submission 499344

import cutlass
import cutlass.cute as cute
import cutlass.utils as utils
import cutlass.pipeline as pipeline
from cutlass.cute.nvgpu import cpasync, tcgen05
import cutlass.utils.blackwell_helpers as sm100_utils
import cutlass.utils.blockscaled_layout as blockscaled_utils
from cutlass.cute.runtime import make_ptr

from typing import Tuple, List, Dict, Any

import torch
from task import input_t, output_t

# Kernel configuration parameters
# Size of tma descriptor in bytes
bytes_per_tensormap = 128
# Number of tensormaps: a, b, sfa, sfb
num_tensormaps = 4
# Tile sizes for M, N, K dimensions
mma_tiler_mnk = (128, 128, 256)  
# Shape of the K dimension for the MMA instruction
mma_inst_shape_k = 64
# FP4 data type for A and B
ab_dtype = cutlass.Float4E2M1FN  
# FP8 data type for scale factors
sf_dtype = cutlass.Float8E4M3FN  
# FP16 output type
c_dtype = cutlass.Float16  
# Scale factor block size (16 elements share one scale)
sf_vec_size = 16  
# Number of threads per CUDA thread block
threads_per_cta = 128  
# Stage numbers of shared memory and tmem
num_acc_stage = 1
num_ab_stage = 2
# Total number of columns in tmem
num_tmem_alloc_cols = 512

# Global cache for compiled kernels (keyed by number of groups)
_compiled_kernel_cache: Dict[int, Any] = {}
# Cache packed launch metadata keyed by problem sizes + tensor addresses
_launch_metadata_cache: Dict[Any, Dict[str, Any]] = {}


# Helper function for ceiling division
def ceil_div(a, b):
    return (a + b - 1) // b


def _build_cta_metadata(problem_sizes: Tuple[Tuple[int, int, int, int], ...]):
    """Flatten grouped tile scheduling metadata into a dense [total_cta, 3] array."""
    cta_meta = []
    total_num_clusters = 0
    tile_m, tile_n = mma_tiler_mnk[0], mma_tiler_mnk[1]

    for group_idx, (m, n, _, _) in enumerate(problem_sizes):
        cta_m = ceil_div(m, tile_m)
        cta_n = ceil_div(n, tile_n)
        total_num_clusters += cta_m * cta_n
        cta_meta.extend(
            (group_idx, coord_x, coord_y)
            for coord_y in range(cta_n)
            for coord_x in range(cta_m)
        )

    return total_num_clusters, cta_meta


@cute.kernel
def init_tensormaps_kernel(
    tma_atom_a: cute.CopyAtom,
    tma_atom_b: cute.CopyAtom,
    tma_atom_sfa: cute.CopyAtom,
    tma_atom_sfb: cute.CopyAtom,
    tensor_of_abc_ptrs: cute.Tensor,
    tensor_of_sfasfb_ptrs: cute.Tensor,
    tensormaps: cute.Tensor,
    tensor_of_problem_sizes: cute.Tensor,
):
    """Initialize one set of A/B/SFA/SFB descriptors per group."""
    _, _, group_idx = cute.arch.block_idx()
    warp_idx = cute.arch.make_warp_uniform(cute.arch.warp_idx())

    size_tensormap_in_i64 = num_tensormaps * bytes_per_tensormap // 8

    @cute.struct
    class SharedStorage:
        tensormap_buffer: cute.struct.MemRange[cutlass.Int64, size_tensormap_in_i64]

    smem = utils.SmemAllocator()
    storage = smem.allocate(SharedStorage)

    tensormap_smem_ptr = storage.tensormap_buffer.data_ptr()
    tensormap_a_smem_ptr = tensormap_smem_ptr
    tensormap_b_smem_ptr = tensormap_a_smem_ptr + bytes_per_tensormap // 8
    tensormap_sfa_smem_ptr = tensormap_b_smem_ptr + bytes_per_tensormap // 8
    tensormap_sfb_smem_ptr = tensormap_sfa_smem_ptr + bytes_per_tensormap // 8

    m = tensor_of_problem_sizes[group_idx, 0]
    n = tensor_of_problem_sizes[group_idx, 1]
    k = tensor_of_problem_sizes[group_idx, 2]
    l = tensor_of_problem_sizes[group_idx, 3]

    mA_mkl_iter = cute.make_ptr(
        ab_dtype, tensor_of_abc_ptrs[group_idx, 0], cute.AddressSpace.gmem
    ).align(32)
    mB_nkl_iter = cute.make_ptr(
        ab_dtype, tensor_of_abc_ptrs[group_idx, 1], cute.AddressSpace.gmem
    ).align(32)
    sfa_mkl_iter = cute.make_ptr(
        sf_dtype, tensor_of_sfasfb_ptrs[group_idx, 0], cute.AddressSpace.gmem
    ).align(32)
    sfb_nkl_iter = cute.make_ptr(
        sf_dtype, tensor_of_sfasfb_ptrs[group_idx, 1], cute.AddressSpace.gmem
    ).align(32)

    mA_mkl_layout = cute.make_layout(
        (m, k, l), stride=(cute.assume(k, 32), 1, cute.assume(m * k, 32))
    )
    mB_nkl_layout = cute.make_layout(
        (n, k, l), stride=(cute.assume(k, 32), 1, cute.assume(n * k, 32))
    )

    atom_shape = ((32, 4), (sf_vec_size, 4))
    atom_stride = ((16, 4), (0, 1))
    sfa_layout = cute.tile_to_shape(
        cute.make_layout(atom_shape, stride=atom_stride),
        mA_mkl_layout.shape,
        (2, 1, 3),
    )
    sfb_layout = cute.tile_to_shape(
        cute.make_layout(atom_shape, stride=atom_stride),
        mB_nkl_layout.shape,
        (2, 1, 3),
    )

    real_tensor_a = cute.make_tensor(mA_mkl_iter, mA_mkl_layout)
    real_tensor_b = cute.make_tensor(mB_nkl_iter, mB_nkl_layout)
    real_tensor_sfa = cute.make_tensor(sfa_mkl_iter, sfa_layout)
    real_tensor_sfb = cute.make_tensor(sfb_nkl_iter, sfb_layout)

