


from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

snake_case      :   Tuple							= TypeVar('T')
snake_case      :   List[Any]							= TypeVar('U')



class  __lowercase	(							Generic[T, U]				):

							"""simple docstring"""


							def __init__(     self					,			A_					,			A_						)->						Optional[int]:
											_SCREAMING_SNAKE_CASE   =			key
											_SCREAMING_SNAKE_CASE   =			val
											_SCREAMING_SNAKE_CASE   =			None
											_SCREAMING_SNAKE_CASE   =			None





							def __repr__(     self						)->						Optional[int]:
											return (
											    F'''Node: key: {self.key}, val: {self.val}, '''
											    F'''has next: {bool(self.next						)}, has prev: {bool(self.prev						)}'''
											)







class  __lowercase	(							Generic[T, U]				):

							"""simple docstring"""


							def __init__(     self						)->						int:
											_SCREAMING_SNAKE_CASE   =			DoubleLinkedListNode(UpperCAmelCase__					,			UpperCAmelCase__						)
											_SCREAMING_SNAKE_CASE   =			DoubleLinkedListNode(UpperCAmelCase__					,			UpperCAmelCase__						)
											_SCREAMING_SNAKE_CASE   =			self.rear, self.head





							def __repr__(     self						)->						Tuple:
											_SCREAMING_SNAKE_CASE   =			['''DoubleLinkedList''']
											_SCREAMING_SNAKE_CASE   =			self.head
											while node.next is not None:
															rep.append(str(UpperCAmelCase__						)						)
															_SCREAMING_SNAKE_CASE   =			node.next
											rep.append(str(self.rear						)						)
											return ",\n    ".join(UpperCAmelCase__						)





							def 		__magic_name__      (     self					,			A_						)->						Union[str, Any]:
											_SCREAMING_SNAKE_CASE   =			self.rear.prev

											# All nodes other than self.head are guaranteed to have non-None previous
											assert previous is not None

											_SCREAMING_SNAKE_CASE   =			node
											_SCREAMING_SNAKE_CASE   =			previous
											_SCREAMING_SNAKE_CASE   =			node
											_SCREAMING_SNAKE_CASE   =			self.rear





							def 		__magic_name__      (     self					,			A_						)->						int:

											if node.prev is None or node.next is None:
															return None

											_SCREAMING_SNAKE_CASE   =			node.next
											_SCREAMING_SNAKE_CASE   =			node.prev
											_SCREAMING_SNAKE_CASE   =			None
											_SCREAMING_SNAKE_CASE   =			None
											return node







class  __lowercase	(							Generic[T, U]				):

							"""simple docstring"""


							SCREAMING_SNAKE_CASE :       Dict	   =    {}





							def __init__(     self					,			A_						)->						Any:
											_SCREAMING_SNAKE_CASE   =			DoubleLinkedList()
											_SCREAMING_SNAKE_CASE   =			capacity
											_SCREAMING_SNAKE_CASE   =			0
											_SCREAMING_SNAKE_CASE   =			0
											_SCREAMING_SNAKE_CASE   =			0
											_SCREAMING_SNAKE_CASE   =			{}





							def __repr__(     self						)->						Optional[int]:
											return (
											    F'''CacheInfo(hits={self.hits}, misses={self.miss}, '''
											    F'''capacity={self.capacity}, current size={self.num_keys})'''
											)





							def __contains__(     self					,			A_						)->						List[str]:
											return key in self.cache





							def 		__magic_name__      (     self					,			A_						)->						Optional[Any]:
											# Note: pythonic interface would throw KeyError rather than return None

											if key in self.cache:
															self.hits += 1
															_SCREAMING_SNAKE_CASE   =			self.cache[key]
															_SCREAMING_SNAKE_CASE   =			self.list.remove(self.cache[key]						)
															assert node == value_node

															# node is guaranteed not None because it is in self.cache
															assert node is not None
															self.list.add(UpperCAmelCase__						)
															return node.val
											self.miss += 1
											return None





							def 		__magic_name__      (     self					,			A_					,			A_						)->						Any:

											if key not in self.cache:
															if self.num_keys >= self.capacity:
																			# delete first node (oldest) when over capacity
																			_SCREAMING_SNAKE_CASE   =			self.list.head.next

