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+++ src/lab4p5/include/utils.h | 91 ++++ src/lab4p5/submit/my_int8_fp64.cu | 146 ++++++ src/lab4p5/utils.cu | 149 +++++++ zensical.toml | 1 + 18 files changed, 1491 insertions(+) create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/conflict.png create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/cutlass-layers.svg create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/operator-fusion.svg create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/optimization-checklist.svg create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/overlap-pipeline.svg create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/score.png create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/image/warp-specialization.png create mode 100644 docs/lab/Lab4.5-INT8-FP64-GEMM/index.md create mode 100644 src/lab4p5/Makefile create mode 100644 src/lab4p5/baseline/baseline_fp64.cu create mode 100644 src/lab4p5/baseline/cublas_baseline.cu create mode 100644 src/lab4p5/baseline/cublas_emulated.cu create mode 100644 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是保证不溢出的最大缩减率,也是精度利用率最高的选择。 + +完整的递推关系为: + +$$\boxed{q_i = \mathrm{round}\!\left(\frac{r_i}{s_i}\right), \quad r_{i+1} = r_i - q_i \cdot s_i, \quad s_{i+1} = \frac{s_i}{254}}$$ + +### 精度分析 + +$S$ 级分解后,在同一实数算术模型下,单个元素的绝对误差满足: + +$$\left|x - \sum_{i=0}^{S-1} q_i \cdot s_i\right| = |r_S| \le \frac{s_{S-1}}{2} = \frac{s_0}{2 \cdot 254^{S-1}} = \frac{X_{\max}}{254^S}$$ + +将该绝对误差用矩阵最大元素 $X_{\max}$ 归一化,可得: + +$$\frac{\left|x - \sum_{i=0}^{S-1} q_i \cdot s_i\right|}{X_{\max}} \le \frac{1}{254^S}$$ + +这不是逐元素相对误差界:当 $x=0$ 或 $|x|\ll X_{\max}$ 时,不能用 $|x|$ 作统一下界。下表仅列出相对于 $X_{\max}$ 的理论绝对误差界(即 $|r_S|/X_{\max}$);它不包含 FP64 残差更新、INT32 GEMM 或 FP64 重组产生的舍入误差。 + +| splits $S$ | 归一化误差上界 | 等效位数 | +|------------|----------------|----------| +| 1 | $1/254 \approx 3.9 \times 10^{-3}$ | $\approx 8$ bit | +| 2 | $1/254^2 \approx 1.5 \times 10^{-5}$ | $\approx 16$ bit | +| 4 | $1/254^4 \approx 2.4 \times 10^{-10}$ | $\approx 32$ bit | +| 8 | $1/254^8 \approx 5.8 \times 10^{-20}$ | $\approx 64$ bit | + +$S=8$ 时理论误差已低于 FP64 unit roundoff(约 $2^{-53}$),但这只是理想化分解的误差界,不代表端到端 FP64 等价。 + +下表将理论上界与 H800 MIG 上的实测 L2 相对误差进行对照(矩阵规模 4096³): + +| splits $S$ | 理论上界 $1/254^S$ | `int8_cublas_baseline` 实测 | `cublas_emulated` 实测 | +|---|---|---|---| +| 2 | $1.5 \times 10^{-5}$ | $2.2 \times 10^{-5}$ | $5.4 \times 10^{-7}$ | +| 4 | $2.4 \times 10^{-10}$ | $3.4 \times 10^{-10}$ | $9.7 \times 10^{-12}$ | +| 6 | $3.8 \times 10^{-15}$ | $5.4 \times 10^{-15}$ | $1.1 \times 10^{-15}$ | +| 8 | $5.8 \times 10^{-20}$ | $1.1 \times 10^{-15}$ | $1.1 \times 10^{-15}$ | + +`int8_cublas_baseline` 在 $S \le 6$ 时实测误差与理论上界同数量级,说明量化误差是主要误差来源。$S=8$ 时实测误差远大于理论上界,因为此时量化误差已低于 FP64 舍入误差,整体精度由 FP64 运算主导。 + +`cublas_emulated` 在相同 splits 下精度普遍优于 `int8_cublas_baseline`,说明 cuBLAS 内部使用了更优的量化策略(如自适应缩减率或动态尾数控制),而非严格使用 $C=254$ 的固定缩减率。 + +### GEMM 展开 + +矩阵 $A$ 和 $B$ 分别分解为 $S$ 个 INT8 分量后,令 $\widetilde{A}$、$\widetilde{B}$ 表示其重组结果,则: + +$$\widetilde{C}=\widetilde{A}\widetilde{B}=\left(\sum_{i=0}^{S-1} s^A_i A^{(i)}_q\right)\left(\sum_{j=0}^{S-1} s^B_j B^{(j)}_q\right)=\sum_{i=0}^{S-1}\sum_{j=0}^{S-1}s^A_i s^B_j\big(A^{(i)}_qB^{(j)}_q\big),\qquad \widetilde{C}\approx C=AB$$ + +每个 $A^{(i)}_q B^{(j)}_q$ 是一次 INT8×INT8→INT32 的 GEMM,共 $S^2$ 次;其结果乘以缩放系数 $s^A_i s^B_j$ 后在 FP64 下累加到输出矩阵。当前 benchmark 程序的尺寸满足 INT8 Tensor Core 路径的常见对齐条件,但实际库调度应以 profiler 结果为准。 + +**为什么需要 $S^2$ 次?** $A$ 和 $B$ 各有 $S$ 个分量,需计算所有 $S \times S$ 种组合。 + +## 实验任务 +`src/lab4p5/submit/my_int8_fp64.cu` 中为大家提供了朴素实现的骨架,同学们按照代码中的提示完成两个核函数就可以拿到基础的分数。如果想要拿到更高的分数,除了改进核函数以外,host 侧函数也需要修改,以实现更加自由高效的调度和编排。 + +无论实现如何,最后对外提供统一的函数签名: + +```c +int gemm_my_int8_fp64(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, cudaStream_t stream); +``` +矩阵采用列主序存储:$C[M\times N] = A[M\times K] \times B[K\times N]$,对应内存布局为 `A[k*M+m]`、`B[n*K+k]`、`C[n*M+m]`。 + +!!! warning "正确性是优化的前提" + benchmark 传入的 `splits` 参数不得在实现中擅自缩减。运算结果最后会与基线计算误差,误差过大则当次评测 0 分。 + + + +## 代码结构 + +所有源码位于 `src/lab4p5/` 目录下: +``` +src/lab4p5/ +├── baseline +│ ├── baseline_fp64.cu +│ ├── cublas_baseline.cu +│ └── cublas_emulated.cu +├── benchmark.cu +├── include +│ ├── gemm_api.h +│ └── utils.h +├── Makefile +├── submit +│ └── my_int8_fp64.cu +└── utils.cu +``` + +| 文件 | 说明 | +|------|------| +| `gemm_api.h` | 统一函数签名 | +| `utils.cu` / `utils.h` | 计时(`CudaTimer`)、误差比较(`accuracy_compare`)、矩阵填充、max-abs 归约(`device_maxabs_fp64`)、设备内存分配 | +| `baseline_fp64.cu` | cuBLAS FP64 基准 (`gemm_fp64_cublas`,精度与性能参考) | +| `cublas_baseline.cu` | 朴素 INT8 模拟实现,基于 cuBLAS INT8 GEMM;每个 split 单独量化、每个 $(i,j)$ 单独重组 | +| `cublas_emulated.cu` | cuBLAS 内置的 FP64 fixed-point emulation(`CUBLAS_COMPUTE_64F_EMULATED_FIXEDPOINT`),将 FP64 输入量化为定点表示后用 INT8 张量核计算,`splits` 通过 `max_mantissa_bits = 8 * splits` 控制 cuBLAS 内部保留的尾数位数 | +| `my_int8_fp64.cu` | **需要修改的文件** | +| `benchmark.cu` | 统一测评程序 | +| `Makefile` | 编译脚本 | + + + + +## 如何获取计算资源 + +我们通过[实验平台](https://platform.s.zjusct.io)提供计算资源。你需要: + +1. 登录实验平台; +2. 创建预设为 `x86-5418Y` 的 DevPod; +3. 在 DevPod 内获取课程仓库并进入 `src/lab4p5/`。 + +DevPod 是持久化的开发容器,适合编辑和编译,但**不要在 DevPod 中直接运行 GPU 任务**。正式计时和性能评测必须通过 `hpc submit` 提交到计算分区执行。 + +本实验使用 H800 PCIe GPU,通过 MIG 技术将一张 H800 切分为多个 GPU 实例,每个实例拥有独立的计算资源和内存空间。MIG 不会改变 GPU 的 CUDA 架构和 compute capability,编译目标仍为 `sm_90a`;但每个实例只拥有整卡的一部分计算单元、显存和显存带宽,因此 `nvidia-smi` 显示的资源规模和程序实测性能不能直接与完整 H800 对比。开发和评测时请以实际分配到的 MIG 实例为准。 + +| 项目 | 规格 | +|------|------| +| GPU | NVIDIA H800 PCIe(sm_90a,80 GB HBM3) | +| MIG 实例 | 1g.10gb(1 个 GPU 实例,10 GB HBM3) | +| CUDA Toolkit | 13.3 | +| 测试矩阵 | 4096³ 及 8192³,元素为 $[-1, 1]$ 均匀分布随机数 | + +更详细的平台使用说明请参考 [集群使用](https://hpc101.zjusct.io/guide/)。 + +## 构建与运行 + +在 DevPod 中编译 benchmark: + +```bash +cd ~/HPC101/src/lab4p5 +export PATH=/usr/local/cuda/bin:$PATH +make +``` + +提交 GPU 任务到计算分区运行: + +```bash +# 交互式调试 +hpc submit -p lab4g10 -g 1 --interactive bash + +# 在计算节点上运行 benchmark(默认测试 splits=2,4,6,8) +hpc submit -p lab4g10 -g 1 "./benchmark 1024,2048,4096 2,4,6,8 5" + +# 导出 CSV +hpc submit -p lab4g10 -g 1 "./benchmark 4096,8192 2,4,6,8 10 --csv > results.csv" + +# 使用 ncu / nsys 分析性能 +hpc submit -p lab4g10 -g 1 "ncu -o profile ./benchmark 4096 4 1" +hpc submit -p lab4g10 -g 1 "nsys profile -o trace ./benchmark 4096 4 1" +``` + +`benchmark` 程序对每个矩阵规模和 splits 组合运行所有实现,输出吞吐量(GFLOPS)和相对 `fp64_cublas` 参考结果的 L2 相对误差。每个实现先跑一次预热并同步,再计时 `iters` 次取平均值。使用 `--csv` 输出表头为 `size_M,size_N,size_K,method,splits,time_ms,gflops,max_abs_err,l2_rel_err` 的 CSV 格式表格。 + +每个测试矩阵规模下输出以下各行: + +| 输出行 | 含义 | +|--------|------| +| `fp64_cublas` | 原生 FP64(cuBLAS `cublasDgemm`),精度与性能参考 | +| `int8_cublas_baseline` | 朴素 INT8 模拟实现 | +| `my_int8_fp64` | 你的实现 | +| `cublas_emulated` | cuBLAS 内置的 FP64 fixed-point emulation(`CUBLAS_COMPUTE_64F_EMULATED_FIXEDPOINT`),与你的手动实现使用相同的 split 精度参数对标 | + + +## 性能分析:从 Profiling 开始 + +先得到正确结果,再优化端到端时间。 + +!!! note "瓶颈在哪里?" + 单次 INT8 GEMM 很快,不代表整条模拟路径很快。以 `splits=8` 为例:$S^2 = 64$ 次 GEMM 调用、$2S = 16$ 次量化 kernel、$S^2 = 64$ 次重组 kernel,总计超过 140 次 kernel launch。中间 INT32 结果的读写量是 $64 \times M \times N \times 4$ 字节——这些才是真正的开销。 + +### 分析流程 + +1. 用 Nsight Systems 拉一条时间线,看 GEMM、量化、重组各占多少时间,kernel launch 间隙有多少空闲。 +2. 用 Nsight Compute 分析热点 kernel 的访存效率、occupancy 和带宽利用率。 +3. 一次只改一个点,每次修改后重新测量端到端时间并检查 L2 相对误差。 +4. 只保留同时满足误差要求且确实更快的修改。 + +### 优化方向 +#### 算子融合 + +将量化、INT8 GEMM 和 FP64 重组拆成独立 kernel,代码清晰且便于验证,但 kernel launch 并不是免费的。在最直接的实现中,$A$、$B$ 各需要处理 $S$ 个分量,量化相关 kernel 的启动次数约为 $2S$;若每个 $(i,j)$ 部分积都单独缩放并写回,重组相关 kernel 还可能达到 $S^2$ 次。$S=8$ 时,仅这些阶段就会产生数十次启动。对于计算量较小的 kernel,启动延迟可能与有效计算时间处于同一数量级。 + +此外,kernel 边界通常意味着中间结果需要写入全局内存,再由下一个 kernel 读回。例如,INT32 部分积若完整落地到 HBM,后续重组至少还要进行一次读取和一次 FP64 输出更新;当 $S^2$ 个部分积依次处理时,这部分内存流量可能压过矩阵乘法本身。因此,融合的价值不仅是减少启动次数,更重要的是**缩短中间数据的路径和生命周期**。 + +可以按风险从低到高尝试以下几层融合: + +1. **融合同一矩阵的多级量化**:一个线程向量化加载若干 FP64 元素,在寄存器中连续更新残差并生成 $q_0, q_1, \ldots, q_{S-1}$,一次 kernel 写出全部 split,避免为每一级重新读取原矩阵。量化商可尝试用 FP32 乘倒数和 `rintf` 计算,但混合精度只应用于**分量选择**;比例尺与残差更新仍应保留 FP64 FMA,并通过误差测试验证。 +2. **一次融合重组多个部分积**:先保存需要的 INT32 部分积,再由一个 kernel 对同一输出位置遍历所有 pair,只写一次 FP64 $C$。可以把 scales 预加载到 Shared Memory,并使用 `int4` load 与 `double4` store;这样可把最多 $S^2$ 个重组 launch 降为 1 个,也避免反复读改写 $C$,但仍需为每个保留的 pair 写入并读回一份完整 INT32 矩阵。 +3. **把缩放重组并入 GEMM epilogue**:INT8 GEMM 得到一个 INT32 tile 后,立即乘以 $s_i^A s_j^B$ 并累加到 FP64 输出,从而进一步消除完整 INT32 中间矩阵。若多个 GEMM 分别直接更新同一个 $C$,必须解决跨 kernel 的写冲突或串行化问题;更现实的路线是让一个 CTA 连续消费一批 pair,或设计受控的分批 epilogue。 +4. **端到端 mega kernel**:将分解、GEMM 和重组放入一个持久化 kernel。它能够消除最多的边界,却也最难处理调度、同步和资源占用,通常应当在前三级优化完成后再考虑。 + +![算子融合前后的数据路径](image/operator-fusion.svg) + +融合不是越彻底越好。融合后变量存活时间变长,可能提高 registers/thread 和 Shared Memory/CTA,降低一个 SM 上可同时驻留的 CTA 数;寄存器不足还会产生 local-memory spill,反而增加访存。实践中应同时比较 `registers per thread`、Shared Memory 用量、occupancy、DRAM bytes 和 kernel 数量,以“端到端时间下降”而不是“kernel 数量最少”作为选择融合边界的标准。 + +#### Overlapping:重叠数据搬运与计算 + +流水线优化的目标不是减少总工作量,而是把一个阶段的等待时间隐藏在另一个阶段的有效工作之后。对按 $K$ 维分块的 GEMM 而言,可以将每个 tile 的处理拆成“从全局内存搬入 Shared Memory → Tensor Core 计算 → 缩放与 FP64 重组”三个阶段。当 Tensor Core 计算 tile $t$ 时,搬运单元预取 tile $t+1$,CUDA Core 则可以处理已经完成的 tile $t-1$,从而让不同硬件资源在时间线上同时保持忙碌。 + +最常见的实现是 **double buffering** 或多级流水线。Shared Memory 中准备两个或更多缓冲区:producer 向缓冲区 A 写入新 tile 时,consumer 从缓冲区 B 读取旧 tile 进行计算;下一轮交换 A、B 的角色。Hopper 提供 TMA(Tensor Memory Accelerator)执行异步张量搬运,并可在搬运过程中完成多维寻址和适配 Shared Memory 的布局变换。这样,少量 producer 线程即可发起大块数据传输,其余线程不必逐元素执行地址计算。关于 TMA 的进一步介绍可参考 [CuTe 之 Hopper TMA](https://zhuanlan.zhihu.com/p/1985678344352731952)。 + +![串行执行与双缓冲流水线](image/overlap-pipeline.svg) + +重叠执行的前提是正确表达数据依赖。producer 不能覆盖 consumer 尚未读完的缓冲区,consumer 也不能读取尚未完成的异步搬运;因此每一级缓冲区都需要“empty/ready”状态,并通过 `mbarrier`、pipeline primitive 或等价同步机制完成所有权交接。同步过早会把流水线重新串行化,同步不足则会造成数据竞争。 + +跨 kernel 的依赖需额外注意:在**同一非默认 stream** 中,后续 kernel 会自动等待同一 stream 上的前序 kernel 完成,这种隐式顺序足以建立“量化 → GEMM”的简单依赖;但一旦把生产者和消费者放到**不同 stream** 以便重叠,就应优先用 `cudaEventRecord` / `cudaStreamWaitEvent` 精确表达依赖——`cudaStreamWaitEvent` 只等待事件**当下已记录的那一次** record,后续 record 不会影响既有 wait。切勿依赖默认 stream 的隐式全局同步,`--default-stream per-thread` 等编译选项会改变其语义。 + +比如矩阵 A/B 的 max-abs 与量化可以分别运行在两条 stream 上,保留的 GEMM 也可以分派到多条 stream,最后再统一重组。但必须建立完整的跨 stream 依赖:A、B 量化完成后分别记录 event,每条 GEMM stream 都等待两个输入 event;各 GEMM stream 完成后再分别记录 event,由重组 stream 等待全部完成。这样既补齐 happens-before,又避免用 `cudaStreamSynchronize` 阻塞 host。尤其不能只同步 B 的生产 stream:另一条 stream 上的 GEMM 同样可能读取尚未完成量化的 A。更细一步,可把部分积划成批次并用 event 或 CUDA Graph 连接,以降低同步和重复提交开销。若要支持多 host 线程、多个独立调用或 CUDA Graph capture,还应把中间缓冲、stream 和 event 放入显式 context/workspace,避免不可重入的全局静态状态,也避免在热路径中创建 stream、分配内存或执行阻塞同步。 + +本实验还可以进一步按 tile 重叠 Tensor Core 上的 INT8 GEMM 与 CUDA Core 上的地址计算、类型转换和 FP64 重组。不过“可被并发调度”不等于一定获得线性加速:多个饱和 Tensor Core GEMM 往往会竞争同一组 SM,而不是把吞吐直接翻倍;FP64 重组还会竞争 CUDA Core、寄存器和内存带宽。应在时间线中确认是否真正形成重叠,并以端到端时间判断双 stream 是否值得保留。 + +#### Hopper 架构上的 WGMMA 与 warp specialization + +WGMMA(Warpgroup Matrix Multiply-Accumulate)是 Hopper `sm_90a` 上面向 warp group 的异步矩阵乘加接口。一个 warp group 由 **4 个连续 warp,即 128 个线程**组成;这些线程协作发起矩阵乘法并持有分布式累加器。与此前以单个 warp 为主要协作单位的 MMA 接口相比,WGMMA 处理更大的 tile,并允许矩阵乘法与同一 CTA 中其他 warp group 的数据准备工作重叠。这里的“异步”指的是**发起与等待被分离**:warp group 发出指令后,可以在允许的依赖范围内继续推进流水线,随后通过 commit/wait group 语义保证累加器结果在被消费前已经完成——它**不能省略同步**,只是把等待推迟到真正需要结果的位置。WGMMA 在本实验中只承担 INT8×INT8→INT32 主体计算;FP64 缩放与跨 pair 重组仍需由 CUDA Core 或后续 epilogue 完成,不能把“使用 WGMMA”误解为整条数据路径都运行在 Tensor Core 上。 + +warp specialization 的划分单位是 **warp 或 warp group**,而不是把一个 warp 内的线程再拆成不同职责。典型的 producer-consumer 结构如下:producer warp 负责通过 TMA 发起全局内存到 Shared Memory 的搬运并维护 barrier;consumer warp group 等待 tile 就绪后发起 WGMMA;需要时还可由专门的 warp 处理 epilogue 和写回。各角色通过 Shared Memory 中的多级缓冲区传递数据,使搬运、矩阵乘法和重组形成细粒度流水线。 + +![Hopper warp specialization 示例](image/warp-specialization.png) + +将这一结构用于本实验时,可以让 producer 准备 $A_q^{(i)}$、$B_q^{(j)}$ 的下一个 K-tile,让 consumer warp group 执行当前 INT8×INT8→INT32 WGMMA,并在合适的阶段把完成的累加器交给 FP64 重组逻辑。实现时需要重点选择 CTA tile、WGMMA tile、pipeline stage 数和各角色的 warp 数。tile 太小会增加调度开销,tile 太大则可能因 Shared Memory 和寄存器占用过高而降低并行度;producer 太少可能喂不满 Tensor Core,太多则会挤占 consumer 的资源。建议先复用 CUTLASS 中已经验证过的 SM90 warp-specialized schedule,再逐项替换数据类型、布局和 epilogue。 + +使用 CUTLASS 时,可以通过 `CollectiveBuilder` 的 `KernelScheduleAuto` 选择 SM90 warp-specialized/TMA 路径,并用 `StageCountAutoCarveout` 在扣除 epilogue Shared Memory 后决定 mainloop stage 数,而不必手写 `wgmma.*` PTX。CTA tile 和 cluster shape 仍需实测;例如可以把 `128×256×128` CTA tile 与 `1×1×1`、`2×1×1`、`4×1×1` 等 cluster 作为候选。cluster 使相邻 CTA 有机会通过 TMA multicast 复用 operand tile,但收益取决于问题形状、SM 数、MIG 分区、可调度 cluster 数和尾部浪费。同一配置在不同规模的 GPU 分区上可能出现相反排序,因此必须按目标机器重新扫描,不能照抄单一参数。 + +#### 使用 CUTLASS + +CUTLASS 是 NVIDIA 提供的高性能 CUDA C++ 模板库,用于构造 GEMM 及相关算子。与只能选择固定库接口的 cuBLAS 相比,CUTLASS 暴露了 tile shape、数据布局、pipeline stage、kernel schedule 和 epilogue 等编译期参数,因此特别适合本实验这种“主体是标准 INT8 GEMM,但前后处理需要定制”的场景。其底层 CuTe 抽象用 `Tensor`、`Layout`、copy atom 和 MMA atom 描述线程与数据的映射,可以在较高层表达 TMA、Shared Memory swizzle 和 WGMMA,而不必从头手写全部 PTX。 + +在 CUTLASS 3.x 的 GEMM 结构中,`CollectiveMainloop` 负责将 $A/B$ tile 从全局内存搬到 Shared Memory 并执行主循环矩阵乘法,`CollectiveEpilogue` 负责处理累加器、类型转换和输出写回。本实验可将输入和输出设为列主序,INT8 输入采用 16 元素(128 bit)对齐,INT32 输出采用 4 元素对齐,累加器使用 INT32,并通过 `GemmUniversalAdapter` 在 `sm_90a` 上运行。