venv/lib/python3.10/site-packages/bitblas/gpu/matmul_analysis.py

# Copyright (c) Microsoft Corporation.
# Licensed under the MIT License.

# pylint: disable=missing-docstring, invalid-name
"""A GEMM schedule rule for GPU operators."""
from dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Set, Union, Tuple, Dict
from tvm import tir
from tvm.ir import Range
from tvm.tir import IterVar, PrimExpr, Var, BufferRegion, IndexMap
from tvm.tir.analysis import undefined_vars
from tvm.tir.schedule.schedule import BlockRV
from ..base.analysis import (
    collect_block_iter_vars_used_in_access_region,
    get_root_block,
    get_reduction_blocks,
)
from tvm.target.target import Target
from tvm.tir.stmt_functor import pre_order_visit
from bitblas.base.arch import get_arch, is_tensorcore_supported_precision
import logging

logger = logging.getLogger(__name__)


def collect_vars_from_expr(prim_expr):
    vars = []

    def callback(node):
        if isinstance(node, Var):
            vars.append(node)
        return True

    pre_order_visit(prim_expr, callback)

    return vars


def _is_one(x: PrimExpr) -> bool:
    return isinstance(x, tir.IntImm) and x.value == 1


def _collect_producers(sch: tir.Schedule, block: tir.schedule.BlockRV):
    result = []
    for producer in sch.get_producers(block):
        result.append(producer)
        result.extend(_collect_producers(sch, producer))
    return result


def _collect_consumers(sch: tir.Schedule, block: tir.schedule.BlockRV):
    result = []
    for consumer in sch.get_consumers(block):
        result.append(consumer)
        result.extend(_collect_consumers(sch, consumer))
    return result


def auto_inline_producers(
    sch: tir.Schedule,
    block: tir.schedule.BlockRV,
    skip_blocks: Optional[List[tir.schedule.BlockRV]] = None,
):
    skip_blocks = skip_blocks or []
    while True:
        inlined_cnt = 0
        producers = _collect_producers(sch, block)
        for producer in producers:
            if any(sch.get(producer) == sch.get(skip_block) for skip_block in skip_blocks):
                continue
            try:
                sch.compute_inline(producer)
                inlined_cnt += 1
            except Exception:  # pylint: disable=bare-except
                continue
        if inlined_cnt == 0:
            return


def auto_inline_consumers(
    sch: tir.Schedule,
    block: tir.schedule.BlockRV,
):
    while True:
        inlined_cnt = 0
        consumers = _collect_consumers(sch, block)
        for consumer in consumers:
            try:
                sch.compute_inline(consumer)
                inlined_cnt += 1
            except Exception:  # pylint: disable=bare-except
                continue
        for consumer in consumers:
            try:
                sch.reverse_compute_inline(consumer)
                inlined_cnt += 1
            except Exception:  # pylint: disable=bare-except
                continue
        if inlined_cnt == 0:
            return


def auto_inline_consumer_chain(
    sch: tir.Schedule,
    block: tir.schedule.BlockRV,
):
    auto_inline_consumers(sch, block)
    remaining_consumers = sch.get_consumers(block)

    if len(remaining_consumers) != 0:
        # Some blocks have failed to be inlined to the producer cache-write stage.
        # This could be due to another producer block that has not been scheduled.
        for c in remaining_consumers:
            for p in sch.get_producers(c):
                if sch.get(p) != sch.get(block):
                    sch.compute_inline(p)

        # Try inlining into the cache-write stage again, this time it should succeed.
        auto_inline_consumers(sch, block)


# used to match the similar region with dequantize op.
def find_first_similar_region(regions: List[BufferRegion], buffer: tir.Buffer):
    for region in regions:
        if len(region.buffer.shape) == len(buffer.shape):
            return region
    return None


# used to match the similar buffer with dequantize op.
def find_first_similar_buffer(regions: List[BufferRegion], buffer: tir.Buffer):
    for region in regions:
        if len(region.buffer.shape) == len(buffer.shape):
            return region.buffer
    return None


