refactor: reorganize CUDA kernels into per-family directories

- move attention kernels to csrc/kernels/attention/ and rotary to rotary/
- add shared common/mma.cuh (mma_sync, ldmatrix) and device.cuh (sm checks)
- split fp8_mm into three-layer fp8/common.h, gemm.cuh, mm.cu
- fix fused FP8 GEMM ldmatrix lane indexing to fix OOB shared reads
- update extension ops, loader, and kernel tests

astrai/extension/fp8.py

@@ -1,161 +1,214 @@
-"""FP8 training: scaling state and aten::linear dispatch.
+"""FP8 training: scaling recipes, per-tensor state, and aten::linear dispatch.
 
 Layered (see also ``ops/fp8.py`` for the CUDA interface adapter):
 
-1. Kernel interface: ``ops.fp8`` - the only module touching the pybind.
+1. Kernel interface: ``ops.fp8`` — the only module touching the pybind.
-2. Training state (this module): per-tensor scales, amax history, delayed
+2. Training state (this module): scaling *recipes* (TE-style delayed scaling
-   scaling, and the ``fp8_autocast`` context (TE-style, like
+   or dynamic current-amax scaling), per-tensor scales + amax history, and
-   ``torch.autocast``).
+   the ``fp8_autocast`` context (like ``torch.autocast``).
 3. aten::linear integration (this module): registers the CUDA impl and the
-   M/N alignment guard.
+   dtype guard.
 
 Usage::
 
     from astrai.extension.fp8 import fp8_autocast
 
-    with fp8_autocast(enabled=True):
+    with fp8_autocast(enabled=True, fp8_format="hybrid"):
         logits = model(input_ids)
         loss.backward()
 
 Importing this module registers the aten::linear CUDA implementation.
+
+Format defaults follow the ecosystem consensus: E4M3 for the forward pass,
+E5M2 for the backward (gradient) pass ("hybrid"); every operand's scale is a
+quantization step derived from its amax history by the active recipe.
 """
 
 from contextlib import contextmanager
+from dataclasses import dataclass
+from enum import Enum
+from typing import Optional
 
 import torch
 from torch.library import Library
 
 from astrai.extension.ops.fp8 import (
-    linear_backward_scaled,
+    linear_backward_fp8,
-    linear_forward_scaled,
+    linear_forward_fp8,
+    mm_fp8,
+    quantize_bf16,
 )
 
-E4M3_MAX = 448.0
+# Max representable value per FP8 format (E4M3: 448, E5M2: 57344).
+FP8_MAX = {"e4m3": 448.0, "e5m2": 57344.0}
+E4M3_MAX = FP8_MAX["e4m3"]  # legacy alias
 
 
-# ---------------------------------------------------------------------------
+class FP8Format(str, Enum):
-# Layer 2: training state (scales, amax history, delayed scaling, autocast)
+    """Per-direction FP8 format. HYBRID = E4M3 forward / E5M2 backward."""
-# ---------------------------------------------------------------------------
+
+    E4M3 = "e4m3"
+    E5M2 = "e5m2"
+    HYBRID = "hybrid"
+
+    def fwd(self) -> str:
+        return "e4m3" if self is FP8Format.HYBRID else self.value
+
+    def bwd(self) -> str:
+        return "e5m2" if self is FP8Format.HYBRID else self.value
+
+
+class FP8Recipe:
+    """Scale-from-amax policy; the scale computation is the injection point.
+
+    ``scale_from_history`` receives the amax tensor for this operand (a ring
+    window for delayed scaling, the current amax for dynamic scaling) and
+    returns the quantization step: ``scale = (amax / FP8_MAX[fmt]) / 2^margin``.
+    """
+
+    history_len: int = 16
+    margin: int = 0
+
+    def scale_from_history(self, amax: torch.Tensor, fmt: str) -> torch.Tensor:
+        raise NotImplementedError
+
+
+@dataclass
+class DelayedScaling(FP8Recipe):
+    """TE-style delayed scaling: max over the amax history window.
+
+    The scale is computed from amax measured in *previous* steps (delayed one
+    step); the window length trades responsiveness against stability.
+    """
+
+    history_len: int = 16
+    margin: int = 0
+
+    def scale_from_history(self, amax: torch.Tensor, fmt: str) -> torch.Tensor:
+        peak = amax.max()
+        return ((peak / FP8_MAX[fmt]) / (2**self.margin)).clamp_min(1e-12)
+
+
+@dataclass
+class DynamicScaling(FP8Recipe):
+    """Current-amax scaling (torchao DYNAMIC): measure, then quantize.
+
+    No history — the scale is derived from the amax of the tensor being
+    quantized in the same step, at the cost of an extra reduction pass.
+    """
+
+    history_len: int = 1
+    margin: int = 0
+
+    def scale_from_history(self, amax: torch.Tensor, fmt: str) -> torch.Tensor:
+        peak = amax.max()
+        return ((peak / FP8_MAX[fmt]) / (2**self.margin)).clamp_min(1e-12)
 
 
 class FP8TensorMeta:
-    """Scales + amax state for one weight tensor and its paired activations.
+    """Per-tensor scaling state: amax history rings + derived scales.
 
-    - weight: delayed scale from a 16-step amax history window (TE style)
+    One ring per operand (weight / activation / gradient). Scales are derived
-    - x/g: delayed one step, reuse the quantize kernel's free atomic amax
+    from the ring by the recipe; fused kernels record the amax while
+    quantizing, so the scale used at step N reflects amax from steps < N
+    (delayed one step).
     """
 
     __slots__ = (
-        "scale",
+        "recipe",
-        "scale_inv",
+        "w_hist",
-        "amax_history",
+        "x_hist",
-        "idx",
+        "g_hist",
-        "x_scale",
+        "w_idx",
-        "x_scale_inv",
-        "x_history",
         "x_idx",
-        "g_scale",
-        "g_scale_inv",
-        "g_history",
         "g_idx",
+        "w_scale",
+        "x_scale",
+        "g_scale",
         "w_init",
         "x_init",
         "g_init",
     )
 
-    def __init__(self, device: torch.device, update_interval: int):
+    def __init__(self, device: torch.device, recipe: FP8Recipe):
-        self.scale = torch.ones(1, device=device, dtype=torch.float32)
+        self.recipe = recipe
-        self.scale_inv = torch.ones(1, device=device, dtype=torch.float32)
+        n = recipe.history_len
-        self.amax_history = torch.ones(
+        self.w_hist = torch.ones(n, device=device, dtype=torch.float32)
-            update_interval, device=device, dtype=torch.float32
+        self.x_hist = torch.ones(n, device=device, dtype=torch.float32)
-        )
+        self.g_hist = torch.ones(n, device=device, dtype=torch.float32)
-        self.idx = 0
+        self.w_idx = self.x_idx = self.g_idx = 0
+        self.w_scale = torch.ones(1, device=device, dtype=torch.float32)
         self.x_scale = torch.ones(1, device=device, dtype=torch.float32)
-        self.x_scale_inv = torch.ones(1, device=device, dtype=torch.float32)
-        self.x_history = torch.ones(update_interval, device=device, dtype=torch.float32)
-        self.x_idx = 0
         self.g_scale = torch.ones(1, device=device, dtype=torch.float32)
-        self.g_scale_inv = torch.ones(1, device=device, dtype=torch.float32)
+        self.w_init = self.x_init = self.g_init = False
-        self.g_history = torch.ones(update_interval, device=device, dtype=torch.float32)
-        self.g_idx = 0
-        self.w_init = False
-        self.x_init = False
-        self.g_init = False
 
-    def init_scale(self, t: torch.Tensor) -> None:
+    # -- ring helpers -------------------------------------------------------
-        """Immediate scale from the current amax; used on the first call.
 