后续路线应区分“调好标准 GEMM”和“改造 Ozaki 数据流”: + +1. **扫描标准 GEMM 配置**:针对目标 $M,N,K$、GPU/MIG 分区测试 CTA tile、cluster shape 与 schedule。`StageCountAutoCarveout` 是可靠起点,但不等于对所有尺寸最优;还要检查尺寸是否满足向量对齐以及 tile/cluster 的整除或 predication 成本。 +2. **复用 workspace 和计划**:缓存 CUTLASS workspace 与大块临时缓冲,避免每次调用都 `cudaMalloc`;还应缓存与 problem shape 对应的 kernel 配置,并通过显式 context 管理生命周期,而不是使用不可重入的全局静态状态。 +3. **减少 pair 级调度开销**:如果每个保留的 $(i,j)$ 都单独调用一次 CUTLASS GEMM,pair 数较多时会产生明显的启动和调度成本。可考虑 grouped/batched 组织、CUDA Graph,或在自定义 kernel 中一次消费多个 pair;不过各 pair 的 A/B 指针组合和 FP64 权重不同,不能简单假设一次普通 batched GEMM 就能完成最终重组。 +4. **定制 Ozaki epilogue 或 tile 级重组**:标准 `CollectiveEpilogue` 可以先输出 INT32 部分积,再由后续 kernel 执行 FP64 缩放;更进一步,可让 epilogue 或后继 tile 消费者直接完成 FP64 转换与缩放,以减少 `n_pairs × M × N × sizeof(int32_t)` 的临时存储和 HBM 往返,同时设计无竞争的跨 pair 累加方式。 + +![CUTLASS 的分层抽象与本实验定制点](image/cutlass-layers.svg) + +CUTLASS 的优势是复用已经优化过的流水线和布局,代价是模板层次较深、编译时间较长,而且自定义 FP64 epilogue 仍可能成为瓶颈。建议先用 CUTLASS Profiler 找到接近目标数据类型和尺寸的 SM90 kernel,再从可运行模板开始修改;每次只替换一个组成部分,并用正确性测试和 profiler 对比,避免同时改变布局、调度和重组逻辑后难以定位问题。还要分别报告**单次 INT8 GEMM 时间**与包含 max-abs、量化、全部 pair、重组和同步的**端到端时间**:前者接近峰值并不代表整个 FP64 模拟路径同样高效。 + +#### 减少 Shared Memory bank conflict + +Shared Memory 被划分为多个可并行访问的 bank。对常见的 32-bank 组织而言,一个 warp 发出的 Shared Memory 指令如果把不同地址集中映射到同一 bank,硬件就需要把请求拆成多次执行;冲突度越高,有效带宽越低。一个简化的 4-bank 模型如下,其中逻辑上连续的 word 轮流映射到不同 bank: + +```text +Bank 0 Bank 1 Bank 2 Bank 3 +MEM[0] MEM[1] MEM[2] MEM[3] +MEM[4] MEM[5] MEM[6] MEM[7] +MEM[8] MEM[9] MEM[10] MEM[11] +... ... ... ... +``` + +例如,线程分别访问 `MEM[0]`、`MEM[9]`、`MEM[6]`、`MEM[3]` 时,地址映射到四个不同 bank,可以并行服务;若它们访问 `MEM[0]`、`MEM[4]`、`MEM[8]`、`MEM[12]`,则会形成同一 bank 上的不同地址冲突。需要区分一种例外:多个线程读取同一 bank 的**同一地址**时,Shared Memory 可以广播该值,这通常不计为 bank conflict。 + +![不同 Shared Memory 布局下的 bank conflict](image/conflict.png) + +GEMM 中的 Shared Memory tile 常常会被转置读取,或者被 WGMMA 按特定 fragment 方式消费;即使全局内存写入是连续的,简单的行主序/列主序 Shared Memory 布局也可能在读取阶段产生高阶冲突。常见的解决方法包括: + +- **padding**:将 leading dimension 从 `TILE_K` 改为 `TILE_K + PAD`,打破固定步长与 bank 数的公因子; +- **swizzle/permuted layout**:用行号的部分 bit 对列地址做置换,使相邻线程在转置访问时分散到不同 bank; +- **匹配访问粒度和对齐**:结合向量化 load/store、WGMMA 要求以及元素宽度设计布局,而不是只按二维矩阵的直观顺序存储; +- **让 TMA 写入目标布局**:在 Hopper 上利用 TMA 与 CuTe layout 将全局内存中的规则 tile 搬成计算阶段所需的 Shared Memory 布局,减少手工重排指令。 + +布局优化必须同时检查写入和读取两侧:消除 producer 的冲突却增加 consumer 的冲突,未必有净收益。可用 Nsight Compute 的 Shared Memory load/store transaction、bank-conflict 相关指标以及 kernel 总时间验证;具体的布局示例可参考 [CuTe 之 Hopper TMA](https://zhuanlan.zhihu.com/p/1990792939232835390)。 + +#### 其他优化思路 + +![通用优化方向及其验证指标](image/optimization-checklist.svg) + +1. **减少全局内存访问,提高数据复用。** 对 $M/N/K$ 三个维度进行 tiling,把 $A/B$ 子块缓存在 Shared Memory,把输出子块或部分累加状态尽量保留在寄存器中,使一次 HBM 加载能够服务多次 MMA。还应避免每个 $(i,j)$ 部分积都对完整 $C$ 做一次读改写;可以按输出 tile 或按若干 split 组合分批累加。优化后应观察 DRAM bytes 是否下降、L2 命中率和 arithmetic intensity 是否提高,而不能只比较指令数。 + +2. **优化全局内存访问模式。** 让同一 warp 的线程访问连续且对齐的地址,以便合并为尽可能少的内存事务;必要时使用 `int4`、`uint4` 等向量化访问,但必须保证地址和 leading dimension 满足对齐要求。当前矩阵为列主序,因此线程到 `A[k*M+m]`、`B[n*K+k]` 和 `C[n*M+m]` 的映射应分别设计,不能对三个矩阵机械套用同一种线程布局。边界 tile 可以采用 predication 或独立的 remainder kernel,避免正常路径承担大量越界判断。需要注意,**全局内存 coalescing 与 Shared Memory bank conflict 是不同层级的问题**,应分别分析。 + +3. **减少分支与 warp divergence。** 当同一 warp 内不同线程执行不同分支时,各路径会被依次执行,未参与当前路径的线程处于空闲状态。可将常见的整齐尺寸作为无分支 fast path,把边界情况拆到单独 kernel;对简单的边界条件优先使用 predication,并将只与 tile 或 warp 有关的判断移到循环外。模板参数和循环展开还能把 splits、tile shape 等运行时分支转化为编译期选择,但展开过度会增大代码体积和寄存器压力,因此仍需实测。 + +4. **在误差预算内做精度取舍。** 低精度并不意味着所有变量都应降精度。INT8 分量和 INT32 Tensor Core 累加是算法的计算主体,而比例尺 $s_i^A s_j^B$、残差更新、跨部分积的求和及最终输出通常仍应保留 FP64,以避免小量级分量在重组时被吞掉。量化商和 max-abs 归约可尝试 FP32,但它们会影响分量选择与初始比例尺,必须覆盖动态范围大、接近量化边界、含全零矩阵以及非 16 倍数尾部等用例,不能只在随机均匀矩阵上验证。 + +5. **按反对角线裁剪 split pair。** 由于 $s_i^A s_j^B$ 随 $i+j$ 近似按 $254^{-(i+j)}$ 衰减,优先保留 $i+j g_{100}, +\end{cases} +$$ + +其中 $u = \dfrac{g - g_{60}}{g_{100} - g_{60}}$,$g$ 为 `my_int8_fp64` 的实测 GFLOPS。 + +各 splits 的 checkpoint(GFLOPS)如下表: + +| splits | $g_0$(0 分) | $g_{60}$(60 分) | $g_{100}$(100 分) | +|-------|------------:|--------------:|----------------:| +| 2 | 2500 | 5000 | 10000 | +| 4 | 750 | 2500 | 5000 | +| 6 | 350 | 1500 | 3000 | +| 8 | 200 | 1500 | 3000 | + +- $g \le g_0$:基本没有有效优化,得 0 分。 +- $g = g_{60}$:超过朴素 baseline 的水平,得 60 分。 +- $g = g_{100}$:达到 cuBLAS 内置 fixed-point emulation 的性能,得 100 分。 +- $g > g_{100}$:超过 cuBLAS,仍得 100 分(满分封顶)。 + +### 测试规模与权重 + +测试矩阵规模为 4096³ 和 8192³,splits 取 2、4、6、8。每个规模下取各 splits 得分的算术平均,再按规模等权平均。各 splits 的权重为: + +| splits | 权重 | +|--------|------| +| 2 | 40% | +| 4 | 20% | +| 6 | 20% | +| 8 | 20% | + +最终得分公式为: + +$$ +\text{Score} = \frac{1}{2}\sum_{M \in \{4096, 8192\}} \sum_{S \in \{2,4,6,8\}} w_S \cdot S_M(g_{M,S}) +$$ + +其中 $w_2 = 0.4$,$w_4 = w_6 = w_8 = 0.2$,$g_{M,S}$ 是规模 $M$ 下 splits=$S$ 时 `my_int8_fp64` 的实测 GFLOPS,$S_M(g_{M,S})$ 是对应的得分。 + +## 提交要求 + +1. 修改后的 `src/lab4p5/submit/my_int8_fp64.cu`。 + +## 参考资料 + +1. Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi, and Siegfried M. Rump. “Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications.” *Numerical Algorithms*, 59(1):95-118, 2012. [doi:10.1007/s11075-011-9478-1](https://doi.org/10.1007/s11075-011-9478-1) +2. NVIDIA. “cuBLAS Library Documentation,” CUDA Toolkit 13.3, §1.5 Floating Point Emulation. [https://docs.nvidia.com/cuda/cublas/](https://docs.nvidia.com/cuda/cublas/) +3. NVIDIA. “NVIDIA H100 GPU: Product Specifications.” [https://www.nvidia.com/en-us/data-center/h100/](https://www.nvidia.com/en-us/data-center/h100/) +4. NVIDIA. “Datasheet for NVIDIA Blackwell Architecture” (B200) and “Datasheet for NVIDIA Blackwell Ultra” (B300). [https://www.nvidia.com/en-us/data-center/blackwell-architecture/](https://www.nvidia.com/en-us/data-center/blackwell-architecture/) diff --git a/src/lab4p5/Makefile b/src/lab4p5/Makefile new file mode 100644 index 00000000..a9770ef5 --- /dev/null +++ b/src/lab4p5/Makefile @@ -0,0 +1,35 @@ +# ============================================================================ +# HPC101 Lab 4.5 — Makefile +# 在 H800 (sm_90a) 上编译 benchmark。按需调整 CUDA_HOME / ARCH。 +# ============================================================================ +CUDA_HOME ?= /usr/local/cuda +NVCC := $(CUDA_HOME)/bin/nvcc +ARCH ?