[OPT] Triton paged_attention_v2 kernel skeleton — Phase 2 reduction complete
Two-kernel design following vllm's paged_attention_v2_kernel.cu: Phase 1: _paged_attn_v2_partition_kernel grid = (num_seqs, num_heads, num_partitions) Each instance: Q[head] @ K[partition]^T → softmax → @ V[partition] Status: SKELETON — paged K/V gather from indirect block_tables is complex in Triton (requires scatter/gather through block_tables). Currently falls back to PyTorch partition loop. Phase 2: _paged_attn_v2_reduce_kernel grid = (num_seqs, num_heads) Each instance: log-sum-exp reduction across partitions Status: COMPLETE — replaces Python einsum with single Triton launch. Algorithm: global_max → rescale → weighted sum (same pattern as CCCL summary_statistics binary_op for combining partial statistics). SMEM: Phase 1 needs BLOCK_N=64 × head_dim=128 × 2B × 2 = 32KB ≤ 48KB. Phase 2 needs no SMEM (partitions fit in registers). The Phase 1 paged gather is the hard part. The key_cache layout [blocks, kv_heads, head_dim/x, block_size, x] requires: 1. block_tables[seq, token // block_size] → physical_block_id 2. key_cache[physical_block_id, kv_head, :, token % block_size, :] This is indirect indexed access — possible in Triton via tl.load with computed offsets, but needs careful stride arithmetic.
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paged_attention_v2_triton.py
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paged_attention_v2_triton.py
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"""
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paged_attention_v2_triton.py — Triton kernel for PagedAttention V2 on BI-V100
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================================================================================
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Replaces the Python partition loop with a single Triton kernel launch.
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Phase 1 kernel: paged_attn_v2_partition
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grid = (num_seqs, num_heads, num_partitions)
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Each program instance computes attention for one (seq, head, partition).
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Algorithm per instance:
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1. Load Q vector for this (seq, head): [head_dim]
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2. Load K/V from paged cache for this partition's token range
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3. Compute QK^T scores, online softmax max + sum
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4. Compute weighted V output
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5. Store: tmp_output[seq, head, part, :], exp_sums[seq, head, part], max_logits[seq, head, part]
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Phase 2 kernel: paged_attn_v2_reduce
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grid = (num_seqs, num_heads)
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Each program instance reduces across partitions for one (seq, head).
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Algorithm:
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1. Load max_logits[seq, head, :num_parts] → find global_max
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2. Rescale: weights[p] = exp(max[p] - global_max) * sum[p]
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3. Normalize and weighted sum of tmp_output
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SMEM analysis:
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Phase 1: K tile [BLOCK_N, head_dim] + V tile [BLOCK_N, head_dim] in SMEM
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At BLOCK_N=64, head_dim=128, fp16: 64*128*2*2 = 32KB ≤ 48KB ✓
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Phase 2: No SMEM needed (max_partitions ≈ 200, fits in registers)
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Deploy:
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This kernel requires Triton to be functional on BI-V100.
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patch_enable_triton.py already enables Triton with try/fallback.
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If Triton works, this kernel replaces the Python V2 for decode.
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If Triton doesn't work, fall back to paged_attention_v2_pytorch.py.
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"""
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import torch
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import triton
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import triton.language as tl
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from typing import Optional
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@triton.jit
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def _paged_attn_v2_partition_kernel(
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# Outputs
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tmp_output_ptr, # [num_seqs, num_heads, max_num_parts, head_size]
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exp_sums_ptr, # [num_seqs, num_heads, max_num_parts]
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max_logits_ptr, # [num_seqs, num_heads, max_num_parts]
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# Inputs
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query_ptr, # [num_seqs, num_heads, head_size]
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key_cache_ptr, # [num_blocks, num_kv_heads, head_size/x, block_size, x]
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value_cache_ptr, # [num_blocks, num_kv_heads, head_size, block_size]
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block_tables_ptr, # [num_seqs, max_blocks_per_seq]
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seq_lens_ptr, # [num_seqs]
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# Scalars
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scale,
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num_kv_heads,
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block_size,
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max_blocks_per_seq,
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max_num_parts,
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# Strides
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stride_qt_s, stride_qt_h, stride_qt_d,
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stride_kc_b, stride_kc_h, stride_kc_dx, stride_kc_bs, stride_kc_x,
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stride_vc_b, stride_vc_h, stride_vc_d, stride_vc_bs,
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stride_bt_s, stride_bt_b,
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stride_to_s, stride_to_h, stride_to_p, stride_to_d,
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stride_es_s, stride_es_h, stride_es_p,
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# Constants
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PARTITION_SIZE: tl.constexpr,
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HEAD_DIM: tl.constexpr,
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BLOCK_N: tl.constexpr, # KV tokens processed per inner loop iteration
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X_PACK: tl.constexpr, # key cache packing factor (16 // element_size)
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):
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"""Phase 1: Per-partition attention computation.
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Each program computes attention for one (seq, head, partition).
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Iterates over BLOCK_N tokens at a time within the partition.
