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Mojo struct

BlackwellMatmulSM100Kernel

struct BlackwellMatmulSM100Kernel[a_type: DType, b_type: DType, c_type: DType, transpose_b: Bool, config: MatmulConfig[a_type, b_type, c_type, transpose_b], cluster_shape: StaticTuple[Int32, Int(3)] = StaticTuple(Int32(1)), elementwise_lambda_fn: Optional[def[dtype: DType, width: SIMDLength, *, alignment: Int = Int(1)](IndexList[Int(2)], SIMD[dtype, width]) capturing thin -> None] = None, elementwise_compute_lambda_fn: Optional[def[dtype: DType, width: SIMDLength, *, alignment: Int = Int(1)](IndexList[Int(2)], SIMD[dtype, width]) capturing thin -> SIMD[dtype, width]] = None, pdl_level: PDLLevel = PDLLevel(), max_profiled_tiles_per_SM: UInt32 = UInt32(0), output_writer_type: OutputWriter = StandardOutputWriter, c_desc_dim0_override: Int = Int(0)]

Blackwell SM100 GEMM kernel with warp specialization.

This struct unifies all parameters and derived types for the SM100 matmul kernel, providing:

  • Compile-time parameter validation
  • Centralized derived type computation
  • Factory methods for kernel components
  • Multiple kernel entry points (standard, split-k)

The SM100 kernel uses:

  • Tensor Memory (TMEM) for MMA accumulators
  • Cluster Launch Control (CLC) for dynamic tile scheduling
  • Warp specialization: Scheduler, TMA Load, MMA, Epilogue warps
  • Software pipelining for overlapping compute and memory operations

Parameters​

Implemented traits​

AnyType, Deinitable, Movable

comptime members​

a_expected_bytes​

comptime a_expected_bytes = (Int((mul (config.block_tile_shape[Int(2)] // (config.a_swizzle.bytes() // size_of[a_type]())), (config.block_tile_shape[Int(0)] // Int(8)), (config.a_swizzle.bytes() // size_of[a_type]()), 8)) * size_of[a_type]())

a_smem_layout​

comptime a_smem_layout = Layout(Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt())), Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt()))).to_layout()

a_swizzle_elems​

comptime a_swizzle_elems = (config.a_swizzle.bytes() // size_of[a_type]())

a_tile_dim0​

comptime a_tile_dim0 = (config.block_tile_shape[Int(0)] // config.cluster_shape[Int(1)])

a_tma_load_size​

comptime a_tma_load_size = ((config.block_tile_shape[Int(0)] // config.cluster_shape[Int(1)]) * (config.a_swizzle.bytes() // size_of[a_type]()))

a_tma_rows​

comptime a_tma_rows = BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].a_tile_dim0

accum_layout​

comptime accum_layout = Layout.row_major(config.mma_shape[Int(0)], config.mma_shape[Int(1)])

accum_pipeline_consumer_arv_count​

comptime accum_pipeline_consumer_arv_count = compute_accum_barrier_counts[Int((mul _resolve_warp_size(), 4)), config.cta_group]()[Int(1)]

accum_pipeline_producer_arv_count​

comptime accum_pipeline_producer_arv_count = compute_accum_barrier_counts[Int((mul _resolve_warp_size(), 4)), config.cta_group]()[Int(0)]

accum_type​

comptime accum_type = MatmulConfig[a_type, b_type, c_type, transpose_b].accum_type

AccumTensor​

comptime AccumTensor = TmemTensor[BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].accum_type, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].accum_layout, cta_group=config.cta_group]

ADescLayout​

comptime ADescLayout = Layout[*(), *()]

ADescLayout_splitk​

comptime ADescLayout_splitk = Layout[*(), *()]

ATileLayout​

comptime ATileLayout = Layout[*(), *()]

ATileLayout_splitk​

comptime ATileLayout_splitk = Layout[*(), *()]

ATmaOp​

comptime ATmaOp = TMATensorTile[a_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()]

