This example demonstrates GEMM with multiple auxiliary tensors (D) and multiple reduction operations. This pattern is used in advanced neural network layers that require additional outputs or statistics (such as sums, means, or other reductions) alongside the main GEMM result.

Mathematical Formulation:

• For each GEMM: $C = A \times B$
• Auxiliary tensors: $D_0, D_1, ...$ (various shapes)
• Reductions: e.g., sum, mean, max over specified axes or outputs

The kernel computes the main GEMM output and additional reductions or statistics in a single pass.

Algorithmic Background:

• The GEMM result is kept in registers, auxiliary tensors are fused in the epilogue, and reductions are computed as part of the output.
• Useful for multi-task learning, attention statistics, and custom neural network layers.

Please follow the instructions in the main Build Guide section as a prerequisite to building and running this example.

cd composable_kernel/example/16_gemm_multi_d_multi_reduces
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j

# Example run
./gemm_multi_d_multi_reduces_xdl --verify=1 --time=1

example/16_gemm_multi_d_multi_reduces/
├── gemm_multi_d_multi_reduces_xdl.cpp         # Main example: sets up, runs, and verifies GEMM with multi-D/multi-reduce
include/ck/tensor_operation/gpu/device/
│   └── device_gemm_multi_d_multi_reduces.hpp       # Device-level API for multi-D/multi-reduce GEMM
include/ck/tensor_operation/gpu/device/impl/
│   └── device_gemm_multi_d_multi_reduces_impl.hpp  # Implementation
include/ck/tensor_operation/gpu/grid/
    └── gridwise_gemm_multi_d_multi_reduces.hpp     # Grid-level kernel

• DeviceGemmMultiDMultiReduces (in device_gemm_multi_d_multi_reduces.hpp):
  Device API for GEMM with multiple outputs and reductions.
• gridwise_gemm_multi_d_multi_reduces (in gridwise_gemm_multi_d_multi_reduces.hpp):
  Implements the tiled/blocking GEMM kernel with multi-output/reduce epilogue.

This example demonstrates how Composable Kernel supports advanced GEMM patterns with multiple outputs and reductions in a single efficient kernel.