




from __future__ import annotations

from collections.abc import MutableSequence



class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					None:




				"""simple docstring"""



				if len(SCREAMING_SNAKE_CASE      ) != degree + 1:
							raise ValueError(
							    'The number of coefficients should be equal to the degree + 1.'      )

				SCREAMING_SNAKE_CASE_								=						list(SCREAMING_SNAKE_CASE      )
				SCREAMING_SNAKE_CASE_								=						degree





	def __add__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				if self.degree > polynomial_a.degree:
							SCREAMING_SNAKE_CASE_								=						self.coefficients[:]
							for i in range(polynomial_a.degree + 1      ):
										coefficients[i] += polynomial_a.coefficients[i]
							return Polynomial(self.degree      ,     SCREAMING_SNAKE_CASE      )
				else:
							SCREAMING_SNAKE_CASE_								=						polynomial_a.coefficients[:]
							for i in range(self.degree + 1      ):
										coefficients[i] += self.coefficients[i]
							return Polynomial(polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def __sub__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				return self + polynomial_a * Polynomial(0      ,     [-1]      )





	def __neg__(							self      )  ->					Polynomial:




				"""simple docstring"""



				return Polynomial(self.degree      ,     [-c for c in self.coefficients]      )





	def __mul__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + polynomial_a.degree + 1)
				for i in range(self.degree + 1      ):
							for j in range(polynomial_a.degree + 1      ):
										coefficients[i + j] += (
										    self.coefficients[i] * polynomial_a.coefficients[j]
										)

				return Polynomial(self.degree + polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					int | float:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						0
				for i in range(self.degree + 1      ):
							result += self.coefficients[i] * (substitution**i)
				return result





	def __str__(							self      )  ->					str:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						''
				for i in range(self.degree      ,     -1      ,     -1      ):
							if self.coefficients[i] == 0:
										continue
							elif self.coefficients[i] > 0:
										if polynomial:
													polynomial += " + "
							else:
										polynomial += " - "

							if i == 0:
										polynomial += str(abs(self.coefficients[i]      )      )
							elif i == 1:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x"
							else:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x^" + str(SCREAMING_SNAKE_CASE      )

				return polynomial





	def __repr__(							self      )  ->					str:




				"""simple docstring"""



				return self.__str__()





	def 						A_(							self      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * self.degree
				for i in range(self.degree      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i + 1] * (i + 1)
				return Polynomial(self.degree - 1      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE = 0      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + 2)
				SCREAMING_SNAKE_CASE_								=						constant
				for i in range(self.degree + 1      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i] / (i + 1)
				return Polynomial(self.degree + 1      ,     SCREAMING_SNAKE_CASE      )





	def __eq__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				if not isinstance(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ):
							return False

				if self.degree != polynomial_a.degree:
							return False

				for i in range(self.degree + 1      ):
							if self.coefficients[i] != polynomial_a.coefficients[i]:
										return False

				return True





	def __ne__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				return not self.__eq__(SCREAMING_SNAKE_CASE      )






from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
				import torch

if is_torch_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm


SCREAMING_SNAKE_CASE__     :     int		    =       logging.get_logger(__name__)



@dataclass
class       a_       (     SCREAMING_SNAKE_CASE__     ):
	A    							= [
	    '''no_inference''',
	    '''no_cuda''',
	    '''no_tpu''',
	    '''no_speed''',
	    '''no_memory''',
	    '''no_env_print''',
	    '''no_multi_process''',
	]





	def __init__(							self      ,     **SCREAMING_SNAKE_CASE      )  ->					Dict:




				"""simple docstring"""



				for deprecated_arg in self.deprecated_args:
							if deprecated_arg in kwargs:
										SCREAMING_SNAKE_CASE_								=						deprecated_arg[3:]
										setattr(self      ,     SCREAMING_SNAKE_CASE      ,     not kwargs.pop(SCREAMING_SNAKE_CASE      )      )
										logger.warning(
										    f'{deprecated_arg} is depreciated. Please use --no_{positive_arg} or'
										    f' {positive_arg}={kwargs[positive_arg]}'      )

				SCREAMING_SNAKE_CASE_								=						kwargs.pop('torchscript'      ,     self.torchscript      )
				SCREAMING_SNAKE_CASE_								=						kwargs.pop('torch_xla_tpu_print_metrics'      ,     self.torch_xla_tpu_print_metrics      )
				SCREAMING_SNAKE_CASE_								=						kwargs.pop('fp16_opt_level'      ,     self.fpaa_opt_level      )
				super().__init__(**SCREAMING_SNAKE_CASE      )

	A    							= field(default=SCREAMING_SNAKE_CASE__  ,    metadata={'''help''': '''Trace the models using torchscript'''}     )
	A    							= field(default=SCREAMING_SNAKE_CASE__  ,    metadata={'''help''': '''Print Xla/PyTorch tpu metrics'''}     )
	A    							= field(
	    default='''O1'''  ,    metadata={
	        '''help''': (
	            '''For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\']. '''
	            '''See details at https://nvidia.github.io/apex/amp.html'''
	        )
	    }  ,    )





	@cached_property
	def 						A_(							self      )  ->					Tuple["torch.device", int]:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				logger.info('PyTorch: setting up devices'      )
				if not self.cuda:
							SCREAMING_SNAKE_CASE_								=						torch.device('cpu'      )
							SCREAMING_SNAKE_CASE_								=						0
				elif is_torch_tpu_available():
							SCREAMING_SNAKE_CASE_								=						xm.xla_device()
							SCREAMING_SNAKE_CASE_								=						0
				else:
							SCREAMING_SNAKE_CASE_								=						torch.device('cuda' if torch.cuda.is_available() else 'cpu'      )
							SCREAMING_SNAKE_CASE_								=						torch.cuda.device_count()
				return device, n_gpu





	@property
	def 						A_(							self      )  ->					Union[str, Any]:




				"""simple docstring"""



				return is_torch_tpu_available() and self.tpu





	@property
	def 						A_(							self      )  ->					int:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				# TODO(PVP): currently only single GPU is supported
				return torch.cuda.current_device()





	@property
	def 						A_(							self      )  ->					"torch.device":




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				return self._setup_devices[0]





	@property
	def 						A_(							self      )  ->					Optional[Any]:




				"""simple docstring"""



				requires_backends(self      ,     ['torch']      )
				return self._setup_devices[1]





	@property
	def 						A_(							self      )  ->					Dict:




				"""simple docstring"""



				return self.n_gpu > 0