# find the block that required to be reindex and scope.
def find_last_producer_from_buffer(sch, main_block, buffer: tir.Buffer) -> Optional[BlockRV]:
    # block that most near to the arguments
    block = main_block
    buffer = buffer

    while True:
        last_buffer = buffer
        producers = sch.get_producers(block)

        if len(producers) == 0:
            # do not have any producer means it is the first block
            break

        for producer in producers:
            for write in sch.get(producer).writes:
                if write.buffer == buffer:
                    block = producer
                    buffer = find_first_similar_buffer(sch.get(producer).reads, last_buffer)
        if buffer == last_buffer:
            break
    return block


def find_arg_idx_from_buffer_chain(sch: tir.Schedule, main_block: tir.schedule.BlockRV,
                                   buffer: tir.Buffer) -> int:
    """traverse to find the arg index from the buffer"""
    producers = sch.get_producers(main_block)

    # a head buffer has no producer blocks
    def find_args_index(sch: tir.Schedule, buffer: tir.Buffer):
        for i, param in enumerate(sch.mod["main"].params):
            if sch.mod["main"].buffer_map[param] == buffer:
                return i
        return None

    is_head_buffer = len(producers) == 0
    if is_head_buffer:
        return find_args_index(sch, buffer)
    for block in sch.get_producers(main_block):
        if len(sch.get(block).reads) != 1 or len(sch.get(block).writes) != 1:
            continue
        for write in sch.get(block).writes:
            if write.buffer == buffer:
                return find_arg_idx_from_buffer_chain(sch, block, buffer)

    # if no buffer producer block found, it means the buffer is an input buffer
    return find_args_index(sch, buffer)


class IterKind(Enum):
    """Iter kinds for GEMM-liked programs.
    We can simplify the computation to C[S, I, J] += A[S, I, K] * B[S, J, K],
    where `I, J, K` are fundamental axes for gemm and `S` represents all
    other spatial axes (e.g. batches)
    kIter_S: spatial axes
    kIter_I: I axes
    kIter_J: J axes
    kIter_K: K axes
    kIter_T: trivial axes (i.e. with extent 1)
    """

    kIter_S = 0
    kIter_I = 1
    kIter_J = 2
    kIter_K = 3
    kIter_T = 4


@dataclass
class IterTrait:
    kind: IterKind
    extent: PrimExpr


def make_iter_fusion_index_map(
    traits: List[IterTrait],
    kind_order: List[IterKind],
) -> tir.IndexMap:
    fused_iters: Dict[IterKind, PrimExpr] = {}
    input_iters: List[tir.Var] = []
    for i, trait in enumerate(traits):
        v_i = tir.Var(f"i{i}", trait.extent.dtype)
        input_iters.append(v_i)
        if trait.kind == IterKind.kIter_T:
            continue
        if trait.kind not in kind_order:
            raise ValueError(f"Unknown iter kind {trait.kind}")
        if trait.kind in fused_iters:
            fused_iters[trait.kind] = fused_iters[trait.kind] * trait.extent + v_i
        else:
            fused_iters[trait.kind] = v_i

    final_indices: List[tir.PrimExpr] = [
        fused_iters.get(kind, tir.IntImm(traits[0].extent.dtype, 0)) for kind in kind_order
    ]

    return tir.IndexMap(input_iters, final_indices, None)


def detect_iter_traits(block: tir.Block) -> Optional[Tuple[List[IterTrait]]]:
    """Detect iter traits based on the pattern C[S, I, J] += A[S, I, K] * B[S, J, K]

    Parameters
    ----------
    block : tir.Block
        The block to be analyzed

    Returns
    -------
    traits : Optional[Tuple[List[IterTrait]]]
        The detected iter traits for axes in A, B and C. None if the block
        does not match the pattern.