-        A scale of 1 would underflow small activations/gradients (e4m3 min
+    def _record(self, hist: torch.Tensor, idx: int, amax: torch.Tensor) -> int:
-        normal is 2^-6); initialize from the actual amax once, then delayed
+        hist[idx] = amax.reshape(())
-        updates take over.
+        return (idx + 1) % hist.numel()
-        """
+
+    def _refresh(self, hist: torch.Tensor, scale: torch.Tensor, fmt: str) -> None:
+        scale.copy_(self.recipe.scale_from_history(hist, fmt))
+
+    def _seed(
+        self, hist: torch.Tensor, scale: torch.Tensor, t: torch.Tensor, fmt: str
+    ) -> None:
         amax = t.abs().amax().to(torch.float32).clamp_min(1e-12)
-        self.scale.copy_(amax / E4M3_MAX)
+        hist.fill_(amax)
-        self.scale_inv.copy_(E4M3_MAX / amax)
+        scale.copy_(self.recipe.scale_from_history(hist, fmt))
-        self.record(amax)
 
-    def push_x_scale(self, amax: torch.Tensor) -> None:
+    # -- per-operand updates (delayed: record now, refresh for next step) ---
-        """Window update for the activation scale (delayed, TE style)."""
-        self.x_history[self.x_idx] = amax.reshape(())
-        self.x_idx = (self.x_idx + 1) % self.x_history.numel()
-        m = self.x_history.max()
-        self.x_scale.copy_(m / E4M3_MAX)
-        self.x_scale_inv.copy_(E4M3_MAX / m)
 
-    def push_g_scale(self, amax: torch.Tensor) -> None:
+    def update_w(self, amax: torch.Tensor, fmt: str) -> None:
-        """Window update for the gradient scale (delayed, TE style)."""
+        self.w_idx = self._record(self.w_hist, self.w_idx, amax)
-        self.g_history[self.g_idx] = amax.reshape(())
+        self._refresh(self.w_hist, self.w_scale, fmt)
-        self.g_idx = (self.g_idx + 1) % self.g_history.numel()
-        m = self.g_history.max()
-        self.g_scale.copy_(m / E4M3_MAX)
-        self.g_scale_inv.copy_(E4M3_MAX / m)
 
-    def record(self, amax: torch.Tensor) -> None:
+    def update_x(self, amax: torch.Tensor, fmt: str) -> None:
-        """Push the latest amax into the ring buffer (device-side copy, no sync)."""
+        self.x_idx = self._record(self.x_hist, self.x_idx, amax)
-        self.amax_history[self.idx] = amax.reshape(())
+        self._refresh(self.x_hist, self.x_scale, fmt)
-        self.idx = (self.idx + 1) % self.amax_history.numel()
 
-    def refresh(self) -> None:
+    def update_g(self, amax: torch.Tensor, fmt: str) -> None:
-        """Recompute scale from the amax history window (delayed scaling)."""
+        self.g_idx = self._record(self.g_hist, self.g_idx, amax)
-        amax = self.amax_history.max()
+        self._refresh(self.g_hist, self.g_scale, fmt)
-        if amax > 0:
+
-            self.scale.copy_(amax / E4M3_MAX)
+    # -- first-use seeding --------------------------------------------------
-            self.scale_inv.copy_(E4M3_MAX / amax)
+
+    def init_w(self, w: torch.Tensor, fmt: str) -> None:
+        self._seed(self.w_hist, self.w_scale, w, fmt)
+        self.w_init = True
+
+    def init_x(self, x: torch.Tensor, fmt: str) -> None:
+        self._seed(self.x_hist, self.x_scale, x, fmt)
+        self.x_init = True
+
+    def init_g(self, g: torch.Tensor, fmt: str) -> None:
+        self._seed(self.g_hist, self.g_scale, g, fmt)
+        self.g_init = True
 
 
 class FP8State:
-    """Global fp8 training state, TE-style."""
+    """Global fp8 training state: active recipe + per-tensor metas."""
 
-    def __init__(self, update_interval: int = 16):
+    def __init__(self):
         self.enabled = False
-        self.update_interval = update_interval
+        self.recipe: FP8Recipe = DelayedScaling()
-        self.step_count = 0
+        self.fp8_format: FP8Format = FP8Format.HYBRID
         self._metas: dict[tuple, FP8TensorMeta] = {}
-        self._last_device: torch.device | None = None
+        self._last_device: Optional[torch.device] = None
-
-    def _get_device(self, t: torch.Tensor) -> torch.device:
-        if self._last_device is None:
-            self._last_device = t.device
-        return t.device
 
     def get_weight_meta(self, w: torch.Tensor) -> FP8TensorMeta:
         key = (w.data_ptr(), w.shape, w.dtype)
         meta = self._metas.get(key)
         if meta is None:
-            meta = FP8TensorMeta(self._get_device(w), self.update_interval)
+            if self._last_device is None:
+                self._last_device = w.device
+            meta = FP8TensorMeta(w.device, self.recipe)
             self._metas[key] = meta
         return meta
 
-    def step(self) -> None:
-        """Advance the counter and refresh all weight scales every N steps."""
-        self.step_count += 1
-        if self.step_count % self.update_interval == 0:
-            for meta in self._metas.values():
-                meta.refresh()
-
     def reset(self) -> None:
         self.enabled = False
-        self.step_count = 0
         self._metas.clear()
         self._last_device = None
 
@@ -171,100 +224,114 @@ def fp8_state() -> FP8State:
 
 
 @contextmanager
-def fp8_autocast(enabled: bool = True, update_interval: int = 16):
+def fp8_autocast(
+    enabled: bool = True,
+    update_interval: int = 16,
+    recipe: Optional[FP8Recipe] = None,
+    fp8_format: str = "hybrid",
+    margin: int = 0,
+):
     """Autocast-style context: fp8 linear dispatch on this thread.
 
     Usage::
 
-        with fp8_autocast(enabled=True):
+        with fp8_autocast(enabled=True, fp8_format="hybrid"):
             logits = model(input_ids)   # aten::linear -> fp8 path
             loss.backward()
 
-    The scale-update counter advances once per ``enter`` (one training step),
+    Args:
-    refreshing weight scales from their amax history every ``update_interval``.
+        enabled: toggle fp8 dispatch for aten::linear.
+        update_interval: legacy alias for the delayed-scaling history window
+            (used only when ``recipe`` is not given).
+        recipe: scaling policy; defaults to ``DelayedScaling(update_interval)``.
+        fp8_format: ``"e4m3"`` / ``"e5m2"`` / ``"hybrid"`` (default) — hybrid
+            means E4M3 forward, E5M2 backward.
+        margin: scale headroom (``scale = (amax / FP8_MAX) / 2^margin``) used
+            with the default delayed recipe.
     """
     state = fp8_state()
-    prev_enabled = state.enabled
+    prev = (state.enabled, state.recipe, state.fp8_format)
-    prev_interval = state.update_interval
+    if recipe is None:
+        recipe = DelayedScaling(history_len=update_interval, margin=margin)
     state.enabled = enabled
-    state.update_interval = update_interval
+    state.recipe = recipe
+    state.fp8_format = FP8Format(fp8_format)
     try:
-        if enabled:
-            state.step()
         yield
     finally:
-        state.enabled = prev_enabled
+        state.enabled, state.recipe, state.fp8_format = prev
-        state.update_interval = prev_interval
+
+
+# ---------------------------------------------------------------------------
+# Strategy-level forward / backward (called from the aten::linear impl)
+# ---------------------------------------------------------------------------
+
+
+def _dynamic_scale(t: torch.Tensor, recipe: FP8Recipe, fmt: str) -> torch.Tensor:
+    amax = t.abs().amax().to(torch.float32).clamp_min(1e-12)
+    return recipe.scale_from_history(amax, fmt)
 
 
 def fp8_linear_forward(x: torch.Tensor, w: torch.Tensor, bias=None):
-    """TE-style scaled fp8 linear forward (called from the aten::linear impl).
+    """Scaled fp8 linear forward (called from the aten::linear impl).
 