ATmaOp_splitk​

comptime ATmaOp_splitk = TMATensorTile[a_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()]

b_expected_bytes​

comptime b_expected_bytes = (Int((mul (config.block_tile_shape[Int(2)] // (config.b_swizzle.bytes() // size_of[b_type]())), (config.block_tile_shape[Int(1)] // Int(8)), (config.b_swizzle.bytes() // size_of[b_type]()), 8)) * size_of[b_type]())

b_smem_layout​

comptime b_smem_layout = Layout(Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt())), Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt()))).to_layout() if transpose_b else Layout(Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt())), Coord(Coord(ComptimeInt(), ComptimeInt()), Coord(ComptimeInt(), ComptimeInt()))).transpose().to_layout()

b_swizzle_elems​

comptime b_swizzle_elems = (config.b_swizzle.bytes() // size_of[b_type]())

b_tile_dim0​

comptime b_tile_dim0 = (config.block_tile_shape[Int(1)] // (config.cluster_shape[Int(0)] // config))

b_tma_load_size​

comptime b_tma_load_size = ((config.block_tile_shape[Int(1)] // (config.cluster_shape[Int(0)] // config)) * (config.b_swizzle.bytes() // size_of[b_type]()))

b_tma_rows​

comptime b_tma_rows = BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].b_tile_dim0

BDescLayout​

comptime BDescLayout = Layout[*(), *()]

BDescLayout_splitk​

comptime BDescLayout_splitk = Layout[*(), *()]

Bias1DTile​

comptime Bias1DTile = TileTensor[c_type, Layout[*(), *()], ImmutAnyOrigin]

Bias1DTileLayout​

comptime Bias1DTileLayout = row_major[Int(1), config.mma_shape[Int(1)]]()

BK​

comptime BK = config.block_tile_shape[Int(2)]

BM​

comptime BM = config.block_tile_shape[Int(0)]

BN​

comptime BN = config.block_tile_shape[Int(1)]

BTileLayout​

comptime BTileLayout = Layout[*(), *()]

BTileLayout_splitk​

comptime BTileLayout_splitk = Layout[*(), *()]

BTmaOp​

comptime BTmaOp = TMATensorTile[b_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()]

BTmaOp_splitk​

comptime BTmaOp_splitk = TMATensorTile[b_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()]

c_desc_dim0​

comptime c_desc_dim0 = c_desc_dim0_override if (c_desc_dim0_override > Int(0)) else config.output_tile_shape[Int(0)] if (eq config.mma_shape[Int(0)], 256) if (eq config.mma_shape[Int(0)], 256) else (eq config.cta_group, 1) or config.AB_swapped else Int(64)

c_desc_inner_elems​

comptime c_desc_inner_elems = BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].c_tile_dim1 if (config == TensorMapSwizzle.SWIZZLE_NONE) else (config.c_swizzle.bytes() // size_of[c_type]())

c_swizzle_elems​

comptime c_swizzle_elems = (config.c_swizzle.bytes() // size_of[c_type]())

c_tile_dim0​

comptime c_tile_dim0 = BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].OutputM if (config.mma_shape[Int(0)] == Int(256)) if (config.mma_shape[Int(0)] == Int(256)) else (config == Int(1)) or config.AB_swapped else Int(64)

c_tile_dim1​

comptime c_tile_dim1 = BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].c_swizzle_elems if config.AB_swapped else BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].OutputN

CDescLayout​

comptime CDescLayout = Layout[*(), *()]

