tpu_model_runner.py 48.7 KB
Newer Older
1
# SPDX-License-Identifier: Apache-2.0
2
import bisect
3
import time
4
from typing import TYPE_CHECKING, Optional, cast
5
6
7
8
9
10
11
12
13
14
from unittest.mock import patch

import numpy as np
import torch
import torch.distributed
import torch.nn as nn
# TPU XLA related
import torch_xla.core.xla_model as xm
import torch_xla.runtime as xr

15
import vllm.envs as envs
16
17
from vllm.attention.backends.abstract import AttentionType
from vllm.attention.layer import Attention
18
from vllm.compilation.wrapper import TorchCompileWrapperWithCustomDispatcher
19
from vllm.config import VllmConfig
20
from vllm.forward_context import set_forward_context
21
22
from vllm.logger import init_logger
from vllm.model_executor.model_loader import get_model
23
24
from vllm.multimodal import MULTIMODAL_REGISTRY
from vllm.multimodal.inputs import MultiModalKwargs, PlaceholderRange
25
from vllm.multimodal.utils import group_mm_inputs_by_modality
26
from vllm.sequence import IntermediateTensors
27
from vllm.utils import LayerBlockType, cdiv, is_pin_memory_available
28
from vllm.v1.attention.backends.pallas import (PallasAttentionBackend,
29
                                               PallasMetadata)
30
from vllm.v1.core.encoder_cache_manager import compute_encoder_budget
31
from vllm.v1.kv_cache_interface import (FullAttentionSpec, KVCacheConfig,
32
                                        KVCacheSpec, SlidingWindowSpec)
33
from vllm.v1.outputs import (EMPTY_MODEL_RUNNER_OUTPUT, LogprobsTensors,
34
                             ModelRunnerOutput)
35
36
from vllm.v1.sample.tpu.metadata import TPUSupportedSamplingMetadata
from vllm.v1.sample.tpu.sampler import Sampler as TPUSampler
37
38
39
from vllm.v1.utils import bind_kv_cache
from vllm.v1.worker.gpu_input_batch import CachedRequestState, InputBatch

40
41
from .utils import (gather_mm_placeholders, sanity_check_mm_encoder_outputs,
                    scatter_mm_placeholders)
42

43
if TYPE_CHECKING:
44
    from vllm.v1.core.sched.output import SchedulerOutput
45
46
47
48
49
50

logger = init_logger(__name__)

# Here we utilize the behavior that out-of-bound index is ignored.
# FIXME(woosuk): Find a more reliable way to prevent possible bugs.
_PAD_SLOT_ID = 1_000_000_000
51
INVALID_TOKEN_ID = -1
52
53
# Smallest output size
MIN_NUM_SEQS = 8
54
55


56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
#########################################################
# Ways to avoid recompilation
#########################################################
#
# The model executor has two primary components:
# 1. preparing the model and sampler inputs
# 2. executing the model and sampler.
# The core idea is to avoid any TPU computation during input preparation. For
# better compilation tracking and increased flexibility, the model execution and
# sampler are divided into several distinct components.
#
# Below are the detailed steps:
#
# Step 1
# It is recommended to avoid TPU operations when preparing the model and sampler
# inputs. CPU tensors can be prepared and transferred to the XLA device using
# cpu_tensor.to(xla_device), which only triggers CPU to TPU transfers and avoids
# compilation.
#
# Step 2
# The TPU execution should be decomposed into subgraphs (4 at the moment):
# 1. the main model
# 2. selecting hidden states for each request
# 3. sampler
# 4. encoder.
# Each subgraph should be decorated in a torch.compile. This is used to make
# sure that we have the same subgraph topology in both dummy_run and
# xecute_model. The results from these subgraphs should either be passed to
# other subgraphs, or transferred from TPU to CPU using xla_tensor.cpu() for
# subsequent processing on the CPU.
#
# Step 3
# The dummy_run should be comprehensive, ensuring all potential input shapes and
# branch predictions are included as subgraph inputs to facilitate
# pre-compilation.
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
class TPUModelRunner:

    def __init__(
        self,
        vllm_config: VllmConfig,
        device: torch.device,
    ):
        self.vllm_config = vllm_config
        self.model_config = vllm_config.model_config
        self.cache_config = vllm_config.cache_config
        self.lora_config = vllm_config.lora_config
        self.load_config = vllm_config.load_config
        self.parallel_config = vllm_config.parallel_config
        self.scheduler_config = vllm_config.scheduler_config
        self.speculative_config = vllm_config.speculative_config
        self.prompt_adapter_config = vllm_config.prompt_adapter_config
        self.observability_config = vllm_config.observability_config
        self.device_config = vllm_config.device_config

        model_config = self.model_config
        cache_config = self.cache_config
        scheduler_config = self.scheduler_config
        parallel_config = self.parallel_config
        self.device = device
115
        self.check_recompilation = envs.VLLM_XLA_CHECK_RECOMPILATION
116

117
        self.enforce_eager = model_config.enforce_eager
118
119
120
121

        self.num_xla_graphs = 0
        self._update_num_xla_graphs("init")

122
123
        self.pin_memory = is_pin_memory_available()
        self.dtype = self.model_config.dtype
124
        self._hidden_states_dtype = self.dtype
125
126
127
128
129
130

        self.is_multimodal_model = model_config.is_multimodal_model
        self.sliding_window = model_config.get_sliding_window()
        self.block_size = cache_config.block_size
        self.max_model_len = model_config.max_model_len
        self.max_num_blocks_per_req = cdiv(self.max_model_len, self.block_size)
131
        self.max_num_tokens = scheduler_config.max_num_batched_tokens
132
133
        # InputBatch needs to work with sampling tensors greater than padding
        # to avoid dynamic shapes. Also, avoid suboptimal alignment.
134
        self.max_num_reqs = max(scheduler_config.max_num_seqs, MIN_NUM_SEQS)
135
136
137
138
139
140
141
142
143
144

        # Model-related.
        self.num_attn_layers = model_config.get_num_layers_by_block_type(
            parallel_config, LayerBlockType.attention)
        self.num_query_heads = model_config.get_num_attention_heads(
            parallel_config)
        self.num_kv_heads = model_config.get_num_kv_heads(parallel_config)
        self.head_size = model_config.get_head_size()
        self.hidden_size = model_config.get_hidden_size()

