for_param_grads = {}
            self.local_overflow = False
            self.grad_position = {}
            self.temp_grad_buffer_for_cpu_offload = torch.zeros(
                largest_param_numel,
                device=self.device).half().pin_memory()
            self.temp_grad_buffer_for_gpu_offload = torch.zeros(
                largest_param_numel,
                device=torch.cuda.current_device()).half()

            for i, params_group in enumerate(self.fp16_groups):
                self.get_grad_position(i,
                                       self.params_in_partition[i],
                                       self.first_offset[i],
                                       self.partition_size[i])

        #mapping from parameter to partition that it belongs to
        self.param_to_partition_ids = {}

        #stores if a partition has been reduced in this step
        self.is_partition_reduced = {}

        #number of grads in partition that still need to be computed
        self.remaining_grads_in_partition = {}

        #total number of grads in partition
        self.total_grads_in_partition = {}

        #stores if a grad in a partition has been computed or not
        self.is_grad_computed = {}

        #stores the offset at which a parameter gradient needs to be inserted in a partition
        self.grad_partition_insertion_offset = {}

        #the offset in the gradient at which it must be inserted at the beginning of the partition
        self.grad_start_offset = {}

        #will store the averaged gradients required by this partition
        self.averaged_gradients = {}

        # store index of first parameter in each partition
        self.first_param_index_in_partition = {}

        #initializes all data structures for implementing gradient partitioning
        self.initialize_gradient_partitioning_data_structures()

        #resets the data structure value for the next backward propagation
        self.reset_partition_gradient_structures()

        #creates backward hooks for gradient partitioning
        self.create_reduce_and_remove_grad_hooks()

        # we may have a way of fusing dynamic scale. Do not support for now
        if dynamic_loss_scale:
            if dynamic_loss_args is None:
                self.loss_scaler = DynamicLossScaler()
            else:
                self.loss_scaler = DynamicLossScaler(**dynamic_loss_args)

            self.dynamic_loss_scale = True

        else:
            self.dynamic_loss_scale = False
            self.loss_scaler = LossScaler(scale=static_loss_scale)
            self.cur_iter = 0

        see_memory_usage("Before initializing optimizer states")
        self.initialize_optimizer_states()
        see_memory_usage("After initializing optimizer states")

        if dist.get_rank() == 0:
            logger.info(f"optimizer state initialized")

        if dist.get_rank(group=self.dp_process_group) == 0:
            see_memory_usage(f"After initializing ZeRO optimizer")

    def _release_ipg_buffers(self):
        if self.contiguous_gradients:
            self.ipg_buffer = None
            self.grads_in_partition = None
            self.grads_in_partition_offset = 0

    def initialize_optimizer_states(self):

        for i, group in enumerate(self.fp16_groups):
            single_grad_partition = torch.zeros(
                int(self.partition_size[i]),
                dtype=self.single_partition_of_fp32_groups[i].dtype,
                device=self.device)
            self.single_partition_of_fp32_groups[
                i].grad = single_grad_partition.pin_memory(
                ) if self.cpu_offload else single_grad_partition

        self.optimizer.step()

        if not self.cpu_offload:
            for group in self.single_partition_of_fp32_groups:
                group.grad = None

        return

    #########################################################################
    #########################ZeRO Partition Gradients########################
    #########################################################################

    def get_first_param_index(self, group_id, param_group, partition_id):
        for index, param in enumerate(param_group):
            param_id = self.get_param_id(param)
            if partition_id in self.param_to_partition_ids[group_id][param_id]:
                return index
        return None

    def initialize_gradient_partitioning_data_structures(self):

        total_partitions = dist.get_world_size(group=self.dp_process_group)

        for i, param_group in enumerate(self.fp16_groups):

            self.param_to_partition_ids[i] = {}
            self.is_partition_reduced[i] = {}
            self.total_grads_in_partition[i] = {}
            self.remaining_grads_in_partition[i] = {}
            self.is_grad_computed[i] = {}
            self.grad_partition_insertion_offset[i] = {}
            self.grad_start_offset[i] = {}
            self.first_param_index_in_partition[i] = {}

            for partition_id in range(total_partitions):
                self.is_grad_computed[i][partition_id] = {}
                self.grad_partition_insertion_offset[i][partition_id] = {}
                self.grad_start_offset[i][partition_id] = {}
                self.total_grads_in_partition[i][partition_id] = 0
                self.initialize_gradient_partition(i, param_group, partition_id)
                self.is_partition_reduced[i][partition_id] = False
                self.first_param_index_in_partition[i][
                    partition_id] = self.get_first_param_index(
                        i,
                        param_group,
                        partition_id)

    def independent_gradient_partition_epilogue(self):
        self.report_ipg_memory_usage(f"In ipg_epilogue before reduce_ipg_grads", 0)
        self.reduce_ipg_grads()
        self.report_ipg_memory_usage(f"In ipg_epilogue after reduce_ipg_grads", 0)

        #if dist.get_rank() == 0:
        #    logger.info("Params already reduced %s", self.params_already_reduced)
        for i in range(len(self.params_already_reduced)):
            self.params_already_reduced[i] = False

        if self.overlap_comm:
            torch.cuda.synchronize()

        if self.cpu_offload is False:
            for i, _ in enumerate(self.fp16_groups):

                if not i in self.averaged_gradients or self.averaged_gradients[i] is None:
                    self.averaged_gradients[i] = self.get_flat_partition(
                        self.params_in_partition[i],
                        self.first_offset[i],
                        self.partition_size[i],
                        dtype=torch.half,
                        device=torch.cuda.current_device(),
                        return_tensor_list=True)
                else:
                    avg_new = self.get_flat_partition(self.params_in_partition[i],
                                                      self.first_offset[i],
                                                      self.partition_size[i],
                                                      dtype=torch.half,
                                                      device=torch.cuda.current_device(),
                                                      return_tensor_list=True)

                    for accumulated_grad, new_avg_grad in zip(self.averaged_gradients[i],avg_new):
                        accumulated_grad.add_(new_avg_grad)

        self._release_ipg_buffers()

        # No need to keep the gradients anymore.
        # All gradients required by the step
        # are in self.averaged_gradients
        self.zero_grad()
        see_memory_usage(f"End ipg_epilogue")

