# original source:
#   https://github.com/AminRezaei0x443/memory-efficient-attention/blob/1bc0d9e6ac5f82ea43a375135c4e1d3896ee1694/memory_efficient_attention/attention_torch.py
# license:
#   MIT
# credit:
#   Amin Rezaei (original author)
#   Alex Birch (optimized algorithm for 3D tensors, at the expense of removing bias, masking and callbacks)
# implementation of:
#   Self-attention Does Not Need O(n2) Memory":
#   https://arxiv.org/abs/2112.05682v2

from functools import partial
import torch
from torch import Tensor
from torch.utils.checkpoint import checkpoint
import math
from typing import Optional, NamedTuple, Protocol, List

from torch import Tensor
from typing import List

def dynamic_slice(
    x: Tensor,
    starts: List[int],
    sizes: List[int],
) -> Tensor:
    slicing = [slice(start, start + size) for start, size in zip(starts, sizes)]
    return x[slicing]

class AttnChunk(NamedTuple):
    exp_values: Tensor
    exp_weights_sum: Tensor
    max_score: Tensor

class SummarizeChunk(Protocol):
    @staticmethod
    def __call__(
        query: Tensor,
        key_t: Tensor,
        value: Tensor,
    ) -> AttnChunk: ...

class ComputeQueryChunkAttn(Protocol):
    @staticmethod
    def __call__(
        query: Tensor,
        key_t: Tensor,
        value: Tensor,
    ) -> Tensor: ...

def _summarize_chunk(
    query: Tensor,
    key_t: Tensor,
    value: Tensor,
    scale: float,
) -> AttnChunk:
    attn_weights = torch.baddbmm(
        torch.empty(1, 1, 1, device=query.device, dtype=query.dtype),
        query,
        key_t,
        alpha=scale,
        beta=0,
    )
    max_score, _ = torch.max(attn_weights, -1, keepdim=True)
    max_score = max_score.detach()
    exp_weights = torch.exp(attn_weights - max_score)
    exp_values = torch.bmm(exp_weights, value)
    max_score = max_score.squeeze(-1)
    return AttnChunk(exp_values, exp_weights.sum(dim=-1), max_score)

def _query_chunk_attention(
    query: Tensor,
    key_t: Tensor,
    value: Tensor,
    summarize_chunk: SummarizeChunk,
    kv_chunk_size: int,
) -> Tensor:
    batch_x_heads, k_channels_per_head, k_tokens = key_t.shape
    _, _, v_channels_per_head = value.shape

    def chunk_scanner(chunk_idx: int) -> AttnChunk:
        key_chunk = dynamic_slice(
            key_t,
            (0, 0, chunk_idx),
            (batch_x_heads, k_channels_per_head, kv_chunk_size)
        )
        value_chunk = dynamic_slice(
            value,
            (0, chunk_idx, 0),
            (batch_x_heads, kv_chunk_size, v_channels_per_head)
        )
        return summarize_chunk(query, key_chunk, value_chunk)

    chunks: List[AttnChunk] = [
        chunk_scanner(chunk) for chunk in torch.arange(0, k_tokens, kv_chunk_size)
    ]
    acc_chunk = AttnChunk(*map(torch.stack, zip(*chunks)))
    chunk_values, chunk_weights, chunk_max = acc_chunk

    global_max, _ = torch.max(chunk_max, 0, keepdim=True)
    max_diffs = torch.exp(chunk_max - global_max)
    chunk_values *= torch.unsqueeze(max_diffs, -1)
    chunk_weights *= max_diffs

    all_values = chunk_values.sum(dim=0)
    all_weights = torch.unsqueeze(chunk_weights, -1).sum(dim=0)
    return all_values / all_weights