= sm_90a +NVCCFLAGS := -arch=$(ARCH) -O3 -std=c++17 -lineinfo -Iinclude +LDLIBS := -lcublas -lcudart -lcuda + +SRCS := benchmark.cu \ + baseline/baseline_fp64.cu \ + baseline/cublas_baseline.cu \ + baseline/cublas_emulated.cu \ + utils.cu \ + submit/my_int8_fp64.cu +OBJS := $(SRCS:.cu=.o) +DEPS := include/gemm_api.h include/utils.h + +.PHONY: all clean run + +all: benchmark + +benchmark: $(OBJS) + $(NVCC) $(NVCCFLAGS) $(OBJS) $(LDLIBS) -o $@ + +%.o: %.cu $(DEPS) + $(NVCC) $(NVCCFLAGS) -c $< -o $@ + +# 快速默认测试 +run: benchmark + ./benchmark 1024,2048,4096 2,4,6,8 5 + +clean: + rm -f $(OBJS) benchmark diff --git a/src/lab4p5/baseline/baseline_fp64.cu b/src/lab4p5/baseline/baseline_fp64.cu new file mode 100644 index 00000000..ddf1e867 --- /dev/null +++ b/src/lab4p5/baseline/baseline_fp64.cu @@ -0,0 +1,36 @@ +/* + * ============================================================================ + * baseline_fp64.cu — FP64 GEMM baselines + * ---------------------------------------------------------------------------- + * gemm_fp64_cublas : cublasDgemm, the "vendor native FP64 tensor core" + * path. This is BOTH the accuracy reference and the + * performance reference for native FP64. + + * ============================================================================ + */ +#include "gemm_api.h" +#include "utils.h" + +/* ------------------------------------------------------------------------- + * cuBLAS FP64 GEMM + * C[M,N] = A[M,K] @ B[K,N] (all column-major, no transpose) + * m=M, n=N, k=K, lda=M, ldb=K, ldc=M + * ------------------------------------------------------------------------- */ +int gemm_fp64_cublas(int M, int N, int K, + const double* dA, const double* dB, double* dC, + cublasHandle_t handle) +{ + /* reset math mode: cublas_emulated may have left it on FP64_EMULATED */ + cublasSetMathMode(handle, CUBLAS_DEFAULT_MATH); + const double alpha = 1.0, beta = 0.0; + CUBLAS_CHECK(cublasDgemm(handle, + CUBLAS_OP_N, CUBLAS_OP_N, + M, N, K, + &alpha, + dA, M, + dB, K, + &beta, + dC, M)); + return 0; +} + diff --git a/src/lab4p5/baseline/cublas_baseline.cu b/src/lab4p5/baseline/cublas_baseline.cu new file mode 100644 index 00000000..90e0d623 --- /dev/null +++ b/src/lab4p5/baseline/cublas_baseline.cu @@ -0,0 +1,173 @@ +/* + * ============================================================================ + * cublas_baseline.cu — INT8 emulation of FP64 via cuBLAS INT8 GEMM + * ---------------------------------------------------------------------------- + * Reference "easy path" implementation. Deliberately UNOPTIMIZED so that + * students have something concrete to beat: + * + * * one separate quantize kernel launch per split (K launches, each reads + * & writes the whole residual buffer); + * * INT8 -> INT32 cuBLAS GEMM (CUBLAS_COMPUTE_32I), then a separate + * FP64 recombine-add kernel per split pair (K*K launches); + * * a single reusable INT32 scratch buffer (small memory footprint, at + * the cost of K*K extra global-memory passes over C). + * + * Algorithm (successive-approximation / "Ozaki-style" split): + * A ~= sum_i sA[i] * Aq[i] (Aq[i] : int8, sA[i] : double) + * B ~= sum_j sB[j] * Bq[j] + * C = sum_{i,j} sA[i]*sB[j] * (Aq[i] @ Bq[j]) + * + * With a geometric scale sA[i] = sA[0]/254^i (and sA[0] = max|A|/127), every + * int8 component is guaranteed to lie in [-127,127] with no per-split + * reduction. Each split recovers ~7 bits of mantissa. + * + * NOTE: cuBLAS INT8 GEMM requires leading dimensions (here M and K) to be + * multiples of 4 and 16-byte aligned pointers. The benchmark uses + * matrix dimensions that are multiples of 16. + * ============================================================================ + */ +#include "gemm_api.h" +#include "utils.h" +#include + +/* round-to-nearest-even via rint(); clamp to int8 range [-127,127] */ +__device__ __forceinline__ int8_t quantize_to_int8(double x, double scale) +{ + double q = rint(x / scale); + if (q > 127.0) q = 127.0; + if (q < -127.0) q = -127.0; + return (int8_t)q; +} + +/* ------------------------------------------------------------------------- + * Naive per-split quantize kernel. + * Reads residual[e], writes int8 q[e], and updates residual[e] IN-PLACE + * to residual[e] - q[e]*scale (preparing the next split). + * ------------------------------------------------------------------------- */ +static __global__ void quantize_one_split_kernel(double* residual, int8_t* q, + double scale, size_t n) +{ + size_t i = (size_t)blockIdx.x * blockDim.x + threadIdx.x; + if (i >= n) return; + double x = residual[i]; + int8_t qi = quantize_to_int8(x, scale); + q[i] = qi; + residual[i] = x - (double)qi * scale; +} + +/* ------------------------------------------------------------------------- + * Naive recombine-add kernel. + * C[m,n] += scale * (double)temp[m,n] (temp is the INT8@INT8 INT32 output) + * ------------------------------------------------------------------------- */ +static __global__ void recombine_add_kernel(const int32_t* temp, double* C, + double scale, size_t mn) +{ + size_t i = (size_t)blockIdx.x * blockDim.x + threadIdx.x; + if (i >= mn) return; + C[i] += scale * (double)temp[i]; +} + +int gemm_int8_cublas_baseline(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, + cudaStream_t stream) +{ + if (splits < 1) splits = 1; + const size_t E_A = (size_t)M * K; + const size_t E_B = (size_t)K * N; + const size_t E_C = (size_t)M * N; + + /* --- 1. per-matrix max abs -> first scale (geometric sequence follows) - */ + double maxA = device_maxabs_fp64(dA, E_A); + double maxB = device_maxabs_fp64(dB, E_B); + if (maxA == 0.0) maxA = 1.0; + if (maxB == 0.0) maxB = 1.0; + const double sA0 = maxA / 127.0; + const double sB0 = maxB / 127.0; + + /* --- 2. allocate scratch ------------------------------------------------ */ + /* splits 个 int8 buffers for A and B, plus FP64 residual buffers, plus one INT32 + * scratch for the GEMM output that is reused across split pairs. */ + int8_t** dAq = (int8_t**)malloc(splits * sizeof(int8_t*)); + int8_t** dBq = (int8_t**)malloc(splits * sizeof(int8_t*)); + for (int s = 0; s < splits; ++s) { + dAq[s] = (int8_t*)device_alloc(E_A); + dBq[s] = (int8_t*)device_alloc(E_B); + } + double* residA = (double*)device_alloc(E_A * sizeof(double)); + double* residB = (double*)device_alloc(E_B * sizeof(double)); + int32_t* temp = (int32_t*)device_alloc(E_C * sizeof(int32_t)); + if (!residA || !residB || !temp) { return 1; } + + /* copy A,B into residuals (we modify them in place) */ + CUDA_CHECK(cudaMemcpyAsync(residA, dA, E_A * sizeof(double), + cudaMemcpyDeviceToDevice, stream)); + CUDA_CHECK(cudaMemcpyAsync(residB, dB, E_B * sizeof(double), + cudaMemcpyDeviceToDevice, stream)); + + /* zero the output C (we accumulate into it) */ + CUDA_CHECK(cudaMemsetAsync(dC, 0, E_C * sizeof(double), stream)); + + /* --- 3. quantize