# Copyright 2025 The HuggingFace Inc. team. # # 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. from math import floor, gcd, sqrt import torch from ...configuration_utils import PreTrainedConfig from ...generation.configuration_utils import GenerationConfig from ...utils.generic import is_flash_attention_requested from ...utils.metrics import attach_tracer, traced from .cache_manager import BlockManager, CacheAllocator, FullAttentionCacheAllocator, SlidingAttentionCacheAllocator from .requests import RequestState, RequestStatus, get_device_and_memory_breakdown, logger def group_layers_by_attn_type(config: PreTrainedConfig) -> tuple[list[list[int]], list[str]]: """ Group layers depending on the attention mix, according to VLLM's hybrid allocator rules: - Layers in each group need to have the same type of attention - All groups have the same number of layers For a model with the following layer types: ["sliding", "full", "full", "sliding", "full", "full", "full", "full"] We would get four groups: [0, 3], [1, 2], [4,5] and [6,7]. """ # If the config has no layer_type attribute, it means all layers are the same attention type layer_types = getattr(config, "layer_types", None) if layer_types is None: attn_type = "sliding_attention" if getattr(config, "sliding_window", None) is not None else "full_attention" layer_types = [attn_type for _ in range(config.num_hidden_layers)] # We then count the number of layers of each type layer_counts = {} for i, layer_type in enumerate(layer_types): layer_counts[layer_type] = layer_counts.get(layer_type, []) + [i] # The size of all groups is the greatest common divisor of the number of layers of each type group_size = gcd(*[len(indices) for indices in layer_counts.values()]) # We then group the layers by type layer_groups = [] for layer_type, indices in layer_counts.items(): for i in range(0, len(indices), group_size): layer_groups.append(indices[i : i + group_size]) # And note the layer types group_types = [layer_types[lg[0]] for lg in layer_groups] return layer_groups, group_types @attach_tracer() class PagedAttentionCache: """ Manages the cache for a paged attention mechanism, inspired by VLLM's hybrid allocator. The cache relies on making groups of layers to reduce the complexity of cache management and fragmentation. The cache uses a three-level hierarchy: - Pages: The smallest unit of cache, a page has a size of [num_heads, head_size], which is the space needed to store the key or value states for one token and one layer. For a model with only full-attention layers, to store the KV cache of one token, we need `2 * num_layers` pages: key and values each take `num_layers` pages. Pages are grouped into blocks: - Blocks: A block is a collection of `block_size` pages, serving as the allocation unit to reduce management complexity and fragmentation. Cache is allocated and freed block by block, not page by page. One block is allocated to one layer group, which only has one attention type, like full-attention or sliding-attention. If all layers in the model have the same attention type, then all layers will be in the same group. There is more than one group if and only if the model has a mixed attention types, like layers with full-attention and layers with sliding-attention. - Cache tensors: The physical supports for the cache. There are as many cache tensors as there are layer in a layer group, and the shape of the cache tensor is `[num_blocks * block_size, num_heads, head_size]`. Grouping layers into groups is useful because when we allocate one block to a group N, the block allocated is the same for all layers in group N, equivalently it is allocated across all cache tensors. This allows us to efficiently allocate and free blocks, and to efficiently read and write key and value states. For instance, imagine we have 8 blocks of cache and a model with two layer groups: a full-attention group with 3 layers and a sliding-attention group with 3 layers. At creation time, the physical cache tensors look like this: cache_tensor_0: □ □ □ □ □ □ □ □ cache_tensor_1: □ □ □ □ □ □ □ □ cache_tensor_2: □ □ □ □ □ □ □ □ where □ means the