aphrodite-engine/aphrodite/processing/block/prefix_caching_block.py

"""Token blocks."""

from os.path import commonprefix
from typing import Dict, FrozenSet, Iterable, List, Optional, Tuple

from aphrodite.common.utils import cdiv
from aphrodite.processing.block.common import (CopyOnWriteTracker,
                                               get_all_blocks_recursively)
from aphrodite.processing.block.interfaces import (Block, BlockAllocator,
                                                   BlockId, Device)
from aphrodite.processing.block.naive_block import (BlockPool, NaiveBlock,
                                                    NaiveBlockAllocator)
from aphrodite.processing.evictor_v2 import (EvictionPolicy, Evictor,
                                             make_evictor)

PrefixHash = int

# By default, we init our block access time as _DEFAULT_LAST_ACCESSED_TIME
# so that if we find one block is still hold _DEFAULT_LAST_ACCESSED_TIME,
# then we know this block hasn't been accessed yet.
_DEFAULT_LAST_ACCESSED_TIME = -1


class BlockTracker:
    """Used to track the status of a block inside the prefix caching allocator
    """
    __slots__ = ("active", "last_accessed", "computed")

    def reset(self):
        self.last_accessed: float = _DEFAULT_LAST_ACCESSED_TIME
        self.computed: bool = False

    def __init__(self):
        self.active: bool = False
        self.reset()

    def enable(self):
        assert not self.active
        self.active = True
        self.reset()

    def disable(self):
        assert self.active
        self.active = False
        self.reset()


class PrefixCachingBlockAllocator(BlockAllocator):
    """A block allocator that implements prefix caching.

    The PrefixCachingBlockAllocator maintains a cache of blocks based on their
    content hash. It reuses blocks with the same content hash to avoid redundant
    memory allocation. The allocator also supports copy-on-write operations.

    Args:
        num_blocks (int): The total number of blocks to manage.
        block_size (int): The size of each block in tokens.
        block_ids(Optional[Iterable[int]], optional): An optional iterable of
            block IDs. If not provided, block IDs will be assigned sequentially
            from 0 to num_blocks - 1.
    """

    def __init__(
        self,
        num_blocks: int,
        block_size: int,
        block_ids: Optional[Iterable[int]] = None,
        eviction_policy: EvictionPolicy = EvictionPolicy.LRU,
    ):
        if block_ids is None:
            block_ids = range(num_blocks)

        self._block_size = block_size

        # A mapping of prefix hash to block index. All blocks which have a
        # prefix hash will be in this dict, even if they have refcount 0.
        self._cached_blocks: Dict[PrefixHash, BlockId] = {}

        # Used to track status of each physical block id
        self._block_tracker: Dict[BlockId, BlockTracker] = {}
        for block_id in block_ids:
            self._block_tracker[block_id] = BlockTracker()

        # Pre-allocate "num_blocks * extra_factor" block objects.
        # The "* extra_factor" is a buffer to allow more block objects
        # than physical blocks
        extra_factor = 4
        self._block_pool = BlockPool(self._block_size, self._create_block,
                                     self, num_blocks * extra_factor)

        # An allocator for blocks that do not have prefix hashes.
        self._hashless_allocator = NaiveBlockAllocator(
            create_block=self._create_block,  # type: ignore
            num_blocks=num_blocks,
            block_size=block_size,
            block_ids=block_ids,
            block_pool=self._block_pool,  # Share block pool here
        )

        # Evitor used to maintain how we want to handle those computed blocks
        # if we find memory pressure is high.
        self.evictor: Evictor = make_evictor(eviction_policy)

        # We share the refcounter between allocators. This allows us to promote
        # blocks originally allocated in the hashless allocator to immutable
        # blocks.
        self._refcounter = self._hashless_allocator.refcounter

        self._cow_tracker = CopyOnWriteTracker(
            refcounter=self._refcounter.as_readonly())

    # Implements Block.Factory.
    def _create_block(
        self,
        prev_block: Optional[Block],
        token_ids: List[int],
        block_size: int,
        allocator: BlockAllocator,
        block_id: Optional[int] = None,
        computed: bool = False,
    ) -> Block:
        # Bind block to self.
        allocator = self

        return PrefixCachingBlock(
            prev_block=prev_block,
            token_ids=token_ids,
            block_size=block_size,
            block_id=block_id,
            allocator=allocator,
            computed=computed,
        )

    def allocate_immutable_block(self,
                                 prev_block: Optional[Block],
                                 token_ids: List[int],
                                 device: Optional[Device] = None) -> Block:
        """Allocates an immutable block with the given token IDs, reusing cached
        blocks if possible.

