composable_kernel/example/46_gemm_add_multiply

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_1
  • D_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

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/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.
• 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.