submission 138838

import torch
from task import input_t, output_t

from typing import Tuple, Type, List, Optional, Union

import cuda.bindings.driver as cuda

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

mma_inst_shape_k = 64
ab_dtype = cutlass.Float4E2M1FN
sf_dtype = cutlass.Float8E4M3FN
c_dtype = cutlass.Float16
sf_vec_size = 16


class Sm100BlockScaledDenseGemmKernel:
    def __init__(
        self,
        mma_tiler_mn: Tuple[int, int],
        cluster_shape_mn: Tuple[int, int],
    ):
        self.ab_dtype = cutlass.Float4E2M1FN
        self.sf_dtype = cutlass.Float8E4M3FN
        self.acc_dtype = cutlass.Float32
        self.c_dtype = cutlass.Float16
        self.sf_vec_size = 16

        self.epilog_warp_id = (0, 1, 2, 3)
        self.mma_warp_id = 4
        self.tma_warp_id = 5
        self.threads_per_cta = 32 * len((self.mma_warp_id, self.tma_warp_id, *self.epilog_warp_id))

        self.mma_tiler_mn = mma_tiler_mn
        self.cluster_shape_mn = cluster_shape_mn

        self.occupancy = 1

        self.smem_capacity = utils.get_smem_capacity_in_bytes("sm_100")
        self.num_tmem_alloc_cols = 512

        self.epilog_sync_barrier = pipeline.NamedBarrier(
            barrier_id=1,
            num_threads=32 * len(self.epilog_warp_id),
        )
        self.tmem_alloc_barrier = pipeline.NamedBarrier(
            barrier_id=2,
            num_threads=32 * len((self.mma_warp_id, *self.epilog_warp_id)),
        )

    def _setup_attributes(self):

        tiled_mma = sm100_utils.make_blockscaled_trivial_tiled_mma(
            self.ab_dtype,
            self.a_major_mode,
            self.b_major_mode,
            self.sf_dtype,
            self.sf_vec_size,
            tcgen05.CtaGroup.ONE,
            self.mma_tiler_mn,
        )

        mma_inst_tile_k = 4
        mma_inst_shape_k = cute.size(tiled_mma.shape_mnk, mode=[2])
        
        self.mma_tiler = (
            self.mma_tiler_mn[0],
            self.mma_tiler_mn[1],
            mma_inst_shape_k * mma_inst_tile_k,
        )
        self.cta_tile_shape_mnk = (
            self.mma_tiler[0] // cute.size(tiled_mma.thr_id.shape),
            self.mma_tiler[1],
            self.mma_tiler[2],
        )
        self.cluster_layout_vmnk = cute.tiled_divide(
            cute.make_layout((*self.cluster_shape_mn, 1)),
            (tiled_mma.thr_id.shape,),
        )

        self.mma_inst_shape_mn_sfb = (
            self.mma_tiler_mn[0],
            cute.round_up(self.mma_tiler_mn[1], 128),
        )
        
        # Create a specific TiledMMA for SFB using the rounded shape
        tiled_mma_sfb = sm100_utils.make_blockscaled_trivial_tiled_mma(
            self.ab_dtype,
            self.a_major_mode,
            self.b_major_mode,
            self.sf_dtype,
            self.sf_vec_size,
            tcgen05.CtaGroup.ONE,
            self.mma_inst_shape_mn_sfb,
        )

        # Create specific tiler for SFB
        self.mma_tiler_sfb = (
            self.mma_inst_shape_mn_sfb[0],
            self.mma_inst_shape_mn_sfb[1],
            mma_inst_shape_k * mma_inst_tile_k,
        )

        # Create specific cluster layout for SFB
        self.cluster_layout_sfb_vmnk = cute.tiled_divide(
            cute.make_layout((*self.cluster_shape_mn, 1)),
            (tiled_mma_sfb.thr_id.shape,),
        )

        self.epi_tile = sm100_utils.compute_epilogue_tile_shape(
            self.cta_tile_shape_mnk,
            False,
            self.c_layout,
            self.c_dtype,
        )
        self.epi_tile_n = cute.size(self.epi_tile[1])
        self.num_acc_stage, self.num_ab_stage, self.num_c_stage = self._compute_stages(
            tiled_mma,
            self.mma_tiler,
            self.a_dtype,
            self.b_dtype,
            self.epi_tile,
            self.c_dtype,
            self.c_layout,
            self.sf_dtype,
            self.sf_vec_size,
            self.smem_capacity,
            self.occupancy,
        )

        self.a_smem_layout_staged = sm100_utils.make_smem_layout_a(
            tiled_mma,
            self.mma_tiler,
            self.ab_dtype,
            self.num_ab_stage,
        )

        self.b_smem_layout_staged = sm100_utils.make_smem_layout_b(
            tiled_mma,
            self.mma_tiler,
            self.ab_dtype,
            self.num_ab_stage,
        )

        self.sfa_smem_layout_staged = blockscaled_utils.make_smem_layout_sfa(
            tiled_mma,
            self.mma_tiler,
            self.sf_vec_size,
            self.num_ab_stage,
        )

        
        self.sfb_smem_layout_staged = blockscaled_utils.make_smem_layout_sfb(
            tiled_mma,
            self.mma_tiler,
            self.sf_vec_size,
            self.num_ab_stage,
        )
        self.c_smem_layout_staged = sm100_utils.make_smem_layout_epi(
            self.c_dtype,
            self.c_layout,
            self.epi_tile,
            self.num_c_stage,
        )

    @cute.jit
    def __call__(
        self,
        a_ptr: cute.Pointer,
        b_ptr: cute.Pointer,
        sfa_ptr: cute.Pointer,
        sfb_ptr: cute.Pointer,
        c_ptr: cute.Pointer,
        problem_size: tuple,
    ):
        self.a_dtype: Type[cutlass.Numeric] = a_ptr.value_type
        self.b_dtype: Type[cutlass.Numeric] = b_ptr.value_type
        self.sf_dtype: Type[cutlass.Numeric] = sfa_ptr.value_type
        self.c_dtype: Type[cutlass.Numeric] = c_ptr.value_type

        self.a_major_mode, self.b_major_mode, self.c_layout = (
            tcgen05.OperandMajorMode.K,
            tcgen05.OperandMajorMode.K,
            utils.LayoutEnum.ROW_MAJOR,
        )
        m, n, k, l = problem_size

        self._setup_attributes()

        a_tensor = cute.make_tensor(
            a_ptr,
            cute.make_ordered_layout(
                (cute.assume(m, 32), k, l), order=(1, 0, 2)
            ),
        )
        b_tensor = cute.make_tensor(
            b_ptr,
            cute.make_ordered_layout(
                (cute.assume(n, 32), k, l), order=(1, 0, 2)
            ),
        )

        c_tensor = cute.make_tensor(
            c_ptr,
            cute.make_ordered_layout(
                (m, cute.assume(n, 32), l), order=(1, 0, 2)
            )
        )

        sfa_layout = blockscaled_utils.tile_atom_to_shape_SF(
            a_tensor.shape, self.sf_vec_size
        )
        sfa_tensor = cute.make_tensor(sfa_ptr, sfa_layout)

        sfb_layout = blockscaled_utils.tile_atom_to_shape_SF(
            b_tensor.shape, self.sf_vec_size
        )
        sfb_tensor = cute.make_tensor(sfb_ptr, sfb_layout)