    """

    if len(block.reads) != 2 or len(block.writes) != 1:
        return None

    def get_access_axes(region: List[Range]) -> Set[Var]:
        axes: Set[Var] = set()
        for r in region:
            if not _is_one(r.extent):
                raise ValueError("Expect elemwise block access")
            axes = axes.union(set(undefined_vars(r.min)))
        return axes

    try:
        A_axes = get_access_axes(block.reads[0].region)
        B_axes = get_access_axes(block.reads[1].region)
        C_axes = get_access_axes(block.writes[0].region)
    except ValueError:
        return None

    traits: Dict[Var, IterTrait] = {}
    for iter_var in block.iter_vars:
        var = iter_var.var
        kind: IterKind
        if _is_one(iter_var.dom.extent):
            if iter_var.iter_type == tir.IterVar.CommReduce:
                # for simplified case (e.g. 1x1 conv kernel)
                kind = IterKind.kIter_K
            else:
                kind = IterKind.kIter_T
        elif iter_var.iter_type == iter_var.DataPar:
            if var in A_axes and var in B_axes and var in C_axes:
                kind = IterKind.kIter_S
            elif var in A_axes and var in C_axes:
                kind = IterKind.kIter_I
            elif var in B_axes and var in C_axes:
                kind = IterKind.kIter_J
            else:
                return None
        elif iter_var.iter_type == tir.IterVar.CommReduce:
            if var in A_axes and var in B_axes and var not in C_axes:
                kind = IterKind.kIter_K
            else:
                return None
        else:
            return None
        traits[var] = IterTrait(kind, iter_var.dom.extent)

    # A Gemm-kernel requires have I, J and K axes
    gemm_traits = {IterKind.kIter_I, IterKind.kIter_J, IterKind.kIter_K}
    if {x.kind for x in traits.values()}.intersection(gemm_traits) != gemm_traits:
        return None

    A_traits = [traits[iter_var.var] for iter_var in block.iter_vars if iter_var.var in A_axes]
    B_traits = [traits[iter_var.var] for iter_var in block.iter_vars if iter_var.var in B_axes]
    C_traits = [traits[iter_var.var] for iter_var in block.iter_vars if iter_var.var in C_axes]
    block_traits = [traits[i.var] for i in block.iter_vars]
    return A_traits, B_traits, C_traits, block_traits


def get_index_map(block: tir.Block,
                  layout: Optional[List[str]] = None) -> Optional[Tuple[tir.IndexMap, ...]]:
    """Get index maps for the block

    Parameters
    ----------
    block : tir.Block
        The block to be analyzed

    layout : List[str]
        the target layout index map to be used.
        'n' for [i, k] layout
        't' for [k, j] layout
        'a' for auto inference based on whether the last axis is reduction.

    Returns
    -------
    index_maps : Optional[Tuple[tir.IndexMap]]
        The index maps for the block, or None if the block is not a gemm-liked kernel
    """
    if layout is None:
        layout = ["n", "t", "n"]
    traits = detect_iter_traits(block)
    if traits is None:
        return None
    A_traits, B_traits, C_traits, block_traits = traits

    def get_ordered_axes(region: List[Range]) -> Set[Var]:
        axes: List[Var] = []
        for r in region:
            if not _is_one(r.extent):
                raise ValueError("Expect elemwise block access")
            axes.append(r.min)
        return axes

    def is_common_reduce(var: Var) -> bool:
        for iter_var in block.iter_vars:
            if iter_var.var == var and iter_var.iter_type == IterVar.CommReduce:
                return True
        return False

    def has_common_reduce(var: Var) -> bool:
        vars = collect_vars_from_expr(var)
        return any(is_common_reduce(v) for v in vars)

    def check_last_trait(region: List[Range]):
        axes = get_ordered_axes(region)
        return has_common_reduce(axes[-1])

    def infer_layout(layout: str, region: List[Range], kind: str = "A"):
        """
        Infer the layout based on the region and the kind of buffer
        kind: "A", "B", "C"
        """
        primary_iter, secondary_iter, reduction_iter = {
            "A": (IterKind.kIter_I, IterKind.kIter_K, IterKind.kIter_K),
            "B": (IterKind.kIter_K, IterKind.kIter_J, IterKind.kIter_K),
            "C": (IterKind.kIter_I, IterKind.kIter_J, None),
        }[kind]

        spatial_iter = {
            "A": IterKind.kIter_I,
            "B": IterKind.kIter_J,
            "C": None,
        }[kind]