    tensormap_manager = utils.TensorMapManager(utils.TensorMapUpdateMode.SMEM, 128)
    tensormap_a_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 0, None)].iterator
    )
    tensormap_b_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 1, None)].iterator
    )
    tensormap_sfa_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 2, None)].iterator
    )
    tensormap_sfb_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 3, None)].iterator
    )

    if warp_idx == 0:
        tensormap_manager.init_tensormap_from_atom(tma_atom_a, tensormap_a_smem_ptr, 0)
        tensormap_manager.init_tensormap_from_atom(tma_atom_b, tensormap_b_smem_ptr, 0)
        tensormap_manager.init_tensormap_from_atom(tma_atom_sfa, tensormap_sfa_smem_ptr, 0)
        tensormap_manager.init_tensormap_from_atom(tma_atom_sfb, tensormap_sfb_smem_ptr, 0)

        tensormap_manager.update_tensormap(
            (real_tensor_a, real_tensor_b, real_tensor_sfa, real_tensor_sfb),
            (tma_atom_a, tma_atom_b, tma_atom_sfa, tma_atom_sfb),
            (
                tensormap_a_gmem_ptr,
                tensormap_b_gmem_ptr,
                tensormap_sfa_gmem_ptr,
                tensormap_sfb_gmem_ptr,
            ),
            0,
            (
                tensormap_a_smem_ptr,
                tensormap_b_smem_ptr,
                tensormap_sfa_smem_ptr,
                tensormap_sfb_smem_ptr,
            ),
        )
        tensormap_manager.fence_tensormap_update(tensormap_a_gmem_ptr)
        tensormap_manager.fence_tensormap_update(tensormap_b_gmem_ptr)
        tensormap_manager.fence_tensormap_update(tensormap_sfa_gmem_ptr)
        tensormap_manager.fence_tensormap_update(tensormap_sfb_gmem_ptr)


def _get_launch_metadata(
    abc_tensors: List[Tuple[torch.Tensor, torch.Tensor, torch.Tensor]],
    sfasfb_reordered_tensors: List[Tuple[torch.Tensor, torch.Tensor]],
    problem_sizes: List[Tuple[int, int, int, int]],
):
    """Build and cache flattened metadata tensors used by the grouped kernel launch."""
    problem_sizes_key = tuple(tuple(int(v) for v in p) for p in problem_sizes)
    abc_ptrs = tuple((a.data_ptr(), b.data_ptr(), c.data_ptr()) for a, b, c in abc_tensors)
    sfasfb_ptrs = tuple(
        (sfa_reordered.data_ptr(), sfb_reordered.data_ptr())
        for sfa_reordered, sfb_reordered in sfasfb_reordered_tensors
    )
    cache_key = (problem_sizes_key, abc_ptrs, sfasfb_ptrs)
    if cache_key in _launch_metadata_cache:
        return _launch_metadata_cache[cache_key]

    total_num_clusters, cta_meta = _build_cta_metadata(problem_sizes_key)
    tensormap_shape = (len(problem_sizes_key), num_tensormaps, bytes_per_tensormap // 8)

    tensor_of_problem_sizes = torch.tensor(
        problem_sizes_key, dtype=torch.int32, device="cuda"
    )
    tensor_of_abc_ptrs = torch.tensor(abc_ptrs, dtype=torch.int64, device="cuda")
    tensor_of_sfasfb_ptrs = torch.tensor(sfasfb_ptrs, dtype=torch.int64, device="cuda")
    tensor_of_cta_metadata = torch.tensor(cta_meta, dtype=torch.int32, device="cuda")
    tensor_of_tensormap = torch.empty(tensormap_shape, dtype=torch.int64, device="cuda")

    launch_metadata = {
        "total_num_clusters": total_num_clusters,
        "tensormaps_initialized": False,
        "tensor_of_problem_sizes": tensor_of_problem_sizes,
        "tensor_of_abc_ptrs": tensor_of_abc_ptrs,
        "tensor_of_sfasfb_ptrs": tensor_of_sfasfb_ptrs,
        "tensor_of_cta_metadata": tensor_of_cta_metadata,
        "tensor_of_tensormap": tensor_of_tensormap,
        "ptr_problem_sizes": make_ptr(
            cutlass.Int32,
            tensor_of_problem_sizes.data_ptr(),
            cute.AddressSpace.gmem,
            assumed_align=16,
        ),
        "ptr_abc_ptrs": make_ptr(
            cutlass.Int64,
            tensor_of_abc_ptrs.data_ptr(),
            cute.AddressSpace.gmem,
            assumed_align=16,
        ),
        "ptr_sfasfb_ptrs": make_ptr(
            cutlass.Int64,
            tensor_of_sfasfb_ptrs.data_ptr(),
            cute.AddressSpace.gmem,
            assumed_align=16,
        ),
        "ptr_cta_metadata": make_ptr(
            cutlass.Int32,
            tensor_of_cta_metadata.data_ptr(),
            cute.AddressSpace.gmem,
            assumed_align=16,
        ),
        "ptr_tensormap": make_ptr(
            cutlass.Int64,
            tensor_of_tensormap.data_ptr(),
            cute.AddressSpace.gmem,
            assumed_align=16,
        ),
    }
    _launch_metadata_cache[cache_key] = launch_metadata
    return launch_metadata


# The CuTe reference implementation for NVFP4 block-scaled GEMM
@cute.kernel
def kernel(
    tiled_mma: cute.TiledMma,
    tma_atom_a: cute.CopyAtom,
    mA_mkl: cute.Tensor,
    tma_atom_b: cute.CopyAtom,
    mB_nkl: cute.Tensor,
    tma_atom_sfa: cute.CopyAtom,
    mSFA_mkl: cute.Tensor,
    tma_atom_sfb: cute.CopyAtom,
    mSFB_nkl: cute.Tensor,
    tensor_of_abc_ptrs: cute.Tensor,
    tensor_of_sfasfb_ptrs: cute.Tensor,
    tensormaps: cute.Tensor,
    tensor_of_problem_sizes: cute.Tensor,
    tensor_of_cta_metadata: cute.Tensor,
    a_smem_layout_staged: cute.ComposedLayout,
    b_smem_layout_staged: cute.ComposedLayout,
    sfa_smem_layout_staged: cute.Layout,
    sfb_smem_layout_staged: cute.Layout,
    num_tma_load_bytes: cutlass.Constexpr[int],
):
    """
    GPU device kernel performing the Group GEMM computation.
    """
    warp_idx = cute.arch.warp_idx()
    warp_idx = cute.arch.make_warp_uniform(warp_idx)
    if warp_idx == 0:
        cpasync.prefetch_descriptor(tma_atom_a)
        cpasync.prefetch_descriptor(tma_atom_b)
        cpasync.prefetch_descriptor(tma_atom_sfa)
        cpasync.prefetch_descriptor(tma_atom_sfb)
    tidx, _, _ = cute.arch.thread_idx()