145
146
147
148
149
150
151
152
153
        # Multi-modal data support
        self.mm_registry = MULTIMODAL_REGISTRY
        self.uses_mrope = model_config.uses_mrope
        # TODO: Support M-RoPE (e.g, Qwen2-VL)
        assert not self.uses_mrope, "TPU does not support M-RoPE yet."

        encoder_compute_budget, encoder_cache_size = compute_encoder_budget(
            model_config=model_config,
            scheduler_config=scheduler_config,
154
            mm_registry=self.mm_registry,
155
156
157
158
159
160
161
162
163
164
165
166
        )
        self.max_num_encoder_input_tokens = encoder_compute_budget
        self.encoder_cache_size = encoder_cache_size

        # Lazy initialization
        # self.model: nn.Module  # Set after load_model
        self.kv_caches: list[torch.Tensor] = []
        # req_id -> (input_id -> encoder_output)
        self.encoder_cache: dict[str, dict[int, torch.Tensor]] = {}

        # Request states.
        self.requests: dict[str, CachedRequestState] = {}
167
168
169
170
171
172
173
        # Persistent batch.
        self.input_batch = InputBatch(
            max_num_reqs=self.max_num_reqs,
            max_model_len=self.max_model_len,
            max_num_blocks_per_req=self.max_num_blocks_per_req,
            device=self.device,
            pin_memory=self.pin_memory,
174
            vocab_size=model_config.get_vocab_size(),
175
176
        )

177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
        # Cached torch/numpy tensor
        # The pytorch tensor and numpy array share the same buffer.
        # Sometimes the numpy op is faster so we create both.
        self.input_ids_cpu = torch.zeros(self.max_num_tokens,
                                         dtype=torch.int32,
                                         device="cpu")
        self.input_ids_np = self.input_ids_cpu.numpy()

        self.positions_cpu = torch.zeros(self.max_num_tokens,
                                         dtype=torch.int32,
                                         device="cpu")
        self.positions_np = self.positions_cpu.numpy()

        self.slot_mapping_cpu = torch.zeros(self.max_num_tokens,
                                            dtype=torch.int64,
                                            device="cpu")
        self.slot_mapping_np = self.slot_mapping_cpu.numpy()
        self.block_table_cpu = torch.zeros(
195
            (self.max_num_tokens, self.max_num_blocks_per_req),
196
197
198
199
200
201
202
203
204
205
206
207
208
209
            dtype=self.input_batch.block_table.get_cpu_tensor().dtype,
            device="cpu")

        self.query_start_loc_cpu = torch.zeros(self.max_num_tokens + 1,
                                               dtype=torch.int32,
                                               device="cpu",
                                               pin_memory=self.pin_memory)
        self.query_start_loc_np = self.query_start_loc_cpu.numpy()

        self.seq_lens_cpu = torch.zeros(self.max_num_tokens,
                                        dtype=torch.int32,
                                        device="cpu",
                                        pin_memory=self.pin_memory)
        self.seq_lens_np = self.seq_lens_cpu.numpy()
210
211
212
213

        # Range tensor with values [0 .. self.max_num_tokens - 1].
        # Used to initialize positions / context_lens / seq_lens
        self.arange_np = np.arange(self.max_num_tokens, dtype=np.int32)
214
        self.num_tokens_paddings = _get_token_paddings(
215
216
217
            min_token_size=16,
            max_token_size=self.max_num_tokens,
            padding_gap=envs.VLLM_TPU_BUCKET_PADDING_GAP)
218
219
        self.num_reqs_paddings = _get_req_paddings(
            min_req_size=MIN_NUM_SEQS, max_req_size=self.max_num_reqs)
220

221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
    def _update_num_xla_graphs(self, case_str):
        check_comp = self.check_recompilation and not self.enforce_eager
        if not check_comp:
            return

        total_cached_graphs = xr.get_num_cached_compilation_graph()
        new_compiled_graphs = total_cached_graphs - self.num_xla_graphs
        if new_compiled_graphs == 0:
            return

        logger.info("Add new %d compiled XLA graphs due to %s",
                    new_compiled_graphs, case_str)
        self.num_xla_graphs += new_compiled_graphs

    def _verify_num_xla_graphs(self, case_str):
        check_comp = self.check_recompilation and not self.enforce_eager
        if not check_comp:
            return

        curr_cached_graph = xr.get_num_cached_compilation_graph()
        assert self.num_xla_graphs == curr_cached_graph, (
            "Recompilation after warm up is detected during {}."
            " num_xla_graphs = {} curr_cached_graph = {}".format(
                case_str, self.num_xla_graphs, curr_cached_graph))

246
247
248
249
250
251
252
253
    def _update_states(self, scheduler_output: "SchedulerOutput") -> bool:
        """Update the cached states and the persistent batch with the scheduler
        output.

        The updated states are used by the `_prepare_inputs` function to create
        the input GPU tensors for the model.

        Returns:
254
            True if there is a new/resumed/paused/finished request.
255
256
257
258
259
            If False, we can skip copying SamplingMetadata to the GPU.
        """
        # Remove finished requests from the cached states.
        for req_id in scheduler_output.finished_req_ids:
            self.requests.pop(req_id, None)
260
            self.encoder_cache.pop(req_id, None)
261
262
263
264
265
266
267

        # Remove the finished requests from the persistent batch.
        # NOTE(woosuk): There could be an edge case where finished_req_ids and
        # scheduled_req_ids overlap. This happens when a request is aborted and
        # then resubmitted with the same ID. In this case, we treat them as two
        # distinct requests - clearing the cached states for the first request
        # and handling the second as a new request.
268
        removed_req_indices: list[int] = []
269
270
271
272
273
        for req_id in scheduler_output.finished_req_ids:
            req_index = self.input_batch.remove_request(req_id)
            if req_index is not None:
                removed_req_indices.append(req_index)