        if layout == "n":
            return [IterKind.kIter_S, primary_iter, secondary_iter]
        elif layout == "t":
            return [IterKind.kIter_S, secondary_iter, primary_iter]
        elif layout == "a":
            # auto inference layout
            # for buffer with reduction axis, we put it as the last axis
            # otherwise, we put it as the first axis
            if kind == "C":
                return [IterKind.kIter_S, primary_iter, secondary_iter]
            else:
                return ([IterKind.kIter_S, spatial_iter, reduction_iter] if check_last_trait(region)
                        else [IterKind.kIter_S, reduction_iter, spatial_iter])
        else:
            raise ValueError(f"Unknown layout {layout}")

    A_index_map = make_iter_fusion_index_map(
        A_traits, infer_layout(layout[0], block.reads[0].region, kind="A"))
    B_index_map = make_iter_fusion_index_map(
        B_traits, infer_layout(layout[1], block.reads[1].region, kind="B"))
    C_index_map = make_iter_fusion_index_map(
        C_traits, infer_layout(layout[2], block.writes[0].region, kind="C"))

    matmul_index_map = make_iter_fusion_index_map(
        block_traits,
        [IterKind.kIter_S, IterKind.kIter_I, IterKind.kIter_J, IterKind.kIter_K],
    )

    return (
        matmul_index_map,
        A_index_map,
        B_index_map,
        C_index_map,
    )


def get_in_out_dtypes(block: tir.Block) -> Tuple[str]:
    """
    Detect In/Out data types for the given block based on the analysis if read/write buffers.
    """
    assert len(block.reads) > 0 and len(block.writes) > 0
    in_dtype = block.reads[0].buffer.dtype
    out_dtype = block.writes[0].buffer.dtype
    return (in_dtype, out_dtype)


def get_dequantize_block(sch, blocks) -> Optional[BlockRV]:
    # check at least two input and one output
    # at lease one input has uint dtype, and the output dtype is float
    def is_dequantize(block: BlockRV) -> bool:
        block_stmt = sch.get(block)
        if len(block_stmt.reads) < 2:
            return False
        has_uint_input = any("uint" in str(region.buffer.dtype) for region in block_stmt.reads)
        if not has_uint_input:
            return False
        return not (len(block_stmt.writes) != 1 or
                    "float" not in str(block_stmt.writes[0].buffer.dtype))

    dequantize_blocks = [block for block in blocks if is_dequantize(block)]
    return dequantize_blocks[0] if len(dequantize_blocks) == 1 else None


def is_identity_or_transpose_block(block_stmt: tir.Block) -> bool:
    iter_types = {iter_var.iter_type for iter_var in block_stmt.iter_vars}
    if iter_types != {IterVar.DataPar}:
        return False, False
    if not isinstance(block_stmt.body, tir.BufferStore):
        return False, False
    if not isinstance(block_stmt.body.value, tir.BufferLoad):
        return False, False

    def get_access_vars(region: List[Range]) -> List[Var]:
        axes: List[Var] = []
        for r in region:
            if not _is_one(r.extent):
                return None
            axes.extend(undefined_vars(r.min))
        # remove trivial axis
        trivial_vars = set(
            iter_var.var for iter_var in block_stmt.iter_vars if _is_one(iter_var.dom.extent))
        axes = [axis for axis in axes if axis not in trivial_vars]
        # remove duplicate axis
        axes = [var for i, var in enumerate(axes) if i == 0 or var != axes[i - 1]]
        return axes

    lhs_access_vars = get_access_vars(block_stmt.reads[0].region)[-2:]
    rhs_access_vars = get_access_vars(block_stmt.writes[0].region)[-2:]
    is_identity = list(lhs_access_vars) == list(rhs_access_vars)
    is_transpose = list(lhs_access_vars) != list(rhs_access_vars) and set(lhs_access_vars) == set(
        rhs_access_vars)
    return is_identity, is_transpose


def is_identity_block(block_stmt: tir.Block) -> bool:
    return is_identity_or_transpose_block(block_stmt)[0]