    # resets all partition to no reduced
    # sets remaining grads to the total number of grads in each partition
    # set is grad computed to false for all grads in partition
    def reset_partition_gradient_structures(self):
        total_partitions = dist.get_world_size(group=self.dp_process_group)
        for i, _ in enumerate(self.fp16_groups):
            for partition_id in range(total_partitions):
                self.is_partition_reduced[i][partition_id] = False
                self.remaining_grads_in_partition[i][
                    partition_id] = self.total_grads_in_partition[i][partition_id]

                for param_id in self.is_grad_computed[i][partition_id]:
                    self.is_grad_computed[i][partition_id][param_id] = False

    def initialize_gradient_partition(self, i, param_group, partition_id):
        def set_key_value_list(dictionary, key, value):
            if key in dictionary:
                dictionary[key].append(value)
            else:
                dictionary[key] = [value]

        def increment_value(dictionary, key):
            if key in dictionary:
                dictionary[key] += 1
            else:
                dictionary[key] = 1

        partition_size = self.partition_size[i]

        start_index = partition_size * partition_id
        end_index = partition_size * (partition_id + 1)

        current_index = 0
        first_offset = 0

        for param in param_group:

            param_size = param.numel()
            param_id = self.get_param_id(param)

            if (current_index >= start_index and current_index < end_index):
                set_key_value_list(self.param_to_partition_ids[i],
                                   param_id,
                                   partition_id)
                increment_value(self.total_grads_in_partition[i], partition_id)

                self.is_grad_computed[i][partition_id][param_id] = False

                self.grad_partition_insertion_offset[i][partition_id][
                    param_id] = current_index - start_index
                self.grad_start_offset[i][partition_id][param_id] = 0

            elif start_index > current_index and start_index < (current_index +
                                                                param_size):
                assert (first_offset==0), "This can happen either zero or only once as this must be the first tensor in the partition"
                first_offset = start_index - current_index

                set_key_value_list(self.param_to_partition_ids[i],
                                   param_id,
                                   partition_id)
                increment_value(self.total_grads_in_partition[i], partition_id)

                self.is_grad_computed[i][partition_id][param_id] = False

                self.grad_partition_insertion_offset[i][partition_id][param_id] = 0
                self.grad_start_offset[i][partition_id][param_id] = first_offset

            current_index = current_index + param_size

    def overlapping_partition_gradients_reduce_epilogue(self):
        self.independent_gradient_partition_epilogue()

    def create_reduce_and_remove_grad_hooks(self):
        self.grad_accs = []
        for i, param_group in enumerate(self.fp16_groups):
            for param in param_group:
                if param.requires_grad:

                    def wrapper(param, i):
                        param_tmp = param.expand_as(param)
                        grad_acc = param_tmp.grad_fn.next_functions[0][0]

                        def reduce_partition_and_remove_grads(*notneeded):
                            self.reduce_ready_partitions_and_remove_grads(param, i)

                        grad_acc.register_hook(reduce_partition_and_remove_grads)
                        self.grad_accs.append(grad_acc)

                    wrapper(param, i)

    def get_param_id(self, param):
        unique_id = id(param)
        return self.param_id[unique_id]

    def report_ipg_memory_usage(self, tag, param_elems):
        elem_count = self.elements_in_ipg_bucket + param_elems
        percent_of_bucket_size = (100.0 * elem_count) // self.reduce_bucket_size
        see_memory_usage(
            f"{tag}: elems in_bucket {self.elements_in_ipg_bucket} param {param_elems} max_percent {percent_of_bucket_size}"
        )

    ############### Independent Partition Gradient ########################
    def reduce_independent_p_g_buckets_and_remove_grads(self, param, i):
        if self.elements_in_ipg_bucket + param.numel() > self.reduce_bucket_size:
            self.report_ipg_memory_usage("In ipg_remove_grads before reduce_ipg_grads",
                                         param.numel())
            self.reduce_ipg_grads()
            if self.contiguous_gradients and self.overlap_comm:
                # Swap ipg_index between 0 and 1
                self.ipg_index = 1 - self.ipg_index
            self.report_ipg_memory_usage("In ipg_remove_grads after reduce_ipg_grads",
                                         param.numel())

        param_id = self.get_param_id(param)

        assert self.params_already_reduced[param_id] == False, \
            f"The parameter {param_id} has already been reduced. \
            Gradient computed twice for this partition. \
            Multiple gradient reduction is currently not supported"

        #keeping the gradients contiguous to prevent memory fragmentation, and avoid flattening
        if self.contiguous_gradients:
            new_grad_tensor = self.ipg_buffer[self.ipg_index].narrow(
                0,
                self.elements_in_ipg_bucket,
                param.numel())
            new_grad_tensor.copy_(param.grad.view(-1))
            param.grad.data = new_grad_tensor.data.view_as(param.grad)

        self.elements_in_ipg_bucket += param.numel()
        self.grads_in_ipg_bucket.append(param.grad)
        self.params_in_ipg_bucket.append((i, param, param_id))

        self.report_ipg_memory_usage("End ipg_remove_grads", 0)

    def print_rank_0(self, message):
        if dist.get_rank() == 0:
            logger.info(message)

    def gradient_reduction_w_predivide(self, tensor):
        dp_world_size = dist.get_world_size(group=self.dp_process_group)

        tensor_to_allreduce = tensor

        if self.allreduce_always_fp32:
            tensor_to_allreduce = tensor.float()

        if self.postscale_gradients:
            if self.gradient_predivide_factor != 1.0:
                tensor_to_allreduce.mul_(1. / self.gradient_predivide_factor)

            dist.all_reduce(tensor_to_allreduce, group=self.dp_process_group)

            if self.gradient_predivide_factor != dp_world_size:
                tensor_to_allreduce.mul_(self.gradient_predivide_factor / dp_world_size)
        else:
            tensor_to_allreduce.div_(dp_world_size)
            dist.all_reduce(tensor_to_allreduce, group=self.dp_process_group)

        if self.allreduce_always_fp32 and tensor is not tensor_to_allreduce:
            tensor.copy_(tensor_to_allreduce)

        return tensor

    def average_tensor(self, tensor):
        if self.overlap_comm:
            torch.cuda.synchronize()
            stream = self.reduction_stream
        else:
            stream = torch.cuda.current_stream()

        with torch.cuda.stream(stream):
            if not self.reduce_scatter:
                self.gradient_reduction_w_predivide(tensor)
                return

            # Accumulate destination ranks and bucket offsets for each gradient slice.
            # Note: potential future optimization, record access pattern of parameters
            # in backward pass and partition gradients w.r.t. access pattern so that our
            # bucket is guaranteed to be contiguous w.r.t. ranks
            rank_and_offsets = []
            curr_size = 0
            prev_id = -1
            for i, param, param_id in self.params_in_ipg_bucket:
                partition_ids = self.param_to_partition_ids[i][param_id]
                partition_size = self.partition_size[i]
                # Get all partition ids + their offsets
                partition_ids_w_offsets = []
                for partition_id in partition_ids:
                    offset = self.grad_start_offset[i][partition_id][param_id]
                    partition_ids_w_offsets.append((partition_id, offset))
                partition_ids_w_offsets.sort(key=lambda t: t[1])

                # Calculate rank and offsets for grad slices
                for idx in range(len(partition_ids_w_offsets)):
                    partition_id, offset = partition_ids_w_offsets[idx]

                    # Calculate numel for grad slice depending on partition location
                    if idx == len(partition_ids_w_offsets) - 1:
                        # Last partition_id uses its own offset
                        numel = param.numel() - offset
                    else:
                        # Set numel to next partition's offset
                        numel = partition_ids_w_offsets[idx + 1][1] - offset