blocks is not allocated to any layer group yet. We have 3 cache tensors because there are 3 layers per group. We allocate 1 block to each group, after allocation, the cache tensors look like this: cache_tensor_0: ✖ ◉ □ □ □ □ □ □ cache_tensor_1: ✖ ◉ □ □ □ □ □ □ cache_tensor_2: ✖ ◉ □ □ □ □ □ □ where ✖ means the block is allocated to the full-attention group, and ◉ means the block is allocated to the sliding-attention group. Now, if we continue to generate, and the sliding window has been reached, we only need to allocate a new block for the full-attention group, and the cache tensors look like this: cache_tensor_0: ✖ ◉ ✖ □ □ □ □ □ cache_tensor_1: ✖ ◉ ✖ □ □ □ □ □ cache_tensor_2: ✖ ◉ ✖ □ □ □ □ □ And after further generation, when we need a new block allocated: cache_tensor_0: ✖ ◉ ✖ ✖ □ □ □ □ cache_tensor_1: ✖ ◉ ✖ ✖ □ □ □ □ cache_tensor_2: ✖ ◉ ✖ ✖ □ □ □ □ This would not have been possible if all layers were in the same group: we would have had to allocate a new block for the sliding-attention group, although it is not needed. """ def __init__( self, config: PreTrainedConfig, generation_config: GenerationConfig, device: torch.device | str, dtype: torch.dtype = torch.float16, tp_size: int | None = None, allow_block_sharing: bool = True, ) -> None: """Initialize a paged attention cache for efficient memory usage. Also turns in prefix sharing if the model has only full attention layers. Args: config: Model configuration generation_config: Generation configuration containing cache parameters device: Device for the cache tensors dtype: Data type of the cache tp_size: Tensor parallelism size allow_block_sharing: A flag to allow block sharing. If the model has some full attention layers, then prefix sharing is enabled as well. """ self.config = config self.dtype = dtype self.device = device # Extract model dimensions kv_heads = getattr(config, "num_key_value_heads", None) self.num_key_value_heads: int = kv_heads if kv_heads is not None else config.num_attention_heads head_dim = getattr(config, "head_dim", None) self.head_dim: int = head_dim if head_dim is not None else config.hidden_size // config.num_attention_heads # Extract cache dimensions self.block_size = getattr(generation_config, "block_size", 32) # Group layers depending on the attention mix layer_groups, group_types = group_layers_by_attn_type(config) group_size = len(layer_groups[0]) self.num_groups = len(layer_groups) self.sliding_windows = {} self.layer_index_to_group_indices = {} for i, group in enumerate(layer_groups): sliding_window = config.sliding_window if group_types[i] == "sliding_attention" else 1 for j, layer in enumerate(group): self.layer_index_to_group_indices[layer] = (i, j) self.sliding_windows[layer] = sliding_window # Handle TP (or dont) if tp_size is not None and tp_size > 1: if self.num_key_value_heads % tp_size != 0: raise ValueError( f"Number of key value heads {self.num_key_value_heads} must be divisible by tensor parallel size {tp_size}." ) # If the model is using tensor parallelism, we need to adjust the number of heads accordingly. # self.num_key_value_heads //= tp_size # TODO: why is this commented out? # Infer number of blocks and max batch tokens page_size = self.head_dim * self.num_key_value_heads if is_flash_attention_requested(self.config): num_attention_masks = 0 # only used to compute the default memory footprint args elif "sliding_attention" in group_types: # TODO: when we generalize to allow for block-attn, we can use `num_attention_masks=sum(set(group_types))` num_attention_masks = 2 else: num_attention_masks = 1 memory_handler = PagedAttentionMemoryHandler( block_size=self.block_size, page_size=page_size, num_groups=self.num_groups, group_size=group_size, peak_activation_per_token=(config.hidden_size + config.vocab_size), num_attention_masks=num_attention_masks, ) num_blocks, max_batch_tokens = memory_handler.infer_num_blocks_and_max_batch_tokens( num_blocks=getattr(generation_config, "num_blocks", None), max_batch_tokens=getattr(generation_config, "max_batch_tokens", None), max_memory_percent=getattr( generation_config, "max_memory", 0.8 ), # FIXME: it seems we overcommit