        Args:
            prev_block (Optional[Block]): The previous block in the sequence.
            token_ids (List[int]): The token IDs to be stored in the block.

        Returns:
            Block: The allocated immutable block.
        """
        assert device is None
        assert_prefix_caching_block_or_none(prev_block)

        # First, try to create a block that points to cached data
        block = self._block_pool.init_block(prev_block=prev_block,
                                            token_ids=token_ids,
                                            block_size=self._block_size,
                                            physical_block_id=None)
        assert block.content_hash is not None

        cached_block_id = self._cached_blocks.get(block.content_hash, None)
        if cached_block_id is not None:
            block.block_id = cached_block_id
            self._incr_refcount_cached_block(block)
            return block
        self._block_pool.free_block(block)

        # No cached block => Allocate a new block
        block = self.allocate_mutable_block(prev_block)
        block.append_token_ids(token_ids)
        return block

    def allocate_immutable_blocks(
            self,
            prev_block: Optional[Block],
            block_token_ids: List[List[int]],
            device: Optional[Device] = None) -> List[Block]:
        blocks = []
        for token_ids in block_token_ids:
            prev_block = self.allocate_immutable_block(prev_block=prev_block,
                                                       token_ids=token_ids,
                                                       device=device)
            blocks.append(prev_block)
        return blocks

    def allocate_mutable_block(self,
                               prev_block: Optional[Block],
                               device: Optional[Device] = None) -> Block:
        """Allocates a mutable block. If there are no free blocks, this will
        evict unused cached blocks.

        Args:
            prev_block (Block): The previous block in the sequence.
                None is not allowed unlike it is super class.

        Returns:
            Block: The allocated mutable block.
        """
        assert device is None
        assert_prefix_caching_block_or_none(prev_block)

        block_id = self._allocate_block_id()
        block = self._block_pool.init_block(prev_block=prev_block,
                                            token_ids=[],
                                            block_size=self._block_size,
                                            physical_block_id=block_id)
        assert not block.computed
        assert block.content_hash is None
        return block

    def _incr_refcount_cached_block(self, block: Block) -> None:
        # Set this block to be "computed" since it is pointing to a
        # cached block id (which was already computed)
        block.computed = True

        block_id = block.block_id
        assert block_id is not None

        refcount = self._refcounter.incr(block_id)
        if refcount == 1:
            # In case a cached block was evicted, restore its tracking
            if block_id in self.evictor:
                self.evictor.remove(block_id)

            self._track_block_id(block_id, computed=True)

    def _decr_refcount_cached_block(self, block: Block) -> None:
        # Ensure this is immutable/cached block
        assert block.content_hash is not None

        block_id = block.block_id
        assert block_id is not None

        refcount = self._refcounter.decr(block_id)
        if refcount > 0:
            block.block_id = None
            return
        else:
            assert refcount == 0

        # No longer used
        assert block.content_hash in self._cached_blocks

        # Add the cached block to the evictor
        # (This keeps the cached block around so it can be reused)
        self.evictor.add(block_id, block.content_hash, block.num_tokens_total,
                         self._block_tracker[block_id].last_accessed)

        # Stop tracking the block
        self._untrack_block_id(block_id)

        block.block_id = None

    def _decr_refcount_hashless_block(self, block: Block) -> None:
        block_id = block.block_id
        assert block_id is not None

        # We may have a fork case where block is shared,
        # in which case, we cannot remove it from tracking
        refcount = self._refcounter.get(block_id)
        if refcount == 1:
            self._untrack_block_id(block_id)

        # Decrement refcount of the block_id, but do not free the block object
        # itself (will be handled by the caller)
        self._hashless_allocator.free(block, keep_block_object=True)

    def _allocate_block_id(self) -> BlockId:
        """First tries to allocate a block id from the hashless allocator,
        and if there are no blocks, then tries to evict an unused cached block.
        """
        hashless_block_id = self._maybe_allocate_hashless_block_id()
        if hashless_block_id is not None:
            return hashless_block_id

        evicted_block_id = self._maybe_allocate_evicted_block_id()
        if evicted_block_id is not None:
            return evicted_block_id