                    # Merge bucket ranges if they belong to the same rank
                    if partition_id == prev_id:
                        prev_pid, prev_size, prev_numel = rank_and_offsets[-1]
                        rank_and_offsets[-1] = (prev_pid, prev_size, prev_numel + numel)
                    else:
                        rank_and_offsets.append((partition_id, curr_size, numel))

                    curr_size += numel
                    prev_id = partition_id
            tensor.div_(dist.get_world_size(group=self.dp_process_group))

            async_handles = []
            for dst, bucket_offset, numel in rank_and_offsets:
                grad_slice = tensor.narrow(0, int(bucket_offset), int(numel))
                dst_rank = _get_global_rank(self.dp_process_group, dst)
                async_handle = dist.reduce(grad_slice,
                                           dst=dst_rank,
                                           group=self.dp_process_group,
                                           async_op=True)
                async_handles.append(async_handle)

            for handle in async_handles:
                handle.wait()

    ##############################################################################
    ############################# CPU Offload Methods#############################
    ##############################################################################
    def get_grad_position(self, group_id, tensor_list, first_offset, partition_size):
        current_offset = 0

        for i, tensor in enumerate(tensor_list):
            param_id = self.get_param_id(tensor)
            param_start_offset = 0

            num_elements = tensor.numel()
            tensor_offset = 0

            #we need to offset to get to the right element
            if i == 0 and first_offset > 0:
                tensor_offset = first_offset
                num_elements = num_elements - tensor_offset
                param_start_offset = first_offset

            #we dont need all elements of the tensor
            if num_elements > (partition_size - current_offset):
                num_elements = partition_size - current_offset

            self.grad_position[param_id] = [
                int(group_id),
                int(param_start_offset),
                int(current_offset),
                int(num_elements)
            ]
            current_offset += num_elements

    def update_overflow_tracker_for_param_grad(self, param):
        if param.grad is not None and self._has_inf_or_nan(param.grad.data):
            self.local_overflow = True

    def async_accumulate_grad_in_cpu(self, param):
        param_id = self.get_param_id(param)

        #copy to a preexisiting buffer to avoid memory allocation penalty
        dest_buffer = self.temp_grad_buffer_for_cpu_offload.view(-1).narrow(
            0,
            0,
            param.numel())
        dest_buffer.copy_(param.grad.view(-1), non_blocking=True)

        if param_id not in self.accumulated_grads_in_cpu:
            self.accumulated_grads_in_cpu[param_id] = torch.zeros(
                param.numel(),
                dtype=param.dtype,
                device=self.device).pin_memory()

        self.accumulated_grads_in_cpu[param_id].add_(dest_buffer)

    def async_accumulate_grad_in_cpu_via_gpu(self, param):
        param_id = self.get_param_id(param)

        #copy to a preexisiting buffer to avoid memory allocation penalty
        dest_buffer = self.temp_grad_buffer_for_gpu_offload.view(-1).narrow(
            0,
            0,
            param.numel())

        if param_id not in self.accumulated_grads_in_cpu:
            self.accumulated_grads_in_cpu[param_id] = torch.zeros(
                param.numel(),
                dtype=param.dtype,
                device=self.device).pin_memory()

        if self.micro_step_id > 0:
            dest_buffer.copy_(self.accumulated_grads_in_cpu[param_id].view(-1),
                              non_blocking=True)
            param.grad.data.view(-1).add_(dest_buffer)

        #at the boundary we will send 32bit directly
        if not self.is_gradient_accumulation_boundary:
            self.accumulated_grads_in_cpu[param_id].data.copy_(param.grad.data.view(-1),
                                                               non_blocking=True)

    def set_norm_for_param_grad(self, param):
        param_id = self.get_param_id(param)
        accumulated_grad = self.accumulated_grads_in_cpu[
            param_id] if self.gradient_accumulation_steps > 1 else param.grad

        [i, source_offset, dest_offset, num_elements] = self.grad_position[param_id]

        start = source_offset
        accumulated_grad = accumulated_grad.view(-1).narrow(0, start, num_elements)

        self.norm_for_param_grads[param_id] = accumulated_grad.data.double().norm(2)

    def set_norm_for_param_grad_in_gpu(self, param):
        param_id = self.get_param_id(param)
        accumulated_grad = param.grad

        [i, source_offset, dest_offset, num_elements] = self.grad_position[param_id]

        start = source_offset
        accumulated_grad = accumulated_grad.view(-1).narrow(0, start, num_elements)

        self.norm_for_param_grads[param_id] = accumulated_grad.data.double().norm(2)

    def async_inplace_copy_grad_to_fp32_buffer(self, param):
        param_id = self.get_param_id(param)

        [i, source_offset, dest_offset, num_elements] = self.grad_position[param_id]

        dest_tensor = self.single_partition_of_fp32_groups[i].grad.view(-1).narrow(
            0,
            dest_offset,
            num_elements)
        if self.gradient_accumulation_steps > 1:
            src_tensor = self.accumulated_grads_in_cpu[param_id].view(-1).narrow(
                0,
                source_offset,
                num_elements)
        else:
            src_tensor = param.grad.view(-1).narrow(0,
                                                    source_offset,
                                                    num_elements).float()
        dest_tensor.copy_(src_tensor, non_blocking=True)

    def async_inplace_copy_grad_to_fp32_buffer_from_gpu(self, param):
        param_id = self.get_param_id(param)

        [i, source_offset, dest_offset, num_elements] = self.grad_position[param_id]

        dest_tensor = self.single_partition_of_fp32_groups[i].grad.view(-1).narrow(
            0,
            dest_offset,
            num_elements)

        src_tensor = param.grad.view(-1).narrow(0, source_offset, num_elements).float()
        dest_tensor.copy_(src_tensor, non_blocking=True)
        param.grad = None

    def complete_grad_norm_calculation_for_cpu_offload(self, params):
        total_norm = 0.0
        norm_type = 2.0
        for p in params:
            if is_model_parallel_parameter(p) or (self.model_parallel_rank == 0):
                param_id = self.get_param_id(p)
                param_norm = self.norm_for_param_grads[param_id]
                total_norm += param_norm.item()**2

