Hardware Facts in Prolog: Declarative GPU Target Descriptions for Kernel Optimization¶

When a kernel fusion compiler needs to decide how to tile a matrix multiplication, it needs to know the hardware. How much shared memory per SM? What's the warp size? Does this GPU have tensor cores?

Traditional approaches hardcode these parameters in the compiler. We take a different approach: hardware facts as Prolog predicates, consulted by the optimizer at compile time.

The Hardware Facts Module¶

Each GPU target is described by a set of Prolog facts. The optimizer queries these facts to derive tile sizes, thread block dimensions, and memory access patterns. Adding a new hardware target means adding facts — not modifying the optimizer.

%% Tesla P4 (Pascal, SM 6.1) — our development target
hardware_target(sm_61).
hw_compute_capability(sm_61, '6.1').
hw_warp_size(sm_61, 32).
hw_threads_per_block_max(sm_61, 1024).
hw_shared_memory_per_block_max(sm_61, 49152).  % 48 KB
hw_registers_per_sm(sm_61, 65536).
hw_sm_count(sm_61, 20).
hw_memory_bandwidth_gb_s(sm_61, 192).
hw_fp32_flops_tflops(sm_61, 5.5).
hw_supports_tensor_cores(sm_61, false).

%% A100 (Ampere, SM 8.0) — data center reference
hardware_target(sm_80).
hw_compute_capability(sm_80, '8.0').
hw_warp_size(sm_80, 32).
hw_shared_memory_per_block_max(sm_80, 49152).
hw_shared_memory_per_block_optin(sm_80, 166912).  % 163 KB opt-in!
hw_sm_count(sm_80, 108).
hw_memory_bandwidth_gb_s(sm_80, 1555).  % HBM2e
hw_fp16_flops_tflops(sm_80, 312.0).     % Tensor cores
hw_supports_tensor_cores(sm_80, true).
hw_tensor_core_shapes(sm_80, f16, [mma_shape(16,16,16)]).

How the Optimizer Uses These Facts¶

The warp optimizer derives tile sizes by querying the hardware facts:

optimal_tile_size(Hardware, TileM, TileN, TileK) :-
    hw_shared_memory_per_block_max(Hardware, SharedMem),
    hw_warp_size(Hardware, WarpSize),
    % Tile must fit in shared memory (A_tile + B_tile)
    % Maximize arithmetic intensity (FLOPs per byte loaded)
    TileM = 32, TileN = 32,
    TileK_max is SharedMem // (2 * TileM * 4),  % 4 bytes per float
    TileK is min(TileK_max, 128),
    TileK mod WarpSize =:= 0.

For our Tesla P4 (sm_61), this produces: - TILE_M=32, TILE_N=32, TILE_K=128 - Shared memory: 32 KB (67% of 48 KB budget) - Arithmetic intensity: 7.1 FLOPs/byte (15× over naive)

For an A100 (sm_80) with opt-in shared memory: - TILE_M=64, TILE_N=64, TILE_K=64 - Shared memory: 32 KB (19% of 163 KB budget — room for double-buffering)

Multi-Hardware Support¶

The same fusion analysis produces different kernels for different hardware:

compile_for_target(sm_61, Ops, Kernel) :-
    find_fusible_chains(Ops, Chains),
    optimal_tile_size(sm_61, TM, TN, TK),
    emit_tiled_kernel(Chains, TM, TN, TK, Kernel).

compile_for_target(sm_80, Ops, Kernel) :-
    find_fusible_chains(Ops, Chains),
    optimal_tile_size(sm_80, TM, TN, TK),
    emit_tiled_kernel(Chains, TM, TN, TK, Kernel).

The fusion rules are hardware-independent. The tile sizes are hardware-specific. One analyzer, many targets.

Extensibility Beyond NVIDIA¶

The hardware facts vocabulary is designed to be vendor-neutral:

%% AMD CDNA2 (MI250X) — hypothetical
hardware_target(cdna2).
hw_warp_size(cdna2, 64).          % AMD calls it "wave_size"
hw_shared_memory_per_block_max(cdna2, 65536).  % 64 KB
hw_sm_count(cdna2, 220).          % AMD calls them "compute units"
hw_supports_tensor_cores(cdna2, true).  % AMD calls them "matrix cores"

The predicate names stay the same. The values change. The optimizer produces different kernels for different vendors — from the same declarative fusion analysis.

Empirical Validation¶

We benchmarked our BPD-generated fused kernel on the Tesla P4:

The fusion saves ~0.1ms per operation (epilogue in registers vs VRAM round-trip). This compounds: 416 eliminated VRAM round-trips per forward pass for a 32-layer transformer.

The Full Source¶

The complete hardware_facts.pl (200 lines, 3 GPU targets, tensor core shapes) is available in our repository.

Part of the BPD ecosystem — a declarative substrate for provably correct kernel fusion.