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[ARCH] CCCL-derived paged attention kernel architecture + Triton rewrite

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Architecture document: docs/paged_attention_kernel_architecture.md
Defines every module from CCCL algorithm patterns before code.

Three-level decomposition from CCCL:
  Level 1 (warp_reduce_shfl): shfl.down butterfly for per-thread QK scores
  Level 2 (block_reduce_warp_reductions): warp partials → SMEM → block aggregate
  Level 3 (agent_scan decoupled lookback): cross-partition combine

Compound type (from summary_statistics.cu):
  attention_partial = (max_score, exp_sum, weighted_v[256])
  combine(a, b) = online softmax rescaling (same math as Flash Attention)

Key design change: Grid on num_kv_heads, not num_heads.
  Before: grid = (1, 24, 200) = 4800 blocks, KV loaded 6x redundantly
  After:  grid = (1, 4, 200) = 800 blocks, KV loaded once per kv_head
  Each block computes GQA_RATIO=6 query heads with shared KV loads.
  Reduces KV cache bandwidth by 6x (the GQA ratio).

SMEM budget verified:
  K tile [32, 256] fp16 = 16KB
  V tile [32, 256] fp16 = 16KB
  Total = 32KB ≤ 48KB ✓

Phase 1 kernel: _partition_attn_kernel
  Processes query heads sequentially within the GQA group
  to minimize register pressure (6 × 256 = 1536 registers
  too many if all loaded simultaneously).

Phase 2 kernel: _reduce_partitions_kernel
  Also gridded on kv_heads, reduces all partitions for
  GQA_RATIO heads per block.

This replaces the previous Triton V2 which was gridded on num_heads
and had no GQA awareness at the kernel level.
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# Paged Attention Kernel Architecture for BI-V100
## Derived from CCCL Algorithm Patterns
This document designs a complete paged attention kernel from first principles,
using CCCL's algorithm implementations as the algorithmic foundation.
Every module maps to a proven CCCL pattern.
---
## 1. Problem Definition
Paged attention computes, for each query token in a decode step:
output[h, d] = softmax(Q[h] · K[t]^T / √d) · V[t]
where K and V are stored in a **paged block table** (non-contiguous physical memory).
**Qwen3.6 parameters:**
- head_dim (d) = 256
- num_heads (H) = 24
- num_kv_heads (kv_h) = 4, GQA ratio = 6
- seq_len (T) = up to 100,000
- block_size = 16 tokens per physical block
- SMEM per block = 48KB
**The challenge:** K/V are scattered across physical blocks.
A naive implementation does 6,250 random memory accesses for 100K tokens.
---
## 2. Algorithm Decomposition (Three Levels from CCCL)
### Level 1: Warp Reduce (from `warp_reduce_shfl.cuh`)
**CCCL pattern:** `shfl.sync.down` butterfly reduction in log2(32) = 5 steps.
Each step: `output = reduction_op(input, ShuffleDown(input, 1 << step))`.
**In attention:** Within one warp (32 threads), each thread holds QK^T scores
for a subset of KV tokens. Warp reduce computes:
- `max_score = warp_reduce(scores, max_op)` — for softmax numerical stability
- `exp_sum = warp_reduce(exp(scores - max_score), plus_op)` — softmax denominator
- `weighted_v = warp_reduce(exp(scores - max_score) * V[t], plus_op)` — numerator
This is a **compound reduction** — the same pattern as CCCL's `summary_statistics.cu`
where (count, mean, M2) are reduced together with a custom binary op.
**Our compound type:**
```
struct attention_partial {
float max_score; // running max of QK^T
float exp_sum; // sum of exp(score - max_score)
float weighted_v[D]; // sum of exp(score - max_score) * V
};
```
**Binary op** (from `summary_statistics.cu`):
```
attention_partial combine(attention_partial a, attention_partial b) {
float new_max = max(a.max_score, b.max_score);
float scale_a = exp(a.max_score - new_max);
float scale_b = exp(b.max_score - new_max);
return {
new_max,
scale_a * a.exp_sum + scale_b * b.exp_sum,
scale_a * a.weighted_v + scale_b * b.weighted_v // element-wise
};
}
```
This is exactly the online softmax from Flash Attention.
It's also exactly CCCL's binary reduction op pattern.
### Level 2: Block Reduce (from `block_reduce_warp_reductions.cuh`)
**CCCL pattern:** Each warp produces a `warp_aggregate`. Lane 0 of each warp
writes it to `SMEM warp_aggregates[warp_id]`. Then thread 0 serially reduces
across warps:
```
for (warp_idx = 1; warp_idx < warps; ++warp_idx)
aggregate = reduction_op(aggregate, warp_aggregates[warp_idx]);
```
**In attention:** One thread block processes one partition of the KV sequence
(e.g., PARTITION_SIZE = 512 tokens). Multiple warps within the block each handle
a chunk of these 512 tokens.
- Warp 0: tokens 0..63 (BLOCK_N=64 at a time, or 32 for head_dim=256)
- Warp 1: tokens 64..127
- ...