        # No block available in hashless allocator, nor in unused cache blocks.
        raise BlockAllocator.NoFreeBlocksError()

    def _maybe_allocate_hashless_block_id(self) -> Optional[BlockId]:
        try:
            # Allocate mutable block and extract its block_id
            block = self._hashless_allocator.allocate_mutable_block(
                prev_block=None)
            block_id = block.block_id
            self._block_pool.free_block(block)

            self._track_block_id(block_id, computed=False)
            return block_id
        except BlockAllocator.NoFreeBlocksError:
            return None

    def _maybe_allocate_evicted_block_id(self) -> Optional[BlockId]:
        if self.evictor.num_blocks == 0:
            return None

        # Here we get an evicted block, which is only added
        # into evictor if its ref counter is 0
        # and since its content would be changed, we need
        # to remove it from _cached_blocks's tracking list
        block_id, content_hash_to_evict = self.evictor.evict()

        # Sanity checks
        assert content_hash_to_evict in self._cached_blocks
        _block_id = self._cached_blocks[content_hash_to_evict]
        assert self._refcounter.get(_block_id) == 0
        assert _block_id == block_id

        self._cached_blocks.pop(content_hash_to_evict)

        self._refcounter.incr(block_id)
        self._track_block_id(block_id, computed=False)

        return block_id

    def _free_block_id(self, block: Block) -> None:
        """Decrements the refcount of the block. The block may be in two 
        possible states: (1) immutable/cached or (2) mutable/hashless. 
        In the first case, the refcount is decremented directly and the block
        may be possibly added to the evictor. In other case, hashless 
        allocator free(..) with keep_block_object=True is called to only free
        the block id (since the block object may be reused by the caller)
        """
        block_id = block.block_id
        assert block_id is not None, "Freeing unallocated block is undefined"

        if block.content_hash is not None:
            # Immutable: This type of block is always cached, and we want to
            # keep it in the evictor for future reuse
            self._decr_refcount_cached_block(block)
        else:
            # Mutable: This type of block is not cached, so we release it
            # directly to the hashless allocator
            self._decr_refcount_hashless_block(block)

        assert block.block_id is None

    def free(self, block: Block, keep_block_object: bool = False) -> None:
        """Release the block (look at free_block_id(..) docs)
        """
        # Release the physical block index
        self._free_block_id(block)

        # Release the block object to the pool
        if not keep_block_object:
            self._block_pool.free_block(block)

    def fork(self, last_block: Block) -> List[Block]:
        """Creates a new sequence of blocks that shares the same underlying
        memory as the original sequence.

        Args:
            last_block (Block): The last block in the original sequence.

        Returns:
            List[Block]: The new sequence of blocks that shares the same memory
                as the original sequence.
        """
        source_blocks = get_all_blocks_recursively(last_block)

        forked_blocks: List[Block] = []
        prev_block = None
        for block in source_blocks:
            block_id = block.block_id
            assert block_id is not None

            refcount = self._refcounter.incr(block_id)
            assert refcount != 1, "can't fork free'd block_id = {}".format(
                block_id)

            forked_block = self._block_pool.init_block(
                prev_block=prev_block,
                token_ids=block.token_ids,
                block_size=self._block_size,
                physical_block_id=block_id)

            forked_blocks.append(forked_block)
            prev_block = forked_blocks[-1]

        return forked_blocks

    def get_num_free_blocks(self, device: Optional[Device] = None) -> int:
        assert device is None
        # The number of free blocks is the number of hashless free blocks
        # plus the number of blocks evictor could free from its list.
        return self._hashless_allocator.get_num_free_blocks(
        ) + self.evictor.num_blocks

    def get_num_total_blocks(self) -> int:
        return self._hashless_allocator.get_num_total_blocks()

    def get_physical_block_id(self, absolute_id: int) -> int:
        """Returns the zero-offset block id on certain block allocator
        given the absolute block id.

        Args:
            absolute_id (int): The absolute block id for the block 
                in whole allocator.

