FFPA(Split-D): Yet another Faster Flash Prefill Attention with Split-D strategy, achieve O(1) SRAM complexity and O(d/4) register complexity for large headdim (> 256), 1.8x~3x 🎉 faster than SDPA. Currently, FFPA supports self-attention, cross-attention, grouped/multi-query attention, causal attention with large headdim (D=320~1024). While the standard FlashAttention-2 only support headdim <= 256.
| Self Attention | Cross/Decode Attention | GQA/MQA Attention | Causal Attention | Headdim |
|---|---|---|---|---|
✔️(Nq = Nkv) |
✔️(Nq != Nkv) |
✔️(Nh_q % Nh_kv == 0) |
✔️(causal mask) |
320~1024 |
Note
FFPA has so far only been tested on Ampere and Ada architectures (e.g. A30, RTX 3080, L20, RTX 4090). It should also work on Hopper and other newer architectures, but performance may not be optimal there since FFPA does not yet leverage TMA for further optimization.
First, clone the repo and build the package from source: (Note: pip uninstall ffpa-attn -y if you want to reinstall after code changes; recommended: PyTorch>=2.11.0, CUDA>=13.0).
git clone https://github.com/xlite-dev/ffpa-attn.git
export MAX_JOBS=32 && python3 setup.py bdist_wheel
pip3 install dist/*.whl # pip uninstall ffpa-attn -yNote
FFPA supports cross-attention where the query seqlen Nq may differ from the key/value seqlen Nkv, GQA / MQA attention where Q has Nh_q heads and K/V have Nh_kv heads (requires Nh_q % Nh_kv == 0; group size = Nh_q / Nh_kv), and causal attention (pass causal=True; queries are aligned to the KV tail, i.e. Q row r attends to k <= r + (Nkv - Nq), which requires Nkv >= Nq). K/V must share the same Nh_kv and Nkv.
Minimal usage example — Self-Attention (B=1, H=32, N=8192, D=512):
import torch
import torch.nn.functional as F
from ffpa_attn import ffpa_attn_func
# D: 32, 64, ..., 320, ..., 1024 (FA-2 <= 256, FFPA supports up to 1024).
B, H, N, D = 1, 32, 8192, 512 # batch_size, num_heads, seq_len, head_dim
q = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
k = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
v = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
# FFPA self attention; layout follows SDPA: (B, H, N, D).
out = ffpa_attn_func(q, k, v) # -> torch.Tensor of shape (B, H, N, D)
print(out.shape, out.dtype)
ref = F.scaled_dot_product_attention(q, k, v)
print(f"vs SDPA max_abs_err={(out - ref).abs().max().item():.4e}")Cross-Attention or Decoding-Attention example (short query, long KV cache; Nq != Nkv):
import torch
import torch.nn.functional as F
from ffpa_attn import ffpa_attn_func
# Short-query / long-KV, e.g. incremental decoding or cross-attention:
# Q: [B, H, Nq, D], K/V: [B, H, Nkv, D]; Nq can differ from Nkv but Nk==Nv required.
B, H, D = 1, 8, 512
Nq, Nkv = 128, 8192
q = torch.randn(B, H, Nq, D, dtype=torch.bfloat16, device="cuda")
k = torch.randn(B, H, Nkv, D, dtype=torch.bfloat16, device="cuda")
v = torch.randn(B, H, Nkv, D, dtype=torch.bfloat16, device="cuda")
out = ffpa_attn_func(q, k, v) # -> (B, H, Nq, D) = (1, 8, 128, 512)
print(out.shape, out.dtype)
ref = F.scaled_dot_product_attention(q, k, v)
print(f"vs SDPA max_abs_err={(out - ref).abs().max().item():.4e}")Grouped-Query / Multi-Query Attention example (Q has more heads than K/V):
import torch
import torch.nn.functional as F
from ffpa_attn import ffpa_attn_func
# GQA: Q has Nh_q heads, K/V share Nh_kv heads; group_size = Nh_q / Nh_kv.
# Typical Llama-3-style 32/8 ratio; MQA is the Nh_kv==1 special case.
# FFPA targets large headdim so we use D=512 here (FA-2 tops out at D=256).
B, D, Nq, Nkv = 1, 512, 1024, 4096
Nh_q, Nh_kv = 32, 8 # group_size = 4
q = torch.randn(B, Nh_q, Nq, D, dtype=torch.bfloat16, device="cuda")
k = torch.randn(B, Nh_kv, Nkv, D, dtype=torch.bfloat16, device="cuda")
v = torch.randn(B, Nh_kv, Nkv, D, dtype=torch.bfloat16, device="cuda")
out = ffpa_attn_func(q, k, v) # -> (B, Nh_q, Nq, D) = (1, 32, 1024, 512)
print(out.shape, out.dtype)
# Reference: replicate K/V along head dim to match Q's head count.
group_size = Nh_q // Nh_kv
k_ref = k.repeat_interleave(group_size, dim=1)
v_ref = v.repeat_interleave(group_size, dim=1)
ref = F.scaled_dot_product_attention(q, k_ref, v_ref)
print(f"vs SDPA max_abs_err={(out - ref).abs().max().item():.4e}")Causal Attention example (self-attention causal; also supports chunked / decoding prefill with Nkv > Nq):
