

"""simple docstring"""






import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation
def       UpperCamelCase					(			_lowerCAmelCase     :						str,  _lowerCAmelCase     :						Union[str, Any],  _lowerCAmelCase     :						Optional[Any] = False,  _lowerCAmelCase     :						Tuple = 1,  _lowerCAmelCase     :						Any = 1,  _lowerCAmelCase     :						Optional[int] = 10000,  )				->			Dict:
	assert len(timesteps.shape ) == 1, "Timesteps should be a 1d-array"

	_UpperCAmelCase    :							Any									=					embedding_dim // 2
	_UpperCAmelCase    :							List[str]									=					-math.log(_lowerCAmelCase ) * torch.arange(
	    start=0,  end=_lowerCAmelCase,  dtype=torch.floataa,  device=timesteps.device )
	_UpperCAmelCase    :							str									=					exponent / (half_dim - downscale_freq_shift)

	_UpperCAmelCase    :							Optional[int]									=					torch.exp(_lowerCAmelCase )
	_UpperCAmelCase    :							List[str]									=					timesteps[:, None].float() * emb[None, :]

	# scale embeddings
	_UpperCAmelCase    :							Optional[Any]									=					scale * emb

	# concat sine and cosine embeddings
	_UpperCAmelCase    :							int									=					torch.cat([torch.sin(_lowerCAmelCase ), torch.cos(_lowerCAmelCase )],  dim=-1 )

	# flip sine and cosine embeddings
	if flip_sin_to_cos:
		_UpperCAmelCase    :							Tuple									=					torch.cat([emb[:, half_dim:], emb[:, :half_dim]],  dim=-1 )

	# zero pad
	if embedding_dim % 2 == 1:
		_UpperCAmelCase    :							Optional[int]									=					torch.nn.functional.pad(_lowerCAmelCase,  (0, 1, 0, 0) )
	return emb
def       UpperCamelCase					(			_lowerCAmelCase     :						Tuple,  _lowerCAmelCase     :						str,  _lowerCAmelCase     :						Union[str, Any]=False,  _lowerCAmelCase     :						Any=0 )				->			Union[str, Any]:
	_UpperCAmelCase    :							List[str]									=					np.arange(_lowerCAmelCase,  dtype=np.floataa )
	_UpperCAmelCase    :							Tuple									=					np.arange(_lowerCAmelCase,  dtype=np.floataa )
	_UpperCAmelCase    :							Optional[int]									=					np.meshgrid(_lowerCAmelCase,  _lowerCAmelCase )  # here w goes first
	_UpperCAmelCase    :							Union[str, Any]									=					np.stack(_lowerCAmelCase,  axis=0 )

	_UpperCAmelCase    :							List[str]									=					grid.reshape([2, 1, grid_size, grid_size] )
	_UpperCAmelCase    :							Dict									=					get_ad_sincos_pos_embed_from_grid(_lowerCAmelCase,  _lowerCAmelCase )
	if cls_token and extra_tokens > 0:
		_UpperCAmelCase    :							Union[str, Any]									=					np.concatenate([np.zeros([extra_tokens, embed_dim] ), pos_embed],  axis=0 )
	return pos_embed
def       UpperCamelCase					(			_lowerCAmelCase     :						int,  _lowerCAmelCase     :						Tuple )				->			Optional[int]:


	if embed_dim % 2 != 0:
		raise ValueError("""embed_dim must be divisible by 2""" )

	# use half of dimensions to encode grid_h
	_UpperCAmelCase    :							Union[str, Any]									=					get_ad_sincos_pos_embed_from_grid(embed_dim // 2,  grid[0] )  # (H*W, D/2)
	_UpperCAmelCase    :							Dict									=					get_ad_sincos_pos_embed_from_grid(embed_dim // 2,  grid[1] )  # (H*W, D/2)

	_UpperCAmelCase    :							int									=					np.concatenate([emb_h, emb_w],  axis=1 )  # (H*W, D)
	return emb
def       UpperCamelCase					(			_lowerCAmelCase     :						int,  _lowerCAmelCase     :						Tuple )				->			List[Any]:


	if embed_dim % 2 != 0:
		raise ValueError("""embed_dim must be divisible by 2""" )

