


"""simple docstring"""
import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			List[Tuple[int, ...]]:
							snake_case_          =						[]
							if isinstance(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
														for v in tree.values():
																					shapes.extend(_fetch_dims(_SCREAMING_SNAKE_CASE			)			)
							elif isinstance(_SCREAMING_SNAKE_CASE			,	(list, tuple)			):
														for t in tree:
																					shapes.extend(_fetch_dims(_SCREAMING_SNAKE_CASE			)			)
							elif isinstance(_SCREAMING_SNAKE_CASE			,	torch.Tensor			):
														shapes.append(tree.shape			)
							else:
														raise ValueError("""Not supported"""			)

							return shapes







@torch.jit.ignore
def   _a			( _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)      ->			Tuple[int, ...]:
							snake_case_          =						[]
							for d in reversed(_SCREAMING_SNAKE_CASE			):
														idx.append(flat_idx % d			)
														snake_case_          =						flat_idx // d

							return tuple(reversed(_SCREAMING_SNAKE_CASE			)			)







@torch.jit.ignore
def   _a			( _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE = None			,	_SCREAMING_SNAKE_CASE = None			,	)      ->			List[Tuple[slice, ...]]:

							# start_edges and end_edges both indicate whether, starting from any given
							# dimension, the start/end index is at the top/bottom edge of the
							# corresponding tensor, modeled as a tree
							def reduce_edge_list(_SCREAMING_SNAKE_CASE			) -> None:
														snake_case_          =						True
														for i in range(len(_SCREAMING_SNAKE_CASE			)			):
																					snake_case_          =						-1 * (i + 1)
																					l[reversed_idx] &= tally
																					snake_case_          =						l[reversed_idx]

							if start_edges is None:
														snake_case_          =						[s == 0 for s in start]
														reduce_edge_list(_SCREAMING_SNAKE_CASE			)
							if end_edges is None:
														snake_case_          =						[e == (d - 1) for e, d in zip(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)]
														reduce_edge_list(_SCREAMING_SNAKE_CASE			)

							# Base cases. Either start/end are empty and we're done, or the final,
							# one-dimensional tensor can be simply sliced
							if len(_SCREAMING_SNAKE_CASE			) == 0:
														return [()]
							elif len(_SCREAMING_SNAKE_CASE			) == 1:
														return [(slice(start[0]			,	end[0] + 1			),)]

							snake_case_          =						[]
							snake_case_          =						[]

							# Dimensions common to start and end can be selected directly
							for s, e in zip(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
														if s == e:
																					path_list.append(slice(_SCREAMING_SNAKE_CASE			,	s + 1			)			)
														else:
																					break

							snake_case_          =						tuple(_SCREAMING_SNAKE_CASE			)
							snake_case_          =						len(_SCREAMING_SNAKE_CASE			)

							# start == end, and we're done
							if divergence_idx == len(_SCREAMING_SNAKE_CASE			):
														return [path]

							def upper() -> Tuple[Tuple[slice, ...], ...]:
														assert start_edges is not None
														assert end_edges is not None

														snake_case_          =						start[divergence_idx]
														return tuple(
														    path + (slice(_SCREAMING_SNAKE_CASE			,	sdi + 1			),) + s
														    for s in _get_minimal_slice_set(
														        start[divergence_idx + 1 :]			,	[d - 1 for d in dims[divergence_idx + 1 :]]			,	dims[divergence_idx + 1 :]			,	start_edges=start_edges[divergence_idx + 1 :]			,	end_edges=[True for _ in end_edges[divergence_idx + 1 :]]			,	)			)

							def lower() -> Tuple[Tuple[slice, ...], ...]:
														assert start_edges is not None
														assert end_edges is not None

														snake_case_          =						end[divergence_idx]
														return tuple(
														    path + (slice(_SCREAMING_SNAKE_CASE			,	edi + 1			),) + s
														    for s in _get_minimal_slice_set(
														        [0 for _ in start[divergence_idx + 1 :]]			,	end[divergence_idx + 1 :]			,	dims[divergence_idx + 1 :]			,	start_edges=[True for _ in start_edges[divergence_idx + 1 :]]			,	end_edges=end_edges[divergence_idx + 1 :]			,	)			)

