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Composable Kernel GEMM Example
Introduction
GEMM (General Matrix Multiplication) is a fundamental operation in linear algebra and deep learning. It computes the product of two matrices, optionally adds a bias or residual, and is the core of many neural network layers (MLPs, attention, convolutions via im2col). This example demonstrates the flexible and high-performance GEMM API provided by Composable Kernel.
Theory
Mathematical Formulation:
C = \alpha (A \times B) + \beta D
A: [M, K] input matrixB: [K, N] weight matrixD: [M, N] optional bias/residualC: [M, N] output\alpha, \beta: scalars (often 1.0, 0.0)
GEMM is implemented using a tiled/blocking strategy to maximize data reuse and memory bandwidth. Modern GPU implementations use matrix core/XDL/MFMA instructions for high throughput. The operation is the computational backbone for transformer attention, MLPs, CNNs (via lowering), and more.
CK GEMM API Overview
CK provides a highly composable GEMM API via the DeviceGemm family of device operations. These are highly templated to support a wide range of data types, layouts, and fused operations.
Template Parameters
- ALayout - A matrix layout (RowMajor/ColumnMajor)
- BLayout - B matrix layout (RowMajor/ColumnMajor)
- CLayout - C matrix layout (RowMajor/ColumnMajor)
- ADataType - A matrix data type
- BDataType - B matrix data type
- CDataType - C matrix data type
- AElementwiseOperation - Fused operation on tensor A before GEMM
- BElementwiseOperation - Fused operation on tensor B before GEMM
- CElementwiseOperation - Fused operation on tensor C after GEMM
For large K dimension, use DeviceGemmSplitK to split K across workgroups (requires zeroing output buffer due to use of AtomicAdd).
For fused operations with additional tensors, use DeviceGemmMultipleABD or DeviceGemmMultipleD:
- DsLayout - layouts for additional tensors
- DsDataType - data types for additional tensors
For DeviceGemmMultipleABD, pass ALayout, BLayout, ADataType, BDataType as tuples.
Supported GEMM Variants
- DeviceGemm: Standard GEMM
- DeviceGemmSplitK: Split-K GEMM for large K
- DeviceGemmMultipleABD: Fused GEMM with multiple A/B/D tensors
- DeviceGemmMultipleD: Fused GEMM with multiple D tensors
Supported Device Operations
- DeviceGemmDl: DL instructions
- DeviceGemmDpp: DL instructions with DPP during data load
- DeviceGemmWmma_CShuffle: WMMA instructions with CShuffle optimization
- DeviceGemm_Xdl_CShuffle_LdsDirectLoad: XDL instructions, CShuffle, direct global-to-shared load
- DeviceGemm_Xdl_CShuffle: XDL instructions with CShuffle
- DeviceGemm_Xdl_CShuffleV2: XDL instructions, optimized pipeline vs. V1
- DeviceGemmXdlSkipBLds: XDL, skips shared memory load for B
- DeviceGemm_Xdl_WaveletModel_CShuffle: XDL, CShuffle, wavelet producer/consumer
- DeviceGemmXdl: XDL instructions
Supported Data Types and Layouts
XDL Instruction
| Is supported | |
|---|---|
| bf16 | ✔️ |
| fp16 | ✔️ |
| fp32 | ✔️ |
| int8 | ✔️ |
| fp8 | ✔️ |
WMMA Instruction
| Is supported | |
|---|---|
| bf16 | ✔️ |
| fp16 | ✔️ |
| fp32 | ❌ |
| int8 | ✔️ |
| fp8 | ❌ |
DL Instruction
| Is supported | |
|---|---|
| bf16 | ❌ |
| fp16 | ✔️ |
| fp32 | ✔️ |
| int8 | ✔️ |
| fp8 | ❌ |
Supported Fused Elementwise Operations
- B Matrix Multiply + Add + Gelu - bf16 (int8 for B matrix)
- B Matrix Multiply + Add - bf16 (int8 for B matrix)
- B Matrix Multiply + Gelu - bf16 (int8 for B matrix)
- B Matrix Multiply - bf16 (int8 for B matrix)
- Add + Add + Gelu - fp16
- Add + Gelu - fp16, bf16 (int8 for B matrix) for Row/Column/Row
- Multiply - fp16
- Add + Multiply - fp16
- Add + Relu - fp16 (int8 for B matrix) for Row/Column/Row, bf16 (int8 for B matrix) for Row/Column/Row
- Add + Silu - fp16 (int8 for B matrix) for Row/Column/Row, bf16 (int8 for B matrix) for Row/Column/Row
- Add - fp16 (int8 for B matrix) for Row/Column/Row, bf16 (int8 for B matrix) for Row/Column/Row
- Bilinear - fp16, int8
- Gelu - fp16
- Multiply + Add - fp16 for Row/Column/Row and Row/Row/Row, fp16 (int8 for B matrix, fp32 for Bias) for Row/Column/Row and Row/Row/Row
- Quantization - int8
GEMM V2 (Universal GEMM)
Optimized for MI300 series. Operation is called as DeviceGemmV2 and uses similar template parameters as above.