	_UpperCAmelCase    :							Optional[int]									=					np.arange(embed_dim // 2,  dtype=np.floataa )
	omega /= embed_dim / 2.0
	_UpperCAmelCase    :							str									=					1.0 / 10000**omega  # (D/2,)

	_UpperCAmelCase    :							Optional[int]									=					pos.reshape(-1 )  # (M,)
	_UpperCAmelCase    :							str									=					np.einsum("""m,d->md""",  _lowerCAmelCase,  _lowerCAmelCase )  # (M, D/2), outer product

	_UpperCAmelCase    :							str									=					np.sin(_lowerCAmelCase )  # (M, D/2)
	_UpperCAmelCase    :							Optional[Any]									=					np.cos(_lowerCAmelCase )  # (M, D/2)

	_UpperCAmelCase    :							Optional[Any]									=					np.concatenate([emb_sin, emb_cos],  axis=1 )  # (M, D)
	return emb






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A=2_24      ,		_A=2_24      ,		_A=16      ,		_A=3      ,		_A=7_68      ,		_A=False      ,		_A=True      ,		_A=True      ,		)    ->    int:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							Optional[Any]									=					(height // patch_size) * (width // patch_size)
				_UpperCAmelCase    :							Tuple									=					flatten
				_UpperCAmelCase    :							int									=					layer_norm

				_UpperCAmelCase    :							Optional[Any]									=					nn.Convad(
				    _A      ,		_A      ,		kernel_size=(patch_size, patch_size)      ,		stride=_A      ,		bias=_A     )
				if layer_norm:
					_UpperCAmelCase    :							List[Any]									=					nn.LayerNorm(_A      ,		elementwise_affine=_A      ,		eps=1e-6     )
				else:
					_UpperCAmelCase    :							Optional[Any]									=					None

				_UpperCAmelCase    :							List[Any]									=					get_ad_sincos_pos_embed(_A      ,		int(num_patches**0.5     )     )
				self.register_buffer("""pos_embed"""      ,		torch.from_numpy(_A     ).float().unsqueeze(0     )      ,		persistent=_A     )
			def 							__snake_case (		self      ,		_A     )    ->    Union[str, Any]:






				'''simple docstring'''







				_UpperCAmelCase    :							List[str]									=					self.proj(_A     )
				if self.flatten:
					_UpperCAmelCase    :							Tuple									=					latent.flatten(2     ).transpose(1      ,		2     )  # BCHW -> BNC
				if self.layer_norm:
					_UpperCAmelCase    :							List[str]									=					self.norm(_A     )
				return latent + self.pos_embed






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A = "silu"      ,		_A = None      ,		_A = None      ,		_A=None      ,		)    ->    Optional[Any]:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							int									=					nn.Linear(_A      ,		_A     )

				if cond_proj_dim is not None:
					_UpperCAmelCase    :							List[str]									=					nn.Linear(_A      ,		_A      ,		bias=_A     )
				else:
					_UpperCAmelCase    :							Tuple									=					None

				_UpperCAmelCase    :							List[Any]									=					get_activation(_A     )

				if out_dim is not None:
					_UpperCAmelCase    :							Tuple									=					out_dim
				else:
					_UpperCAmelCase    :							Any									=					time_embed_dim
				_UpperCAmelCase    :							Optional[int]									=					nn.Linear(_A      ,		_A     )

				if post_act_fn is None:
					_UpperCAmelCase    :							str									=					None
				else:
					_UpperCAmelCase    :							int									=					get_activation(_A     )
			def 							__snake_case (		self      ,		_A      ,		_A=None     )    ->    Tuple:






				'''simple docstring'''







				if condition is not None:
					_UpperCAmelCase    :							Union[str, Any]									=					sample + self.cond_proj(_A     )
				_UpperCAmelCase    :							List[Any]									=					self.linear_a(_A     )

				if self.act is not None:
					_UpperCAmelCase    :							Union[str, Any]									=					self.act(_A     )

				_UpperCAmelCase    :							List[Any]									=					self.linear_a(_A     )

				if self.post_act is not None:
					_UpperCAmelCase    :							Tuple									=					self.post_act(_A     )
				return sample






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A     )    ->    int:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							int									=					num_channels
				_UpperCAmelCase    :							int									=					flip_sin_to_cos
				_UpperCAmelCase    :							Optional[Any]									=					downscale_freq_shift
			def 							__snake_case (		self      ,		_A     )    ->    List[str]:






