






from math import pi, sqrt



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			float    )						->      float:





    """simple docstring"""

    if num <= 0:
        raise ValueError("""math domain error"""    )
    if num > 171.5:
        raise OverflowError("""math range error"""    )
    elif num - int(__lowercase    ) not in (0, 0.5):
        raise NotImplementedError("""num must be an integer or a half-integer"""    )
    elif num == 0.5:
        return sqrt(__lowercase    )
    else:
        return 1.0 if num == 1 else (num - 1) * gamma(num - 1    )



def 			_SCREAMING_SNAKE_CASE						( )						->      None:





    """simple docstring"""

    assert gamma(0.5    ) == sqrt(__lowercase    )
    assert gamma(1    ) == 1.0
    assert gamma(2    ) == 1.0


if __name__ == "__main__":
  from doctest import testmod

  testmod()
  __a      :       str				  =   1.0
  while num:
    __a      :       Tuple				  =   float(input("Gamma of: "))
    print(f"""gamma({num}) = {gamma(num)}""")
    print("\nEnter 0 to exit...")












from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast
from ...utils import logging


__a      :       List[Any]				  =   logging.get_logger(__name__)

__a      :       List[str]				  =   {
    "EleutherAI/gpt-neo-1.3B": "https://huggingface.co/EleutherAI/gpt-neo-1.3B/resolve/main/config.json",
    # See all GPTNeo models at https://huggingface.co/models?filter=gpt_neo
}


class       __lowercase      (	lowercase_  ):







     '''simple docstring'''
     SCREAMING_SNAKE_CASE   						=				"gpt_neo"
     SCREAMING_SNAKE_CASE   						=				["past_key_values"]
     SCREAMING_SNAKE_CASE   						=				{"num_attention_heads": "num_heads", "num_hidden_layers": "num_layers"}




     def __init__(				self       :			Optional[Any] ,	UpperCamelCase_       :			List[Any]=50_257 ,	UpperCamelCase_       :			Union[str, Any]=2_048 ,	UpperCamelCase_       :			List[str]=2_048 ,	UpperCamelCase_       :			Optional[int]=24 ,	UpperCamelCase_       :			Any=[[["global", "local"], 12]] ,	UpperCamelCase_       :			Tuple=16 ,	UpperCamelCase_       :			List[Any]=None ,	UpperCamelCase_       :			Optional[Any]=256 ,	UpperCamelCase_       :			List[str]="gelu_new" ,	UpperCamelCase_       :			str=0.0 ,	UpperCamelCase_       :			Optional[Any]=0.0 ,	UpperCamelCase_       :			str=0.0 ,	UpperCamelCase_       :			List[Any]=0.1 ,	UpperCamelCase_       :			str=1e-5 ,	UpperCamelCase_       :			Optional[Any]=0.02 ,	UpperCamelCase_       :			Union[str, Any]=True ,	UpperCamelCase_       :			Union[str, Any]=50_256 ,	UpperCamelCase_       :			Dict=50_256 ,	**UpperCamelCase_       :			Union[str, Any] ,	):


         """simple docstring"""



         __A         =	vocab_size
         __A         =	max_position_embeddings
         __A         =	hidden_size
         __A         =	num_layers
         __A         =	num_heads
         __A         =	intermediate_size
         __A         =	window_size
         __A         =	activation_function
         __A         =	resid_dropout
         __A         =	embed_dropout
         __A         =	attention_dropout
         __A         =	classifier_dropout
         __A         =	layer_norm_epsilon
         __A         =	initializer_range
         __A         =	use_cache

         __A         =	bos_token_id
         __A         =	eos_token_id

         __A         =	attention_types
         __A         =	self.expand_attention_types_params(UpperCamelCase_				)

         if len(self.attention_layers				) != self.num_layers:
             raise ValueError(
                 """Configuration for convolutional module is incorrect. """
                 """It is required that `len(config.attention_layers)` == `config.num_layers` """
                 F"but is `len(config.attention_layers) = {len(self.attention_layers				)}`, "
                 F"`config.num_layers = {self.num_layers}`. "
                 """`config.attention_layers` is prepared using `config.attention_types`. """
                 """Please verify the value of `config.attention_types` argument."""				)

         super().__init__(bos_token_id=UpperCamelCase_ ,	eos_token_id=UpperCamelCase_ ,	**UpperCamelCase_				)