        Returns:
            int: The rzero-offset block id on certain device.
        """
        return sorted(self.all_block_ids).index(absolute_id)

    @property
    def all_block_ids(self) -> FrozenSet[int]:
        return self._hashless_allocator.all_block_ids

    def is_block_cached(self, block: Block) -> bool:
        assert block.content_hash is not None
        if block.content_hash in self._cached_blocks:
            return True
        return False

    def promote_to_immutable_block(self, block: Block) -> BlockId:
        """Once a mutable block is full, it can be promoted to an immutable
        block. This means that its content can be referenced by future blocks
        having the same prefix.

        Note that if we already have a cached block with the same content, we
        will replace the newly-promoted block's mapping with the existing cached
        block id.

        Args:
            block: The mutable block to be promoted.

        Returns:
            BlockId: Either the original block index, or the block index of
                the previously cached block matching the same content.
        """
        # Ensure block can be promoted
        assert block.content_hash is not None
        assert block.block_id is not None
        assert self._refcounter.get(block.block_id) > 0

        if block.content_hash not in self._cached_blocks:
            # No cached content hash => Set this block as cached
            # (Note that this block is not computed yet =>
            #  Will be computed after free())
            self._cached_blocks[block.content_hash] = block.block_id
            return block.block_id

        # Reuse the cached content hash
        self._decr_refcount_hashless_block(block)
        block.block_id = self._cached_blocks[block.content_hash]

        # Increment refcount of the cached block and (possibly) restore
        # it from the evictor.
        # Note that in this case, the block is marked as computed
        self._incr_refcount_cached_block(block)

        return block.block_id

    def cow_block_if_not_appendable(self, block: Block) -> BlockId:
        """Performs a copy-on-write operation on the given block if it is not
        appendable.

        Args:
            block (Block): The block to check for copy-on-write.

        Returns:
            BlockId: The block index of the new block if a copy-on-write 
                operation was performed, or the original block index if
                no copy-on-write was necessary.
        """
        src_block_id = block.block_id
        assert src_block_id is not None

        if self._cow_tracker.is_appendable(block):
            return src_block_id

        self._free_block_id(block)
        trg_block_id = self._allocate_block_id()

        self._cow_tracker.record_cow(src_block_id, trg_block_id)

        return trg_block_id

    def clear_copy_on_writes(self) -> List[Tuple[BlockId, BlockId]]:
        """Returns the copy-on-write source->destination mapping and clears it.

        Returns:
            List[Tuple[BlockId, BlockId]]: A list mapping source
                block indices to destination block indices.
        """
        return self._cow_tracker.clear_cows()

    def mark_blocks_as_accessed(self, block_ids: List[int],
                                now: float) -> None:
        """Mark blocks as accessed, used in prefix caching.

        If the block is added into evictor, we need to update corresponding
        info in evictor's metadata.
        """

        for block_id in block_ids:
            if self._block_tracker[block_id].active:
                self._block_tracker[block_id].last_accessed = now
            elif block_id in self.evictor:
                self.evictor.update(block_id, now)
            else:
                raise ValueError(
                    "Mark block as accessed which is not belonged to GPU")

    def mark_blocks_as_computed(self, block_ids: List[int]) -> None:
        raise NotImplementedError("Marking as computed is incremental")

    def _track_block_id(self, block_id: Optional[BlockId],
                        computed: bool) -> None:
        assert block_id is not None
        self._block_tracker[block_id].enable()
        self._block_tracker[block_id].computed = computed

    def _untrack_block_id(self, block_id: Optional[BlockId]) -> None:
        assert block_id is not None
        self._block_tracker[block_id].disable()

    def block_is_computed(self, block_id: int) -> bool:
        if self._block_tracker[block_id].active:
            return self._block_tracker[block_id].computed
        else:
            return block_id in self.evictor

    def get_computed_block_ids(self,
                               prev_computed_block_ids: List[int],
                               block_ids: List[int],
                               skip_last_block_id: bool = True) -> List[int]:
        prev_prefix_size = len(prev_computed_block_ids)
        cur_size = len(block_ids)
        if skip_last_block_id:
            cur_size -= 1

        # Sanity checks
        assert cur_size >= 0
        assert prev_prefix_size <= cur_size

        ret = prev_computed_block_ids
        for i in range(prev_prefix_size, cur_size):
            block_id = block_ids[i]
            if self.block_is_computed(block_id):
                ret.append(block_id)
        return ret

    def get_common_computed_block_ids(
            self, computed_seq_block_ids: List[List[int]]) -> List[int]:
        """Return the block ids that are common for a given sequence group.