def is_transpose_block(block_stmt: tir.Block) -> bool:
    return is_identity_or_transpose_block(block_stmt)[1]


def inline_transpose_block(sch: tir.Schedule, blocks: List[tir.schedule.BlockRV]):
    result_blocks = []
    for block in blocks:
        if not is_transpose_block(sch.get(block)):
            result_blocks.append(block)
            continue
        try:
            sch.compute_inline(block)
        except Exception:
            try:
                sch.reverse_compute_inline(block)
            except Exception:
                result_blocks.append(block)
    return result_blocks


def normalize_to_matmul(sch: tir.Schedule,
                        main_block: BlockRV,
                        layout: Optional[List[str]] = None) -> Optional[tir.Schedule]:
    if layout is None:
        layout = ["n", "t", "n"]
    block_stmt = sch.get(main_block)

    # let layout be 'a' to auto inference the layout
    index_maps = get_index_map(block_stmt, layout=layout)
    if index_maps is None:
        logger.debug("Cannot find the appropriate index map for tensorcore")
        return None

    matmul_index_map, a_index_map, b_index_map, c_index_map = index_maps

    # `skip_simplify` to  avoid the bug in the 1x1 conv
    block = sch.reindex(main_block, ("read", 0), skip_simplify=True)
    sch.transform_layout(block, ("write", 0), a_index_map)
    block = sch.reindex(main_block, ("read", 1), skip_simplify=True)
    sch.transform_layout(block, ("write", 0), b_index_map)
    block = sch.reindex(main_block, ("write", 0), skip_simplify=True)
    sch.transform_layout(block, ("read", 0), c_index_map)
    sch.transform_block_layout(main_block, matmul_index_map)
    sch.mod["main"] = sch.mod["main"].with_attr("dlight.tensorcore_prenormlized", True)
    return sch


def get_tensorized_func_and_tags(
    func: tir.PrimFunc,
    target: Target,
    layout: Optional[List[str]] = None,
    skip_normalize: bool = False,
    allow_gemv: bool = False,
) -> Tuple[tir.PrimFunc, Dict[str, Union[List[int], int]]]:
    """
        transform function to matmul if necessary (e.g. transform conv2d with im2col)
    """
    if layout is None:
        layout = ["a", "a", "a"]
    # step1. detect whether the function can utilize tensorcore
    sch = tir.Schedule(func)
    root_block = get_root_block(sch)
    blocks = sch.get_child_blocks(root_block)
    reduction_blocks = get_reduction_blocks(sch, blocks)
    if not reduction_blocks or len(reduction_blocks) != 1:
        return func, None

    def _can_be_tensorized(sch: tir.Schedule, block: BlockRV) -> bool:
        block_stmt = sch.get(block)
        conditions = []
        conditions.append(len(block_stmt.reads) == 2)
        conditions.append(len(block_stmt.writes) == 1)
        conditions.append(
            len(
                collect_block_iter_vars_used_in_access_region(block_stmt,
                                                              block_stmt.writes[0].region)) > 0)
        return all(conditions)

    # step2. transform function to tensorcore matmul (e.g. conv2d with im2col)
    def check_sm_version(arch: str) -> int:
        sm_version = arch.replace("sm_", "")
        return int(sm_version) if sm_version.isdigit() else -1

    def analysis_tensorcore_tags(sch: tir.Schedule, block: BlockRV,
                                 target: Target) -> Union[bool, Dict]:
        tags: Dict[str, Union[List[int], int]] = {}
        block_stmt = sch.get(block)

        # Nvidia Only Support Tensor Core for
        # devices greater than 70.
        if check_sm_version(target.arch) < 70:
            return False
        # analysis tensorcore axis
        # todo(lei): maybe we can remove this in the future
        (write_buffer_region,) = block_stmt.writes
        out_axis = len(write_buffer_region.buffer.shape)
        tags["tensorcore_config"] = [out_axis - 2, out_axis - 1]

        # analysis pipeline stage
        # todo(lei): maybe we can integrate this into policy in the future
        tags["pipeline_stage"] = 1
        if target.kind.name == "cuda" and check_sm_version(target.arch) == 80:
            # enable pipeline stage only for sm_80 devices
            tags["pipeline_stage"] = 2

