composable_kernel/tutorial/ck_tile/gemm/01_naive_gemm

CK Tile Naive GEMM Tutorial

A minimal GEMM (C = A × B) using the CK Tile API. No optimizations — just the core data flow through the three-level hierarchy: host → block → warp.

Key Terms

Term	What it is
Problem	Shape, data types, and layout of the GEMM matrices
Policy	How data and computation are mapped to threads (tile distributions, warp configs)
Pipeline	The loop that moves data through DRAM → VGPRs → LDS → MFMA and accumulates C
Epilogue	Post-GEMM work (e.g. activation, scaling). Not used in this tutorial

Execution Hierarchy

practice_gemm.cpp          ← host: parse args, allocate, launch, verify
  └─ grid_gemm.hpp         ← host-level: block-to-tile mapping, create tile windows
      └─ block_gemm_pipeline_agmem_bgmem_creg.hpp
         │                  ← block-level: loop over K, DRAM→VGPR→LDS, call warp GEMM
         └─ block_gemm_asmem_bsmem_creg.hpp
                            ← warp-level: LDS→VGPR, MFMA m32n32k8, accumulate C

Data flow per K-iteration:

A,B in DRAM ──load_tile──► VGPRs ──store_tile──► LDS ──sync──► warp GEMM (MFMA) ──► C in VGPRs

After all K-iterations, C is stored back to DRAM.

File Guide

File	Role
practice_gemm.cpp	Entry point: sizes, host tensors, kernel launch, verification
practice_gemm.hpp	Composes GridGemmProblem, BlockGemmPipelineProblem, and Gemm struct
reference_gemm.hpp	CPU reference for correctness checking
grid_gemm.hpp	Host-level pipeline: maps blockIdx to tile coordinates, creates A/B/C tile windows
block_gemm_pipeline_agmem_bgmem_creg.hpp	Block-level pipeline: K-loop, DRAM→LDS data movement
block_gemm_pipeline_agmem_bgmem_creg_policy.hpp	Policy: A/B DRAM tile distributions, LDS descriptors
block_gemm_asmem_bsmem_creg.hpp	Warp-level: reads A/B from LDS, runs MFMA, accumulates C
block_gemm_asmem_bsmem_creg_policy.hpp	Policy: WarpGemm type selection (standard vs transposed C)

Tile Sizes

From practice_gemm.cpp (fp16, BlockSize=256):

Matrix	Block tile	Description
A	256 × 32	M × K per block
B	128 × 32	N × K per block
C	256 × 128	M × N per block (accumulated in registers)

Each block tile is further split across 4 warps (MWarp=4, NWarp=1). The warp-level MFMA instruction is m32n32k8.

Tile Distributions

The policy files define how threads map to tile elements:

A and B DRAM loads (block_gemm_pipeline_agmem_bgmem_creg_policy.hpp):

• Factor M (or N) into M0 × M1 × M2, K into K0 × K1
• P0 = warp_id → M1, P1 = lane_id → M2 × K0 (merged for coalescing)
• Y0 = M0 (iterations), Y1 = K1 (vector load width = 8 for fp16)
• See the tile_distribution/ tutorials for worked examples with these exact shapes

C register layout (block_gemm_asmem_bsmem_creg_policy.hpp):

• Determined by the WarpGemm type (MFMA instruction output mapping)
• Standard: M-dimension in Hs[0], N-dimension in Hs[1]
• Transposed: swaps M/N dimensions, changes which lanes hold which C elements

Transposed C Distribution Switch

The macro CK_TILE_ENABLE_TRANSPOSED_C_DISTRIBUTION (default: 1) selects between two WarpGemm variants:

Value	WarpGemm	C layout
1 (default)	WarpGemmMfma*TransposedCDistribution	Swapped A/B in MFMA, transposed C register layout
0	WarpGemmMfma*	Standard MFMA, standard C register layout

To build with the standard (non-transposed) variant, pass the define via compiler flags:

cmake -DCMAKE_CXX_FLAGS="-DCK_TILE_ENABLE_TRANSPOSED_C_DISTRIBUTION=0" ..

Both variants produce correct results — they differ only in how C elements are distributed across thread registers, which affects downstream store coalescing.

Building and Running

cd <repo-root>/projects/composablekernel/build

# Configure (first time)
../script/cmake-ck-dev.sh ../ <arch>

# Build
make tile_tutorial_naive_gemm -j
# or: ninja tile_tutorial_naive_gemm

# Run (default: M=3328, N=4096, K=4096)
./bin/tile_tutorial_naive_gemm

# Custom sizes (positional args: verification M N K)
./bin/tile_tutorial_naive_gemm 0 1024 512 256

Reference

• Tile distribution encoding: include/ck_tile/core/tensor/tile_distribution_encoding.hpp
• MFMA warp gemm: include/ck_tile/ops/gemm/warp/warp_gemm_attribute_mfma.hpp
• Production GEMM pipeline: include/ck_tile/ops/gemm/pipeline/gemm_pipeline_agmem_bgmem_creg_v1_default_policy.hpp