        Only those blocks that are immutable and already be marked
        compyted would be taken consideration.
        """

        # NOTE We exclude the last block to avoid the case where the entire
        # prompt is cached. This would cause erroneous behavior in model
        # runner.

        # It returns a list of int although type annotation says list of string.
        if len(computed_seq_block_ids) == 1:
            return computed_seq_block_ids[0]

        return commonprefix([
            ids for ids in computed_seq_block_ids  # type: ignore
            if ids
        ])

    def get_num_blocks_touched(self,
                               blocks: List[Block],
                               num_lookahead_slots: int = 0) -> int:
        """Determine the number of blocks that will be touched by
        swapping in/out the given blocks from certain sequence
        group with the provided num_lookahead_slots.

        Args:
            blocks (List[Block]): The potential blocks to swap.
            num_lookahead_slots (int): number of lookahead slots (0 for 
                swap out).
        
        Returns:
            int: the number of blocks that will be touched by
                swapping in/out the given blocks and num_lookahead_slots.
        """
        num_touched_blocks = 0
        for block in blocks:
            if not block.is_full:
                if block.num_empty_slots >= num_lookahead_slots:
                    num_touched_blocks += 1
                else:
                    num_touched_blocks += cdiv(
                        num_lookahead_slots - block.num_empty_slots,
                        self._block_size)
            else:
                if not self.is_block_cached(block):
                    num_touched_blocks += 1
        return num_touched_blocks

    def swap_out(self, blocks: List[Block]) -> None:
        """Execute the swap out actions. Basically just free the 
        given blocks.

        Args:
            blocks: List of blocks to be swapped out.
        """
        for block in blocks:
            self._free_block_id(block)

    def swap_in(self, blocks: List[Block]) -> None:
        """Execute the swap in actions. Change the block id from 
        old allocator to current allocator for each block to finish 
        the block table update. 

        Args:
            blocks: List of blocks to be swapped in.
        """
        for block in blocks:
            # Here we allocate either immutable or mutable block and then
            # extract its block_id. Note that the block object is released
            # and the block_id is assigned to "block" to allow reusing the
            # existing "block" object
            if block.is_full:
                tmp_block = self.allocate_immutable_block(
                    prev_block=block.prev_block, token_ids=block.token_ids)
            else:
                tmp_block = self.allocate_mutable_block(
                    prev_block=block.prev_block)
                tmp_block.append_token_ids(block.token_ids)

            block_id = tmp_block.block_id
            self._block_pool.free_block(tmp_block)

            block.block_id = block_id  # Assign block_id


class PrefixCachingBlock(Block):
    """A block implementation that supports prefix caching.

    The PrefixCachingBlock class represents a block of token IDs with prefix
    caching capabilities. It wraps a NaiveBlock internally and provides
    additional functionality for content hashing and promoting immutable blocks
    with the prefix caching allocator.

    Args:
        prev_block (Optional[PrefixCachingBlock]): The previous block in the
            sequence.
        token_ids (List[int]): The initial token IDs to be stored in the block.
        block_size (int): The maximum number of token IDs that can be stored in
            the block.
        allocator (BlockAllocator): The prefix
            caching block allocator associated with this block.
        block_id (Optional[int], optional): The physical block index
            of this block. Defaults to None.
    """

    def __init__(
        self,
        prev_block: Optional[Block],
        token_ids: List[int],
        block_size: int,
        allocator: BlockAllocator,
        block_id: Optional[int] = None,
        computed: bool = False,
    ):
        assert isinstance(allocator, PrefixCachingBlockAllocator), (
            "Currently this class is only tested with "
            "PrefixCachingBlockAllocator. Got instead allocator = {}".format(
                allocator))
        assert_prefix_caching_block_or_none(prev_block)

        self._prev_block = prev_block
        self._cached_content_hash: Optional[int] = None
        self._cached_num_tokens_total: int = 0
        self._allocator = allocator
        self._last_accessed: float = _DEFAULT_LAST_ACCESSED_TIME
        self._computed = computed