				'''simple docstring'''







				_UpperCAmelCase    :							List[str]									=					get_timestep_embedding(
				    _A      ,		self.num_channels      ,		flip_sin_to_cos=self.flip_sin_to_cos      ,		downscale_freq_shift=self.downscale_freq_shift      ,		)
				return t_emb






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 2_56      ,		_A = 1.0      ,		_A=True      ,		_A=True      ,		_A=False     )    ->    Optional[int]:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Tuple									=					nn.Parameter(torch.randn(_A     ) * scale      ,		requires_grad=_A     )
				_UpperCAmelCase    :							str									=					log
				_UpperCAmelCase    :							Dict									=					flip_sin_to_cos

				if set_W_to_weight:
					# to delete later
					_UpperCAmelCase    :							Tuple									=					nn.Parameter(torch.randn(_A     ) * scale      ,		requires_grad=_A     )

					_UpperCAmelCase    :							List[str]									=					self.W
			def 							__snake_case (		self      ,		_A     )    ->    Optional[Any]:






				'''simple docstring'''







				if self.log:
					_UpperCAmelCase    :							Optional[Any]									=					torch.log(_A     )

				_UpperCAmelCase    :							Any									=					x[:, None] * self.weight[None, :] * 2 * np.pi

				if self.flip_sin_to_cos:
					_UpperCAmelCase    :							Optional[int]									=					torch.cat([torch.cos(_A     ), torch.sin(_A     )]      ,		dim=-1     )
				else:
					_UpperCAmelCase    :							int									=					torch.cat([torch.sin(_A     ), torch.cos(_A     )]      ,		dim=-1     )
				return out






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A      ,		_A      ,		)    ->    List[str]:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							Tuple									=					height
				_UpperCAmelCase    :							Any									=					width
				_UpperCAmelCase    :							str									=					num_embed
				_UpperCAmelCase    :							Any									=					embed_dim

				_UpperCAmelCase    :							Optional[int]									=					nn.Embedding(self.num_embed      ,		_A     )
				_UpperCAmelCase    :							List[str]									=					nn.Embedding(self.height      ,		_A     )
				_UpperCAmelCase    :							List[Any]									=					nn.Embedding(self.width      ,		_A     )
			def 							__snake_case (		self      ,		_A     )    ->    str:






				'''simple docstring'''







				_UpperCAmelCase    :							Dict									=					self.emb(_A     )

				_UpperCAmelCase    :							Any									=					self.height_emb(torch.arange(self.height      ,		device=index.device     ).view(1      ,		self.height     )     )

				# 1 x H x D -> 1 x H x 1 x D
				_UpperCAmelCase    :							str									=					height_emb.unsqueeze(2     )

				_UpperCAmelCase    :							Optional[Any]									=					self.width_emb(torch.arange(self.width      ,		device=index.device     ).view(1      ,		self.width     )     )

				# 1 x W x D -> 1 x 1 x W x D
				_UpperCAmelCase    :							Dict									=					width_emb.unsqueeze(1     )

				_UpperCAmelCase    :							Union[str, Any]									=					height_emb + width_emb

				# 1 x H x W x D -> 1 x L xD
				_UpperCAmelCase    :							List[Any]									=					pos_emb.view(1      ,		self.height * self.width      ,		-1     )

				_UpperCAmelCase    :							Any									=					emb + pos_emb[:, : emb.shape[1], :]

				return emb






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A     )    ->    Union[str, Any]:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Union[str, Any]									=					dropout_prob > 0
				_UpperCAmelCase    :							str									=					nn.Embedding(num_classes + use_cfg_embedding      ,		_A     )
				_UpperCAmelCase    :							Optional[int]									=					num_classes
				_UpperCAmelCase    :							int									=					dropout_prob
			def 							__snake_case (		self      ,		_A      ,		_A=None     )    ->    Dict:






				'''simple docstring'''







				if force_drop_ids is None:
					_UpperCAmelCase    :							Union[str, Any]									=					torch.rand(labels.shape[0]      ,		device=labels.device     ) < self.dropout_prob
				else:
					_UpperCAmelCase    :							Tuple									=					torch.tensor(force_drop_ids == 1     )
				_UpperCAmelCase    :							Optional[int]									=					torch.where(_A      ,		self.num_classes      ,		_A     )
				return labels
			def 							__snake_case (		self      ,		_A      ,		_A=None     )    ->    Dict:






				'''simple docstring'''







				_UpperCAmelCase    :							Optional[int]									=					self.dropout_prob > 0
				if (self.training and use_dropout) or (force_drop_ids is not None):
					_UpperCAmelCase    :							str									=					self.token_drop(_A      ,		_A     )
				_UpperCAmelCase    :							Any									=					self.embedding_table(_A     )
				return embeddings






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 10_24      ,		_A = 7_68      ,		_A = 7_68      ,		_A = 10      ,		)    ->    Optional[int]:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							Optional[int]									=					num_image_text_embeds
				_UpperCAmelCase    :							str									=					nn.Linear(_A      ,		self.num_image_text_embeds * cross_attention_dim     )
				_UpperCAmelCase    :							List[str]									=					nn.Linear(_A      ,		_A     )
			def 							__snake_case (		self      ,		_A      ,		_A     )    ->    Optional[int]:






				'''simple docstring'''







				_UpperCAmelCase    :							Dict									=					text_embeds.shape[0]

				# image
				_UpperCAmelCase    :							str									=					self.image_embeds(_A     )
				_UpperCAmelCase    :							str									=					image_text_embeds.reshape(_A      ,		self.num_image_text_embeds      ,		-1     )

				# text
				_UpperCAmelCase    :							Tuple									=					self.text_proj(_A     )

				return torch.cat([image_text_embeds, text_embeds]      ,		dim=1     )






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 7_68      ,		_A = 7_68      ,		_A = 32      ,		)    ->    Dict:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							Tuple									=					num_image_text_embeds
				_UpperCAmelCase    :							Any									=					nn.Linear(_A      ,		self.num_image_text_embeds * cross_attention_dim     )
				_UpperCAmelCase    :							Union[str, Any]									=					nn.LayerNorm(_A     )
			def 							__snake_case (		self      ,		_A     )    ->    Tuple:






				'''simple docstring'''







				_UpperCAmelCase    :							Optional[int]									=					image_embeds.shape[0]

				# image
				_UpperCAmelCase    :							Dict									=					self.image_embeds(_A     )
				_UpperCAmelCase    :							Optional[Any]									=					image_embeds.reshape(_A      ,		self.num_image_text_embeds      ,		-1     )
				_UpperCAmelCase    :							Tuple									=					self.norm(_A     )
				return image_embeds






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A=0.1     )    ->    int:






				'''simple docstring'''







				super().__init__()

				_UpperCAmelCase    :							Dict									=					Timesteps(num_channels=2_56      ,		flip_sin_to_cos=_A      ,		downscale_freq_shift=1     )
				_UpperCAmelCase    :							Optional[int]									=					TimestepEmbedding(in_channels=2_56      ,		time_embed_dim=_A     )
				_UpperCAmelCase    :							Dict									=					LabelEmbedding(_A      ,		_A      ,		_A     )
			def 							__snake_case (		self      ,		_A      ,		_A      ,		_A=None     )    ->    List[str]:






				'''simple docstring'''







				_UpperCAmelCase    :							List[Any]									=					self.time_proj(_A     )
				_UpperCAmelCase    :							Optional[Any]									=					self.timestep_embedder(timesteps_proj.to(dtype=_A     )     )  # (N, D)

				_UpperCAmelCase    :							Optional[Any]									=					self.class_embedder(_A     )  # (N, D)

				_UpperCAmelCase    :							int									=					timesteps_emb + class_labels  # (N, D)

				return conditioning






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A = 64     )    ->    str:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							str									=					nn.LayerNorm(_A     )
				_UpperCAmelCase    :							Optional[int]									=					AttentionPooling(_A      ,		_A     )
				_UpperCAmelCase    :							Any									=					nn.Linear(_A      ,		_A     )
				_UpperCAmelCase    :							List[str]									=					nn.LayerNorm(_A     )
			def 							__snake_case (		self      ,		_A     )    ->    Dict:






				'''simple docstring'''







				_UpperCAmelCase    :							List[str]									=					self.norma(_A     )
				_UpperCAmelCase    :							Tuple									=					self.pool(_A     )
				_UpperCAmelCase    :							List[Any]									=					self.proj(_A     )
				_UpperCAmelCase    :							Optional[int]									=					self.norma(_A     )
				return hidden_states