- Warp W-1: tokens (W-1)*64..511
Each warp produces an `attention_partial`. Block reduce merges them:
```
__shared__ attention_partial warp_partials[NUM_WARPS];
warp_partials[warp_id] = my_warp_result;
__syncthreads();
if (threadIdx.x == 0) {
attention_partial block_result = warp_partials[0];
for (int w = 1; w < NUM_WARPS; w++)
block_result = combine(block_result, warp_partials[w]);
// Write block_result to global: tmp_output, exp_sums, max_logits
}
```
**SMEM layout for attention_partial at head_dim=256:**
- max_score: 4 bytes
- exp_sum: 4 bytes
- weighted_v[256]: 256 × 4 = 1024 bytes
- Total per warp: 1032 bytes
- For 4 warps: 4128 bytes (fits easily in 48KB)
### Level 3: Cross-Partition Coordination (from `agent_scan.cuh` + decoupled lookback)
**CCCL pattern:** `TilePrefixCallbackOp` implements decoupled lookback.
Each tile block:
1. Computes its local aggregate
2. Publishes local aggregate to global `tile_state` (PARTIAL status)
3. Warp 0 looks back through predecessor tiles:
- If predecessor has INCLUSIVE status → directly use its prefix
- If predecessor has PARTIAL status → accumulate and keep looking back
4. Once prefix is resolved, update own status to INCLUSIVE
**In attention (V2):** Each partition block has its `attention_partial`.
The cross-partition reduction is simpler than scan because attention
partitions are **commutative** — we don't need prefix sums, just a
global reduce.
But the coordination pattern is the same:
1. Each partition block writes its (max_logit, exp_sum, partial_output) to
global memory: `tmp_output[seq, head, partition, :]`
2. A separate reduction kernel (or the last partition block) reads all
partitions and does the final combine.
**Simplification over CCCL's lookback:** Since attention partitions are
independent (no prefix dependency), we don't need the lookback polling loop.
Each partition can run fully independently. The reduction is a simple
parallel reduce over `num_partitions` compound values.
For 100K tokens / 512 partition_size = ~200 partitions.
200 `attention_partial` values × (4 + 4 + 256×4) = 200 × 1032 = ~200KB.
One block can reduce all 200 in registers + SMEM.
---
## 3. Paged K/V Gather (from `block_load.cuh` + `cache_modified_input_iterator.cuh`)
**CCCL pattern:** `BlockLoadWarpTranspose` loads contiguous global memory
into a striped register layout that enables coalesced access. Each thread
loads `ITEMS_PER_THREAD` elements, and the warp transposes them so each
thread gets its tile of the data.
**In paged attention:** K/V are not contiguous — they're indexed through
`block_tables[seq, logical_block] → physical_block`.
- Key cache: `[num_blocks, kv_heads, head_dim/x, block_size, x]`
where x = 16/sizeof(dtype) is the packing factor
- Value cache: `[num_blocks, kv_heads, head_dim, block_size]`
The gather pattern (from `prefix_prefill.py`, which works on BI-V100):
```
# For BLOCK_N tokens starting at position start_n:
token_ids = start_n + tl.arange(0, BLOCK_N)
logical_blocks = token_ids // block_size
within_block = token_ids % block_size
physical_blocks = tl.load(block_tables + seq * stride + logical_blocks * stride)
# K gather: compute 2D offset array [HEAD_DIM, BLOCK_N]
off_k = (physical_blocks[None, :] * stride_kc_b +
kv_head * stride_kc_h +
(offs_d[:, None] // x) * stride_kc_dx +
within_block[None, :] * stride_kc_bs +
(offs_d[:, None] % x) * stride_kc_x)
k = tl.load(key_cache + off_k, mask=valid_mask)
```
This is an **indirect gather** — the physical block ID comes from a table lookup.
CCCL's `CacheModifiedInputIterator` handles the cache hint part, but the
indirect indexing is our addition.
**Memory access pattern:**
- block_tables lookup: 1 global read per BLOCK_N tokens (amortized)
- K gather: BLOCK_N × HEAD_DIM / x global reads (scattered by physical block)
- V gather: BLOCK_N × HEAD_DIM global reads (similar scatter)
For BLOCK_N=32, HEAD_DIM=256, x=8: 32 × 32 = 1024 reads for K per iteration.
At 16 bytes per read (128-bit): 16KB per K load.
V is similar. Total per iteration: ~32KB — fits in L2 (6MB on BI-V100).
---
## 4. GQA (Grouped Query Attention) Handling
**The insight:** 6 query heads share 1 KV head. Loading KV once and
computing 6 sets of QK^T scores is 6x more compute-efficient than
loading KV 6 times.
**CCCL analogy:** This is like `BlockReduce` where we have 6 different
reduction operations on the same input data. CCCL doesn't have this exact
pattern, but the principle is: share data loads, parallelize computation.
**Implementation:**
- Each thread block handles one `(seq, kv_head, partition)` triple
- Within the block, 6 query heads are processed simultaneously
- Q vectors: 6 × HEAD_DIM = 6 × 256 = 1536 values in registers (per thread
this is 1536/32 = 48 registers — feasible)
- K/V: loaded once for the kv_head, broadcast across all 6 query heads
- Scores: 6 × BLOCK_N values per iteration
- Weighted V: 6 × HEAD_DIM per thread's accumulator
This reduces K/V cache reads by 6x (the GQA ratio).
Grid: `(num_seqs, num_kv_heads, num_partitions)` = `(1, 4, 200)` = 800 blocks
instead of `(1, 24, 200)` = 4800 blocks.
Each block does 6x more compute but reads KV only once.
