



'''simple docstring'''





from math import factorial






class __A     :



 '''simple docstring'''







 def __init__(self					,  A					,  A			)       ->	str:


      """simple docstring"""



      _a           =    real
      if isinstance(A					,  A			):
           _a           =    [1] * rank
      else:
           _a           =    rank



 def __repr__(self			)       ->	List[Any]:


      """simple docstring"""



      return (
          f'''{self.real}+'''
          f'''{'+'.join(str(A			)+'E'+str(n+1			)for n,dual in enumerate(self.duals			)			)}'''
      )



 def    a__    (self			)       ->	List[Any]:


      """simple docstring"""



      _a           =    self.duals.copy()
      while cur[-1] == 0:
           cur.pop(-1			)
      return Dual(self.real					,  A			)



 def __add__(self					,  A			)       ->	int:


      """simple docstring"""



      if not isinstance(A					,  A			):
           return Dual(self.real + other					,  self.duals			)
      _a           =    self.duals.copy()
      _a           =    other.duals.copy()
      if len(A			) > len(A			):
           o_dual.extend([1] * (len(A			) - len(A			))			)
      elif len(A			) < len(A			):
           s_dual.extend([1] * (len(A			) - len(A			))			)
      _a           =    []
      for i in range(len(A			)			):
           new_duals.append(s_dual[i] + o_dual[i]			)
      return Dual(self.real + other.real					,  A			)

 __lowerCamelCase       :			Optional[Any]		=			__add__



 def __sub__(self					,  A			)       ->	Optional[Any]:


      """simple docstring"""



      return self + other * -1



 def __mul__(self					,  A			)       ->	Union[str, Any]:


      """simple docstring"""



      if not isinstance(A					,  A			):
           _a           =    []
           for i in self.duals:
                new_duals.append(i * other			)
           return Dual(self.real * other					,  A			)
      _a           =    [0] * (len(self.duals			) + len(other.duals			) + 1)
      for i, item in enumerate(self.duals			):
           for j, jtem in enumerate(other.duals			):
                new_duals[i + j + 1] += item * jtem
      for k in range(len(self.duals			)			):
           new_duals[k] += self.duals[k] * other.real
      for index in range(len(other.duals			)			):
           new_duals[index] += other.duals[index] * self.real
      return Dual(self.real * other.real					,  A			)

 __lowerCamelCase       :			Optional[Any]		=			__mul__



 def __truediv__(self					,  A			)       ->	Optional[Any]:


      """simple docstring"""



      if not isinstance(A					,  A			):
           _a           =    []
           for i in self.duals:
                new_duals.append(i / other			)
           return Dual(self.real / other					,  A			)
      raise ValueError



 def __floordiv__(self					,  A			)       ->	str:


      """simple docstring"""



      if not isinstance(A					,  A			):
           _a           =    []
           for i in self.duals:
                new_duals.append(i // other			)
           return Dual(self.real // other					,  A			)
      raise ValueError



 def __pow__(self					,  A			)       ->	Optional[Any]:


      """simple docstring"""



      if n < 0 or isinstance(A					,  A			):
           raise ValueError('''power must be a positive integer'''			)
      if n == 0:
           return 1
      if n == 1:
           return self
      _a           =    self
      for _ in range(n - 1			):
           x *= self
      return x





def lowerCAmelCase    (__A    ,      __A    ,      __A):



     """simple docstring"""



     if not callable(__A):
          raise ValueError('''differentiate() requires a function as input for func''')
     if not isinstance(__A    ,      (float, int)):
          raise ValueError('''differentiate() requires a float as input for position''')
     if not isinstance(__A    ,      __A):
          raise ValueError('''differentiate() requires an int as input for order''')
     _a           =    Dual(__A    ,      1)
     _a           =    func(__A)
     if order == 0:
          return result.real
     return result.duals[order - 1] * factorial(__A)


if __name__ == "__main__":
  import doctest

  doctest.testmod()




  def lowerCAmelCase    (__A):



       """simple docstring"""



       return y**2 * y**4
  print(differentiate(f, 9, 2))








'''simple docstring'''





import inspect
import unittest

import torch
import torch.nn as nn

from accelerate.hooks import (
    AlignDevicesHook,
    ModelHook,
    SequentialHook,
    add_hook_to_module,
    attach_align_device_hook,
    remove_hook_from_module,
    remove_hook_from_submodules,
)
from accelerate.test_utils import require_multi_gpu






class __A     (    nn.Module		):



 '''simple docstring'''







 def __init__(self			)       ->	Dict:


      """simple docstring"""



      super().__init__()
      _a           =    nn.Linear(3					,  4			)
      _a           =    nn.BatchNormad(4			)
      _a           =    nn.Linear(4					,  5			)



 def    a__    (self					,  A			)       ->	Dict:


      """simple docstring"""



      return self.lineara(self.batchnorm(self.lineara(A			)			)			)






class __A     (    A		):