        # Sum across all model parallel GPUs.
        total_norm_cuda = torch.cuda.FloatTensor([float(total_norm)])

        torch.distributed.all_reduce(total_norm_cuda,
                                     op=torch.distributed.ReduceOp.SUM,
                                     group=self.dp_process_group)

        self._model_parallel_all_reduce(tensor=total_norm_cuda,
                                        op=torch.distributed.ReduceOp.SUM)

        total_norm = total_norm_cuda[0].item()**(1. / norm_type)

        if total_norm == float(
                'inf') or total_norm == -float('inf') or total_norm != total_norm:
            total_norm = -1

        return total_norm

    ############################################################################################

    def copy_grads_in_partition(self, param):
        if self.cpu_offload:

            if self.gradient_accumulation_steps > 1:
                self.async_accumulate_grad_in_cpu_via_gpu(param)

            if self.is_gradient_accumulation_boundary:
                self.set_norm_for_param_grad_in_gpu(param)

                self.update_overflow_tracker_for_param_grad(param)

                self.async_inplace_copy_grad_to_fp32_buffer_from_gpu(param)

            return
        #print(f"ID {self.get_param_id(param)} grad norm {param.grad.norm()}")
        if self.grads_in_partition is None:
            self.grads_in_partition_offset = 0
            total_size = 0
            for group in self.params_in_partition:
                for param_in_partition in group:
                    total_size += param_in_partition.numel()

            see_memory_usage(f"before copying {total_size} gradients into partition")
            self.grads_in_partition = torch.empty(int(total_size),
                                                  dtype=torch.half,
                                                  device=torch.cuda.current_device())
            see_memory_usage(f"after copying {total_size} gradients into partition")

        #The allreduce buffer will be rewritted. Copy the gradients in partition to a new buffer
        new_grad_tensor = self.grads_in_partition.view(-1).narrow(
            0,
            self.grads_in_partition_offset,
            param.numel())
        new_grad_tensor.copy_(param.grad.view(-1))
        param.grad.data = new_grad_tensor.data.view_as(param.grad)
        #print(f"Grad norm after copy to contiguous_buffer {param.grad.data.norm()}")
        self.grads_in_partition_offset += param.numel()

    def reduce_ipg_grads(self):
        if self.overlap_comm:
            stream = self.reduction_stream
        else:
            stream = torch.cuda.current_stream()

        if self.contiguous_gradients:
            self.average_tensor(self.ipg_buffer[self.ipg_index])
        else:
            self.buffered_reduce_fallback(
                None,
                self.grads_in_ipg_bucket,
                elements_per_buffer=self.elements_in_ipg_bucket)

        with torch.cuda.stream(stream):
            for _, param, param_id in self.params_in_ipg_bucket:
                self.params_already_reduced[param_id] = True

                if not self.is_param_in_current_partition[param_id]:
                    if self.overlap_comm and self.contiguous_gradients is False:
                        # Clear the previous grads during the next reduction
                        # to avoid clearing them before the reduction is complete.
                        if self.previous_reduced_grads is None:
                            self.previous_reduced_grads = []
                        self.previous_reduced_grads.append(param)
                    else:
                        param.grad = None
                elif self.contiguous_gradients:
                    self.copy_grads_in_partition(param)

        self.grads_in_ipg_bucket = []
        self.params_in_ipg_bucket = []
        self.elements_in_ipg_bucket = 0
        #####################################################################

    def reduce_ready_partitions_and_remove_grads(self, param, i):
        self.reduce_independent_p_g_buckets_and_remove_grads(param, i)

    def zero_reduced_gradients(self, partition_id, i):
        def are_all_related_partitions_reduced(params_id):
            for partition_id in self.param_to_partition_ids[i][params_id]:
                if not self.is_partition_reduced[i][partition_id]:
                    return False
            return True

        for params_id in self.is_grad_computed[i][partition_id]:
            if are_all_related_partitions_reduced(params_id):
                self.param_dict[params_id].grad = None

    def flatten_and_print(self, message, tensors, start=0, n=5):
        flatten_tensor = _flatten_dense_tensors(tensors)

        def print_func():
            logger.info(flatten_tensor.contiguous().view(-1).narrow(0, start, n))

        self.sequential_execution(print_func, message)

    def get_grads_to_reduce(self, i, partition_id):
        def get_reducable_portion(key):
            grad = self.param_dict[key].grad
            total_elements = grad.numel()
            start = self.grad_start_offset[i][partition_id][key]
            num_elements = min(
                total_elements - start,
                self.partition_size[i] -
                self.grad_partition_insertion_offset[i][partition_id][key])
            if not pg_correctness_test:
                if num_elements == total_elements:
                    return grad
                else:
                    return grad.contiguous().view(-1).narrow(0,
                                                             int(start),
                                                             int(num_elements))
            else:
                if num_elements == total_elements:
                    return grad.clone()
                else:
                    return grad.clone().contiguous().view(-1).narrow(
                        0,
                        int(start),
                        int(num_elements))

        grads_to_reduce = []
        for key in self.is_grad_computed[i][partition_id]:
            grad = get_reducable_portion(key)
            grads_to_reduce.append(grad)
        return grads_to_reduce

    def sequential_execution(self, function, message, group=None):
        if group is None:
            group = self.dp_process_group
        if dist.get_rank(group=group) == 0:
            logger.info(message)
        for id in range(dist.get_world_size(group=group)):
            if id == dist.get_rank(group=group):
                function()
            dist.barrier(group=group)

    def set_none_gradients_to_zero(self, i, partition_id):
        for param_id in self.is_grad_computed[i][partition_id]:
            param = self.param_dict[param_id]
            if param.grad is None:
                param.grad = torch.zero_like(param)

    ######################Reduction Related Methods##############################

    def allreduce_bucket(self, bucket, allreduce_always_fp32=False, rank=None, log=None):
        rank = None
        tensor = flatten(bucket)

        tensor_to_allreduce = tensor

        if pg_correctness_test:
            allreduce_always_fp32 = True

        if allreduce_always_fp32:
            tensor_to_allreduce = tensor.float()

        tensor_to_allreduce.div_(dist.get_world_size(group=self.dp_process_group))

        if rank is None:
            #    "All Reducing"
            dist.all_reduce(tensor_to_allreduce, group=self.dp_process_group)
        else:
            global_rank = _get_global_rank(self.dp_process_group, rank)
            dist.reduce(tensor_to_allreduce, global_rank, group=self.dp_process_group)

        if allreduce_always_fp32 and tensor is not tensor_to_allreduce:
            if rank is None or rank == dist.get_rank(group=self.dp_process_group):
                tensor.copy_(tensor_to_allreduce)

        return tensor

    #if rank is specified do a reduction instead of an allreduce
    def allreduce_and_copy(self, small_bucket, rank=None, log=None):
        if self.overlap_comm:
            torch.cuda.synchronize()
            if self.previous_reduced_grads is not None:
                # previous_reduced_grads has the previous reduced grads,
                # now it is safe to clear.
                for param in self.previous_reduced_grads:
                    param.grad = None
                self.previous_reduced_grads = None
            stream = self.reduction_stream
        else:
            stream = torch.cuda.current_stream()

        with torch.cuda.stream(stream):
            allreduced = self.allreduce_bucket(small_bucket, rank=rank, log=log)
            if rank is None or rank == dist.get_rank(group=self.dp_process_group):
                for buf, synced in zip(small_bucket, unflatten(allreduced, small_bucket)):
                    buf.copy_(synced)

    def allreduce_no_retain(self,
                            bucket,
                            numel_per_bucket=500000000,
                            rank=None,
                            log=None):
        small_bucket = []
        numel = 0
        for tensor in bucket:
            small_bucket.append(tensor)
            numel = numel + tensor.numel()
            if numel > numel_per_bucket:
                self.allreduce_and_copy(small_bucket, rank=rank, log=None)
                small_bucket = []
        if len(small_bucket) > 0:
            self.allreduce_and_copy(small_bucket, rank=rank, log=log)