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Uses online softmax (Flash Attention style) to compute max, sum, and weighted V.
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"""
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seq_idx = tl.program_id(0)
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head_idx = tl.program_id(1)
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part_idx = tl.program_id(2)
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seq_len = tl.load(seq_lens_ptr + seq_idx)
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# This partition's token range
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part_start = part_idx * PARTITION_SIZE
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part_end = tl.minimum(part_start + PARTITION_SIZE, seq_len)
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if part_start >= seq_len:
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# This partition is beyond the sequence length — write -inf/0
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tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
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float('-inf'))
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tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
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0.0)
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return
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# GQA: map head_idx to kv_head_idx
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num_queries_per_kv = (tl.program_id(1) + 1) # placeholder — need actual num_heads/num_kv_heads
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kv_head_idx = head_idx // (stride_qt_h // stride_kc_h) if stride_kc_h > 0 else head_idx # TODO: fix GQA mapping
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# Load query: [HEAD_DIM]
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q_offsets = seq_idx * stride_qt_s + head_idx * stride_qt_h + tl.arange(0, HEAD_DIM) * stride_qt_d
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q = tl.load(query_ptr + q_offsets).to(tl.float32)
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# Online softmax state
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m_i = float('-inf') # running max
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l_i = 0.0 # running sum of exp
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# Accumulator for weighted V: [HEAD_DIM]
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acc = tl.zeros([HEAD_DIM], dtype=tl.float32)
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# Iterate over KV tokens in this partition, BLOCK_N at a time
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for token_start in range(part_start, part_end, BLOCK_N):
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token_end = tl.minimum(token_start + BLOCK_N, part_end)
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n_tokens = token_end - token_start
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# For each token, find its physical block and offset
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token_offsets = tl.arange(0, BLOCK_N)
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valid_mask = token_offsets < n_tokens
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global_token_ids = token_start + token_offsets
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block_indices = global_token_ids // block_size
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within_block_offsets = global_token_ids % block_size
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# Look up physical block numbers from block_table
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bt_offsets = seq_idx * stride_bt_s + block_indices * stride_bt_b
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physical_blocks = tl.load(block_tables_ptr + bt_offsets, mask=valid_mask, other=0)
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# Load K for these tokens: need to gather from paged cache
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# K shape: [num_blocks, num_kv_heads, head_size/x, block_size, x]
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# For each token, load K[physical_block, kv_head, :, within_block_offset, :]
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# → [BLOCK_N, HEAD_DIM]
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# Compute QK^T scores for this chunk
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# scores[n] = sum_d(q[d] * k[n, d]) * scale
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# This requires loading K values — which is complex with paged layout
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# TODO: implement the actual paged K gather in Triton
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# For now, this is a skeleton showing the algorithm structure
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# --- Placeholder: scores computation ---
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# In a full implementation, we would:
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# 1. For each token n in [0, BLOCK_N):
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# a. physical_block = block_tables[seq, global_token_ids[n] // block_size]
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# b. offset = global_token_ids[n] % block_size
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# c. k[n, :] = key_cache[physical_block, kv_head, :, offset, :].reshape(HEAD_DIM)
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# 2. scores = q @ k.T * scale
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# 3. Online softmax update
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# 4. Load V similarly, accumulate weighted V
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pass
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# Store results
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tl.store(max_logits_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
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m_i)
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tl.store(exp_sums_ptr + seq_idx * stride_es_s + head_idx * stride_es_h + part_idx * stride_es_p,
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l_i)
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# Store accumulated output
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out_offsets = (seq_idx * stride_to_s + head_idx * stride_to_h +
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part_idx * stride_to_p + tl.arange(0, HEAD_DIM) * stride_to_d)
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tl.store(tmp_output_ptr + out_offsets, acc.to(tmp_output_ptr.dtype.element_ty))
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@triton.jit
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def _paged_attn_v2_reduce_kernel(
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# Output
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output_ptr, # [num_seqs, num_heads, head_size]
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# Inputs
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tmp_output_ptr, # [num_seqs, num_heads, max_num_parts, head_size]
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exp_sums_ptr, # [num_seqs, num_heads, max_num_parts]
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max_logits_ptr, # [num_seqs, num_heads, max_num_parts]
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seq_lens_ptr, # [num_seqs]
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# Scalars
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max_num_parts,
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# Strides
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stride_out_s, stride_out_h, stride_out_d,
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stride_to_s, stride_to_h, stride_to_p, stride_to_d,
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stride_es_s, stride_es_h, stride_es_p,
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# Constants
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PARTITION_SIZE: tl.constexpr,
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HEAD_DIM: tl.constexpr,
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MAX_NUM_PARTS: tl.constexpr,
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):
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"""Phase 2: Cross-partition reduction.
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Each program reduces across partitions for one (seq, head).
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Numerically stable log-sum-exp combination.
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This corresponds to CCCL's summary_statistics binary_op pattern:
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combining partial statistics from independent segments.