							# If both start and end are at the edges of the subtree rooted at
							# divergence_idx, we can just select the whole subtree at once
							if start_edges[divergence_idx] and end_edges[divergence_idx]:
														slices.append(path + (slice(start[divergence_idx]			,	end[divergence_idx] + 1			),)			)
							# If just start is at the edge, we can grab almost all of the subtree,
							# treating only the ragged bottom edge as an edge case
							elif start_edges[divergence_idx]:
														slices.append(path + (slice(start[divergence_idx]			,	end[divergence_idx]			),)			)
														slices.extend(lower()			)
							# Analogous to the previous case, but the top is ragged this time
							elif end_edges[divergence_idx]:
														slices.extend(upper()			)
														slices.append(path + (slice(start[divergence_idx] + 1			,	end[divergence_idx] + 1			),)			)
							# If both sides of the range are ragged, we need to handle both sides
							# separately. If there's contiguous meat in between them, we can index it
							# in one big chunk
							else:
														slices.extend(upper()			)
														snake_case_          =						end[divergence_idx] - start[divergence_idx]
														if middle_ground > 1:
																					slices.append(path + (slice(start[divergence_idx] + 1			,	end[divergence_idx]			),)			)
														slices.extend(lower()			)

							return slices







@torch.jit.ignore
def   _a			( _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)      ->			torch.Tensor:
							snake_case_          =						t.shape[:no_batch_dims]
							snake_case_          =						list(_flat_idx_to_idx(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)			)
							# _get_minimal_slice_set is inclusive
							snake_case_          =						list(_flat_idx_to_idx(flat_end - 1			,	_SCREAMING_SNAKE_CASE			)			)

							# Get an ordered list of slices to perform
							snake_case_          =						_get_minimal_slice_set(
							    _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	)

							snake_case_          =						[t[s] for s in slices]

							return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]			) for s in sliced_tensors]			)







def   _a			( _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE = False			,	_SCREAMING_SNAKE_CASE = None			,	_SCREAMING_SNAKE_CASE = False			,	)      ->			Any:
							if not (len(_SCREAMING_SNAKE_CASE			) > 0):
														raise ValueError("""Must provide at least one input"""			)

							snake_case_          =						[shape[:no_batch_dims] for shape in _fetch_dims(_SCREAMING_SNAKE_CASE			)]
							snake_case_          =						tuple([max(_SCREAMING_SNAKE_CASE			) for s in zip(*_SCREAMING_SNAKE_CASE			)]			)

							def _prep_inputs(_SCREAMING_SNAKE_CASE			) -> torch.Tensor:
														if not low_mem:
																					if not sum(t.shape[:no_batch_dims]			) == no_batch_dims:
																												snake_case_          =						t.expand(orig_batch_dims + t.shape[no_batch_dims:]			)
																					snake_case_          =						t.reshape(-1			,	*t.shape[no_batch_dims:]			)
														else:
																					snake_case_          =						t.expand(orig_batch_dims + t.shape[no_batch_dims:]			)
														return t

							snake_case_          =						tensor_tree_map(_prep_inputs			,	_SCREAMING_SNAKE_CASE			)
							snake_case_          =						None
							if _out is not None:
														snake_case_          =						tensor_tree_map(lambda _SCREAMING_SNAKE_CASE			: t.view([-1] + list(t.shape[no_batch_dims:]			)			)			,	_out			)

							snake_case_          =						1
							for d in orig_batch_dims:
														flat_batch_dim *= d

							snake_case_          =						flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

							def _select_chunk(_SCREAMING_SNAKE_CASE			) -> torch.Tensor:
														return t[i : i + chunk_size] if t.shape[0] != 1 else t

							snake_case_          =						0
							snake_case_          =						prepped_outputs
							for _ in range(_SCREAMING_SNAKE_CASE			):
														# Chunk the input
														if not low_mem:
																					snake_case_          =						_select_chunk
														else:
																					snake_case_          =						partial(
																					    _chunk_slice			,	flat_start=_SCREAMING_SNAKE_CASE			,	flat_end=min(_SCREAMING_SNAKE_CASE			,	i + chunk_size			)			,	no_batch_dims=len(_SCREAMING_SNAKE_CASE			)			,	)

														snake_case_          =						tensor_tree_map(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)

														# Run the layer on the chunk
														snake_case_          =						layer(**_SCREAMING_SNAKE_CASE			)

														# Allocate space for the output
														if out is None:
																					snake_case_          =						tensor_tree_map(lambda _SCREAMING_SNAKE_CASE			: t.new_zeros((flat_batch_dim,) + t.shape[1:]			)			,	_SCREAMING_SNAKE_CASE			)

														# Put the chunk in its pre-allocated space
														if isinstance(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):

																					def assign(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			) -> None:
																												for k, v in da.items():
																																			if isinstance(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
																																										assign(_SCREAMING_SNAKE_CASE			,	da[k]			)
																																			else:
																																										if _add_into_out:
																																																	v[i : i + chunk_size] += da[k]
																																										else:
																																																	snake_case_          =						da[k]

																					assign(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)
														elif isinstance(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
																					for xa, xa in zip(_SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			):
																												if _add_into_out:
																																			xa[i : i + chunk_size] += xa
																												else:
																																			snake_case_          =						xa
														elif isinstance(_SCREAMING_SNAKE_CASE			,	torch.Tensor			):
																					if _add_into_out:
																												out[i : i + chunk_size] += output_chunk
																					else:
																												snake_case_          =						output_chunk
														else:
																					raise ValueError("""Not supported"""			)

														i += chunk_size

							snake_case_          =						tensor_tree_map(lambda _SCREAMING_SNAKE_CASE			: t.view(orig_batch_dims + t.shape[1:]			)			,	_SCREAMING_SNAKE_CASE			)

							return out





class        __A       :





