diffusers/models/autoencoders/autoencoder_kl_hunyuanimage.py

# Copyright 2025 The Hunyuan Team and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.utils.checkpoint

from ...configuration_utils import ConfigMixin, register_to_config
from ...loaders import FromOriginalModelMixin
from ...utils import logging
from ...utils.accelerate_utils import apply_forward_hook
from ..activations import get_activation
from ..modeling_outputs import AutoencoderKLOutput
from ..modeling_utils import ModelMixin
from .vae import AutoencoderMixin, DecoderOutput, DiagonalGaussianDistribution


logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


class HunyuanImageResnetBlock(nn.Module):
    r"""
    Residual block with two convolutions and optional channel change.

    Args:
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
        non_linearity (str, optional): Type of non-linearity to use. Default is "silu".
    """

    def __init__(self, in_channels: int, out_channels: int, non_linearity: str = "silu") -> None:
        super().__init__()
        self.in_channels = in_channels
        self.out_channels = out_channels
        self.nonlinearity = get_activation(non_linearity)

        # layers
        self.norm1 = nn.GroupNorm(num_groups=32, num_channels=in_channels, eps=1e-6, affine=True)
        self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=1, padding=1)
        self.norm2 = nn.GroupNorm(num_groups=32, num_channels=out_channels, eps=1e-6, affine=True)
        self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, stride=1, padding=1)
        if in_channels != out_channels:
            self.conv_shortcut = nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=1, padding=0)
        else:
            self.conv_shortcut = None

    def forward(self, x):
        # Apply shortcut connection
        residual = x

        # First normalization and activation
        x = self.norm1(x)
        x = self.nonlinearity(x)

        x = self.conv1(x)
        x = self.norm2(x)
        x = self.nonlinearity(x)
        x = self.conv2(x)

        if self.conv_shortcut is not None:
            x = self.conv_shortcut(x)
        # Add residual connection
        return x + residual


class HunyuanImageAttentionBlock(nn.Module):
    r"""
    Self-attention with a single head.

    Args:
        in_channels (int): The number of channels in the input tensor.
    """

    def __init__(self, in_channels: int):
        super().__init__()

        # layers
        self.norm = nn.GroupNorm(num_groups=32, num_channels=in_channels, eps=1e-6, affine=True)
        self.to_q = nn.Conv2d(in_channels, in_channels, 1)
        self.to_k = nn.Conv2d(in_channels, in_channels, 1)
        self.to_v = nn.Conv2d(in_channels, in_channels, 1)
        self.proj = nn.Conv2d(in_channels, in_channels, 1)

    def forward(self, x):
        identity = x
        x = self.norm(x)

        # compute query, key, value
        query = self.to_q(x)
        key = self.to_k(x)
        value = self.to_v(x)

        batch_size, channels, height, width = query.shape
        query = query.permute(0, 2, 3, 1).reshape(batch_size, height * width, channels).contiguous()
        key = key.permute(0, 2, 3, 1).reshape(batch_size, height * width, channels).contiguous()
        value = value.permute(0, 2, 3, 1).reshape(batch_size, height * width, channels).contiguous()

        # apply attention
        x = F.scaled_dot_product_attention(query, key, value)

        x = x.reshape(batch_size, height, width, channels).permute(0, 3, 1, 2)
        # output projection
        x = self.proj(x)

        return x + identity


class HunyuanImageDownsample(nn.Module):
    """
    Downsampling block for spatial reduction.

