import mpmath  # for roots of unity
import numpy as np






class 		a__						:

					def __init__(    self      :       int,_A      :       Optional[int]=None,_A      :       Any=None    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    list(poly_a or [0]    )[:]
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    list(poly_b or [0]    )[:]

							# Remove leading zero coefficients
							while self.polyA[-1] == 0:
									self.polyA.pop()
							SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    len(self.polyA    )

							while self.polyB[-1] == 0:
									self.polyB.pop()
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    len(self.polyB    )

							# Add 0 to make lengths equal a power of 2
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    int(
							    2 ** np.ceil(np.loga(len(self.polyA    ) + len(self.polyB    ) - 1    )    )    )

							while len(self.polyA    ) < self.c_max_length:
									self.polyA.append(0    )
							while len(self.polyB    ) < self.c_max_length:
									self.polyB.append(0    )
							# A complex root used for the fourier transform
							SCREAMING_SNAKE_CASE_  :		List[str]				      =    complex(mpmath.root(x=1,n=self.c_max_length,k=1    )    )

							# The product
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    self.__multiply()

					def 				__UpperCamelCase   (    self      :       str,_A      :       str    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Any				      =    [[x] for x in self.polyA] if which == "A" else [[x] for x in self.polyB]
							# Corner case
							if len(_A    ) <= 1:
									return dft[0]
							#
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    self.c_max_length // 2
							while next_ncol > 0:
									SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    [[] for i in range(_A    )]
									SCREAMING_SNAKE_CASE_  :		str				      =    self.root**next_ncol

									# First half of next step
									SCREAMING_SNAKE_CASE_  :		int				      =    1
									for j in range(self.c_max_length // (next_ncol * 2)    ):
											for i in range(_A    ):
													new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]    )
											current_root *= root
									# Second half of next step
									SCREAMING_SNAKE_CASE_  :		Dict				      =    1
									for j in range(self.c_max_length // (next_ncol * 2)    ):
											for i in range(_A    ):
													new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]    )
											current_root *= root
									# Update
									SCREAMING_SNAKE_CASE_  :		Dict				      =    new_dft
									SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    next_ncol // 2
							return dft[0]

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







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		int				      =    self.__dft("A"    )
							SCREAMING_SNAKE_CASE_  :		Any				      =    self.__dft("B"    )
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    [[dft_a[i] * dft_b[i] for i in range(self.c_max_length    )]]
							del dft_a
							del dft_b

							# Corner Case
							if len(inverce_c[0]    ) <= 1:
									return inverce_c[0]
							# Inverse DFT
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    2
							while next_ncol <= self.c_max_length:
									SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    [[] for i in range(_A    )]
									SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    self.root ** (next_ncol // 2)
									SCREAMING_SNAKE_CASE_  :		Dict				      =    1
									# First half of next step
									for j in range(self.c_max_length // next_ncol    ):
											for i in range(next_ncol // 2    ):
													# Even positions
													new_inverse_c[i].append(
													    (
													        inverce_c[i][j]
													        + inverce_c[i][j + self.c_max_length // next_ncol]
													    )
													    / 2    )
													# Odd positions
													new_inverse_c[i + next_ncol // 2].append(
													    (
													        inverce_c[i][j]
													        - inverce_c[i][j + self.c_max_length // next_ncol]
													    )
													    / (2 * current_root)    )
											current_root *= root
									# Update
									SCREAMING_SNAKE_CASE_  :		Dict				      =    new_inverse_c
									next_ncol *= 2
							# Unpack
							SCREAMING_SNAKE_CASE_  :		int				      =    [round(x[0].real,8    ) + round(x[0].imag,8    ) * 1j for x in inverce_c]

							# Remove leading 0's
							while inverce_c[-1] == 0:
									inverce_c.pop()
							return inverce_c






					def __str__(    self      :       Dict    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[str]				      =    "A = " + " + ".join(
							    F'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]    )    )
							SCREAMING_SNAKE_CASE_  :		int				      =    "B = " + " + ".join(
							    F'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    "A*B = " + " + ".join(
							    F'{coef}*x^{i}' for coef, i in enumerate(self.product    )    )

							return F'{a}\n{b}\n{c}'