							'''simple docstring'''

							def __init__(			self							: Optional[int]						,    UpperCAmelCase_							: int = 512						,    )   ->List[Any]:



														"""simple docstring"""



														snake_case_          =						max_chunk_size
														snake_case_          =						None
														snake_case_          =						None



							def 						lowerCAmelCase    (			self							: Optional[int]						,    UpperCAmelCase_							: Callable						,    UpperCAmelCase_							: tuple						,    UpperCAmelCase_							: int    )   ->int:



														"""simple docstring"""



														logging.info("""Tuning chunk size..."""    )

														if min_chunk_size >= self.max_chunk_size:
																					return min_chunk_size

														snake_case_          =						[2**l for l in range(int(math.log(self.max_chunk_size						,    2    )    ) + 1    )]
														snake_case_          =						[c for c in candidates if c > min_chunk_size]
														snake_case_          =						[min_chunk_size] + candidates
														candidates[-1] += 4

														def test_chunk_size(UpperCAmelCase_							: int    ) -> bool:
																					try:
																												with torch.no_grad():
																																			fn(*UpperCAmelCase_						,    chunk_size=UpperCAmelCase_    )
																												return True
																					except RuntimeError:
																												return False

														snake_case_          =						0
														snake_case_          =						len(UpperCAmelCase_    ) - 1
														while i > min_viable_chunk_size_index:
																					snake_case_          =						test_chunk_size(candidates[i]    )
																					if not viable:
																												snake_case_          =						(min_viable_chunk_size_index + i) // 2
																					else:
																												snake_case_          =						i
																												snake_case_          =						(i + len(UpperCAmelCase_    ) - 1) // 2

														return candidates[min_viable_chunk_size_index]



							def 						lowerCAmelCase    (			self							: Union[str, Any]						,    UpperCAmelCase_							: Iterable						,    UpperCAmelCase_							: Iterable    )   ->bool:



														"""simple docstring"""



														snake_case_          =						True
														for aa, aa in zip(UpperCAmelCase_						,    UpperCAmelCase_    ):
																					assert type(UpperCAmelCase_    ) == type(UpperCAmelCase_    )
																					if isinstance(UpperCAmelCase_						,    (list, tuple)    ):
																												consistent &= self._compare_arg_caches(UpperCAmelCase_						,    UpperCAmelCase_    )
																					elif isinstance(UpperCAmelCase_						,    UpperCAmelCase_    ):
																												snake_case_          =						[v for _, v in sorted(aa.items()						,    key=lambda UpperCAmelCase_    : x[0]    )]
																												snake_case_          =						[v for _, v in sorted(aa.items()						,    key=lambda UpperCAmelCase_    : x[0]    )]
																												consistent &= self._compare_arg_caches(UpperCAmelCase_						,    UpperCAmelCase_    )
																					else:
																												consistent &= aa == aa

														return consistent



							def 						lowerCAmelCase    (			self							: List[Any]						,    UpperCAmelCase_							: Callable						,    UpperCAmelCase_							: tuple						,    UpperCAmelCase_							: int						,    )   ->int:



														"""simple docstring"""



														snake_case_          =						True
														snake_case_          =						tree_map(lambda UpperCAmelCase_    : a.shape if isinstance(UpperCAmelCase_						,    torch.Tensor    ) else a						,    UpperCAmelCase_						,    UpperCAmelCase_    )
														if self.cached_arg_data is not None:
																					# If args have changed shape/value, we need to re-tune
																					assert len(self.cached_arg_data    ) == len(UpperCAmelCase_    )
																					snake_case_          =						self._compare_arg_caches(self.cached_arg_data						,    UpperCAmelCase_    )
														else:
																					# Otherwise, we can reuse the precomputed value
																					snake_case_          =						False

														if not consistent:
																					snake_case_          =						self._determine_favorable_chunk_size(
																					    UpperCAmelCase_						,    UpperCAmelCase_						,    UpperCAmelCase_						,    )
																					snake_case_          =						arg_data

														assert self.cached_chunk_size is not None

														return self.cached_chunk_size







"""simple docstring"""
def   _a			( _SCREAMING_SNAKE_CASE			,	_SCREAMING_SNAKE_CASE			)      ->			str:
							return "\n".join(
							    f"""{number} * {i} = {number * i}""" for i in range(1			,	number_of_terms + 1			)			)


if __name__ == "__main__":
				print(multiplication_table(number=5, number_of_terms=10))