        # Standard TiledMMA
        tiled_mma = sm100_utils.make_blockscaled_trivial_tiled_mma(
            self.ab_dtype,
            self.a_major_mode,
            self.b_major_mode,
            self.sf_dtype,
            self.sf_vec_size,
            tcgen05.CtaGroup.ONE,
            self.mma_tiler_mn,
        )

        # SFB Specific TiledMMA (Re-created here or stored in self)
        tiled_mma_sfb = sm100_utils.make_blockscaled_trivial_tiled_mma(
            self.ab_dtype,
            self.a_major_mode,
            self.b_major_mode,
            self.sf_dtype,
            self.sf_vec_size,
            tcgen05.CtaGroup.ONE,
            self.mma_inst_shape_mn_sfb,
        )

        a_op = sm100_utils.cluster_shape_to_tma_atom_A(
            self.cluster_shape_mn, tiled_mma.thr_id
        )
        a_smem_layout = cute.slice_(
            self.a_smem_layout_staged, (None, None, None, 0)
        )
        tma_atom_a, tma_tensor_a = cute.nvgpu.make_tiled_tma_atom_A(
            a_op,
            a_tensor,
            a_smem_layout,
            self.mma_tiler,
            tiled_mma,
            self.cluster_layout_vmnk.shape,
        )

        b_op = sm100_utils.cluster_shape_to_tma_atom_B(
            self.cluster_shape_mn, tiled_mma.thr_id
        )
        b_smem_layout = cute.slice_(
            self.b_smem_layout_staged, (None, None, None, 0)
        )
        tma_atom_b, tma_tensor_b = cute.nvgpu.make_tiled_tma_atom_B(
            b_op,
            b_tensor,
            b_smem_layout,
            self.mma_tiler,
            tiled_mma,
            self.cluster_layout_vmnk.shape,
        )

        sfa_op = sm100_utils.cluster_shape_to_tma_atom_A(
            self.cluster_shape_mn, tiled_mma.thr_id
        )
        sfa_smem_layout = cute.slice_(
            self.sfa_smem_layout_staged, (None, None, None, 0)
        )
        tma_atom_sfa, tma_tensor_sfa = cute.nvgpu.make_tiled_tma_atom_A(
            sfa_op,
            sfa_tensor,
            sfa_smem_layout,
            self.mma_tiler,
            tiled_mma,
            self.cluster_layout_vmnk.shape,
            internal_type=cutlass.Int16,
        )

        sfb_op = sm100_utils.cluster_shape_to_tma_atom_SFB(
            self.cluster_shape_mn, tiled_mma.thr_id
        )
        sfb_smem_layout = cute.slice_(
            self.sfb_smem_layout_staged, (None, None, None, 0)
        )
        tma_atom_sfb, tma_tensor_sfb = cute.nvgpu.make_tiled_tma_atom_B(
            sfb_op,
            sfb_tensor,
            sfb_smem_layout,
            self.mma_tiler_sfb,           # Use SFB tiler
            tiled_mma_sfb,                # Use SFB tiled_mma
            self.cluster_layout_sfb_vmnk.shape, # Use SFB cluster layout
            internal_type=cutlass.Int16,
        )

        atom_thr_size = cute.size(tiled_mma.thr_id.shape)
        a_copy_size = cute.size_in_bytes(self.ab_dtype, a_smem_layout)
        b_copy_size = cute.size_in_bytes(self.ab_dtype, b_smem_layout)
        sfa_copy_size = cute.size_in_bytes(self.sf_dtype, sfa_smem_layout)
        sfb_copy_size = cute.size_in_bytes(self.sf_dtype, sfb_smem_layout)
        self.num_tma_load_bytes = (
            a_copy_size + b_copy_size + sfa_copy_size + sfb_copy_size
        ) * atom_thr_size

        epi_smem_layout = cute.slice_(self.c_smem_layout_staged, (None, None, 0))
        tma_atom_c, tma_tensor_c = cpasync.make_tiled_tma_atom(
            cpasync.CopyBulkTensorTileS2GOp(),
            c_tensor,
            epi_smem_layout,
            self.epi_tile,
        )

        grid = self._compute_grid(
            c_tensor, self.cta_tile_shape_mnk, self.cluster_shape_mn
        )

        self.buffer_align_bytes = 1024

        @cute.struct
        class SharedStorage:
            ab_full_mbar_ptr: cute.struct.MemRange[cutlass.Int64, self.num_ab_stage]
            ab_empty_mbar_ptr: cute.struct.MemRange[cutlass.Int64, self.num_ab_stage]
            acc_full_mbar_ptr: cute.struct.MemRange[cutlass.Int64, self.num_acc_stage]
            tmem_dealloc_mbar_ptr: cutlass.Int64
            tmem_holding_buf: cutlass.Int32
            # (EPI_TILE_M, EPI_TILE_N, STAGE)
            sC: cute.struct.Align[
                cute.struct.MemRange[
                    self.c_dtype, cute.cosize(self.c_smem_layout_staged.outer)
                ],
                self.buffer_align_bytes,
            ]
            # (MMA, MMA_M, MMA_K, STAGE)
            sA: cute.struct.Align[
                cute.struct.MemRange[
                    self.a_dtype, cute.cosize(self.a_smem_layout_staged.outer)
                ],
                self.buffer_align_bytes,
            ]
            # (MMA, MMA_N, MMA_K, STAGE)
            sB: cute.struct.Align[
                cute.struct.MemRange[
                    self.b_dtype, cute.cosize(self.b_smem_layout_staged.outer)
                ],
                self.buffer_align_bytes,
            ]
            # (MMA, MMA_M, MMA_K, STAGE)
            sSFA: cute.struct.Align[
                cute.struct.MemRange[
                    self.sf_dtype, cute.cosize(self.sfa_smem_layout_staged)
                ],
                self.buffer_align_bytes,
            ]
            # (MMA, MMA_N, MMA_K, STAGE)
            sSFB: cute.struct.Align[
                cute.struct.MemRange[
                    self.sf_dtype, cute.cosize(self.sfb_smem_layout_staged)
                ],
                self.buffer_align_bytes,
            ]

        self.shared_storage = SharedStorage

        self.kernel(
            tiled_mma,
            tiled_mma_sfb,                  # Pass specialized SFB MMA
            tma_atom_a,
            tma_tensor_a,
            tma_atom_b,
            tma_tensor_b,
            tma_atom_sfa,
            tma_tensor_sfa,
            tma_atom_sfb,
            tma_tensor_sfb,
            tma_atom_c,
            tma_tensor_c,
            self.cluster_layout_vmnk,
            self.cluster_layout_sfb_vmnk,   # Pass specialized SFB Cluster Layout
            self.a_smem_layout_staged,
            self.b_smem_layout_staged,
            self.sfa_smem_layout_staged,
            self.sfb_smem_layout_staged,
            self.c_smem_layout_staged,
            self.epi_tile,
        ).launch(
            grid=grid,
            block=[self.threads_per_cta, 1, 1],
            cluster=(*self.cluster_shape_mn, 1),
            smem=self.shared_storage.size_in_bytes(),
        )
        return

