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Batched GEMM
Theory
This example demonstrates batched GEMM: performing multiple independent matrix multiplications (all with the same shape) in a single kernel launch. Batched GEMM is used in multi-head attention, RNNs, and other models requiring parallel matrix multiplications.
Mathematical Formulation:
For B batches:
C_b = A_b \times B_b \quad \text{for} \quad b = 1, 2, ..., B
A_b: [M, K] input matrix for batchbB_b: [K, N] weight matrix for batchbC_b: [M, N] output matrix for batchb
Algorithmic Background:
- All matrices in the batch have the same shape and strides.
- The kernel launches a grid covering all batches, with each block assigned to a batch.
- Used for multi-head attention, parallel MLPs, and more.
How to Run
Prerequisites
cd composable_kernel/build
make -j install
Build and Execute
cd composable_kernel/example/24_batched_gemm
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j
# Example run
./batched_gemm_xdl --verify=1 --time=1
Source Code Structure
Directory Layout
example/24_batched_gemm/
├── batched_gemm_xdl.cpp # Main example: sets up, runs, and verifies batched GEMM
include/ck/tensor_operation/gpu/device/
│ └── device_batched_gemm_xdl.hpp # Device-level batched GEMM API
include/ck/tensor_operation/gpu/grid/
│ └── gridwise_batched_gemm_xdl.hpp # Grid-level batched GEMM kernel
Key Classes and Functions
- DeviceBatchedGemmXdl (in
device_batched_gemm_xdl.hpp):
Device API for batched GEMM.template <typename ALayout, typename BLayout, typename CLayout, typename ADataType, typename BDataType, typename CDataType, typename AElementwiseOperation, typename BElementwiseOperation, typename CElementwiseOperation, typename GemmSpecialization> struct DeviceBatchedGemmXdl : public BaseOperator - gridwise_batched_gemm_xdl (in
gridwise_batched_gemm_xdl.hpp):
Implements the tiled/blocking batched GEMM kernel.
This example demonstrates how Composable Kernel supports efficient parallel matrix multiplication for batched and multi-head workloads.