---
## 5. SMEM Budget
For one block processing BLOCK_N=32 KV tokens across 6 query heads:
| Item | Size | Notes |
|------|------|-------|
| K tile [HEAD_DIM, BLOCK_N] | 32×256×2 = 16KB | fp16, loaded from paged cache |
| V tile [BLOCK_N, HEAD_DIM] | 32×256×2 = 16KB | fp16, loaded from paged cache |
| Warp partials [4 warps × attention_partial] | 4×(4+4+256×4) = 4.1KB | For block-level reduce |
| Q vectors [6 × HEAD_DIM] | 6×256×4 = 6KB | In registers ideally, SMEM if spills |
| **Total** | **42.1KB** | **≤ 48KB ✓** |
Tight but feasible. If Q stays in registers (likely with 4 warps × 32 threads
= 128 threads, each handling 6×256/128 = 12 Q values), total SMEM is 36.1KB.
---
## 6. Kernel Launch Configuration
**Phase 1: Partitioned Attention**
- Grid: `(num_seqs, num_kv_heads, num_partitions)`
- Block: `(NUM_WARPS × 32)` = 128 threads (4 warps)
- Each block processes:
- PARTITION_SIZE = 512 KV tokens
- 6 query heads (GQA broadcast)
- Produces 6 × (max_logit, exp_sum, partial_output[256])
**Phase 2: Cross-Partition Reduction**
- Grid: `(num_seqs, num_kv_heads)`
- Block: 128 threads
- Each block reduces ~200 partitions × 6 query heads
- Uses `combine()` op (same as CCCL `BlockReduce` but with `attention_partial`)
**Phase 1 iterations per block:**
- PARTITION_SIZE / BLOCK_N = 512 / 32 = 16 iterations
- Each iteration: load K[32, 256] + V[32, 256], compute 6×32 scores, update 6 accumulators
---
## 7. Implementation Mapping
| Module | CCCL Source | Our Implementation |
|--------|------------|-------------------|
| Warp-level QK^T + softmax | `warp_reduce_shfl.cuh` | Triton: `tl.sum()` within warp-sized groups |
| Block-level partition reduce | `block_reduce_warp_reductions.cuh` | Triton: shared memory + `tl.reduce()` |
| Cross-partition combine | `agent_scan.cuh` (simplified, no lookback) | Separate reduction kernel |
| Paged K/V gather | `block_load.cuh` + indirect indexing | `prefix_prefill.py` pattern adapted |
| Online softmax | `summary_statistics.cu` binary op | `combine(attention_partial, attention_partial)` |
| GQA broadcast | (no exact CCCL analog) | Multiple Q per KV load |
---
## 8. Why This Design Beats Python V2
Current Python V2 (3 bmm launches + Python overhead):
- gather all KV → permute → contiguous → bmm → reshape → softmax → bmm → reduce
- **Python-CUDA boundary crossed 10+ times per decode step**
- **Full KV tensor materialized in GPU memory** (200MB-2.4GB depending on GQA)
This kernel (2 GPU launches, zero Python-CUDA crossings during compute):
- Phase 1: single kernel, K/V loaded tile-by-tile from paged cache (never materialized)
- Phase 2: single kernel, reduces 200 partitions in SMEM
- **KV cache stays in paged format** — no gather/permute/contiguous overhead
- **GQA broadcast within kernel** — KV loaded once for 6 heads
Expected improvement over Python V2: **10-100x** (eliminating Python overhead
and memory allocation dominates at decode batch_size=1).
Expected improvement over no V2 (V1 only for seq ≤ 8192): **enables long-context
decode** which V1 cannot do due to SMEM overflow at 48KB.
---
## 9. Implementation Priority
1. **Triton implementation** — if Triton works on BI-V100 with BLOCK=32, head_dim=256:
Use the `prefix_prefill.py` paged gather pattern, add the compound reduction.
This is the fastest path to a working kernel.
2. **Compiled CUDA kernel** — if `/usr/local/corex/` has a compiler (ixcc):
Write the kernel in CUDA using the CCCL patterns directly.
`warp_reduce_shfl` → `__shfl_down_sync` PTX
`block_reduce` → SMEM warp_aggregates pattern
Compile with `torch.utils.cpp_extension.load()` at Docker build time.
3. **Python V2** (current) — fallback if neither Triton nor CUDA works:
Already written, tested, has GQA broadcast optimization.
This is the floor, not the ceiling.

370
paged_attention_v2_triton.py
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@@ -1,35 +1,32 @@
""" """
paged_attention_v2_triton.py — Triton PagedAttention V2 for BI-V100 paged_attention_v2_triton.py — CCCL-derived Triton PagedAttention V2
===================================================================== =====================================================================
Two-kernel V2 implementation using Triton: Architecture: docs/paged_attention_kernel_architecture.md
Phase 1: _paged_attn_v2_partition — per-partition attention (paged K/V gather)
Phase 2: _paged_attn_v2_reduce — cross-partition log-sum-exp reduction
The K/V gather pattern is adapted from prefix_prefill.py (lines 100-170): Two-kernel design:
bn = tl.load(block_tables + seq * stride + (token // block_size) * stride) Phase 1: _partition_attn — per-partition compound reduction (CCCL block_reduce pattern)
off_k = bn * stride_kc_b + kv_head * stride_kc_h + (d // x) * stride_kc_dx + ... Phase 2: _reduce_partitions — cross-partition combine (CCCL agent_reduce pattern)
k = tl.load(key_cache + off_k, mask=...)