    # GPU device kernel
    @cute.kernel
    def kernel(
        self,
        tiled_mma: cute.TiledMma,
        tiled_mma_sfb: cute.TiledMma,       # Receive SFB Tiled MMA
        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,
        tma_atom_c: Optional[cute.CopyAtom],
        mC_mnl: cute.Tensor,
        cluster_layout_vmnk: cute.Layout,
        cluster_layout_sfb_vmnk: cute.Layout, # Receive SFB Cluster Layout
        a_smem_layout_staged: cute.ComposedLayout,
        b_smem_layout_staged: cute.ComposedLayout,
        sfa_smem_layout_staged: cute.Layout,
        sfb_smem_layout_staged: cute.Layout,
        c_smem_layout_staged: Union[cute.Layout, cute.ComposedLayout, None],
        epi_tile: cute.Tile,
    ):
        warp_idx = cute.arch.warp_idx()
        warp_idx = cute.arch.make_warp_uniform(warp_idx)

        # Prefetch descriptors with dedicated TMA warp
        if warp_idx == self.tma_warp_id:
            cpasync.prefetch_descriptor(tma_atom_a)
            cpasync.prefetch_descriptor(tma_atom_b)
            cpasync.prefetch_descriptor(tma_atom_sfa)
            cpasync.prefetch_descriptor(tma_atom_sfb)
            cpasync.prefetch_descriptor(tma_atom_c)

        bidx, bidy, bidz = cute.arch.block_idx()
        mma_tile_coord_v = bidx % cute.size(tiled_mma.thr_id.shape)
        cta_rank_in_cluster = cute.arch.make_warp_uniform(
            cute.arch.block_idx_in_cluster()
        )
        block_in_cluster_coord_vmnk = cluster_layout_vmnk.get_flat_coord(
            cta_rank_in_cluster
        )
        block_in_cluster_coord_sfb_vmnk = cluster_layout_sfb_vmnk.get_flat_coord(
            cta_rank_in_cluster
        )

        cta_coord = (bidx, bidy, bidz)
        mma_tile_coord_mnl = (
            cta_coord[0] // cute.size(tiled_mma.thr_id.shape),
            cta_coord[1],
            cta_coord[2],
        )

        tidx, _, _ = cute.arch.thread_idx()

        smem = utils.SmemAllocator()
        storage = smem.allocate(self.shared_storage)

        ab_pipeline_producer_group = pipeline.CooperativeGroup(pipeline.Agent.Thread)
        ab_pipeline_consumer_group = pipeline.CooperativeGroup(
            pipeline.Agent.Thread, 1
        )
        ab_pipeline = pipeline.PipelineTmaUmma.create(
            barrier_storage=storage.ab_full_mbar_ptr.data_ptr(),
            num_stages=self.num_ab_stage,
            producer_group=ab_pipeline_producer_group,
            consumer_group=ab_pipeline_consumer_group,
            tx_count=self.num_tma_load_bytes,
            cta_layout_vmnk=cluster_layout_vmnk,
            defer_sync=True,
        )

        acc_pipeline_producer_group = pipeline.CooperativeGroup(pipeline.Agent.Thread)
        num_acc_consumer_threads = len(self.epilog_warp_id)
        acc_pipeline_consumer_group = pipeline.CooperativeGroup(
            pipeline.Agent.Thread, num_acc_consumer_threads,
        )
        acc_pipeline = pipeline.PipelineUmmaAsync.create(
            barrier_storage=storage.acc_full_mbar_ptr.data_ptr(),
            num_stages=self.num_acc_stage,
            producer_group=acc_pipeline_producer_group,
            consumer_group=acc_pipeline_consumer_group,
            cta_layout_vmnk=cluster_layout_vmnk,
        )
        
        tmem = utils.TmemAllocator(
            storage.tmem_holding_buf,
            barrier_for_retrieve=self.tmem_alloc_barrier,
            allocator_warp_id=self.epilog_warp_id[0],
        )

        pipeline_init_arrive(cluster_shape_mn=self.cluster_shape_mn, is_relaxed=True)

        # (EPI_TILE_M, EPI_TILE_N, STAGE)=((8,16),(32,1),(1,3))
        sC = storage.sC.get_tensor(
            c_smem_layout_staged.outer, swizzle=c_smem_layout_staged.inner
        )
        # (MMA, MMA_M, MMA_K, STAGE)= ((128,64),1,4,7)
        sA = storage.sA.get_tensor(
            a_smem_layout_staged.outer, swizzle=a_smem_layout_staged.inner
        )
        # (MMA, MMA_N, MMA_K, STAGE)=((64,64),1,4,7)
        sB = storage.sB.get_tensor(
            b_smem_layout_staged.outer, swizzle=b_smem_layout_staged.inner
        )
        # (MMA, MMA_M, MMA_K, STAGE)= ((((32,4),1),(16,4)),1,4,7)
        sSFA = storage.sSFA.get_tensor(sfa_smem_layout_staged)
        # (MMA, MMA_N, MMA_K, STAGE)= ((((32,4),1),(16,4)),1,4,7)
        sSFB = storage.sSFB.get_tensor(sfb_smem_layout_staged)

        #
        # Local_tile partition global tensors
        #
        # (bM, bK, RestM, RestK, RestL)=(128,256,?,?,?)
        gA_mkl = cute.local_tile(
            mA_mkl, cute.slice_(self.mma_tiler, (None, 0, None)), (None, None, None)
        )
        # (bN, bK, RestN, RestK, RestL)=(64,256,?,?,?)
        gB_nkl = cute.local_tile(
            mB_nkl, cute.slice_(self.mma_tiler, (0, None, None)), (None, None, None)
        )
        # (bM, bK, RestM, RestK, RestL)=((32,4),(16,4,4),?,?,(1,?))
        gSFA_mkl = cute.local_tile(
            mSFA_mkl, cute.slice_(self.mma_tiler, (None, 0, None)), (None, None, None)
        )
        # (bN, bK, RestN, RestK, RestL)=((32,4),(16,4,4),?,?,(1,?))
        gSFB_nkl = cute.local_tile(
            mSFB_nkl,
            cute.slice_(self.mma_tiler_sfb, (0, None, None)),
            (None, None, None),
        )
        # (bM, bN, RestM, RestN, RestL)=(128,64,?,?,?)
        gC_mnl = cute.local_tile(
            mC_mnl, cute.slice_(self.mma_tiler, (None, None, 0)), (None, None, None)
        )
        k_block_cnt = cute.size(gA_mkl, mode=[3])

        thr_mma = tiled_mma.get_slice(0)
        thr_mma_sfb = tiled_mma_sfb.get_slice(0) # Get slice for SFB