    #
    # Read flattened CTA metadata: (group_idx, tile_coord_m, tile_coord_n)
    #
    bidx, bidy, bidz = cute.arch.block_idx()
    group_idx = cutlass.Int32(tensor_of_cta_metadata[bidz, 0])
    coord_x = cutlass.Int32(tensor_of_cta_metadata[bidz, 1])
    coord_y = cutlass.Int32(tensor_of_cta_metadata[bidz, 2])
    group_idx = cute.arch.make_warp_uniform(group_idx)
    coord_x = cute.arch.make_warp_uniform(coord_x)
    coord_y = cute.arch.make_warp_uniform(coord_y)

    #
    # Construct C Tensor for each CTA
    #
    mC_mnl_iter = cute.make_ptr(
        c_dtype, tensor_of_abc_ptrs[group_idx, 2], cute.AddressSpace.gmem
    ).align(32)
    m = tensor_of_problem_sizes[group_idx, 0]
    n = tensor_of_problem_sizes[group_idx, 1]
    k = tensor_of_problem_sizes[group_idx, 2]
    l = tensor_of_problem_sizes[group_idx, 3]

    mC_mnl_layout = cute.make_layout(
        (m, n, l),
        stride=(cute.assume(n, 32), 1, cute.assume(m * n, 32),))
    mC_mnl = cute.make_tensor(mC_mnl_iter, mC_mnl_layout)
    # Local partition for global C Tensor
    # (bM, bN, RestM, RestN, RestL)
    gC_mnl = cute.local_tile(
        mC_mnl, cute.slice_(mma_tiler_mnk, (None, None, 0)), (coord_x, coord_y, 0)
    )

    #
    # Define shared storage for kernel
    #
    @cute.struct
    class SharedStorage:
        ab_mbar_ptr: cute.struct.MemRange[cutlass.Int64, num_ab_stage * 2]
        acc_mbar_ptr: cute.struct.MemRange[cutlass.Int64, num_acc_stage * 2]
        tmem_holding_buf: cutlass.Int32
    smem = utils.SmemAllocator()
    storage = smem.allocate(SharedStorage)

    # Setup smem tensor for A, B, SFA, SFB
    # (MMA, MMA_M, MMA_K, STAGE)
    sA = smem.allocate_tensor(
        element_type=ab_dtype,
        layout=a_smem_layout_staged.outer,
        byte_alignment=128,
        swizzle=a_smem_layout_staged.inner,
    )
    # (MMA, MMA_N, MMA_K, STAGE)
    sB = smem.allocate_tensor(
        element_type=ab_dtype,
        layout=b_smem_layout_staged.outer,
        byte_alignment=128,
        swizzle=b_smem_layout_staged.inner,
    )
    # (MMA, MMA_M, MMA_K, STAGE)
    sSFA = smem.allocate_tensor(
        element_type=sf_dtype,
        layout=sfa_smem_layout_staged,
        byte_alignment=128,
    )
    # (MMA, MMA_N, MMA_K, STAGE)
    sSFB = smem.allocate_tensor(
        element_type=sf_dtype,
        layout=sfb_smem_layout_staged,
        byte_alignment=128,
    )

    # Initialize mainloop ab_pipeline, acc_pipeline and their states
    ab_pipeline_producer_group = pipeline.CooperativeGroup(pipeline.Agent.Thread)
    ab_pipeline_consumer_group = pipeline.CooperativeGroup(pipeline.Agent.Thread, 1)
    ab_producer, ab_consumer = pipeline.PipelineTmaUmma.create(
        barrier_storage=storage.ab_mbar_ptr.data_ptr(),
        num_stages=num_ab_stage,
        producer_group=ab_pipeline_producer_group,
        consumer_group=ab_pipeline_consumer_group,
        tx_count=num_tma_load_bytes,
    ).make_participants()
    acc_producer, acc_consumer = pipeline.PipelineUmmaAsync.create(
        barrier_storage=storage.acc_mbar_ptr.data_ptr(),
        num_stages=num_acc_stage,
        producer_group=pipeline.CooperativeGroup(pipeline.Agent.Thread),
        consumer_group=pipeline.CooperativeGroup(
            pipeline.Agent.Thread,
            threads_per_cta,
        ),
    ).make_participants()

    #
    # Local_tile partition global tensors
    #
    # (bM, bK, RestM, RestK, RestL)
    gA_mkl = cute.local_tile(
        mA_mkl, cute.slice_(mma_tiler_mnk, (None, 0, None)), (None, None, None)
    )
    # (bN, bK, RestN, RestK, RestL)
    gB_nkl = cute.local_tile(
        mB_nkl, cute.slice_(mma_tiler_mnk, (0, None, None)), (None, None, None)
    )
    # (bM, bK, RestM, RestK, RestL)
    gSFA_mkl = cute.local_tile(
        mSFA_mkl, cute.slice_(mma_tiler_mnk, (None, 0, None)), (None, None, None)
    )
    # (bN, bK, RestN, RestK, RestL)
    gSFB_nkl = cute.local_tile(
        mSFB_nkl, cute.slice_(mma_tiler_mnk, (0, None, None)), (None, None, None)
    )
    #
    # Partition global tensor for TiledMMA_A/B/C
    #
    thr_mma = tiled_mma.get_slice(tidx)
    # (MMA, MMA_M, MMA_K, RestM, RestK, RestL)
    tCgA = thr_mma.partition_A(gA_mkl)
    # (MMA, MMA_N, MMA_K, RestN, RestK, RestL)
    tCgB = thr_mma.partition_B(gB_nkl)
    # (MMA, MMA_M, MMA_K, RestM, RestK, RestL)
    tCgSFA = thr_mma.partition_A(gSFA_mkl)
    # (MMA, MMA_N, MMA_K, RestN, RestK, RestL)
    tCgSFB = thr_mma.partition_B(gSFB_nkl)
    # (MMA, MMA_M, MMA_N, RestM, RestN, RestL)
    tCgC = thr_mma.partition_C(gC_mnl)

