





'''simple docstring'''

import gc
import importlib.metadata
import tempfile
import unittest

from packaging import version

from transformers import (
    AutoModel,
    AutoModelForCausalLM,
    AutoModelForSeqaSeqLM,
    AutoModelForSequenceClassification,
    AutoTokenizer,
    BitsAndBytesConfig,
    pipeline,
)
from transformers.testing_utils import (
    is_torch_available,
    require_accelerate,
    require_bitsandbytes,
    require_torch,
    require_torch_gpu,
    require_torch_multi_gpu,
    slow,
)

def     __magic_name__							(				__UpperCAmelCase   )    ->       Union[str, Any]:

   '''simple docstring'''







   if model.config.model_type == "gpt2":
      return model.transformer.h[0].mlp.c_fc
   return model.transformer.h[0].mlp.dense_ah_to_h


if is_torch_available():
    import torch
    import torch.nn as nn







    class __a			( nn.Module      ):





       def __init__(       self					:      int					,lowerCamelCase					:      nn.Module					,lowerCamelCase					:      int     ):

          '''simple docstring'''

          super().__init__()
          __SCREAMING_SNAKE_CASE   				=							module
          __SCREAMING_SNAKE_CASE   				=							nn.Sequential(
              nn.Linear(module.in_features					,lowerCamelCase					,bias=lowerCamelCase     )					,nn.Linear(lowerCamelCase					,module.out_features					,bias=lowerCamelCase     )					,)
          __SCREAMING_SNAKE_CASE   				=							(2.0 / (5 * min(module.in_features					,module.out_features     ))) ** 0.5
          nn.init.normal_(self.adapter[0].weight					,std=lowerCamelCase     )
          nn.init.zeros_(self.adapter[1].weight     )
          self.adapter.to(module.weight.device     )





       def   UpperCAmelCase__  (       self					:      Optional[int]					,lowerCamelCase					:      int					,*lowerCamelCase					:      List[str]					,**lowerCamelCase					:      List[Any]     ):

          '''simple docstring'''

          return self.module(lowerCamelCase					,*lowerCamelCase					,**lowerCamelCase     ) + self.adapter(lowerCamelCase     )







@require_bitsandbytes
@require_accelerate
@require_torch
@require_torch_gpu
@slow
class __a			( unittest.TestCase      ):
   # We keep the constants inside the init function and model loading inside setUp function

   # We need to test on relatively large models (aka >1b parameters otherwise the quantiztion may not work as expected)
   # Therefore here we use only bloom-1b3 to test our module
   __UpperCamelCase :			Dict						   =						'bigscience/bloom-1b7'

   # Constant values
   __UpperCamelCase :			Union[str, Any]						   =						2.109_659_552_692_574

   __UpperCamelCase :			List[str]						   =						'Hello my name is'
   __UpperCamelCase :			Union[str, Any]						   =						set()
   EXPECTED_OUTPUTS.add('Hello my name is John and I am a professional photographer. I'      )
   EXPECTED_OUTPUTS.add('Hello my name is John.\nI am a friend of your father.\n'      )
   EXPECTED_OUTPUTS.add('Hello my name is John Doe, I am a student at the University'      )
   __UpperCamelCase :			Any						   =						10





   def   UpperCAmelCase__  (       self					:      Optional[Any]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							AutoTokenizer.from_pretrained(self.model_name     )







class __a			( _snake_case      ):





   def   UpperCAmelCase__  (       self					:      Union[str, Any]     ):

      '''simple docstring'''

      super().setUp()

      # Models and tokenizer
      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(
          self.model_name					,torch_dtype=torch.floataa					,device_map="""auto"""     )
      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )





   def   UpperCAmelCase__  (       self					:      Union[str, Any]     ):

      '''simple docstring'''

      del self.model_fpaa
      del self.model_abit

      gc.collect()
      torch.cuda.empty_cache()





   def   UpperCAmelCase__  (       self					:      Tuple     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.model_abit.config

      self.assertTrue(hasattr(lowerCamelCase					,"""quantization_config"""     )     )

      __SCREAMING_SNAKE_CASE   				=							config.to_dict()
      __SCREAMING_SNAKE_CASE   				=							config.to_diff_dict()

      __SCREAMING_SNAKE_CASE   				=							config.to_json_string()





   def   UpperCAmelCase__  (       self					:      Optional[Any]     ):

      '''simple docstring'''

      from bitsandbytes.nn import Paramsabit

      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.get_memory_footprint()
      __SCREAMING_SNAKE_CASE   				=							self.model_abit.get_memory_footprint()

      self.assertAlmostEqual(mem_fpaa / mem_abit					,self.EXPECTED_RELATIVE_DIFFERENCE     )
      __SCREAMING_SNAKE_CASE   				=							get_some_linear_layer(self.model_abit     )
      self.assertTrue(linear.weight.__class__ == Paramsabit     )