274
275
276
277
278
279
280
281
        # Free the cached encoder outputs.
        for req_id, input_id in scheduler_output.free_encoder_input_ids:
            encoder_outputs = self.encoder_cache.get(req_id)
            if encoder_outputs is not None:
                encoder_outputs.pop(input_id, None)
                if not encoder_outputs:
                    self.encoder_cache.pop(req_id, None)

282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
        # Remove the unscheduled requests from the persistent batch.
        # NOTE(woosuk): The unscheduled requests are either preempted requests
        # or running requests that are not scheduled in this step. We remove
        # them from the persistent batch but keep their cached states since
        # they will be scheduled again sometime in the future.
        scheduled_req_ids = scheduler_output.num_scheduled_tokens.keys()
        cached_req_ids = self.input_batch.req_id_to_index.keys()
        unscheduled_req_ids = cached_req_ids - scheduled_req_ids
        # NOTE(woosuk): The persistent batch optimization assumes that
        # consecutive batches contain mostly the same requests. If batches
        # have low request overlap (e.g., alternating between two distinct
        # sets of requests), this optimization becomes very inefficient.
        for req_id in unscheduled_req_ids:
            req_index = self.input_batch.remove_request(req_id)
            assert req_index is not None
            removed_req_indices.append(req_index)

299
        req_ids_to_add: list[str] = []
300
301
302
303
304
305
306
307
308
309
310
311
        # Add new requests to the cached states.
        for new_req_data in scheduler_output.scheduled_new_reqs:
            req_id = new_req_data.req_id
            sampling_params = new_req_data.sampling_params

            self.requests[req_id] = CachedRequestState(
                req_id=req_id,
                prompt_token_ids=new_req_data.prompt_token_ids,
                prompt=new_req_data.prompt,
                mm_inputs=new_req_data.mm_inputs,
                mm_positions=new_req_data.mm_positions,
                sampling_params=sampling_params,
312
                generator=None,
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
                block_ids=new_req_data.block_ids,
                num_computed_tokens=new_req_data.num_computed_tokens,
                output_token_ids=[],
                lora_request=new_req_data.lora_request,
            )

            req_ids_to_add.append(req_id)

        # Update the states of the running/resumed requests.
        for req_data in scheduler_output.scheduled_cached_reqs:
            req_id = req_data.req_id
            req_state = self.requests[req_id]

            # Update the cached states.
            req_state.num_computed_tokens = req_data.num_computed_tokens
            if not req_data.resumed_from_preemption:
                # Append the new blocks to the existing block IDs.
                req_state.block_ids.extend(req_data.new_block_ids)
            else:
                # The request is resumed from preemption.
                # Replace the existing block IDs with the new ones.
                req_state.block_ids = req_data.new_block_ids

            req_index = self.input_batch.req_id_to_index.get(req_id)
            if req_index is None:
                # The request is not in the persistent batch.
                # The request was either preempted and resumed later, or was not
                # scheduled in the previous step and needs to be added again.
                req_ids_to_add.append(req_id)
                continue

            # Update the persistent batch.
            self.input_batch.num_computed_tokens_cpu[req_index] = (
                req_data.num_computed_tokens)
347
348
            self.input_batch.block_table.append_row(req_data.new_block_ids,
                                                    req_index)
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365

        # Add the new or resumed requests to the persistent batch.
        # The smaller empty indices are filled first.
        removed_req_indices = sorted(removed_req_indices, reverse=True)
        for req_id in req_ids_to_add:
            req_state = self.requests[req_id]
            if removed_req_indices:
                # Fill the empty index.
                req_index = removed_req_indices.pop()
            else:
                # Append to the end.
                req_index = None
            self.input_batch.add_request(req_state, req_index)

        # Condense the batched states if there are empty indices.
        if removed_req_indices:
            self.input_batch.condense(removed_req_indices)
366

367
368
369
370
371
372
        return len(unscheduled_req_ids) > 0 or len(req_ids_to_add) > 0

    def get_model(self) -> nn.Module:
        assert self.model is not None
        return self.model

373
    def get_kv_cache_spec(self) -> dict[str, KVCacheSpec]:
374
        """
375
        Generates the KVCacheSpec by parsing the kv cache format from each
376
377
        Attention module in the static forward context.
        Returns:
378
            KVCacheSpec: A dictionary mapping layer names to their KV cache
379
380
381
382
383
            format. Layers that do not need KV cache are not included.
        """

        forward_ctx = self.vllm_config.compilation_config.static_forward_context
        block_size = self.vllm_config.cache_config.block_size
384
        kv_cache_spec: dict[str, KVCacheSpec] = {}
385
386
387
        for layer_name, attn_module in forward_ctx.items():
            assert isinstance(attn_module, Attention)
            if attn_module.attn_type == AttentionType.DECODER:
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
                if attn_module.sliding_window is not None:
                    kv_cache_spec[layer_name] = SlidingWindowSpec(
                        block_size=block_size,
                        num_kv_heads=attn_module.num_kv_heads,
                        head_size=attn_module.head_size,
                        dtype=attn_module.dtype,
                        sliding_window=attn_module.sliding_window,
                        use_mla=False,
                    )
                else:
                    kv_cache_spec[layer_name] = FullAttentionSpec(
                        block_size=block_size,
                        num_kv_heads=attn_module.num_kv_heads,
                        head_size=attn_module.head_size,
                        dtype=attn_module.dtype,
                        use_mla=False,
                    )
405
406
407
408
409
410
411
412
413
414
415
416
            elif attn_module.attn_type in (AttentionType.ENCODER,
                                           AttentionType.ENCODER_ONLY):
                # encoder-only attention does not need KV cache.
                continue
            elif attn_module.attn_type == AttentionType.ENCODER_DECODER:
                raise NotImplementedError
            else:
                raise ValueError(
                    f"Unknown attention type: {attn_module.attn_type}")

        return kv_cache_spec

417
    def _prepare_inputs(self, scheduler_output: "SchedulerOutput"):
418
419
420
421
422
        total_num_scheduled_tokens = scheduler_output.total_num_scheduled_tokens
        assert total_num_scheduled_tokens > 0
        num_reqs = self.input_batch.num_reqs
        assert num_reqs > 0