CDescLayout_splitk​

comptime CDescLayout_splitk = Layout[*(), *()]

clc_consumer_arv_count​

comptime clc_consumer_arv_count = compute_clc_barrier_counts[_resolve_warp_size(), _resolve_warp_size(), _resolve_warp_size(), (Int((mul _resolve_warp_size(), 4)) + _resolve_warp_size() if config.use_tma_epilogue_load else Int(0)), Int((mul config.cluster_shape[Int(0)], config.cluster_shape[Int(1)])), config.cta_group]()[Int(1)]

clc_producer_arv_count​

comptime clc_producer_arv_count = compute_clc_barrier_counts[_resolve_warp_size(), _resolve_warp_size(), _resolve_warp_size(), (Int((mul _resolve_warp_size(), 4)) + _resolve_warp_size() if config.use_tma_epilogue_load else Int(0)), Int((mul config.cluster_shape[Int(0)], config.cluster_shape[Int(1)])), config.cta_group]()[Int(0)]

clc_throttle_consumer_arv_count​

comptime clc_throttle_consumer_arv_count = compute_clc_barrier_counts[_resolve_warp_size(), _resolve_warp_size(), _resolve_warp_size(), (Int((mul _resolve_warp_size(), 4)) + _resolve_warp_size() if config.use_tma_epilogue_load else Int(0)), Int((mul config.cluster_shape[Int(0)], config.cluster_shape[Int(1)])), config.cta_group]()[Int(3)]

clc_throttle_producer_arv_count​

comptime clc_throttle_producer_arv_count = compute_clc_barrier_counts[_resolve_warp_size(), _resolve_warp_size(), _resolve_warp_size(), (Int((mul _resolve_warp_size(), 4)) + _resolve_warp_size() if config.use_tma_epilogue_load else Int(0)), Int((mul config.cluster_shape[Int(0)], config.cluster_shape[Int(1)])), config.cta_group]()[Int(2)]

CLUSTER_M​

comptime CLUSTER_M = config.cluster_shape[Int(0)]

CLUSTER_N​

comptime CLUSTER_N = config.cluster_shape[Int(1)]

CLUSTER_SIZE​

comptime CLUSTER_SIZE = (config.cluster_shape[Int(0)] * config.cluster_shape[Int(1)])

Context​

comptime Context = KernelContext[config.num_clc_pipeline_stages, config.cta_group, config.cluster_shape[Int(0)], config.cluster_shape[Int(1)]]

cta_group​

comptime cta_group = config.cta_group

CTileLayout​

comptime CTileLayout = Layout[*(), *()]

CTileLayout_splitk​

comptime CTileLayout_splitk = Layout[*(), *()]

CTmaOp​

comptime CTmaOp = TMATensorTile[c_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()]

CTmaOp_splitk​

comptime CTmaOp_splitk = TMATensorTile[c_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()]

epi_load_consumer_arv_count​

comptime epi_load_consumer_arv_count = SIMD(Int((mul _resolve_warp_size(), 4)))

epi_load_producer_arv_count​

comptime epi_load_producer_arv_count = SIMD(ceildiv(config.block_tile_shape[Int(0)] if config.AB_swapped else config.mma_shape[Int(1)], Int(8))) if config.epilogue_is_1d else Int32(1)

epi_load_swizzle​

comptime epi_load_swizzle = config.epi_load_swizzle

epi_load_swizzle_elems​

comptime epi_load_swizzle_elems = (config.epi_load_swizzle.bytes() // size_of[c_type]())

EPILOGUE_LOAD_THREADS​

comptime EPILOGUE_LOAD_THREADS = WARP_SIZE if config.use_tma_epilogue_load else Int(0)

EPILOGUE_THREADS​

comptime EPILOGUE_THREADS = (Int(4) * _resolve_warp_size())

EpilogueCtx​

comptime EpilogueCtx = EpilogueWarpContext[BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].opc, _resolve_warp_size(), Int((mul _resolve_warp_size(), 4))]

EpilogueLoadDescLayout​

comptime EpilogueLoadDescLayout = Layout[*(), *()]

EpilogueLoadTileLayout​

comptime EpilogueLoadTileLayout = Layout[*(), *()]