memory, was changed from 0.9 which caused OOMs in our benchmarking CI cache_dtype=self.dtype, ) # Add the inferred attributes to the class self.num_blocks = num_blocks self.max_batch_tokens = max_batch_tokens self.num_pages = self.num_blocks * self.block_size logger.info( f"PagedAttentionCache initialized with {self.num_blocks = }, {self.block_size = }, {page_size = }, " f"{self.max_batch_tokens = } {num_attention_masks = }" ) # Initialize the cache self.key_cache: list[torch.Tensor] = [] self.value_cache: list[torch.Tensor] = [] # We add two extra tokens to the cache to handle padding and generally discard unwanted tokens self.cache_shape = ((num_blocks + 2) * self.block_size, self.num_key_value_heads, self.head_dim) for _ in range(group_size): new_layer_key_cache = torch.empty(self.cache_shape, dtype=self.dtype, device=self.device) new_layer_value_cache = torch.empty(self.cache_shape, dtype=self.dtype, device=self.device) torch._dynamo.mark_static_address(new_layer_key_cache) torch._dynamo.mark_static_address(new_layer_value_cache) self.key_cache.append(new_layer_key_cache) self.value_cache.append(new_layer_value_cache) logger.info(f"{self.cache_shape = } {self.key_cache[0].shape = } {self.key_cache[0].numel() = }") # Block management data structures self.allow_block_sharing = allow_block_sharing self.group_cache_managers: list[CacheAllocator] = [] self.num_full_attention_groups = 0 self.num_sliding_attention_groups = 0 self.max_sliding_window_blocks_per_request = 0 for i, group_type in enumerate(group_types): if group_type == "full_attention": cm = FullAttentionCacheAllocator(i, self.block_size, allow_block_sharing=allow_block_sharing) self.num_full_attention_groups += 1 elif group_type == "sliding_attention": cm = SlidingAttentionCacheAllocator(i, self.block_size, config.sliding_window) self.num_sliding_attention_groups += 1 self.max_sliding_window_blocks_per_request = cm._max_blocks_per_request else: raise ValueError(f"Invalid group type: {group_type}") self.group_cache_managers.append(cm) # We only use prefix sharing if the whole model has only full attention layers and block sharing is allowed self.use_prefix_sharing = allow_block_sharing and group_types == ["full_attention"] self._block_manager = BlockManager(num_blocks, self.block_size) self._total_prefix_length: int = 0 # a counter to measure the impact of prefix sharing, also used in tests def will_allocation_be_successful(self, num_requested_blocks: int, allocated_blocks: int) -> bool: """Returns a boolean indicating if the allocation of (num_requested_blocks) blocks will be successful. The number of newly allocated blocks needed is predicted by the following rules: - for full attention groups: since there is no sliding window for full attention layers, one requested block is always equivalent to one newly allocated block for EACH full attention group - for sliding window groups: because of the sliding window, the number of blocks allocated to a request is capped. Using the number of already (allocated_blocks) we can compute the number of new blocks to actually allocate to the request, which can be lower than the number of requested blocks. That number is the same for all sliding window groups, as only one sliding window size is supported. """ # This is not in a branch, because it is very rare to have zero full attention layer needed_blocks = num_requested_blocks * self.num_full_attention_groups # Only take this branch if the model has sliding window attention layers if self.num_sliding_attention_groups: blocks_left = max(self.max_sliding_window_blocks_per_request - allocated_blocks, 0) needed_blocks += min(blocks_left, num_requested_blocks) * self.num_sliding_attention_groups return needed_blocks <= self.get_num_free_blocks() @traced def allocate_blocks(self, n_blocks: int, request_id: str, allocated_blocks: int) -> int | None: """Allocate cache blocks across all layer groups for a given request. Actual allocation is done by the cache managers, and this method only returns the maximum number of blocks actually allocated across all managers.""" # First check allocation will be successful before