        # analysis async copy
        # todo(lei): maybe we can integrate this into policy in the future
        tags["use_async_copy"] = False
        if tags["pipeline_stage"] == 2 and check_sm_version(target.arch) >= 80:
            # async copy only works in software pipeline.
            tags["use_async_copy"] = True

        # analysis intrin information
        def get_ordered_axes(region: List[Range]) -> Set[Var]:
            axes: List[Var] = []
            for r in region:
                if not _is_one(r.extent):
                    raise ValueError("Expect elemwise block access")
                axes.append(r.min)
            return axes

        def is_common_reduce(var: Var) -> bool:
            for iter_var in block_stmt.iter_vars:
                if iter_var.var == var and iter_var.iter_type == IterVar.CommReduce:
                    return True
            return False

        def has_common_reduce(var: Var) -> bool:
            vars = collect_vars_from_expr(var)
            return any(is_common_reduce(v) for v in vars)

        def check_last_trait(region: List[Range]):
            axes = get_ordered_axes(region)
            return has_common_reduce(axes[-1])

        intrin_info: dict = {}
        in_dtype, out_dtype = get_in_out_dtypes(block_stmt)
        intrin_info["in_dtype"] = in_dtype
        intrin_info["out_dtype"] = out_dtype

        if 70 <= check_sm_version(target.arch) < 80 and out_dtype == "int32":
            # INT32 Accum TensorCore only supports SM Version > 32.
            return False

        # if the last dimension is reduce axis, the B is transposed
        intrin_info["trans_b"] = check_last_trait(block_stmt.reads[1].region)
        if func.attrs is not None and "input_transform_kind" in func.attrs:
            intrin_info["input_transform_kind"] = func.attrs["input_transform_kind"]
        if func.attrs is not None and "weight_transform_kind" in func.attrs:
            intrin_info["weight_transform_kind"] = func.attrs["weight_transform_kind"]
        tags["intrin_info"] = intrin_info
        # Analysis Block Reduction Optimization
        # Currently, we only support block reduction depth 2 for small M
        # When the func is a dequantize like ops, we should consider the M
        require_block_reduce = False
        # And we only support float16 for now
        if (hasattr(func.attrs, "dequantize_info") and in_dtype in ["bfloat16", "float16"]):
            for arg in func.params:
                inp_shape = func.buffer_map[arg].shape
                M = inp_shape[0]
                if isinstance(M, tir.IntImm) and M <= 128:
                    require_block_reduce = True
                break
        if require_block_reduce and check_sm_version(target.arch) == 80:
            tags["block_reduction_depth"] = 2
        return tags

    (main_block,) = reduction_blocks
    if _can_be_tensorized(sch, main_block) is None:
        return func, None

    block_stmt = sch.get(main_block)
    if target.kind.name == "cuda" and check_sm_version(target.arch) >= 70:
        in_dtype, out_dtype = get_in_out_dtypes(block_stmt)
        if not is_tensorcore_supported_precision(in_dtype, out_dtype, arch=get_arch(target)):
            logger.debug("The input and output dtype is not supported by tensorcore")
            return func, None

        # reindex and transform functions
        # Normalize tensor functions to C[S, I, J] += A[S, I, K] * B[S, J, K]
        # or C[S, I, J] += A[S, I, K] * B[S, K, J]
        # skip normalize when we want to detect tags only.
        if not skip_normalize:
            sch = normalize_to_matmul(sch, main_block, layout)
            if sch is None:
                return func, None

        block_stmt = sch.get(main_block)