# Unit tests
if __name__ == "__main__":
		import doctest

		doctest.testmod()

import unittest

import numpy as np

from transformers.testing_utils import require_flax, require_tf, require_torch
from transformers.utils import (
    expand_dims,
    flatten_dict,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    reshape,
    squeeze,
    transpose,
)


if is_flax_available():
		import jax.numpy as jnp

if is_tf_available():
		import tensorflow as tf

if is_torch_available():
		import torch






class 		a__						(					unittest.TestCase					):

					def 				__UpperCamelCase   (    self      :       List[str]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Dict				      =    {
							    "task_specific_params": {
							        "summarization": {"length_penalty": 1.0, "max_length": 128, "min_length": 12, "num_beams": 4},
							        "summarization_cnn": {"length_penalty": 2.0, "max_length": 142, "min_length": 56, "num_beams": 4},
							        "summarization_xsum": {"length_penalty": 1.0, "max_length": 62, "min_length": 11, "num_beams": 6},
							    }
							}
							SCREAMING_SNAKE_CASE_  :		Any				      =    {
							    "task_specific_params.summarization.length_penalty": 1.0,
							    "task_specific_params.summarization.max_length": 128,
							    "task_specific_params.summarization.min_length": 12,
							    "task_specific_params.summarization.num_beams": 4,
							    "task_specific_params.summarization_cnn.length_penalty": 2.0,
							    "task_specific_params.summarization_cnn.max_length": 142,
							    "task_specific_params.summarization_cnn.min_length": 56,
							    "task_specific_params.summarization_cnn.num_beams": 4,
							    "task_specific_params.summarization_xsum.length_penalty": 1.0,
							    "task_specific_params.summarization_xsum.max_length": 62,
							    "task_specific_params.summarization_xsum.min_length": 11,
							    "task_specific_params.summarization_xsum.num_beams": 6,
							}

							self.assertEqual(flatten_dict(_A    ),_A    )

					def 				__UpperCamelCase   (    self      :       str    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Dict				      =    np.random.randn(3,4    )
							self.assertTrue(np.allclose(transpose(_A    ),x.transpose()    )    )

							SCREAMING_SNAKE_CASE_  :		Tuple				      =    np.random.randn(3,4,5    )
							self.assertTrue(np.allclose(transpose(_A,axes=(1, 2, 0)    ),x.transpose((1, 2, 0)    )    )    )

					@require_torch
					def 				__UpperCamelCase   (    self      :       List[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[str]				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Any				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(transpose(_A    ),transpose(_A    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		Dict				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(transpose(_A,axes=(1, 2, 0)    ),transpose(_A,axes=(1, 2, 0)    ).numpy()    )    )

					@require_tf
					def 				__UpperCamelCase   (    self      :       List[str]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Tuple				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(transpose(_A    ),transpose(_A    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		List[str]				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(transpose(_A,axes=(1, 2, 0)    ),transpose(_A,axes=(1, 2, 0)    ).numpy()    )    )

					@require_flax
					def 				__UpperCamelCase   (    self      :       List[str]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		str				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(transpose(_A    ),np.asarray(transpose(_A    )    )    )    )

							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(transpose(_A,axes=(1, 2, 0)    ),np.asarray(transpose(_A,axes=(1, 2, 0)    )    )    )    )

					def 				__UpperCamelCase   (    self      :       Dict    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Tuple				      =    np.random.randn(3,4    )
							self.assertTrue(np.allclose(reshape(_A,(4, 3)    ),np.reshape(_A,(4, 3)    )    )    )

							SCREAMING_SNAKE_CASE_  :		Any				      =    np.random.randn(3,4,5    )
							self.assertTrue(np.allclose(reshape(_A,(12, 5)    ),np.reshape(_A,(12, 5)    )    )    )

