📚 Modern CUDA Learn Notes with PyTorch for Beginners: It includes Tensor/CUDA Cores, TF32/F16/BF16/F8, 📖200+ CUDA Kernels🔥🔥(Easy -> Hard++) with PyTorch bindings, 📖100+ LLM/VLM/CV/CUDA/CuTe🔥 blogs, 📖toy-hgemm⚡️⚡️ which can achieve 98%~100% performance of cuBLAS, and 📖flash-attention-mma⚡️⚡️ using Tensor Cores with pure MMA PTX. Welcome to 🌟👆🏻star this repo to support me, many thanks ~ 🎉🎉
- [2025-01-08]: 📚Split Q + Fully QKV Fine-grained Tiling has been refactored into 🤖ffpa-attn-mma: 📚FFPA - Yet another Faster Flash Prefill Attention with O(1)🎉SRAM complexity for headdim > 256, 1.8x~3x🎉faster than SDPA EA: 📈L20 ~1.9x↑🎉, 📈 A30 ~1.8x↑🎉, 📈3080 ~2.9x↑🎉, 📈4090 ~2.1x↑🎉.
- [2024-12-02]: HGEMM MMA kernels has been refactored into 🤖hgemm-mma: ⚡️Write HGEMM from scratch using Tensor Cores with WMMA, MMA and CuTe API, achieve peak⚡️ performance.
Currently, on NVIDIA L20, RTX 4090 and RTX 3080 Laptop, compared with cuBLAS's default Tensor Cores algorithm, the HGEMM (WMMA/MMA/CuTe) in this repo (blue🔵) can achieve 98%~100% of its (orange🟠) performance. Please check toy-hgemm library⚡️⚡️ or hgemm-mma⚡️⚡️ repo for more details.
| 📚Feature | 📚Feature | 📚Feature | 📚Feature |
|---|---|---|---|
| ✔️CUDA/Tensor Cores | ✔️Loop over K | ✔️Tile Block(BMxBK) | ✔️Tile Threads(T 8x8) |
| ✔️WMMA(m16n16k16) | ✔️MMA(m16n8k16) | ✔️Pack LDST(128 bits) | ✔️SMEM Padding |
| ✔️Copy Async | ✔️Tile MMAs | ✔️Tile Warps | ✔️Multi Stages(2~4) |
| ✔️Register Double Buffers | ✔️Block Swizzle | ✔️Warp Swizzle | ✔️SMEM Swizzle(CuTe/MMA) |
| ✔️Collective Store(Shfl) | ✔️Layout NN | ✔️Layout TN | ✔️SGEMM FP32/TF32 |
I have also implemented FlashAttention-2 using pure MMA PTX instructions, which supports features such as Multi-Stages, Tile MMA, Tile Warp, Shared KV SMEM, Fully Shared QKV SMEM, Prefetch Q s2r, Prefetch K/V g2s, QKV Fine-grained Tiling, Collective Store, etc. Please refer to flash-attention-mma⚡️⚡️ for more details.
| 📚Feature | 📚Feature | 📚Feature | 📚Feature |
|---|---|---|---|
| ✔️Tensor Cores | ✔️Loop over N/D | ✔️Tile Block(Br, Bc) | ✔️MMA(m16n8k16) |
| ✔️Pack LDST(128 bits) | ✔️SMEM Swizzle/Padding | ✔️Copy Async | ✔️Tile MMAs |
| ✔️Tile Warps | ✔️Multi Stages(1/2) | ✔️Collective Store(Shfl) | ✔️Split KV/Q |
| ✔️Shared QKV SMEM | ✔️Prefetch Q s2r | ✔️Prefetch KV g2s | ✔️QKV Fine-grained Tiling |
Currently, for small-scale attention (B<=4, H <=48, SeqLen <= 8192, D <= 64) it can run faster than FA2/SDPA on some Devices. For example, on NVIDIA RTX 3080 Laptop, 📚 Split Q + Fully Shared QKV SMEM method can achieve 55 TFLOPS (D=64) that almost ~1.5x 🎉 faster than FA2. On NVIDIA L20, 🤖ffpa-attn-mma method can achieve 104 TFLOPS (D=512) that almost ~1.8x 🎉 faster than SDPA (EFFICIENT ATTENTION). However, for large-scale attention, there remains a performance gap. Stay tuned for updates ~ (MMA Acc F16/F32, softmax Acc F32 vs FA2 MMA/softmax Acc F32, 👇Benchmark)
| Algorithm | (B,H,N,D) | RTX 3080 Laptop | L20 | RTX 4090 |
|---|---|---|---|---|
| FlashAttention-2 | (1,8,8192,64) | 37 TFLOPS | 100 TFLOPS | 145 TFLOPS |
| share-qkv+stage2 | (1,8,8192,64) | 55 TFLOPS | 99 TFLOPS | 221 TFLOPS |
| FlashAttention-2 | (1,48,8192,64) | 37 TFLOPS | 109 TFLOPS | 163 TFLOPS |
| share-qkv+stage2 | (1,48,8192,64) | 48 TFLOPS | 107 TFLOPS | 224 TFLOPS |
| SDPA(EFFICIENT ATTENTION) | (1,48,8192,512) | 16 TFLOPS | 58 TFLOPS | 85 TFLOPS |
| 🤖ffpa-attn-mma | (1,48,8192,512) | 39 TFLOPS | 104 TFLOPS | 200 TFLOPS |
| Precision Errors vs FA2/SDPA | / | max: < ~1e-3 | min: ~0.0 | mean: < ~1e-5 |
The Split KV and Split Q implementations have been carried out in flash-attention-mma⚡️⚡️ for performance comparison. The Split KV method, which involves splitting all QKV across MMA (Warps), is slower than Split Q method, which splitting Q across MMA(Warps) and keep access KV for all MMA(Warps).