423
424
425
426
        # Get the number of scheduled tokens for each request.
        num_scheduled_tokens_per_req = []
        max_num_scheduled_tokens_all_reqs = 0
        for req_id in self.input_batch.req_ids[:num_reqs]:
427
            assert req_id is not None
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
            num_tokens = scheduler_output.num_scheduled_tokens[req_id]
            num_scheduled_tokens_per_req.append(num_tokens)
            max_num_scheduled_tokens_all_reqs = max(
                max_num_scheduled_tokens_all_reqs, num_tokens)
        num_scheduled_tokens_per_req = np.array(num_scheduled_tokens_per_req,
                                                dtype=np.int32)
        assert max_num_scheduled_tokens_all_reqs > 0

        # Get request indices.
        # E.g., [2, 5, 3] -> [0, 0, 1, 1, 1, 1, 1, 2, 2, 2]
        # For each scheduled token, what are the corresponding req index.
        req_indices = np.repeat(self.arange_np[:num_reqs],
                                num_scheduled_tokens_per_req)

        # Get batched arange.
        # E.g., [2, 5, 3] -> [0, 1, 0, 1, 2, 3, 4, 0, 1, 2]
        # For each scheduled token, what is its position in corresponding req.
        arange = np.concatenate(
            [self.arange_np[:n] for n in num_scheduled_tokens_per_req])

        # Get positions.
        positions_np = self.positions_np[:total_num_scheduled_tokens]
        np.add(self.input_batch.num_computed_tokens_cpu[req_indices],
               arange,
               out=positions_np)

        # Get token indices.
        # E.g., [0, 1, 0, 1, 2, 3, 4, 0, 1, 2]
        # -> [0, 1, M, M + 1, M + 2, M + 3, M + 4, 2 * M, 2 * M + 1, 2 * M + 2]
        # where M is the max_model_len.
        token_indices = (positions_np +
                         req_indices * self.input_batch.token_ids_cpu.shape[1])

        # NOTE(woosuk): We use torch.index_select instead of np.take here
        # because torch.index_select is much faster than np.take for large
        # tensors.
464
465
        torch.index_select(self.input_batch.token_ids_cpu_tensor.flatten(),
                           0,
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
                           torch.from_numpy(token_indices),
                           out=self.input_ids_cpu[:total_num_scheduled_tokens])

        # Calculate the slot mapping.
        # E.g., [0, 1, 0, 1, 2, 3, 4, 0, 1, 2]
        # -> [0, 0, K, K, K + 1, K + 1, K + 2, 2 * K, 2 * K, 2 * K + 1]
        # where K is the max_num_blocks_per_req and the block size is 2.
        # NOTE(woosuk): We can't simply use `token_indices // block_size` here
        # because M (max_model_len) is not necessarily divisible by block_size.
        # req_indices: # E.g., [2, 5, 3] -> [0, 0, 1, 1, 1, 1, 1, 2, 2, 2]
        block_table_indices = (req_indices * self.max_num_blocks_per_req +
                               positions_np // self.block_size)
        # NOTE(woosuk): We use torch.index_select instead of np.take here
        # because torch.index_select is much faster than np.take for large
        # tensors.
481
        block_table_cpu = self.input_batch.block_table.get_cpu_tensor()
482
483
484
485
486
487
488
489
490
491
        block_numbers = block_table_cpu.flatten()[block_table_indices].numpy()
        block_offsets = positions_np % self.block_size
        np.add(block_numbers * self.block_size,
               block_offsets,
               out=self.slot_mapping_np[:total_num_scheduled_tokens])

        # Prepare the attention metadata.
        self.query_start_loc_np[0] = 0
        np.cumsum(num_scheduled_tokens_per_req,
                  out=self.query_start_loc_np[1:num_reqs + 1])
492
        self.query_start_loc_np[num_reqs + 1:] = 1
493
494
495
496
497
498

        self.seq_lens_np[:num_reqs] = (
            self.input_batch.num_computed_tokens_cpu[:num_reqs] +
            num_scheduled_tokens_per_req)

        # Do the padding and copy the tensors to the TPU.
499
        padded_total_num_scheduled_tokens = _get_padded_token_len(
500
            self.num_tokens_paddings, total_num_scheduled_tokens)
501
502
503
        # Zero out to avoid spurious values from prev iteration (last cp chunk)
        self.input_ids_cpu[
            total_num_scheduled_tokens:padded_total_num_scheduled_tokens] = 0
504
505
506
507
508
509
510
511
512
513
        self.input_ids = self.input_ids_cpu[:
                                            padded_total_num_scheduled_tokens].to(
                                                self.device)
        self.position_ids = self.positions_cpu[:
                                               padded_total_num_scheduled_tokens].to(
                                                   self.device)
        self.slot_mapping_cpu[total_num_scheduled_tokens:] = _PAD_SLOT_ID
        slot_mapping = self.slot_mapping_cpu[:
                                             padded_total_num_scheduled_tokens].to(
                                                 self.device)
514
515
        block_tables = self.block_table_cpu[:self.max_num_reqs]
        block_tables[:num_reqs, :self.max_num_blocks_per_req] = (
516
            self.input_batch.block_table.get_cpu_tensor()[:num_reqs])
517
518
        block_tables = block_tables.to(self.device)
        query_start_loc = self.query_start_loc_cpu[:self.max_num_reqs + 1].to(
519
            self.device)
520
        seq_lens = self.seq_lens_cpu[:self.max_num_reqs].to(self.device)
521
522
523

        attn_metadata = PallasMetadata(
            slot_mapping=slot_mapping,
524
            block_tables=block_tables,
525
526
            context_lens=seq_lens,
            query_start_loc=query_start_loc,
527
528
529
            num_seqs=torch.tensor([num_reqs],
                                  dtype=torch.int32,
                                  device=self.device),
530
        )
531
532
533
534
535
        # NOTE(woosuk): Due to chunked prefills, there can be at most 1 partial
        # request in the batch. While we should not sample any token from this
        # partial request, we do so for simplicity. We will ignore the sampled
        # token from the partial request.
        # TODO: Support prompt logprobs.
536
537
        padded_num_reqs = _get_padded_num_reqs_with_upper_limit(
            num_reqs, self.max_num_reqs)
538
539
        # Indices at which we sample (positions of last token in the sequence).
        # Padded to avoid recompiling when `num_reqs` varies.
540
541
        logits_indices = self.query_start_loc_cpu[1:padded_num_reqs + 1] - 1
        logits_indices = logits_indices.to(self.device)
542
        return attn_metadata, logits_indices, padded_num_reqs
543