					@require_torch
					def 				__UpperCamelCase   (    self      :       Optional[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		List[str]				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(reshape(_A,(4, 3)    ),reshape(_A,(4, 3)    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		Dict				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		int				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(reshape(_A,(12, 5)    ),reshape(_A,(12, 5)    ).numpy()    )    )

					@require_tf
					def 				__UpperCamelCase   (    self      :       Dict    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(reshape(_A,(4, 3)    ),reshape(_A,(4, 3)    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		int				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		Any				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(reshape(_A,(12, 5)    ),reshape(_A,(12, 5)    ).numpy()    )    )

					@require_flax
					def 				__UpperCamelCase   (    self      :       Tuple    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[str]				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		int				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(reshape(_A,(4, 3)    ),np.asarray(reshape(_A,(4, 3)    )    )    )    )

							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    np.random.randn(3,4,5    )
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(reshape(_A,(12, 5)    ),np.asarray(reshape(_A,(12, 5)    )    )    )    )

					def 				__UpperCamelCase   (    self      :       Optional[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		int				      =    np.random.randn(1,3,4    )
							self.assertTrue(np.allclose(squeeze(_A    ),np.squeeze(_A    )    )    )

							SCREAMING_SNAKE_CASE_  :		Any				      =    np.random.randn(1,4,1,5    )
							self.assertTrue(np.allclose(squeeze(_A,axis=2    ),np.squeeze(_A,axis=2    )    )    )

					@require_torch
					def 				__UpperCamelCase   (    self      :       List[str]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[str]				      =    np.random.randn(1,3,4    )
							SCREAMING_SNAKE_CASE_  :		Any				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(squeeze(_A    ),squeeze(_A    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		Any				      =    np.random.randn(1,4,1,5    )
							SCREAMING_SNAKE_CASE_  :		Dict				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(squeeze(_A,axis=2    ),squeeze(_A,axis=2    ).numpy()    )    )

					@require_tf
					def 				__UpperCamelCase   (    self      :       Union[str, Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		str				      =    np.random.randn(1,3,4    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(squeeze(_A    ),squeeze(_A    ).numpy()    )    )

							SCREAMING_SNAKE_CASE_  :		Any				      =    np.random.randn(1,4,1,5    )
							SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(squeeze(_A,axis=2    ),squeeze(_A,axis=2    ).numpy()    )    )

					@require_flax
					def 				__UpperCamelCase   (    self      :       List[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    np.random.randn(1,3,4    )
							SCREAMING_SNAKE_CASE_  :		List[str]				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(squeeze(_A    ),np.asarray(squeeze(_A    )    )    )    )

							SCREAMING_SNAKE_CASE_  :		str				      =    np.random.randn(1,4,1,5    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(squeeze(_A,axis=2    ),np.asarray(squeeze(_A,axis=2    )    )    )    )

					def 				__UpperCamelCase   (    self      :       List[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Tuple				      =    np.random.randn(3,4    )
							self.assertTrue(np.allclose(expand_dims(_A,axis=1    ),np.expand_dims(_A,axis=1    )    )    )

					@require_torch
					def 				__UpperCamelCase   (    self      :       Dict    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Tuple				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    torch.tensor(_A    )
							self.assertTrue(np.allclose(expand_dims(_A,axis=1    ),expand_dims(_A,axis=1    ).numpy()    )    )

					@require_tf
					def 				__UpperCamelCase   (    self      :       Union[str, Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    tf.constant(_A    )
							self.assertTrue(np.allclose(expand_dims(_A,axis=1    ),expand_dims(_A,axis=1    ).numpy()    )    )






					@require_flax
					def 				__UpperCamelCase   (    self      :       List[Any]    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		int				      =    np.random.randn(3,4    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    jnp.array(_A    )
							self.assertTrue(np.allclose(expand_dims(_A,axis=1    ),np.asarray(expand_dims(_A,axis=1    )    )    )    )