- 📚 Split KV (Basic, FlashAttention-1)
// Split QKV across MMA(Warps) using naive matmul MMA&Warp tiling policy.
// case: The layout of 8 MMA(2x4) [after] kWarpTileSeqLenQxkWarpTileSeqLenK(2x2) -> 32x2,32x2=64x64:
// | [64,64] | warp_KV 0 | warp_KV 1 | warp_KV 2 | warp_KV 3 |
// | warp_QP 0 |-- MMA 0,MMA 0 --|-- MMA 2,MMA 2 --|-- MMA 4,MMA 4 --|-- MMA 6,MMA 6 --|
// | warp_QP 0 |-- MMA 0,MMA 0 --|-- MMA 2,MMA 2 --|-- MMA 4,MMA 4 --|-- MMA 6,MMA 6 --|
// | warp_QP 1 |-- MMA 1,MMA 1 --|-- MMA 3,MMA 2 --|-- MMA 5,MMA 5 --|-- MMA 7,MMA 7 --|
// | warp_QP 1 |-- MMA 1,MMA 1 --|-- MMA 3,MMA 2 --|-- MMA 5,MMA 5 --|-- MMA 7,MMA 7 --|
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_kv_kernel(half* Q, half* K, half* V, half* O, ...);- 📚 Split Q (Faster, FlashAttention-2)
// Split Q across MMA(Warps) and keep access KV for all MMA(Warps),
// in order to reduce the comm between warps via smem and warp shuffle.
// case: MMA = m16n8k16, Br=16x4=64, Bc=8x8=64, layout: 4 warps
// | 64x64 | warp_KV 0 |
// | warp_QP 0 | MMA 0 ... MMA 0 (x8) |
// | warp_QP 1 | MMA 1 ... MMA 1 (x8) |
// | warp_QP 2 | MMA 2 ... MMA 2 (x8) |
// | warp_QP 3 | MMA 3 ... MMA 3 (x8) |
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_q_kernel(half* Q, half* K, half* V, half* O, ...);- 📚 Split Q + Shared KV SMEM (1/2 SRAM vs FA2)
// K, V shared the same shared memory, improve block occupancy.
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_q_shared_kv_kernel(half* Q, half* K, half* V, half* O, ...);- 📚 Split Q + Fully Shared QKV SMEM (1/4 SRAM vs FA2)
// Q, K, V fully shared the same shared memory and prefetch Q s2r, improve block occupancy
// and reduce Q SMEM IO-Access.
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_q_shared_qkv_kernel(half* Q, half* K, half* V, half* O, ...);- 📚 Split Q + QK Fine-grained Tiling (O(16xd) SRAM vs FA2 O(4xBrxd) SRAM,
Headdim -> 1024)
// Fine-grained tiling at the MMA level for Q@K^T results in a constant SRAM usage of
// 64 * kMmaAtomK for Q and K. For V, the SRAM complexity is O(kMmaAtomK * d), leading to
// an overall SRAM complexity of O(kMmaAtomK * d). Consequently, this approach allows us to
// extend D (head dimension) up to 1024.
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_q_tiling_qk_kernel(half* Q, half* K, half* V, half* O, ...);- 📚 Split Q + Fully QKV Fine-grained Tiling (O(2xBrx16)~O(1) SRAM vs FA2 O(4xBrxd) SRAM)
// Fine-grained tiling at the MMA level for all Q@K^T and P@V results in a constant SRAM usage of
// Br * 16 or Bc * 16 for Q, K, V, leading to an overall SRAM complexity of O(Br * 16). Consequently,
// this approach allows us to run faster than SDPA w or w/o MMA Acc F32.