import torch
import torch.nn.functional as F
from ffpa_attn import ffpa_attn_func
# Causal self-attention: Q row r attends to k <= r (standard triangular mask).
# FFPA is tuned for large headdim, so we keep D=512 as in the self-attn example.
B, H, N, D = 1, 8, 4096, 512
q = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
k = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
v = torch.randn(B, H, N, D, dtype=torch.bfloat16, device="cuda")
out = ffpa_attn_func(q, k, v, causal=True)
print(out.shape, out.dtype)
ref = F.scaled_dot_product_attention(q, k, v, is_causal=True)
print(f"vs SDPA max_abs_err={(out - ref).abs().max().item():.4e}")
# Chunked / decoding prefill: Nq < Nkv, queries aligned to the KV tail
# so Q row r attends to k <= r + (Nkv - Nq). Requires Nkv >= Nq.
Nq, Nkv = 128, 8192
q = torch.randn(B, H, Nq, D, dtype=torch.bfloat16, device="cuda")
k = torch.randn(B, H, Nkv, D, dtype=torch.bfloat16, device="cuda")
v = torch.randn(B, H, Nkv, D, dtype=torch.bfloat16, device="cuda")
out = ffpa_attn_func(q, k, v, causal=True)
print(out.shape, out.dtype) # (1, 8, 128, 512)A runnable end-to-end example (with SDPA accuracy/perf comparison, both aligned N=8192 and non-aligned N=8191 cases) is provided under examples/run_ffpa_attn.py:
CUDA_VISIBLE_DEVICES=0 python3 examples/run_ffpa_attn.pyWe have extended FlashAttention for large headdim (D > 256) by implementing Fine-grained Tiling at the MMA level (GEMM style) for the Q@K^T and P@V matmul. This approach results in a constant SRAM usage of Br * 16 or Bc * 16 (Br = Bc) for Q, K, and V, leading to an overall SRAM complexity of O(2 * Br * 16) ≈ O(1) and a register complexity of O(d/4). Consequently, this method allows us to extend headdim beyond 256 and achieve faster performance compared to SDPA with or without MMA Accumulation F32 (1.8x~3x 🎉 faster than SDPA EA).
We have named this new attention tiling technique FFPA: Faster Flash Prefill Attention. FFPA does not introduce any additional VRAM requirement, so the HBM memory complexity remains the same as FlashAttention.
By leveraging this approach, we can achieve better performance than SDPA EA for very large headdim (D > 256, FA-2 not supported). Approximate SRAM and register complexity analysis for FFPA is as follows: (d=headdim, C,Br,Bc=Constant, Br=Bc, let O(C)≈O(1)) 👇
| 📚Complexity Analysis | 📚FFPA Attention (Split-D) | 📚FlashAttention-2 |
|---|---|---|
| SRAM | O(2xBrx16)≈O(1) | ≈O(3xBrxd), d↑ |
| Register | ≈O(d/4), d↑ | ≈O(d/2), d↑ |
| HBM | ≈FA2≈O(Nd), O | ≈O(Nd), O |
| Extra HBM | ≈FA2≈O(N), m,l | ≈O(N), m,l |
📚Implementation: FFPA is implemented using pure MMA PTX instructions, which supports many features such as Split-Q, SMEM Swizzle/Padding, QKV Multi-Stages(1~4), Tile MMAs/Warps, Mixed MMA F32/F16 Acc (Q@K^T MMA Acc F32 + P@V MMA Acc F16), Fully Shared QKV SMEM, Prefetch QKV g2s, Persist Q s2r/g2s, Fully QKV Fine-grained Tiling(GEMM style), Collective Store, etc.
| ✔️Tensor Cores | ✔️MMA(m16n8k16) | ✔️Tile Block(Br, Bc) | ✔️Tile MMA/Warp |
|---|---|---|---|
| ✔️Split Q(FA-2) | ✔️Pack LDST(128 bits) | ✔️SMEM Swizzle/Pad | ✔️Copy Async |
| ✔️Reg Double Buffers | ✔️QKV Multi-Stages(1~4) | ✔️Collective Store(Shfl) | ✔️Prefetch QKV g2s |
| ✔️QKV Fine-grained Tiling | ✔️Shared QKV SMEM | ✔️Mixed MMA Acc | ✔️Persist Q s2r/g2s |
GNU General Public License v3.0
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@misc{ffpa-attn@2025,
title={FFPA: Yet another Faster Flash Prefill Attention for large headdim.},
url={https://github.com/xlite-dev/ffpa-attn.git},
note={Open-source software available at https://github.com/xlite-dev/ffpa-attn.git},
author={DefTruth},
year={2025}
}