    Args:
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
    """

    def __init__(self, in_channels: int, out_channels: int):
        super().__init__()
        factor = 4
        if out_channels % factor != 0:
            raise ValueError(f"out_channels % factor != 0: {out_channels % factor}")

        self.conv = nn.Conv2d(in_channels, out_channels // factor, kernel_size=3, stride=1, padding=1)
        self.group_size = factor * in_channels // out_channels

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        h = self.conv(x)

        B, C, H, W = h.shape
        h = h.reshape(B, C, H // 2, 2, W // 2, 2)
        h = h.permute(0, 3, 5, 1, 2, 4)  # b, r1, r2, c, h, w
        h = h.reshape(B, 4 * C, H // 2, W // 2)

        B, C, H, W = x.shape
        shortcut = x.reshape(B, C, H // 2, 2, W // 2, 2)
        shortcut = shortcut.permute(0, 3, 5, 1, 2, 4)  # b, r1, r2, c, h, w
        shortcut = shortcut.reshape(B, 4 * C, H // 2, W // 2)

        B, C, H, W = shortcut.shape
        shortcut = shortcut.view(B, h.shape[1], self.group_size, H, W).mean(dim=2)
        return h + shortcut


class HunyuanImageUpsample(nn.Module):
    """
    Upsampling block for spatial expansion.

    Args:
        in_channels (int): Number of input channels.
        out_channels (int): Number of output channels.
    """

    def __init__(self, in_channels: int, out_channels: int):
        super().__init__()
        factor = 4
        self.conv = nn.Conv2d(in_channels, out_channels * factor, kernel_size=3, stride=1, padding=1)
        self.repeats = factor * out_channels // in_channels

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        h = self.conv(x)

        B, C, H, W = h.shape
        h = h.reshape(B, 2, 2, C // 4, H, W)  # b, r1, r2, c, h, w
        h = h.permute(0, 3, 4, 1, 5, 2)  # b, c, h, r1, w, r2
        h = h.reshape(B, C // 4, H * 2, W * 2)

        shortcut = x.repeat_interleave(repeats=self.repeats, dim=1)

        B, C, H, W = shortcut.shape
        shortcut = shortcut.reshape(B, 2, 2, C // 4, H, W)  # b, r1, r2, c, h, w
        shortcut = shortcut.permute(0, 3, 4, 1, 5, 2)  # b, c, h, r1, w, r2
        shortcut = shortcut.reshape(B, C // 4, H * 2, W * 2)
        return h + shortcut


class HunyuanImageMidBlock(nn.Module):
    """
    Middle block for HunyuanImageVAE encoder and decoder.

    Args:
        in_channels (int): Number of input channels.
        num_layers (int): Number of layers.
    """

    def __init__(self, in_channels: int, num_layers: int = 1):
        super().__init__()

        resnets = [HunyuanImageResnetBlock(in_channels=in_channels, out_channels=in_channels)]

        attentions = []
        for _ in range(num_layers):
            attentions.append(HunyuanImageAttentionBlock(in_channels))
            resnets.append(HunyuanImageResnetBlock(in_channels=in_channels, out_channels=in_channels))

        self.resnets = nn.ModuleList(resnets)
        self.attentions = nn.ModuleList(attentions)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x = self.resnets[0](x)

        for attn, resnet in zip(self.attentions, self.resnets[1:]):
            x = attn(x)
            x = resnet(x)

        return x


class HunyuanImageEncoder2D(nn.Module):
    r"""
    Encoder network that compresses input to latent representation.

    Args:
        in_channels (int): Number of input channels.
        z_channels (int): Number of latent channels.
        block_out_channels (list of int): Output channels for each block.
        num_res_blocks (int): Number of residual blocks per block.
        spatial_compression_ratio (int): Spatial downsampling factor.
        non_linearity (str): Type of non-linearity to use. Default is "silu".
        downsample_match_channel (bool): Whether to match channels during downsampling.
    """

    def __init__(
        self,
        in_channels: int,
        z_channels: int,
        block_out_channels: tuple[int, ...],
        num_res_blocks: int,
        spatial_compression_ratio: int,
        non_linearity: str = "silu",
        downsample_match_channel: bool = True,
    ):
        super().__init__()
        if block_out_channels[-1] % (2 * z_channels) != 0:
            raise ValueError(
                f"block_out_channels[-1 has to be divisible by 2 * out_channels, you have block_out_channels = {block_out_channels[-1]} and out_channels = {z_channels}"
            )

        self.in_channels = in_channels
        self.z_channels = z_channels
        self.block_out_channels = block_out_channels
        self.num_res_blocks = num_res_blocks
        self.spatial_compression_ratio = spatial_compression_ratio

        self.group_size = block_out_channels[-1] // (2 * z_channels)
        self.nonlinearity = get_activation(non_linearity)

