"""
Lookup Free Quantization
Proposed in https://arxiv.org/abs/2310.05737

In the simplest setup, each dimension is quantized into {-1, 1}.
An entropy penalty is used to encourage utilization.

Refer to 
https://github.com/lucidrains/vector-quantize-pytorch/blob/master/vector_quantize_pytorch/lookup_free_quantization.py
https://github.com/theAdamColton/ijepa-enhanced/blob/7edef5f7288ae8f537f0db8a10044a2a487f70c9/ijepa_enhanced/lfq.py
"""

from math import log2, ceil
from collections import namedtuple

import torch
from torch import nn, einsum
import torch.nn.functional as F
from torch.nn import Module

from einops import rearrange, reduce, pack, unpack

# constants
LossBreakdown = namedtuple('LossBreakdown', ['per_sample_entropy', 'codebook_entropy', 'commitment', 'avg_probs'])

# helper functions
def exists(v):
    return v is not None

def default(*args):
    for arg in args:
        if exists(arg):
            return arg() if callable(arg) else arg
    return None

def pack_one(t, pattern):
    return pack([t], pattern)

def unpack_one(t, ps, pattern):
    return unpack(t, ps, pattern)[0]

# entropy
def entropy(prob):
    return (-prob * torch.log(prob + 1e-5)).sum(dim=-1)

# class
def mult_along_first_dims(x, y):
    """
    returns x * y elementwise along the leading dimensions of y
    """
    ndim_to_expand = x.ndim - y.ndim
    for _ in range(ndim_to_expand):
        y = y.unsqueeze(-1)
    return x * y

def masked_mean(x, m):
    """
    takes the mean of the elements of x that are not masked
    the mean is taken along the shared leading dims of m
    equivalent to: x[m].mean(tuple(range(m.ndim)))

    The benefit of using masked_mean rather than using
    tensor indexing is that masked_mean is much faster
    for torch-compile on batches.

    The drawback is larger floating point errors
    """
    x = mult_along_first_dims(x, m)
    x = x / m.sum()
    return x.sum(tuple(range(m.ndim)))


def entropy_loss(
    logits,
    mask=None,
    temperature=0.01,
    sample_minimization_weight=1.0,
    batch_maximization_weight=1.0,
    eps=1e-5,
):
    """
    Entropy loss of unnormalized logits

    logits: Affinities are over the last dimension

    https://github.com/google-research/magvit/blob/05e8cfd6559c47955793d70602d62a2f9b0bdef5/videogvt/train_lib/losses.py#L279
    LANGUAGE MODEL BEATS DIFFUSION — TOKENIZER IS KEY TO VISUAL GENERATION (2024)
    """
    probs = F.softmax(logits / temperature, -1)
    log_probs = F.log_softmax(logits / temperature + eps, -1)

    if mask is not None:
        # avg_probs = probs[mask].mean(tuple(range(probs.ndim - 1)))
        # avg_probs = einx.mean("... D -> D", probs[mask])

        avg_probs = masked_mean(probs, mask)
        # avg_probs = einx.mean("... D -> D", avg_probs)
    else:
        avg_probs = reduce(probs, "... D -> D", "mean")

    avg_entropy = -torch.sum(avg_probs * torch.log(avg_probs + eps))

    sample_entropy = -torch.sum(probs * log_probs, -1)
    if mask is not None:
        # sample_entropy = sample_entropy[mask].mean()
        sample_entropy = masked_mean(sample_entropy, mask).mean()
    else:
        sample_entropy = torch.mean(sample_entropy)

    loss = (sample_minimization_weight * sample_entropy) - (
        batch_maximization_weight * avg_entropy
    )

    return sample_entropy, avg_entropy, loss


class GFQ(Module):
    def __init__(
        self,
        *,
        dim,
        num_codebooks = 1,
        sample_minimization_weight=1.0,
        batch_maximization_weight=1.0,
    ):
        super().__init__()
        self.token_factorization = num_codebooks > 1
        self.codebook_dim = dim // num_codebooks
        self.codebook_size = 2 ** self.codebook_dim
        self.dim = dim
        self.num_codebooks = num_codebooks
        self.vocab_size = num_codebooks * self.codebook_size
        
        # for entropy loss
        self.sample_minimization_weight = sample_minimization_weight
        self.batch_maximization_weight = batch_maximization_weight
        self.factorized_bits = [self.codebook_dim] * num_codebooks
        for i, factorized_bit in enumerate(self.factorized_bits):
            self.register_buffer(f"mask_{i}", 2 ** torch.arange(factorized_bit), persistent=False)
        
        # codes
        all_codes = torch.arange(self.codebook_size)
        bits = self.indices_to_bits(all_codes)
        codebook = bits * 2.0 - 1.0
        self.register_buffer('codebook', codebook, persistent = False)
        self.register_buffer('zero', torch.tensor(0.), persistent = False)