        # 16 for 16 bits tensor core while 32 for 8bits tensorcore.
        minimal_tensorize_spatial_threshold = 16
        minimal_tensorize_reduce_threshold = 16 if in_dtype in ["bfloat16", "float16"] else 32
        # the batch dimension is not taken into consideration.
        for item_var in block_stmt.iter_vars[1:]:
            extent = item_var.dom.extent
            iter_type = item_var.iter_type

            if iter_type is IterVar.DataPar:
                minimal_tensorize_threshold = minimal_tensorize_spatial_threshold
            elif iter_type is IterVar.CommReduce:
                minimal_tensorize_threshold = minimal_tensorize_reduce_threshold
            else:
                raise ValueError(f"Unknown IterVar type {iter_type}")

            if (isinstance(extent, tir.expr.IntImm) and extent.value < minimal_tensorize_threshold):
                return func, None
        tags = analysis_tensorcore_tags(sch, main_block, target)
        return sch.mod["main"], tags

    return func, None


def get_propagate_map(trans: bool = True, dtype="float16", matrix_name="A", index_dtype="int32"):
    from bitblas.tl.mma_layout import (  # pylint: disable=import-outside-toplevel
        ldmatrix_32x8_to_shared_16x16_layout, ldmatrix_trans_32x8_to_shared_16x16_layout,
        ldmatrix_32x16_to_shared_16x32_layout_a, ldmatrix_32x16_to_shared_16x32_layout_b,
    )

    assert dtype in [
        "bfloat16",
        "float16",
        "int8",
        "e4m3_float8",
        "e5m2_float8",
    ], "Only support bfloat16, float16, int8, e4m3_float8, e5m2_float8"
    # TODO(lei): actually should analyze based on bits instead of dtype
    if dtype in ["bfloat16", "float16"]:
        ldmatrix_layout = ldmatrix_32x8_to_shared_16x16_layout
        ldmatrix_layout_trans = ldmatrix_trans_32x8_to_shared_16x16_layout
    elif dtype in ["int8", "e4m3_float8", "e5m2_float8"]:
        # int8 mma only support 32x16 to 16x32 layout
        if matrix_name == "A" and trans is False:
            ldmatrix_layout = ldmatrix_32x16_to_shared_16x32_layout_a
        elif matrix_name == "B" and trans is True:
            ldmatrix_layout = ldmatrix_32x16_to_shared_16x32_layout_b
        else:
            raise ValueError("Unknown matrix name ", matrix_name)

    # IntraWarp memory layout was occurred by ldmatrix, we should lift the ld_matrix out
    def ldmatrix_permutation_16x16_32x8_16x16(kernel_i, kernel_j):
        thread_id = kernel_i * 2 + kernel_j // 8
        local_id = kernel_j % 8
        return ldmatrix_layout(thread_id, local_id)

    def ldmatrix_trans_permutation_16x16_32x8_16x16(kernel_i, kernel_j):
        thread_id = kernel_i * 2 + kernel_j // 8
        local_id = kernel_j % 8
        return ldmatrix_layout_trans(thread_id, local_id)

    def ldmatrix_permutation_16x32_32x16_32x16(kernel_i, kernel_j):
        thread_id = kernel_i * 2 + kernel_j // 16
        local_id = kernel_j % 16
        return ldmatrix_layout(thread_id, local_id)

    if dtype in ["bfloat16", "float16"]:
        ldmatrix_index_map = (
            ldmatrix_trans_permutation_16x16_32x8_16x16
            if trans else ldmatrix_permutation_16x16_32x8_16x16)
    else:
        ldmatrix_index_map = ldmatrix_permutation_16x32_32x16_32x16

    ldmatrix_index_map = IndexMap.from_func(ldmatrix_index_map, index_dtype=index_dtype)
    # TODO(lei): index_dtype should be analyzed from the schedule
    row, col = [16, 16] if dtype in ["bfloat16", "float16"] else [16, 32]
    inversed_index_map = ldmatrix_index_map.inverse([row, col])
    return ldmatrix_index_map, inversed_index_map


