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GEMM with Add and Multiply Fusion
Theory
This example demonstrates GEMM fused with addition and multiplication operations. This pattern is used in neural networks for bias addition, scaling, gating, and other elementwise transformations after a linear layer.
Mathematical Formulation:
- GEMM:
Y = A \times B - Add:
Z = Y + D_0 - Multiply:
E = Z \odot D_1D_0,D_1: auxiliary tensors (e.g., bias, scale, gate)
Algorithmic Background:
- The GEMM result is kept in registers, addition and multiplication are fused in the epilogue.
- No intermediate results are written to global memory.
- Used for bias+scale, gating, and other fused epilogue patterns.
How to Run
Prerequisites
cd composable_kernel/build
make -j install
Build and Execute
cd composable_kernel/example/46_gemm_add_multiply
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j
Run example_gemm_add_multiply_dl_fp16
#arg1: verification (0=no, 1=yes)
#arg2: initialization (0=no init, 1=integer value, 2=decimal value)
#arg3: time kernel (0=no, 1=yes)
#arg4 to 11: M (256x), N(128x), K(32x), StrideA, StrideB, StrideD0, StrideD1, StrideE"
./bin/example_gemm_add_multiply_dl_fp16 1 1 1
Source Code Structure
Directory Layout
example/46_gemm_add_multiply/
├── gemm_add_multiply_xdl.cpp # Main example: sets up, runs, and verifies GEMM+Add+Multiply
include/ck/tensor_operation/gpu/device/
│ └── device_gemm_multiple_d.hpp # Device-level API for multi-tensor GEMM
include/ck/tensor_operation/gpu/device/impl/
│ └── device_gemm_add_multiply_impl.hpp # Add+Multiply implementation
include/ck/tensor_operation/gpu/grid/
│ └── gridwise_gemm_multiple_d_xdl.hpp # Grid-level multi-stage GEMM
include/ck/tensor_operation/gpu/element/
└── element_wise_operation.hpp # Elementwise operation definitions
Key Classes and Functions
- DeviceGemmMultipleD (in
device_gemm_multiple_d.hpp):
Device API for GEMM with multiple auxiliary tensors and fused epilogues.template <typename ALayout, typename BLayout, typename DsLayout, typename ELayout, typename ADataType, typename BDataType, typename DsDataType, typename EDataType, typename AElementwiseOperation, typename BElementwiseOperation, typename CDEElementwiseOperation> struct DeviceGemmMultipleD : public BaseOperator - gridwise_gemm_multiple_d_xdl (in
gridwise_gemm_multiple_d_xdl.hpp):
Implements the tiled/blocking GEMM kernel with multi-stage epilogue. - element_wise_operation (in
element_wise_operation.hpp):
Defines addition, multiplication, and other elementwise operations.
This example demonstrates how Composable Kernel supports efficient fusion of addition and multiplication with GEMM for deep learning and scientific computing.