📚 Modern CUDA Learn Notes with PyTorch for Beginners: It includes Tensor/CUDA Cores, TF32/F16/BF16/F8, 📖150+ 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 ~ 🎉🎉
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-tensorcores-mma⚡️⚡️ repo for more details.
| CUDA Cores | Sliced K (Loop over K) | Tile Block (BMxBK) | Tile Thread (t 8x8) |
|---|---|---|---|
| ✔️ | ✔️ | ✔️ | ✔️ |
| WMMA (m16n16k16) | MMA (m16n8k16) | Pack LDST (128 bits) | SMEM Padding |
| ✔️ | ✔️ | ✔️ | ✔️ |
| Copy Async | Tile MMA (More Threads) | Tile Warp (More Values) | Multi Stages (2/3/4) |
| ✔️ | ✔️ | ✔️ | ✔️ |
| Reg Double Buffers | Block Swizzle | Warp Swizzle | SMEM Swizzle (CuTe/MMA) |
| ✔️ | ✔️ | ✔️ | ✔️ |
| Collective Store (Shfl) | Row Major (NN) | Col Major (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, QK Fine-grained Tiling, Collective Store, etc. Please refer to flash-attention-mma⚡️⚡️ for more details.
| Tensor Cores | Loop over Seqlen/Headdim | Tile Block (Br, Bc) | MMA (m16n8k16) |
|---|---|---|---|
| ✔️ | ✔️ | ✔️ | ✔️ |
| Pack LDST (128 bits) | SMEM Swizzle/Padding | Copy Async | Tile MMA (More Threads) |
| ✔️ | ✔️ | ✔️ | ✔️ |
| Tile Warp (More Values) | Multi Stages (1/2) | Collective Store (Shfl) | Split KV/Q |
| ✔️ | ✔️ | ✔️ | ✔️ |
| Shared QKV/KV SMEM | Prefetch Q s2r | Prefetch K/V g2s | QK Fine-grained Tiling |
| ✔️ | ✔️ | ✔️ | ✔️ |
Currently, for small-scale attention (B<=4, H <=48, SeqLen <= 8192) it can run faster than FA2/SDPA on some Devices. For example, on NVIDIA RTX 3080 Laptop, 📚 Split Q + Fully Shared QKV SMEM can achieve 55 TFLOPS (D=64) that almost ~1.5x 🎉 faster than FA2. On NVIDIA L20, 📚 Split Q + QK Fine-grained Tiling can achieve 81 TFLOPS (D=512) that almost ~1.4x 🎉 faster than SDPA (EFFICIENT ATTENTION). However, for large-scale attention, there remains a performance gap. Stay tuned for updates ~ (👇Benchmark)
| Algorithm | (B,H,N,D) | RTX 3080 Laptop | L20 | RTX 4090 |
|---|---|---|---|---|
| FlashAttention-2 | (1,8,8192,64) | 37 TFLOPS | 100 TFLOPS | 145 TFLOPS |
| mma(split-q+share-qkv+stage2) | (1,8,8192,64) | 55 TFLOPS | 96 TFLOPS | 218 TFLOPS |
| FlashAttention-2 | (1,48,8192,64) | 37 TFLOPS | 109 TFLOPS | 163 TFLOPS |
| mma(split-q+share-qkv+stage2) | (1,48,8192,64) | 35 TFLOPS | 104 TFLOPS | 223 TFLOPS |
| SDPA(EFFICIENT ATTENTION) | (1,48,8192,512) | 16 TFLOPS | 58 TFLOPS | 85 TFLOPS |
| mma(split-q+tiling-qk+stage2) | (1,48,8192,512) | 23 TFLOPS | 81 TFLOPS | 120 TFLOPS |
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 and K 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. Stay tuned for updates ~
__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, ...);@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}
}📖 150+ 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👆🏻)
| 📖 CUDA Kernel | 📖 Elem DType | 📖 Acc DType | 📖 Docs | 📖 Level |
|---|---|---|---|---|
| ✔️ flash_attn_mma_stages_split_kv* | f16 | f16 | link | ⭐️⭐️⭐️⭐️ |
| ✔️ flash_attn_mma_stages_split_q* | f16 | f16 | link | ⭐️⭐️⭐️⭐️ |
| ✔️ flash_attn_mma_stages...shared_kv* | f16 | f16 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ✔️ flash_attn_mma_stages...shared_qkv* | f16 | f16 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ✔️ flash_attn_mma_stages...tiling_qk* | f16 | f16 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ✔️ flash_attn_mma...tiling_qk_swizzle{+smem}* | f16 | f16 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ? flash_attn_mma_stages_split_kv{f32}* | f16 | f32 | link | ⭐️⭐️⭐️⭐️ |
| ? flash_attn_mma_stages_split_q{f32}* | f16 | f32 | link | ⭐️⭐️⭐️⭐️ |
| ? flash_attn_mma_stages...shared_kv{f32}* | f16 | f32 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ? flash_attn_mma_stages...shared_qkv{f32}* | f16 | f32 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ? flash_attn_mma_stages...tiling_qk{f32}* | f16 | f32 | link | ⭐️⭐️⭐️⭐️⭐️ |
| ✔️ How to implement MMA smem swizzle* | f16 | f16 | link | ⭐️⭐️⭐️⭐️ |
📚 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
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How to contribute? Star this repo or check 🌤🌤CONTRIBUTE🎉🎉.