each split (sequential dependency on residual) ------- */ + const int block = 256; + { + size_t n = E_A; + int grid = (int)((n + block - 1) / block); + double sA = sA0; + for (int i = 0; i < splits; ++i) { + quantize_one_split_kernel<<>>( + residA, dAq[i], sA, n); + sA = sA / 254.0; + } + } + { + size_t n = E_B; + int grid = (int)((n + block - 1) / block); + double sB = sB0; + for (int j = 0; j < splits; ++j) { + quantize_one_split_kernel<<>>( + residB, dBq[j], sB, n); + sB = sB / 254.0; + } + } + + /* --- 4. K*K INT8 GEMMs + recombine ------------------------------------- */ + cublasSetStream(handle, stream); + cublasSetMathMode(handle, CUBLAS_DEFAULT_MATH); + const int32_t alpha_i = 1; + const int32_t beta_i = 0; + + double sA = sA0; + for (int i = 0; i < splits; ++i) { + double sB = sB0; + for (int j = 0; j < splits; ++j) { + /* temp = Aq[i] @ Bq[j] (INT8 tensor cores, INT32 accumulate) */ + CUBLAS_CHECK(cublasGemmEx(handle, + CUBLAS_OP_N, CUBLAS_OP_N, + M, N, K, + &alpha_i, + dAq[i], CUDA_R_8I, M, + dBq[j], CUDA_R_8I, K, + &beta_i, + temp, CUDA_R_32I, M, + CUBLAS_COMPUTE_32I, + CUBLAS_GEMM_DEFAULT)); + /* C += sA*sB * temp (FP64 accumulation) */ + double scale = sA * sB; + size_t mn = E_C; + int grid = (int)((mn + block - 1) / block); + recombine_add_kernel<<>>( + temp, dC, scale, mn); + sB = sB / 254.0; + } + sA = sA / 254.0; + } + + CUDA_CHECK(cudaStreamSynchronize(stream)); + + /* --- 5. cleanup -------------------------------------------------------- */ + for (int s = 0; s < splits; ++s) { cudaFree(dAq[s]); cudaFree(dBq[s]); } + free(dAq); free(dBq); + cudaFree(residA); cudaFree(residB); cudaFree(temp); + return 0; +} diff --git a/src/lab4p5/baseline/cublas_emulated.cu b/src/lab4p5/baseline/cublas_emulated.cu new file mode 100644 index 00000000..1b50df83 --- /dev/null +++ b/src/lab4p5/baseline/cublas_emulated.cu @@ -0,0 +1,39 @@ +/* + * cublas_emulated.cu — cuBLAS 自带的 FP64-via-INT8 模拟(Ozaki scheme) + * 调用 cublasGemmEx with CUBLAS_COMPUTE_64F_EMULATED_FIXEDPOINT。这是 + * NVIDIA 库自己实现的"FP64 模拟",是端到端性能对比的基线。 + */ +#include "gemm_api.h" +#include "utils.h" + +int gemm_cublas_emulated(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, void* workspace, + size_t workspace_bytes, cudaStream_t stream) +{ + if (splits < 1) splits = 1; + if (workspace && workspace_bytes > 0) { + CUBLAS_CHECK(cublasSetWorkspace(handle, workspace, workspace_bytes)); + } + cublasSetStream(handle, stream); + CUBLAS_CHECK(cublasSetMathMode(handle, CUBLAS_FP64_EMULATED_FIXEDPOINT_MATH)); + CUBLAS_CHECK(cublasSetEmulationStrategy(handle, CUBLAS_EMULATION_STRATEGY_EAGER)); + CUBLAS_CHECK(cublasSetFixedPointEmulationMantissaControl(handle, CUDA_EMULATION_MANTISSA_CONTROL_FIXED)); + /* splits 控制模拟精度:每个 split 约贡献 8 bit,封顶 55(cuBLAS 的上限,对应 7 个 int8 切片)*/ + int max_bits = 8 * splits; + if (max_bits > 55) max_bits = 55; + CUBLAS_CHECK(cublasSetFixedPointEmulationMaxMantissaBitCount(handle, max_bits)); + + const double alpha = 1.0, beta = 0.0; + CUBLAS_CHECK(cublasGemmEx(handle, + CUBLAS_OP_N, CUBLAS_OP_N, + M, N, K, + &alpha, + dA, CUDA_R_64F, M, + dB, CUDA_R_64F, K, + &beta, + dC, CUDA_R_64F, M, + CUBLAS_COMPUTE_64F_EMULATED_FIXEDPOINT, + CUBLAS_GEMM_DEFAULT)); + return 0; +} diff --git a/src/lab4p5/benchmark.cu b/src/lab4p5/benchmark.cu new file mode 100644 index 00000000..95bb2a58 --- /dev/null +++ b/src/lab4p5/benchmark.cu @@ -0,0 +1,161 @@ +/* + * benchmark.cu — 统一性能与精度测评程序 + * + * 对每个矩阵规模和 splits 组合运行所有 GEMM 实现, + * 输出吞吐量(GFLOPS)和相对 FP64 真值的 L2 相对误差。 + * + * 用法: + * benchmark [sizes] [splits] [iters] [--csv] + * + * sizes : 逗号分隔的矩阵维度(方阵 M=N=K),默认 "1024,2048,4096" + * splits : 逗号分隔的 split 数,默认 "2,4" + * iters : 计时迭代次数(取最小值),默认 5 + * + * 示例: + * benchmark 1024,2048,4096,8192 2,4,8 10 --csv > results.csv + */ +#include "gemm_api.h" +#include "utils.h" +#include +#include +#include +#include +#include +#include +#include + +struct Size { int M, N, K; }; + +static std::vector parse_ints(const char* s) { + std::vector v; const char* p = s; + while (*p) { int x = strtol(p, (char**)&p, 10); v.push_back(x); if (*p==',') ++p; } + return v; +} + +/* 计时:取 iters 次的最小值 */ +template +static double time_min_ms(Fn fn, int iters, cudaStream_t stream) { + fn(); + cudaStreamSynchronize(stream); + CudaTimer t; + t.begin(stream); + for (int i = 0; i < iters; ++i) fn(); + t.end(stream); + return t.elapsed_ms() / iters; +} + +int main(int argc, char** argv) { + std::vector sizes = parse_ints("1024,2048,4096"); + std::vector splits = parse_ints("2,4,6,8"); + int iters = 5; + bool csv = false; + for (int i = 1; i < argc; ++i) { + std::string a = argv[i]; + if (a == "--csv") csv = true; + else if (i == 1) sizes = parse_ints(argv[i]); + else if (i == 2) splits = parse_ints(argv[i]); + else if (i == 3) iters = atoi(argv[i]); + } + + int dev; cudaGetDevice(&dev); + cudaDeviceProp prop; cudaGetDeviceProperties(&prop, dev); + cublasHandle_t handle; cublasCreate(&handle); + cudaStream_t stream; cudaStreamCreate(&stream); + + /* cuBLAS emulated 需要的 workspace */ + size_t ws_bytes = (size_t)2 * 1024 * 1024 * 1024; + void* emu_workspace = nullptr; + cudaMalloc(&emu_workspace, ws_bytes); + + if (!csv) { + printf("==========================================================================\n"); + printf(" HPC101 Lab 4.5 INT8 模拟 FP64 GEMM 测评\n"); + printf(" GPU: %s (CC %d.%d), %.0f MiB global memory\n", + prop.name, prop.major, prop.minor, + prop.totalGlobalMem / (1024.0*1024.0)); + printf(" iters=%d (取最小值), 存储格式: 列主序\n", iters); + printf("==========================================================================\n"); + } else { + printf("size_M,size_N,size_K,method,splits,time_ms,gflops,max_abs_err,l2_rel_err\n"); + } + + for (int S : sizes) { + Size sz{ S, S, S }; + int M = sz.M, N = sz.N, K = sz.K; + size_t EA = (size_t)M*K, EB = (size_t)K*N, EC = (size_t)M*N; + + std::vector hA(EA), hB(EB); + fill_matrix(hA.data(), EA, 0x1234ULL + 7*S); + fill_matrix(hB.data(), EB, 0x5678ULL + 7*S); + + double *dA, *dB, *dCref, *dCtest; + cudaMalloc(&dA, EA*sizeof(double)); + cudaMalloc(&dB, EB*sizeof(double)); + cudaMalloc(&dCref, EC*sizeof(double)); + cudaMalloc(&dCtest, EC*sizeof(double)); + cudaMemcpy(dA, hA.data(), EA*sizeof(double), cudaMemcpyHostToDevice); + cudaMemcpy(dB, hB.data(), EB*sizeof(double), cudaMemcpyHostToDevice); + + double flops = 2.0 * (double)M * (double)N * (double)K; + + /* FP64 cuBLAS 参考基准(精度参考 + 性能参考) */ + double ms_ref = time_min_ms([&](){ + gemm_fp64_cublas(M,N,K,dA,dB,dCref,handle); }, iters, stream); + double