    # Update tma descriptor with the correct shapes and strides
    tensormap_manager = utils.TensorMapManager(
        utils.TensorMapUpdateMode.SMEM,
        128,
    )
    tensormap_a_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 0, None)].iterator
    )
    tensormap_b_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 1, None)].iterator
    )
    tensormap_sfa_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 2, None)].iterator
    )
    tensormap_sfb_gmem_ptr = tensormap_manager.get_tensormap_ptr(
        tensormaps[(group_idx, 3, None)].iterator
    )

    #
    # Partition global/shared tensor for TMA load A/B/SFA/SFB
    #
    # TMA Partition_S/D for A
    # ((atom_v, rest_v), STAGE)
    # ((atom_v, rest_v), RestM, RestK, RestL)
    tAsA, tAgA = cpasync.tma_partition(
        tma_atom_a,
        0,
        cute.make_layout(1),
        cute.group_modes(sA, 0, 3),
        cute.group_modes(tCgA, 0, 3),
    )
    # TMA Partition_S/D for B
    # ((atom_v, rest_v), STAGE)
    # ((atom_v, rest_v), RestN, RestK, RestL)
    tBsB, tBgB = cpasync.tma_partition(
        tma_atom_b,
        0,
        cute.make_layout(1),
        cute.group_modes(sB, 0, 3),
        cute.group_modes(tCgB, 0, 3),
    )
    #  TMA Partition_S/D for SFA
    # ((atom_v, rest_v), STAGE)
    # ((atom_v, rest_v), RestM, RestK, RestL)
    tAsSFA, tAgSFA = cpasync.tma_partition(
        tma_atom_sfa,
        0,
        cute.make_layout(1),
        cute.group_modes(sSFA, 0, 3),
        cute.group_modes(tCgSFA, 0, 3),
    )
    tAsSFA = cute.filter_zeros(tAsSFA)
    tAgSFA = cute.filter_zeros(tAgSFA)
    # TMA Partition_S/D for SFB
    # ((atom_v, rest_v), STAGE)
    # ((atom_v, rest_v), RestN, RestK, RestL)
    tBsSFB, tBgSFB = cpasync.tma_partition(
        tma_atom_sfb,
        0,
        cute.make_layout(1),
        cute.group_modes(sSFB, 0, 3),
        cute.group_modes(tCgSFB, 0, 3),
    )
    tBsSFB = cute.filter_zeros(tBsSFB)
    tBgSFB = cute.filter_zeros(tBgSFB)

    #
    # Partition shared/tensor memory tensor for TiledMMA_A/B/C
    #
    # (MMA, MMA_M, MMA_K, STAGE)
    tCrA = tiled_mma.make_fragment_A(sA)
    # (MMA, MMA_N, MMA_K, STAGE)
    tCrB = tiled_mma.make_fragment_B(sB)
    # (MMA, MMA_M, MMA_N)
    acc_shape = tiled_mma.partition_shape_C(mma_tiler_mnk[:2])
    # (MMA, MMA_M, MMA_N)
    tCtAcc_fake = tiled_mma.make_fragment_C(acc_shape)
    #
    # Alloc tensor memory buffer
    #
    tmem_alloc_barrier = pipeline.NamedBarrier(
        barrier_id=1,
        num_threads=threads_per_cta,
    )
    tmem = utils.TmemAllocator(
        storage.tmem_holding_buf,
        barrier_for_retrieve=tmem_alloc_barrier,
    )
    tmem.allocate(num_tmem_alloc_cols)
    tmem.wait_for_alloc()
    acc_tmem_ptr = tmem.retrieve_ptr(cutlass.Float32)
    tCtAcc = cute.make_tensor(acc_tmem_ptr, tCtAcc_fake.layout)

    #
    # Make SFA/SFB tmem tensor
    #
    # Get SFA tmem ptr
    sfa_tmem_ptr = cute.recast_ptr(
        acc_tmem_ptr + tcgen05.find_tmem_tensor_col_offset(tCtAcc),
        dtype=sf_dtype,
    )
    # (MMA, MMA_M, MMA_K)
    tCtSFA_layout = blockscaled_utils.make_tmem_layout_sfa(
        tiled_mma,
        mma_tiler_mnk,
        sf_vec_size,
        cute.slice_(sfa_smem_layout_staged, (None, None, None, 0)),
    )
    tCtSFA = cute.make_tensor(sfa_tmem_ptr, tCtSFA_layout)
    # Get SFB tmem ptr
    sfb_tmem_ptr = cute.recast_ptr(
        acc_tmem_ptr
        + tcgen05.find_tmem_tensor_col_offset(tCtAcc)
        + tcgen05.find_tmem_tensor_col_offset(tCtSFA),
        dtype=sf_dtype,
    )
    # (MMA, MMA_N, MMA_K)
    tCtSFB_layout = blockscaled_utils.make_tmem_layout_sfb(
        tiled_mma,
        mma_tiler_mnk,
        sf_vec_size,
        cute.slice_(sfb_smem_layout_staged, (None, None, None, 0)),
    )
    tCtSFB = cute.make_tensor(sfb_tmem_ptr, tCtSFB_layout)

    #
    # Partition for S2T copy of SFA/SFB
    #
    # Make S2T CopyAtom
    copy_atom_s2t = cute.make_copy_atom(
        tcgen05.Cp4x32x128bOp(tcgen05.CtaGroup.ONE),
        sf_dtype,
    )
    # (MMA, MMA_MN, MMA_K, STAGE)
    tCsSFA_compact = cute.filter_zeros(sSFA)
    tCtSFA_compact = cute.filter_zeros(tCtSFA)
    tiled_copy_s2t_sfa = tcgen05.make_s2t_copy(copy_atom_s2t, tCtSFA_compact)
    thr_copy_s2t_sfa = tiled_copy_s2t_sfa.get_slice(0)
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
    tCsSFA_compact_s2t_ = thr_copy_s2t_sfa.partition_S(tCsSFA_compact)
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
    tCsSFA_compact_s2t = tcgen05.get_s2t_smem_desc_tensor(
        tiled_copy_s2t_sfa, tCsSFA_compact_s2t_
    )
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K)
    tCtSFA_compact_s2t = thr_copy_s2t_sfa.partition_D(tCtSFA_compact)