        #
        # Partition global tensor for TiledMMA_A/B/C
        #
        thr_mma = tiled_mma.get_slice(mma_tile_coord_v)
        thr_mma_sfb = tiled_mma_sfb.get_slice(mma_tile_coord_v)
        # (MMA, MMA_M, MMA_K, RestM, RestK, RestL)= ((128,64),1,4,?,?,?)
        tCgA = thr_mma.partition_A(gA_mkl)
        # (MMA, MMA_N, MMA_K, RestN, RestK, RestL)=((64,64),1,4,?,?,?)
        tCgB = thr_mma.partition_B(gB_nkl)
        # (MMA, MMA_M, MMA_K, RestM, RestK, RestL)=(((32,4),(16,4)),1,4,?,?,(1,?))
        tCgSFA = thr_mma.partition_A(gSFA_mkl)
        # (MMA, MMA_N, MMA_K, RestN, RestK, RestL)=(((32,4),(16,4)),1,4,?,?,(1,?))
        tCgSFB = thr_mma_sfb.partition_B(gSFB_nkl)
        # (MMA, MMA_M, MMA_N, RestM, RestN, RestL)=((128,64),1,1,?,?,?)
        tCgC = thr_mma.partition_C(gC_mnl)

        #
        # Partition global/shared tensor for TMA load A/B
        #
        # TMA load A partition_S/D
        a_cta_layout = cute.make_layout(
            cute.slice_(cluster_layout_vmnk, (0, 0, None, 0)).shape
        )
        # ((atom_v, rest_v), STAGE)
        # ((atom_v=(256,128), rest_v), RestM, RestK, RestL)
        tAsA, tAgA = cpasync.tma_partition(
            tma_atom_a,
            block_in_cluster_coord_vmnk[2],
            a_cta_layout,
            cute.group_modes(sA, 0, 3),
            cute.group_modes(tCgA, 0, 3),
        )
        # TMA load B partition_S/D
        b_cta_layout = cute.make_layout(
            cute.slice_(cluster_layout_vmnk, (0, None, 0, 0)).shape
        )
        # ((atom_v, rest_v), STAGE)
        # ((atom_v=(256,64), rest_v), RestN, RestK, RestL)
        tBsB, tBgB = cpasync.tma_partition(
            tma_atom_b,
            block_in_cluster_coord_vmnk[1],
            b_cta_layout,
            cute.group_modes(sB, 0, 3),
            cute.group_modes(tCgB, 0, 3),
        )
        #  TMALDG_SFA partition_S/D
        sfa_cta_layout = a_cta_layout
        # ((atom_v, rest_v), STAGE)
        # ((atom_v=(512,4), rest_v=16->1(after filter)), RestM, RestK, RestL)
        tAsSFA, tAgSFA = cute.nvgpu.cpasync.tma_partition(
            tma_atom_sfa,
            block_in_cluster_coord_vmnk[2],
            sfa_cta_layout,
            cute.group_modes(sSFA, 0, 3),
            cute.group_modes(tCgSFA, 0, 3),
        )
        tAsSFA = cute.filter_zeros(tAsSFA)
        tAgSFA = cute.filter_zeros(tAgSFA)

        # TMALDG_SFB partition_S/D
        sfb_cta_layout = cute.make_layout(
            cute.slice_(cluster_layout_sfb_vmnk, (0, None, 0, 0)).shape
        )
        # ((atom_v, rest_v), STAGE)
        # ((atom_v=(512,4), rest_v=16->1(after filter)), RestM, RestK, RestL)
        tBsSFB, tBgSFB = cute.nvgpu.cpasync.tma_partition(
            tma_atom_sfb,
            block_in_cluster_coord_sfb_vmnk[1],
            sfb_cta_layout,
            cute.group_modes(sSFB, 0, 3),
            cute.group_modes(tCgSFB, 0, 3),
        )
        tBsSFB = cute.filter_zeros(tBsSFB)
        tBgSFB = cute.filter_zeros(tBgSFB)

        # (MMA, MMA_M, MMA_K, STAGE) = (1,1,4,7)
        tCrA = tiled_mma.make_fragment_A(sA)
        # (MMA, MMA_N, MMA_K, STAGE) = (1,1,4,7)
        tCrB = tiled_mma.make_fragment_B(sB)
        # (MMA, MMA_M, MMA_N)=((128, 64), 1, 1)
        acc_shape = tiled_mma.partition_shape_C(self.mma_tiler[:2])
        # (MMA, MMA_M, MMA_N)=((128,64),1,1)
        tCtAcc_fake = tiled_mma.make_fragment_C(acc_shape)

        pipeline_init_wait(cluster_shape_mn=self.cluster_shape_mn)


        # ---------- TMA warp: AB producer ----------
        if warp_idx == self.tma_warp_id:
            # ((atom_v, rest_v), RestK)= (((256,128),1),?)
            tAgA_slice = tAgA[(None, mma_tile_coord_mnl[0], None, mma_tile_coord_mnl[2])]
            # ((atom_v, rest_v), RestK)=(((256,64),1),?)
            tBgB_slice = tBgB[(None, mma_tile_coord_mnl[1], None, mma_tile_coord_mnl[2])]
            # ((atom_v, rest_v), RestK)=(((512,4),1),?)
            tAgSFA_slice = tAgSFA[(None, mma_tile_coord_mnl[0], None, mma_tile_coord_mnl[2])]
            slice_n = mma_tile_coord_mnl[1]
            if cutlass.const_expr(self.cta_tile_shape_mnk[1] == 64):
                slice_n = mma_tile_coord_mnl[1] // 2
            # ((atom_v, rest_v), RestK)=(((512,4),1),?)
            tBgSFB_slice = tBgSFB[(None, slice_n, None, mma_tile_coord_mnl[2])]
            
            ab_producer_state = pipeline.make_pipeline_state(
                pipeline.PipelineUserType.Producer, self.num_ab_stage
            )

            peek_ab_empty_status = ab_pipeline.producer_try_acquire(
                ab_producer_state
            )

            for k_block_idx in cutlass.range(0, k_block_cnt, 1, unroll=1):
                ab_pipeline.producer_acquire(ab_producer_state, peek_ab_empty_status)

                cute.copy(
                    tma_atom_a,
                    tAgA_slice[(None, ab_producer_state.count)],
                    tAsA[(None, ab_producer_state.index)],
                    tma_bar_ptr=ab_pipeline.producer_get_barrier(ab_producer_state),
                )
                cute.copy(
                    tma_atom_b,
                    tBgB_slice[(None, ab_producer_state.count)],
                    tBsB[(None, ab_producer_state.index)],
                    tma_bar_ptr=ab_pipeline.producer_get_barrier(ab_producer_state),
                )
                cute.copy(
                    tma_atom_sfa,
                    tAgSFA_slice[(None, ab_producer_state.count)],
                    tAsSFA[(None, ab_producer_state.index)],
                    tma_bar_ptr=ab_pipeline.producer_get_barrier(ab_producer_state),
                )
                cute.copy(
                    tma_atom_sfb,
                    tBgSFB_slice[(None, ab_producer_state.count)],
                    tBsSFB[(None, ab_producer_state.index)],
                    tma_bar_ptr=ab_pipeline.producer_get_barrier(ab_producer_state),
                )

                ab_producer_state.advance()
                if ab_producer_state.count < k_block_cnt:
                    peek_ab_empty_status = ab_pipeline.producer_try_acquire(
                        ab_producer_state
                    )

            ab_pipeline.producer_tail(ab_producer_state)