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 7_68      ,		_A = 7_68      ,		_A = 15_36     )    ->    Union[str, Any]:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Tuple									=					nn.Linear(_A      ,		_A     )
				_UpperCAmelCase    :							Optional[Any]									=					nn.LayerNorm(_A     )
				_UpperCAmelCase    :							List[Any]									=					nn.Linear(_A      ,		_A     )
			def 							__snake_case (		self      ,		_A      ,		_A     )    ->    List[Any]:






				'''simple docstring'''







				_UpperCAmelCase    :							str									=					self.text_proj(_A     )
				_UpperCAmelCase    :							List[str]									=					self.text_norm(_A     )

				# image
				_UpperCAmelCase    :							Dict									=					self.image_proj(_A     )

				return time_image_embeds + time_text_embeds






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 7_68      ,		_A = 15_36     )    ->    List[str]:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Tuple									=					nn.Linear(_A      ,		_A     )
				_UpperCAmelCase    :							Optional[Any]									=					nn.LayerNorm(_A     )
			def 							__snake_case (		self      ,		_A     )    ->    Any:






				'''simple docstring'''







				_UpperCAmelCase    :							List[Any]									=					self.image_proj(_A     )
				_UpperCAmelCase    :							Optional[int]									=					self.image_norm(_A     )
				return time_image_embeds






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A = 7_68      ,		_A = 15_36     )    ->    str:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Optional[Any]									=					nn.Linear(_A      ,		_A     )
				_UpperCAmelCase    :							Union[str, Any]									=					nn.LayerNorm(_A     )
				_UpperCAmelCase    :							Optional[Any]									=					nn.Sequential(
				    nn.Convad(3      ,		16      ,		3      ,		padding=1     )      ,		nn.SiLU()      ,		nn.Convad(16      ,		16      ,		3      ,		padding=1     )      ,		nn.SiLU()      ,		nn.Convad(16      ,		32      ,		3      ,		padding=1      ,		stride=2     )      ,		nn.SiLU()      ,		nn.Convad(32      ,		32      ,		3      ,		padding=1     )      ,		nn.SiLU()      ,		nn.Convad(32      ,		96      ,		3      ,		padding=1      ,		stride=2     )      ,		nn.SiLU()      ,		nn.Convad(96      ,		96      ,		3      ,		padding=1     )      ,		nn.SiLU()      ,		nn.Convad(96      ,		2_56      ,		3      ,		padding=1      ,		stride=2     )      ,		nn.SiLU()      ,		nn.Convad(2_56      ,		4      ,		3      ,		padding=1     )      ,		)
			def 							__snake_case (		self      ,		_A      ,		_A     )    ->    Any:






				'''simple docstring'''







				_UpperCAmelCase    :							List[str]									=					self.image_proj(_A     )
				_UpperCAmelCase    :							Optional[int]									=					self.image_norm(_A     )
				_UpperCAmelCase    :							Any									=					self.input_hint_block(_A     )
				return time_image_embeds, hint






class     _UpperCAmelCase			(		nn.Module):
			def __init__(		self      ,		_A      ,		_A      ,		_A=None     )    ->    Optional[Any]:






				'''simple docstring'''







				super().__init__()
				_UpperCAmelCase    :							Optional[Any]									=					dtype
				_UpperCAmelCase    :							Dict									=					nn.Parameter(torch.randn(1      ,		_A     ) / embed_dim**0.5     )
				_UpperCAmelCase    :							str									=					nn.Linear(_A      ,		_A      ,		dtype=self.dtype     )
				_UpperCAmelCase    :							Optional[Any]									=					nn.Linear(_A      ,		_A      ,		dtype=self.dtype     )
				_UpperCAmelCase    :							Any									=					nn.Linear(_A      ,		_A      ,		dtype=self.dtype     )
				_UpperCAmelCase    :							Optional[int]									=					num_heads
				_UpperCAmelCase    :							Dict									=					embed_dim // self.num_heads
			def 							__snake_case (		self      ,		_A     )    ->    List[str]:






				'''simple docstring'''