        # init block
        self.conv_in = nn.Conv2d(in_channels, block_out_channels[0], kernel_size=3, stride=1, padding=1)

        # downsample blocks
        self.down_blocks = nn.ModuleList([])

        block_in_channel = block_out_channels[0]
        for i in range(len(block_out_channels)):
            block_out_channel = block_out_channels[i]
            # residual blocks
            for _ in range(num_res_blocks):
                self.down_blocks.append(
                    HunyuanImageResnetBlock(in_channels=block_in_channel, out_channels=block_out_channel)
                )
                block_in_channel = block_out_channel

            # downsample block
            if i < np.log2(spatial_compression_ratio) and i != len(block_out_channels) - 1:
                if downsample_match_channel:
                    block_out_channel = block_out_channels[i + 1]
                self.down_blocks.append(
                    HunyuanImageDownsample(in_channels=block_in_channel, out_channels=block_out_channel)
                )
                block_in_channel = block_out_channel

        # middle blocks
        self.mid_block = HunyuanImageMidBlock(in_channels=block_out_channels[-1], num_layers=1)

        # output blocks
        # Output layers
        self.norm_out = nn.GroupNorm(num_groups=32, num_channels=block_out_channels[-1], eps=1e-6, affine=True)
        self.conv_out = nn.Conv2d(block_out_channels[-1], 2 * z_channels, kernel_size=3, stride=1, padding=1)

        self.gradient_checkpointing = False

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x = self.conv_in(x)

        ## downsamples
        for down_block in self.down_blocks:
            if torch.is_grad_enabled() and self.gradient_checkpointing:
                x = self._gradient_checkpointing_func(down_block, x)
            else:
                x = down_block(x)

        ## middle
        if torch.is_grad_enabled() and self.gradient_checkpointing:
            x = self._gradient_checkpointing_func(self.mid_block, x)
        else:
            x = self.mid_block(x)

        ## head
        B, C, H, W = x.shape
        residual = x.view(B, C // self.group_size, self.group_size, H, W).mean(dim=2)

        x = self.norm_out(x)
        x = self.nonlinearity(x)
        x = self.conv_out(x)
        return x + residual


class HunyuanImageDecoder2D(nn.Module):
    r"""
    Decoder network that reconstructs output from latent representation.

    Args:
    z_channels : int
        Number of latent channels.
    out_channels : int
        Number of output channels.
    block_out_channels : tuple[int, ...]
        Output channels for each block.
    num_res_blocks : int
        Number of residual blocks per block.
    spatial_compression_ratio : int
        Spatial upsampling factor.
    upsample_match_channel : bool
        Whether to match channels during upsampling.
    non_linearity (str): Type of non-linearity to use. Default is "silu".
    """

    def __init__(
        self,
        z_channels: int,
        out_channels: int,
        block_out_channels: tuple[int, ...],
        num_res_blocks: int,
        spatial_compression_ratio: int,
        upsample_match_channel: bool = True,
        non_linearity: str = "silu",
    ):
        super().__init__()
        if block_out_channels[0] % z_channels != 0:
            raise ValueError(
                f"block_out_channels[0] should be divisible by z_channels but has block_out_channels[0] = {block_out_channels[0]} and z_channels = {z_channels}"
            )

        self.z_channels = z_channels
        self.block_out_channels = block_out_channels
        self.num_res_blocks = num_res_blocks
        self.repeat = block_out_channels[0] // z_channels
        self.spatial_compression_ratio = spatial_compression_ratio
        self.nonlinearity = get_activation(non_linearity)

        self.conv_in = nn.Conv2d(z_channels, block_out_channels[0], kernel_size=3, stride=1, padding=1)

        # Middle blocks with attention
        self.mid_block = HunyuanImageMidBlock(in_channels=block_out_channels[0], num_layers=1)