gf_ref = flops / (ms_ref*1e-3) / 1e9; + AccuracyReport acc_self{}; + accuracy_compare(dCref, dCref, M, N, &acc_self); + + if (!csv) { + printf("\n[M=%d N=%d K=%d] (2*MNK FLOPs = %.3g)\n", M,N,K, flops); + printf(" %-26s %6s %10s %10s %12s %12s\n", + "method","splits","time(ms)","GFLOPS","maxAbsErr","L2RelErr"); + printf(" %-26s %6s %10.3f %10.1f %12.3e %12.3e\n", + "fp64_cublas (REF)","-", ms_ref, gf_ref, 0.0, 0.0); + } else { + printf("%d,%d,%d,fp64_cublas,0,%.4f,%.2f,0,0\n", M,N,K, ms_ref, gf_ref); + } + + /* INT8 模拟: baseline / student / cublas_emulated */ + const char* names[3] = { "int8_cublas_baseline", + "my_int8_fp64", + "cublas_emulated" }; + for (int sp : splits) { + for (int m = 0; m < 3; ++m) { + double ms = 0; + switch (m) { + case 0: gemm_int8_cublas_baseline(M,N,K,dA,dB,dCtest,sp,handle,stream); break; + case 1: gemm_my_int8_fp64 (M,N,K,dA,dB,dCtest,sp,handle,stream); break; + case 2: gemm_cublas_emulated (M,N,K,dA,dB,dCtest,sp,handle,emu_workspace,ws_bytes,stream); break; + } + cudaStreamSynchronize(stream); + CudaTimer t; t.begin(stream); + for (int it=0; it +#include +#include + +#ifdef __cplusplus +extern "C" { +#endif + +/* ---- FP64 基准 ---- */ + +/* cuBLAS FP64 GEMM (cublasDgemm),精度与性能参考 */ +int gemm_fp64_cublas(int M, int N, int K, + const double* dA, const double* dB, double* dC, + cublasHandle_t handle); + +/* 朴素实现:逐 split 量化 + cuBLAS INT8 GEMM + 逐次重组,未优化 */ +int gemm_int8_cublas_baseline(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, + cudaStream_t stream); + +/* 学生实现 */ +int gemm_my_int8_fp64(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, cudaStream_t stream); + +/* cuBLAS 自带 FP64 模拟 (CUBLAS_COMPUTE_64F_EMULATED_FIXEDPOINT),基线 */ +int gemm_cublas_emulated(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, void* workspace, + size_t workspace_bytes, cudaStream_t stream); + +#ifdef __cplusplus +} +#endif + +#endif /* GEMM_API_H */ diff --git a/src/lab4p5/include/utils.h b/src/lab4p5/include/utils.h new file mode 100644 index 00000000..2984903b --- /dev/null +++ b/src/lab4p5/include/utils.h @@ -0,0 +1,91 @@ +#ifndef UTILS_H +#define UTILS_H + +#include +#include +#include +#include + +/* ----------------------------------------------------------------------- */ +/* Error-checking macros */ +/* ----------------------------------------------------------------------- */ + +#define CUDA_CHECK(call) \ + do { \ + cudaError_t _e = (call); \ + if (_e != cudaSuccess) { \ + fprintf(stderr, "CUDA error %s:%d: %s (%s)\n", \ + __FILE__, __LINE__, cudaGetErrorName(_e), \ + cudaGetErrorString(_e)); \ + return (int)_e; \ + } \ + } while (0) + +#define CUBLAS_CHECK(call) \ + do { \ + cublasStatus_t _s = (call); \ + if (_s != CUBLAS_STATUS_SUCCESS) { \ + fprintf(stderr, "cuBLAS error %s:%d: status=%d\n", \ + __FILE__, __LINE__, (int)_s); \ + return (int)(0x10000 + (int)_s); \ + } \ + } while (0) + +/* ----------------------------------------------------------------------- */ +/* Timing */ +/* ----------------------------------------------------------------------- */ + +struct CudaTimer { + cudaEvent_t start, stop; + CudaTimer() { + cudaEventCreate(&start); + cudaEventCreate(&stop); + } + ~CudaTimer() { + cudaEventDestroy(start); + cudaEventDestroy(stop); + } + void begin(cudaStream_t s = 0) { cudaEventRecord(start, s); } + void end(cudaStream_t s = 0) { cudaEventRecord(stop, s); } + /* returns milliseconds (blocks until stop recorded) */ + float elapsed_ms() { + float ms = 0.f; + cudaEventSynchronize(stop); + cudaEventElapsedTime(&ms, start, stop); + return ms; + } +}; + +/* ----------------------------------------------------------------------- */ +/* Accuracy metrics */ +/* ----------------------------------------------------------------------- */ + +struct AccuracyReport { + double max_abs_err; /* max |C_ref - C_test| */ + double max_rel_err; /* max |C_ref - C_test| / |C_ref| over non-tiny */ + double l2_rel_err; /* ||C_ref - C_test||_2 / ||C_ref||_2 */ +}; + +/* Compare a test (device, FP64) GEMM output against a reference (device, FP64) + * output. Both are M*N column-major. */ +void accuracy_compare(const double* d_ref, const double* d_test, + int M, int N, AccuracyReport* rep); + +/* ----------------------------------------------------------------------- */ +/* Matrix helpers */ +/* ----------------------------------------------------------------------- */ + +/* Fill a host buffer with a deterministic, reproducible FP64 matrix in a sane + * range (values uniformly in [-1, 1] with a fixed seed). */ +void fill_matrix(double* h, size_t n, uint64_t seed); + +/* Allocate a device buffer of `bytes` bytes and return the device pointer. + * Returns nullptr on failure. */ +void* device_alloc(size_t bytes); +void device_free(void* p); + +/* Compute max |x| over a device FP64 buffer of `n` elements. Synchronizes. + * Returns 0.0 for an empty buffer. */ +double device_maxabs_fp64(const double* dx, size_t n); + +#endif /* UTILS_H */ diff --git a/src/lab4p5/submit/my_int8_fp64.cu b/src/lab4p5/submit/my_int8_fp64.cu new file mode 100644 index 00000000..37826433 --- /dev/null +++ b/src/lab4p5/submit/my_int8_fp64.cu @@ -0,0 +1,146 @@ +#include "gemm_api.h" +#include "utils.h" +#include + +/* ====================================================================== */ +/* TODO (1): 量化一个 split */ +/* 用你的实现替换下面的占位代码 */ +/* ====================================================================== */ +static __global__ void quantize_split_kernel(double* residual, int8_t* q, + double scale, size_t n) +{ + size_t i = (size_t)blockIdx.x * blockDim.x + threadIdx.x; + if (i >= n) return; + + /* TODO(student): + * double x = residual[i]; + * double qf = rint(x / scale); + * if (qf > 127.0) qf = 127.0; + * if (qf < -127.0) qf = -127.0; + * int8_t qi = (int8_t)qf; + * q[i] = qi; + * residual[i] = x - (double)qi * scale; + */ + + /* --- 占位代码:避免编译器报错。完成后请删除。 --- */ + q[i] = 0; + residual[i] = residual[i]; + (void)scale; +} + +/* ====================================================================== */ +/* TODO (2): 将一次 split-pair 的 INT32 结果累加到 FP64 C */ +/* 用你的实现替换下面的占位代码 */ +/* ====================================================================== */ +static __global__ void recombine_add_kernel(const int32_t* temp, double* C, + double scale, size_t mn) +{ + size_t i = (size_t)blockIdx.x * blockDim.x + threadIdx.x; + if (i >= mn) return; + + /* TODO(student): + * C[i] += scale * (double)temp[i]; + */ + + /* --- 占位代码: 避免编译器报错。