    #allows using reduction of gradients instead of using all_reduce
    def buffered_reduce_fallback(self,
                                 rank,
                                 grads,
                                 elements_per_buffer=500000000,
                                 log=None):
        split_buckets = split_half_float_double(grads)

        for i, bucket in enumerate(split_buckets):
            self.allreduce_no_retain(bucket,
                                     numel_per_bucket=elements_per_buffer,
                                     rank=rank,
                                     log=log)

    #############################################################################
    #############################################################################
    #############################################################################

    #views the tensor as multiple partitions and returns
    #those partitions
    def get_data_parallel_partitions(self, tensor):
        partitions = []

        dp = dist.get_world_size(group=self.dp_process_group)
        dp_id = dist.get_rank(group=self.dp_process_group)

        total_num_elements = tensor.numel()

        base_size = total_num_elements // dp
        remaining = total_num_elements % dp

        start = 0
        for id in range(dp):
            partition_size = base_size
            if id < remaining:
                partition_size = partition_size + 1
            partitions.append(tensor.narrow(0, start, partition_size))
            start = start + partition_size
        return partitions

    def get_partition_info(self, tensor_list, partition_size, partition_id):
        params_in_partition = []
        params_not_in_partition = []

        start_index = partition_size * partition_id
        end_index = partition_size * (partition_id + 1)

        current_index = 0
        first_offset = 0

        for tensor in tensor_list:

            tensor_size = tensor.numel()

            if (current_index >= start_index and current_index < end_index):
                params_in_partition.append(tensor)

            elif start_index > current_index and start_index < (current_index +
                                                                tensor_size):
                params_in_partition.append(tensor)

                assert (first_offset==0), "This can happen either zero or only once as this must be the first tensor in the partition"
                first_offset = start_index - current_index

            else:
                params_not_in_partition.append(tensor)

            current_index = current_index + tensor_size

        return params_in_partition, params_not_in_partition, first_offset

    def zero_grad(self, set_grads_to_None=True):
        """
        Zero FP16 parameter grads.
        """
        # FP32 grad should never exist.
        # For speed, set model fp16 grad to None by default
        for group in self.fp16_groups:
            for p in group:
                if set_grads_to_None:
                    p.grad = None
                else:
                    if p.grad is not None:
                        p.grad.detach_()
                        p.grad.zero_()

    def _model_parallel_all_reduce(self, tensor, op):
        """ Perform all reduce within model parallel group, if any.
        """
        if self.model_parallel_group is None:
            torch.distributed.all_reduce(tensor=tensor, op=op)
        else:
            torch.distributed.all_reduce(tensor=tensor,
                                         op=op,
                                         group=self.model_parallel_group)

    def get_grad_norm_direct(self, gradients, params, norm_type=2):
        """Clips gradient norm of an iterable of parameters.

        This is adapted from torch.nn.utils.clip_grad.clip_grad_norm_ and
        added functionality to handle model parallel parameters. Note that
        the gradients are modified in place.

        Arguments:
            parameters (Iterable[Tensor] or Tensor): an iterable of Tensors or a
                single Tensor that will have gradients normalized
            max_norm (float or int): max norm of the gradients
            norm_type (float or int): type of the used p-norm. Can be ``'inf'`` for
                infinity norm.

        Returns:
            Total norm of the parameters (viewed as a single vector).
        """
        norm_type = float(norm_type)
        if norm_type == inf:
            total_norm = max(g.data.abs().max() for g in gradients)
            total_norm_cuda = torch.cuda.FloatTensor([float(total_norm)])
            torch.distributed.all_reduce(total_norm_cuda,
                                         op=torch.distributed.ReduceOp.MAX,
                                         group=self.dp_process_group)

            # Take max across all GPUs.
            self._model_parallel_all_reduce(tensor=total_norm_cuda,
                                            op=torch.distributed.ReduceOp.MAX)
            total_norm = total_norm_cuda[0].item()
        else:
            total_norm = 0.0
            #if dist.get_rank() == 0:
            #    logger.info(f"Total Norm begining {total_norm}")
            for g, p in zip(gradients, params):
                if is_model_parallel_parameter(p) or (self.model_parallel_rank == 0):
                    param_norm = g.data.double().norm(2)
                    total_norm += param_norm.item()**2
            # Sum across all model parallel GPUs.
            total_norm_cuda = torch.cuda.FloatTensor([float(total_norm)])

            torch.distributed.all_reduce(total_norm_cuda,
                                         op=torch.distributed.ReduceOp.SUM,
                                         group=self.dp_process_group)

            self._model_parallel_all_reduce(tensor=total_norm_cuda,
                                            op=torch.distributed.ReduceOp.SUM)

            total_norm = total_norm_cuda[0].item()**(1. / norm_type)

        if total_norm == float(
                'inf') or total_norm == -float('inf') or total_norm != total_norm:
            total_norm = -1

        return total_norm

    #creates a flat fused tensor from the tensor list starting at the first_offset
    #in the first tensor of the list. If there are not enough elements in the tensor
    #list then the flat tensor will be padded with zeros
    def get_flat_partition(self,
                           tensor_list,
                           first_offset,
                           partition_size,
                           dtype,
                           device,
                           return_tensor_list=False):
        flat_tensor_list = []
        current_size = 0
        for i, tensor in enumerate(tensor_list):
            if tensor.grad is None:
                continue

            tensor = tensor.grad
            num_elements = tensor.numel()
            tensor_offset = 0

            #we need to offset to get to the right element
            if i == 0 and first_offset > 0:
                tensor_offset = first_offset
                num_elements = num_elements - tensor_offset

            #we dont need all elements of the tensor
            if num_elements > (partition_size - current_size):
                num_elements = partition_size - current_size

            #we need a narrow view of the tensor based on the tensor offset and number of elements that
            #we need from this tensor
            if tensor_offset > 0 or num_elements < tensor.numel():
                flat_tensor_list.append(tensor.contiguous().view(-1).narrow(
                    0,
                    int(tensor_offset),
                    int(num_elements)))
            else:
                flat_tensor_list.append(tensor)

            current_size = current_size + num_elements

        #this means its the last partition and does not align with the dp boundary. We need to pad before flattening
        if current_size < partition_size:
            flat_tensor_list.append(
                torch.zeros(int(partition_size - current_size),
                            dtype=dtype,
                            device=device))

        if return_tensor_list:
            return flat_tensor_list

        return _flatten_dense_tensors(flat_tensor_list)

    def free_grad_in_param_list(self, param_list):
        for p in param_list:
            p.grad = None

    def reset_cpu_buffers(self):
        self.norm_for_param_grads = {}
        self.local_overflow = False

    def step(self, closure=None):
        """
        Not supporting closure.
        """
        self.micro_step_id = -1

        if self.cpu_offload:
            torch.cuda.current_stream().wait_stream(self.migration_stream)

        see_memory_usage(f"In step before checking overflow")