-    x uses the delayed scale of its paired weight meta (amax from the previous
+    Delayed scaling uses the fused BF16->E4M3 GEMM (quantize + amax inside the
-    forward of this linear); the quantize kernel emits the current amax for the
+    kernel); dynamic scaling measures the current amax first and runs the
-    next step. No extra abs/max reduce.
+    pre-quantized path.
     """
     if bias is None:
         bias = torch.empty(0, device=x.device, dtype=x.dtype)
     state = fp8_state()
+    fmt = state.fp8_format.fwd()
     meta = state.get_weight_meta(w)
     if not meta.w_init:
-        meta.init_scale(w)
+        meta.init_w(w, fmt)
-        meta.w_init = True
+    if isinstance(state.recipe, DynamicScaling):
+        x_2d = x.reshape(-1, w.size(1))
+        sx = _dynamic_scale(x_2d, state.recipe, fmt)
+        sw = _dynamic_scale(w, state.recipe, fmt)
+        x8, _ = quantize_bf16(x_2d, sx, fmt)
+        w8, _ = quantize_bf16(w, sw, fmt)
+        out = mm_fp8(x8, w8, sx, sw)
+        out = out.reshape(*x.shape[:-1], w.size(0))
+        if bias.numel():
+            out = out + bias
+        return out
     if not meta.x_init:
-        amax = x.abs().amax().to(torch.float32).clamp_min(1e-12)
+        meta.init_x(x, fmt)
-        meta.x_history.fill_(amax)
+    out, amax_x, amax_w = linear_forward_fp8(x, w, bias, meta.x_scale, meta.w_scale)
-        meta.x_scale.copy_(amax / E4M3_MAX)
+    meta.update_x(amax_x, fmt)
-        meta.x_scale_inv.copy_(E4M3_MAX / amax)
+    meta.update_w(amax_w, fmt)
-        meta.x_init = True
-    amax_x = torch.empty(1, device=x.device, dtype=torch.float32)
-    amax_w = torch.empty(1, device=x.device, dtype=torch.float32)
-    out = linear_forward_scaled(
-        x,
-        w,
-        bias,
-        meta.x_scale,
-        meta.scale,
-        meta.x_scale_inv,
-        meta.scale_inv,
-        amax_x,
-        amax_w,
-    )
-    meta.record(amax_w)
-    meta.push_x_scale(amax_x)
     return out
 
 
-def fp8_linear_backward(g, x, w, masks):
+def fp8_linear_backward(g: torch.Tensor, x: torch.Tensor, w: torch.Tensor, masks):
-    """TE-style scaled fp8 linear backward (called from aten::linear_backward)."""
+    """Scaled fp8 linear backward (called from aten::linear_backward).
+
+    The gradient is quantized to the backward format (E5M2 in hybrid mode)
+    and the dX / dW GEMMs share that single quantization.
+    """
     state = fp8_state()
+    fmt = state.fp8_format.bwd()
     meta = state.get_weight_meta(w)
-    if not meta.g_init:
+    if isinstance(state.recipe, DynamicScaling):
-        amax = g.abs().amax().to(torch.float32).clamp_min(1e-12)
+        sg = _dynamic_scale(g, state.recipe, fmt)
-        meta.g_history.fill_(amax)
+        sw = _dynamic_scale(w, state.recipe, fmt)
-        meta.g_scale.copy_(amax / E4M3_MAX)
+        sx = _dynamic_scale(x, state.recipe, fmt)
-        meta.g_scale_inv.copy_(E4M3_MAX / amax)
+    else:
-        meta.g_init = True
+        if not meta.g_init:
-    amax_g = torch.empty(1, device=g.device, dtype=torch.float32)
+            meta.init_g(g, fmt)
-    out = linear_backward_scaled(
+        sg, sw, sx = meta.g_scale, meta.w_scale, meta.x_scale
-        g,
+    grad_x, grad_w, grad_b, amax_g = linear_backward_fp8(
-        x,
+        g, x, w, masks, sg, sw, sx, fmt
-        w,
-        masks,
-        meta.g_scale,
-        meta.scale,
-        meta.x_scale,
-        meta.g_scale_inv,
-        meta.scale_inv,
-        meta.x_scale_inv,
-        amax_g,
     )
-    meta.push_g_scale(amax_g)
+    if not isinstance(state.recipe, DynamicScaling):
-    return out
+        meta.update_g(amax_g, fmt)
+    return grad_x, grad_w, grad_b
 
 
 # ---------------------------------------------------------------------------
-# Layer 3: aten::linear integration
+# aten::linear integration
 # ---------------------------------------------------------------------------
 
 
@@ -279,9 +346,14 @@ def fp8_linear_enabled() -> bool:
 
 
 def _fp8_supported(x: torch.Tensor, w: torch.Tensor) -> bool:
-    """cuBLASLt fp8 requires M % 16 == 0 and N % 16 == 0 (K is padded)."""
+    """Shape guard for the fp8 linear path.
-    m = x.numel() // x.size(-1)
+
-    return m % 16 == 0 and w.size(0) % 16 == 0
+    Unlike a strict 16-alignment requirement, the fp8 kernels handle unaligned
+    M/N via boundary checks (slower but correct) — so no whole-call bf16
+    fallback for small decode batches. Only the K-dimension contraction must
+    match, and the weight must be 2D.
+    """
+    return x.dim() >= 2 and w.dim() == 2 and x.size(-1) == w.size(1)
 
 
 def _linear_cuda_impl(x: torch.Tensor, w: torch.Tensor, bias=None):

astrai/extension/loader.py

@@ -1,24 +1,35 @@
 """Dynamic discovery and loading of compiled CUDA kernel modules.
 
-Each kernel is registered in ``csrc/build.py`` and built into a ``.so`` placed
+Each kernel is built by the CMake build in ``csrc/CMakeLists.txt`` into a
-in this package directory. On import we try to load each one; kernels that
+``.so`` placed in ``astrai/extension/lib/`` — the module name equals the
-failed to build (or are running on a CPU-only machine) are marked unavailable
+``.so`` name equals the pybind name (e.g. ``attn_decode``, defined via
-so the wrapper functions can fall back to ``torch`` SDPA.
+``TORCH_EXTENSION_NAME``). ``KERNEL_NAMES`` is discovered automatically from
+the ``.so`` files present, so adding a kernel to the CMake ``KERNELS``
+registry needs no change here. On import we try to load each one; kernels
+that failed to build (or are running on a CPU-only machine) are marked
+unavailable so the wrapper functions can fall back to ``torch`` SDPA.
 """
 
+import glob
 import importlib
 import logging
+import os
 
 logger = logging.getLogger(__name__)
 
-KERNEL_NAMES = [
+_LIB_DIR = os.path.join(os.path.dirname(__file__), "lib")
-    "attn_decode",
+
-    "attn_prefill",
+
-    "attn_paged_decode",
+def _discover_kernel_names() -> list[str]:
-    "attn_paged_prefill",
+    """Return the module names of the compiled kernel ``.so`` files in lib/."""
-    "rotary_emb",
+    names: list[str] = []
-    "fp8_mm",
+    for path in glob.glob(os.path.join(_LIB_DIR, "*.so")):
-]
+        # strip the "<soabi>.so" suffix, e.g. attn_decode.cpython-312-...so
+        names.append(os.path.basename(path).split(".", 1)[0])
+    return sorted(names)
+
+
+KERNEL_NAMES = _discover_kernel_names()
 
 _available: dict[str, bool] = {}
 _modules: dict[str, object] = {}

astrai/extension/ops/fp8.py

@@ -1,9 +1,16 @@
-"""FP8 CUDA kernel interface adapter (the only module touching the pybind.
+"""FP8 CUDA kernel interface adapter (the only module touching the pybind).
 
-Isolates the ``fp8_mm`` CUDA extension behind stable Python functions:
+Isolates the ``fp8_mm`` CUDA extension behind stable Python primitives:
-- availability / dtype checks and clear errors
+
-- torch.library ``custom::fp8_mm`` registration (meta + CPU fallback)
+- ``quantize_bf16(x, scale, fmt) -> (x8, amax)`` — BF16 → FP8 with fused amax
-- quantize-in-GEMM primitives used by ``fp8.py`` training state
+- ``mm_fp8(a8, b8, sa, sb) -> out`` — pre-quantized FP8 GEMM (BF16 output)
+- ``linear_forward_fp8(x, w, bias, sx, sw) -> (out, amax_x, amax_w)``
+- ``linear_backward_fp8(g, x, w, masks, sg, sw, sx, fmt) -> (gx, gw, gb, amax_g)``
+
+Scale semantics: scales are *quantization steps* — the value divided out when
+quantizing (``x8 = x / scale``). Every primitive computes its own inverse
+internally; callers never pass ``scale_inv``. ``amax`` values are *returned*,
+never passed as output arguments. ``fmt`` is ``"e4m3"`` or ``"e5m2"``.
 
