code: import torch
  from torch import nn
  from torch.autograd import Variable
  from torch.nn.parameter import Parameter
  from torch._utils import _flatten_dense_tensors, _unflatten_dense_tensors
  
  from .loss_scaler import DynamicLossScaler, LossScaler
  
  FLOAT_TYPES = (torch.FloatTensor, torch.cuda.FloatTensor)
  HALF_TYPES = (torch.HalfTensor, torch.cuda.HalfTensor)
  
  def conversion_helper(val, conversion):
      """Apply conversion to val. Recursively apply conversion if `val` is a nested tuple/list structure."""
      if not isinstance(val, (tuple, list)):
          return conversion(val)
      rtn =  [conversion_helper(v, conversion) for v in val]
      if isinstance(val, tuple):
          rtn = tuple(rtn)
      return rtn
  
  def fp32_to_fp16(val):
      """Convert fp32 `val` to fp16"""
      def half_conversion(val):
          val_typecheck = val
          if isinstance(val_typecheck, (Parameter, Variable)):
              val_typecheck = val.data
          if isinstance(val_typecheck, FLOAT_TYPES):
              val = val.half()
          return val
      return conversion_helper(val, half_conversion)
  
  def fp16_to_fp32(val):
      """Convert fp16 `val` to fp32"""
      def float_conversion(val):
          val_typecheck = val
          if isinstance(val_typecheck, (Parameter, Variable)):
              val_typecheck = val.data
          if isinstance(val_typecheck, HALF_TYPES):
              val = val.float()
          return val
      return conversion_helper(val, float_conversion)
  
  class FP16_Module(nn.Module):
      def __init__(self, module):
          super(FP16_Module, self).__init__()
          self.add_module('module', module.half())
  
      def forward(self, *inputs, **kwargs):
          return fp16_to_fp32(self.module(*(fp32_to_fp16(inputs)), **kwargs))
  
      def load_state_dict(self, state_dict, strict=True):
          self.module.load_state_dict(state_dict, strict=strict)
  
      def state_dict(self, destination=None, prefix='', keep_vars=False):
          return self.module.state_dict(destination=destination, prefix=prefix, keep_vars=keep_vars)
  
  class FP16_Optimizer(object):
      """
      FP16_Optimizer is designed to wrap an existing PyTorch optimizer, 
      and enable an fp16 model to be trained using a master copy of fp32 weights.
  
      Args:
          optimizer (torch.optim.optimizer):  Existing optimizer containing initialized fp16 parameters.  Internally, FP16_Optimizer replaces the passed optimizer's fp16 parameters with new fp32 parameters copied from the original ones.  FP16_Optimizer also stores references to the original fp16 parameters, and updates these fp16 parameters from the master fp32 copy after each step.  
          static_loss_scale (float, optional, default=1.0):  Loss scale used internally to scale fp16 gradients computed by the model.  Scaled gradients will be copied to fp32, then downscaled before being applied to the fp32 master params, so static_loss_scale should not affect learning rate.
          dynamic_loss_scale (bool, optional, default=False):  Use dynamic loss scaling.  If True, this will override any static_loss_scale option.
  
      """
  
      def __init__(self, optimizer, static_loss_scale=1.0, dynamic_loss_scale=False):
          if not torch.cuda.is_available:
              raise SystemError('Cannot use fp16 without CUDA')
  
          self.fp16_param_groups = []
          self.fp32_param_groups = []
          for param_group in optimizer.param_groups:
              fp16_params_this_group = [param for param in param_group['params'] if param.requires_grad]
          
              fp32_params_this_group = _flatten_dense_tensors(
                  [param.detach().data.clone().float() for param in fp16_params_this_group])
              fp32_params_this_group = Variable(fp32_params_this_group, requires_grad = True)
              fp32_params_this_group.grad = fp32_params_this_group.new(*fp32_params_this_group.size())
          
              param_group['params'] = [fp32_params_this_group]
  
              self.fp16_param_groups.append(fp16_params_this_group)
              self.fp32_param_groups.append(fp32_params_this_group)
  
          self.optimizer = optimizer.__class__(optimizer.param_groups)
  