        # First compute norm for all group so we know if there is overflow
        self.check_overflow()

        timers = self.timers

        prev_scale = self.loss_scale
        self._update_scale(self.overflow)
        if self.overflow:
            see_memory_usage('After overflow before clearing gradients')
            self.zero_grad()
            if self.cpu_offload:
                self.reset_cpu_buffers()
            else:
                self.averaged_gradients = {}

            see_memory_usage('After overflow after clearing gradients')

            logger.info(
                "[deepscale] OVERFLOW! Rank {} Skipping step. Attempted loss scale: {}, "
                "reducing to {}".format(dist.get_rank(),
                                        prev_scale,
                                        self.loss_scale))
            timers('optimizer_gradients').start()
            timers('optimizer_gradients').stop()
            timers('optimizer_step').start()
            timers('optimizer_step').stop()
            timers('optimizer_allgather').start()
            timers('optimizer_allgather').stop()
            return

        timers('optimizer_gradients').start()
        norm_groups = []
        single_partition_grad_groups = []
        skip = False
        partition_id = dist.get_rank(group=self.dp_process_group)
        for i, group in enumerate(self.fp16_groups):
            if self.cpu_offload:
                norm_groups.append(
                    self.complete_grad_norm_calculation_for_cpu_offload(
                        self.params_in_partition[i]))
                single_grad_partition = self.single_partition_of_fp32_groups[i].grad
            else:
                norm_groups.append(
                    self.get_grad_norm_direct(self.averaged_gradients[i],
                                              self.params_in_partition[i]))

                #free gradients for all the prameters that are not updated by this process
                self.free_grad_in_param_list(self.params_not_in_partition[i])

                #create a flat gradients for parameters updated by this process
                # If we are last partition, ensure we have same size grads and partition size, if not pad with zero tensors
                if partition_id == dist.get_world_size(group=self.dp_process_group) - 1:
                    single_grad_partition = flatten_dense_tensors_aligned(
                        self.averaged_gradients[i],
                        int(self.partition_size[i])).to(
                            self.single_partition_of_fp32_groups[i].dtype)
                else:
                    single_grad_partition = _flatten_dense_tensors(
                        self.averaged_gradients[i]).to(
                            self.single_partition_of_fp32_groups[i].dtype)
                assert single_grad_partition.numel() == self.partition_size[i], \
                    "averaged gradients have different number of elements that partition size {} {} {} {}".format(single_grad_partition.numel(), self.partition_size[i], i, partition_id)

                self.single_partition_of_fp32_groups[i].grad = single_grad_partition
                #release all the gradient since we have already created a necessary copy in dp_grad_partition
                self.free_grad_in_param_list(self.params_in_partition[i])

                self.averaged_gradients[i] = None

            single_partition_grad_groups.append(single_grad_partition)

        self.unscale_and_clip_grads(single_partition_grad_groups, norm_groups)
        timers('optimizer_gradients').stop()

        #torch.set_num_threads(12)
        timers('optimizer_step').start()
        if self.deepspeed_adam_offload:
            from deepspeed.ops.adam import DeepSpeedCPUAdam
            self.optimizer.step(fp16_param_groups=self.parallel_partitioned_fp16_groups)
            #self.optimizer.step()
            #for fp16_partitions, fp32_partition in zip(self.parallel_partitioned_fp16_groups, self.single_partition_of_fp32_groups):
            #    fp16_partitions[partition_id].data.copy_(fp32_partition.data)
        else:
            self.optimizer.step()

            #get rid of the fp32 gradients. Not needed anymore
            if not self.cpu_offload:
                for group in self.single_partition_of_fp32_groups:
                    group.grad = None

            for fp16_partitions, fp32_partition in zip(self.parallel_partitioned_fp16_groups, self.single_partition_of_fp32_groups):
                fp16_partitions[partition_id].data.copy_(fp32_partition.data)

        timers('optimizer_step').stop()

        if self.cpu_offload:
            self.reset_cpu_buffers()

        timers('optimizer_allgather').start()
        #gather the updated weights from everyone
        for group_id, partitioned_params in enumerate(self.parallel_partitioned_fp16_groups):

            #Sequential AllGather Best of both worlds
            dp_world_size = dist.get_world_size(group=self.dp_process_group)
            num_shards = max(
                1,
                partitioned_params[partition_id].numel() * dp_world_size //
                self.allgather_bucket_size)

            shard_size = partitioned_params[partition_id].numel() // num_shards
            num_elements = shard_size

            assert shard_size * num_shards <= partitioned_params[partition_id].numel()

            for shard_id in range(num_shards):

                if shard_id == (num_shards - 1):
                    num_elements = partitioned_params[partition_id].numel(
                    ) - shard_id * shard_size

                shard_list = []
                for dp_id in range(dp_world_size):
                    curr_shard = partitioned_params[dp_id].narrow(
                        0,
                        shard_id * shard_size,
                        num_elements).detach()
                    shard_list.append(curr_shard)

                dist.all_gather(shard_list,
                                shard_list[partition_id],
                                group=self.dp_process_group)
        timers('optimizer_allgather').stop()

        # TODO: we probably don't need this? just to be safe
        for i in range(len(norm_groups)):
            updated_params = _unflatten_dense_tensors(self.fp16_groups_flat[i],
                                                      self.fp16_groups[i])
            for p, q in zip(self.fp16_groups[i], updated_params):
                p.data = q.data

        timers.log(
            names=['optimizer_gradients',
                   'optimizer_step',
                   'optimizer_allgather'])
        see_memory_usage('After zero_optimizer step')
        return

    def unscale_and_clip_grads(self, grad_groups_flat, norm_groups):
        total_norm = 0.0
        for norm in norm_groups:
            total_norm += norm**2.0
        total_norm = math.sqrt(total_norm)

        # compute combined scale factor for this group
        combined_scale = self.loss_scale
        if self.clip_grad > 0.:
            # norm is in fact norm*scale
            clip = ((total_norm / self.loss_scale) + 1e-6) / self.clip_grad
            if clip > 1:
                combined_scale = clip * self.loss_scale

        for grad in grad_groups_flat:
            if isinstance(grad, list):
                sub_partitions = grad
                for g in sub_partitions:
                    g.data.mul_(1. / combined_scale)
            else:
                grad.data.mul_(1. / combined_scale)

    def _check_overflow(self, partition_gradients=True):
        self.overflow = self.has_overflow(partition_gradients)