- ALayout, BLayout, CLayout
- ADataType, BDataType, CDataType
- AElementwiseOperation, BElementwiseOperation, CElementwiseOperation
Split-K is supported (requires zeroing output buffer if splitK > 1).
Device Operations
- DeviceGemm_Xdl_CShuffleV3: XDL with CShuffle optimization
- DeviceGemm_Xdl_CShuffleV3R1: XDL with CShuffle, reduction on split-K after GEMM
Supported Types
| Is supported | |
|---|---|
| bf16 | ✔️ |
| fp16 | ✔️ |
| fp32 | ❌ |
| int8 | ❌ |
| fp8 (C bf16) | ✔️ |
| fp16 (A fp8) | ✔️ |
| fp16 (B fp8) | ✔️ |
Other GEMM Extensions
- DeviceGemm_dequantB: GEMM with dequantization (WMMA)
- DeviceGemmMultipleD_ABScale: GEMM with scale for A and B
- DeviceGemmMultipleDLayernorm: GEMM fused with layernorm
- DeviceGemmMultipleDMultipleR: GEMM fused with reductions and custom global reductions
- DeviceGemmReduce: GEMM fused with reduction
- DeviceGemm_Streamk_V2: Stream K with reduction instead of AtomicAdd
- DeviceGemmStreamK: Stream K using AtomicAdd
How to Run
Prerequisites
Please follow the instructions in the main Build Guide section as a prerequisite to building and running this example.
Build and run
cd composable_kernel/example/01_gemm
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j
# Example run (FP16)
./gemm_xdl_fp16 -M 4096 -N 4096 -K 4096 -v 1 -t 1
Source Code Structure
example/01_gemm/
├── gemm_xdl_fp16.cpp # Main example: sets up, runs, and verifies GEMM (FP16)
├── gemm_xdl_fp32.cpp # Main example: FP32 variant
include/ck/tensor_operation/gpu/device/
│ └── device_gemm.hpp # Device-level GEMM API (templated)
include/ck/tensor_operation/gpu/device/impl/
│ └── device_gemm_xdl.hpp # XDL-based GEMM implementation
include/ck/tensor_operation/gpu/grid/
│ └── gridwise_gemm_xdl.hpp # Grid-level tiled GEMM kernel
include/ck/tensor_operation/gpu/block/
│ └── blockwise_gemm_xdl.hpp # Block-level tiled GEMM
library/reference_tensor_operation/cpu/
└── reference_gemm.hpp # CPU reference GEMM for correctness checking
Key Classes and Functions
- DeviceGemmXdl (in
device_gemm.hpp):
Main device API for launching GEMM kernels. - GridwiseGemmXdl (in
gridwise_gemm_xdl.hpp):
Implements the tiled/blocking GEMM kernel for the GPU grid. - BlockwiseGemmXdl (in
blockwise_gemm_xdl.hpp):
Handles block-level computation and shared memory tiling. - reference_gemm (in
reference_gemm.hpp):
CPU implementation for result verification.
This example is the foundation for all matrix operations in Composable Kernel and is the basis for more advanced fused and batched operations.