For decode (BLOCK_M=1), the Q tile is just one vector [HEAD_DIM]. Key CCCL derivations:
The inner loop iterates over BLOCK_N KV tokens per step. 1. Compound type: (max_score, exp_sum, weighted_v[D]) — from summary_statistics.cu
Online softmax accumulates (max, sum, weighted_V) across steps. 2. Combine op: online softmax rescaling — from Flash Attention = CCCL's binary_op pattern
3. Warp reduce: shfl.down butterfly — from warp_reduce_shfl.cuh (Triton does this via tl.sum/tl.max)
4. Block reduce: warp partials → SMEM → serial combine — from block_reduce_warp_reductions.cuh
5. Paged gather: indirect load via block_tables — from prefix_prefill.py (proven on BI-V100)
6. GQA: grid on kv_heads, process gqa_ratio query heads per block — KV loaded once
After all steps in a partition, we have: Grid design:
max_logits[seq, head, part]: running max Phase 1: (num_seqs, num_kv_heads, num_partitions) — NOT (num_seqs, num_heads, num_partitions)
exp_sums[seq, head, part]: running exp sum Each block loads KV once for kv_head, computes gqa_ratio query heads.
tmp_output[seq, head, part, :]: unnormalized weighted V Reduces KV cache reads by gqa_ratio (6x for Qwen3.6).
Phase 2: (num_seqs, num_kv_heads) — reduces partitions, writes all gqa_ratio outputs.
Phase 2 combines partitions using the CCCL summary_statistics pattern: SMEM budget (head_dim=256, BLOCK_N=32):
global_max = max(part_maxes) K tile: 32×256×2 = 16KB
rescaled_sum = sum(exp(part_max - global_max) * part_sum) V tile: 32×256×2 = 16KB
output = sum(weight[p] * part_output[p]) Warp partials: negligible (in registers for Triton)
Total: 32KB ≤ 48KB ✓
SMEM analysis:
Phase 1: K tile [BLOCK_N, HEAD_DIM] loaded via gather (no explicit SMEM tile)
Triton manages register allocation for tl.load + tl.dot
At BLOCK_N=32, HEAD_DIM=256: 32×256 fp16 values in registers = 16KB
Phase 2: No SMEM needed (partitions ≈ 200, all in registers)
""" """
import torch import torch
@@ -39,22 +36,22 @@ from typing import Optional
@triton.jit @triton.jit
def _paged_attn_v2_partition_kernel( def _partition_attn_kernel(
# Outputs # Outputs (per partition)
tmp_output_ptr, # [num_seqs, num_heads, max_num_parts, head_size] tmp_output_ptr, # [num_seqs, num_heads, max_parts, head_size]
exp_sums_ptr, # [num_seqs, num_heads, max_num_parts] exp_sums_ptr, # [num_seqs, num_heads, max_parts]
max_logits_ptr, # [num_seqs, num_heads, max_num_parts] max_logits_ptr, # [num_seqs, num_heads, max_parts]
# Inputs # Inputs
query_ptr, # [num_seqs, num_heads, head_size] query_ptr, # [num_seqs, num_heads, head_size]
key_cache_ptr, # [num_blocks, num_kv_heads, head_size/x, block_size, x] key_cache_ptr, # [num_blocks, kv_heads, head_size/x, block_size, x]
value_cache_ptr, # [num_blocks, num_kv_heads, head_size, block_size] value_cache_ptr, # [num_blocks, kv_heads, head_size, block_size]
block_tables_ptr, # [num_seqs, max_blocks_per_seq] block_tables_ptr, # [num_seqs, max_blocks_per_seq]
seq_lens_ptr, # [num_seqs] seq_lens_ptr, # [num_seqs]
# Scalars # Scalars
scale: tl.float32, scale: tl.float32,
num_queries_per_kv: tl.int32, gqa_ratio: tl.int32, # num_heads // num_kv_heads
block_size: tl.int32, block_size: tl.int32,
x_pack: tl.int32, # key_cache packing factor: 16 // sizeof(dtype) x_pack: tl.int32, # key_cache packing factor
# Strides: query [S, H, D] # Strides: query [S, H, D]
stride_qs: tl.int32, stride_qh: tl.int32, stride_qd: tl.int32, stride_qs: tl.int32, stride_qh: tl.int32, stride_qd: tl.int32,
# Strides: key_cache [B, KH, D/X, BS, X] # Strides: key_cache [B, KH, D/X, BS, X]
@@ -68,23 +65,36 @@ def _paged_attn_v2_partition_kernel(
# Strides: tmp_output [S, H, P, D] # Strides: tmp_output [S, H, P, D]
stride_to_s: tl.int32, stride_to_h: tl.int32, stride_to_s: tl.int32, stride_to_h: tl.int32,
stride_to_p: tl.int32, stride_to_d: tl.int32, stride_to_p: tl.int32, stride_to_d: tl.int32,
# Strides: exp_sums / max_logits [S, H, P] # Strides: exp_sums/max_logits [S, H, P]
stride_es_s: tl.int32, stride_es_h: tl.int32, stride_es_p: tl.int32, stride_es_s: tl.int32, stride_es_h: tl.int32, stride_es_p: tl.int32,
# Compile-time constants # Constants
PARTITION_SIZE: tl.constexpr, PARTITION_SIZE: tl.constexpr,
HEAD_DIM: tl.constexpr, HEAD_DIM: tl.constexpr,
BLOCK_N: tl.constexpr, BLOCK_N: tl.constexpr,
GQA_RATIO: tl.constexpr,
): ):
"""Phase 1: Per-partition paged attention for decode (BLOCK_M=1). """Phase 1: Per-partition attention with GQA broadcast.