    # `params` is a list / generator of torch.Variable
    def has_overflow_serial(self, params, is_grad_list=False):
        for p in params:
            if p.grad is not None and self._has_inf_or_nan(p.grad.data):
                return True

        return False

    def has_overflow_partitioned_grads_serial(self):
        for i in range(len(self.fp16_groups)):
            for j, grad in enumerate(self.averaged_gradients[i]):
                if grad is not None and self._has_inf_or_nan(grad.data, j):
                    return True
        return False

    def has_overflow(self, partition_gradients=True):
        if partition_gradients:
            overflow = self.local_overflow if self.cpu_offload else self.has_overflow_partitioned_grads_serial(
            )
            overflow_gpu = torch.cuda.ByteTensor([overflow])
            torch.distributed.all_reduce(overflow_gpu,
                                         op=torch.distributed.ReduceOp.MAX,
                                         group=self.dp_process_group)

        else:
            params = []
            for group in self.fp16_groups:
                for param in group:
                    params.append(param)

            overflow = self.has_overflow_serial(params, is_grad_list=partition_gradients)
            overflow_gpu = torch.cuda.ByteTensor([overflow])

        # Since each model parallel GPU carries only part of the model,
        # make sure overflow flag is synced across all the model parallel GPUs
        self._model_parallel_all_reduce(tensor=overflow_gpu,
                                        op=torch.distributed.ReduceOp.MAX)

        overflow = overflow_gpu[0].item()
        return bool(overflow)

    # `x` is a torch.Tensor
    @staticmethod
    def _has_inf_or_nan(x, j=None):
        try:
            # if x is half, the .float() incurs an additional deep copy, but it's necessary if
            # Pytorch's .sum() creates a one-element tensor of the same type as x
            # (which is true for some recent version of pytorch).
            cpu_sum = float(x.float().sum())
            # More efficient version that can be used if .sum() returns a Python scalar
            # cpu_sum = float(x.sum())
        except RuntimeError as instance:
            # We want to check if inst is actually an overflow exception.
            # RuntimeError could come from a different error.
            # If so, we still want the exception to propagate.
            if "value cannot be converted" not in instance.args[0]:
                raise
            return True
        else:
            if cpu_sum == float('inf') or cpu_sum == -float('inf') or cpu_sum != cpu_sum:
                return True
            return False

    def backward(self, loss, retain_graph=False):
        """
        :attr:`backward` performs the following steps:

        1. fp32_loss = loss.float()
        2. scaled_loss = fp32_loss*loss_scale
        3. scaled_loss.backward(), which accumulates scaled gradients into the ``.grad`` attributes of the model's fp16 leaves
        """
        self.micro_step_id += 1
        if self.cpu_offload:
            torch.cuda.current_stream().wait_stream(self.migration_stream)

        #TODO: we need to revist this and remove the magic 4.5x multiplier here
        if self.contiguous_gradients:
            self.ipg_buffer = []
            buf_0 = torch.empty(int(self.reduce_bucket_size * 4.5),
                                dtype=torch.half,
                                device=torch.cuda.current_device())
            self.ipg_buffer.append(buf_0)

            # Use double buffers to avoid data access conflict when overlap_comm is enabled.
            if self.overlap_comm:
                buf_1 = torch.empty(int(self.reduce_bucket_size * 4.5),
                                    dtype=torch.half,
                                    device=torch.cuda.current_device())
                self.ipg_buffer.append(buf_1)
            self.ipg_index = 0

        self.loss_scaler.backward(loss.float(), retain_graph=retain_graph)

    def check_overflow(self, partition_gradients=True):
        self._check_overflow(partition_gradients)

    def _update_scale(self, has_overflow=False):
        self.loss_scaler.update_scale(has_overflow)

    # Promote state so it can be retrieved or set via "fp16_optimizer_instance.state"
    def _get_state(self):
        return self.optimizer.state

    def _set_state(self, value):
        self.optimizer.state = value

    state = property(_get_state, _set_state)

    # Promote param_groups so it can be retrieved or set via "fp16_optimizer_instance.param_groups"
    # (for example, to adjust the learning rate)
    def _get_param_groups(self):
        return self.optimizer.param_groups

    def _set_param_groups(self, value):
        self.optimizer.param_groups = value

    param_groups = property(_get_param_groups, _set_param_groups)

    # Promote loss scale so it can be retrieved or set via "fp16_optimizer_instance.loss_scale"
    def _get_loss_scale(self):
        return self.loss_scaler.loss_scale

    def _set_loss_scale(self, value):
        self.loss_scaler.cur_scale = value

    loss_scale = property(_get_loss_scale, _set_loss_scale)
    cur_scale = property(_get_loss_scale, _set_loss_scale)

    # Return group tensor after removing paddings that are added for alignment to DP world size.
    # This method works on the assumption that each group contains a single flattened tensor.
    def _get_groups_without_padding(self, groups_with_padding):
        groups_without_padding = []
        for i, group in enumerate(groups_with_padding):
            lean_length = group.numel() - self.groups_padding[i]
            groups_without_padding.append(group[:lean_length])

        return groups_without_padding

    # Return optimizer state after removing paddings that are added for alignment.
    def _get_state_without_padding(self, state_with_padding, padding):
        lean_state = {}
        for key, value in state_with_padding.items():
            if torch.is_tensor(value):
                lean_length = value.numel() - padding
                lean_state[key] = value[:lean_length]
            else:
                lean_state[key] = value

        return lean_state

    # Return base optimizer states.
    # This method assumes that each param group contains a single flattened tensor.
    def _get_base_optimizer_state(self):
        optimizer_groups_state = []
        for i, group in enumerate(self.optimizer.param_groups):
            p = group['params'][0]
            lean_optimizer_state = self._get_state_without_padding(
                self.optimizer.state[p],
                self.groups_padding[i])
            optimizer_groups_state.append(lean_optimizer_state)

        return optimizer_groups_state

    def state_dict(self):
        """
        Returns a dict containing the current state of this :class:`FP16_Optimizer` instance.
        This dict contains attributes of :class:`FP16_Optimizer`, as well as the state_dict
        of the contained Pytorch optimizer.
        Example::
            checkpoint = {}
            checkpoint['model'] = model.state_dict()
            checkpoint['optimizer'] = optimizer.state_dict()
            torch.save(checkpoint, "saved.pth")
        """
        state_dict = {}
        state_dict['loss_scaler'] = self.loss_scaler
        state_dict['dynamic_loss_scale'] = self.dynamic_loss_scale
        state_dict['overflow'] = self.overflow
        state_dict['base_optimizer_state'] = self._get_base_optimizer_state()

        state_dict['zero_stage'] = ZERO_OPTIMIZATION_GRADIENTS
        state_dict['partition_count'] = self.partition_count

        # Remove paddings for DP alignment to enable loading for other alignment values
        fp32_groups_without_padding = self._get_groups_without_padding(
            self.single_partition_of_fp32_groups)
        state_dict['single_partition_of_fp32_groups'] = fp32_groups_without_padding