          # self.optimizer.load_state_dict(optimizer.state_dict())
  
          self.param_groups = self.optimizer.param_groups
  
          if dynamic_loss_scale:
              self.dynamic_loss_scale = True
              self.loss_scaler = DynamicLossScaler()
          else:
              self.dynamic_loss_scale = False
              self.loss_scaler = LossScaler(static_loss_scale)
  
          self.overflow = False
          self.first_closure_call_this_step = True
  
      def zero_grad(self):
          """
          Zero fp32 and fp16 parameter grads.
          """
          self.optimizer.zero_grad()
          for fp16_group in self.fp16_param_groups:
              for param in fp16_group:
                  if param.grad is not None:
                      param.grad.detach_() # This does appear in torch.optim.optimizer.zero_grad(), 
                                           # but I'm not sure why it's needed.
                      param.grad.zero_()
  
      def _check_overflow(self):
          fp16_params = [] 
          for fp16_group in self.fp16_param_groups:
              for param in fp16_group:
                  fp16_params.append(param)
          self.overflow = self.loss_scaler.has_overflow(fp16_params)
  
      def _update_scale(self, has_overflow=False):
          self.loss_scaler.update_scale(has_overflow)
  
      def _copy_grads_fp16_to_fp32(self):
          for fp32_group, fp16_group in zip(self.fp32_param_groups, self.fp16_param_groups):
              # This might incur one more deep copy than is necessary.
              fp32_group.grad.data.copy_(
                  _flatten_dense_tensors([fp16_param.grad.data for fp16_param in fp16_group]))
  
      def _downscale_fp32(self):
          for param_group in self.optimizer.param_groups:
              param_group['params'][0].grad.data.mul_(1./self.loss_scale)
  
      def clip_fp32_grads(self, clip=-1):
          if clip > 0:
              torch.nn.utils.clip_grad_norm(self.fp32_param_groups, clip)
  
      def _copy_params_fp32_to_fp16(self):
          for fp16_group, fp32_group in zip(self.fp16_param_groups, self.fp32_param_groups):
              for fp16_param, fp32_param in zip(fp16_group, 
                  _unflatten_dense_tensors(fp32_group, fp16_group)):
                  fp16_param.data.copy_(fp32_param.data)
  
      def state_dict(self):
          """
          Returns a dict containing the current state of this FP16_Optimizer instance.
          This dict contains attributes of FP16_Optimizer, as well as the state_dict
          of the contained Pytorch optimizer.
  
          Untested.
          """
          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['first_closure_call_this_step'] = self.first_closure_call_this_step
          state_dict['optimizer_state_dict'] = self.optimizer.state_dict()
          return state_dict
  
      def load_state_dict(self, state_dict):
          """
          Loads a state_dict created by an earlier call to state_dict. 
  
          Untested.
          """
          self.loss_scaler = state_dict['loss_scaler']
          self.dynamic_loss_scale = state_dict['dynamic_loss_scale']
          self.overflow = state_dict['overflow']
          self.first_closure_call_this_step = state_dict['first_closure_call_this_step']
          self.optimizer.load_state_dict(state_dict['optimizer_state_dict'])
  
      def step(self, closure=None): # could add clip option.
          """
          If no closure is supplied, step should be called after fp16_optimizer_obj.backward(loss).
          step updates the fp32 master copy of parameters using the optimizer supplied to
          FP16_Optimizer's constructor, then copies the updated fp32 params into the fp16 params
          originally referenced by Fp16_Optimizer's constructor, so the user may immediately run
          another forward pass using their model.
  
          If a closure is supplied, step may be called without a prior call to self.backward(loss).
          However, the user should take care that any loss.backward() call within the closure
          has been replaced by fp16_optimizer_obj.backward(loss).
  
          Args:
             closure (optional):  Closure that will be supplied to the underlying optimizer originally passed to FP16_Optimizer's constructor.  closure should call zero_grad on the FP16_Optimizer object, compute the loss, call .backward(loss), and return the loss.
  
          Closure example::
  
              # optimizer is assumed to be an FP16_Optimizer object, previously constructed from an 
              # existing pytorch optimizer.
              for input, target in dataset:
                  def closure():
                      optimizer.zero_grad()
                      output = model(input)
                      loss = loss_fn(output, target)
                      optimizer.backward(loss)
                      return loss
                  optimizer.step(closure)
  
          .. note::
              The only changes that need to be made compared to 
              `ordinary optimizer closures`_ are that "optimizer" itself should be an instance of 
              FP16_Optimizer, and that the call to loss.backward should be replaced by 
              optimizer.backward(loss). 
  
          .. warning::
              Currently, calling step with a closure is not compatible with dynamic loss scaling.
  
          .. _`ordinary optimizer closures`:
              http://pytorch.org/docs/master/optim.html#optimizer-step-closure
          """
          if closure is not None and isinstance(self.loss_scaler, DynamicLossScaler):
              raise TypeError("Using step with a closure is currently not "
                              "compatible with dynamic loss scaling.")
  