 Policy (scales, amax history, delayed scaling, autocast) lives in ``fp8.py``;
 this module is stateless.
@@ -14,106 +21,158 @@ from torch.library import custom_op
 
 from astrai.extension.loader import get_module, is_available
 
+# fmt string -> kernel int (0 = E4M3, 1 = E5M2)
+_FMT_TO_INT = {"e4m3": 0, "e5m2": 1}
 
-def _mod():
+# The pybind module is loaded once at first use and cached: the loader
-    if not is_available("fp8_mm"):
+# resolves modules at import time and never reloads them, so every call
-        raise RuntimeError(
+# after the first is a single None check.
-            "CUDA kernel 'fp8_mm' is not available. Build with CSRC_KERNELS=true."
+_MOD: object | None = None
-        )
-    return get_module("fp8_mm")
 
 
-@custom_op("custom::fp8_mm", mutates_args=())
+def _mod() -> object:
-def fp8_mm(
+    global _MOD
-    a: torch.Tensor, b: torch.Tensor, sx: torch.Tensor, sw: torch.Tensor
+    if _MOD is None:
-) -> torch.Tensor:
+        if not is_available("fp8_mm"):
-    """BF16 inputs, fused FP8 GEMM with FP32 accumulation and BF16 output."""
+            raise RuntimeError(
+                "CUDA kernel 'fp8_mm' is not available. Build with CSRC_KERNELS=true."
+            )
+        _MOD = get_module("fp8_mm")
+    return _MOD
 
 
-@fp8_mm.register_fake
+def _fmt_int(fmt: str) -> int:
-def _fp8_mm_fake(a, b, sx, sw):
+    try:
-    return torch.empty((a.size(0), b.size(0)), device=a.device, dtype=torch.bfloat16)
+        return _FMT_TO_INT[fmt]
+    except KeyError:
+        raise ValueError(f"unsupported fp8 format {fmt!r} (expected 'e4m3' or 'e5m2')")
 
 
-@fp8_mm.register_kernel("cuda")
+def _fmt_dtype(fmt: str) -> torch.dtype:
-def _fp8_mm_cuda(a, b, sx, sw):
+    return torch.float8_e5m2 if _fmt_int(fmt) else torch.float8_e4m3fn
-    if not (a.dtype == torch.bfloat16 and b.dtype == torch.bfloat16):
-        raise TypeError(f"bf16 GEMM requires bf16 inputs, got {a.dtype}/{b.dtype}")
-    return _mod().fp8_mm(a, b, sx, sw)
 
 
-@fp8_mm.register_kernel("cpu")
+@custom_op("custom::fp8_quantize", mutates_args=())
-def _fp8_mm_cpu(a, b, sx, sw):
+def fp8_quantize(
-    return torch.mm(a.float(), b.float().t()).to(torch.bfloat16)
+    x: torch.Tensor, scale: torch.Tensor, fmt: int
+) -> tuple[torch.Tensor, torch.Tensor]:
+    """BF16 -> FP8 quantize with fused amax; returns ``(x8, amax)``."""
 
 
-@custom_op("custom::fp8_mm_prequant", mutates_args=())
+@fp8_quantize.register_fake
-def fp8_mm_prequant(
+def _fp8_quantize_fake(x, scale, fmt):
-    a: torch.Tensor, b: torch.Tensor, scale: torch.Tensor
+    dtype = torch.float8_e5m2 if fmt else torch.float8_e4m3fn
-) -> torch.Tensor:
+    return (
-    """Pre-quantized FP8 inputs, fused FP8 GEMM, FP32 accumulation, BF16 out."""
+        torch.empty(x.shape, device=x.device, dtype=dtype),
-
+        torch.empty(1, device=x.device, dtype=torch.float32),
-
-@fp8_mm_prequant.register_fake
-def _fp8_mm_prequant_fake(a, b, scale):
-    return torch.empty((a.size(0), b.size(0)), device=a.device, dtype=torch.bfloat16)
-
-
-@fp8_mm_prequant.register_kernel("cuda")
-def _fp8_mm_prequant_cuda(a, b, scale):
-    if not (a.dtype == torch.float8_e4m3fn and b.dtype == torch.float8_e4m3fn):
-        raise TypeError(
-            f"pre-quantized FP8 GEMM requires fp8 inputs, got {a.dtype}/{b.dtype}"
-        )
-    return _mod().fp8_mm_prequant(a, b, scale)
-
-
-@fp8_mm_prequant.register_kernel("cpu")
-def _fp8_mm_prequant_cpu(a, b, scale):
-    return (a.float() @ b.float().t() * scale).to(torch.bfloat16)
-
-
-@custom_op("custom::fp8_mm_prequant_fp8", mutates_args=())
-def fp8_mm_prequant_fp8(
-    a: torch.Tensor, b: torch.Tensor, scale: torch.Tensor, out_scale: torch.Tensor
-) -> torch.Tensor:
-    """FP8 inputs and FP8 output: fused FP8 GEMM with FP32 accumulation."""
-
-
-@fp8_mm_prequant_fp8.register_fake
-def _fp8_mm_prequant_fp8_fake(a, b, scale, out_scale):
-    return torch.empty((a.size(0), b.size(0)), device=a.device, dtype=a.dtype)
-
-
-@fp8_mm_prequant_fp8.register_kernel("cuda")
-def _fp8_mm_prequant_fp8_cuda(a, b, scale, out_scale):
-    if not (a.dtype == torch.float8_e4m3fn and b.dtype == torch.float8_e4m3fn):
-        raise TypeError(
-            f"pre-quantized FP8 GEMM requires fp8 inputs, got {a.dtype}/{b.dtype}"
-        )
-    return _mod().fp8_mm_prequant_fp8(a, b, scale, out_scale)
-
-
-@fp8_mm_prequant_fp8.register_kernel("cpu")
-def _fp8_mm_prequant_fp8_cpu(a, b, scale, out_scale):
-    return (a.float() @ b.float().t() * scale * out_scale).to(torch.float8_e4m3fn)
-
-
-def linear_forward_scaled(x, w, bias, sx, sw, sx_inv, sw_inv, amax_x, amax_w):
-    """Quantize BF16 inputs to FP8, accumulate in FP32, and return BF16.
-
-    x/w: [..., K] / [N, K] bf16; sx/sw and their inverses control the fused
-    E4M3 conversion; amax_x/amax_w receive the input max-abs values.
-    """
-    if not (x.dtype == torch.bfloat16 and w.dtype == torch.bfloat16):
-        raise TypeError(f"fp8 forward requires bf16 inputs, got {x.dtype}/{w.dtype}")
-    return _mod().fp8_linear_forward_scaled(
-        x, w, bias, sx, sw, sx_inv, sw_inv, amax_x, amax_w
     )
 