EpilogueLoadTmaOp​

comptime EpilogueLoadTmaOp = TMATensorTile[c_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()]

input_expected_bytes​

comptime input_expected_bytes = (Int((add (mul (config.block_tile_shape[Int(2)] // (config.a_swizzle.bytes() // size_of[a_type]())), (config.block_tile_shape[Int(0)] // Int(8)), (config.a_swizzle.bytes() // size_of[a_type]()), size_of[a_type](), config.cta_group, 8), (mul (config.block_tile_shape[Int(2)] // (config.b_swizzle.bytes() // size_of[b_type]())), (config.block_tile_shape[Int(1)] // Int(8)), (config.b_swizzle.bytes() // size_of[b_type]()), size_of[b_type](), config.cta_group, 8))) * config)

InputTilePipeline​

comptime InputTilePipeline = InputTilePipeline[StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size]

MMA_K​

comptime MMA_K = config.mma_shape[Int(2)]

MMA_M​

comptime MMA_M = config.mma_shape[Int(0)]

MMA_N​

comptime MMA_N = config.mma_shape[Int(1)]

MMA_THREADS​

comptime MMA_THREADS = WARP_SIZE

MmaCtx​

comptime MmaCtx = MmaWarpContext[BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].opc, _resolve_warp_size(), Int((mul _resolve_warp_size(), 4))]

MmaEpilogueSync​

comptime MmaEpilogueSync = WarpGroupBarrier[(_resolve_warp_size() + Int((mul _resolve_warp_size(), 4))), Int(1)]

MmaOp​

comptime MmaOp = MmaOpSM100_SS[c_type, a_type, b_type, config.block_tile_shape, config.mma_shape, accum_type=BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].accum_type, cta_group=config.cta_group, cluster_shape=config.cluster_shape, a_swizzle=config.a_swizzle, b_swizzle=config.b_swizzle, transpose_b=transpose_b]

num_accum_pipeline_stages​

comptime num_accum_pipeline_stages = config.num_accum_pipeline_stages

num_c_tma_descriptors​

comptime num_c_tma_descriptors = output_writer_type.num_peers

num_clc_pipeline_stages​

comptime num_clc_pipeline_stages = config.num_clc_pipeline_stages

num_group_pipeline_stages​

comptime num_group_pipeline_stages = (config // config)

num_k_mmas​

comptime num_k_mmas = (config.block_tile_shape[Int(2)] // config.mma_shape[Int(2)])

num_m_mmas​

comptime num_m_mmas = (config.block_tile_shape[Int(0)] // (config.mma_shape[Int(0)] // config))

num_n_mmas​

comptime num_n_mmas = (config.block_tile_shape[Int(1)] // (config.mma_shape[Int(1)] // config))

num_output_stages​

comptime num_output_stages = config.num_output_stages

num_output_warps​

comptime num_output_warps = 4

num_pipeline_stages​

comptime num_pipeline_stages = config.num_pipeline_stages

NUM_THREADS​

comptime NUM_THREADS = (Int((mul _resolve_warp_size(), 7)) + _resolve_warp_size() if config.use_tma_epilogue_load else Int(0))

NUM_TMEM_COLS​

comptime NUM_TMEM_COLS = 512

opc​

comptime opc = OutputPipelineConfig(BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].num_accum_pipeline_stages, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].stage_stride_cols, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].cta_group)

OutputM​

comptime OutputM = config.output_tile_shape[Int(0)]

OutputN​

comptime OutputN = config.output_tile_shape[Int(1)]

OutputPipeline​

comptime OutputPipeline = OutputTilePipeline[BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].opc]

register_based_epilogue​

comptime register_based_epilogue = config.register_based_epilogue

Scheduler​

comptime Scheduler = TileScheduler[config.num_clc_pipeline_stages, Index[Int, Int, Int, dtype=DType.uint32](config.cluster_shape[Int(0)], config.cluster_shape[Int(1)], config.cluster_shape[Int(2)]), config.raster_order, config.block_swizzle_size]

SCHEDULER_THREADS​

comptime SCHEDULER_THREADS = WARP_SIZE

SmemType​

comptime SmemType = B200MatmulSmem[a_type, b_type, c_type, transpose_b, config=config]

stage_stride_cols​

comptime stage_stride_cols = (Int(512) // config)