     @staticmethod
     def 		lowerCAmelCase_     (				UpperCamelCase_       :			str				):


         """simple docstring"""



         __A         =	[]
         for item in attention_types:
             for _ in range(item[1]				):
                 attentions.extend(item[0]				)
         return attentions



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





    """simple docstring"""

    import torch

    __A         =	input.size()
    __A         =	len(__lowercase    )
    __A         =	shape[dimension]

    __A         =	torch.arange(0			,				__lowercase			,				__lowercase    )
    __A         =	torch.div(sizedim - size			,				__lowercase			,				rounding_mode="""floor"""    ) + 1
    __A         =	torch.arange(__lowercase    ) + low_indices[:min_length][:, None]

    __A         =	[slice(__lowercase    )] * rank
    __A         =	indices
    __A         =	input[s]

    __A         =	list(range(0			,				rank + 1    )    )
    perm.append(perm.pop(dimension + 1    )    )

    return sliced.permute(__lowercase    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Dict			,				__lowercase   :			Any    )						->      Union[str, Any]:





    """simple docstring"""

    import torch

    __A         =	torch.arange(1			,				__lowercase    )
    __A         =	torch.remainder(__lowercase			,				__lowercase    )
    __A         =	remainders == 0
    __A         =	candidates[divisor_indices]
    __A         =	torch.max(__lowercase    )
    return largest_divisor, torch.div(__lowercase			,				__lowercase			,				rounding_mode="""floor"""    )






class       __lowercase      (	lowercase_  ):







     '''simple docstring'''




     @property
     def 		lowerCAmelCase_     (				self       :			Dict				):


         """simple docstring"""



         __A         =	OrderedDict({"""input_ids""": {0: """batch""", 1: """sequence"""}}				)
         if self.use_past:
             self.fill_with_past_key_values_(UpperCamelCase_ ,	direction="""inputs"""				)
             __A         =	{0: """batch""", 1: """past_sequence + sequence"""}
         else:
             __A         =	{0: """batch""", 1: """sequence"""}

         return common_inputs




     @property
     def 		lowerCAmelCase_     (				self       :			Optional[int]				):


         """simple docstring"""



         return self._config.num_heads




     def 		lowerCAmelCase_     (				self       :			Union[str, Any] ,	UpperCamelCase_       :			PreTrainedTokenizer ,	UpperCamelCase_       :			int = -1 ,	UpperCamelCase_       :			int = -1 ,	UpperCamelCase_       :			bool = False ,	UpperCamelCase_       :			Optional[TensorType] = None ,	):


         """simple docstring"""



         __A         =	super(UpperCamelCase_ ,	self				).generate_dummy_inputs(
             UpperCamelCase_ ,	batch_size=UpperCamelCase_ ,	seq_length=UpperCamelCase_ ,	is_pair=UpperCamelCase_ ,	framework=UpperCamelCase_				)

         # We need to order the input in the way they appears in the forward()
         __A         =	OrderedDict({"""input_ids""": common_inputs["""input_ids"""]}				)

         # Need to add the past_keys
         if self.use_past:
             if not is_torch_available():
                 raise ValueError("""Cannot generate dummy past_keys inputs without PyTorch installed."""				)
             else:
                 import torch

                 __A    ,	__A         =	common_inputs["""input_ids"""].shape
                 # Not using the same length for past_key_values
                 __A         =	seqlen + 2
                 __A         =	(
                     batch,
                     self.num_attention_heads,
                     past_key_values_length,
                     self._config.hidden_size // self.num_attention_heads,
                 )
                 __A         =	[
                     (torch.zeros(UpperCamelCase_				), torch.zeros(UpperCamelCase_				)) for _ in range(self.num_layers				)
                 ]

         __A         =	common_inputs["""attention_mask"""]
         if self.use_past:
             __A         =	ordered_inputs["""attention_mask"""].dtype
             __A         =	torch.cat(
                 [ordered_inputs["""attention_mask"""], torch.ones(UpperCamelCase_ ,	UpperCamelCase_ ,	dtype=UpperCamelCase_				)] ,	dim=1				)

         return ordered_inputs





     @property
     def 		lowerCAmelCase_     (				self       :			Tuple				):


         """simple docstring"""



         return 13




