



from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean


def A						(       __UpperCamelCase					)						->      Optional[int]:

			# A local function to see if a dot lands in the circle.
			def is_in_circle(__UpperCamelCase ,	__UpperCamelCase					) -> bool:
						A__       =    sqrt((x**2) + (y**2)					)
						# Our circle has a radius of 1, so a distance
						# greater than 1 would land outside the circle.
						return distance_from_centre <= 1

			# The proportion of guesses that landed in the circle
			A__       =    mean(
			    int(is_in_circle(uniform(-1.0 ,	1.0					) ,	uniform(-1.0 ,	1.0					)					)					)
			    for _ in range(__UpperCamelCase					)					)
			# The ratio of the area for circle to square is pi/4.
			A__       =    proportion * 4
			print(f'''The estimated value of pi is {pi_estimate}'''					)
			print(f'''The numpy value of pi is {pi}'''					)
			print(f'''The total error is {abs(pi - pi_estimate					)}'''					)


def A						(       __UpperCamelCase ,	__UpperCamelCase ,	__UpperCamelCase = 0.0 ,	__UpperCamelCase = 1.0 ,	)						->      float:
			return mean(
			    function_to_integrate(uniform(__UpperCamelCase ,	__UpperCamelCase					)					) for _ in range(__UpperCamelCase					)					) * (max_value - min_value)


def A						(       __UpperCamelCase ,	__UpperCamelCase = 0.0 ,	__UpperCamelCase = 1.0					)						->      None:

			def identity_function(__UpperCamelCase					) -> float:
						return x

			A__       =    area_under_curve_estimator(
			    __UpperCamelCase ,	__UpperCamelCase ,	__UpperCamelCase ,	__UpperCamelCase					)
			A__       =    (max_value * max_value - min_value * min_value) / 2

			print('******************'					)
			print(f'''Estimating area under y=x where x varies from {min_value} to {max_value}'''					)
			print(f'''Estimated value is {estimated_value}'''					)
			print(f'''Expected value is {expected_value}'''					)
			print(f'''Total error is {abs(estimated_value - expected_value					)}'''					)
			print('******************'					)


def A						(       __UpperCamelCase					)						->      None:

			def function_to_integrate(__UpperCamelCase					) -> float:
						return sqrt(4.0 - x * x					)

			A__       =    area_under_curve_estimator(
			    __UpperCamelCase ,	__UpperCamelCase ,	0.0 ,	2.0					)

			print('******************'					)
			print('Estimating pi using area_under_curve_estimator'					)
			print(f'''Estimated value is {estimated_value}'''					)
			print(f'''Expected value is {pi}'''					)
			print(f'''Total error is {abs(estimated_value - pi					)}'''					)
			print('******************'					)


if __name__ == "__main__":
							import doctest

							doctest.testmod()









import unittest

from transformers import is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, require_torch, slow


if is_flax_available():
							import optax
							from flax.training.common_utils import onehot

							from transformers import AutoTokenizer, FlaxMTaForConditionalGeneration
							from transformers.models.ta.modeling_flax_ta import shift_tokens_right


@require_torch
@require_sentencepiece
@require_tokenizers
@require_flax
class      __lowerCAmelCase     (		unittest.TestCase      ):
					"""simple docstring"""






					@slow
					def     _a							(     self					:       int					):






								"""simple docstring"""


								A__       =    FlaxMTaForConditionalGeneration.from_pretrained('google/mt5-small'					)
								A__       =    AutoTokenizer.from_pretrained('google/mt5-small'					)

								A__       =    tokenizer('Hello there'				,					return_tensors='np'					).input_ids
								A__       =    tokenizer('Hi I am'				,					return_tensors='np'					).input_ids

								A__       =    shift_tokens_right(_snake_case				,					model.config.pad_token_id				,					model.config.decoder_start_token_id					)

								A__       =    model(_snake_case				,					decoder_input_ids=_snake_case					).logits
								A__       =    optax.softmax_cross_entropy(_snake_case				,					onehot(_snake_case				,					logits.shape[-1]					)					).mean()

								A__       =    -(labels.shape[-1] * loss.item())

								A__       =    -84.9127
								self.assertTrue(abs(mtf_score - EXPECTED_SCORE					) < 1E-4					)