TilePayload​

comptime TilePayload = StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages]

TileWriterType​

comptime TileWriterType = TileWriter[a_type, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].accum_type, config.block_tile_shape, config.mma_shape, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].opc, config.c_swizzle, config.AB_swapped, config.output_tile_shape[Int(0)], config.output_tile_shape[Int(1)], config.num_output_stages, Int(4), elementwise_lambda_fn, elementwise_compute_lambda_fn, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].register_based_epilogue, True]

TileWriterType_splitk​

comptime TileWriterType_splitk = TileWriter[a_type, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].accum_type, config.block_tile_shape, config.mma_shape, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].opc, config.c_swizzle, config.AB_swapped, config.output_tile_shape[Int(0)], config.output_tile_shape[Int(1)], config.num_output_stages, Int(4), elementwise_lambda_fn, elementwise_compute_lambda_fn, BlackwellMatmulSM100Kernel[a_type, b_type, c_type, transpose_b, config, cluster_shape, elementwise_lambda_fn, elementwise_compute_lambda_fn, pdl_level, max_profiled_tiles_per_SM, output_writer_type, c_desc_dim0_override].register_based_epilogue]

TMA_LOAD_THREADS​

comptime TMA_LOAD_THREADS = WARP_SIZE

Tmem​

comptime Tmem = TmemAllocation[OutputPipelineConfig(config.num_accum_pipeline_stages, (Int(512) // config), config.cta_group).cta_group]

TmemDealloc​

comptime TmemDealloc = TmemDeallocBarrier[OutputPipelineConfig(config.num_accum_pipeline_stages, (Int(512) // config), config.cta_group).cta_group]

WorkIter​

comptime WorkIter = WorkIterator[config.num_clc_pipeline_stages, Index[Int, Int, Int, dtype=DType.uint32](config.cluster_shape[Int(0)], config.cluster_shape[Int(1)], config.cluster_shape[Int(2)]), config.raster_order, config.block_swizzle_size]

Methods​

write_output_tile​

static def write_output_tile[tma_origin: ImmOrigin](c_tma_ops: Pointer[Array[TMATensorTile[c_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], output_writer_type.num_peers], tma_origin], c_tiles: SMemTileArray2DRowMajor[c_type, config.output_tile_shape[Int(0)], config.output_tile_shape[Int(1)], config.num_output_stages], stage: OutputStage[Self.opc], tile_coord: Tuple[UInt32, UInt32, UInt32], shape: Tuple[UInt32, UInt32])

Write one batched output tile through the injected writer policy.

Construction of the concrete tile writer happens inside Self.output_writer_type.write_batched

Parameters:

  • ​tma_origin (ImmOrigin): Origin type for the C TMA descriptor memory.

Args:

validate_constraints​

static def validate_constraints()

Validate parameter constraints at compile time.

init_barriers​

static def init_barriers[use_tma_epilogue_load: Bool = False](ctx: KernelContext[config.num_clc_pipeline_stages, config.cta_group, config.cluster_shape[Int(0)], config.cluster_shape[Int(1)]], input_barriers: SMemArray[SharedMemBarrier, ((config // config) * Int(2))], accum_barriers: SMemArray[SharedMemBarrier, (config * Int(2))], clc_throttle: SMemArray[SharedMemBarrier, (config * Int(2))], clc_full: SMemArray[SharedMemBarrier, config.num_clc_pipeline_stages], clc_empty: SMemArray[SharedMemBarrier, config.num_clc_pipeline_stages], tmem_dealloc: SMemArray[SharedMemBarrier, Int(1)], epi_load_barriers: SMemArray[SharedMemBarrier, (config.num_accum_pipeline_stages if config.AB_swapped or config.epilogue_is_1d else config.num_tma_epilogue_pipeline_stages if config.use_tma_epilogue_load else Int(0) * Int(2))] = SMemArray(Pointer.unsafe_dangling()))

Initialize barriers. TMA descriptor prefetch is done by each kernel entry point before calling this method.