				_UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase    :							Union[str, Any]									=					x.size()

				def shape(_A     ):
					# (bs, length, width) --> (bs, length, n_heads, dim_per_head)
					_UpperCAmelCase    :							Dict									=					x.view(_A      ,		-1      ,		self.num_heads      ,		self.dim_per_head     )
					# (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
					_UpperCAmelCase    :							Optional[Any]									=					x.transpose(1      ,		2     )
					# (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
					_UpperCAmelCase    :							str									=					x.reshape(bs * self.num_heads      ,		-1      ,		self.dim_per_head     )
					# (bs*n_heads, length, dim_per_head) --> (bs*n_heads, dim_per_head, length)
					_UpperCAmelCase    :							List[str]									=					x.transpose(1      ,		2     )
					return x

				_UpperCAmelCase    :							Optional[Any]									=					x.mean(dim=1      ,		keepdim=_A     ) + self.positional_embedding.to(x.dtype     )
				_UpperCAmelCase    :							str									=					torch.cat([class_token, x]      ,		dim=1     )  # (bs, length+1, width)

				# (bs*n_heads, class_token_length, dim_per_head)
				_UpperCAmelCase    :							int									=					shape(self.q_proj(_A     )     )
				# (bs*n_heads, length+class_token_length, dim_per_head)
				_UpperCAmelCase    :							str									=					shape(self.k_proj(_A     )     )
				_UpperCAmelCase    :							Optional[int]									=					shape(self.v_proj(_A     )     )

				# (bs*n_heads, class_token_length, length+class_token_length):
				_UpperCAmelCase    :							Dict									=					1 / math.sqrt(math.sqrt(self.dim_per_head     )     )
				_UpperCAmelCase    :							List[str]									=					torch.einsum("""bct,bcs->bts"""      ,		q * scale      ,		k * scale     )  # More stable with f16 than dividing afterwards
				_UpperCAmelCase    :							List[Any]									=					torch.softmax(weight.float()      ,		dim=-1     ).type(weight.dtype     )

				# (bs*n_heads, dim_per_head, class_token_length)
				_UpperCAmelCase    :							Optional[Any]									=					torch.einsum("""bts,bcs->bct"""      ,		_A      ,		_A     )

				# (bs, length+1, width)
				_UpperCAmelCase    :							Optional[int]									=					a.reshape(_A      ,		-1      ,		1     ).transpose(1      ,		2     )

				return a[:, 0, :]  # cls_token






"""simple docstring"""






def       UpperCamelCase					(			_lowerCAmelCase     :						int,  _lowerCAmelCase     :						int = 1000 )				->			str:
	if (not isinstance(_lowerCAmelCase,  _lowerCAmelCase )) or (digit_position <= 0):
		raise ValueError("""Digit position must be a positive integer""" )
	elif (not isinstance(_lowerCAmelCase,  _lowerCAmelCase )) or (precision < 0):
		raise ValueError("""Precision must be a nonnegative integer""" )

	# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
	# accurate
	_UpperCAmelCase    :							List[Any]									=					(
	    4 * _subsum(_lowerCAmelCase,  1,  _lowerCAmelCase )
	    - 2 * _subsum(_lowerCAmelCase,  4,  _lowerCAmelCase )
	    - _subsum(_lowerCAmelCase,  5,  _lowerCAmelCase )
	    - _subsum(_lowerCAmelCase,  6,  _lowerCAmelCase )
	)

	# return the first hex digit of the fractional part of the result
	return hex(int((sum_result % 1) * 16 ) )[2:]
def       UpperCamelCase					(			_lowerCAmelCase     :						int,  _lowerCAmelCase     :						int,  _lowerCAmelCase     :						int )				->			float:
	_UpperCAmelCase    :							Optional[int]									=					0.0
	for sum_index in range(digit_pos_to_extract + precision ):
		_UpperCAmelCase    :							Optional[Any]									=					8 * sum_index + denominator_addend
		if sum_index < digit_pos_to_extract:
			# if the exponential term is an integer and we mod it by the denominator
			# before dividing, only the integer part of the sum will change;
			# the fractional part will not
			_UpperCAmelCase    :							Optional[Any]									=					pow(
			    16,  digit_pos_to_extract - 1 - sum_index,  _lowerCAmelCase )
		else:
			_UpperCAmelCase    :							int									=					pow(16,  digit_pos_to_extract - 1 - sum_index )
		total += exponential_term / denominator
	return total


if __name__ == "__main__":
						import doctest

						doctest.testmod()