544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
    def _scatter_placeholders(
        self,
        embeds: torch.Tensor,
        is_embed: Optional[torch.Tensor],
    ) -> torch.Tensor:
        if is_embed is None:
            return embeds

        placeholders = embeds.new_full(
            (is_embed.shape[0], embeds.shape[-1]),
            fill_value=torch.nan,
        )
        placeholders[is_embed] = embeds
        return placeholders

    def _gather_placeholders(
        self,
        placeholders: torch.Tensor,
        is_embed: Optional[torch.Tensor],
    ) -> torch.Tensor:
        if is_embed is None:
            return placeholders

        return placeholders[is_embed]

    def _execute_mm_encoder(self, scheduler_output: "SchedulerOutput"):
570
571
572
573
574
        scheduled_encoder_inputs = scheduler_output.scheduled_encoder_inputs
        if not scheduled_encoder_inputs:
            return

        # Batch the multi-modal inputs.
575
576
        mm_inputs = list[MultiModalKwargs]()
        req_ids_pos = list[tuple[str, int, PlaceholderRange]]()
577
578
        for req_id, encoder_input_ids in scheduled_encoder_inputs.items():
            req_state = self.requests[req_id]
579
580
581
582
583

            for mm_input_id in encoder_input_ids:
                mm_inputs.append(req_state.mm_inputs[mm_input_id])
                req_ids_pos.append(
                    (req_id, mm_input_id, req_state.mm_positions[mm_input_id]))
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609

        # Batch mm inputs as much as we can: if a request in the batch has
        # multiple modalities or a different modality than the previous one,
        # we process it separately to preserve item order.
        # FIXME(ywang96): This is a hacky way to deal with multiple modalities
        # in the same batch while still being able to benefit from batching
        # multimodal inputs. The proper solution should be reordering the
        # encoder outputs.
        grouped_mm_inputs_list = group_mm_inputs_by_modality(mm_inputs)

        encoder_outputs = []
        for grouped_mm_inputs in grouped_mm_inputs_list:
            batched_mm_inputs = MultiModalKwargs.batch(grouped_mm_inputs)
            batched_mm_inputs = MultiModalKwargs.as_kwargs(batched_mm_inputs,
                                                           device=self.device)

            # Run the encoder.
            # `curr_group_outputs` is either of the following:
            # 1. A tensor of shape (num_items, feature_size, hidden_size)
            # in case feature_size is fixed across all multimodal items.
            # 2. A list or tuple (length: num_items) of tensors, each of shape
            # (feature_size, hidden_size) in case the feature size is dynamic
            # depending on the input multimodal items.
            curr_group_outputs = self.model.get_multimodal_embeddings(
                **batched_mm_inputs)

610
611
612
613
614
            sanity_check_mm_encoder_outputs(
                curr_group_outputs,
                expected_num_items=len(grouped_mm_inputs),
            )

615
616
617
618
            for output in curr_group_outputs:
                encoder_outputs.append(output)

        # Cache the encoder outputs.
619
620
621
622
        for (req_id, input_id, pos_info), output in zip(
                req_ids_pos,
                encoder_outputs,
        ):
623
624
625
            if req_id not in self.encoder_cache:
                self.encoder_cache[req_id] = {}

626
627
628
629
630
631
            self.encoder_cache[req_id][input_id] = scatter_mm_placeholders(
                output,
                is_embed=pos_info.is_embed,
            )

    def _gather_mm_embeddings(
632
633
634
        self,
        scheduler_output: "SchedulerOutput",
    ) -> list[torch.Tensor]:
635
        mm_embeds: list[torch.Tensor] = []
636
637
638
639
640
641
642
        for req_id in self.input_batch.req_ids:
            num_scheduled_tokens = scheduler_output.num_scheduled_tokens[
                req_id]
            req_state = self.requests[req_id]
            num_computed_tokens = req_state.num_computed_tokens
            mm_positions = req_state.mm_positions
            for i, pos_info in enumerate(mm_positions):
643
644
                start_pos = pos_info.offset
                num_encoder_tokens = pos_info.length
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665

                # The encoder output is needed if the two ranges overlap:
                # [num_computed_tokens,
                #  num_computed_tokens + num_scheduled_tokens) and
                # [start_pos, start_pos + num_encoder_tokens)
                if start_pos >= num_computed_tokens + num_scheduled_tokens:
                    # The encoder output is not needed in this step.
                    break
                if start_pos + num_encoder_tokens <= num_computed_tokens:
                    # The encoder output is already processed and stored
                    # in the decoder's KV cache.
                    continue

                start_idx = max(num_computed_tokens - start_pos, 0)
                end_idx = min(
                    num_computed_tokens - start_pos + num_scheduled_tokens,
                    num_encoder_tokens)
                assert start_idx < end_idx
                assert req_id in self.encoder_cache
                assert i in self.encoder_cache[req_id]
                encoder_output = self.encoder_cache[req_id][i]
666
667
668
669
670
671
672
673
674
675

                if (is_embed := pos_info.is_embed) is not None:
                    is_embed = is_embed[start_idx:end_idx]

                mm_embeds_item = gather_mm_placeholders(
                    encoder_output[start_idx:end_idx],
                    is_embed=is_embed,
                )
                mm_embeds.append(mm_embeds_item)
        return mm_embeds
676

677
678
679
680
    @torch.no_grad()
    def execute_model(
        self,
        scheduler_output: "SchedulerOutput",
681
        intermediate_tensors: Optional[IntermediateTensors] = None,
682
683
684
    ) -> ModelRunnerOutput:
        # Update cached state
        self._update_states(scheduler_output)
685
        if not scheduler_output.total_num_scheduled_tokens:
686
            # Return empty ModelRunnerOutput if there's no work to do.
687
            return EMPTY_MODEL_RUNNER_OUTPUT
688

