
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  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Union[str, Any]:
			lowerCAmelCase__      :      List[str]         =		[]
			if isinstance(lowerCAmelCase_       ,							lowerCAmelCase_     ):
						for v in tree.values():
									shapes.extend(_fetch_dims(lowerCAmelCase_     )     )
			elif isinstance(lowerCAmelCase_       ,							(list, tuple)     ):
						for t in tree:
									shapes.extend(_fetch_dims(lowerCAmelCase_     )     )
			elif isinstance(lowerCAmelCase_       ,							torch.Tensor     ):
						shapes.append(tree.shape     )
			else:
						raise ValueError('Not supported'     )

			return shapes
@torch.jit.ignore
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		Union[str, Any]:
			lowerCAmelCase__      :      Union[str, Any]         =		[]
			for d in reversed(lowerCAmelCase_     ):
						idx.append(flat_idx % d     )
						lowerCAmelCase__      :      Dict         =		flat_idx // d

			return tuple(reversed(lowerCAmelCase_     )     )
@torch.jit.ignore
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_ = None       ,							SCREAMING_SNAKE_CASE_ = None       ,							)				->		Tuple:

			# 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:
						lowerCAmelCase__      :      Tuple         =		True
						for i in range(len(lowerCAmelCase_     )     ):
									lowerCAmelCase__      :      List[str]         =		-1 * (i + 1)
									l[reversed_idx] &= tally
									lowerCAmelCase__      :      List[str]         =		l[reversed_idx]

			if start_edges is None:
						lowerCAmelCase__      :      Union[str, Any]         =		[s == 0 for s in start]
						reduce_edge_list(lowerCAmelCase_     )
			if end_edges is None:
						lowerCAmelCase__      :      Any         =		[e == (d - 1) for e, d in zip(lowerCAmelCase_       ,							lowerCAmelCase_     )]
						reduce_edge_list(lowerCAmelCase_     )

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

			lowerCAmelCase__      :      List[Tuple[slice, ...]]         =		[]
			lowerCAmelCase__      :      List[slice]         =		[]

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

			lowerCAmelCase__      :      Tuple[slice, ...]         =		tuple(lowerCAmelCase_     )
			lowerCAmelCase__      :      Any         =		len(lowerCAmelCase_     )

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

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

						lowerCAmelCase__      :      Tuple         =		start[divergence_idx]
						return tuple(
						    path + (slice(lowerCAmelCase_       ,							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

						lowerCAmelCase__      :      Dict         =		end[divergence_idx]
						return tuple(
						    path + (slice(lowerCAmelCase_       ,							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()     )
						lowerCAmelCase__      :      Optional[Any]         =		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  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		Any:
			lowerCAmelCase__      :      Union[str, Any]         =		t.shape[:no_batch_dims]
			lowerCAmelCase__      :      Optional[int]         =		list(_flat_idx_to_idx(lowerCAmelCase_       ,							lowerCAmelCase_     )     )
			# _get_minimal_slice_set is inclusive
			lowerCAmelCase__      :      Optional[Any]         =		list(_flat_idx_to_idx(flat_end - 1       ,							lowerCAmelCase_     )     )

			# Get an ordered list of slices to perform
			lowerCAmelCase__      :      Any         =		_get_minimal_slice_set(
			    lowerCAmelCase_       ,							lowerCAmelCase_       ,							lowerCAmelCase_       ,							)

			lowerCAmelCase__      :      Optional[Any]         =		[t[s] for s in slices]

			return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]     ) for s in sliced_tensors]     )
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_ = False       ,							SCREAMING_SNAKE_CASE_ = None       ,							SCREAMING_SNAKE_CASE_ = False       ,							)				->		Optional[int]:
			if not (len(lowerCAmelCase_     ) > 0):
						raise ValueError('Must provide at least one input'     )

			lowerCAmelCase__      :      Union[str, Any]         =		[shape[:no_batch_dims] for shape in _fetch_dims(lowerCAmelCase_     )]
			lowerCAmelCase__      :      int         =		tuple([max(lowerCAmelCase_     ) for s in zip(*lowerCAmelCase_     )]     )

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

			lowerCAmelCase__      :      Dict[str, Any]         =		tensor_tree_map(_prep_inputs       ,							lowerCAmelCase_     )
			lowerCAmelCase__      :      Optional[int]         =		None
			if _out is not None:
						lowerCAmelCase__      :      Tuple         =		tensor_tree_map(lambda SCREAMING_SNAKE_CASE_     : t.view([-1] + list(t.shape[no_batch_dims:]     )     )       ,							_out     )

			lowerCAmelCase__      :      Union[str, Any]         =		1
			for d in orig_batch_dims:
						flat_batch_dim *= d

			lowerCAmelCase__      :      int         =		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

			lowerCAmelCase__      :      str         =		0
			lowerCAmelCase__      :      Optional[int]         =		prepped_outputs
			for _ in range(lowerCAmelCase_     ):
						# Chunk the input
						if not low_mem:
									lowerCAmelCase__      :      Optional[int]         =		_select_chunk
						else:
									lowerCAmelCase__      :      Optional[Any]         =		partial(
									    _chunk_slice       ,							flat_start=lowerCAmelCase_       ,							flat_end=min(lowerCAmelCase_       ,							i + chunk_size     )       ,							no_batch_dims=len(lowerCAmelCase_     )       ,							)

						lowerCAmelCase__      :      Dict[str, Any]         =		tensor_tree_map(lowerCAmelCase_       ,							lowerCAmelCase_     )