    @property
    def dtype(self):
        return self.codebook.dtype
    
    def indices_to_bits(self, x):
        """
        x: long tensor of indices

        returns big endian bits
        """
        mask = 2 ** torch.arange(self.codebook_dim, device=x.device, dtype=torch.long)
        x = (x.unsqueeze(-1) & mask) != 0       # x is now big endian bits, the last dimension being the bits
        return x

    def get_codebook_entry(self, x, bhwc, index_order): #0610
        mask = getattr(self, f"mask_{index_order}") if self.token_factorization else self.mask
        mask = mask.to(device=x.device, dtype=torch.long)
        
        x = (x.unsqueeze(-1) & mask) != 0
        x = x * 2.0 - 1.0                #back to the float
        b, h, w, c = bhwc
        x = rearrange(x, "b (h w) c -> b h w c", h=h, w=w, c=c)
        x = rearrange(x, "b h w c -> b c h w")      ## scale back 
        return x

    def bits_to_indices(self, bits):
        """
        bits: bool tensor of big endian bits, where the last dimension is the bit dimension

        returns indices, which are long integers from 0 to self.codebook_size
        """
        assert bits.shape[-1] == self.codebook_dim
        indices = 2 ** torch.arange(
            0,
            self.codebook_dim,
            1,
            dtype=torch.long,
            device=bits.device,
        )
        return (bits * indices).sum(-1)
    
    def decode(self, x):
        """
        x: ... NH
            where NH is number of codebook heads
            A longtensor of codebook indices, containing values from
            0 to self.codebook_size
        """
        x = self.indices_to_bits(x)
        x = x.to(self.dtype)        # to some sort of float
        x = x * 2 - 1               # -1 or 1
        x = rearrange(x, "... NC Z-> ... (NC Z)")
        return x

    def forward(
        self,
        x,
        inv_temperature = 100.,
        return_loss_breakdown = False,
        mask = None,
        return_loss = True,
    ):
        """
        einstein notation
        b - batch
        n - sequence (or flattened spatial dimensions)
        d - feature dimension, which is also log2(codebook size)
        c - number of codebook dim
        """
        x = rearrange(x, 'b d ... -> b ... d')
        x, ps = pack_one(x, 'b * d')
        x = rearrange(x, 'b n (c d) -> b n c d', c = self.num_codebooks)    # split out number of codebooks

        codebook_value = torch.Tensor([1.0]).to(device=x.device, dtype=x.dtype)
        quantized = torch.where(x > 0, codebook_value, -codebook_value)      # higher than 0 filled 

        # calculate indices
        if self.token_factorization:
            quantized = rearrange(quantized, 'b n c d -> b n 1 (c d)')
            indices_list = []
            begin = 0
            end = 0
            for i, factorized_bit in enumerate(self.factorized_bits):
                end += factorized_bit
                mask_name = f"mask_{i}"
                mask = getattr(self, mask_name)
                indices = reduce((quantized[..., begin:end] > 0).int() * mask.int(), "b n c d -> b n c", "sum")
                indices_list.append(indices)
                begin += factorized_bit
            quantized = rearrange(quantized, 'b n 1 (c d) -> b n c d', c = self.num_codebooks)
        else:
            indices = reduce((quantized > 0).int() * self.mask.int(), 'b n c d -> b n c', 'sum')

        # entropy aux loss
        if self.training and return_loss:
            logits = 2 * einsum('... i d, j d -> ... i j', x, self.codebook)
            # the same as euclidean distance up to a constant
            per_sample_entropy, codebook_entropy, entropy_aux_loss = entropy_loss(
                logits = logits,
                sample_minimization_weight = self.sample_minimization_weight,
                batch_maximization_weight = self.batch_maximization_weight
            )

            avg_probs = self.zero
        else:
            per_sample_entropy = codebook_entropy = self.zero
            entropy_aux_loss = self.zero
            avg_probs = self.zero

        # commit loss
        if self.training:
            commit_loss = F.mse_loss(x, quantized.detach(), reduction = 'none')

            if exists(mask):
                commit_loss = commit_loss[mask]

            commit_loss = commit_loss.mean()
        else:
            commit_loss = self.zero


        # use straight-through gradients (optionally with custom activation fn) if training
        if self.training:
            quantized = x + (quantized - x).detach() #transfer to quantized

        # merge back codebook dim
        quantized = rearrange(quantized, 'b n c d -> b n (c d)')

        # reconstitute image or video dimensions
        quantized = unpack_one(quantized, ps, 'b * d')
        quantized = rearrange(quantized, 'b ... d -> b d ...')
        
        if self.token_factorization:
            indices_ = []
            for i, indices in enumerate(indices_list):
                indices = unpack_one(indices, ps, "b * c")
                indices = indices.flatten()
                indices_.append(indices)
            indices = indices_
        else:
            indices = unpack_one(indices, ps, 'b * c')
            indices = indices.flatten()

        ret = (quantized, entropy_aux_loss, indices)

        if not return_loss_breakdown:
            return ret

        return ret, LossBreakdown(per_sample_entropy, codebook_entropy, commit_loss, avg_probs)


if __name__ == "__main__":
    quantizer = GFQ(
    codebook_size = 2**18,      # codebook size, must be a power of 2
    dim = 18,                   # this is the input feature dimension, defaults to log2(codebook_size) if not defined
    sample_minimization_weight = 1.0,        # within entropy loss, how much weight to give to diversity of codes, taken from https://arxiv.org/abs/1911.05894
    batch_maximization_weight = 1.0
)

    image_feats = torch.randn(2, 18, 16, 16) #16 is dim, must be power of 2 of codebook_size

    quantized, indices, entropy_aux_loss = quantizer(image_feats, inv_temperature=100.)  # you may want to experiment with temperature

    assert image_feats.shape == quantized.shape
    assert (quantized == quantizer.indices_to_codes(indices)).all()