Parameters:

  • ​use_tma_epilogue_load (Bool): Whether to initialize epilogue load barriers (defaults to False).

Args:

  • ​ctx (KernelContext[config.num_clc_pipeline_stages, config.cta_group, config.cluster_shape[Int(0)], config.cluster_shape[Int(1)]]): Kernel context with election vars and CTA coordinates.
  • ​input_barriers (SMemArray[SharedMemBarrier, ((config // config) * Int(2))]): Barriers for the input (A/B) tile producer-consumer pipeline.
  • ​accum_barriers (SMemArray[SharedMemBarrier, (config * Int(2))]): Barriers for the MMA-to-epilogue accumulator pipeline.
  • ​clc_throttle (SMemArray[SharedMemBarrier, (config * Int(2))]): Throttle barriers for CLC scheduling.
  • ​clc_full (SMemArray[SharedMemBarrier, config.num_clc_pipeline_stages]): Full barriers signaling CLC pipeline stage occupancy.
  • ​clc_empty (SMemArray[SharedMemBarrier, config.num_clc_pipeline_stages]): Empty barriers signaling CLC pipeline stage availability.
  • ​tmem_dealloc (SMemArray[SharedMemBarrier, Int(1)]): Barrier for TMEM deallocation synchronization across the cluster.
  • ​epi_load_barriers (SMemArray[SharedMemBarrier, (config.num_accum_pipeline_stages if config.AB_swapped or config.epilogue_is_1d else config.num_tma_epilogue_pipeline_stages if config.use_tma_epilogue_load else Int(0) * Int(2))]): Barriers for the epilogue load producer-consumer pipeline (defaults to a dangling pointer when use_tma_epilogue_load is False).

mma​

static def mma[tiles_origin: MutOrigin, //](tmem_stage: TmemStage[Self.opc], tiles: ConsumerTiles[tiles_origin, StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size], mma_op: MmaOpSM100_SS[accum_type=mma_op.accum_type, cta_group=mma_op.cta_group, cluster_shape=mma_op.cluster_shape, a_swizzle=mma_op.a_swizzle, b_swizzle=mma_op.b_swizzle, transpose_b=mma_op.transpose_b], elect_one_warp: Bool, iter_idx: UInt32, k_start: UInt32)

Execute MMA operations for one pipeline stage.

This is the core MMA function designed to be called within a consumer stage context:

with consumer.acquire() as tiles:
    Self.mma(stage.tmem, tiles, mma_op, ...)

Parameters:

  • ​tiles_origin (MutOrigin): Origin type for the mutable tile payload memory (inferred).

Args:

load_input_tiles​

static def load_input_tiles[tiles_origin: MutOrigin, //](a_tma_op: TMATensorTile[a_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], b_tma_op: TMATensorTile[b_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], tiles: ProducerTiles[tiles_origin, StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size], peer_cta_coord: Tuple[Int, Int, Int], work_tile_coord: Tuple[Int, Int, Int], a_multicast_mask: UInt16, b_multicast_mask: UInt16, iter_idx: UInt32, elect_one_cta: Bool)

Load A and B tiles using 3D TMA.

Uses async_multicast_load_3d with batch coordinate from work_tile_coord[2]. For non-batched calls, batch coord is 0 (grid_dim.z = 1).

Parameters:

  • ​tiles_origin (MutOrigin): Origin type for the mutable tile payload memory (inferred).

Args:

prefetch_a_tiles​

static def prefetch_a_tiles[tiles_origin: MutOrigin, //](a_tma_op: TMATensorTile[a_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], tiles: ProducerTiles[tiles_origin, StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size], peer_cta_coord: Tuple[Int, Int, Int], work_tile_coord: Tuple[Int, Int, Int], a_multicast_mask: UInt16, iter_idx: UInt32, elect_one_cta: Bool)

Load A tiles only; set full expected bytes (A+B) on the barrier.