 
-def linear_backward_scaled(g, x, w, masks, sg, sw, sx, sg_inv, sw_inv, sx_inv, amax_g):
+@fp8_quantize.register_kernel("cuda")
-    """dX = g @ W, dW = g^T @ X, dB = sum(g) with per-tensor scales."""
+def _fp8_quantize_cuda(x, scale, fmt):
+    if x.dtype != torch.bfloat16:
+        raise TypeError(f"fp8 quantize requires bf16 input, got {x.dtype}")
+    return _mod().quantize_bf16(x, scale, int(fmt))
+
+
+@fp8_quantize.register_kernel("cpu")
+def _fp8_quantize_cpu(x, scale, fmt):
+    x8 = (x.float() / scale).to(_fmt_dtype("e5m2" if fmt else "e4m3"))
+    amax = x.abs().amax().float().reshape(1).clamp_min(1e-12)
+    return x8, amax
+
+
+@custom_op("custom::fp8_gemm", mutates_args=())
+def fp8_gemm(
+    a: torch.Tensor,
+    b: torch.Tensor,
+    sa: torch.Tensor,
+    sb: torch.Tensor,
+    out_dtype: int = 0,
+    out_scale: torch.Tensor | None = None,
+) -> torch.Tensor:
+    """FP8 GEMM: ``a @ b^T * (sa * sb)`` with FP32 accumulation.
+
+    ``out_dtype``: 0 = BF16 (default), 1 = FP8 E4M3 (requires ``out_scale``,
+    the quantization step for the output — mirrors ``torch._scaled_mm``).
+    """
+
+
+@fp8_gemm.register_fake
+def _fp8_gemm_fake(a, b, sa, sb, out_dtype=0, out_scale=None):
+    dtype = torch.float8_e4m3fn if out_dtype else torch.bfloat16
+    return torch.empty((a.size(0), b.size(0)), device=a.device, dtype=dtype)
+
+
+@fp8_gemm.register_kernel("cuda")
+def _fp8_gemm_cuda(a, b, sa, sb, out_dtype=0, out_scale=None):
+    if a.dtype != b.dtype or a.dtype not in (torch.float8_e4m3fn, torch.float8_e5m2):
+        raise TypeError(
+            f"fp8 GEMM requires matching fp8 inputs, got {a.dtype}/{b.dtype}"
+        )
+    return _mod().mm_fp8(a, b, sa, sb, int(out_dtype), out_scale)
+
+
+@fp8_gemm.register_kernel("cpu")
+def _fp8_gemm_cpu(a, b, sa, sb, out_dtype=0, out_scale=None):
+    acc = a.float() @ b.float().t() * sa * sb
+    if out_dtype:
+        os_ = 1.0 if out_scale is None else out_scale
+        return (acc * os_).to(torch.float8_e4m3fn)
+    return acc.to(torch.bfloat16)
+
+
+def quantize_bf16(x: torch.Tensor, scale: torch.Tensor, fmt: str = "e4m3"):
+    """BF16 -> FP8 quantize with fused amax; returns ``(x8, amax)``.
+
+    ``scale`` is the quantization step (device scalar); ``fmt`` selects
+    E4M3 or E5M2. ``amax`` is a fresh 1-element float32 tensor — the caller
+    never clears it.
+    """
+    return fp8_quantize(x, scale, _fmt_int(fmt))
+
+
+def mm_fp8(
+    a: torch.Tensor,
+    b: torch.Tensor,
+    sa: torch.Tensor,
+    sb: torch.Tensor,
+    out_dtype: str = "bf16",
+    out_scale: torch.Tensor | None = None,
+) -> torch.Tensor:
+    """Pre-quantized FP8 GEMM: ``a @ b^T * (sa * sb)``.
+
+    ``a``/``b`` must be FP8 tensors of the same format (E4M3 or E5M2);
+    ``sa``/``sb`` are their quantization steps. ``out_dtype`` is ``"bf16"``
+    (default) or ``"e4m3"`` — FP8 output for layer-to-layer pipelines, which
+    requires ``out_scale`` (the output quantization step).
+    """
+    if out_dtype not in ("bf16", "e4m3"):
+        raise ValueError(
+            f"unsupported out_dtype {out_dtype!r} (expected 'bf16' or 'e4m3')"
+        )
+    return fp8_gemm(a, b, sa, sb, int(out_dtype == "e4m3"), out_scale)
+
+
+def linear_forward_fp8(x, w, bias, sx, sw):
+    """BF16 linear forward, quantizing x/w to E4M3 inside the GEMM.
+
+    Returns ``(out, amax_x, amax_w)``. ``bias`` may be ``None``.
+    """
+    if not (x.dtype == torch.bfloat16 and w.dtype == torch.bfloat16):
+        raise TypeError(f"fp8 forward requires bf16 inputs, got {x.dtype}/{w.dtype}")
+    if bias is None:
+        bias = torch.empty(0, device=x.device, dtype=x.dtype)
+    return _mod().linear_forward_fp8(x, w, bias, sx, sw)
+
+
+def linear_backward_fp8(g, x, w, masks, sg, sw, sx, fmt: str = "e5m2"):
+    """FP8 linear backward; returns ``(grad_input, grad_weight, grad_bias, amax_g)``.
+
+    The gradient (and the transposed w/x operands) are quantized to ``fmt``
+    (default E5M2 — larger dynamic range for gradients) and the two GEMMs run
+    as FP8 tensor-core products sharing a single gradient quantization.
+    """
     if not (
         g.dtype == torch.bfloat16
         and x.dtype == torch.bfloat16
@@ -122,6 +181,4 @@ def linear_backward_scaled(g, x, w, masks, sg, sw, sx, sg_inv, sw_inv, sx_inv, a
         raise TypeError(
             f"fp8 backward requires bf16 inputs, got {g.dtype}/{x.dtype}/{w.dtype}"
         )
-    return _mod().fp8_linear_backward_scaled(
+    return _mod().linear_backward_fp8(g, x, w, list(masks), sg, sw, sx, _fmt_int(fmt))
-        g, x, w, masks, sg, sw, sx, sg_inv, sw_inv, sx_inv, amax_g
-    )

csrc/CMakeLists.txt

@@ -48,10 +48,33 @@ set(TORCH_LIBS
 
 set(CMAKE_CUDA_ARCHITECTURES "${ASTRAI_CUDA_ARCH}")
 
-set(KERNELS attn_decode attn_prefill attn_paged_decode attn_paged_prefill rotary_emb fp8_mm)
+# Kernel registry — parallel lists of module names (.so / pybind names,
+# globally unique across families) and their per-family source paths under
+# kernels/. `loader.py` auto-discovers the .so files in astrai/extension/lib/,
+# so this CMake registry is the single place to register a new kernel.
+set(KERNEL_NAMES
+    attn_decode
+    attn_prefill
+    attn_paged_decode
+    attn_paged_prefill
+    rotary_emb
+    fp8_mm
+)
+set(KERNEL_SRCS
+    attention/decode.cu
+    attention/prefill.cu
+    attention/paged_decode.cu
+    attention/paged_prefill.cu
+    rotary/rotary_emb.cu
+    fp8/mm.cu
+)
 
-foreach(name ${KERNELS})
+list(LENGTH KERNEL_NAMES _kernel_count)
-    add_library(${name} MODULE "${CMAKE_CURRENT_SOURCE_DIR}/kernels/${name}.cu")
+math(EXPR _kernel_last "${_kernel_count} - 1")
+foreach(i RANGE ${_kernel_last})
+    list(GET KERNEL_NAMES ${i} name)
+    list(GET KERNEL_SRCS ${i} src)
+    add_library(${name} MODULE "${CMAKE_CURRENT_SOURCE_DIR}/kernels/${src}")
 
     target_compile_definitions(${name} PRIVATE TORCH_EXTENSION_NAME=${name})
 

csrc/__init__.py

@@ -1,2 +1,2 @@
 # Source directory for CUDA kernels — build-time only.
-# Compiled .so files live in astrAI/_ext/.
+# Compiled .so files live in astrai/extension/lib/ (see csrc/CMakeLists.txt).

csrc/kernels/attention/common.h

@@ -13,7 +13,7 @@ enum TensorLayout : int {
 //   - Contiguous K/V: dense [batch, kv_head, kv_len, head_dim] tensors (k/v).
 //   - Paged (SGLang-style): flat pool [size, kv_head, head_dim] + req_to_token.
 // Each kernel selects the addressing via a KVSource policy (see
-// attn_layout_policies.cuh); a given call only touches the fields of one mode, so
+// layout_policies.cuh); a given call only touches the fields of one mode, so
 // this is a POD shared by both paths rather than two parallel structs that
 // drift out of sync.
 template<typename T, typename AT = float>

csrc/kernels/attention/decode.cu

@@ -1,5 +1,5 @@
-#include "attn_dispatchers.cuh"
+#include "dispatchers.cuh"
-#include "attn_entry_utils.cuh"
+#include "entry_utils.cuh"
 
 torch::Tensor attn_decode(
     torch::Tensor q,

csrc/kernels/attention/decode_split_kv.cuh

@@ -1,9 +1,9 @@
 #pragma once
 #include <cuda_bf16.h>
 #include <float.h>
-#include "attn_common.h"
+#include "common.h"
-#include "attn_layout_policies.cuh"
+#include "layout_policies.cuh"
-#include "attn_warp_utils.cuh"
+#include "warp_utils.cuh"
 constexpr int DC_CHUNK = 64;
 