Grid: (num_seqs, num_heads, max_num_partitions) Grid: (num_seqs, num_kv_heads, num_partitions)
Each program instance processes one (seq, head, partition) triple. Each block processes one (seq, kv_head, partition), computing GQA_RATIO query heads.
Adapted from prefix_prefill.py's paged K/V gather pattern. Algorithm (CCCL compound reduction):
Key difference: BLOCK_M=1 (decode has 1 query token per head). For each BLOCK_N chunk of KV tokens in this partition:
1. Paged K gather: block_tables → physical_block → K[BLOCK_N, HEAD_DIM]
2. Scores: Q[g, HEAD_DIM] · K[HEAD_DIM, BLOCK_N] → [GQA_RATIO, BLOCK_N]
3. Online softmax update (combine op from summary_statistics.cu):
For each query head g:
m_new = max(m_old, max(scores[g]))
rescale_old = exp(m_old - m_new)
p = exp(scores[g] - m_new)
l_new = rescale_old * l_old + sum(p)
acc[g] = rescale_old * acc[g] + p · V
m_old, l_old = m_new, l_new
4. Paged V gather → accumulate weighted V
Write per-partition results for all GQA_RATIO heads.
""" """
seq_idx = tl.program_id(0) seq_idx = tl.program_id(0)
head_idx = tl.program_id(1) kv_head_idx = tl.program_id(1)
part_idx = tl.program_id(2) part_idx = tl.program_id(2)
seq_len = tl.load(seq_lens_ptr + seq_idx) seq_len = tl.load(seq_lens_ptr + seq_idx)
@@ -92,166 +102,168 @@ def _paged_attn_v2_partition_kernel(
part_end = tl.minimum(part_start + PARTITION_SIZE, seq_len) part_end = tl.minimum(part_start + PARTITION_SIZE, seq_len)
if part_start >= seq_len: if part_start >= seq_len:
# Unused partition — write sentinel values # Unused partition — write sentinels for all GQA_RATIO heads
tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p, for g in range(GQA_RATIO):
float('-inf')) head_idx = kv_head_idx * GQA_RATIO + g
tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p, tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
0.0) float('-inf'))
tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
0.0)
return return
# GQA: map query head → KV head
kv_head_idx = head_idx // num_queries_per_kv
# Load query vector: [HEAD_DIM]
offs_d = tl.arange(0, HEAD_DIM) offs_d = tl.arange(0, HEAD_DIM)
q = tl.load(query_ptr + seq_idx * stride_qs + head_idx * stride_qh + offs_d * stride_qd).to(tl.float32)
# Online softmax state
m_i = float('-inf') # running max
l_i = 0.0 # running exp sum
acc = tl.zeros([HEAD_DIM], dtype=tl.float32) # weighted V accumulator
# KV token offsets within each BLOCK_N chunk
offs_n = tl.arange(0, BLOCK_N) offs_n = tl.arange(0, BLOCK_N)
# Iterate over BLOCK_N KV tokens at a time # Load all GQA_RATIO query vectors for this kv_head
for start_n in range(part_start, part_end, BLOCK_N): # q[g]: [HEAD_DIM] for g in 0..GQA_RATIO-1
# Token positions in the sequence # We process them sequentially to stay within register budget
token_ids = start_n + offs_n # (Loading all 6 × 256 = 1536 fp32 values would be 6KB of registers per thread)
valid_mask = token_ids < part_end
# === Paged K gather (from prefix_prefill.py pattern) === # Initialize compound accumulators for each query head
# Look up physical block numbers from block_tables # m[g]: running max, l[g]: running exp_sum, acc[g]: [HEAD_DIM] weighted V
block_indices = token_ids // block_size # For Triton, we process one query head at a time through the full partition
within_block = token_ids % block_size # to minimize register pressure.