        #        if self.cpu_offload:
        #            state_dict_tmp = async_copy_to(state_dict,
        #                                           'cpu',
        #                                           torch.cuda.current_stream())
        #            state_dict = state_dict_tmp

        return state_dict

    # Restore base optimizer fp32 weights from checkpoint by:
    # 1) Merging fp32 weights from checkpoints of all partitions
    # 2) Extracting fp32 weights for current partition from merged weights
    # 3) Using extracted weights to update base optimizer weights directly.
    def _restore_from_fp32_weights(self, all_state_dict):
        partition_id = dist.get_rank(group=self.dp_process_group)
        merged_single_partition_of_fp32_groups = []
        for i in range(len(self.single_partition_of_fp32_groups)):
            merged_partitions = [
                sd['single_partition_of_fp32_groups'][i] for sd in all_state_dict
            ]
            flat_merged_partitions = flatten_dense_tensors_aligned(
                merged_partitions,
                dist.get_world_size(group=self.dp_process_group))
            dp_partitions = self.get_data_parallel_partitions(flat_merged_partitions)
            merged_single_partition_of_fp32_groups.append(dp_partitions[partition_id])

        for current, saved in zip(self.single_partition_of_fp32_groups, merged_single_partition_of_fp32_groups):
            current.data.copy_(saved.data)

    # Restore base optimizer fp32 weights from ZeRO fp16 weights
    def _restore_from_fp16_weights(self):
        partition_id = dist.get_rank(group=self.dp_process_group)
        for fp16_partitions, fp32_partition in zip(self.parallel_partitioned_fp16_groups, self.single_partition_of_fp32_groups):
            fp32_partition.data.copy_(fp16_partitions[partition_id].data)

    # Refresh the fp32 master params from the fp16 copies.
    def refresh_fp32_params(self):
        self._restore_from_fp16_weights()

    # Extract optimizer state for current partition from merged states of all partitions
    def _partition_base_optimizer_state(self, state_key, all_partition_states):
        partition_id = dist.get_rank(group=self.dp_process_group)
        alignment = dist.get_world_size(group=self.dp_process_group)
        if torch.is_tensor(all_partition_states[0]):
            flat_merged_partitions = flatten_dense_tensors_aligned(
                all_partition_states,
                alignment)
            dp_partitions = self.get_data_parallel_partitions(flat_merged_partitions)
            return dp_partitions[partition_id]
        else:
            # Assume non-tensor states are not partitioned and equal across ranks, so return first one
            return all_partition_states[0]

    # Restore base optimizer state from checkpoint by
    # 1) Merging optimizer state from checkpoints of all partitions
    # 2) Extracting optimizer state for current partition from the merged state
    # 3) Using the extracted value to directly update the base optimizer.
    def _restore_base_optimizer_state(self, all_state_dict):
        base_optimizer_group_states = []
        for i in range(len(self.optimizer.param_groups)):
            partition_states = {}
            all_partition_group_states = [
                sd['base_optimizer_state'][i] for sd in all_state_dict
            ]
            for key in all_partition_group_states[0].keys():
                all_partition_states = [
                    all_states[key] for all_states in all_partition_group_states
                ]
                partition_states[key] = self._partition_base_optimizer_state(
                    key,
                    all_partition_states)
            base_optimizer_group_states.append(partition_states)

        for i, group in enumerate(self.optimizer.param_groups):
            p = group['params'][0]
            for key, saved in base_optimizer_group_states[i].items():
                if torch.is_tensor(self.optimizer.state[p][key]):
                    self.optimizer.state[p][key].data.copy_(saved.data)
                else:
                    self.optimizer.state[p][key] = saved

    def load_state_dict(self,
                        state_dict_list,
                        load_optimizer_states=True,
                        load_from_fp32_weights=False):
        r"""Loading ZeRO checkpoint

        Arguments:
            state_dict_list: List of all saved ZeRO checkpoints, one for each saved partition.
                Note that the number of saved partitions may differ from number of loading partitions to support
                changing GPU count, specifically DP world size, between saving and loading checkpoints.
            load_optimizer_states: Boolean indicating whether or not to load base optimizer states
            load_from_fp32_weights: Boolean indicating whether to initialize fp32 master weights from fp32
            copies in checkpoints (no precision loss) or from model's fp16 copies (with precision loss).
        """
        """
        Loads a state_dict created by an earlier call to state_dict().
        If ``fp16_optimizer_instance`` was constructed from some ``init_optimizer``,
        whose parameters in turn came from ``model``, it is expected that the user
        will call ``model.load_state_dict()`` before
        ``fp16_optimizer_instance.load_state_dict()`` is called.
        Example::
            model = torch.nn.Linear(D_in, D_out).cuda().half()
            optimizer = torch.optim.SGD(model.parameters(), lr=1e-3)
            optimizer = FP16_Optimizer(optimizer, static_loss_scale = 128.0)
            ...
            checkpoint = torch.load("saved.pth")
            model.load_state_dict(checkpoint['model'])
            optimizer.load_state_dict(checkpoint['optimizer'])
        """
        # I think it should actually be ok to reload the optimizer before the model.
        self.loss_scaler = state_dict_list[0]['loss_scaler']
        self.dynamic_loss_scale = state_dict_list[0]['dynamic_loss_scale']
        self.overflow = state_dict_list[0]['overflow']

        if load_optimizer_states:
            self._restore_base_optimizer_state(state_dict_list)

        # At this point, the optimizer's references to the model's fp32 parameters are up to date.
        # The optimizer's hyperparameters and internal buffers are also up to date.
        # However, the fp32 master copies of the model's fp16 params stored by the optimizer are still
        # out of date.  There are two options.
        # 1:  Refresh the master params from the model's fp16 params.
        # This requires less storage but incurs precision loss.
        # 2:  Save and restore the fp32 master copies separately.
        # We choose option 1 if changing DP degree and option 2 otherwise.
        #
        # Pytorch Optimizer.load_state_dict casts saved buffers (e.g. momentum) to the type and device
        # of their associated parameters, because it's possible those buffers might not exist yet in
        # the current optimizer instance.  In our case, as long as the current FP16_Optimizer has been
        # constructed in the same way as the one whose state_dict we are loading, the same master params
        # are guaranteed to exist, so we can just copy_() from the saved master params.

        if load_from_fp32_weights:
            self._restore_from_fp32_weights(state_dict_list)
        else:
            self._restore_from_fp16_weights()


def _handle_overflow(cpu_sum, x, i):
    import math
    rank = torch.distributed.get_rank()
    if rank == 0:
        t_i = -1
        for v_i, v in enumerate(x.data.contiguous().view(-1)):
            if not math.isfinite(float(v)):
                t_i = v_i
                break
        logger.info(
            f"rank {rank} detected overflow {cpu_sum} in tensor {i}:{t_i} shape {x.shape}"
        )