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      from transformers import TaPreTrainedModel

      self.model_fpaa.get_memory_footprint()
      self.model_abit.get_memory_footprint()

      for name, module in self.model_abit.named_modules():
         if isinstance(lowerCamelCase					,torch.nn.Linear     ):
            if name not in ["lm_head"] + TaPreTrainedModel._keep_in_fpaa_modules:
               # 4-bit parameters are packed in uint8 variables
               self.assertTrue(module.weight.dtype == torch.uinta     )





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     )
      __SCREAMING_SNAKE_CASE   				=							self.model_abit.generate(input_ids=encoded_input["""input_ids"""].to(0     )					,max_new_tokens=10     )

      self.assertIn(self.tokenizer.decode(output_sequences[0]					,skip_special_tokens=lowerCamelCase     )					,self.EXPECTED_OUTPUTS     )





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							BitsAndBytesConfig()
      __SCREAMING_SNAKE_CASE   				=							True

      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(
          self.model_name					,quantization_config=lowerCamelCase					,device_map="""auto"""     )

      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     )
      __SCREAMING_SNAKE_CASE   				=							model_abit_from_config.generate(
          input_ids=encoded_input["""input_ids"""].to(0     )					,max_new_tokens=10     )

      self.assertIn(self.tokenizer.decode(output_sequences[0]					,skip_special_tokens=lowerCamelCase     )					,self.EXPECTED_OUTPUTS     )





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      with self.assertRaises(lowerCamelCase     ), tempfile.TemporaryDirectory() as tmpdirname:
         self.model_abit.save_pretrained(lowerCamelCase     )





   def   UpperCAmelCase__  (       self					:      Optional[Any]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							BitsAndBytesConfig()

      with self.assertRaises(lowerCamelCase     ):
         __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(
             self.model_name					,quantization_config=lowerCamelCase					,load_in_abit=lowerCamelCase					,device_map="""auto"""					,bnb_abit_quant_type="""nf4"""					,)





   def   UpperCAmelCase__  (       self					:      List[Any]     ):

      '''simple docstring'''

      with self.assertRaises(lowerCamelCase     ):
         # Tries with `str`
         self.model_abit.to("""cpu"""     )

      with self.assertRaises(lowerCamelCase     ):
         # Tries with a `dtype``
         self.model_abit.to(torch.floataa     )

      with self.assertRaises(lowerCamelCase     ):
         # Tries with a `device`
         self.model_abit.to(torch.device("""cuda:0"""     )     )

      with self.assertRaises(lowerCamelCase     ):
         # Tries with a `device`
         self.model_abit.float()

      with self.assertRaises(lowerCamelCase     ):
         # Tries with a `device`
         self.model_abit.half()

      # Test if we did not break anything
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     )

      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.to(torch.floataa     )
      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.generate(input_ids=encoded_input["""input_ids"""].to(0     )					,max_new_tokens=10     )

      # Check this does not throw an error
      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.to("""cpu"""     )

      # Check this does not throw an error
      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.half()

      # Check this does not throw an error
      __SCREAMING_SNAKE_CASE   				=							self.model_fpaa.float()





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							AutoModelForSeqaSeqLM.from_pretrained("""t5-small"""					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      self.assertTrue(model.decoder.block[0].layer[2].DenseReluDense.wo.weight.dtype == torch.floataa     )







@require_bitsandbytes
@require_accelerate
@require_torch
@require_torch_gpu
@slow
class __a			( unittest.TestCase      ):





   @classmethod
   def   UpperCAmelCase__  (       cls					:      Dict     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							"""t5-small"""
      __SCREAMING_SNAKE_CASE   				=							"""google/flan-t5-small"""  # flan-t5 uses dense-act instead of dense-relu-dense
      __SCREAMING_SNAKE_CASE   				=							AutoTokenizer.from_pretrained(cls.model_name     )
      __SCREAMING_SNAKE_CASE   				=							"""Translate in German: Hello, my dog is cute"""





   def   UpperCAmelCase__  (       self					:      int     ):

      '''simple docstring'''

      gc.collect()
      torch.cuda.empty_cache()





   def   UpperCAmelCase__  (       self					:      Any     ):

      '''simple docstring'''

      from transformers import TaForConditionalGeneration

      __SCREAMING_SNAKE_CASE   				=							TaForConditionalGeneration._keep_in_fpaa_modules
      __SCREAMING_SNAKE_CASE   				=							None

      # test with `t5-small`
      __SCREAMING_SNAKE_CASE   				=							TaForConditionalGeneration.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     ).to(0     )
      __SCREAMING_SNAKE_CASE   				=							model.generate(**lowerCamelCase     )