 '''simple docstring'''







 def    a__    (self					,  A					,  *A					,  **A			)       ->	Optional[Any]:


      """simple docstring"""



      return (args[0] + 1,) + args[1:], kwargs






class __A     (    A		):



 '''simple docstring'''







 def    a__    (self					,  A					,  A			)       ->	int:


      """simple docstring"""



      return output + 1






class __A     (    unittest.TestCase		):



 '''simple docstring'''







 def    a__    (self			)       ->	Union[str, Any]:


      """simple docstring"""



      _a           =    ModelForTest()
      _a           =    ModelHook()

      add_hook_to_module(A					,  A			)
      self.assertEqual(test_model._hf_hook					,  A			)
      self.assertTrue(hasattr(A					,  '''_old_forward'''			)			)

      # Check adding the hook did not change the name or the signature
      self.assertEqual(test_model.forward.__name__					,  '''forward'''			)
      self.assertListEqual(list(inspect.signature(test_model.forward			).parameters			)					,  ['''x''']			)

      remove_hook_from_module(A			)
      self.assertFalse(hasattr(A					,  '''_hf_hook'''			)			)
      self.assertFalse(hasattr(A					,  '''_old_forward'''			)			)



 def    a__    (self			)       ->	Any:


      """simple docstring"""



      _a           =    ModelForTest()
      _a           =    ModelHook()

      add_hook_to_module(A					,  A			)
      add_hook_to_module(A					,  A					,  append=A			)

      self.assertEqual(isinstance(test_model._hf_hook					,  A			)					,  A			)
      self.assertEqual(len(test_model._hf_hook.hooks			)					,  2			)
      self.assertTrue(hasattr(A					,  '''_old_forward'''			)			)

      # Check adding the hook did not change the name or the signature
      self.assertEqual(test_model.forward.__name__					,  '''forward'''			)
      self.assertListEqual(list(inspect.signature(test_model.forward			).parameters			)					,  ['''x''']			)

      remove_hook_from_module(A			)
      self.assertFalse(hasattr(A					,  '''_hf_hook'''			)			)
      self.assertFalse(hasattr(A					,  '''_old_forward'''			)			)



 def    a__    (self			)       ->	Union[str, Any]:


      """simple docstring"""



      _a           =    ModelForTest()
      _a           =    torch.randn(2					,  3			)
      _a           =    test_model(x + 1			)
      _a           =    test_model(x + 2			)

      _a           =    PreForwardHook()
      add_hook_to_module(A					,  A			)
      _a           =    test_model(A			)
      self.assertTrue(torch.allclose(A					,  A					,  atol=1E-5			)			)

      # Attaching a hook to a model when it already has one replaces, does not chain
      _a           =    PreForwardHook()
      add_hook_to_module(A					,  A			)
      _a           =    test_model(A			)
      self.assertTrue(torch.allclose(A					,  A					,  atol=1E-5			)			)

      # You need to use the sequential hook to chain two or more hooks
      _a           =    SequentialHook(PreForwardHook()					,  PreForwardHook()			)
      add_hook_to_module(A					,  A			)

      _a           =    test_model(A			)
      assert torch.allclose(A					,  A					,  atol=1E-5			)



 def    a__    (self			)       ->	str:


      """simple docstring"""



      _a           =    ModelForTest()
      _a           =    torch.randn(2					,  3			)
      _a           =    test_model(A			)

      _a           =    PostForwardHook()
      add_hook_to_module(A					,  A			)
      _a           =    test_model(A			)
      self.assertTrue(torch.allclose(A					,  output + 1					,  atol=1E-5			)			)

      # Attaching a hook to a model when it already has one replaces, does not chain
      _a           =    PostForwardHook()
      add_hook_to_module(A					,  A			)
      _a           =    test_model(A			)
      self.assertTrue(torch.allclose(A					,  output + 1					,  atol=1E-5			)			)

      # You need to use the sequential hook to chain two or more hooks
      _a           =    SequentialHook(PostForwardHook()					,  PostForwardHook()			)
      add_hook_to_module(A					,  A			)

      _a           =    test_model(A			)
      assert torch.allclose(A					,  output + 2					,  atol=1E-5			)



 def    a__    (self			)       ->	List[str]:


      """simple docstring"""



      _a           =    ModelForTest()
      _a           =    torch.randn(2					,  3			)
      _a           =    test_model(A			)

      _a           =    PostForwardHook()
      add_hook_to_module(A					,  A			)
      _a           =    test_model(A			)
      self.assertTrue(torch.allclose(A					,  output + 1			)			)
      self.assertTrue(outputa.requires_grad			)

      _a           =    True
      _a           =    test_model(A			)
      self.assertFalse(outputa.requires_grad			)



 @require_multi_gpu
 def    a__    (self			)       ->	List[Any]:


      """simple docstring"""