Called before wait_on_dependent_grids() to prefetch the static weight matrix (kernel-A in swapAB mode). The barrier will not fire until the matching complete_b_tiles() call delivers the remaining B bytes.

Parameters:

  • ​tiles_origin (MutOrigin): Origin type for the mutable tile payload memory (inferred).

Args:

complete_b_tiles​

static def complete_b_tiles(b_tma_op: TMATensorTile[b_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], stage: UInt32, barrier: Pointer[SharedMemBarrier, MutUntrackedOrigin, address_space=AddressSpace.SHARED], payload: StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], peer_cta_coord: Tuple[Int, Int, Int], work_tile_coord: Tuple[Int, Int, Int], b_multicast_mask: UInt16, iter_idx: UInt32)

Load B tiles into a previously prefetched stage.

Delivers the remaining B bytes so that the stage barrier fires and the consumer can proceed. Pair with prefetch_a_tiles().

Args:

prefetch_b_tiles​

static def prefetch_b_tiles[tiles_origin: MutOrigin, //](b_tma_op: TMATensorTile[b_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], tiles: ProducerTiles[tiles_origin, StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size], peer_cta_coord: Tuple[Int, Int, Int], work_tile_coord: Tuple[Int, Int, Int], b_multicast_mask: UInt16, iter_idx: UInt32, elect_one_cta: Bool)

Load B tiles only; set full expected bytes (A+B) on the barrier.

Called before wait_on_dependent_grids() to prefetch the static weight matrix (kernel-B in non-swapAB mode). The barrier will not fire until the matching complete_a_tiles() call delivers the remaining A bytes.

Parameters:

  • ​tiles_origin (MutOrigin): Origin type for the mutable tile payload memory (inferred).

Args:

complete_a_tiles​

static def complete_a_tiles(a_tma_op: TMATensorTile[a_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], stage: UInt32, barrier: Pointer[SharedMemBarrier, MutUntrackedOrigin, address_space=AddressSpace.SHARED], payload: StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], peer_cta_coord: Tuple[Int, Int, Int], work_tile_coord: Tuple[Int, Int, Int], a_multicast_mask: UInt16, iter_idx: UInt32)

Load A tiles into a previously prefetched stage.

Delivers the remaining A bytes so that the stage barrier fires and the consumer can proceed. Pair with prefetch_b_tiles().

Args:

load_input_tiles_splitk​

static def load_input_tiles_splitk[a_tma_origin: ImmOrigin, b_tma_origin: ImmOrigin, tiles_origin: MutOrigin, //](a_loader: TileLoader[a_tma_origin, a_type, Layout[*(), *()], Layout[*(), *()], cta_group=config.cta_group], b_loader: TileLoader[b_tma_origin, b_type, Layout[*(), *()], Layout[*(), *()], cta_group=config.cta_group], tiles: ProducerTiles[tiles_origin, StandardTilePayload[a_type, b_type, IndexList(config.block_tile_shape[Int(0)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), IndexList(config.block_tile_shape[Int(1)], config.block_tile_shape[Int(2)], __list_literal__=NoneType(None)), config.num_pipeline_stages], (config // config), config.k_group_size], iter_idx: UInt32, work_m_coord: Int, work_n_coord: Int, peer_cta_coord: Tuple[Int, Int, Int], elect_one_cta: Bool)

Load k_group_size A and B tiles using 2D TMA (for split-K only).

Orchestrates the tile loading operation including:

  • expect_bytes signaling
  • k-group iteration
  • Peer CTA slicing for 2-SM MMA

Parameters:

  • ​a_tma_origin (ImmOrigin): Origin type for the A matrix TMA descriptor memory (inferred).
  • ​b_tma_origin (ImmOrigin): Origin type for the B matrix TMA descriptor memory (inferred).
  • ​tiles_origin (MutOrigin): Origin type for the mutable tile payload memory (inferred).