starting, to avoid partial allocations if not self.will_allocation_be_successful(n_blocks, allocated_blocks): return None # Allocate blocks across all cache managers max_allocated = 0 for cm in self.group_cache_managers: num_allocated_blocks = cm.allocate_blocks(n_blocks, request_id, self._block_manager) if num_allocated_blocks is None: raise ValueError(f"Failed to allocate {n_blocks} blocks for request {request_id}") max_allocated = max(max_allocated, num_allocated_blocks) return max_allocated @traced def free_blocks(self, request_id: str) -> None: """Free all allocated cache blocks for a given request across all layer groups. Actual deallocation is done by the cache managers.""" for cm in self.group_cache_managers: cm.free_blocks(request_id, self._block_manager) def get_num_free_blocks(self) -> int: """Get the current number of unallocated blocks available for new requests.""" return self._block_manager.num_free_blocks @traced def extend_read_and_write_indices( self, request_id: str, past_length: int, query_length: int, read_index: list[list[int]], write_index: list[list[int]], ) -> None: """Retrieve physical cache indices for reading KV states in the cache across all layer groups. This method coordinates with all cache managers to build the complete set of read indices needed for attention computation. """ for cm, read_indices, write_indices in zip(self.group_cache_managers, read_index, write_index): indices = cm.get_read_indices(request_id, past_length, query_length) read_indices.extend(indices) indices = cm.get_write_indices(request_id, past_length, query_length) write_indices.extend(indices) @traced def get_seqlens_k(self, past_length: int, query_length: int) -> dict[str, int]: """Retrieve the key sequence length for the given request_id across all layer types. Returns a dictionary of layer types to their corresponding key sequence lengths.""" seqlens_k = {} if self.num_full_attention_groups > 0: seqlens_k["full_attention"] = past_length + query_length if self.num_sliding_attention_groups > 0: seqlens_k["sliding_attention"] = query_length + min(past_length, self.config.sliding_window - 1) # NOTE: when we add more attention types / different sliding windows, we can go back to looping over CMs return seqlens_k @traced def update( self, key_states: torch.Tensor, # shape [1, num_kv_heads, seqlen_kv, head_dim] value_states: torch.Tensor, # shape [1, num_kv_heads, seqlen_kv, head_dim] layer_idx: int, read_index: list[torch.Tensor], # shape [num_layer_groups, seqlen_kv + past_length] write_index: list[torch.Tensor], # shape [num_layer_groups, seqlen_q] ) -> tuple[torch.Tensor, torch.Tensor]: # shape [seqlen_kv + past_length, num_kv_heads, head_dim] """Update the cache with new key-value states for a specific layer. This method writes new KV states to the appropriate cache locations. The behavior differs based on the layer's attention type: - Full attention: New KV states are written to cache, then complete sequence is read from cache - Sliding window: Old KV is read from cache along with extra spaces for the new KV, then new KV is written to cache. This is because new KV might overwrite the old KV, so we need to read the old KV first. Returns the complete KV states (cached + new) for attention computation. """ # Retrieve the layer read and write indices, and if there is a sliding window group_idx, layer_idx_in_group = self.layer_index_to_group_indices[layer_idx] layer_read_index = read_index[group_idx] layer_write_index = write_index[group_idx] # Select the correct cache k_cache = self.key_cache[layer_idx_in_group] v_cache = self.value_cache[layer_idx_in_group] # Transpose the key and value states to match the cache shape, after which shape is [seqlen_kv, num_kv_heads, head_dim] key_states = key_states.transpose(1, 2).squeeze(0) value_states = value_states.transpose(1, 2).squeeze(0) # Case: full attention sliding_window = self.sliding_windows[layer_idx] if sliding_window == 1: k_cache[layer_write_index, :, :] = key_states v_cache[layer_write_index, :, :] = value_states key_states_with_cache = k_cache[layer_read_index, :, :] value_states_with_cache = v_cache[layer_read_index, :, :] # Case: sliding window -- we need to be careful of read/write order because of chunked prefill, because it's # the only case where you may write over cache you need to use else: # Add the cache to the key and value states mask = (layer_read_index == -1).unsqueeze(-1).unsqueeze(-1) # TODO: should this be precomputed? key_states_with_cache = k_cache[layer_read_index, :, :] key_states_with_cache.masked_scatter_(mask, key_states) value_states_with_cache = v_cache[layer_read_index, :, :] value_states_with_cache.masked_scatter_(mask, value_states) # Write new KV values to the cache k_cache[layer_write_index, :, :] = key_states v_cache[layer_write_index, :, :] = value_states # Return the new KV values return key_states_with_cache, value_states_with_cache def search_prefix_match(self, request_id: str, prompt_ids: list[int]) -> int: """Searches for a prefix match in the cache for the given (prompts_ids). If one is found, we reference the matching blocks in the (request_id), increase the reference count of the blocks and return the number of blocks that match. If no prefix match is found, we return 0.""" current_hash = None allocated_blocks = [] for b in range(len(prompt_ids) // self.block_size): tokens = prompt_ids[b * self.block_size : (b + 1) * self.block_size] # Prefix sharing is only supported when there is only one full attention layer group, so group_id=0. current_hash = self._block_manager.compute_hash(current_hash, tokens, group_id=0) block_id = self._block_manager._hash_to_id.get(current_hash) if block_id is not None: allocated_blocks.append(block_id) self._block_manager.increase_ref_count(block_id) else: break # If we found a matching prefix, we reference the blocks in the request if allocated_blocks: logger.debug(f"Found prefix match for request {request_id} with {len(allocated_blocks)} blocks") cm = self.group_cache_managers[0] cm.block_table[request_id] = allocated_blocks prefix_length = len(allocated_blocks) * self.block_size self._total_prefix_length += prefix_length return prefix_length def mark_shareable_blocks_as_complete(self, state: RequestState, num_complete_blocks: int) -> None: """Marks the blocks allocated to a request (state) as complete if they are shareable and they have been computed in the forward pass. A complete block is a block where the KV cache has been fully computed: if the block has enough space to hold the cache for N tokens, the block is marked as complete when the cache data is present for the N tokens. If block sharing is off, this is a no-op.""" # The status can be FINISHED in async mode, because batch N+1 offloaded the request before batch N was over. So # we need to check for this case to avoid looking in the block table for blocks that no longer exist. if num_complete_blocks == 0 or state.status == RequestStatus.FINISHED: return None for cm in self.group_cache_managers: if cm.uses_block_sharing: self._block_manager.mark_shareable_blocks_as_complete( num_complete_blocks=num_complete_blocks, allocated_blocks=cm.block_table[state.request_id], prompt_ids=(state.initial_tokens + state.generated_tokens), ) def copy_cache(self, list_source_blocks: list[int], list_forked_blocks: list[int]) -> None: """Copy the cache from the source blocks to the forked blocks.""" source_blocks = torch.tensor(list_source_blocks, device=self.device, dtype=torch.int32) forked_blocks = torch.tensor(list_forked_blocks, device=self.device, dtype=torch.int32) for key_cache, value_cache in zip(self.key_cache, self.value_cache): key_cache = key_cache.view(-1, self.block_size, self.num_key_value_heads, self.head_dim) value_cache = value_cache.view(-1, self.block_size, self.num_key_value_heads, self.head_dim) key_cache[forked_blocks] = key_cache[source_blocks] value_cache[forked_blocks] = value_cache[source_blocks] # FIXME: consolidate the cache into a single tensor of shape (group_size, 2, *self.k_or_v_cache_shape) # This will allow for better .update and a single copy instead of one per cache tensor def fork_request(self, source_request_id: str, destination_request_ids: list[str]) -> tuple[list[int], list[int]]: """Fork the cache of a request (state) into the one of a list of requests with the given (dst_request_ids).""" # These lists will be the accumulators for the source and destination blocks for the cache copy source_blocks, destination_blocks = [], [] # Main fork loop for cm in self.group_cache_managers: src_blocks, dst_blocks = cm.fork_blocks(source_request_id, destination_request_ids, self._block_manager) source_blocks.extend(src_blocks) destination_blocks.extend(dst_blocks) return source_blocks, destination_blocks # TODO: rework computation with the groups and their sizes class PagedAttentionMemoryHandler: """A helper class to determine the best number of pages and maximum number of tokens per batch for the paged attention cache, providing automatic sizing based on available GPU memory. The helper works using the number of pages, which is tied to the number of blocks by: num_blocks = num_pages // block_size The memory footprint consists of three main components: - Cache memory: the space needed to store the cache tensors: 2 * layer_group_size * [num_pages, page_size] * cache_dtype - Activation memory: the space temporarily taken by the largest activation during the model forward pass: peak_activation_per_token * max_tokens_per_batch * activation_dtype_size - Static tensors: the space taken by the input/output buffers and metadata tensors for batch processing, sum of: - inputs_ids + outputs_ids + position_ids + logits_indices: 4 * max_tokens_per_batch * int32_size - attention_mask: num_attention_masks * num_pages * max_tokens_per_batch * activation_dtype_size - cumulative_seqlens_q + cumulative_seqlens_k: (1 + 2) * max_tokens_per_batch * int32_size - write_index_tensor: num_groups * max_tokens_per_batch * int32_size - read_index_tensor: num_groups * (num_pages + max_tokens_per_batch) * int32_size The handler can operate in three modes: 1. Auto-sizing: Determines both number of pages and maximum number of tokens per batch using quadratic optimization 2. Fixed cache: Calculates max batch tokens given a fixed number of pages 3. Fixed batch: Calculates number of pages given a fixed maximum batch size """ _activation_dtype = torch.bfloat16 _input_dtype = torch.int32 _upper_bound_max_batch_tokens = 256 _upper_bound_num_blocks = 4096 def __init__( self, block_size: int, page_size: int, num_groups: int, group_size: int, peak_activation_per_token: int, num_attention_masks: int, ) -> None: """Initialize the memory handler with the parameters that cannot be automatically inferred. Args: block_size: Size of the cache blocks page_size: Size of the cache pages num_groups: Number of layer groups group_size: Number of layers per layer group peak_activation_per_token: Maximum size of activation tensor per token, = hidden_size + vocab_size num_attention_masks: Number of attention masks, 0 if no attention mask is used, 2 if hybrid model, else 1 """ self.block_size = block_size self.page_size = page_size self.num_groups = num_groups self.group_size = group_size self.peak_activation_per_token = peak_activation_per_token self.num_attention_masks = num_attention_masks @staticmethod def get_available_memory(max_memory_percent: float = 1.0) -> int: """Calculate available GPU memory for cache allocation, accounting for already allocated tensors. This method queries the current memory state and applies the specified percentage limit to determine how much memory can be safely used for the paged attention cache. Args: max_memory_percent: Fraction of available memory to use (0.0-1.0). 1.0 means use all available memory. Returns: int: Available memory in bytes for cache allocation """ _, total, reserved, allocated = get_device_and_memory_breakdown() available_memory = total - max(allocated, reserved) available_memory = int(available_memory * max_memory_percent) return available_memory def infer_num_blocks_and_max_batch_tokens( self, num_blocks: int | None = None, max_batch_tokens: int | None = None, max_memory_percent: float = 0.8, # FIXME: it seems we overcommit memory, was changed from 0.9 which caused OOMs in our benchmarking CI cache_dtype: torch.dtype = torch.float16, ) -> tuple[int, int]: """Determine optimal