        # ---------- MMA warp: AB consumer + GEMM + ACC producer ----------
        if warp_idx == self.mma_warp_id:

            tmem.wait_for_alloc()
            #
            # Retrieving tensor memory ptr and make accumulator/SFA/SFB tensor
            #
            acc_tmem_ptr = tmem.retrieve_ptr(self.acc_dtype) # tcgen05.find_tmem_tensor_col_offset(tCtAcc) = 64
            # Make accumulator tmem tensor
            # (MMA, MMA_M, MMA_N, STAGE)= ((128,64),1,1)
            tCtAcc = cute.make_tensor(acc_tmem_ptr, tCtAcc_fake.layout)
            # Make SFA tmem tensor    
            sfa_tmem_ptr = cute.recast_ptr(
                acc_tmem_ptr + tcgen05.find_tmem_tensor_col_offset(tCtAcc),
                dtype=self.sf_dtype,
            )
            # (MMA, MMA_M, MMA_K)=((((32,4),4),(16,4)),1,4)
            tCtSFA_layout = blockscaled_utils.make_tmem_layout_sfa(
                tiled_mma,
                self.mma_tiler,
                self.sf_vec_size,
                cute.slice_(sfa_smem_layout_staged, (None, None, None, 0)),
            )
            tCtSFA = cute.make_tensor(sfa_tmem_ptr, tCtSFA_layout) #tcgen05.find_tmem_tensor_col_offset(tCtSFA) = 16
            # Make SFB tmem tensor
            sfb_tmem_ptr = cute.recast_ptr(
                acc_tmem_ptr
                + tcgen05.find_tmem_tensor_col_offset(tCtAcc)
                + tcgen05.find_tmem_tensor_col_offset(tCtSFA),
                dtype=self.sf_dtype,
            )
            # (MMA, MMA_N, MMA_K)=((((32,4),4),(16,4)),1,4)
            tCtSFB_layout = blockscaled_utils.make_tmem_layout_sfb(
                tiled_mma,
                self.mma_tiler,
                self.sf_vec_size,
                cute.slice_(sfb_smem_layout_staged, (None, None, None, 0)),
            )
            tCtSFB = cute.make_tensor(sfb_tmem_ptr, tCtSFB_layout) #tcgen05.find_tmem_tensor_col_offset(tCtSFB)=16
            #
            # Partition for S2T copy of SFA/SFB
            #
            # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)=((((32, 1, 1), 4), 1), 1, 1, 4, 7)
            # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K)=(((32, 16, 4), 1), 1, 1, 4)
            tiled_copy_s2t_sfa, tCsSFA_compact_s2t, tCtSFA_compact_s2t = (
                self.mainloop_s2t_copy_and_partition(sSFA, tCtSFA)
            )
            # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)=((((32, 1, 1), 4), 1), 1, 1, 4, 7)
            # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K)=(((32, 16, 4), 1), 1, 1, 4)
            tiled_copy_s2t_sfb, tCsSFB_compact_s2t, tCtSFB_compact_s2t = (
                self.mainloop_s2t_copy_and_partition(sSFB, tCtSFB)
            )
            ab_consumer_state = pipeline.make_pipeline_state(
                pipeline.PipelineUserType.Consumer, self.num_ab_stage
            )
            acc_producer_state = pipeline.make_pipeline_state(
                pipeline.PipelineUserType.Producer, self.num_acc_stage
            )

            # Peek initial full
            peek_ab_full_status = ab_pipeline.consumer_try_wait(
                ab_consumer_state
            )
            
            tCtSFB_mma = tCtSFB
            if cutlass.const_expr(self.cta_tile_shape_mnk[1] == 64):
                # Move in increments of 64 columns of SFB
                offset = cutlass.Int32((mma_tile_coord_mnl[1] % 2) * 2)
                shifted_ptr = cute.recast_ptr(
                    acc_tmem_ptr
                    + tcgen05.find_tmem_tensor_col_offset(tCtAcc)
                    + tcgen05.find_tmem_tensor_col_offset(tCtSFA)
                    + offset,
                    dtype=self.sf_dtype,
                )
                tCtSFB_mma = cute.make_tensor(shifted_ptr, tCtSFB_layout)


            tiled_mma.set(tcgen05.Field.ACCUMULATE, False)

            for _ in range(k_block_cnt):
                ab_pipeline.consumer_wait(ab_consumer_state, peek_ab_full_status)

                s2t_stage_coord = (
                    None,
                    None,
                    None,
                    None,
                    ab_consumer_state.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,
                )

                num_kphases = cute.size(tCrA, mode=[2])
                for kphase_idx in cutlass.range(num_kphases, unroll_full=True):
                    kphase_coord = (
                        None,
                        None,
                        kphase_idx,
                        ab_consumer_state.index,
                    )
                    sf_kphase_coord = (None, None, kphase_idx)
                    tiled_mma.set(
                        tcgen05.Field.SFA,
                        tCtSFA[sf_kphase_coord].iterator,
                    )
                    tiled_mma.set(
                        tcgen05.Field.SFB,
                        tCtSFB_mma[sf_kphase_coord].iterator,
                    )

                    cute.gemm(
                        tiled_mma,
                        tCtAcc,
                        tCrA[kphase_coord],
                        tCrB[kphase_coord],
                        tCtAcc,
                    )
                    tiled_mma.set(tcgen05.Field.ACCUMULATE, True)

                ab_pipeline.consumer_release(ab_consumer_state)

                ab_consumer_state.advance()
                if ab_consumer_state.count < k_block_cnt:
                    peek_ab_full_status = ab_pipeline.consumer_try_wait(
                        ab_consumer_state
                    )

            acc_pipeline.producer_commit(acc_producer_state)
        
        if warp_idx in self.epilog_warp_id:

            tmem.allocate(self.num_tmem_alloc_cols)
            #
            # Bar sync for retrieve tensor memory ptr from shared memory
            #
            tmem.wait_for_alloc()