    # (MMA, MMA_MN, MMA_K, STAGE)
    tCsSFB_compact = cute.filter_zeros(sSFB)
    # (MMA, MMA_MN, MMA_K)
    tCtSFB_compact = cute.filter_zeros(tCtSFB)
    tiled_copy_s2t_sfb = tcgen05.make_s2t_copy(copy_atom_s2t, tCtSFB_compact)
    thr_copy_s2t_sfb = tiled_copy_s2t_sfb.get_slice(0)
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
    tCsSFB_compact_s2t_ = thr_copy_s2t_sfb.partition_S(tCsSFB_compact)
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
    tCsSFB_compact_s2t = tcgen05.get_s2t_smem_desc_tensor(
        tiled_copy_s2t_sfb, tCsSFB_compact_s2t_
    )
    # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K)
    tCtSFB_compact_s2t = thr_copy_s2t_sfb.partition_D(tCtSFB_compact)

    # Number of K loops
    k_tile_cnt = cute.ceil_div(k, mma_tiler_mnk[2])

    #
    # Slice to per mma tile index
    #
    mma_tile_coord_mnl = (coord_x, coord_y, 0)
    # ((atom_v, rest_v), RestK)
    tAgA = tAgA[(None, mma_tile_coord_mnl[0], None, mma_tile_coord_mnl[2])]
    # ((atom_v, rest_v), RestK)
    tBgB = tBgB[(None, mma_tile_coord_mnl[1], None, mma_tile_coord_mnl[2])]
    # ((atom_v, rest_v), RestK)
    tAgSFA = tAgSFA[(None, mma_tile_coord_mnl[0], None, mma_tile_coord_mnl[2])]
    # ((atom_v, rest_v), RestK)
    tBgSFB = tBgSFB[(None, mma_tile_coord_mnl[1], None, mma_tile_coord_mnl[2])]

    #
    # Main loop
    #
    if warp_idx == 0:
        # Wait for accumulator buffer empty
        acc_empty = acc_producer.acquire_and_advance()
        # Set ACCUMULATE field to False for the first k_tile iteration
        tiled_mma.set(tcgen05.Field.ACCUMULATE, False)
        if k_tile_cnt > 0:
            # Prologue: prefetch the first k-tile.
            ab_empty = ab_producer.acquire_and_advance()
            cute.copy(
                tma_atom_a,
                tAgA[(None, 0)],
                tAsA[(None, ab_empty.index)],
                tma_bar_ptr=ab_empty.barrier,
                tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                    tensormap_a_gmem_ptr, cute.AddressSpace.generic
                ),
            )
            cute.copy(
                tma_atom_b,
                tBgB[(None, 0)],
                tBsB[(None, ab_empty.index)],
                tma_bar_ptr=ab_empty.barrier,
                tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                    tensormap_b_gmem_ptr, cute.AddressSpace.generic
                ),
            )
            cute.copy(
                tma_atom_sfa,
                tAgSFA[(None, 0)],
                tAsSFA[(None, ab_empty.index)],
                tma_bar_ptr=ab_empty.barrier,
                tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                    tensormap_sfa_gmem_ptr, cute.AddressSpace.generic
                ),
            )
            cute.copy(
                tma_atom_sfb,
                tBgSFB[(None, 0)],
                tBsSFB[(None, ab_empty.index)],
                tma_bar_ptr=ab_empty.barrier,
                tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                    tensormap_sfb_gmem_ptr, cute.AddressSpace.generic
                ),
            )

            # Steady state: overlap next prefetch with current compute.
            for k_tile in range(k_tile_cnt):
                next_k_tile = k_tile + 1
                if next_k_tile < k_tile_cnt:
                    ab_next_empty = ab_producer.acquire_and_advance()
                    cute.copy(
                        tma_atom_a,
                        tAgA[(None, next_k_tile)],
                        tAsA[(None, ab_next_empty.index)],
                        tma_bar_ptr=ab_next_empty.barrier,
                        tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                            tensormap_a_gmem_ptr, cute.AddressSpace.generic
                        ),
                    )
                    cute.copy(
                        tma_atom_b,
                        tBgB[(None, next_k_tile)],
                        tBsB[(None, ab_next_empty.index)],
                        tma_bar_ptr=ab_next_empty.barrier,
                        tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                            tensormap_b_gmem_ptr, cute.AddressSpace.generic
                        ),
                    )
                    cute.copy(
                        tma_atom_sfa,
                        tAgSFA[(None, next_k_tile)],
                        tAsSFA[(None, ab_next_empty.index)],
                        tma_bar_ptr=ab_next_empty.barrier,
                        tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                            tensormap_sfa_gmem_ptr, cute.AddressSpace.generic
                        ),
                    )
                    cute.copy(
                        tma_atom_sfb,
                        tBgSFB[(None, next_k_tile)],
                        tBsSFB[(None, ab_next_empty.index)],
                        tma_bar_ptr=ab_next_empty.barrier,
                        tma_desc_ptr=tensormap_manager.get_tensormap_ptr(
                            tensormap_sfb_gmem_ptr, cute.AddressSpace.generic
                        ),
                    )

                # Wait for AB buffer full for current tile.
                ab_full = ab_consumer.wait_and_advance()

                # Copy SFA/SFB from shared memory to TMEM
                s2t_stage_coord = (None, None, None, None, ab_full.index)
                tCsSFA_compact_s2t_staged = tCsSFA_compact_s2t[s2t_stage_coord]
                tCsSFB_compact_s2t_staged = tCsSFB_compact_s2t[s2t_stage_coord]
                cute.copy(
                    tiled_copy_s2t_sfa,
                    tCsSFA_compact_s2t_staged,
                    tCtSFA_compact_s2t,
                )
                cute.copy(
                    tiled_copy_s2t_sfb,
                    tCsSFB_compact_s2t_staged,
                    tCtSFB_compact_s2t,
                )

                # tCtAcc += tCrA * tCrSFA * tCrB * tCrSFB
                num_kblocks = cute.size(tCrA, mode=[2])
                for kblock_idx in cutlass.range(num_kblocks, unroll_full=True):
                    kblock_coord = (
                        None,
                        None,
                        kblock_idx,
                        ab_full.index,
                    )