 // Scalar split-KV decode (fallback for sm < 80, no tensor cores), unified

csrc/kernels/attention/decode_split_kv_mma.cuh

@@ -1,10 +1,10 @@
 #pragma once
 #include <cfloat>
 #include <cuda_bf16.h>
-#include "attn_common.h"
+#include "common.h"
-#include "attn_layout_policies.cuh"
+#include "layout_policies.cuh"
-#include "attn_mma_utils.cuh"
+#include "mma_utils.cuh"
-#include "attn_warp_utils.cuh"
+#include "warp_utils.cuh"
 
 // Split-K (FlashDecoding) tensor-core decode via GQA head-packing, unified
 // across contiguous and paged (SGLang flat-pool) K/V via the KV template

csrc/kernels/attention/dispatchers.cuh

@@ -3,20 +3,20 @@
 // No torch dependency; pure CUDA.
 //
 // The paged and contiguous kernels are unified by the KVSource policy
-// (ContigKV / PagedKV from attn_layout_policies.cuh), so each launcher struct
+// (ContigKV / PagedKV from layout_policies.cuh), so each launcher struct
 // below is templated on KV and the paged dispatch is just the same launcher
 // instantiated with PagedKV.  Only the grid/split math differs, and that is
 // covered by KV::host_q_len / KV::host_kv_len.
 
 #include <cuda_runtime.h>
 #include <algorithm>
-#include "attn_warp_utils.cuh"
+#include "warp_utils.cuh"
-#include "attn_layout_policies.cuh"
+#include "layout_policies.cuh"
-#include "attn_prefill_split_q.cuh"
+#include "prefill_split_q.cuh"
-#include "attn_decode_split_kv.cuh"
+#include "decode_split_kv.cuh"
 #ifndef ASTRAI_NO_MMA
-#include "attn_prefill_split_q_mma.cuh"
+#include "prefill_split_q_mma.cuh"
-#include "attn_decode_split_kv_mma.cuh"
+#include "decode_split_kv_mma.cuh"
 #endif
 
 // Split-KV: compute number of splits to fill all SMs for small-batch decode.

csrc/kernels/attention/entry_utils.cuh

@@ -2,8 +2,8 @@
 #include <float.h>
 #include <torch/extension.h>
 #include <c10/cuda/CUDAGuard.h>
-#include "attn_common.h"
+#include "common.h"
-#include "attn_warp_utils.cuh"
+#include "warp_utils.cuh"
 
 using bf16 = __nv_bfloat16;
 

csrc/kernels/attention/layout_policies.cuh

@@ -1,6 +1,6 @@
 #pragma once
 #include <cuda_bf16.h>
-#include "attn_common.h"
+#include "common.h"
 
 // ============================================================================
 // Attention layout policies keep Q scheduling independent from K/V storage.

csrc/kernels/attention/mma_utils.cuh

@@ -3,6 +3,8 @@
 #include <cuda_fp16.h>
 #include <cuda_runtime.h>
 
+#include "../common/mma.cuh"
+
 // Predicated cp.async (4-operand form) requires CUDA 11.2+.
 // bf16 mma.sync requires sm_80+ (guarded at build time by ASTRAI_NO_MMA).
 #if CUDART_VERSION < 11020
@@ -24,10 +26,10 @@ struct KernelTraits {
 
     static constexpr int BR = 16;             // Q rows per warp (mma M=16)
 
-    // Derived: mma.sync.m16n8k16 tile counts
+    // Derived: mma tile counts from the shared mma_shape (m16n8k16 for bf16)
-    static constexpr int KD  = HEAD_DIM / 16;  // Q/K k-slides
+    static constexpr int KD  = HEAD_DIM / astrai::mma_shape<bf16>::k;  // Q/K k-slides
     static constexpr int NC8 = BC / 8;          // S n-tiles (N=8)
-    static constexpr int KT2 = BC / 16;         // P k-tiles (K=16)
+    static constexpr int KT2 = BC / astrai::mma_shape<bf16>::k;        // P k-tiles (K=16)
     static constexpr int DN8 = HEAD_DIM / 8;    // O n-tiles (N=8)
 
     static constexpr int LD = HEAD_DIM;         // smem leading dim
@@ -43,16 +45,7 @@ struct KernelTraits {
 
 // ---- PTX wrappers ----
 using bf16 = __nv_bfloat16;
-
+// bf16 mma.sync lives in the shared astrai::mma_sync template (common/mma.cuh).
-__device__ __forceinline__ void mma16816(float* d, const unsigned* a,
-                                          const unsigned* b, const float* c) {
-    asm volatile(
-        "mma.sync.aligned.m16n8k16.row.col.f32.bf16.bf16.f32 "
-        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%10,%11,%12,%13};"
-        : "=f"(d[0]), "=f"(d[1]), "=f"(d[2]), "=f"(d[3])
-        : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]), "r"(b[0]), "r"(b[1]),
-          "f"(c[0]), "f"(c[1]), "f"(c[2]), "f"(c[3]));
-}
 
 // read two adjacent bf16 from smem as one packed .b32 (elem0 low, elem1 high)
 __device__ __forceinline__ unsigned ld2(const bf16* p) {
@@ -73,26 +66,9 @@ __device__ __forceinline__ unsigned pkb(bf16 a, bf16 b) {
     return *reinterpret_cast<unsigned*>(&v);
 }
 
-// ldmatrix: cooperatively load mma fragments from smem (one instruction per
+// ldmatrix lives in the shared template (common/mma.cuh):
-// 16x16 / 16x8 tile) with the exact register layout mma expects.
+// `astrai::ldmatrix_x2<bf16>` / `<bf16, /*Trans=*/true>` load the K/V
-__device__ __forceinline__ void ldmatrix_x4(unsigned* r, const bf16* p) {
+// fragments with the exact register layout mma expects.
-    unsigned a = __cvta_generic_to_shared(p);
-    asm volatile("ldmatrix.sync.aligned.m8n8.x4.shared.b16 {%0,%1,%2,%3}, [%4];"
-                 : "=r"(r[0]), "=r"(r[1]), "=r"(r[2]), "=r"(r[3])
-                 : "r"(a));
-}
-__device__ __forceinline__ void ldmatrix_x2(unsigned* r, const bf16* p) {
-    unsigned a = __cvta_generic_to_shared(p);
-    asm volatile("ldmatrix.sync.aligned.m8n8.x2.shared.b16 {%0,%1}, [%2];"
-                 : "=r"(r[0]), "=r"(r[1])
-                 : "r"(a));
-}
-__device__ __forceinline__ void ldmatrix_x2_trans(unsigned* r, const bf16* p) {
-    unsigned a = __cvta_generic_to_shared(p);
-    asm volatile("ldmatrix.sync.aligned.m8n8.x2.trans.shared.b16 {%0,%1}, [%2];"
-                 : "=r"(r[0]), "=r"(r[1])
-                 : "r"(a));
-}
 
 // XOR swizzle for shared-memory column at 8-bf16 chunk granularity.
 __device__ __forceinline__ int swiz_col(int d, int r, int mask = 7) {
@@ -180,9 +156,9 @@ __device__ inline void mma_compute_scores(
         #pragma unroll
         for (int kt = 0; kt < Traits::KD; kt++) {
             unsigned b[2];
-            ldmatrix_x2(b, &sK[krow_l * Traits::LD
+            astrai::ldmatrix_x2<bf16>(b, &sK[krow_l * Traits::LD
                 + swiz_col(kt * 16 + kcol_h, krow_l, Traits::SWIZ_MASK)]);
-            mma16816(Sacc[n8], Qa[kt], b, Sacc[n8]);
+            astrai::mma_sync<bf16>(Sacc[n8], Qa[kt], b, Sacc[n8]);
         }
     }
 }
@@ -290,9 +266,9 @@ __device__ inline void mma_pv_accumulate(
         #pragma unroll
         for (int dn8 = 0; dn8 < Traits::DN8; dn8++) {
             unsigned b[2];
-            ldmatrix_x2_trans(b, &sV[vrow_l * Traits::LD
+            astrai::ldmatrix_x2<bf16, true>(b, &sV[vrow_l * Traits::LD
                 + swiz_col(dn8 * 8, vrow_l, Traits::SWIZ_MASK)]);
-            mma16816(Oacc[dn8], Pa, b, Oacc[dn8]);
+            astrai::mma_sync<bf16>(Oacc[dn8], Pa, b, Oacc[dn8]);
         }
     }
 }