            #
            # Retrieving tensor memory ptr and make accumulator tensor
            #
            acc_tmem_ptr = tmem.retrieve_ptr(self.acc_dtype)
            # (MMA, MMA_M, MMA_N, STAGE)
            tCtAcc = cute.make_tensor(acc_tmem_ptr, tCtAcc_fake.layout)

            tiled_copy_t2r, tTR_tAcc, tTR_rAcc = self.epilog_tmem_copy_and_partition(
                tidx, tCtAcc, tCgC, epi_tile
            )

            tTR_rC = cute.make_fragment(tTR_rAcc.shape, self.c_dtype)
            tiled_copy_r2s, tRS_rC, tRS_sC = self.epilog_smem_copy_and_partition(
                tiled_copy_t2r, tTR_rC, tidx, sC
            )
            tma_atom_c, bSG_sC, bSG_gC = self.epilog_gmem_copy_and_partition(
                tidx, tma_atom_c, tCgC, epi_tile, sC
            )
            bSG_gC = bSG_gC[(None, None, None, *mma_tile_coord_mnl)]

            acc_consumer_state = pipeline.make_pipeline_state(
                pipeline.PipelineUserType.Consumer, self.num_acc_stage
            )

            c_producer_group = pipeline.CooperativeGroup(
                pipeline.Agent.Thread,
                32 * len(self.epilog_warp_id),
                32 * len(self.epilog_warp_id),
            )

            c_pipeline = pipeline.PipelineTmaStore.create(
                num_stages=self.num_c_stage,
                producer_group=c_producer_group,
            )

            tmem.relinquish_alloc_permit()
            acc_pipeline.consumer_wait(acc_consumer_state)

            tTR_tAcc = cute.group_modes(tTR_tAcc, 3, cute.rank(tTR_tAcc))
            bSG_gC = cute.group_modes(bSG_gC, 1, cute.rank(bSG_gC))

            #
            # Store accumulator to global memory in subtiles
            #
            subtile_cnt = cute.size(tTR_tAcc.shape, mode=[3])

            for subtile_idx in range(subtile_cnt):
                #
                # Load accumulator from tensor memory buffer to register
                #
                tTR_tAcc_mn = tTR_tAcc[(None, None, None, subtile_idx)]
                cute.copy(tiled_copy_t2r, tTR_tAcc_mn, tTR_rAcc)

                #
                # Perform epilogue op on accumulator and convert to C type
                #
                acc_vec = tiled_copy_r2s.retile(tTR_rAcc).load()
                acc_vec = acc_vec.to(self.c_dtype)
                tRS_rC.store(acc_vec)

                #
                # Store C to shared memory
                #
                c_buffer = subtile_idx % self.num_c_stage
                cute.copy(tiled_copy_r2s, tRS_rC, tRS_sC[(None, None, None, c_buffer)])
                # Fence and barrier to make sure shared memory store is visible to TMA store
                cute.arch.fence_proxy(
                    cute.arch.ProxyKind.async_shared,
                    space=cute.arch.SharedSpace.shared_cta,
                )

                self.epilog_sync_barrier.arrive_and_wait()

                if warp_idx == self.epilog_warp_id[0]:
                    cute.copy(
                        tma_atom_c,
                        bSG_sC[(None, c_buffer)],
                        bSG_gC[(None, subtile_idx)],
                    )
                    c_pipeline.producer_commit()
                    c_pipeline.producer_acquire()
                self.epilog_sync_barrier.arrive_and_wait()


            self.epilog_sync_barrier.arrive_and_wait()
            tmem.free(acc_tmem_ptr)
    
    def mainloop_s2t_copy_and_partition(
        self,
        sSF: cute.Tensor,
        tSF: cute.Tensor,
    ) -> Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]:
        """
        Make tiledCopy for smem to tmem load for scale factor tensor, then use it to partition smem memory (source) and tensor memory (destination).

        :param sSF: The scale factor tensor in smem
        :type sSF: cute.Tensor
        :param tSF: The scale factor tensor in tmem
        :type tSF: cute.Tensor

        :return: A tuple containing (tiled_copy_s2t, tCsSF_compact_s2t, tCtSF_compact_s2t) where:
            - tiled_copy_s2t: The tiled copy operation for smem to tmem load for scale factor tensor(s2t)
            - tCsSF_compact_s2t: The partitioned scale factor tensor in smem
            - tSF_compact_s2t: The partitioned scale factor tensor in tmem
        :rtype: Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]
        """
        # (MMA, MMA_MN, MMA_K, STAGE)
        tCsSF_compact = cute.filter_zeros(sSF)
        # (MMA, MMA_MN, MMA_K)
        tCtSF_compact = cute.filter_zeros(tSF)

        # Make S2T CopyAtom and tiledCopy
        copy_atom_s2t = cute.make_copy_atom(
            tcgen05.Cp4x32x128bOp(tcgen05.CtaGroup.ONE),
            self.sf_dtype,
        )
        tiled_copy_s2t = tcgen05.make_s2t_copy(copy_atom_s2t, tCtSF_compact)
        thr_copy_s2t = tiled_copy_s2t.get_slice(0)

        # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
        tCsSF_compact_s2t_ = thr_copy_s2t.partition_S(tCsSF_compact)
        # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K, STAGE)
        tCsSF_compact_s2t = tcgen05.get_s2t_smem_desc_tensor(
            tiled_copy_s2t, tCsSF_compact_s2t_
        )
        # ((ATOM_V, REST_V), Rest_Tiler, MMA_MN, MMA_K)
        tCtSF_compact_s2t = thr_copy_s2t.partition_D(tCtSF_compact)

        return tiled_copy_s2t, tCsSF_compact_s2t, tCtSF_compact_s2t

    def epilog_tmem_copy_and_partition(
        self,
        tidx: cutlass.Int32,
        tAcc: cute.Tensor,
        gC_mnl: cute.Tensor,
        epi_tile: cute.Tile,
    ) -> Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]:
        """
        Make tiledCopy for tensor memory load, then use it to partition tensor memory (source) and register array (destination).

        :param tidx: The thread index in epilogue warp groups
        :type tidx: cutlass.Int32
        :param tAcc: The accumulator tensor to be copied and partitioned
        :type tAcc: cute.Tensor
        :param gC_mnl: The global tensor C
        :type gC_mnl: cute.Tensor
        :param epi_tile: The epilogue tiler
        :type epi_tile: cute.Tile

        :return: A tuple containing (tiled_copy_t2r, tTR_tAcc, tTR_rAcc) where:
            - tiled_copy_t2r: The tiled copy operation for tmem to register copy(t2r)
            - tTR_tAcc: The partitioned accumulator tensor
            - tTR_rAcc: The accumulated tensor in register used to hold t2r results
        :rtype: Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]
        """
        # Make tiledCopy for tensor memory load
        copy_atom_t2r = sm100_utils.get_tmem_load_op(
            self.cta_tile_shape_mnk,
            self.c_layout,
            self.c_dtype,
            self.acc_dtype,
            epi_tile,
            False
        )
        # (EPI_TILE_M, EPI_TILE_N, EPI_M, EPI_N)
        tAcc_epi = cute.flat_divide(
            tAcc[((None, None), 0, 0)],
            epi_tile,
        )
        # (EPI_TILE_M, EPI_TILE_N)
        tiled_copy_t2r = tcgen05.make_tmem_copy(
            copy_atom_t2r, tAcc_epi[(None, None, 0, 0)]
        )

        thr_copy_t2r = tiled_copy_t2r.get_slice(tidx)
        # (T2R, T2R_M, T2R_N, EPI_M, EPI_M)
        tTR_tAcc = thr_copy_t2r.partition_S(tAcc_epi)