                    # Set SFA/SFB tensor to tiled_mma
                    sf_kblock_coord = (None, None, kblock_idx)
                    tiled_mma.set(
                        tcgen05.Field.SFA,
                        tCtSFA[sf_kblock_coord].iterator,
                    )
                    tiled_mma.set(
                        tcgen05.Field.SFB,
                        tCtSFB[sf_kblock_coord].iterator,
                    )

                    cute.gemm(
                        tiled_mma,
                        tCtAcc,
                        tCrA[kblock_coord],
                        tCrB[kblock_coord],
                        tCtAcc,
                    )
                    # Enable accumulate on tCtAcc after first kblock
                    tiled_mma.set(tcgen05.Field.ACCUMULATE, True)

                # Async arrive AB buffer empty
                ab_full.release()
        acc_empty.commit()

    #
    # Epilogue
    # Partition for epilogue
    #
    op = tcgen05.Ld32x32bOp(tcgen05.Repetition.x128, tcgen05.Pack.NONE)
    copy_atom_t2r = cute.make_copy_atom(op, cutlass.Float32)
    tiled_copy_t2r = tcgen05.make_tmem_copy(copy_atom_t2r, tCtAcc[None,0,0])
    thr_copy_t2r = tiled_copy_t2r.get_slice(tidx)
    # (TmemCpy, NumTmemCpy)
    tDtAcc = thr_copy_t2r.partition_S(tCtAcc[None,0,0])
    # (TmemCpy, NumTmemCpy)
    tDgC = thr_copy_t2r.partition_D(tCgC[None,0,0])

    # (TmemCpy, NumTmemCpy)
    tDrAcc = cute.make_rmem_tensor(tDgC.shape, cutlass.Float32)
    # (TmemCpy, NumTmemCpy)
    tDrC = cute.make_rmem_tensor(tDgC.shape, c_dtype)

    # Release TMEM allocation lock
    tmem.relinquish_alloc_permit()
    # Wait for accumulator buffer full
    acc_full = acc_consumer.wait_and_advance()

    # Copy accumulator to register
    cute.copy(tiled_copy_t2r, tDtAcc, tDrAcc)
    acc_vec = tDrAcc.load()
    tDrC.store(acc_vec.to(c_dtype))

    # STG Atom, just to ensure functionality
    # For performance optimization, better to use Tma store operation to
    # reduce address calculation and predicate calulation instructions
    simt_atom = cute.make_copy_atom(
        cute.nvgpu.CopyUniversalOp(), c_dtype, num_bits_per_copy=16
    )
    thread_layout = cute.make_layout(
        (1, threads_per_cta), stride=(threads_per_cta, 1))
    value_layout = cute.make_layout((1, 1))
    tiled_copy_r2g = cute.make_tiled_copy_tv(
        simt_atom, thread_layout, value_layout
    )
    thr_copy_r2g = tiled_copy_r2g.get_slice(tidx)
    cC = cute.make_identity_tensor(gC_mnl.shape)
    # ((atom_v, rest_v), NumGmemCpy)
    tDcC = thr_copy_r2g.partition_D(cC)

    # ((atom_v, rest_v), NumGmemCpy)
    tDpC = cute.make_rmem_tensor(tDrC.shape, cutlass.Boolean)
    residue_m = mC_mnl.shape[0] - cutlass.Int32(coord_x) * mma_tiler_mnk[0]
    residue_n = mC_mnl.shape[1] - cutlass.Int32(coord_y) * mma_tiler_mnk[1]
    for i in range(cute.size(tDrC.shape)):
        # Swap residue_m and residue_n to match the order of tDcC
        tDpC[i] = cute.elem_less(tDcC[i], (residue_n, residue_m))
    cute.copy(simt_atom, cute.flatten(tDrC), cute.flatten(tDgC), pred=cute.flatten(tDpC))

    acc_full.release()
    # Deallocate TMEM
    cute.arch.barrier()
    tmem.free(acc_tmem_ptr)
    pass


# Host-side JIT function to prepare tensors and launch GPU kernel.
@cute.jit
def my_kernel(
    ptr_of_tensor_of_problem_sizes: cute.Pointer,
    ptr_of_tensor_of_abc_ptrs: cute.Pointer,
    ptr_of_tensor_of_sfasfb_ptrs: cute.Pointer,
    ptr_of_tensor_of_cta_metadata: cute.Pointer,
    ptr_of_tensor_of_tensormap: cute.Pointer,
    total_num_clusters: cutlass.Int32,
    num_groups: cutlass.Int32,
    init_tensormaps: cutlass.Boolean,
):

    tensor_of_abc_ptrs = cute.make_tensor(
        ptr_of_tensor_of_abc_ptrs, cute.make_layout((num_groups, 3), stride=(3, 1))
    )
    tensor_of_sfasfb_ptrs = cute.make_tensor(
        ptr_of_tensor_of_sfasfb_ptrs, cute.make_layout((num_groups, 2), stride=(2, 1))
    )
    tensor_of_problem_sizes = cute.make_tensor(
        ptr_of_tensor_of_problem_sizes, cute.make_layout((num_groups, 4), stride=(4, 1))
    )
    tensor_of_cta_metadata = cute.make_tensor(
        ptr_of_tensor_of_cta_metadata, cute.make_layout((total_num_clusters, 3), stride=(3, 1))
    )
    tensor_of_tensormap = cute.make_tensor(
        ptr_of_tensor_of_tensormap, cute.make_layout((num_groups, 4, 16), stride=(64, 16, 1))
    )

    # Use fake shape for initial Tma descriptor and atom setup
    # The real Tma desc and atom will be updated during kernel execution.
    min_a_shape = (cutlass.Int32(64), cutlass.Int32(64), cutlass.Int32(64), cutlass.Int32(1))
    min_b_shape = (cutlass.Int32(64), cutlass.Int32(64), cutlass.Int32(64), cutlass.Int32(1))
    initial_a = cute.make_tensor(
        cute.make_ptr(ab_dtype, 0, cute.AddressSpace.gmem, assumed_align=16,),
        cute.make_layout(
            (min_a_shape[0], cute.assume(min_a_shape[2], 32), min_a_shape[3]),
            stride=(
                cute.assume(min_a_shape[2], 32),
                1,
                cute.assume(min_a_shape[0] * min_a_shape[2], 32),
            ),
        ),
    )
    initial_b = cute.make_tensor(
        cute.make_ptr(ab_dtype, 0, cute.AddressSpace.gmem, assumed_align=16,),
        cute.make_layout(
            (min_b_shape[1], cute.assume(min_b_shape[2], 32), min_b_shape[3]),
            stride=(
                cute.assume(min_b_shape[2], 32),
                1,
                cute.assume(min_b_shape[1] * min_b_shape[2], 32),
            ),
        ),
    )