csrc/kernels/attention/paged_decode.cu

@@ -1,5 +1,5 @@
-#include "attn_dispatchers.cuh"
+#include "dispatchers.cuh"
-#include "attn_entry_utils.cuh"
+#include "entry_utils.cuh"
 
 torch::Tensor attn_paged_decode(
     torch::Tensor q,

csrc/kernels/attention/paged_prefill.cu

@@ -1,5 +1,5 @@
-#include "attn_dispatchers.cuh"
+#include "dispatchers.cuh"
-#include "attn_entry_utils.cuh"
+#include "entry_utils.cuh"
 
 torch::Tensor attn_paged_prefill(
     torch::Tensor q,

csrc/kernels/attention/prefill.cu

@@ -1,5 +1,5 @@
-#include "attn_dispatchers.cuh"
+#include "dispatchers.cuh"
-#include "attn_entry_utils.cuh"
+#include "entry_utils.cuh"
 
 torch::Tensor attn_prefill(
     torch::Tensor q,

csrc/kernels/attention/prefill_split_q.cuh

@@ -1,8 +1,8 @@
 #pragma once
 #include <cfloat>
 #include <cuda_bf16.h>
-#include "attn_common.h"
+#include "common.h"
-#include "attn_layout_policies.cuh"
+#include "layout_policies.cuh"
 
 using bf16 = __nv_bfloat16;
 

csrc/kernels/attention/prefill_split_q_mma.cuh

@@ -1,9 +1,9 @@
 #pragma once
 #include <cfloat>
 #include <cuda_bf16.h>
-#include "attn_common.h"
+#include "common.h"
-#include "attn_layout_policies.cuh"
+#include "layout_policies.cuh"
-#include "attn_mma_utils.cuh"
+#include "mma_utils.cuh"
 
 // Tensor-core prefill flash attention (raw mma.sync PTX), unified across
 // contiguous and paged (SGLang flat-pool) K/V via the KV template parameter.

csrc/kernels/common/device.cuh

@@ -0,0 +1,23 @@
+// Pure-CUDA device helpers shared across kernel families (no torch).
+//
+// Family-local headers under kernels/<family>/ own their POD params and
+// strategy traits; anything cross-cutting (compute-capability checks, device
+// constants) lives here.
+
+#pragma once
+
+namespace astrai {
+
+// Compute-capability comparison: is the device at least (major, minor)?
+inline bool sm_at_least(int device_major, int device_minor, int major,
+                        int minor) {
+    return device_major > major ||
+           (device_major == major && device_minor >= minor);
+}
+
+// FP8 tensor-core MMA (`mma.sync.aligned.m16n8k32` with fp8 inputs) exists on
+// Ada (sm_89) and Hopper (sm_90+); sm_80 has no fp8 instructions.
+inline constexpr int kMinSmForFp8Major = 8;
+inline constexpr int kMinSmForFp8Minor = 9;
+
+}  // namespace astrai

csrc/kernels/common/mma.cuh

@@ -0,0 +1,143 @@
+// Shared mma.sync wrappers — pure CUDA, no torch.
+//
+// One template for every tensor-core MMA used by the kernel families. The
+// instruction shape follows from the input element type:
+//   __nv_bfloat16        -> mma.sync.aligned.m16n8k16 (sm_80+), A = 4x b32, B = 2x b32
+//   __nv_fp8_e4m3/e5m2   -> mma.sync.aligned.m16n8k32 (sm_89+), A = 4x b32, B = 2x b32
+// All variants accumulate into fp32: d = a*b + c, with the PTX mnemonic and
+// the K dimension differing per type. `d` may alias `c` (in-place accumulate,
+// as the FP8 GEMM does).
+
+#pragma once
+
+#include <cuda_bf16.h>
+#include <cuda_fp8.h>
+#include <cuda_runtime.h>
+#include <type_traits>
+
+namespace astrai {
+
+// Compute capability of the current compilation pass: 0 in the host pass,
+// the numeric CC (e.g. 890) in device passes where __CUDA_ARCH__ is defined.
+// Defined() cannot appear in expressions, so this macro lets mma_sync use
+// the arch in a static_assert instead of per-branch #if guards.
+#ifndef __CUDA_ARCH__
+#define ASTRAI_DEVICE_ARCH 0
+#else
+#define ASTRAI_DEVICE_ARCH __CUDA_ARCH__
+#endif
+
+// Compile-time shape of the MMA instruction for an input element type.
+// `min_arch` is the numeric compute capability the instruction requires —
+// the single place that encodes the hardware floor for each type.
+template <typename InT>
+struct mma_shape {
+    static constexpr int k = 16;         // m16n8k16
+    static constexpr int a_regs = 4;     // A fragment: 4x b32
+    static constexpr int b_regs = 2;     // B fragment: 2x b32
+    static constexpr int min_arch = 800; // bf16 mma.sync, sm_80+
+};
+
+template <>
+struct mma_shape<__nv_fp8_e4m3> {
+    static constexpr int k = 32;         // m16n8k32
+    static constexpr int a_regs = 4;
+    static constexpr int b_regs = 2;
+    static constexpr int min_arch = 890; // fp8 mma.sync, sm_89+ (Ada/Hopper)
+};
+
+template <>
+struct mma_shape<__nv_fp8_e5m2> {
+    static constexpr int k = 32;
+    static constexpr int a_regs = 4;
+    static constexpr int b_regs = 2;
+    static constexpr int min_arch = 890;
+};
+
+// d[4] = a[4] x b[2] + c[4], row-major A, col-major B, fp32 accumulator.
+// The PTX mnemonic is selected from InT. Building for a compute capability
+// below `mma_shape<InT>::min_arch` is a **compile error** — the instruction
+// does not exist there, and a silent no-op would produce wrong results.
+template <typename InT>
+__device__ __forceinline__ void mma_sync(float d[4], const unsigned a[4],
+                                         const unsigned b[2],
+                                         const float c[4]) {
+    static_assert(ASTRAI_DEVICE_ARCH == 0 ||
+                      ASTRAI_DEVICE_ARCH >= mma_shape<InT>::min_arch,
+                  "mma_sync: this MMA shape requires a newer compute "
+                  "capability than the build target");
+    if constexpr (std::is_same_v<InT, __nv_bfloat16>) {
+        asm volatile(
+            "mma.sync.aligned.m16n8k16.row.col.f32.bf16.bf16.f32 "
+            "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%10,%11,%12,%13};"
+            : "=f"(d[0]), "=f"(d[1]), "=f"(d[2]), "=f"(d[3])
+            : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]), "r"(b[0]), "r"(b[1]),
+              "f"(c[0]), "f"(c[1]), "f"(c[2]), "f"(c[3]));
+    } else if constexpr (std::is_same_v<InT, __nv_fp8_e5m2>) {
+        asm volatile(
+            "mma.sync.aligned.m16n8k32.row.col.f32.e5m2.e5m2.f32 "
+            "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%10,%11,%12,%13};"
+            : "=f"(d[0]), "=f"(d[1]), "=f"(d[2]), "=f"(d[3])
+            : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]), "r"(b[0]), "r"(b[1]),
+              "f"(c[0]), "f"(c[1]), "f"(c[2]), "f"(c[3]));
+    } else {
+        asm volatile(
+            "mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32 "
+            "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%10,%11,%12,%13};"
+            : "=f"(d[0]), "=f"(d[1]), "=f"(d[2]), "=f"(d[3])
+            : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]), "r"(b[0]), "r"(b[1]),
+              "f"(c[0]), "f"(c[1]), "f"(c[2]), "f"(c[3]));
+    }
+}
+
+#undef ASTRAI_DEVICE_ARCH
+
+// ---------------------------------------------------------------------------
+// ldmatrix — cooperatively load 8x8 b16 matrices from smem into registers.
+//
+// The instruction is identical for every 16-bit-storage element type: bf16
+// maps 1:1 onto b16 slots; fp8 is stored packed two-per-slot (see
+// fp8/gemm.cuh), so one b16 slot holds two fp8 values. `T` is the element
+// type and only serves as a semantic tag.
+//
+//   x2 (single address): matrix0 = p (8 rows), matrix1 = p + 8*16 bytes
+//   x4:                  four matrices at p, +128, +256, +384 bytes
+//   Trans:               transpose variant (V fragments of attention)
+//
+// ldmatrix takes a *single* smem address per thread, but the addresses of
+// the 32 lanes are *not* all the same: lane i supplies the start address of
+// matrix-row i (modulo 8) for matrix (i/8) — lanes 0-7 feed matrix 0's rows,
+// lanes 8-15 matrix 1's rows (x2/x4), lanes 16-23 / 24-31 matrix 2 / 3's rows
+// (x4 only; their addresses are ignored by x2). Each matrix is 8 rows x 16
+// bytes, and consecutive matrices of one instruction are contiguous at
+// 128-byte strides. fp8 fragment layouts in fp8/gemm.cuh are arranged around
+// this constraint.
+// ---------------------------------------------------------------------------
+
+template <typename T, bool Trans = false>
+__device__ __forceinline__ void ldmatrix_x2(unsigned r[2], const T* p) {
+    const unsigned a = __cvta_generic_to_shared(p);
+    if constexpr (Trans) {
+        asm volatile(
+            "ldmatrix.sync.aligned.m8n8.x2.trans.shared.b16 {%0,%1}, [%2];"
+            : "=r"(r[0]), "=r"(r[1])
+            : "r"(a));
+    } else {
+        asm volatile(
+            "ldmatrix.sync.aligned.m8n8.x2.shared.b16 {%0,%1}, [%2];"
+            : "=r"(r[0]), "=r"(r[1])
+            : "r"(a));
+    }
+}
+
+// Four matrices at p, p+128, p+256, p+384 bytes (16-byte row stride).
+template <typename T>
+__device__ __forceinline__ void ldmatrix_x4(unsigned r[4], const T* p) {
+    const unsigned a = __cvta_generic_to_shared(p);
+    asm volatile(
+        "ldmatrix.sync.aligned.m8n8.x4.shared.b16 {%0,%1,%2,%3}, [%4];"
+        : "=r"(r[0]), "=r"(r[1]), "=r"(r[2]), "=r"(r[3])
+        : "r"(a));
+}
+
+}  // namespace astrai