        # (EPI_TILE_M, EPI_TILE_N, EPI_M, EPI_N, RestM, RestN, RestL)
        gC_mnl_epi = cute.flat_divide(
            gC_mnl[((None, None), 0, 0, None, None, None)], epi_tile
        )
        # (T2R, T2R_M, T2R_N, EPI_M, EPI_N, RestM, RestN, RestL)
        tTR_gC = thr_copy_t2r.partition_D(gC_mnl_epi)
        # (T2R, T2R_M, T2R_N)
        tTR_rAcc = cute.make_fragment(
            tTR_gC[(None, None, None, 0, 0, 0, 0, 0)].shape, self.acc_dtype
        )
        return tiled_copy_t2r, tTR_tAcc, tTR_rAcc

    def epilog_smem_copy_and_partition(
        self,
        tiled_copy_t2r: cute.TiledCopy,
        tTR_rC: cute.Tensor,
        tidx: cutlass.Int32,
        sC: cute.Tensor,
    ) -> Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]:
        """
        Make tiledCopy for shared memory store, then use it to partition register array (source) and shared memory (destination).

        :param tiled_copy_t2r: The tiled copy operation for tmem to register copy(t2r)
        :type tiled_copy_t2r: cute.TiledCopy
        :param tTR_rC: The partitioned accumulator tensor
        :type tTR_rC: cute.Tensor
        :param tidx: The thread index in epilogue warp groups
        :type tidx: cutlass.Int32
        :param sC: The shared memory tensor to be copied and partitioned
        :type sC: cute.Tensor

        :return: A tuple containing (tiled_copy_r2s, tRS_rC, tRS_sC) where:
            - tiled_copy_r2s: The tiled copy operation for register to smem copy(r2s)
            - tRS_rC: The partitioned tensor C (register source)
            - tRS_sC: The partitioned tensor C (smem destination)
        :rtype: Tuple[cute.TiledCopy, cute.Tensor, cute.Tensor]
        """
        copy_atom_r2s = sm100_utils.get_smem_store_op(
            self.c_layout, self.c_dtype, self.acc_dtype, tiled_copy_t2r
        )
        tiled_copy_r2s = cute.make_tiled_copy_D(copy_atom_r2s, tiled_copy_t2r)
        # (R2S, R2S_M, R2S_N, PIPE_D)
        thr_copy_r2s = tiled_copy_r2s.get_slice(tidx)
        tRS_sC = thr_copy_r2s.partition_D(sC)
        # (R2S, R2S_M, R2S_N)
        tRS_rC = tiled_copy_r2s.retile(tTR_rC)
        return tiled_copy_r2s, tRS_rC, tRS_sC

    def epilog_gmem_copy_and_partition(
        self,
        tidx: cutlass.Int32,
        atom: Union[cute.CopyAtom, cute.TiledCopy],
        gC_mnl: cute.Tensor,
        epi_tile: cute.Tile,
        sC: cute.Tensor,
    ) -> Tuple[cute.CopyAtom, cute.Tensor, cute.Tensor]:
        """Make tiledCopy for global memory store, then use it to:
        partition shared memory (source) and global memory (destination) for TMA store version.

        :param tidx: The thread index in epilogue warp groups
        :type tidx: cutlass.Int32
        :param atom: The copy_atom_c to be used for TMA store version, or tiled_copy_t2r for none TMA store version
        :type atom: cute.CopyAtom or cute.TiledCopy
        :param gC_mnl: The global tensor C
        :type gC_mnl: cute.Tensor
        :param epi_tile: The epilogue tiler
        :type epi_tile: cute.Tile
        :param sC: The shared memory tensor to be copied and partitioned
        :type sC: cute.Tensor

        :return: A tuple containing (tma_atom_c, bSG_sC, bSG_gC) where:
            - tma_atom_c: The TMA copy atom
            - bSG_sC: The partitioned shared memory tensor C
            - bSG_gC: The partitioned global tensor C
        :rtype: Tuple[cute.CopyAtom, cute.Tensor, cute.Tensor]
        """
        # (EPI_TILE_M, EPI_TILE_N, EPI_M, EPI_N, RestM, RestN, RestL)
        gC_epi = cute.flat_divide(
            gC_mnl[((None, None), 0, 0, None, None, None)], epi_tile
        )

        tma_atom_c = atom
        sC_for_tma_partition = cute.group_modes(sC, 0, 2)
        gC_for_tma_partition = cute.group_modes(gC_epi, 0, 2)
        # ((ATOM_V, REST_V), EPI_M, EPI_N)
        # ((ATOM_V, REST_V), EPI_M, EPI_N, RestM, RestN, RestL)
        bSG_sC, bSG_gC = cpasync.tma_partition(
            tma_atom_c,
            0,
            cute.make_layout(1),
            sC_for_tma_partition,
            gC_for_tma_partition,
        )
        return tma_atom_c, bSG_sC, bSG_gC
    
    @staticmethod
    def _compute_stages(
        tiled_mma: cute.TiledMma,
        mma_tiler_mnk: Tuple[int, int, int],
        a_dtype: Type[cutlass.Numeric],
        b_dtype: Type[cutlass.Numeric],
        epi_tile: cute.Tile,
        c_dtype: Type[cutlass.Numeric],
        c_layout: utils.LayoutEnum,
        sf_dtype: Type[cutlass.Numeric],
        sf_vec_size: int,
        smem_capacity: int,
        occupancy: int,
    ) -> Tuple[int, int, int]:
        """Computes the number of stages for A/B/C operands based on heuristics.

        :param tiled_mma: The tiled MMA object defining the core computation.
        :type tiled_mma: cute.TiledMma
        :param mma_tiler_mnk: The shape (M, N, K) of the MMA tiler.
        :type mma_tiler_mnk: tuple[int, int, int]
        :param a_dtype: Data type of operand A.
        :type a_dtype: type[cutlass.Numeric]
        :param b_dtype: Data type of operand B.
        :type b_dtype: type[cutlass.Numeric]
        :param epi_tile: The epilogue tile shape.
        :type epi_tile: cute.Tile
        :param c_dtype: Data type of operand C (output).
        :type c_dtype: type[cutlass.Numeric]
        :param c_layout: Layout enum of operand C.
        :type c_layout: utils.LayoutEnum
        :param sf_dtype: Data type of Scale factor.
        :type sf_dtype: type[cutlass.Numeric]
        :param sf_vec_size: Scale factor vector size.
        :type sf_vec_size: int
        :param smem_capacity: Total available shared memory capacity in bytes.
        :type smem_capacity: int
        :param occupancy: Target number of CTAs per SM (occupancy).
        :type occupancy: int