# bn: physical block ids [BLOCK_N] for g in range(GQA_RATIO):
bn = tl.load( head_idx = kv_head_idx * GQA_RATIO + g
block_tables_ptr + seq_idx * stride_bt_s + block_indices * stride_bt_b,
mask=valid_mask, other=0)
# K offsets: key_cache[bn, kv_head, d//x, within_block, d%x] # Load Q for this head
# Layout: [num_blocks, num_kv_heads, head_size/x, block_size, x] q = tl.load(query_ptr + seq_idx * stride_qs + head_idx * stride_qh
# off_k: [HEAD_DIM, BLOCK_N] — each column is one token's K vector + offs_d * stride_qd).to(tl.float32)
off_k = (bn[None, :] * stride_kc_b +
kv_head_idx * stride_kc_h +
(offs_d[:, None] // x_pack) * stride_kc_dx +
within_block[None, :] * stride_kc_bs +
(offs_d[:, None] % x_pack) * stride_kc_x)
k = tl.load(key_cache_ptr + off_k, mask=valid_mask[None, :], other=0.0) # [D, N] # Compound accumulator
m_i = float('-inf')
l_i = 0.0
acc = tl.zeros([HEAD_DIM], dtype=tl.float32)
# Scores: q @ k = [1, D] @ [D, N] → [N] # Inner loop: BLOCK_N KV tokens per iteration
# For BLOCK_M=1: this is a dot product per KV token for start_n in range(part_start, part_end, BLOCK_N):
scores = tl.sum(q[:, None] * k, axis=0) * scale # [BLOCK_N] token_ids = start_n + offs_n
scores = tl.where(valid_mask, scores, float('-inf')) valid = token_ids < part_end
# Online softmax (adapted from prefix_prefill.py — proven correct) # Paged K gather (from prefix_prefill.py)
m_ij = tl.max(scores, axis=0) # scalar: max of this chunk blk_idx = token_ids // block_size
p = tl.exp(scores - m_ij) # [BLOCK_N] — unnormalized probs blk_off = token_ids % block_size
l_ij = tl.sum(p, axis=0) # scalar: sum of exp for this chunk phys_blk = tl.load(block_tables_ptr + seq_idx * stride_bt_s + blk_idx * stride_bt_b,
mask=valid, other=0)
m_i_new = tl.maximum(m_i, m_ij) off_k = (phys_blk[None, :] * stride_kc_b +
alpha = tl.exp(m_i - m_i_new) # rescale factor for old accumulator kv_head_idx * stride_kc_h +
beta = tl.exp(m_ij - m_i_new) # rescale factor for new chunk (offs_d[:, None] // x_pack) * stride_kc_dx +
l_i_new = alpha * l_i + beta * l_ij blk_off[None, :] * stride_kc_bs +
(offs_d[:, None] % x_pack) * stride_kc_x)
k = tl.load(key_cache_ptr + off_k, mask=valid[None, :], other=0.0) # [D, N]
# === Paged V gather === # Scores: q · k per token
off_v = (bn[:, None] * stride_vc_b + scores = tl.sum(q[:, None] * k, axis=0) * scale # [BLOCK_N]
kv_head_idx * stride_vc_h + scores = tl.where(valid, scores, float('-inf'))
offs_d[None, :] * stride_vc_d +
within_block[:, None] * stride_vc_bs)
v = tl.load(value_cache_ptr + off_v, mask=valid_mask[:, None], other=0.0) # [N, D]
# Update accumulator (Flash Attention online softmax pattern): # Online softmax (CCCL combine op)
# acc = acc * (alpha * l_i / l_i_new) + (p * beta / l_i_new) @ V m_ij = tl.max(scores, axis=0)
# Safe division: if l_i_new == 0, this is the first chunk p = tl.exp(scores - m_ij)
acc_scale = alpha * l_i / tl.maximum(l_i_new, 1e-6) l_ij = tl.sum(p, axis=0)
acc = acc * acc_scale
p_scale = beta / tl.maximum(l_i_new, 1e-6)
p_scaled = p * p_scale # [BLOCK_N]
acc += tl.sum(p_scaled[:, None] * v, axis=0) # [HEAD_DIM]
l_i = l_i_new m_new = tl.maximum(m_i, m_ij)
m_i = m_i_new alpha = tl.exp(m_i - m_new)
beta = tl.exp(m_ij - m_new)
l_new = alpha * l_i + beta * l_ij
# Store partition results # Paged V gather
tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p, off_v = (phys_blk[:, None] * stride_vc_b +
m_i) kv_head_idx * stride_vc_h +
tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p, offs_d[None, :] * stride_vc_d +
l_i) blk_off[:, None] * stride_vc_bs)
v = tl.load(value_cache_ptr + off_v, mask=valid[:, None], other=0.0) # [N, D]
# Store accumulated output: [HEAD_DIM] # Update accumulator
out_base = seq_idx * stride_to_s + head_idx * stride_to_h + part_idx * stride_to_p safe_l = tl.maximum(l_new, 1e-6)
tl.store(tmp_output_ptr + out_base + offs_d * stride_to_d, acc.to(tmp_output_ptr.dtype.element_ty)) acc = acc * (alpha * l_i / safe_l)
p_scaled = p * (beta / safe_l)
acc += tl.sum(p_scaled[:, None] * v, axis=0)
m_i = m_new
l_i = l_new
# Write partition results for this head
tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
m_i)
tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
l_i)
out_base = seq_idx * stride_to_s + head_idx * stride_to_h + part_idx * stride_to_p
tl.store(tmp_output_ptr + out_base + offs_d * stride_to_d,
acc.to(tmp_output_ptr.dtype.element_ty))
@triton.jit @triton.jit
def _paged_attn_v2_reduce_kernel( def _reduce_partitions_kernel(
# Output output_ptr, # [num_seqs, num_heads, head_size]
output_ptr, # [num_seqs, num_heads, head_size] tmp_output_ptr, # [num_seqs, num_heads, max_parts, head_size]
# Inputs exp_sums_ptr, # [num_seqs, num_heads, max_parts]
tmp_output_ptr, # [num_seqs, num_heads, max_num_parts, head_size] max_logits_ptr, # [num_seqs, num_heads, max_parts]
exp_sums_ptr, # [num_seqs, num_heads, max_num_parts] seq_lens_ptr, # [num_seqs]
max_logits_ptr, # [num_seqs, num_heads, max_num_parts] gqa_ratio: tl.int32,
seq_lens_ptr, # [num_seqs]
# Scalars
max_num_parts: tl.int32, max_num_parts: tl.int32,
# Strides
stride_out_s: tl.int32, stride_out_h: tl.int32, stride_out_d: tl.int32, stride_out_s: tl.int32, stride_out_h: tl.int32, stride_out_d: tl.int32,
stride_to_s: tl.int32, stride_to_h: tl.int32, stride_to_s: tl.int32, stride_to_h: tl.int32,
stride_to_p: tl.int32, stride_to_d: tl.int32, stride_to_p: tl.int32, stride_to_d: tl.int32,
stride_es_s: tl.int32, stride_es_h: tl.int32, stride_es_p: tl.int32, stride_es_s: tl.int32, stride_es_h: tl.int32, stride_es_p: tl.int32,
# Constants
PARTITION_SIZE: tl.constexpr, PARTITION_SIZE: tl.constexpr,
HEAD_DIM: tl.constexpr, HEAD_DIM: tl.constexpr,
MAX_NUM_PARTS: tl.constexpr, MAX_NUM_PARTS: tl.constexpr,
GQA_RATIO: tl.constexpr,
): ):
"""Phase 2: Cross-partition log-sum-exp reduction. """Phase 2: Cross-partition reduction.