# TODO: refactor CrossAttention#get_attention_scores to share code with this
def _get_attention_scores_no_kv_chunking(
    query: Tensor,
    key_t: Tensor,
    value: Tensor,
    scale: float,
) -> Tensor:
    attn_scores = torch.baddbmm(
        torch.empty(1, 1, 1, device=query.device, dtype=query.dtype),
        query,
        key_t,
        alpha=scale,
        beta=0,
    )
    attn_probs = attn_scores.softmax(dim=-1)
    del attn_scores
    hidden_states_slice = torch.bmm(attn_probs, value)
    return hidden_states_slice

class ScannedChunk(NamedTuple):
    chunk_idx: int
    attn_chunk: AttnChunk

def efficient_dot_product_attention(
    query: Tensor,
    key_t: Tensor,
    value: Tensor,
    query_chunk_size=1024,
    kv_chunk_size: Optional[int] = None,
    kv_chunk_size_min: Optional[int] = None,
    use_checkpoint=True,
):
    """Computes efficient dot-product attention given query, transposed key, and value.
      This is efficient version of attention presented in
      https://arxiv.org/abs/2112.05682v2 which comes with O(sqrt(n)) memory requirements.
      Args:
        query: queries for calculating attention with shape of
          `[batch * num_heads, tokens, channels_per_head]`.
        key_t: keys for calculating attention with shape of
          `[batch * num_heads, channels_per_head, tokens]`.
        value: values to be used in attention with shape of
          `[batch * num_heads, tokens, channels_per_head]`.
        query_chunk_size: int: query chunks size
        kv_chunk_size: Optional[int]: key/value chunks size. if None: defaults to sqrt(key_tokens)
        kv_chunk_size_min: Optional[int]: key/value minimum chunk size. only considered when kv_chunk_size is None. changes `sqrt(key_tokens)` into `max(sqrt(key_tokens), kv_chunk_size_min)`, to ensure our chunk sizes don't get too small (smaller chunks = more chunks = less concurrent work done).
        use_checkpoint: bool: whether to use checkpointing (recommended True for training, False for inference)
      Returns:
        Output of shape `[batch * num_heads, query_tokens, channels_per_head]`.
      """
    batch_x_heads, q_tokens, q_channels_per_head = query.shape
    _, _, k_tokens = key_t.shape
    scale = q_channels_per_head ** -0.5

    kv_chunk_size = min(kv_chunk_size or int(math.sqrt(k_tokens)), k_tokens)
    if kv_chunk_size_min is not None:
        kv_chunk_size = max(kv_chunk_size, kv_chunk_size_min)

    def get_query_chunk(chunk_idx: int) -> Tensor:
        return dynamic_slice(
            query,
            (0, chunk_idx, 0),
            (batch_x_heads, min(query_chunk_size, q_tokens), q_channels_per_head)
        )
    
    summarize_chunk: SummarizeChunk = partial(_summarize_chunk, scale=scale)
    summarize_chunk: SummarizeChunk = partial(checkpoint, summarize_chunk) if use_checkpoint else summarize_chunk
    compute_query_chunk_attn: ComputeQueryChunkAttn = partial(
        _get_attention_scores_no_kv_chunking,
        scale=scale
    ) if k_tokens <= kv_chunk_size else (
        # fast-path for when there's just 1 key-value chunk per query chunk (this is just sliced attention btw)
        partial(
            _query_chunk_attention,
            kv_chunk_size=kv_chunk_size,
            summarize_chunk=summarize_chunk,
        )
    )

    if q_tokens <= query_chunk_size:
        # fast-path for when there's just 1 query chunk
        return compute_query_chunk_attn(
            query=query,
            key_t=key_t,
            value=value,
        )
    
    # TODO: maybe we should use torch.empty_like(query) to allocate storage in-advance,
    # and pass slices to be mutated, instead of torch.cat()ing the returned slices
    res = torch.cat([
        compute_query_chunk_attn(
            query=get_query_chunk(i * query_chunk_size),
            key_t=key_t,
            value=value,
        ) for i in range(math.ceil(q_tokens / query_chunk_size))
    ], dim=1)
    return res