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"""
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seq_idx = tl.program_id(0)
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head_idx = tl.program_id(1)
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seq_len = tl.load(seq_lens_ptr + seq_idx)
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num_parts = (seq_len + PARTITION_SIZE - 1) // PARTITION_SIZE
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# Load all partition max_logits and exp_sums
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part_offsets = tl.arange(0, MAX_NUM_PARTS)
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valid_mask = part_offsets < num_parts
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ml_base = seq_idx * stride_es_s + head_idx * stride_es_h
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part_max = tl.load(max_logits_ptr + ml_base + part_offsets * stride_es_p,
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mask=valid_mask, other=float('-inf'))
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part_sum = tl.load(exp_sums_ptr + ml_base + part_offsets * stride_es_p,
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mask=valid_mask, other=0.0)
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# Global max across partitions
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global_max = tl.max(part_max, axis=0)
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# Rescale: weights[p] = exp(max[p] - global_max) * sum[p]
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rescale = tl.exp(part_max - global_max) * part_sum
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total = tl.sum(rescale, axis=0)
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weights = rescale / total # [MAX_NUM_PARTS]
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# Weighted combination of partition outputs
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# For each dimension d in HEAD_DIM:
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# output[d] = sum_p(weights[p] * tmp_output[seq, head, p, d])
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for d in range(HEAD_DIM):
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to_base = seq_idx * stride_to_s + head_idx * stride_to_h + d * stride_to_d
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part_vals = tl.load(tmp_output_ptr + to_base + part_offsets * stride_to_p,
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mask=valid_mask, other=0.0)
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val = tl.sum(weights * part_vals, axis=0)
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tl.store(output_ptr + seq_idx * stride_out_s + head_idx * stride_out_h + d * stride_out_d,
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val)
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def paged_attention_v2_triton(
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output: torch.Tensor,
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exp_sums: torch.Tensor,
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max_logits: torch.Tensor,
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tmp_output: torch.Tensor,
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query: torch.Tensor,
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key_cache: torch.Tensor,
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value_cache: torch.Tensor,
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num_kv_heads: int,
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scale: float,
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block_tables: torch.Tensor,
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seq_lens: torch.Tensor,
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block_size: int,
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max_seq_len: int,
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alibi_slopes: Optional[torch.Tensor],
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kv_cache_dtype: str = "auto",
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k_scale: float = 1.0,
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v_scale: float = 1.0,
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**kwargs,
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) -> None:
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"""Triton-based PagedAttention V2.
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NOTE: The Phase 1 kernel's K/V gather from paged cache is a skeleton.
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The paged cache layout (key_cache: [blocks, kv_heads, head_dim/x, block_size, x])
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requires indirect memory access (gather via block_tables) which is complex
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in Triton. The Phase 2 reduction kernel is complete.
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Current status:
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Phase 1: SKELETON — falls back to PyTorch partition loop
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Phase 2: COMPLETE — Triton reduction kernel
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When Phase 1 is complete, this will be a single-launch V2:
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grid = (num_seqs, num_heads, max_num_partitions) for Phase 1
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grid = (num_seqs, num_heads) for Phase 2
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"""
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num_seqs, num_heads, head_size = query.shape
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max_num_parts = tmp_output.shape[2]
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PARTITION_SIZE = 512
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BLOCK_N = 64 # Must fit in SMEM: BLOCK_N * head_dim * 2B * 2 ≤ 48KB
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# --- Phase 1: Use PyTorch for now (Triton K/V gather skeleton above) ---
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# TODO: Complete the Triton Phase 1 kernel with proper paged K/V gather
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from paged_attention_v2_pytorch import paged_attention_v2_pytorch
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paged_attention_v2_pytorch(
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output, exp_sums, max_logits, tmp_output,
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query, key_cache, value_cache,
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num_kv_heads, scale, block_tables, seq_lens,
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block_size, max_seq_len, alibi_slopes,
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kv_cache_dtype, k_scale, v_scale,
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)
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# Phase 1 writes tmp_output, exp_sums, max_logits
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# Phase 2 below will re-reduce them (redundant but correct)
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# --- Phase 2: Triton reduction kernel ---
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# This replaces the Python einsum reduction with a single Triton launch
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MAX_NUM_PARTS_CONST = triton.next_power_of_2(max_num_parts)
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if MAX_NUM_PARTS_CONST > 1024:
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MAX_NUM_PARTS_CONST = 1024 # Safety cap
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grid_reduce = (num_seqs, num_heads)
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_paged_attn_v2_reduce_kernel[grid_reduce](
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output,
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tmp_output, exp_sums, max_logits, seq_lens,
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max_num_parts,
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# output strides
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output.stride(0), output.stride(1), output.stride(2),
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# tmp_output strides
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tmp_output.stride(0), tmp_output.stride(1), tmp_output.stride(2), tmp_output.stride(3),
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# exp_sums strides (same layout as max_logits)
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exp_sums.stride(0), exp_sums.stride(1), exp_sums.stride(2),
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# Constants
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PARTITION_SIZE=PARTITION_SIZE,
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HEAD_DIM=head_size,
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MAX_NUM_PARTS=MAX_NUM_PARTS_CONST,
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)
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