number of blocks and maximum number of tokens per batch based on available memory and constraints. Check the class docstring for more details. Naming the number of pages as N and the maximum number of tokens per batch as M, the equation solved is: available_memory = sum([ MN * num_attention_masks * activation_dtype_size, 2N * (layer_group_size * page_size * cache_dtype + 2 * num_group), M * (peak_activation_per_token * activation_dtype + 28 + 4 * num_group), ]) where we already simplified int32_size = 4. """ if num_blocks is None: if max_batch_tokens is None: # If neither num_blocks nor max_batch_tokens are provided, we use a second-order polynomial num_blocks, max_batch_tokens = self.compute_num_blocks_and_max_batch_tokens( max_memory_percent, cache_dtype ) else: # If only max_batch_tokens is provided, we infer the num_blocks num_blocks = self.compute_num_blocks(max_batch_tokens, max_memory_percent, cache_dtype) elif max_batch_tokens is None: # If only num_blocks is provided, we infer the max_batch_tokens max_batch_tokens = self.compute_max_batch_tokens(num_blocks, max_memory_percent, cache_dtype) else: # If both num_blocks and max_batch_tokens are provided, we use them (useless, but helps with typing) max_batch_tokens = max_batch_tokens # We check if the memory footprint is too large in all cases available_memory = self.get_available_memory(max_memory_percent) memory_footprint = self.compute_memory_footprint( max_batch_tokens=max_batch_tokens, num_blocks=num_blocks, cache_dtype=cache_dtype ) if memory_footprint > available_memory: raise MemoryError(f"Memory footprint {memory_footprint} is more than available memory {available_memory}") return num_blocks, max_batch_tokens def compute_num_blocks_and_max_batch_tokens( self, max_memory_percent: float, cache_dtype: torch.dtype = torch.float16, m: float = 0.01, ) -> tuple[int, int]: """Calculate optimal number of blocks and maximum number of tokens per batch using quadratic optimization when neither is fixed. This method assumes a relationship M = m * N where m is a small ratio below 1 and solves the resulting quadratic equation to find the optimal N that maximizes utilization within memory constraints. m is the amount of cache we can fill with one batch: m=0.01 means a batch fills at most 1% of the cache. The equation to solve is: available_memory = sum([ m * N^2 * num_attention_masks * activation_dtype_size, 2N * (layer_group_size * page_size * cache_dtype + 2 * num_group), m * N * (peak_activation_per_token * activation_dtype + 28 + 4 * num_group), ]) If num_attention_masks is 0, the equation simplifies to a 1st degree polynomial. """ cache_memory = self.get_available_memory(max_memory_percent) logger.info(f"Cache memory: {cache_memory}") # Compute second-degree polynomial coefficients a = m * self.num_attention_masks * self._activation_dtype.itemsize b = 2 * (self.group_size * self.page_size * cache_dtype.itemsize + 2 * self.num_groups) b += m * (self.peak_activation_per_token * self._activation_dtype.itemsize + 28 + 4 * self.num_groups) c = -cache_memory logger.debug(f"Coefficients of 2nd degree polynomial: {a = }, {b = }, {c = }") # If num_attention_masks is 0, the equation simplifies to a 1st degree polynomial if self.num_attention_masks == 0: greatest_solution = -c / b # Otherwise, we solve the quadratic equation else: discriminant = b**2 - 4 * a * c if discriminant < 0: raise ValueError(f"Discriminant is negative: {discriminant = }") greatest_solution = (-b + sqrt(discriminant)) / (2 * a) if greatest_solution < 0: raise ValueError(f"Greatest solution is negative: {greatest_solution = }") # Infer number of blocks and max batch tokens num_pages = floor(greatest_solution) num_blocks = num_pages // self.block_size if num_blocks > self._upper_bound_num_blocks: logger.info(f"{num_blocks = } is too large, setting to {self._upper_bound_num_blocks = }") num_blocks = self._upper_bound_num_blocks max_batch_tokens = int(greatest_solution * m) if max_batch_tokens > self._upper_bound_max_batch_tokens: logger.info(f"{max_batch_tokens = } is too large, setting to {self._upper_bound_max_batch_tokens = }") max_batch_tokens = self._upper_bound_max_batch_tokens return num_blocks, max_batch_tokens def compute_max_batch_tokens( self, num_blocks: int, max_memory_percent: float, cache_dtype: torch.dtype = torch.float16, ) -> int: """Calculate maximum batch tokens M given a fixed number of cache blocks. The formula for M is given by: M = (available_memory - 2N * (layer_group_size * page_size * cache_dtype + 2 * num_group)) / (activation_dtype_size * (N * num_attention_masks + peak_activation_per_token) + 28 + 4 * num_group) """ cache_memory = self.get_available_memory(max_memory_percent) num_pages = num_blocks * self.block_size # Compute numerator num = cache_memory num -= 2 * num_pages * (self.group_size * self.page_size * cache_dtype.itemsize + 2 * self.num_groups) # Compute denominator denum = self._activation_dtype.itemsize * ( num_pages * self.num_attention_masks + self.peak_activation_per_token ) denum += 28 + 4 * self.num_groups # Compute max batch tokens and return max_batch_tokens = floor(num / denum) if max_batch_tokens > self._upper_bound_max_batch_tokens: logger.info(f"{max_batch_tokens = } is too large, setting to {self._upper_bound_max_batch_tokens = }") max_batch_tokens = self._upper_bound_max_batch_tokens return max_batch_tokens def compute_num_blocks( self, max_batch_tokens: int, max_memory_percent: float, cache_dtype: torch.dtype = torch.float16, ) -> int: """Calculate number of cache blocks N given a fixed maximum token per token M. The formula for N is given by: N = (available_memory - M * (peak_activation_per_token * activation_dtype + 28 + 4 * num_group)) / (2 * (layer_group_size * page_size * cache_dtype + 2 * num_group) + M * (num_attention_masks * activation_dtype_size)) """ cache_memory = self.get_available_memory(max_memory_percent) # Compute numerator num = cache_memory num -= max_batch_tokens * self.peak_activation_per_token * self._activation_dtype.itemsize num -= max_batch_tokens * (28 + 4 * self.num_groups) # Compute denominator denum = 2 * (self.group_size * self.page_size * cache_dtype.itemsize + 2 * self.num_groups) denum += max_batch_tokens * (self.num_attention_masks * self._activation_dtype.itemsize) denum += max_batch_tokens * self._activation_dtype.itemsize # Compute cache size and return number of blocks num_pages = floor(num / denum) num_blocks = num_pages // self.block_size if num_blocks > self._upper_bound_num_blocks: logger.info(f"{num_blocks = } is too large, setting to {self._upper_bound_num_blocks = }") num_blocks = self._upper_bound_num_blocks return num_blocks def compute_memory_footprint( self, num_blocks: int, max_batch_tokens: int, cache_dtype: torch.dtype, ) -> int: """Calculate the memory footprint breakdown for a given number of blocks and maximum batch tokens. The memory footprint is given by: available_memory = sum([ MN * num_attention_masks * activation_dtype_size, 2N * (layer_group_size * page_size * cache_dtype + 2 * num_group), M * (peak_activation_per_token * activation_dtype + 28 + 4 * num_group), ]) but is broken down below. """ num_pages = num_blocks * self.block_size cache_memory_footprint = 2 * self.group_size * num_pages * self.page_size * cache_dtype.itemsize activation_memory_footprint = self.peak_activation_per_token * self._activation_dtype.itemsize activation_memory_footprint *= max_batch_tokens inputs_outputs_positions_and_logits_memory_footprint = 4 * max_batch_tokens * 4 # second 4 is for int32 size attention_memory_footprint = self.num_attention_masks * self._activation_dtype.itemsize attention_memory_footprint *= num_pages * max_batch_tokens cumulative_seqlens_memory_footprint = 3 * max_batch_tokens * 4 # 4 is for int32 size write_index_memory_footprint = self.num_groups * max_batch_tokens * 4 # 4 is for int32 size read_index_memory_footprint = self.num_groups * (num_pages + max_batch_tokens) * 4 # 4 is for int32 size total_memory_footprint = sum( [ cache_memory_footprint, activation_memory_footprint, inputs_outputs_positions_and_logits_memory_footprint, attention_memory_footprint, cumulative_seqlens_memory_footprint, write_index_memory_footprint, read_index_memory_footprint, ] ) return total_memory_footprint