        # Upsampling blocks
        block_in_channel = block_out_channels[0]
        self.up_blocks = nn.ModuleList()
        for i in range(len(block_out_channels)):
            block_out_channel = block_out_channels[i]
            for _ in range(self.num_res_blocks + 1):
                self.up_blocks.append(
                    HunyuanImageResnetBlock(in_channels=block_in_channel, out_channels=block_out_channel)
                )
                block_in_channel = block_out_channel

            if i < np.log2(spatial_compression_ratio) and i != len(block_out_channels) - 1:
                if upsample_match_channel:
                    block_out_channel = block_out_channels[i + 1]
                self.up_blocks.append(HunyuanImageUpsample(block_in_channel, block_out_channel))
                block_in_channel = block_out_channel

        # Output layers
        self.norm_out = nn.GroupNorm(num_groups=32, num_channels=block_out_channels[-1], eps=1e-6, affine=True)
        self.conv_out = nn.Conv2d(block_out_channels[-1], out_channels, kernel_size=3, stride=1, padding=1)

        self.gradient_checkpointing = False

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        h = self.conv_in(x) + x.repeat_interleave(repeats=self.repeat, dim=1)

        if torch.is_grad_enabled() and self.gradient_checkpointing:
            h = self._gradient_checkpointing_func(self.mid_block, h)
        else:
            h = self.mid_block(h)

        for up_block in self.up_blocks:
            if torch.is_grad_enabled() and self.gradient_checkpointing:
                h = self._gradient_checkpointing_func(up_block, h)
            else:
                h = up_block(h)
        h = self.norm_out(h)
        h = self.nonlinearity(h)
        h = self.conv_out(h)
        return h


class AutoencoderKLHunyuanImage(ModelMixin, AutoencoderMixin, ConfigMixin, FromOriginalModelMixin):
    r"""
    A VAE model for 2D images with spatial tiling support.

    This model inherits from [`ModelMixin`]. Check the superclass documentation for it's generic methods implemented
    for all models (such as downloading or saving).
    """

    _supports_gradient_checkpointing = False

    # fmt: off
    @register_to_config
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        latent_channels: int,
        block_out_channels: tuple[int, ...],
        layers_per_block: int,
        spatial_compression_ratio: int,
        sample_size: int,
        scaling_factor: float = None,
        downsample_match_channel: bool = True,
        upsample_match_channel: bool = True,
    ) -> None:
    # fmt: on
        super().__init__()

        self.encoder = HunyuanImageEncoder2D(
            in_channels=in_channels,
            z_channels=latent_channels,
            block_out_channels=block_out_channels,
            num_res_blocks=layers_per_block,
            spatial_compression_ratio=spatial_compression_ratio,
            downsample_match_channel=downsample_match_channel,
        )

        self.decoder = HunyuanImageDecoder2D(
            z_channels=latent_channels,
            out_channels=out_channels,
            block_out_channels=list(reversed(block_out_channels)),
            num_res_blocks=layers_per_block,
            spatial_compression_ratio=spatial_compression_ratio,
            upsample_match_channel=upsample_match_channel,
        )

        # Tiling and slicing configuration
        self.use_slicing = False
        self.use_tiling = False

        # Tiling parameters
        self.tile_sample_min_size = sample_size
        self.tile_latent_min_size = sample_size // spatial_compression_ratio
        self.tile_overlap_factor = 0.25

    def enable_tiling(
        self,
        tile_sample_min_size: int | None = None,
        tile_overlap_factor: float | None = None,
    ) -> None:
        r"""
        Enable spatial tiled VAE decoding. When this option is enabled, the VAE will split the input tensor into tiles
        to compute decoding and encoding in several steps. This is useful for saving a large amount of memory and to
        allow processing larger images.