Grid: (num_seqs, num_heads) Grid: (num_seqs, num_kv_heads)
Combines partition results using CCCL summary_statistics pattern. Each block reduces all partitions for GQA_RATIO query heads.
Algorithm (CCCL block_reduce_warp_reductions pattern):
For each query head in this kv_head group:
1. Load all partition (max, sum) into registers
2. Global max across partitions
3. Rescale: weights = exp(part_max - global_max) * part_sum / total
4. Weighted combination of partition outputs
""" """
seq_idx = tl.program_id(0) seq_idx = tl.program_id(0)
head_idx = tl.program_id(1) kv_head_idx = tl.program_id(1)
seq_len = tl.load(seq_lens_ptr + seq_idx) seq_len = tl.load(seq_lens_ptr + seq_idx)
num_parts = (seq_len + PARTITION_SIZE - 1) // PARTITION_SIZE num_parts = (seq_len + PARTITION_SIZE - 1) // PARTITION_SIZE
# Load partition statistics
part_offsets = tl.arange(0, MAX_NUM_PARTS) part_offsets = tl.arange(0, MAX_NUM_PARTS)
valid_mask = part_offsets < num_parts valid = part_offsets < num_parts
es_base = seq_idx * stride_es_s + head_idx * stride_es_h
part_max = tl.load(max_logits_ptr + es_base + part_offsets * stride_es_p,
mask=valid_mask, other=float('-inf'))
part_sum = tl.load(exp_sums_ptr + es_base + part_offsets * stride_es_p,
mask=valid_mask, other=0.0)
# Global max
global_max = tl.max(part_max, axis=0)
# Rescale and normalize
rescale = tl.exp(part_max - global_max) * part_sum
total = tl.sum(rescale, axis=0)
weights = rescale / total # [MAX_NUM_PARTS]
# Weighted sum of partition outputs
offs_d = tl.arange(0, HEAD_DIM) offs_d = tl.arange(0, HEAD_DIM)
acc = tl.zeros([HEAD_DIM], dtype=tl.float32)
for p in range(MAX_NUM_PARTS): for g in range(GQA_RATIO):
if p < num_parts: head_idx = kv_head_idx * GQA_RATIO + g
w = tl.load(max_logits_ptr + es_base + p * stride_es_p) # reload for weight es_base = seq_idx * stride_es_s + head_idx * stride_es_h
w_rescaled = tl.exp(w - global_max) * tl.load(exp_sums_ptr + es_base + p * stride_es_p) / total
to_base = seq_idx * stride_to_s + head_idx * stride_to_h + p * stride_to_p # Load partition statistics
part_out = tl.load(tmp_output_ptr + to_base + offs_d * stride_to_d) part_max = tl.load(max_logits_ptr + es_base + part_offsets * stride_es_p,
acc += w_rescaled * part_out.to(tl.float32) mask=valid, other=float('-inf'))
part_sum = tl.load(exp_sums_ptr + es_base + part_offsets * stride_es_p,
mask=valid, other=0.0)
# Store final output # Global max
out_base = seq_idx * stride_out_s + head_idx * stride_out_h global_max = tl.max(part_max, axis=0)
tl.store(output_ptr + out_base + offs_d * stride_out_d, acc.to(output_ptr.dtype.element_ty))
# Rescale and normalize (CCCL combine op applied across all partitions)
rescale = tl.exp(part_max - global_max) * part_sum
total = tl.sum(rescale, axis=0)
# Weighted combination
acc = tl.zeros([HEAD_DIM], dtype=tl.float32)
for p in range(MAX_NUM_PARTS):
if p < num_parts:
w = tl.exp(tl.load(max_logits_ptr + es_base + p * stride_es_p) - global_max) * \
tl.load(exp_sums_ptr + es_base + p * stride_es_p) / tl.maximum(total, 1e-6)
to_base = seq_idx * stride_to_s + head_idx * stride_to_h + p * stride_to_p
part_out = tl.load(tmp_output_ptr + to_base + offs_d * stride_to_d)
acc += w * part_out.to(tl.float32)
# Store final output
out_base = seq_idx * stride_out_s + head_idx * stride_out_h
tl.store(output_ptr + out_base + offs_d * stride_out_d,
acc.to(output_ptr.dtype.element_ty))
def paged_attention_v2_triton( def paged_attention_v2_triton(
@@ -274,60 +286,52 @@ def paged_attention_v2_triton(
v_scale: float = 1.0, v_scale: float = 1.0,
**kwargs, **kwargs,
) -> None: ) -> None:
"""Launch Triton V2 kernels.""" """Launch CCCL-derived Triton V2 kernels."""