        :return: A tuple containing the computed number of stages for:
                 (ACC stages, A/B operand stages, C stages)
        :rtype: tuple[int, int, int]
        """
        # ACC stages
        num_acc_stage = 1 if mma_tiler_mnk[1] == 256 else 2

        # Default C stages
        num_c_stage = 2

        # Calculate smem layout and size for one stage of A, B, SFA, SFB and C
        a_smem_layout_stage_one = sm100_utils.make_smem_layout_a(
            tiled_mma,
            mma_tiler_mnk,
            a_dtype,
            1,  # a tmp 1 stage is provided
        )
        b_smem_layout_staged_one = sm100_utils.make_smem_layout_b(
            tiled_mma,
            mma_tiler_mnk,
            b_dtype,
            1,  # a tmp 1 stage is provided
        )
        sfa_smem_layout_staged_one = blockscaled_utils.make_smem_layout_sfa(
            tiled_mma,
            mma_tiler_mnk,
            sf_vec_size,
            1,  # a tmp 1 stage is provided
        )
        sfb_smem_layout_staged_one = blockscaled_utils.make_smem_layout_sfb(
            tiled_mma,
            mma_tiler_mnk,
            sf_vec_size,
            1,  # a tmp 1 stage is provided
        )

        c_smem_layout_staged_one = sm100_utils.make_smem_layout_epi(
            c_dtype,
            c_layout,
            epi_tile,
            1,
        )

        ab_bytes_per_stage = (
            cute.size_in_bytes(a_dtype, a_smem_layout_stage_one)
            + cute.size_in_bytes(b_dtype, b_smem_layout_staged_one)
            + cute.size_in_bytes(sf_dtype, sfa_smem_layout_staged_one)
            + cute.size_in_bytes(sf_dtype, sfb_smem_layout_staged_one)
        )
        mbar_helpers_bytes = 1024
        c_bytes_per_stage = cute.size_in_bytes(c_dtype, c_smem_layout_staged_one)
        c_bytes = c_bytes_per_stage * num_c_stage

        # Calculate A/B/SFA/SFB stages:
        # Start with total smem per CTA (capacity / occupancy)
        # Subtract reserved bytes and initial C stages bytes
        # Divide remaining by bytes needed per A/B/SFA/SFB stage
        num_ab_stage = (
            smem_capacity // occupancy - (mbar_helpers_bytes + c_bytes)
        ) // ab_bytes_per_stage

        # Refine epilogue stages:
        # Calculate remaining smem after allocating for A/B/SFA/SFB stages and reserved bytes
        # Add remaining unused smem to epilogue
        num_c_stage += (
            smem_capacity
            - occupancy * ab_bytes_per_stage * num_ab_stage
            - occupancy * (mbar_helpers_bytes + c_bytes)
        ) // (occupancy * c_bytes_per_stage)

        return num_acc_stage, num_ab_stage, num_c_stage

    @staticmethod
    def _compute_grid(
        c: cute.Tensor,
        cta_tile_shape_mnk: Tuple[int, int, int],
        cluster_shape_mn: Tuple[int, int],
    ) -> Tuple[int, int, int]:
        """Compute grid shape for the output tensor C.

        :param c: The output tensor C
        :type c: cute.Tensor
        :param cta_tile_shape_mnk: The shape (M, N, K) of the CTA tile.
        :type cta_tile_shape_mnk: tuple[int, int, int]
        :param cluster_shape_mn: Shape of each cluster in M, N dimensions.
        :type cluster_shape_mn: tuple[int, int]

        :return: Grid shape for kernel launch.
        :rtype: tuple[int, int, int]
        """

        cluster_shape_mnl = (*cluster_shape_mn, 1)

        grid = cute.round_up(
            (
                cute.ceil_div(c.layout.shape[0], cta_tile_shape_mnk[0]),
                cute.ceil_div(c.layout.shape[1], cta_tile_shape_mnk[1]),
                c.layout.shape[2],
            ),
            cluster_shape_mnl,
        )

        return grid
    


_compiled_kernel_cache = None

def compile_kernel():
    """
    Compile the GEMM kernel once and cache it.
    Returns the compiled kernel function.
    """
    global _compiled_kernel_cache
    if _compiled_kernel_cache is not None:
        return _compiled_kernel_cache

    # Dummy pointers just for compilation
    a_ptr = make_ptr(ab_dtype, 0, cute.AddressSpace.gmem, assumed_align=16)
    b_ptr = make_ptr(ab_dtype, 0, cute.AddressSpace.gmem, assumed_align=16)
    c_ptr = make_ptr(c_dtype, 0, cute.AddressSpace.gmem, assumed_align=16)
    sfa_ptr = make_ptr(sf_dtype, 0, cute.AddressSpace.gmem, assumed_align=32)
    sfb_ptr = make_ptr(sf_dtype, 0, cute.AddressSpace.gmem, assumed_align=32)

    _compiled_kernel_cache = cute.compile(
        Sm100BlockScaledDenseGemmKernel((128,64), (1,1)),
        a_ptr,
        b_ptr,
        sfa_ptr,
        sfb_ptr,
        c_ptr,
        (0, 0, 0, 0),
    )
    return _compiled_kernel_cache

def custom_kernel(data: input_t) -> output_t:
    """
    Execute the block-scaled GEMM kernel.


    Args:
        data: Tuple of (a, b, sfa, sfb, c) PyTorch tensors
            a: [m, k/2, l] in float4_e2m1_x2 (logical K = 2 * a.shape[1])
            b: [n, k/2, l] in float4_e2m1_x2
            sfa: [m, k, l] scale factors in float8_e4m3fn
            sfb: [n, k, l] scale factors in float8_e4m3fn
            c: [m, n, l] output in float16


    Returns:
        The output tensor c with computed GEMM results.
    """
    a, b, _, _, sfa, sfb, c = data

    # Logical sizes: PyTorch fp4 uses x2 packing on K dimension
    m, k_packed, l = a.shape
    n, k_packed_b, l_b = b.shape
    k = k_packed * 2  # logical K

    compiled_func = compile_kernel()

    # CuTe pointers for A/B/C/SFA/SFB via torch tensor data pointer
    a_ptr = make_ptr(ab_dtype, a.data_ptr(), cute.AddressSpace.gmem, assumed_align=16)
    b_ptr = make_ptr(ab_dtype, b.data_ptr(), cute.AddressSpace.gmem, assumed_align=16)
    c_ptr = make_ptr(c_dtype, c.data_ptr(), cute.AddressSpace.gmem, assumed_align=16)
    sfa_ptr = make_ptr(
        sf_dtype, sfa.data_ptr(), cute.AddressSpace.gmem, assumed_align=32
    )
    sfb_ptr = make_ptr(
        sf_dtype, sfb.data_ptr(), cute.AddressSpace.gmem, assumed_align=32
    )

    # Execute the compiled kernel
    compiled_func(a_ptr, b_ptr, sfa_ptr, sfb_ptr, c_ptr, (m, n, k, l))

    return c