689
690
        if self.is_multimodal_model:
            # Run the multimodal encoder if any.
691
692
            self._execute_mm_encoder(scheduler_output)
            mm_embeds = self._gather_mm_embeddings(scheduler_output)
693
        else:
694
            mm_embeds = []
695

696
        # Prepare inputs
697
698
        attn_metadata, logits_indices, padded_num_reqs = self._prepare_inputs(
            scheduler_output)
699
700
701
702
        if self.is_multimodal_model:
            # NOTE(woosuk): To unify token ids and soft tokens (vision
            # embeddings), we always use embeddings (rather than token ids)
            # as input to the multimodal model, even when the input is text.
703
            if mm_embeds:
704
                inputs_embeds = self.model.get_input_embeddings(
705
                    self.input_ids, mm_embeds)
706
707
708
709
710
711
712
713
714
715
            else:
                inputs_embeds = self.model.get_input_embeddings(self.input_ids)
            input_ids = None
        else:
            # For text-only models, we use token ids as input.
            # While it is possible to use embeddings as input just like the
            # multimodal models, it is not desirable for performance since
            # then the embedding layer is not included in the CUDA graph.
            input_ids = self.input_ids
            inputs_embeds = None
716
        num_reqs = self.input_batch.num_reqs
717
718
719
        # Run the decoder
        with set_forward_context(attn_metadata, self.vllm_config):
            hidden_states = self.model(
720
721
722
                input_ids=input_ids,
                positions=self.position_ids,
                inputs_embeds=inputs_embeds,
723
            )
724
725
726
727
        hidden_states = self.select_hidden_states(hidden_states,
                                                  logits_indices)
        tpu_sampling_metadata = TPUSupportedSamplingMetadata.\
            from_input_batch(self.input_batch, padded_num_reqs, self.device)
728
729
        selected_token_ids = self.sample_from_hidden(hidden_states,
                                                     tpu_sampling_metadata)
730
        # Remove padding on cpu and keep dynamic op outside of xla graph.
731
        selected_token_ids = selected_token_ids.cpu()[:num_reqs]
732

733
734
        # Update the cache state concurrently. Code above will not block until
        # we use `selected_token_ids`. Add mark_step if post-processing changes
735
        request_seq_lens: list[tuple[int, CachedRequestState, int]] = []
736
        discard_sampled_tokens_req_indices = []
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
        for i, req_id in zip(range(num_reqs), self.input_batch.req_ids):
            assert req_id is not None
            req_state = self.requests[req_id]
            seq_len = (req_state.num_computed_tokens +
                       scheduler_output.num_scheduled_tokens[req_id])
            if seq_len >= req_state.num_tokens:
                request_seq_lens.append((i, req_state, seq_len))
            else:
                # Ignore the sampled token from the partial request.
                # Rewind the generator state as if the token was not sampled.
                generator = self.input_batch.generators.get(i)
                if generator is not None:
                    # This relies on cuda-specific torch-internal impl details
                    generator.set_offset(generator.get_offset() - 4)

752
753
754
755
                # Record the index of the request that should not be sampled,
                # so that we could clear the sampled tokens before returning.
                discard_sampled_tokens_req_indices.append(i)

756
757
758
        assert all(
            req_id is not None for req_id in
            self.input_batch.req_ids[:num_reqs]), "req_ids contains None"
759
        req_ids = cast(list[str], self.input_batch.req_ids[:num_reqs])
760

761
        prompt_logprobs_dict: dict[str, Optional[LogprobsTensors]] = {}
762
        for req_id in self.input_batch.req_ids[:num_reqs]:
763
764
            prompt_logprobs_dict[req_id] = None

765
766
767
        max_gen_len = selected_token_ids.shape[-1]
        if max_gen_len == 1:
            valid_sampled_token_ids = selected_token_ids.tolist()
768

769
770
771
772
773
774
775
            # Mask out the sampled tokens that should not be sampled.
            # TODO: Keep in sync with gpu_model_runner.py, in particular
            #       the "else" case here
            for i in discard_sampled_tokens_req_indices:
                valid_sampled_token_ids[i].clear()

            # Append sampled tokens
776
777
778
779
780
            for i, req_state, seq_len in request_seq_lens:
                token_id = valid_sampled_token_ids[i][0]
                self.input_batch.token_ids_cpu[i, seq_len] = token_id
                req_state.output_token_ids.append(token_id)
                self.input_batch.num_tokens[i] += 1
781

782
783
784
785
786
787
788
789
790
791
792
793
794
795
        else:
            valid_mask = selected_token_ids != INVALID_TOKEN_ID
            gen_lens = valid_mask.sum(dim=1).tolist()
            valid_sampled_token_ids = [
                seq.tolist()
                for seq in selected_token_ids[valid_mask].split(gen_lens)
            ]
            self.input_batch.num_tokens[:num_reqs] += gen_lens
            for i, req_state, seq_len in request_seq_lens:
                target_slice = slice(seq_len - gen_lens[i] + 1, seq_len + 1)
                self.input_batch.token_ids_cpu[
                    i, target_slice] = valid_sampled_token_ids[i]
                req_state.output_token_ids.extend(valid_sampled_token_ids[i])

796
        model_runner_output = ModelRunnerOutput(
797
            req_ids=req_ids,
798
            req_id_to_index=self.input_batch.req_id_to_index,
799
            sampled_token_ids=valid_sampled_token_ids,
800
            spec_token_ids=None,
801
            logprobs=None,
802
            prompt_logprobs_dict=prompt_logprobs_dict,
803
        )
804
805
806
807
808

        # Check there are no new graphs compiled - all the graphs should be
        # captured and compiled during warm up.
        self._verify_num_xla_graphs("execute_model")