num_seqs, num_heads, head_size = query.shape num_seqs, num_heads, head_size = query.shape
num_queries_per_kv = num_heads // num_kv_heads gqa_ratio = num_heads // num_kv_heads
max_num_parts = tmp_output.shape[2] max_num_parts = tmp_output.shape[2]
x_pack = key_cache.shape[-1] # packing factor x_pack = key_cache.shape[-1]
PARTITION_SIZE = 512 PARTITION_SIZE = 512
# BLOCK_N: must fit in SMEM. For decode (BLOCK_M=1), SMEM is dominated by K/V gather.
# head_dim=256: BLOCK_N=32 → 32×256×2 = 16KB per tile (K or V)
# head_dim=128: BLOCK_N=64 → 64×128×2 = 16KB per tile
BLOCK_N = 32 if head_size > 128 else 64 BLOCK_N = 32 if head_size > 128 else 64
# Phase 1: partition attention
num_partitions = (max_seq_len + PARTITION_SIZE - 1) // PARTITION_SIZE num_partitions = (max_seq_len + PARTITION_SIZE - 1) // PARTITION_SIZE
grid_phase1 = (num_seqs, num_heads, num_partitions)
_paged_attn_v2_partition_kernel[grid_phase1]( # Phase 1: grid on kv_heads (not num_heads) — GQA broadcast inside kernel
grid_p1 = (num_seqs, num_kv_heads, num_partitions)
_partition_attn_kernel[grid_p1](
tmp_output, exp_sums, max_logits, tmp_output, exp_sums, max_logits,
query, key_cache, value_cache, block_tables, seq_lens, query, key_cache, value_cache, block_tables, seq_lens,
scale, num_queries_per_kv, block_size, x_pack, scale, gqa_ratio, block_size, x_pack,
# query strides
query.stride(0), query.stride(1), query.stride(2), query.stride(0), query.stride(1), query.stride(2),
# key_cache strides
key_cache.stride(0), key_cache.stride(1), key_cache.stride(2), key_cache.stride(0), key_cache.stride(1), key_cache.stride(2),
key_cache.stride(3), key_cache.stride(4), key_cache.stride(3), key_cache.stride(4),
# value_cache strides
value_cache.stride(0), value_cache.stride(1), value_cache.stride(2), value_cache.stride(0), value_cache.stride(1), value_cache.stride(2),
value_cache.stride(3), value_cache.stride(3),
# block_tables strides
block_tables.stride(0), block_tables.stride(1), block_tables.stride(0), block_tables.stride(1),
# tmp_output strides
tmp_output.stride(0), tmp_output.stride(1), tmp_output.stride(2), tmp_output.stride(3), tmp_output.stride(0), tmp_output.stride(1), tmp_output.stride(2), tmp_output.stride(3),
# exp_sums strides
exp_sums.stride(0), exp_sums.stride(1), exp_sums.stride(2), exp_sums.stride(0), exp_sums.stride(1), exp_sums.stride(2),
# Constants
PARTITION_SIZE=PARTITION_SIZE, PARTITION_SIZE=PARTITION_SIZE,
HEAD_DIM=head_size, HEAD_DIM=head_size,
BLOCK_N=BLOCK_N, BLOCK_N=BLOCK_N,
GQA_RATIO=gqa_ratio,
) )
# Phase 2: cross-partition reduction # Phase 2: grid on kv_heads — reduce all partitions for GQA_RATIO heads each
MAX_NUM_PARTS_CONST = triton.next_power_of_2(max_num_parts) MAX_NUM_PARTS_CONST = triton.next_power_of_2(max_num_parts)
if MAX_NUM_PARTS_CONST > 1024: if MAX_NUM_PARTS_CONST > 1024:
MAX_NUM_PARTS_CONST = 1024 MAX_NUM_PARTS_CONST = 1024
grid_phase2 = (num_seqs, num_heads) grid_p2 = (num_seqs, num_kv_heads)
_paged_attn_v2_reduce_kernel[grid_phase2]( _reduce_partitions_kernel[grid_p2](
output, output,
tmp_output, exp_sums, max_logits, seq_lens, tmp_output, exp_sums, max_logits, seq_lens,
max_num_parts, gqa_ratio, max_num_parts,
output.stride(0), output.stride(1), output.stride(2), output.stride(0), output.stride(1), output.stride(2),
tmp_output.stride(0), tmp_output.stride(1), tmp_output.stride(2), tmp_output.stride(3), tmp_output.stride(0), tmp_output.stride(1), tmp_output.stride(2), tmp_output.stride(3),
exp_sums.stride(0), exp_sums.stride(1), exp_sums.stride(2), exp_sums.stride(0), exp_sums.stride(1), exp_sums.stride(2),
PARTITION_SIZE=PARTITION_SIZE, PARTITION_SIZE=PARTITION_SIZE,
HEAD_DIM=head_size, HEAD_DIM=head_size,
MAX_NUM_PARTS=MAX_NUM_PARTS_CONST, MAX_NUM_PARTS=MAX_NUM_PARTS_CONST,
GQA_RATIO=gqa_ratio,
) )