          scale = self.loss_scaler.loss_scale
          self._update_scale(self.overflow)
  
          if self.overflow:
              print("OVERFLOW! Skipping step. Attempted loss scale: {}".format(scale))
              return
          
          if closure is not None:
              self._step_with_closure(closure)
          else:
              self.optimizer.step()
  
          self._copy_params_fp32_to_fp16()
  
          return
  
      def _step_with_closure(self, closure):
          def wrapped_closure():
              if self.first_closure_call_this_step:
                  """
                  We expect that the fp16 params are initially fresh on entering self.step(),
                  so _copy_params_fp32_to_fp16() is unnecessary the first time wrapped_closure()
                  is called within self.optimizer.step().
                  """
                  self.first_closure_call_this_step = False
              else:
                  """ 
                  If self.optimizer.step() internally calls wrapped_closure more than once,
                  it may update the fp32 params after each call.  However, self.optimizer 
                  doesn't know about the fp16 params at all.  If the fp32 params get updated,
                  we can't rely on self.optimizer to refresh the fp16 params.  We need
                  to handle that manually:
                  """
                  self._copy_params_fp32_to_fp16()
              
              """
              Our API expects the user to give us ownership of the backward() call by
              replacing all calls to loss.backward() with optimizer.backward(loss).
              This requirement holds whether or not the call to backward() is made within
              a closure.
              If the user is properly calling optimizer.backward(loss) within "closure," 
              calling closure() here will give the fp32 master params fresh gradients
              for the optimizer to play with, 
              so all wrapped_closure needs to do is call closure() and return the loss.
              """
              temp_loss = closure() 
              return temp_loss
  
          self.optimizer.step(wrapped_closure)
  
          self.first_closure_call_this_step = True
  
      def backward(self, loss, update_fp32_grads=True):
          """ 
          fp16_optimizer_obj.backward performs the following conceptual operations:
  
          fp32_loss = loss.float() (see first Note below)
  
          scaled_loss = fp32_loss*loss_scale
  
          scaled_loss.backward(), which accumulates scaled gradients into the .grad attributes of the
          fp16 model's leaves.
  
          fp16 grads are then copied to the stored fp32 params' .grad attributes (see second Note).
  
          Finally, fp32 grads are divided by loss_scale.
  
          In this way, after fp16_optimizer_obj.backward, the fp32 parameters have fresh gradients,
          and fp16_optimizer_obj.step may be called.
  
          .. note::
              Converting the loss to fp32 before applying the loss scale provides some
              additional safety against overflow if the user has supplied an fp16 value.  
              However, for maximum overflow safety, the user should
              compute the loss criterion (MSE, cross entropy, etc) in fp32 before supplying it to 
              fp16_optimizer_obj.backward.
  
          .. note::
              The gradients found in an fp16 model's leaves after a call to 
              fp16_optimizer_obj.backward should not be regarded as valid in general, 
              because it's possible 
              they have been scaled (and in the case of dynamic loss scaling, 
              the scale factor may silently change over time).  
              If the user wants to inspect gradients after a call to fp16_optimizer_obj.backward,  
              he/she should query the .grad attribute of FP16_Optimizer's stored fp32 parameters.
  
          Args:
              loss:  The loss output by the user's model.  loss may be either float or half (but see first Note above).
              update_fp32_grads (bool, optional, default=True):  Option to copy fp16 grads to fp32 grads on this call.  By setting this to False, the user can delay this copy, which is useful to eliminate redundant fp16->fp32 grad copies if fp16_optimizer_obj.backward is being called on multiple losses in one iteration.  If set to False, the user becomes responsible for calling fp16_optimizer_obj.update_fp32_grads before calling fp16_optimizer_obj.step.
  
          Example::
  
              # Ordinary operation:
              optimizer.backward(loss)
  
              # Naive operation with multiple losses (technically valid, but less efficient):
              # fp32 grads will be correct after the second call,  but 
              # the first call incurs an unnecessary fp16->fp32 grad copy.
              optimizer.backward(loss1)
              optimizer.backward(loss2)
  
              # More efficient way to handle multiple losses:
              # The fp16->fp32 grad copy is delayed until fp16 grads from all 
              # losses have been accumulated.
              optimizer.backward(loss1, update_fp32_grads=False)
              optimizer.backward(loss2, update_fp32_grads=False)
              optimizer.update_fp32_grads()
          """ 
          self.loss_scaler.backward(loss.float())
          if update_fp32_grads:
              self.update_fp32_grads()
  
      def update_fp32_grads(self):
          """
          Copy the .grad attribute from stored references to fp16 parameters to 
          the .grad attribute of the master fp32 parameters that are directly 
          updated by the optimizer.  :attr:`update_fp32_grads` only needs to be called if
          fp16_optimizer_obj.backward was called with update_fp32_grads=False.
          """
          if self.dynamic_loss_scale:
              self._check_overflow()
              if self.overflow: return
          self._copy_grads_fp16_to_fp32()
          self._downscale_fp32()
  
      @property
      def loss_scale(self):
          return self.loss_scaler.loss_scale
  
apis: torch._utils._unflatten_dense_tensors torch._utils._flatten_dense_tensors torch.autograd.Variable torch.nn.utils.clip_grad_norm