__global__ void // Q, K, V, O -> [B, H, N, D]
flash_attn_mma_stages_split_q_tiling_qkv_kernel(half* Q, half* K, half* V, half* O, ...);💡NOTE: 📚Split Q + Fully QKV Fine-grained Tiling has been refactored into 🤖ffpa-attn-mma.
@misc{CUDA-Learn-Notes@2024,
title={CUDA-Learn-Notes: A Modern CUDA Learn Notes with PyTorch for Beginners},
url={https://github.com/DefTruth/CUDA-Learn-Notes},
note={Open-source software available at https://github.com/DefTruth/CUDA-Learn-Notes},
author={DefTruth etc},
year={2024}
}📖 200+ CUDA Kernels 🔥🔥 (Easy -> Hard++) (©️back👆🏻)
The kernels listed here will guide you through a step-by-step progression, ranging from easy to very challenging topics. The workflow for each topic will be as follows: custom CUDA kernel implementation -> PyTorch Python bindings -> Run tests. 👉TIPS: * = Tensor Cores (WMMA, MMA, CuTe), otherwise, CUDA Cores; / = not supported; ✔️ = supported; ❔ = TODO. Contents are listed as follows:
📚 Easy and 📚 Medium sections cover operations such as element-wise, mat_trans, warp/block reduce, nms, relu, gelu, swish, layer-norm, rms-norm, online-softmax, dot-prod, embedding and basic usage for FP32, FP16, BF16 and FP8 . 📚 Hard, 📚 Hard+ and 📚 Hard++ sections delve deeper into advanced topics, primarily focusing on operations like sgemv, sgemm, hgemv, hgemm and flash-attention. These sections also provide numerous kernels implemented using Tensor Cores with pure MMA PTX.
📚 Easy ⭐️ & Medium ⭐️⭐️ (©️back👆🏻)
📚 Hard ⭐⭐⭐️ (©️back👆🏻)
📚 Hard+ ⭐️⭐️⭐️⭐️ & Hard++ ⭐️⭐️⭐️⭐️⭐️ (©️back👆🏻)
- 📚 FlashAttention-2 MMA (MMA Acc F32/F16, swizzle, QKV smem share, fine-grained tiling, etc.🎉)
💡NOTE: rr: means reduce registers usage (for d>128); f32: means MMA accumulate with FP32 dtype, otherwise, FP16. softmax Acc dtype is always be FP32 for high precision; swizzle: now, only support smem swizzle for MMA.
- 📚 FFPA Attention MMA (1.8x~3x🎉faster vs SDPA EA, D > 256, FA2 not supported)
| 📖 CUDA Kernel | 📖 Elem DType | 📖 Acc DType | 📖 Docs | 📖 Level |
|---|---|---|---|---|
| ✔️ ffpa_mma_stages_split_q_L1_F16F16F16 | f16 | f16 | link | ⭐️⭐️⭐️⭐️ |
| ✔️ ffpa_mma_stages_split_q_L1_F16F16F32 | f16 | f32 | link | ⭐️⭐️⭐️⭐️ |
| ✔️ ffpa_mma_stages_split_q_L1_mixed_acc | f16 | QK f32, PV f16 | link | ⭐️⭐️⭐️⭐️ |
| f16 | f16 | link | ⭐️⭐️⭐️⭐️ | |
| f16 | f32 | link | ⭐️⭐️⭐️⭐️ | |
| f16 | QK f32, PV f16 | link | ⭐️⭐️⭐️⭐️ | |
| f16 | f16 | link | ⭐️⭐️⭐️⭐️ | |
| f16 | f32 | link | ⭐️⭐️⭐️⭐️ | |
| f16 | QK f32, PV f16 | link | ⭐️⭐️⭐️⭐️ |
💡NOTE: 🤖ffpa-attn-mma: 📚FFPA - Yet another Faster Flash Prefill Attention with O(1)🎉SRAM complexity for headdim > 256, 1.8x~3x🎉faster than SDPA EA: 📈L20 ~1.9x↑🎉, 📈 A30 ~1.8x↑🎉, 📈3080 ~2.9x↑🎉, 📈4090 ~2.1x↑🎉.
📚 大模型|多模态|Diffusion|推理优化 (本人作者) (©️back👆🏻)
📚 CV推理部署|C++|算法|技术随笔 (本人作者) (©️back👆🏻)
📚 CUTLASS|CuTe|NCCL|CUDA|文章推荐 (其他作者) (©️back👆🏻)
💡说明: 本小节整理一些自己比较喜欢的文章。欢迎大家提PR推荐更多优秀的文章！
©️License (©️back👆🏻)
GNU General Public License v3.0
🎉Contribute (©️back👆🏻)
How to contribute? Star this repo or check 🌤🌤CONTRIBUTE🎉🎉.
