


"""simple docstring"""







import mpmath  # for roots of unity
import numpy as np




class  UpperCamelCase_	:

	"""simple docstring"""





	def __init__( self			:				List[Any]			,			UpperCAmelCase__			:				Optional[Any]=None			,			UpperCAmelCase__			:				int=None   )       ->	str:
						# Input as list
						__SCREAMING_SNAKE_CASE						   =				list(poly_a or [0]   )[:]
						__SCREAMING_SNAKE_CASE						   =				list(poly_b or [0]   )[:]

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

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

						# Add 0 to make lengths equal a power of 2
						__SCREAMING_SNAKE_CASE						   =				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						   =				complex(mpmath.root(x=1			,			n=self.c_max_length			,			k=1   )   )

						# The product
						__SCREAMING_SNAKE_CASE						   =				self.__multiply()




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

											# First half of next step
											__SCREAMING_SNAKE_CASE						   =				1
											for j in range(self.c_max_length // (next_ncol * 2)   ):
																for i in range(UpperCAmelCase__   ):
																					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						   =				1
											for j in range(self.c_max_length // (next_ncol * 2)   ):
																for i in range(UpperCAmelCase__   ):
																					new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]   )
																current_root *= root
											# Update
											__SCREAMING_SNAKE_CASE						   =				new_dft
											__SCREAMING_SNAKE_CASE						   =				next_ncol // 2
						return dft[0]




	def   UpperCAmelCase_      ( self			:				Union[str, Any]   )       ->	Any:
						__SCREAMING_SNAKE_CASE						   =				self.__dft("A"   )
						__SCREAMING_SNAKE_CASE						   =				self.__dft("B"   )
						__SCREAMING_SNAKE_CASE						   =				[[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						   =				2
						while next_ncol <= self.c_max_length:
											__SCREAMING_SNAKE_CASE						   =				[[] for i in range(UpperCAmelCase__   )]
											__SCREAMING_SNAKE_CASE						   =				self.root ** (next_ncol // 2)
											__SCREAMING_SNAKE_CASE						   =				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						   =				new_inverse_c
											next_ncol *= 2
						# Unpack
						__SCREAMING_SNAKE_CASE						   =				[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			:				Optional[int]   )       ->	Any:
						__SCREAMING_SNAKE_CASE						   =				"A = " + " + ".join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]   )   )
						__SCREAMING_SNAKE_CASE						   =				"B = " + " + ".join(
						    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]   )   )
						__SCREAMING_SNAKE_CASE						   =				"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()




"""simple docstring"""







import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
		import torch

		from transformers.generation import DisjunctiveConstraint




@require_torch
class  UpperCamelCase_	( unittest.TestCase):

	"""simple docstring"""





	def   UpperCAmelCase_      ( self			:				Optional[int]   )       ->	List[str]:
						# For consistency across different places the DisjunctiveConstraint is called,
						# dc.token_ids is a list of integers. It is also initialized only by integers.

						__SCREAMING_SNAKE_CASE						   =				[[1, 2, 4], [1, 2, 3, 4]]
						__SCREAMING_SNAKE_CASE						   =				DisjunctiveConstraint(UpperCAmelCase__   )
						self.assertTrue(isinstance(dc.token_ids			,			UpperCAmelCase__   )   )

						with self.assertRaises(UpperCAmelCase__   ):
											DisjunctiveConstraint(torch.LongTensor([[1, 2, 4], [1, 2, 3]]   )   )

						with self.assertRaises(UpperCAmelCase__   ):
											DisjunctiveConstraint([torch.LongTensor([1, 2, 4]   ), torch.LongTensor([1, 2, 3, 4, 5]   )]   )




	def   UpperCAmelCase_      ( self			:				Any   )       ->	int:
						# We can't have constraints that are complete subsets of another. This leads to a preverse
						# interpretation of "constraint fulfillment": does generating [1,2,3] fulfill the constraint?
						# It would mean that it generated [1,2] which fulfills it, but it's in the middle of potentially
						# fulfilling [1,2,3,4]. If we believe that [1,2,3] does fulfill the constraint, then the algorithm
						# will necessarily never reach [1,2,3,4], giving users a false sense of control (better to just not allow it).
						__SCREAMING_SNAKE_CASE						   =				[[1, 2], [1, 2, 3, 4]]

						with self.assertRaises(UpperCAmelCase__   ):
											DisjunctiveConstraint(UpperCAmelCase__   )  # fails here




	def   UpperCAmelCase_      ( self			:				List[Any]   )       ->	Any:
						__SCREAMING_SNAKE_CASE						   =				[[1, 2, 3], [1, 2, 4]]

						__SCREAMING_SNAKE_CASE						   =				DisjunctiveConstraint(UpperCAmelCase__   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(1   )
						__SCREAMING_SNAKE_CASE						   =				stepped is True and completed is False and reset is False
						self.assertTrue(UpperCAmelCase__   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.current_seq == [1]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(2   )
						__SCREAMING_SNAKE_CASE						   =				stepped is True and completed is False and reset is False
						self.assertTrue(UpperCAmelCase__   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.current_seq == [1, 2]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(3   )
						__SCREAMING_SNAKE_CASE						   =				stepped is True and completed is True and reset is False
						self.assertTrue(UpperCAmelCase__   )
						self.assertTrue(dc.completed   )  # Completed!
						self.assertTrue(dc.current_seq == [1, 2, 3]   )




	def   UpperCAmelCase_      ( self			:				str   )       ->	List[str]:
						__SCREAMING_SNAKE_CASE						   =				[[1, 2, 3], [1, 2, 4, 5], [1, 2, 5]]

						__SCREAMING_SNAKE_CASE						   =				DisjunctiveConstraint(UpperCAmelCase__   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(1   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.current_seq == [1]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(2   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.current_seq == [1, 2]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(4   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.current_seq == [1, 2, 4]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(5   )
						self.assertTrue(dc.completed   )  # Completed!
						self.assertTrue(dc.current_seq == [1, 2, 4, 5]   )

						dc.reset()

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(1   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.remaining() == 3   )
						self.assertTrue(dc.current_seq == [1]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(2   )
						self.assertTrue(not dc.completed   )
						self.assertTrue(dc.remaining() == 2   )
						self.assertTrue(dc.current_seq == [1, 2]   )

						__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				dc.update(5   )
						self.assertTrue(dc.completed   )  # Completed!
						self.assertTrue(dc.remaining() == 0   )
						self.assertTrue(dc.current_seq == [1, 2, 5]   )