        Args:
            tile_sample_min_size (`int`, *optional*):
                The minimum size required for a sample to be separated into tiles across the spatial dimension.
            tile_overlap_factor (`float`, *optional*):
                The overlap factor required for a latent to be separated into tiles across the spatial dimension.
        """
        self.use_tiling = True
        self.tile_sample_min_size = tile_sample_min_size or self.tile_sample_min_size
        self.tile_overlap_factor = tile_overlap_factor or self.tile_overlap_factor
        self.tile_latent_min_size = self.tile_sample_min_size // self.config.spatial_compression_ratio

    def _encode(self, x: torch.Tensor):

        batch_size, num_channels, height, width = x.shape

        if self.use_tiling and (width > self.tile_sample_min_size or height > self.tile_sample_min_size):
            return self.tiled_encode(x)

        enc = self.encoder(x)

        return enc

    @apply_forward_hook
    def encode(
        self, x: torch.Tensor, return_dict: bool = True
    ) -> AutoencoderKLOutput | tuple[DiagonalGaussianDistribution]:
        r"""
        Encode a batch of images into latents.

        Args:
            x (`torch.Tensor`): Input batch of images.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether to return a [`~models.autoencoder_kl.AutoencoderKLOutput`] instead of a plain tuple.

        Returns:
                The latent representations of the encoded videos. If `return_dict` is True, a
                [`~models.autoencoder_kl.AutoencoderKLOutput`] is returned, otherwise a plain `tuple` is returned.
        """
        if self.use_slicing and x.shape[0] > 1:
            encoded_slices = [self._encode(x_slice) for x_slice in x.split(1)]
            h = torch.cat(encoded_slices)
        else:
            h = self._encode(x)
        posterior = DiagonalGaussianDistribution(h)

        if not return_dict:
            return (posterior,)
        return AutoencoderKLOutput(latent_dist=posterior)

    def _decode(self, z: torch.Tensor, return_dict: bool = True):

        batch_size, num_channels, height, width = z.shape

        if self.use_tiling and (width > self.tile_latent_min_size or height > self.tile_latent_min_size):
            return self.tiled_decode(z, return_dict=return_dict)

        dec = self.decoder(z)

        if not return_dict:
            return (dec,)

        return DecoderOutput(sample=dec)

    @apply_forward_hook
    def decode(self, z: torch.Tensor, return_dict: bool = True) -> DecoderOutput | torch.Tensor:
        r"""
        Decode a batch of images.

        Args:
            z (`torch.Tensor`): Input batch of latent vectors.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether to return a [`~models.vae.DecoderOutput`] instead of a plain tuple.

        Returns:
            [`~models.vae.DecoderOutput`] or `tuple`:
                If return_dict is True, a [`~models.vae.DecoderOutput`] is returned, otherwise a plain `tuple` is
                returned.
        """
        if self.use_slicing and z.shape[0] > 1:
            decoded_slices = [self._decode(z_slice).sample for z_slice in z.split(1)]
            decoded = torch.cat(decoded_slices)
        else:
            decoded = self._decode(z).sample

        if not return_dict:
            return (decoded,)
        return DecoderOutput(sample=decoded)


    def blend_v(self, a: torch.Tensor, b: torch.Tensor, blend_extent: int) -> torch.Tensor:
        blend_extent = min(a.shape[-2], b.shape[-2], blend_extent)
        for y in range(blend_extent):
            b[:, :, y, :] = a[:, :, -blend_extent + y, :] * (1 - y / blend_extent) + b[:, :, y, :] * (
                y / blend_extent
            )
        return b

    def blend_h(self, a: torch.Tensor, b: torch.Tensor, blend_extent: int) -> torch.Tensor:
        blend_extent = min(a.shape[-1], b.shape[-1], blend_extent)
        for x in range(blend_extent):
            b[:, :, :, x] = a[:, :, :, -blend_extent + x] * (1 - x / blend_extent) + b[:, :, :, x] * (
                x / blend_extent
            )
        return b

    def tiled_encode(self, x: torch.Tensor) -> torch.Tensor:
        """
        Encode input using spatial tiling strategy.

        Args:
            x (`torch.Tensor`): Input tensor of shape (B, C, T, H, W).