809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
        return model_runner_output

    def load_model(self) -> None:
        self.device = self.device_config.device

        # NOTE(woosuk): While the executor assigns the TP ranks to the worker
        # process, the ranks can be different from the ranks internally assigned
        # by the xm runtime. Therefore, there is a mismatch in the rank
        # assignment between the gloo (cpu) runtime and the xm (tpu) runtime.
        # This is not a problem in linear layers because all-reduce is
        # rank-agnostic. However, it matters for all-gather as the ranks
        # determine the order of concatenating the output tensors.
        # As a workaround, we use the xm's rank assignment only when loading
        # the embedding weights.
        xm_tp_rank = xr.global_ordinal()
        with patch(
                "vllm.model_executor.layers.vocab_parallel_embedding."
                "get_tensor_model_parallel_rank",
                return_value=xm_tp_rank):
            model = get_model(vllm_config=self.vllm_config)
829
830
        # Sync all pending XLA execution during model initialization and weight
        # loading.
831
832
        xm.mark_step()
        xm.wait_device_ops()
833
834
        self.model = model
        self.sampler = TPUSampler()
835

836
    @torch.no_grad()
837
    def _dummy_run(self, num_tokens: int) -> None:
838
839
840
841
842
843
844
845
846
847
        if self.is_multimodal_model:
            input_ids = None
            inputs_embeds = torch.zeros((num_tokens, self.hidden_size),
                                        dtype=self.dtype,
                                        device=self.device)
        else:
            input_ids = torch.zeros((num_tokens),
                                    dtype=torch.int32,
                                    device=self.device)
            inputs_embeds = None
848
        actual_num_reqs = min(num_tokens, self.max_num_reqs)
849
850
851
852
853
854
        position_ids = torch.zeros(num_tokens,
                                   dtype=torch.int32,
                                   device=self.device)
        slot_mapping = torch.zeros(num_tokens,
                                   dtype=torch.int64,
                                   device=self.device)
855
856
857
858
859
        block_tables = torch.zeros(
            (self.max_num_reqs, self.block_table_cpu.shape[1]),
            dtype=torch.int32,
            device=self.device)
        query_lens = [1] * self.max_num_reqs
860
861
862
863
        query_start_loc = torch.cumsum(torch.tensor([0] + query_lens,
                                                    dtype=torch.int32),
                                       dim=0,
                                       dtype=torch.int32).to(self.device)
864
        context_lens = torch.ones((self.max_num_reqs, ),
865
866
                                  dtype=torch.int32,
                                  device=self.device)
867
868
869
        num_seqs = torch.tensor([actual_num_reqs],
                                dtype=torch.int32,
                                device=self.device)
870
871
872
873
874
        attn_metadata = PallasMetadata(
            slot_mapping=slot_mapping,
            block_tables=block_tables,
            context_lens=context_lens,
            query_start_loc=query_start_loc,
875
            num_seqs=num_seqs,
876
        )
877

878
879
880
881
        if self.is_multimodal_model:
            torch._dynamo.mark_dynamic(inputs_embeds, 0)
        else:
            torch._dynamo.mark_dynamic(input_ids, 0)
882
883
        torch._dynamo.mark_dynamic(position_ids, 0)
        torch._dynamo.mark_dynamic(attn_metadata.slot_mapping, 0)
884
885

        with set_forward_context(attn_metadata, self.vllm_config, 0):
886
887
888
889
            out = self.model(input_ids=input_ids,
                             positions=position_ids,
                             inputs_embeds=inputs_embeds)
        self._hidden_states_dtype = out.dtype
890

891
    def _precompile_backbone(self) -> None:
892
893
894
        logger.info("Compiling the model with different input shapes.")

        start = time.perf_counter()
895
        for num_tokens in self.num_tokens_paddings:
896
            logger.info("  -- num_tokens: %d", num_tokens)
897
            self._dummy_run(num_tokens)
898
899
900
        xm.wait_device_ops()
        end = time.perf_counter()
        logger.info("Compilation finished in in %.2f [secs].", end - start)
901
        self._update_num_xla_graphs("model backbone")
902

903
904
905
906
907
    def _precompile_select_hidden_states(self) -> None:
        # Compile hidden state selection function for bucketed
        # n_tokens x max_num_reqs. Graph is really small so this is fine.
        logger.info(
            "Compiling select_hidden_states with different input shapes.")
908
909
        start = time.perf_counter()
        hsize = self.model_config.get_hidden_size()
910
        for num_tokens in self.num_tokens_paddings:
911
912
            dummy_hidden = torch.zeros((num_tokens, hsize),
                                       device=self.device,
913
                                       dtype=self._hidden_states_dtype)
914
915
916
917
918
919
920
921
            torch._dynamo.mark_dynamic(dummy_hidden, 0)
            for num_reqs in self.num_reqs_paddings:
                indices = torch.zeros(num_reqs,
                                      dtype=torch.int32,
                                      device=self.device)
                torch._dynamo.mark_dynamic(indices, 0)
                self.select_hidden_states(dummy_hidden, indices)
            logger.info("  -- num_tokens: %d", num_tokens)
922
        xm.wait_device_ops()
923
        end = time.perf_counter()
924
925
        logger.info("Compilation finished in in %.2f [secs].", end - start)
        self._update_num_xla_graphs("select_hidden_states")
926

927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
    def _precompile_sample_from_hidden(self) -> None:
        logger.info("Compiling sampling with different input shapes.")
        start = time.perf_counter()
        hsize = self.model_config.get_hidden_size()
        for num_reqs in self.num_reqs_paddings:
            dummy_hidden = torch.zeros((num_reqs, hsize),
                                       device=self.device,
                                       dtype=self._hidden_states_dtype)
            # The first dimension of dummy_hidden cannot be mark_dynamic because
            # some operations in the sampler require it to be static.
            for all_greedy in [False, True]:
                generate_params_if_all_greedy = not all_greedy
                sampling_metadata = (
                    TPUSupportedSamplingMetadata.from_input_batch(
                        self.input_batch,
                        num_reqs,
                        self.device,
                        generate_params_if_all_greedy,
                    ))
                sampling_metadata.all_greedy = all_greedy
                self.sample_from_hidden(dummy_hidden, sampling_metadata)
            logger.info("  -- num_seqs: %d", num_reqs)
        xm.wait_device_ops()
        end = time.perf_counter()
951
952
        logger.info("Compilation finished in in %.2f [secs].", end - start)
        self._update_num_xla_graphs("sampling")
953

954
955
956
957
958
959
960
961
962
    def capture_model(self) -> None:
        """
        Precompile all the subgraphs with possible input shapes.
        """
        # TODO: precompile encoder
        self._precompile_backbone()
        self._precompile_select_hidden_states()
        self._precompile_sample_from_hidden()

963
964
965
966
    def initialize_kv_cache(self, kv_cache_config: KVCacheConfig) -> None:
        """
        Initialize KV cache based on `kv_cache_config`.
        Args:
967
            kv_cache_config: Configuration for the KV cache, including the KV
968
969
            cache size of each layer
        """
970
        if len(kv_cache_config.kv_cache_groups) > 1:
971
972
973
974
            raise NotImplementedError(
                "Hybrid models with more than one KV cache type are not "
                "supported yet.")

