gpu-opt-tier1-block-tiling

name	gpu-opt-tier1-block-tiling
description	Chooses block/tile dimensions, warp counts, pipeline stages, and L2-aware block grouping for GPU kernels (Triton/CUDA/HIP). Use when autotuning matmul-like kernels, tuning occupancy, or aligning tile geometry with M/N/K and NVIDIA vs AMD thread models.

Tier 1: Block, Tile, and Warp Configuration

This skill is Tier 1 in AutoKernel's tiered optimization playbook: fix launch geometry before memory micro-optimizations.

BLOCK_SIZE_M / N / K

• Eligibility: For tensor/MMA paths, BLOCK_K is often ≥16 (NVIDIA WMMA/WGMMA) or ≥32 (AMD MFMA on CDNA).
• Square vs rectangular: Wider BLOCK_N helps B reuse in row layouts; taller BLOCK_M helps A reuse. Balance against register/SMEM pressure.
• Dimension-driven rules:
  • Small M or N (e.g. <128): prefer smaller tiles (64×64, 64×128) so enough blocks exist to fill the GPU.
  • Very large K: larger BLOCK_K can amortize loads but raises SMEM/regs; validate occupancy.
  • Skinny matrices: prioritize the large dimension in tile width/height so warps stay busy.

num_warps and num_stages

• num_warps: More warps hide latency but increase register footprint and can lower occupancy. Typical search: 2, 4, 8 on NVIDIA; on AMD, remember wavefront-64 — num_warps=4 ⇒ 256 threads per block.
• num_stages: Software-pipelined loads (cp.async, multi-buffer SMEM) need num_stages≥2 on NVIDIA. On HIP/ROCm, num_stages must be ≥1 (0 is invalid).
• Coordination: High num_stages + large tiles can spill registers; co-tune with num_warps.

Occupancy tuning

• If DRAM/L2 metrics are low and warps are often stalled on memory, try more warps or smaller tiles first.
• If compute units are underfed and occupancy is already high, favor larger tiles or better instruction mix (later tiers).

GROUP_SIZE_M (L2-aware tiling)

• Process GROUP_SIZE_M consecutive block-rows before advancing along N to reuse B slices in L2.
• Common search space: 4, 8, 16; 8 is a strong default on Ampere/Hopper-class workloads.

Typical autotune search spaces

Vendor	BLOCK_M×N×K (examples)	num_warps	num_stages	Notes
NVIDIA	64–256 each axis, K often 32–64	2, 4, 8	2–5	WGMMA kernels may need arch-specific caps
AMD	64–256, K often 32	2, 4, 8 (×64 threads/warp)	1–3	Add waves_per_eu (e.g. 2–8) when supported

AMD: wavefront-64

• One warp = 64 threads. Tile shapes that are multiples of 64 along the thread-dependent axis often map more cleanly.
• Pair with waves_per_eu hints: 2–4 when compute-bound, 4–8 when memory-bound (empirical starting points).

Triton-oriented defaults (starting points)

• NVIDIA GEMM-style grids often center on 128×256×64, 128×128×32, 64×128×32 with GROUP_SIZE_M=8; shrink M/N when grid is too coarse.
• AMD CDNA grids often center on 128×128×32 or 256×128×32 with num_warps 4 or 8; always include at least one 64×64×32 candidate when occupancy is poor.
• Keep total threads per block compatible with hardware limits (e.g. 1024 max); on AMD, multiples of 64 per warp axis reduce tail divergence in loads.

Dividers, padding, and grid coverage

• If M, N, or K are not divisible by tile sizes, ensure masks or epilogue tiles; autotune should still evaluate rounded-down main path configs.
• Prefer BLOCK_ divisors* that match MMA instruction shapes (e.g. 16/32 multiples) over arbitrary primes unless sparsity or fusion forces otherwise.

Relationship to other skills

• Pairs with gemm-kernel-optimization for concrete config tuples; this file is the decision logic behind those tuples.
• After Tier 1 sweeps plateau, hand off to tier2-memory-access if loads are sector-inefficient or L2 metrics are poor.

Agent Instructions

1. Read problem sizes M, N, K and pick a tile scale (small M/N → smaller blocks).
2. Build a compact config grid: 3–6 (BLOCK_M, BLOCK_N, BLOCK_K) candidates × num_warps × num_stages (respect HIP num_stages≥1).
3. Always sweep GROUP_SIZE_M (e.g. 4/8/16) for GEMM-like kernels with large inner dimension.
4. After a winner emerges, confirm occupancy and register/SMEM limits before locking configs.
5. Cross-check deeper tuning against AutoKernel Tier 2+ (memory hierarchy) if bandwidth or bank conflicts dominate.