        Returns:
            `torch.Tensor`:
                The latent representation of the encoded images.
        """
        _, _, _, height, width = x.shape
        overlap_size = int(self.tile_sample_min_size * (1 - self.tile_overlap_factor))
        blend_extent = int(self.tile_latent_min_size * self.tile_overlap_factor)
        row_limit = self.tile_latent_min_size - blend_extent

        rows = []
        for i in range(0, height, overlap_size):
            row = []
            for j in range(0, width, overlap_size):
                tile = x[:, :, :, i : i + self.tile_sample_min_size, j : j + self.tile_sample_min_size]
                tile = self.encoder(tile)
                row.append(tile)
            rows.append(row)

        result_rows = []
        for i, row in enumerate(rows):
            result_row = []
            for j, tile in enumerate(row):
                if i > 0:
                    tile = self.blend_v(rows[i - 1][j], tile, blend_extent)
                if j > 0:
                    tile = self.blend_h(row[j - 1], tile, blend_extent)
                result_row.append(tile[:, :, :, :row_limit, :row_limit])
            result_rows.append(torch.cat(result_row, dim=-1))

        moments = torch.cat(result_rows, dim=-2)

        return moments

    def tiled_decode(self, z: torch.Tensor, return_dict: bool = True) -> DecoderOutput | torch.Tensor:
        """
        Decode latent using spatial tiling strategy.

        Args:
            z (`torch.Tensor`): Latent tensor of shape (B, C, H, W).
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`~models.vae.DecoderOutput`] instead of a plain tuple.

        Returns:
            [`~models.vae.DecoderOutput`] or `tuple`:
                If return_dict is True, a [`~models.vae.DecoderOutput`] is returned, otherwise a plain `tuple` is
                returned.
        """
        _, _, height, width = z.shape
        overlap_size = int(self.tile_latent_min_size * (1 - self.tile_overlap_factor))
        blend_extent = int(self.tile_sample_min_size * self.tile_overlap_factor)
        row_limit = self.tile_sample_min_size - blend_extent

        rows = []
        for i in range(0, height, overlap_size):
            row = []
            for j in range(0, width, overlap_size):
                tile = z[:, :, i : i + self.tile_latent_min_size, j : j + self.tile_latent_min_size]
                decoded = self.decoder(tile)
                row.append(decoded)
            rows.append(row)

        result_rows = []
        for i, row in enumerate(rows):
            result_row = []
            for j, tile in enumerate(row):
                if i > 0:
                    tile = self.blend_v(rows[i - 1][j], tile, blend_extent)
                if j > 0:
                    tile = self.blend_h(row[j - 1], tile, blend_extent)
                result_row.append(tile[:, :, :row_limit, :row_limit])
            result_rows.append(torch.cat(result_row, dim=-1))

        dec = torch.cat(result_rows, dim=-2)
        if not return_dict:
            return (dec,)
        return DecoderOutput(sample=dec)


    def forward(
        self,
        sample: torch.Tensor,
        sample_posterior: bool = False,
        return_dict: bool = True,
        generator: torch.Generator | None = None,
    ) -> DecoderOutput | torch.Tensor:
        """
        Args:
            sample (`torch.Tensor`): Input sample.
            sample_posterior (`bool`, *optional*, defaults to `False`):
                Whether to sample from the posterior.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`DecoderOutput`] instead of a plain tuple.
            generator (`torch.Generator`, *optional*):
                A [`torch.Generator`](https://pytorch.org/docs/stable/generated/torch.Generator.html) to make sampling
                deterministic.

        Returns:
            [`~models.vae.DecoderOutput`] or `tuple`:
                If `return_dict` is True, a [`~models.vae.DecoderOutput`] is returned, otherwise a plain `tuple` is
                returned.
        """
        posterior = self.encode(sample).latent_dist
        if sample_posterior:
            z = posterior.sample(generator=generator)
        else:
            z = posterior.mode()
        dec = self.decode(z, return_dict=return_dict)

        return dec