# This function is used to get the index map for the stage3 of the
# Ladder weight propagation, which can be used to avoid the ldmatrix
# Instructions.
def get_ladder_stage3_map(dtype="float16", index_dtype="int32"):

    def shared_32x8_to_mma_32x8_layout(i, j):
        thread_id = (i % 8) * 4 + (j // 2)
        local_id = (i // 8) * 2 + (j % 2)
        return thread_id, local_id

    def shared_32x16_to_mma_32x16_layout(i, j):
        thread_id = (i % 8) * 4 + (j // 4)
        local_id = (i // 8) * 4 + (j % 4)
        return thread_id, local_id

    assert dtype in [
        "bfloat16",
        "float16",
        "int8",
        "e4m3_float8",
        "e5m2_float8",
    ], "Only support float16, int8, e4m3_float8, e5m2_float8"
    if dtype in ["bfloat16", "float16"]:
        stage3_layout = shared_32x8_to_mma_32x8_layout
    elif dtype in ["int8", "e4m3_float8", "e5m2_float8"]:
        stage3_layout = shared_32x16_to_mma_32x16_layout
    else:
        raise ValueError("Unknown dtype ", dtype)

    # IntraWarp memory layout was occurred by ldmatrix, we should lift the ld_matrix out
    def ladder_stage3_permutation_16x16_32x8_32x8_16x16(kernel_i, kernel_j):
        thread_id = kernel_i * 2 + kernel_j // 8
        local_id = kernel_j % 8
        new_thread_id, new_local_id = stage3_layout(thread_id, local_id)
        new_kernel_i = (new_thread_id * 8 + new_local_id) // 16
        new_kernel_j = (new_thread_id * 8 + new_local_id) % 16
        return new_kernel_i, new_kernel_j

    def ladder_stage3_permutation_16x32_32x16_32x16_16x32(kernel_i, kernel_j):
        thread_id = kernel_i * 2 + kernel_j // 16
        local_id = kernel_j % 16
        new_thread_id, new_local_id = stage3_layout(thread_id, local_id)
        new_kernel_i = (new_thread_id * 16 + new_local_id) // 32
        new_kernel_j = (new_thread_id * 16 + new_local_id) % 32
        return new_kernel_i, new_kernel_j

    if dtype in ["bfloat16", "float16"]:
        stage3_index_map = ladder_stage3_permutation_16x16_32x8_32x8_16x16
    else:
        stage3_index_map = ladder_stage3_permutation_16x32_32x16_32x16_16x32

    stage3_index_map = IndexMap.from_func(stage3_index_map, index_dtype=index_dtype)
    # TODO(lei): index_dtype should be analyzed from the schedule
    row, col = [16, 16] if dtype in ["bfloat16", "float16"] else [16, 32]
    inversed_index_map = stage3_index_map.inverse([row, col])
    return stage3_index_map, inversed_index_map


def layout_propagate_chain(
    sch: tir.Schedule,
    start_block: BlockRV,
    start_buffer: tir.Buffer,
    end_block: BlockRV,
    index_map: IndexMap,
):
    # some layout transformation may only apply to the last n dimensions
    # propagate the layout transformation to the chain of blocks
    block = start_block
    buffer = start_buffer
    index_map = index_map
    while True:
        last_buffer = buffer
        producers = sch.get_producers(block)
        if len(producers) == 0:
            break
        for producer in producers:
            if len(sch.get(producer).writes) != 1:
                return index_map
            if sch.get(producer) == sch.get(end_block):
                return index_map
            (write,) = sch.get(producer).writes

            read = find_first_similar_region(sch.get(producer).reads, last_buffer)
            if write.buffer == buffer:
                block = producer
                buffer = read.buffer
                write_indices = [r.min for r in write.region]
                read_indices = [r.min for r in read.region]
                # reverse index map from [vi // x] -> [vi * x] to match the inconsistent layout
                tmp_index_map = IndexMap(write_indices, read_indices, None)
                tmp_index_map = tmp_index_map.non_surjective_inverse(write.buffer.shape)[0]

                # if dequantize like ops are used, the scaling factor should be considered
                # to be applied to the final indices
                scaling_factor = 1
                for i, j in zip(write.buffer.shape, read.buffer.shape):
                    scaling_factor *= i // j
                final_indices = list(
                    index_map.map_indices(tmp_index_map.map_indices(write_indices)))
                final_indices[-1] = final_indices[-1] // scaling_factor
                index_map = IndexMap(
                    write_indices,
                    final_indices,
                    None,
                )
        if buffer == last_buffer:
            break
    return index_map