        # On the first time, we create the block object, and next we only
        # reinitialize it
        if hasattr(self, "_block"):
            self._block.__init__(  # type: ignore[has-type]
                prev_block=prev_block,
                token_ids=token_ids,
                block_size=block_size,
                block_id=block_id,
                allocator=self._allocator)
        else:
            self._block = NaiveBlock(prev_block=prev_block,
                                     token_ids=token_ids,
                                     block_size=block_size,
                                     block_id=block_id,
                                     allocator=self._allocator)

        self._update_num_tokens_total()

    def _update_num_tokens_total(self):
        """Incrementally computes the number of tokens that there is
        till the current block (included)
        """
        res = 0

        # Add all previous blocks
        if self._prev_block is not None:
            res += self._prev_block.num_tokens_total

        # Add current block
        res += len(self.token_ids)

        self._cached_num_tokens_total = res

    @property
    def computed(self) -> bool:
        return self._computed

    @computed.setter
    def computed(self, value) -> None:
        self._computed = value

    @property
    def last_accessed(self) -> float:
        return self._last_accessed

    @last_accessed.setter
    def last_accessed(self, last_accessed_ts: float):
        self._last_accessed = last_accessed_ts

    def append_token_ids(self, token_ids: List[int]) -> None:
        """Appends the given token IDs to the block and registers the block as
        immutable if the block becomes full.

        Args:
            token_ids (List[int]): The token IDs to be appended to the block.
        """
        # Ensure this is mutable block (not promoted)
        assert self.content_hash is None
        assert not self.computed

        if len(token_ids) == 0:
            return

        # Ensure there are input tokens
        assert token_ids, "Got token_ids = {}".format(token_ids)

        # Naive block handles CoW.
        self._block.append_token_ids(token_ids)
        self._update_num_tokens_total()

        # If the content hash is present, then the block can be made immutable.
        # Register ourselves with the allocator, potentially replacing the
        # physical block index.
        if self.content_hash is not None:
            self.block_id = self._allocator.promote_to_immutable_block(self)

    @property
    def block_id(self) -> Optional[int]:
        return self._block.block_id

    @block_id.setter
    def block_id(self, value) -> None:
        self._block.block_id = value

    @property
    def is_full(self) -> bool:
        return self._block.is_full

    @property
    def num_empty_slots(self) -> int:
        return self._block.num_empty_slots

    @property
    def num_tokens_total(self) -> int:
        return self._cached_num_tokens_total

    @property
    def block_size(self) -> int:
        return self._block.block_size

    @property
    def token_ids(self) -> List[int]:
        return self._block.token_ids

    @property
    def prev_block(self) -> Optional[Block]:
        return self._prev_block

    @property
    def content_hash(self) -> Optional[int]:
        """Return the content-based hash of the current block, or None if it is
        not yet defined.

        For the content-based hash to be defined, the current block must be
        full.
        """
        # If the hash is already computed, return it.
        if self._cached_content_hash is not None:
            return self._cached_content_hash

        # We cannot compute a hash for the current block because it is not full.
        if not self.is_full:
            return None

        is_first_block = self._prev_block is None
        prev_block_hash = (
            None if is_first_block else
            self._prev_block.content_hash  # type: ignore
        )

        # Previous block exists but does not yet have a hash.
        # Return no hash in this case.
        if prev_block_hash is None and not is_first_block:
            return None

        self._cached_content_hash = PrefixCachingBlock.hash_block_tokens(
            is_first_block,
            prev_block_hash,
            cur_block_token_ids=self.token_ids)
        return self._cached_content_hash

    @staticmethod
    def hash_block_tokens(is_first_block: bool, prev_block_hash: Optional[int],
                          cur_block_token_ids: List[int]) -> int:
        """Computes a hash value corresponding to the contents of a block and
        the contents of the preceding block(s). The hash value is used for
        prefix caching.

        NOTE: Content-based hashing does not yet support LoRA.

        Parameters:
        - is_first_block (bool): A flag indicating if the block is the first in
            the sequence.
        - prev_block_hash (Optional[int]): The hash of the previous block. None
            if this is the first block.
        - cur_block_token_ids (List[int]): A list of token ids in the current
            block. The current block is assumed to be full.