975
        kv_caches: dict[str, torch.Tensor] = {}
976

977
978
979
980
981
982
983
984
985
986
987
988
        for kv_cache_group in kv_cache_config.kv_cache_groups:
            kv_cache_spec = kv_cache_group.kv_cache_spec
            for layer_name in kv_cache_group.layer_names:
                tensor_config = kv_cache_config.tensors[layer_name]
                assert tensor_config.size % kv_cache_spec.page_size_bytes == 0
                num_blocks = tensor_config.size // kv_cache_spec.page_size_bytes
                if isinstance(kv_cache_spec, FullAttentionSpec):
                    kv_cache_shape = PallasAttentionBackend.get_kv_cache_shape(
                        num_blocks, kv_cache_spec.block_size,
                        kv_cache_spec.num_kv_heads, kv_cache_spec.head_size)
                    dtype = kv_cache_spec.dtype

989
990
991
                    tpu_kv_cache = torch.zeros(kv_cache_shape,
                                               dtype=dtype,
                                               device=self.device)
992

993
                    kv_caches[layer_name] = tpu_kv_cache
994
995
                else:
                    raise NotImplementedError
996
997
998
999
1000
1001

        bind_kv_cache(
            kv_caches,
            self.vllm_config.compilation_config.static_forward_context,
            self.kv_caches)

1002
1003
    def reset_dynamo_cache(self):
        if self.is_multimodal_model:
1004
            compiled_model = self.model.get_language_model().model
1005
1006
1007
1008
1009
1010
1011
        else:
            compiled_model = self.model.model
        if isinstance(compiled_model, TorchCompileWrapperWithCustomDispatcher):
            logger.info("Clear dynamo cache and cached dynamo bytecode.")
            torch._dynamo.eval_frame.remove_from_cache(
                compiled_model.original_code_object)
            compiled_model.compiled_codes.clear()
1012

1013
1014
1015
1016
1017
    @torch.compile(backend="openxla", fullgraph=True, dynamic=False)
    def select_hidden_states(self, hidden_states, indices_do_sample):
        return hidden_states[indices_do_sample]

    @torch.compile(backend="openxla", fullgraph=True, dynamic=False)
1018
    def sample_from_hidden(
1019
        self,
1020
        sample_hidden_states: torch.Tensor,
1021
1022
1023
        sampling_metadata: TPUSupportedSamplingMetadata,
    ) -> torch.Tensor:
        """
1024
1025
1026
        Sample with xla-friendly function. This function is to be traced 
        separately from `forward` for lighter compilation overhead.
        """
1027
        logits = self.model.compute_logits(sample_hidden_states, None)
1028
1029
1030
1031
1032
        if sampling_metadata.all_greedy:
            out_tokens = torch.argmax(logits, dim=-1, keepdim=True)
        else:
            out_tokens = self.sampler(logits,
                                      sampling_metadata).sampled_token_ids
1033
1034
        return out_tokens

1035
1036
    def get_multimodal_embeddings(self, *args, **kwargs):
        return self.model.get_multimodal_embeddings(*args, **kwargs)
1037

1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
    def get_input_embeddings(self, *args, **kwargs):
        return self.model.get_input_embeddings(*args, **kwargs)


def _get_req_paddings(min_req_size: int, max_req_size: int) -> list[int]:
    logger.info("Preparing request paddings:")
    # assert min_req_size is power of 2
    assert (min_req_size & (min_req_size - 1) == 0) and min_req_size > 0
    paddings: list = []
    num = max(MIN_NUM_SEQS, min_req_size)
    while num <= max_req_size and (len(paddings) == 0 or paddings[-1] != num):
        paddings.append(num)
        logger.info("    %d", num)
        num = _get_padded_num_reqs_with_upper_limit(num + 1, max_req_size)
    return paddings
1053
1054


1055
def _get_padded_num_reqs_with_upper_limit(x: int, upper_limit: int) -> int:
1056
    res = MIN_NUM_SEQS if x <= MIN_NUM_SEQS else 1 << (x - 1).bit_length()
1057
    return min(res, upper_limit)
1058
1059


1060
1061
def _get_token_paddings(min_token_size: int, max_token_size: int,
                        padding_gap: int) -> list[int]:
1062
1063
    """Generate a list of padding size, starting from min_token_size, 
    ending with a number that can cover max_token_size
1064
1065
1066
1067
1068
1069
    
    If padding_gap == 0 then:
        increase 2X each time (exponential)
    else:
        first increase the size to twice, 
        then increase the padding size by padding_gap.
1070
    """
1071
1072
    # assert min_token_size is power of 2
    assert (min_token_size & (min_token_size - 1) == 0) and min_token_size > 0
1073
1074
    paddings = []
    num = min_token_size
1075
1076

    if padding_gap == 0:
1077
        logger.info("Using exponential token paddings:")
1078
        while True:
1079
1080
            logger.info("    %d", num)
            paddings.append(num)
1081
1082
            if num >= max_token_size:
                break
1083
1084
1085
            num *= 2

    else:
1086
        logger.info("Using incremental token paddings:")
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
        while num <= padding_gap:
            logger.info("    %d", num)
            paddings.append(num)
            num *= 2
        num //= 2
        while num < max_token_size:
            num += padding_gap
            logger.info("    %d", num)
            paddings.append(num)

1097
1098
1099
1100
1101
1102
1103
1104
1105
    return paddings


def _get_padded_token_len(paddings: list[int], x: int) -> int:
    """Return the first element in paddings list greater or equal to x.
    """
    index = bisect.bisect_left(paddings, x)
    assert index < len(paddings)
    return paddings[index]