
"""simple docstring"""




# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING, Dict, Optional

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.logging import get_logger
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
					import jax
					import jaxlib

UpperCAmelCase__      :    Any    							= get_logger()

UpperCAmelCase__      :    Optional[dict]    							= None



class 	lowerCAmelCase_						(TensorFormatter[Mapping, '''jax.Array''', Mapping]  ):


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__=None   ,       SCREAMING_SNAKE_CASE__=None   ,       **SCREAMING_SNAKE_CASE__    )					->		List[str]:



											"""simple docstring"""




											super().__init__(features=SCREAMING_SNAKE_CASE__    )
											import jax
											from jaxlib.xla_client import Device

											if isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ):
																		raise ValueError(
																		    F'''Expected {device} to be a `str` not {type(SCREAMING_SNAKE_CASE__    )}, as `jaxlib.xla_extension.Device` '''
																		    """is not serializable neither with `pickle` nor with `dill`. Instead you can surround """
																		    """the device with `str()` to get its string identifier that will be internally mapped """
																		    """to the actual `jaxlib.xla_extension.Device`."""    )
											SCREAMING_SNAKE_CASE__						:       Tuple           =   device if isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ) else str(jax.devices()[0]    )
											# using global variable since `jaxlib.xla_extension.Device` is not serializable neither
											# with `pickle` nor with `dill`, so we need to use a global variable instead
											global DEVICE_MAPPING
											if DEVICE_MAPPING is None:
																		SCREAMING_SNAKE_CASE__						:       List[Any]           =   self._map_devices_to_str()
											if self.device not in list(DEVICE_MAPPING.keys()    ):
																		logger.warning(
																		    F'''Device with string identifier {self.device} not listed among the available '''
																		    F'''devices: {list(DEVICE_MAPPING.keys()    )}, so falling back to the default '''
																		    F'''device: {str(jax.devices()[0]    )}.'''    )
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   str(jax.devices()[0]    )
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   jnp_array_kwargs



				@staticmethod
				def 	__magic_name__    ()					->		Dict[str, "jaxlib.xla_extension.Device"]:



											"""simple docstring"""




											import jax

											return {str(SCREAMING_SNAKE_CASE__    ): device for device in jax.devices()}



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Tuple:



											"""simple docstring"""




											import jax
											import jax.numpy as jnp

											if isinstance(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__    ) and column:
																		if all(
																		    isinstance(SCREAMING_SNAKE_CASE__   ,       jax.Array    ) and x.shape == column[0].shape and x.dtype == column[0].dtype for x in column    ):
																									return jnp.stack(SCREAMING_SNAKE_CASE__   ,       axis=0    )
											return column



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Optional[int]:



											"""simple docstring"""




											import jax
											import jax.numpy as jnp

											if isinstance(SCREAMING_SNAKE_CASE__   ,       (str, bytes, type(SCREAMING_SNAKE_CASE__    ))    ):
																		return value
											elif isinstance(SCREAMING_SNAKE_CASE__   ,       (np.character, np.ndarray)    ) and np.issubdtype(value.dtype   ,       np.character    ):
																		return value.tolist()

											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   {}

											if isinstance(SCREAMING_SNAKE_CASE__   ,       (np.number, np.ndarray)    ) and np.issubdtype(value.dtype   ,       np.integer    ):
																		# the default int precision depends on the jax config
																		# see https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#double-64bit-precision
																		if jax.config.jax_enable_xaa:
																									SCREAMING_SNAKE_CASE__						:       int           =   {"""dtype""": jnp.intaa}
																		else:
																									SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   {"""dtype""": jnp.intaa}
											elif isinstance(SCREAMING_SNAKE_CASE__   ,       (np.number, np.ndarray)    ) and np.issubdtype(value.dtype   ,       np.floating    ):
																		SCREAMING_SNAKE_CASE__						:       int           =   {"""dtype""": jnp.floataa}
											elif config.PIL_AVAILABLE and "PIL" in sys.modules:
																		import PIL.Image

																		if isinstance(SCREAMING_SNAKE_CASE__   ,       PIL.Image.Image    ):
																									SCREAMING_SNAKE_CASE__						:       Any           =   np.asarray(SCREAMING_SNAKE_CASE__    )

        # using global variable since `jaxlib.xla_extension.Device` is not serializable neither
        # with `pickle` nor with `dill`, so we need to use a global variable instead
											global DEVICE_MAPPING
											if DEVICE_MAPPING is None:
																		SCREAMING_SNAKE_CASE__						:       Optional[int]           =   self._map_devices_to_str()

											with jax.default_device(DEVICE_MAPPING[self.device]    ):
																		# calling jnp.array on a np.ndarray does copy the data
																		# see https://github.com/google/jax/issues/4486
																		return jnp.array(SCREAMING_SNAKE_CASE__   ,       **{**default_dtype, **self.jnp_array_kwargs}    )