      # test with `flan-t5-small`
      __SCREAMING_SNAKE_CASE   				=							TaForConditionalGeneration.from_pretrained(
          self.dense_act_model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     ).to(0     )
      __SCREAMING_SNAKE_CASE   				=							model.generate(**lowerCamelCase     )
      __SCREAMING_SNAKE_CASE   				=							modules





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      import bitsandbytes as bnb

      from transformers import TaForConditionalGeneration

      # test with `t5-small`
      __SCREAMING_SNAKE_CASE   				=							TaForConditionalGeneration.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )

      # there was a bug with decoders - this test checks that it is fixed
      self.assertTrue(isinstance(model.decoder.block[0].layer[0].SelfAttention.q					,bnb.nn.Linearabit     )     )

      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     ).to(0     )
      __SCREAMING_SNAKE_CASE   				=							model.generate(**lowerCamelCase     )

      # test with `flan-t5-small`
      __SCREAMING_SNAKE_CASE   				=							TaForConditionalGeneration.from_pretrained(
          self.dense_act_model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     ).to(0     )
      __SCREAMING_SNAKE_CASE   				=							model.generate(**lowerCamelCase     )







class __a			( _snake_case      ):





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      super().setUp()
      # model_name
      __SCREAMING_SNAKE_CASE   				=							"""bigscience/bloom-560m"""
      __SCREAMING_SNAKE_CASE   				=							"""t5-small"""

      # Different types of model

      __SCREAMING_SNAKE_CASE   				=							AutoModel.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      # Sequence classification model
      __SCREAMING_SNAKE_CASE   				=							AutoModelForSequenceClassification.from_pretrained(
          self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      # CausalLM model
      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )
      # Seq2seq model
      __SCREAMING_SNAKE_CASE   				=							AutoModelForSeqaSeqLM.from_pretrained(
          self.seq_to_seq_name					,load_in_abit=lowerCamelCase					,device_map="""auto"""     )





   def   UpperCAmelCase__  (       self					:      Optional[Any]     ):

      '''simple docstring'''

      del self.base_model
      del self.sequence_model
      del self.model_abit
      del self.seq_to_seq_model

      gc.collect()
      torch.cuda.empty_cache()





   def   UpperCAmelCase__  (       self					:      str     ):

      '''simple docstring'''

      from bitsandbytes.nn import Paramsabit

      self.assertTrue(self.base_model.h[-1].mlp.dense_ah_to_h.weight.__class__ == Paramsabit     )

      # Other heads should be nn.Parameter
      self.assertTrue(self.model_abit.lm_head.weight.__class__ == torch.nn.Parameter     )
      self.assertTrue(self.sequence_model.score.weight.__class__ == torch.nn.Parameter     )
      self.assertTrue(self.seq_to_seq_model.lm_head.weight.__class__ == torch.nn.Parameter     )







class __a			( _snake_case      ):





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      super().setUp()





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      del self.pipe

      gc.collect()
      torch.cuda.empty_cache()





   def   UpperCAmelCase__  (       self					:      Tuple     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							pipeline(
          """text-generation"""					,model=self.model_name					,model_kwargs={"""device_map""": """auto""", """load_in_4bit""": True, """torch_dtype""": torch.floataa}					,max_new_tokens=self.MAX_NEW_TOKENS					,)

      # Real second forward pass
      __SCREAMING_SNAKE_CASE   				=							self.pipe(self.input_text     )
      self.assertIn(pipeline_output[0]["""generated_text"""]					,self.EXPECTED_OUTPUTS     )







@require_torch_multi_gpu
class __a			( _snake_case      ):





   def   UpperCAmelCase__  (       self					:      Dict     ):

      '''simple docstring'''

      super().setUp()





   def   UpperCAmelCase__  (       self					:      Optional[int]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(
          self.model_name					,load_in_abit=lowerCamelCase					,device_map="""balanced"""     )

      # Check correct device map
      self.assertEqual(set(model_parallel.hf_device_map.values()     )					,{0, 1}     )

      # Check that inference pass works on the model
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer(self.input_text					,return_tensors="""pt"""     )

      # Second real batch
      __SCREAMING_SNAKE_CASE   				=							model_parallel.generate(input_ids=encoded_input["""input_ids"""].to(0     )					,max_new_tokens=10     )
      self.assertIn(self.tokenizer.decode(output_parallel[0]					,skip_special_tokens=lowerCamelCase     )					,self.EXPECTED_OUTPUTS     )







class __a			( _snake_case      ):





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE   				=							"""facebook/opt-350m"""
      super().setUp()





   def   UpperCAmelCase__  (       self					:      List[str]     ):

      '''simple docstring'''

      if version.parse(importlib.metadata.version("""bitsandbytes"""     )     ) < version.parse("""0.37.0"""     ):
         return