Args:

epilogue_load_producer​

static def epilogue_load_producer[_epi_pipeline_stages: Int](epi_load_iter: WorkIterator[config.num_clc_pipeline_stages, Index[Int, Int, Int, dtype=DType.uint32](config.cluster_shape[Int(0)], config.cluster_shape[Int(1)], config.cluster_shape[Int(2)]), config.raster_order, config.block_swizzle_size], mut epilogue_load_pipeline: ProducerConsumerPipeline[_epi_pipeline_stages], epilogue_load_tma_op: TMATensorTile[c_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()], bias_1d_tile: TileTensor[c_type, Layout[*(), *()], ImmutAnyOrigin], epilogue_load_tiles: SMemTileArray2DRowMajor[c_type, Int(1) if config.epilogue_is_1d else config.mma_shape[Int(1)] if config.AB_swapped else config.block_tile_shape[Int(0)], config.block_tile_shape[Int(0)] if config.AB_swapped else config.mma_shape[Int(1)] if config.epilogue_is_1d else config.block_tile_shape[Int(0)] if config.AB_swapped else config.output_tile_shape[Int(1)], config.num_accum_pipeline_stages if config.AB_swapped or config.epilogue_is_1d else config.num_tma_epilogue_pipeline_stages if config.use_tma_epilogue_load else Int(0)], mnk: StaticTuple[UInt32, Int(3)])

Load epilogue tiles (bias) from GMEM to SMEM for each output tile.

Handles three cases based on config:

  • 1D bias: warp-wide cp.async with zero-fill for OOB elements
  • AB_swapped: full MMA_N x BM TMA per output tile
  • non-AB_swapped: BM x stageN strips in stage-outer/col_wg-inner order

Parameters:

  • ​_epi_pipeline_stages (Int): Number of stages in the epilogue load producer-consumer pipeline.

Args:

run​

static def run(a_tma_op: TMATensorTile[a_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], b_tma_op: TMATensorTile[b_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], c_tma_ops: Array[TMATensorTile[c_type, Int(3), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(3), Layout[*(), *()]]()], output_writer_type.num_peers], epilogue_load_tma_op: TMATensorTile[c_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()], bias_1d_tile: TileTensor[c_type, Layout[*(), *()], ImmutAnyOrigin], cluster_dim: StaticTuple[Int32, Int(3)], mnk: StaticTuple[UInt32, Int(3)], workspace: Span[UInt64, MutAnyOrigin], rank_sigs: Optional[Array[Pointer[Signal, MutAnyOrigin], Int(8)]] = None, my_rank_dev: Int32 = Int32(0))

Main kernel entry point for SM100 matrix multiplication.

Always uses 3D TMA descriptors. For non-batched inputs, batch=1 and batch_coord=0 (from k_start = block_idx.z = 0 when grid_dim.z = 1). For batched inputs, grid_dim.z = batch_size and batch_coord from k_start.

Args:

run_splitk​

static def run_splitk[reduction_layout: TensorLayout](a_tma_op: TMATensorTile[a_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()], b_tma_op: TMATensorTile[b_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()], c_tma_op: TMATensorTile[c_type, Int(2), _to_index_list[Layout[*(), *()]](), _to_index_list[Int(2), Layout[*(), *()]]()], reduction_tensor: TileTensor[MatmulConfig[a_type, b_type, c_type, transpose_b].accum_type, reduction_layout, MutAnyOrigin], lock_ptr: Pointer[UInt8, MutUnsafeAnyOrigin], cluster_dim: StaticTuple[Int32, Int(3)], mnk: StaticTuple[UInt32, Int(3)], workspace: Span[UInt64, MutAnyOrigin])

Split-K kernel entry point for better parallelism on small problems.

Split-K divides the K dimension across multiple CTAs, with each CTA computing a partial result that is then reduced.

Parameters:

  • ​reduction_layout (TensorLayout): Memory layout of the reduction workspace tensor, must match the layout of reduction_tensor.

Args:

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