      _a           =    ModelForTest()
      # Everything is on CPU
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # This will move each submodule on different devices
      add_hook_to_module(model.lineara					,  AlignDevicesHook(execution_device=0			)			)
      add_hook_to_module(model.batchnorm					,  AlignDevicesHook(execution_device=0			)			)
      add_hook_to_module(model.lineara					,  AlignDevicesHook(execution_device=1			)			)

      self.assertEqual(model.lineara.weight.device					,  torch.device(0			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device(0			)			)
      self.assertEqual(model.batchnorm.running_mean.device					,  torch.device(0			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device(1			)			)

      # We can still make a forward pass. The input does not need to be on any particular device
      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  torch.device(1			)			)

      # We can add a general hook to put back output on same device as input.
      add_hook_to_module(A					,  AlignDevicesHook(io_same_device=A			)			)
      _a           =    torch.randn(2					,  3			).to(0			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  torch.device(0			)			)



 def    a__    (self			)       ->	List[str]:


      """simple docstring"""



      _a           =    ModelForTest()

      # Everything is on CPU
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # This will move each submodule on different devices
      _a           =    {'''execution_device''': 0 if torch.cuda.is_available() else '''cpu''', '''offload''': True}

      add_hook_to_module(model.lineara					,  AlignDevicesHook(**A			)			)
      add_hook_to_module(model.batchnorm					,  AlignDevicesHook(**A			)			)
      add_hook_to_module(model.lineara					,  AlignDevicesHook(**A			)			)

      # Parameters have been offloaded, so on the meta device
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      # Buffers are not included in the offload by default, so are on the execution device
      _a           =    torch.device(hook_kwargs['''execution_device''']			)
      self.assertEqual(model.batchnorm.running_mean.device					,  A			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_module(model.lineara			)
      remove_hook_from_module(model.batchnorm			)
      remove_hook_from_module(model.lineara			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # Now test with buffers included in the offload
      _a           =    {
          '''execution_device''': 0 if torch.cuda.is_available() else '''cpu''',
          '''offload''': True,
          '''offload_buffers''': True,
      }

      add_hook_to_module(model.lineara					,  AlignDevicesHook(**A			)			)
      add_hook_to_module(model.batchnorm					,  AlignDevicesHook(**A			)			)
      add_hook_to_module(model.lineara					,  AlignDevicesHook(**A			)			)

      # Parameters have been offloaded, so on the meta device, buffers included
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.running_mean.device					,  torch.device('''meta'''			)			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_module(model.lineara			)
      remove_hook_from_module(model.batchnorm			)
      remove_hook_from_module(model.lineara			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)



 def    a__    (self			)       ->	Optional[int]:


      """simple docstring"""



      _a           =    ModelForTest()

      # Everything is on CPU
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # This will move each submodule on different devices
      _a           =    0 if torch.cuda.is_available() else '''cpu'''
      attach_align_device_hook(A					,  execution_device=A					,  offload=A			)

      # Parameters have been offloaded, so on the meta device
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      # Buffers are not included in the offload by default, so are on the execution device
      _a           =    torch.device(A			)
      self.assertEqual(model.batchnorm.running_mean.device					,  A			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_submodules(A			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # Now test with buffers included in the offload
      attach_align_device_hook(A					,  execution_device=A					,  offload=A					,  offload_buffers=A			)

      # Parameters have been offloaded, so on the meta device, buffers included
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.running_mean.device					,  torch.device('''meta'''			)			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_submodules(A			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)



 def    a__    (self			)       ->	Any:


      """simple docstring"""



      _a           =    ModelForTest()

      # Everything is on CPU
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # This will move each submodule on different devices
      _a           =    0 if torch.cuda.is_available() else '''cpu'''
      attach_align_device_hook(
          A					,  execution_device=A					,  offload=A					,  weights_map=model.state_dict()			)

      # Parameters have been offloaded, so on the meta device
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      # Buffers are not included in the offload by default, so are on the execution device
      _a           =    torch.device(A			)
      self.assertEqual(model.batchnorm.running_mean.device					,  A			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_submodules(A			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)

      # Now test with buffers included in the offload
      attach_align_device_hook(
          A					,  execution_device=A					,  offload=A					,  weights_map=model.state_dict()					,  offload_buffers=A					,  )

      # Parameters have been offloaded, so on the meta device, buffers included
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''meta'''			)			)
      self.assertEqual(model.batchnorm.running_mean.device					,  torch.device('''meta'''			)			)

      _a           =    torch.randn(2					,  3			)
      _a           =    model(A			)
      self.assertEqual(output.device					,  A			)

      # Removing hooks loads back the weights in the model.
      remove_hook_from_submodules(A			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.batchnorm.weight.device					,  torch.device('''cpu'''			)			)
      self.assertEqual(model.lineara.weight.device					,  torch.device('''cpu'''			)			)