完成后请删除。 --- */ + (void)temp; (void)C; (void)scale; +} + +/* ====================================================================== */ +/* Host侧代码: 完整实现,无需修改配合上面两个kernel即可获得正确的结果。 */ +/* 可以自由修改以获得更高的性能。 */ +/* ====================================================================== */ +int gemm_my_int8_fp64(int M, int N, int K, + const double* dA, const double* dB, double* dC, + int splits, cublasHandle_t handle, cudaStream_t stream) +{ + if (splits < 1) splits = 1; + const size_t E_A = (size_t)M * K; + const size_t E_B = (size_t)K * N; + const size_t E_C = (size_t)M * N; + + /* 1. 计算比例尺: sA0 = max|dA|/127, sB0 = max|dB|/127 */ + double maxA = device_maxabs_fp64(dA, E_A); + double maxB = device_maxabs_fp64(dB, E_B); + if (maxA == 0.0) maxA = 1.0; + if (maxB == 0.0) maxB = 1.0; + const double sA0 = maxA / 127.0; + const double sB0 = maxB / 127.0; + + /* 2. 分配临时缓冲 */ + int8_t** dAq = (int8_t**)malloc(splits * sizeof(int8_t*)); + int8_t** dBq = (int8_t**)malloc(splits * sizeof(int8_t*)); + for (int s = 0; s < splits; ++s) { + dAq[s] = (int8_t*)device_alloc(E_A); + dBq[s] = (int8_t*)device_alloc(E_B); + } + double* residA = (double*)device_alloc(E_A * sizeof(double)); + double* residB = (double*)device_alloc(E_B * sizeof(double)); + int32_t* temp = (int32_t*)device_alloc(E_C * sizeof(int32_t)); + + /* 3. 拷贝 A,B 到残差缓冲(量化会原地修改), 清零 C */ + CUDA_CHECK(cudaMemcpyAsync(residA, dA, E_A * sizeof(double), + cudaMemcpyDeviceToDevice, stream)); + CUDA_CHECK(cudaMemcpyAsync(residB, dB, E_B * sizeof(double), + cudaMemcpyDeviceToDevice, stream)); + CUDA_CHECK(cudaMemsetAsync(dC, 0, E_C * sizeof(double), stream)); + + const int block = 256; + + /* 4. 量化 A 的 splits 个 split */ + { + int grid = (int)((E_A + block - 1) / block); + double sA = sA0; + for (int i = 0; i < splits; ++i) { + quantize_split_kernel<<>>( + residA, dAq[i], sA, E_A); + sA = sA / 254.0; + } + } + /* 量化 B 的 splits 个 split */ + { + int grid = (int)((E_B + block - 1) / block); + double sB = sB0; + for (int j = 0; j < splits; ++j) { + quantize_split_kernel<<>>( + residB, dBq[j], sB, E_B); + sB = sB / 254.0; + } + } + + /* 5. K² 次 INT8 GEMM + 重组累加 */ + cublasSetStream(handle, stream); + const int32_t alpha_i = 1, beta_i = 0; + double sA = sA0; + for (int i = 0; i < splits; ++i) { + double sB = sB0; + for (int j = 0; j < splits; ++j) { + /* temp = Aq[i] @ Bq[j] (INT8 张量核, INT32 累加) */ + CUBLAS_CHECK(cublasGemmEx(handle, + CUBLAS_OP_N, CUBLAS_OP_N, + M, N, K, + &alpha_i, + dAq[i], CUDA_R_8I, M, + dBq[j], CUDA_R_8I, K, + &beta_i, + temp, CUDA_R_32I, M, + CUBLAS_COMPUTE_32I, + CUBLAS_GEMM_DEFAULT)); + /* C += sA*sB * temp (FP64 累加) */ + double scale = sA * sB; + int grid = (int)((E_C + block - 1) / block); + recombine_add_kernel<<>>( + temp, dC, scale, E_C); + sB = sB / 254.0; + } + sA = sA / 254.0; + } + + CUDA_CHECK(cudaStreamSynchronize(stream)); + + /* 6. 释放临时缓冲 */ + for (int s = 0; s < splits; ++s) { cudaFree(dAq[s]); cudaFree(dBq[s]); } + free(dAq); free(dBq); + cudaFree(residA); cudaFree(residB); cudaFree(temp); + return 0; +} diff --git a/src/lab4p5/utils.cu b/src/lab4p5/utils.cu new file mode 100644 index 00000000..4c775184 --- /dev/null +++ b/src/lab4p5/utils.cu @@ -0,0 +1,149 @@ +#include "utils.h" +#include +#include +#include +#include + +/* ----------------------------------------------------------------------- */ +/* Device memory helpers */ +/* ----------------------------------------------------------------------- */ +void* device_alloc(size_t bytes) { + void* p = nullptr; + cudaError_t e = cudaMalloc(&p, bytes); + if (e != cudaSuccess) return nullptr; + return p; +} +void device_free(void* p) { if (p) cudaFree(p); } + +/* ----------------------------------------------------------------------- */ +/* Device max-abs reduction (FP64) */ +/* ----------------------------------------------------------------------- */ +static __global__ void maxabs_block_kernel(const double* x, size_t n, double* partial) +{ + /* one block reduces a chunk; uses shared-memory tree reduction */ + extern __shared__ double smem[]; + double t = 0.0; + for (size_t i = blockIdx.x * blockDim.x + threadIdx.x; + i < n; i += gridDim.x * blockDim.x) { + double v = fabs(x[i]); + if (v > t) t = v; + } + smem[threadIdx.x] = t; + __syncthreads(); + for (int s = blockDim.x / 2; s > 0; s >>= 1) { + if (threadIdx.x < s) { + double a = smem[threadIdx.x], b = smem[threadIdx.x + s]; + smem[threadIdx.x] = (a > b) ? a : b; + } + __syncthreads(); + } + if (threadIdx.x == 0) partial[blockIdx.x] = smem[0]; +} + +double device_maxabs_fp64(const double* dx, size_t n) +{ + if (n == 0) return 0.0; + int block = 256; + /* cap grid to avoid tiny blocks on huge inputs */ + size_t grid = (n + (size_t)block - 1) / block; + if (grid > 4096) grid = 4096; + double* partial = nullptr; + cudaMalloc(&partial, grid * sizeof(double)); + maxabs_block_kernel<<<(unsigned)grid, block, block * sizeof(double)>>>( + dx, n, partial); + /* final reduce on host (grid <= 4096 doubles = 32KB, cheap) */ + double* h_partial = (double*)malloc(grid * sizeof(double)); + cudaMemcpy(h_partial, partial, grid * sizeof(double), + cudaMemcpyDeviceToHost); + double m = 0.0; + for (size_t i = 0; i < grid; ++i) + if (h_partial[i] > m) m = h_partial[i]; + cudaFree(partial); + free(h_partial); + return m; +} + +/* ----------------------------------------------------------------------- */ +/* Deterministic matrix fill */ +/* ----------------------------------------------------------------------- */ +/* Simple xorshift64 PRNG so the lab is fully reproducible without linking + * against a host RNG library. Values are mapped to [-1, 1]. */ +static inline uint64_t xs64_next(uint64_t* s) { + uint64_t x = *s; + x ^= x << 13; + x ^= x >> 7; + x ^= x << 17; + *s = x; + return x; +} + +void fill_matrix(double* h, size_t n, uint64_t seed) { + uint64_t s = seed ? seed : 0x9E3779B97F4A7C15ull; + for (size_t i = 0; i < n; ++i) { + uint64_t u = xs64_next(&s); + /* map 53 bits of u to [0,1) */ + double r = (double)(u >> 11) * (1.0 / 9007199254740992.0); + h[i] = 2.0 * r - 1.0; /* [-1, 1] */ + } +} + +/* ----------------------------------------------------------------------- */ +/* Accuracy comparison */ +/* ----------------------------------------------------------------------- */ +/* We compute everything on the GPU to avoid large host<->device copies. */ + +static __global__ void acc_diff_kernel(const double* ref, const double* test, int mn, + double* out_absmax, /* scratch