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		int:



											"""simple docstring"""




											import jax

											# support for torch, tf, jax etc.
											if config.TORCH_AVAILABLE and "torch" in sys.modules:
																		import torch

																		if isinstance(SCREAMING_SNAKE_CASE__   ,       torch.Tensor    ):
																									return self._tensorize(data_struct.detach().cpu().numpy()[()]    )
											if hasattr(SCREAMING_SNAKE_CASE__   ,       """__array__"""    ) and not isinstance(SCREAMING_SNAKE_CASE__   ,       jax.Array    ):
																		SCREAMING_SNAKE_CASE__						:       List[Any]           =   data_struct.__array__()
											# support for nested types like struct of list of struct
											if isinstance(SCREAMING_SNAKE_CASE__   ,       np.ndarray    ):
																		if data_struct.dtype == object:  # jax arrays cannot be instantied from an array of objects
																									return self._consolidate([self.recursive_tensorize(SCREAMING_SNAKE_CASE__    ) for substruct in data_struct]    )
											elif isinstance(SCREAMING_SNAKE_CASE__   ,       (list, tuple)    ):
																		return self._consolidate([self.recursive_tensorize(SCREAMING_SNAKE_CASE__    ) for substruct in data_struct]    )
											return self._tensorize(SCREAMING_SNAKE_CASE__    )



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		str:



											"""simple docstring"""




											return map_nested(self._recursive_tensorize   ,       SCREAMING_SNAKE_CASE__   ,       map_list=SCREAMING_SNAKE_CASE__    )



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Mapping:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[Any]           =   self.numpy_arrow_extractor().extract_row(SCREAMING_SNAKE_CASE__    )
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   self.python_features_decoder.decode_row(SCREAMING_SNAKE_CASE__    )
											return self.recursive_tensorize(SCREAMING_SNAKE_CASE__    )



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		"jax.Array":



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[Any]           =   self.numpy_arrow_extractor().extract_column(SCREAMING_SNAKE_CASE__    )
											SCREAMING_SNAKE_CASE__						:       int           =   self.python_features_decoder.decode_column(SCREAMING_SNAKE_CASE__   ,       pa_table.column_names[0]    )
											SCREAMING_SNAKE_CASE__						:       str           =   self.recursive_tensorize(SCREAMING_SNAKE_CASE__    )
											SCREAMING_SNAKE_CASE__						:       Any           =   self._consolidate(SCREAMING_SNAKE_CASE__    )
											return column



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Mapping:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self.numpy_arrow_extractor().extract_batch(SCREAMING_SNAKE_CASE__    )
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   self.python_features_decoder.decode_batch(SCREAMING_SNAKE_CASE__    )
											SCREAMING_SNAKE_CASE__						:       Tuple           =   self.recursive_tensorize(SCREAMING_SNAKE_CASE__    )
											for column_name in batch:
																		SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self._consolidate(batch[column_name]    )
											return batch






"""simple docstring"""




import mpmath  # for roots of unity
import numpy as np



class 	lowerCAmelCase_						:


				"""simple docstring"""



				def __init__(self   ,       SCREAMING_SNAKE_CASE__=None   ,       SCREAMING_SNAKE_CASE__=None    )					->		Dict:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   list(poly_a or [0]    )[:]
											SCREAMING_SNAKE_CASE__						:       Tuple           =   list(poly_b or [0]    )[:]

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

											while self.polyB[-1] == 0:
																		self.polyB.pop()
											SCREAMING_SNAKE_CASE__						:       List[str]           =   len(self.polyB    )

											# Add 0 to make lengths equal a power of 2
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   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__						:       Tuple           =   self.__multiply()



				def 	__magic_name__    (self   ,       SCREAMING_SNAKE_CASE__    )					->		Union[str, Any]:



											"""simple docstring"""




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

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



				def 	__magic_name__    (self    )					->		int:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       Union[str, Any]           =   self.__dft("""A"""    )
											SCREAMING_SNAKE_CASE__						:       Dict           =   self.__dft("""B"""    )
											SCREAMING_SNAKE_CASE__						:       List[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__						:       List[str]           =   [[] for i in range(SCREAMING_SNAKE_CASE__    )]
																		SCREAMING_SNAKE_CASE__						:       Tuple           =   self.root ** (next_ncol // 2)
																		SCREAMING_SNAKE_CASE__						:       Any           =   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__						:       Optional[Any]           =   new_inverse_c
																		next_ncol *= 2
											# Unpack
											SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   [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    )					->		List[str]:



											"""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__						:       Union[str, Any]           =   """B = """ + """ + """.join(
											    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]    )    )
											SCREAMING_SNAKE_CASE__						:       int           =   """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()