																			# guaranteed to have a non-None first node when num_keys > 0
																			# explain to type checker via assertions
																			assert first_node is not None
																			assert first_node.key is not None
																			assert (
																			    self.list.remove(UpperCAmelCase__						) is not None
																			)  # node guaranteed to be in list assert node.key is not None

																			del self.cache[first_node.key]
																			self.num_keys -= 1
															_SCREAMING_SNAKE_CASE   =			DoubleLinkedListNode(UpperCAmelCase__					,			UpperCAmelCase__						)
															self.list.add(self.cache[key]						)
															self.num_keys += 1

											else:
															# bump node to the end of the list, update value
															_SCREAMING_SNAKE_CASE   =			self.list.remove(self.cache[key]						)
															assert node is not None  # node guaranteed to be in list
															_SCREAMING_SNAKE_CASE   =			value
															self.list.add(UpperCAmelCase__						)





							@classmethod
							def 		__magic_name__      (     cls					,			A_ = 128						)->						Optional[int]:

											def cache_decorator_inner(A_						) -> Callable[..., U]:
															def cache_decorator_wrapper(*A_						) -> U:
																			if func not in cls.decorator_function_to_instance_map:
																							_SCREAMING_SNAKE_CASE   =			LRUCache(UpperCAmelCase__						)

																			_SCREAMING_SNAKE_CASE   =			cls.decorator_function_to_instance_map[func].get(args[0]						)
																			if result is None:
																							_SCREAMING_SNAKE_CASE   =			func(*UpperCAmelCase__						)
																							cls.decorator_function_to_instance_map[func].put(args[0]					,			UpperCAmelCase__						)
																			return result

															def cache_info() -> LRUCache[T, U]:
																			return cls.decorator_function_to_instance_map[func]

															setattr(UpperCAmelCase__					,			'cache_info'					,			UpperCAmelCase__						)  # noqa: B010

															return cache_decorator_wrapper

											return cache_decorator_inner


if __name__ == "__main__":
							import doctest

							doctest.testmod()



'''simple docstring'''





import math

import flax.linen as nn
import jax.numpy as jnp






def 				_lowerCAmelCase			(   __magic_name__						:     jnp.ndarray   , __magic_name__						:     int   , __magic_name__						:     float = 1   , __magic_name__						:     float = 1   , __magic_name__						:     float = 1.0E4   , __magic_name__						:     bool = False   , __magic_name__						:     float = 1.0   , )				->  jnp.ndarray:
						assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
						assert embedding_dim % 2 == 0, f'''Embedding dimension {embedding_dim} should be even'''
						lowercase :							int    		=float(embedding_dim // 2						)
						lowercase :							Optional[int]    		=math.log(max_timescale / min_timescale						) / (num_timescales - freq_shift)
						lowercase :							Any    		=min_timescale * jnp.exp(jnp.arange(__magic_name__   , dtype=jnp.floataa						) * -log_timescale_increment						)
						lowercase :							List[Any]    		=jnp.expand_dims(__magic_name__   , 1						) * jnp.expand_dims(__magic_name__   , 0						)

						# scale embeddings
						lowercase :							Tuple    		=scale * emb

						if flip_sin_to_cos:
												lowercase :							Dict    		=jnp.concatenate([jnp.cos(__magic_name__						), jnp.sin(__magic_name__						)]   , axis=1						)
						else:
												lowercase :							Any    		=jnp.concatenate([jnp.sin(__magic_name__						), jnp.cos(__magic_name__						)]   , axis=1						)
						lowercase :							List[str]    		=jnp.reshape(__magic_name__   , [jnp.shape(__magic_name__						)[0], embedding_dim]						)
						return signal





class 		__SCREAMING_SNAKE_CASE							(			nn.Module      ):
				lowerCamelCase_		       =    32
				lowerCamelCase_		       =    jnp.floataa







				@nn.compact
				def __call__(       self     :		Tuple		,					UpperCAmelCase__     :		int   ):
										'''simple docstring'''
										lowercase :							List[Any]    		=nn.Dense(self.time_embed_dim		,					dtype=self.dtype		,					name='''linear_1'''   )(UpperCAmelCase__   )
										lowercase :							Any    		=nn.silu(UpperCAmelCase__   )
										lowercase :							int    		=nn.Dense(self.time_embed_dim		,					dtype=self.dtype		,					name='''linear_2'''   )(UpperCAmelCase__   )
										return temb





class 		__SCREAMING_SNAKE_CASE							(			nn.Module      ):
				lowerCamelCase_		       =    32
				lowerCamelCase_		       =    False
				lowerCamelCase_		       =    1







				@nn.compact
				def __call__(       self     :		int		,					UpperCAmelCase__     :		str   ):
										'''simple docstring'''
										return get_sinusoidal_embeddings(
										    UpperCAmelCase__		,					embedding_dim=self.dim		,					flip_sin_to_cos=self.flip_sin_to_cos		,					freq_shift=self.freq_shift   )