atomic */ + double* out_l2_num, /* sum of squares of diff */ + double* out_l2_den) /* sum of squares of ref */ +{ + int i = blockIdx.x * blockDim.x + threadIdx.x; + if (i >= mn) return; + double r = ref[i]; + double t = test[i]; + double d = r - t; + double ad = fabs(d); + /* atomic max for abs error */ + /* implement atomic max on double via atomicCAS */ + unsigned long long* addr = (unsigned long long*)out_absmax; + unsigned long long assumed, old = *addr; + do { + assumed = old; + double cur = __longlong_as_double(assumed); + old = atomicCAS(addr, assumed, __double_as_longlong(fmax(cur, ad))); + } while (assumed != old); + atomicAdd(out_l2_num, d * d); + atomicAdd(out_l2_den, r * r); +} + +void accuracy_compare(const double* d_ref, const double* d_test, + int M, int N, AccuracyReport* rep) +{ + int mn = M * N; + double *d_absmax, *d_l2n, *d_l2d; + cudaMalloc(&d_absmax, sizeof(double)); + cudaMalloc(&d_l2n, sizeof(double)); + cudaMalloc(&d_l2d, sizeof(double)); + double z = 0.0; + cudaMemcpy(d_absmax, &z, sizeof(double), cudaMemcpyHostToDevice); + cudaMemcpy(d_l2n, &z, sizeof(double), cudaMemcpyHostToDevice); + cudaMemcpy(d_l2d, &z, sizeof(double), cudaMemcpyHostToDevice); + + int block = 256; + int grid = (mn + block - 1) / block; + acc_diff_kernel<<>>(d_ref, d_test, mn, d_absmax, d_l2n, d_l2d); + cudaDeviceSynchronize(); + + double h_absmax = 0, h_l2n = 0, h_l2d = 0; + cudaMemcpy(&h_absmax, d_absmax, sizeof(double), cudaMemcpyDeviceToHost); + cudaMemcpy(&h_l2n, d_l2n, sizeof(double), cudaMemcpyDeviceToHost); + cudaMemcpy(&h_l2d, d_l2d, sizeof(double), cudaMemcpyDeviceToHost); + + rep->max_abs_err = h_absmax; + rep->l2_rel_err = (h_l2d > 0.0) ? sqrt(h_l2n / h_l2d) : 0.0; + rep->max_rel_err = 0.0; /* computed below for non-tiny entries */ + + cudaFree(d_absmax); + cudaFree(d_l2n); + cudaFree(d_l2d); +} diff --git a/zensical.toml b/zensical.toml index bb2cd9e2..4a9134a4 100644 --- a/zensical.toml +++ b/zensical.toml @@ -27,6 +27,7 @@ nav = [ { "Lab 2: MoE 的向量化计算" = "lab/Lab2-Vectorization/index.md"}, { "Lab 3: GDN Prefill 前向优化" = "lab/Lab3-GDN-Prefill/index.md" }, { "Lab 4: AMSS-NCKU 数值相对论程序优化" = "lab/Lab4-AMSS-NCKU/index.md"}, + { "Lab 4.5: INT8 张量核模拟 FP64 GEMM" = "lab/Lab4.5-INT8-FP64-GEMM/index.md" }, { "Lab 5: Gemma4 端到端推理优化" = "lab/Lab5-Gemma4/index.md"} ] }, ]

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z55D#GGONucVWPLsq*XBCWfDoyIXtQ1Ci3I(ouR%s;6r^&PPqQhG;4x zSltW{ARD|U3P@fLcUz_P98~{`5(M!MF)ns^O3+aeK2&e&?$6s?Rdr3CJ)N=k9_f|W zw=^|R`_B32qZGmSK~X9&G>piH?xX+zR1(ug{@W)x-aFr!OpD%HvtjiID1}=r1&uBh z&kCZ`gfaQS%wL4m2bDjnx4?VQXzd1*r*9xeP|%}}oOQ)duLq|08VA7k`ozNgu@3uB z^tC@$#Q)Y$;P1mE7!nZ4{AG4+S^Ml$k7`wT_X|~&If6r7#X{QUu!RzKnvpL5w~zl% zduP*w1<@i)5jAqAvFE*4 z)I|$#F7+bAAoFqOo{xLZx#zr>d;^E;z2J#$7fO|C5agdueC~OplMt3 zNot=9eYs^KgPI1^UH;4Esi%-SPYXtw;!&@DQ9G~IeN$LrBmUNk#PLUQk4?+@K6ml% zX09|^JF(j^vw#6rhtb{5b@J62^r$26XL9&dgV-mgMBu36L|+w;YK|T0k)QQqz(aRL#ev}ekr&PAFvB}Lsc^DP) z7Zsg4xV(6J1c+?5n!OSr1kejGjqk3%j*CNPfhkyrO|%CBR6w9PB18f@5aY~v1Q0=O zWNWK1M@&b|G7dtjW`HkAwc5RGPI=8l8pxlu(PtYIAUKPUh00!PZH?MLn&>F&45x>g zmj{s9M;?KuN=3EV(~512z^ekalQJAGQ7qn}xyt+SfrLJ9mA3!_4D|^q!6B5PiM!Z1 niC5D(v)lrQaWaV@jeGSAviTpHR?!k)00000NkvXXu0mjf + CUTLASS 的分层抽象与可调参数 + 图中从设备接口、GEMM kernel、collective mainloop 和 epilogue、CuTe 布局与拷贝、Hopper 指令五层展示 CUTLASS 的组成,并列出适用于本实验的定制点。 + + + + + CUTLASS:在性能模板中替换本实验需要的部件 + + + Device / Adapter参数检查、workspace、kernel launch 与统一 API 封装 + + GEMM Kernelproblem shape、tile/cluster shape、persistent 或常规调度策略 + + CollectiveMainloopTMA/cp.async 搬运、pipeline stage、warp-specialized schedule、WGMMA + CollectiveEpilogue缩放、类型转换、FP64 重组与写回 + + CuTeTensor/Layout、线程与数据分块、copy atom、MMA atom + + Hopper SM90 指令TMA · mbarrier · WGMMA · shared-memory swizzle + + + 本实验的定制点 + INT8 × INT8 → INT32 + 列主序 A/B/C 布局 + CTA / cluster tile shape + pipeline stage count + Shared Memory swizzle + 自定义 FP64 epilogue + 按 M/N/K 与 splits 调参 + Profiler / Nsight 验证 + + + 建议路径:先复用可运行的 SM90 GEMM 模板,再逐步替换 layout、schedule 与 epilogue;每次只改变一个变量。 + diff --git a/docs/lab/Lab4.5-INT8-FP64-GEMM/image/operator-fusion.svg b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/operator-fusion.svg new file mode 100644 index 00000000..f4342284 --- /dev/null +++ b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/operator-fusion.svg @@ -0,0 +1,39 @@ + + + + + + + + + + 融合前 + + 量化 kernel + + 全局内存 + + INT8 GEMM + + 全局内存 + + FP64 重组 + + + + + + 分层融合 + + 一次量化多个 split + + GEMM + 缩放重组 epilogue + + 输出 C + + + diff --git a/docs/lab/Lab4.5-INT8-FP64-GEMM/image/optimization-checklist.svg b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/optimization-checklist.svg new file mode 100644 index 00000000..79fde4fc --- /dev/null +++ b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/optimization-checklist.svg @@ -0,0 +1,56 @@ + + 四类通用 GPU 优化思路 + 四个象限分别展示数据复用与减少全局访存、连续合并访问与布局优化、减少 warp 分支发散、根据误差预算选择精度。 + + + + + + 通用优化的四个问题:搬多少、怎么搬、谁在空转、精度花在哪 + + + 1. 数据复用:减少 HBM 往返 + HBMA/B tile + Shared多次复用 + Registeracc tile + + 目标:提高 arithmetic intensity;让一次加载服务多个 MMA。 + 观察:DRAM bytes、L2 hit rate、Tensor Core 利用率。 + + + 2. 访问布局:让线程访问可合并 + + T0T1T2T3T4T5T6T7 + + 连续地址 → 少量合并事务 + 同时处理对齐、leading dimension 和边界 tile。 + 注意:全局内存合并与 Shared Memory bank 冲突是两层问题。 + + + 3. 控制流:减少 warp divergence + + + + + 统一 fast path:所有 lane 执行同一路径 + 将边界处理拆成独立 kernel,或用 predication 替代复杂分支。 + 观察:branch efficiency、warp execution efficiency。 + + + 4. 精度预算:把 FP64 用在关键路径 + FP64 输入 + INT8 分量 + FP64 累加 + + 先确定误差目标,再选择 splits、缩放系数精度与累加顺序。 + 任何降精度都要同时报告吞吐和 L2 相对误差。 + 禁止只凭“位宽更低”推断端到端一定更快。 + + 优化闭环:profile → 提出一个瓶颈假设 → 单变量修改 → 同时验证性能与精度。 + diff --git a/docs/lab/Lab4.5-INT8-FP64-GEMM/image/overlap-pipeline.svg b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/overlap-pipeline.svg new file mode 100644 index 00000000..fd303d7d --- /dev/null +++ b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/overlap-pipeline.svg @@ -0,0 +1,49 @@ + + + + + + + 串行执行 + 搬运 + 计算 + 重组 + + + + + + + + load tile 0 + load tile 1 + GEMM tile 0 + GEMM tile 1 + recompose 0 + recompose 1 + + 双缓冲流水线 + TMA + WGMMA + CUDA Core + + + + + + + + load tile 0 → buf A + load tile 1 → buf B + load tile 2 → buf A + GEMM tile 0 + GEMM tile 1 + GEMM tile 2 + recompose 0 + recompose 1 + recompose 2 + diff --git a/docs/lab/Lab4.5-INT8-FP64-GEMM/image/score.png b/docs/lab/Lab4.5-INT8-FP64-GEMM/image/score.png new file mode 100644 index 0000000000000000000000000000000000000000..1870a37e57b5b20f755d7482a796aa29873c34c8 GIT binary patch literal 92404 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