    # Setup sfa/sfb tensor by filling A/B tensor to scale factor atom layout
    # ((Atom_M, Rest_M),(Atom_K, Rest_K),RestL)
    sfa_layout = blockscaled_utils.tile_atom_to_shape_SF(
        initial_a.shape, sf_vec_size
    )
    # ((Atom_N, Rest_N),(Atom_K, Rest_K),RestL)
    sfb_layout = blockscaled_utils.tile_atom_to_shape_SF(
        initial_b.shape, sf_vec_size
    )
    # Create initial SFA and SFB tensors with fake shape and null pointer.
    initial_sfa = cute.make_tensor(
        cute.make_ptr(sf_dtype, 0, cute.AddressSpace.gmem, assumed_align=16,), sfa_layout)
    initial_sfb = cute.make_tensor(
        cute.make_ptr(sf_dtype, 0, cute.AddressSpace.gmem, assumed_align=16,), sfb_layout)

    # Select MMA operation
    mma_op = tcgen05.MmaMXF4NVF4Op(
        sf_dtype,
        (mma_tiler_mnk[0], mma_tiler_mnk[1], mma_inst_shape_k),
        tcgen05.CtaGroup.ONE,
        tcgen05.OperandSource.SMEM,
    )
    tiled_mma = cute.make_tiled_mma(mma_op)

    cluster_layout_vmnk = cute.tiled_divide(
        cute.make_layout((1, 1, 1)),
        (tiled_mma.thr_id.shape,),
    )

    # Compute A/B/SFA/SFB/C shared memory layout
    a_smem_layout_staged = sm100_utils.make_smem_layout_a(
        tiled_mma,
        mma_tiler_mnk,
        ab_dtype,
        num_ab_stage,
    )
    b_smem_layout_staged = sm100_utils.make_smem_layout_b(
        tiled_mma,
        mma_tiler_mnk,
        ab_dtype,
        num_ab_stage,
    )
    sfa_smem_layout_staged = blockscaled_utils.make_smem_layout_sfa(
        tiled_mma,
        mma_tiler_mnk,
        sf_vec_size,
        num_ab_stage,
    )
    sfb_smem_layout_staged = blockscaled_utils.make_smem_layout_sfb(
        tiled_mma,
        mma_tiler_mnk,
        sf_vec_size,
        num_ab_stage,
    )
    atom_thr_size = cute.size(tiled_mma.thr_id.shape)

    # Setup TMA for A
    a_smem_layout = cute.slice_(a_smem_layout_staged, (None, None, None, 0))
    tma_atom_a, tma_tensor_a = cute.nvgpu.make_tiled_tma_atom_A(
        cpasync.CopyBulkTensorTileG2SOp(tcgen05.CtaGroup.ONE),
        initial_a,
        a_smem_layout,
        mma_tiler_mnk,
        tiled_mma,
        cluster_layout_vmnk.shape,
    )
    # Setup TMA for B
    b_smem_layout = cute.slice_(b_smem_layout_staged, (None, None, None, 0))
    tma_atom_b, tma_tensor_b = cute.nvgpu.make_tiled_tma_atom_B(
        cpasync.CopyBulkTensorTileG2SOp(tcgen05.CtaGroup.ONE),
        initial_b,
        b_smem_layout,
        mma_tiler_mnk,
        tiled_mma,
        cluster_layout_vmnk.shape,
    )
    # Setup TMA for SFA
    sfa_smem_layout = cute.slice_(
        sfa_smem_layout_staged, (None, None, None, 0)
    )
    tma_atom_sfa, tma_tensor_sfa = cute.nvgpu.make_tiled_tma_atom_A(
        cpasync.CopyBulkTensorTileG2SOp(tcgen05.CtaGroup.ONE),
        initial_sfa,
        sfa_smem_layout,
        mma_tiler_mnk,
        tiled_mma,
        cluster_layout_vmnk.shape,
        internal_type=cutlass.Int16,
    )
    # Setup TMA for SFB
    sfb_smem_layout = cute.slice_(
        sfb_smem_layout_staged, (None, None, None, 0)
    )
    tma_atom_sfb, tma_tensor_sfb = cute.nvgpu.make_tiled_tma_atom_B(
        cpasync.CopyBulkTensorTileG2SOp(tcgen05.CtaGroup.ONE),
        initial_sfb,
        sfb_smem_layout,
        mma_tiler_mnk,
        tiled_mma,
        cluster_layout_vmnk.shape,
        internal_type=cutlass.Int16,
    )

    # Compute TMA load bytes
    a_copy_size = cute.size_in_bytes(ab_dtype, a_smem_layout)
    b_copy_size = cute.size_in_bytes(ab_dtype, b_smem_layout)
    sfa_copy_size = cute.size_in_bytes(sf_dtype, sfa_smem_layout)
    sfb_copy_size = cute.size_in_bytes(sf_dtype, sfb_smem_layout)
    num_tma_load_bytes = (
        a_copy_size + b_copy_size + sfa_copy_size + sfb_copy_size
    ) * atom_thr_size

    # Compute grid size
    grid = (1, 1, total_num_clusters)

    if init_tensormaps:
        # Initialize A/B/SFA/SFB tensormaps once per group.
        init_tensormaps_kernel(
            tma_atom_a,
            tma_atom_b,
            tma_atom_sfa,
            tma_atom_sfb,
            tensor_of_abc_ptrs,
            tensor_of_sfasfb_ptrs,
            tensor_of_tensormap,
            tensor_of_problem_sizes,
        ).launch(
            grid=(1, 1, num_groups),
            block=[32, 1, 1],
            cluster=(1, 1, 1),
        )

    # Launch the kernel
    kernel(
        # MMA (Matrix Multiply-Accumulate) configuration
        tiled_mma,                  # Tiled MMA object defining NVFP4 GEMM compute pattern
        