        Returns:
        - int: The computed hash value for the block.
        """
        assert (prev_block_hash is None) == is_first_block
        return hash((is_first_block, prev_block_hash, *cur_block_token_ids))


class ComputedBlocksTracker:
    """Handles caching of per-sequence computed block ids. 
        When a sequence appears for the first time, it traverses all of the 
        blocks and detects the prefix of blocks that is computed. On the
        subsequent times, it only traverses the new blocks that were added 
        and updates the already recorded prefix of blocks with the newly 
        computed blocks.

        To avoid redundant traversals, the algorithm also detects when there
        is a "gap" in the computed prefix. For example, if we have blocks =
        [1,2,3,4,5], and we have detected [1,2,3] as the computed prefix, then
        we won't try to add more computed blocks to [1,2,3] in this sequence
        iteration, and will add more computed blocks only after the sequence is
        freed and reused again.

        Note that currently, for a given sequence, we also skip the last 
        block id for caching purposes, to avoid caching of a full sequence
    """

    def __init__(self, allocator):
        self._allocator = allocator
        self._cached_computed_seq_blocks: Dict[int, Tuple[List[int],
                                                          bool]] = {}

    def add_seq(self, seq_id: int) -> None:
        """Start tracking seq_id
        """
        assert seq_id not in self._cached_computed_seq_blocks
        self._cached_computed_seq_blocks[seq_id] = ([], False)

    def remove_seq(self, seq_id: int) -> None:
        """Stop tracking seq_id
        """
        assert seq_id in self._cached_computed_seq_blocks
        del self._cached_computed_seq_blocks[seq_id]

    def get_cached_computed_blocks_and_update(
            self, seq_id: int, block_ids: List[int]) -> List[int]:
        """ Look at the class documentation for details
        """
        # Ensure seq_id is already tracked
        assert seq_id in self._cached_computed_seq_blocks

        # Get cached data (may be empty on the first time)
        prev_computed_block_ids, has_gap = self._cached_computed_seq_blocks[
            seq_id]

        if has_gap:
            # When gap is detected, we do not add more computed blocks at this
            # sequence iteration
            return prev_computed_block_ids

        # We do not consider the last block id for caching purposes.
        num_cur_blocks = len(block_ids) - 1
        assert num_cur_blocks >= 0

        if len(prev_computed_block_ids) >= num_cur_blocks:
            # Cache HIT
            assert len(prev_computed_block_ids) == num_cur_blocks
            return prev_computed_block_ids

        # If here, then we may possibly add more computed blocks. As a result,
        # traverse the additional blocks after prev_computed_block_ids to
        # detect more computed blocks and add them.

        # Incremental init for seq_id => Look only at the new blocks
        computed_block_ids = self._allocator.get_computed_block_ids(  # noqa: E501
            prev_computed_block_ids,
            block_ids,
            skip_last_block_id=
            True,  # We skip last block id to avoid caching of full seq
        )

        # Detect if there is a "gap"
        has_gap = len(computed_block_ids) < num_cur_blocks

        # Record
        self._cached_computed_seq_blocks[seq_id] = (computed_block_ids,
                                                    has_gap)

        return computed_block_ids


class LastAccessBlocksTracker:
    """Manages the last access time of the tracked sequences, in order to allow
    an efficient update of allocator's block last access times
    """

    def __init__(self, allocator):
        self._allocator = allocator
        self._seq_last_access: Dict[int, Optional[float]] = {}

    def add_seq(self, seq_id: int) -> None:
        """Start tracking seq_id
        """
        assert seq_id not in self._seq_last_access
        self._seq_last_access[seq_id] = None

    def remove_seq(self, seq_id: int) -> None:
        """Stop tracking seq_id
        """
        assert seq_id in self._seq_last_access
        del self._seq_last_access[seq_id]

    def update_last_access(self, seq_id: int, time: float) -> None:
        assert seq_id in self._seq_last_access
        self._seq_last_access[seq_id] = time

    def update_seq_blocks_last_access(self, seq_id: int,
                                      block_ids: List[int]) -> None:
        assert seq_id in self._seq_last_access

        ts = self._seq_last_access[seq_id]

        if ts is None:
            # No last access was recorded, no need to update.
            return

        self._allocator.mark_blocks_as_accessed(block_ids, ts)


def assert_prefix_caching_block_or_none(block: Optional[Block]):
    if block is None:
        return
    assert isinstance(block,
                      PrefixCachingBlock), "Got block = {}".format(block)