      # Step 1: freeze all parameters
      __SCREAMING_SNAKE_CASE   				=							AutoModelForCausalLM.from_pretrained(self.model_name					,load_in_abit=lowerCamelCase     )

      self.assertEqual(set(model.hf_device_map.values()     )					,{torch.cuda.current_device()}     )

      for param in model.parameters():
         __SCREAMING_SNAKE_CASE   				=							False  # freeze the model - train adapters later
         if param.ndim == 1:
            # cast the small parameters (e.g. layernorm) to fp32 for stability
            __SCREAMING_SNAKE_CASE   				=							param.data.to(torch.floataa     )

        # Step 2: add adapters
      for _, module in model.named_modules():
         if "OPTAttention" in repr(type(lowerCamelCase     )     ):
            __SCREAMING_SNAKE_CASE   				=							LoRALayer(module.q_proj					,rank=16     )
            __SCREAMING_SNAKE_CASE   				=							LoRALayer(module.k_proj					,rank=16     )
            __SCREAMING_SNAKE_CASE   				=							LoRALayer(module.v_proj					,rank=16     )

        # Step 3: dummy batch
      __SCREAMING_SNAKE_CASE   				=							self.tokenizer("""Test batch """					,return_tensors="""pt"""     ).to(0     )

      # Step 4: Check if the gradient is not None
      with torch.cuda.amp.autocast():
         __SCREAMING_SNAKE_CASE   				=							model.forward(**lowerCamelCase     )
         out.logits.norm().backward()

      for module in model.modules():
         if isinstance(lowerCamelCase					,lowerCamelCase     ):
            self.assertTrue(module.adapter[1].weight.grad is not None     )
            self.assertTrue(module.adapter[1].weight.grad.norm().item() > 0     )
         elif isinstance(lowerCamelCase					,nn.Embedding     ):
            self.assertTrue(module.weight.grad is None     )







class __a			( _snake_case      ):
   __UpperCamelCase :			Tuple						   =						'gpt2-xl'
   __UpperCamelCase :			Dict						   =						3.3_191_854_854_152_187










"""simple docstring"""






from math import factorial



class      A__  :




	'''simple docstring'''





	def __init__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple			,     _SCREAMING_SNAKE_CASE:						Any)							->			str:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			real
				if isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    Optional[int]				=			[1] * rank
				else:
							__lowerCAmelCase :    Optional[Any]				=			rank

	def __repr__(	self:						Optional[int])							->			List[str]:

				"""simple docstring"""

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

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

				"""simple docstring"""

				__lowerCAmelCase :    List[str]				=			self.duals.copy()
				while cur[-1] == 0:
							cur.pop(-1)
				return Dual(self.real			,     _SCREAMING_SNAKE_CASE)

	def __add__(	self:						Optional[int]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Union[str, Any]:

				"""simple docstring"""

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

	SCREAMING_SNAKE_CASE        =      __add__

	def __sub__(	self:						Dict			,     _SCREAMING_SNAKE_CASE:						str)							->			Optional[Any]:

				"""simple docstring"""

				return self + other * -1

	def __mul__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Optional[int]:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    List[Any]				=			[]
							for i in self.duals:
										new_duals.append(i * other)
							return Dual(self.real * other			,     _SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    List[str]				=			[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			,     _SCREAMING_SNAKE_CASE)

	SCREAMING_SNAKE_CASE        =      __mul__

	def __truediv__(	self:						Any			,     _SCREAMING_SNAKE_CASE:						str)							->			Dict:

				"""simple docstring"""

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

	def __floordiv__(	self:						List[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			str:

				"""simple docstring"""

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







	def __pow__(	self:						Optional[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			List[Any]:

				"""simple docstring"""

				if n < 0 or isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							raise ValueError("power must be a positive integer")
				if n == 0:
							return 1
				if n == 1:
							return self
				__lowerCAmelCase :    List[Any]				=			self
				for _ in range(n - 1):
							x *= self
				return x






def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case      )		->  Any:
			if not callable(__snake_case      ):
						raise ValueError("differentiate() requires a function as input for func"      )
			if not isinstance(__snake_case   ,(float, int)      ):
						raise ValueError("differentiate() requires a float as input for position"      )
			if not isinstance(__snake_case   ,__snake_case      ):
						raise ValueError("differentiate() requires an int as input for order"      )
			__lowerCAmelCase :    Any				=			Dual(__snake_case   ,1      )
			__lowerCAmelCase :    Tuple				=			func(__snake_case      )
			if order == 0:
						return result.real
			return result.duals[order - 1] * factorial(__snake_case      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()


	def      _lowercase							(    __snake_case      )		->  Tuple:
				return y**2 * y**4





	print(differentiate(f, 9, 2))