						# Run the layer on the chunk
						lowerCAmelCase__      :      Tuple         =		layer(**lowerCAmelCase_     )

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

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

									def assign(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ) -> None:
												for k, v in da.items():
															if isinstance(lowerCAmelCase_       ,							lowerCAmelCase_     ):
																		assign(lowerCAmelCase_       ,							da[k]     )
															else:
																		if _add_into_out:
																					v[i : i + chunk_size] += da[k]
																		else:
																					lowerCAmelCase__      :      List[str]         =		da[k]

									assign(lowerCAmelCase_       ,							lowerCAmelCase_     )
						elif isinstance(lowerCAmelCase_       ,							lowerCAmelCase_     ):
									for xa, xa in zip(lowerCAmelCase_       ,							lowerCAmelCase_     ):
												if _add_into_out:
															xa[i : i + chunk_size] += xa
												else:
															lowerCAmelCase__      :      Tuple         =		xa
						elif isinstance(lowerCAmelCase_       ,							torch.Tensor     ):
									if _add_into_out:
												out[i : i + chunk_size] += output_chunk
									else:
												lowerCAmelCase__      :      List[str]         =		output_chunk
						else:
									raise ValueError('Not supported'     )

						i += chunk_size

			lowerCAmelCase__      :      Any         =		tensor_tree_map(lambda SCREAMING_SNAKE_CASE_     : t.view(orig_batch_dims + t.shape[1:]     )       ,							lowerCAmelCase_     )

			return out







class      A__							:






				def __init__(						self					:      int    ,     a					:      int = 512    ,     ):






							'''simple docstring'''







							lowerCAmelCase__      :      Union[str, Any]         =		max_chunk_size
							lowerCAmelCase__      :      Optional[int]         =		None
							lowerCAmelCase__      :      Optional[tuple]         =		None






				def 							_lowerCamelCase		(						self					:      Optional[Any]    ,     a					:      Callable    ,     a					:      tuple    ,     a					:      int   ):






							'''simple docstring'''







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

							if min_chunk_size >= self.max_chunk_size:
										return min_chunk_size

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

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

							lowerCAmelCase__      :      int         =		0
							lowerCAmelCase__      :      Tuple         =		len(__a   ) - 1
							while i > min_viable_chunk_size_index:
										lowerCAmelCase__      :      Dict         =		test_chunk_size(candidates[i]   )
										if not viable:
													lowerCAmelCase__      :      List[str]         =		(min_viable_chunk_size_index + i) // 2
										else:
													lowerCAmelCase__      :      Any         =		i
													lowerCAmelCase__      :      str         =		(i + len(__a   ) - 1) // 2

							return candidates[min_viable_chunk_size_index]






				def 							_lowerCamelCase		(						self					:      Optional[Any]    ,     a					:      Iterable    ,     a					:      Iterable   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Any         =		True
							for aa, aa in zip(__a    ,     __a   ):
										assert type(__a   ) == type(__a   )
										if isinstance(__a    ,     (list, tuple)   ):
													consistent &= self._compare_arg_caches(__a    ,     __a   )
										elif isinstance(__a    ,     __a   ):
													lowerCAmelCase__      :      str         =		[v for _, v in sorted(aa.items()    ,     key=lambda a   : x[0]   )]
													lowerCAmelCase__      :      Optional[int]         =		[v for _, v in sorted(aa.items()    ,     key=lambda a   : x[0]   )]
													consistent &= self._compare_arg_caches(__a    ,     __a   )
										else:
													consistent &= aa == aa

							return consistent






				def 							_lowerCamelCase		(						self					:      Union[str, Any]    ,     a					:      Callable    ,     a					:      tuple    ,     a					:      int    ,     ):






							'''simple docstring'''







							lowerCAmelCase__      :      int         =		True
							lowerCAmelCase__      :      tuple         =		tree_map(lambda a   : a.shape if isinstance(__a    ,     torch.Tensor   ) else a    ,     __a    ,     __a   )
							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(__a   )
										lowerCAmelCase__      :      str         =		self._compare_arg_caches(self.cached_arg_data    ,     __a   )
							else:
										# Otherwise, we can reuse the precomputed value
										lowerCAmelCase__      :      List[Any]         =		False

							if not consistent:
										lowerCAmelCase__      :      int         =		self._determine_favorable_chunk_size(
										    __a    ,     __a    ,     __a    ,     )
										lowerCAmelCase__      :      Dict         =		arg_data

							assert self.cached_chunk_size is not None

							return self.cached_chunk_size







from math import pi
def 					snake_case_						(   lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  int					):
							return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
	print(arc_length(90, 10))