        # TMA (Tensor Memory Accelerator) atoms and tensors for input matrix A
        tma_atom_a,                 # TMA copy atom defining how to load A from global memory
        tma_tensor_a,               # Tensor descriptor for A (created from smallest A tensor)
        
        # TMA atoms and tensors for input matrix B
        tma_atom_b,                 # TMA copy atom defining how to load B from global memory
        tma_tensor_b,               # Tensor descriptor for B (created from smallest B tensor)
        
        # TMA atoms and tensors for scale factor A
        tma_atom_sfa,               # TMA copy atom for loading scale factors for A
        tma_tensor_sfa,             # Tensor descriptor for SFA (block scale factors for A)
        
        # TMA atoms and tensors for scale factor B
        tma_atom_sfb,               # TMA copy atom for loading scale factors for B
        tma_tensor_sfb,             # Tensor descriptor for SFB (block scale factors for B)
        
        # Runtime tensor metadata for dynamic group access
        tensor_of_abc_ptrs,         # Device tensor containing pointers to A, B, C for all groups
        tensor_of_sfasfb_ptrs,      # Device tensor containing pointers to SFA, SFB for all groups
        tensor_of_tensormap,        # Pre-allocated buffer for tensormap descriptors per group
        tensor_of_problem_sizes,    # Device tensor containing (m, n, k, l) for each group
        tensor_of_cta_metadata,     # Device tensor containing (group_idx, tile_m, tile_n) per CTA
        
        # Shared memory layouts with staging for pipelined execution
        a_smem_layout_staged,       # Staged shared memory layout for A (includes stage dimension)
        b_smem_layout_staged,       # Staged shared memory layout for B (includes stage dimension)
        sfa_smem_layout_staged,     # Staged shared memory layout for SFA (includes stage dimension)
        sfb_smem_layout_staged,     # Staged shared memory layout for SFB (includes stage dimension)
        
        # Pipeline synchronization parameter
        num_tma_load_bytes,         # Total bytes to load per TMA transaction (for barrier setup)
    ).launch(
        grid=grid,
        block=[threads_per_cta, 1, 1],
        cluster=(1, 1, 1),
    )
    return


# Compile once per group-count specialization and reuse compiled callable.
def compile_kernel(num_groups: int):
    """
    Compile the kernel once and cache it by group count.
    This should be called before any timing measurements.

    Returns:
        The compiled kernel function
    """
    global _compiled_kernel_cache
    
    cache_key = num_groups

    if cache_key in _compiled_kernel_cache:
        return _compiled_kernel_cache[cache_key]

    cute_ptr_of_tensor_of_problem_sizes = make_ptr(
        cutlass.Int32, 0, cute.AddressSpace.gmem, assumed_align=16,
    )
    cute_ptr_of_tensor_of_abc_ptrs = make_ptr(
        cutlass.Int64, 0, cute.AddressSpace.gmem, assumed_align=16,
    )
    cute_ptr_of_tensor_of_sfasfb_ptrs = make_ptr(
        cutlass.Int64, 0, cute.AddressSpace.gmem, assumed_align=16,
    )
    cute_ptr_of_tensor_of_cta_metadata = make_ptr(
        cutlass.Int32, 0, cute.AddressSpace.gmem, assumed_align=16,
    )
    # Fake cluster numbers for compile only.
    total_num_clusters = cutlass.Int32(1)
    num_groups = cutlass.Int32(num_groups)
    cute_ptr_of_tensor_of_tensormap = make_ptr(
        cutlass.Int64, 0, cute.AddressSpace.gmem, assumed_align=16,
    )
    compiled_func = cute.compile(
        my_kernel,
        cute_ptr_of_tensor_of_problem_sizes,
        cute_ptr_of_tensor_of_abc_ptrs,
        cute_ptr_of_tensor_of_sfasfb_ptrs,
        cute_ptr_of_tensor_of_cta_metadata,
        cute_ptr_of_tensor_of_tensormap,
        total_num_clusters,
        num_groups,
        cutlass.Boolean(False),
    )
    _compiled_kernel_cache[cache_key] = compiled_func
    return compiled_func


def custom_kernel(data: input_t) -> output_t:
    """
    Execute the block-scaled group GEMM kernel.
    
    This is the main entry point called by the evaluation framework.
    It converts PyTorch tensors to CuTe tensors, launches the kernel,
    and returns the result.
    
    Args:
        data: Tuple of (abc_tensors, sfasfb_tensors, problem_sizes) where:
            abc_tensors: list of tuples (a, b, c) where 
                a is torch.Tensor[float4e2m1fn_x2] of shape [m, k // 2, l]
                b is torch.Tensor[float4e2m1fn_x2] of shape [n, k // 2, l]
                c is torch.Tensor[float16] of shape [m, n, l]
            sfasfb_tensors: list of tuples (sfa, sfb) where 
                sfa is torch.Tensor[float8_e4m3fnuz] of shape [m, k // 16, l]
                sfb is torch.Tensor[float8_e4m3fnuz] of shape [n, k // 16, l]
            problem_sizes: list of tuples (m, n, k, l)
            each group has its own a, b, c, sfa, sfb with different m, n, k, l problem sizes
            l should always be 1 for each group.
            list size is the number of groups.
    
    Returns:
        list of c tensors where c is torch.Tensor[float16] of shape [m, n, l] for each group
    """
    abc_tensors, _, sfasfb_reordered_tensors, problem_sizes = data

    num_groups = len(problem_sizes)
    compiled_func = compile_kernel(num_groups)
    launch_metadata = _get_launch_metadata(
        abc_tensors,
        sfasfb_reordered_tensors,
        problem_sizes,
    )

    init_tensormaps = not launch_metadata["tensormaps_initialized"]
    compiled_func(
        launch_metadata["ptr_problem_sizes"],
        launch_metadata["ptr_abc_ptrs"],
        launch_metadata["ptr_sfasfb_ptrs"],
        launch_metadata["ptr_cta_metadata"],
        launch_metadata["ptr_tensormap"],
        launch_metadata["total_num_clusters"],
        num_groups,
        cutlass.Boolean(init_tensormaps),
    )
    if init_tensormaps:
        launch_metadata["tensormaps_initialized"] = True

    return [c for _, _, c in abc_tensors]