csrc/kernels/fp8/common.h

@@ -0,0 +1,62 @@
+#pragma once
+
+#include <cuda_bf16.h>
+#include <cuda_fp8.h>
+#include <cuda_runtime.h>
+#include <cstdint>
+
+// Compile-time FP8 format: E4M3 (forward / high precision, max 448) or
+// E5M2 (gradient / large dynamic range, max 57344).
+enum class FP8Format : int {
+    E4M3 = 0,
+    E5M2 = 1,
+};
+
+// Compile-time tile configuration, mirroring KernelTraits<HEAD_DIM, BC,
+// WARPS, STAGES> in the attention kernels. `Fmt` selects the FP8 conversion
+// and the MMA PTX mnemonic; the remaining parameters shape the CTA tile and
+// the cp.async pipeline depth.
+template <FP8Format Fmt, int BlockM, int BlockN, int K, int Stages>
+struct Fp8GemmTraits {
+    static constexpr FP8Format kFormat = Fmt;
+    static constexpr int kBlockM = BlockM;
+    static constexpr int kBlockN = BlockN;
+    static constexpr int kK = K;
+    static constexpr int kStages = Stages;
+    static constexpr bool kIsE5M2 = (Fmt == FP8Format::E5M2);
+    static constexpr __nv_fp8_interpretation_t kNvFormat =
+        kIsE5M2 ? __NV_E5M2 : __NV_E4M3;
+    static constexpr float kFp8Max = kIsE5M2 ? 57344.0f : 448.0f;
+
+    // Saturated float -> FP8 conversion for this format.
+    __device__ __forceinline__ static unsigned char cvt(float f) {
+        return static_cast<unsigned char>(
+            __nv_cvt_float_to_fp8(f, __NV_SATFINITE, kNvFormat));
+    }
+};
+
+// Unified GEMM parameter POD, mirroring AttentionParams: one struct flows
+// through quantize / fused / pre-quantized kernels. Each kernel touches only
+// the fields it needs; buffers are raw pointers packed by the torch binding.
+struct FP8Params {
+    // Inputs: a/b are BF16 for the fused (quantize-in-GEMM) path, FP8 for
+    // the pre-quantized path. Scales are quantization steps (device scalars).
+    const void* __restrict__ a_ptr;
+    const void* __restrict__ b_ptr;
+    const float* __restrict__ scale_a;
+    const float* __restrict__ scale_b;
+
+    // Output: BF16 or FP8 (E4M3). out_scale is the output quantization step
+    // (FP8 output only).
+    void* __restrict__ out_ptr;
+    const float* __restrict__ out_scale;
+
+    // Fused forward extras: bias (may be null) and amax slots (may be null).
+    const __nv_bfloat16* __restrict__ bias;
+    float* __restrict__ amax_a;
+    float* __restrict__ amax_b;
+
+    // Shapes. total is only used by the elementwise quantize kernel.
+    int64_t m, n, k;
+    int64_t total;
+};

csrc/kernels/fp8/gemm.cuh

@@ -0,0 +1,668 @@
+#pragma once
+// FP8 GEMM device code — pure CUDA, no torch. Mirrors the attention kernel
+// layout (attn_*_mma.cuh): kernels take the FP8Params POD, tile shape and
+// FP8 format ride on compile-time template parameters, and launchers are
+// plain functions usable from both the torch binding and pure C tests.
+
+#include <cuda_bf16.h>
+#include <cuda_fp8.h>
+#include <cuda_runtime.h>
+#include <type_traits>
+
+#include "common.h"
+#include "../common/mma.cuh"
+
+namespace fp8 {
+
+// m16n8k32 (see astrai::mma_shape<fp8 type>::k in common/mma.cuh)
+constexpr int kMmaK = 32;
+constexpr int kWarps = 8;  // 128x64 CTA = 8 warps
+
+// Map the FP8Format enum to the CUDA fp8 element type consumed by mma_sync.
+template <FP8Format Fmt>
+struct fp8_input {
+    using type = __nv_fp8_e4m3;
+};
+template <>
+struct fp8_input<FP8Format::E5M2> {
+    using type = __nv_fp8_e5m2;
+};
+
+// ---------------------------------------------------------------------------
+// Shared device helpers
+// ---------------------------------------------------------------------------
+
+__device__ __forceinline__ unsigned pack_fp8x4_vector(
+    float x0, float x1, float x2, float x3,
+    __nv_fp8_interpretation_t fmt = __NV_E4M3) {
+    const auto low = __nv_cvt_float2_to_fp8x2(make_float2(x0, x1),
+                                              __NV_SATFINITE, fmt);
+    const auto high = __nv_cvt_float2_to_fp8x2(make_float2(x2, x3),
+                                               __NV_SATFINITE, fmt);
+    return static_cast<unsigned>(low) | (static_cast<unsigned>(high) << 16);
+}
+
+// FP8 MMA lives in the shared astrai::mma_sync template (common/mma.cuh);
+// instantiate it with fp8_input<Fmt>::type. Accumulates in-place: callers
+// pass the same accumulator array as both `d` and `c`.
+
+__device__ __forceinline__ void atomic_max_float(float* destination,
+                                                  float value) {
+    if (destination)
+        atomicMax(reinterpret_cast<unsigned*>(destination),
+                  __float_as_uint(value));
+}
+
+__device__ __forceinline__ float warp_reduce_max(float value) {
+#pragma unroll
+    for (int offset = 16; offset; offset >>= 1) {
+        value = fmaxf(value, __shfl_xor_sync(0xffffffffu, value, offset));
+    }
+    return value;
+}
+
+// Block-wide max reduction of a per-warp tracked value, then an atomic
+// update of the global amax slot when `track` is set.
+template <int NWarps>
+__device__ __forceinline__ void block_reduce_amax(float& local, float* slots,
+                                                  int warp, int lane,
+                                                  bool track, float* global) {
+    local = warp_reduce_max(local);
+    if (lane == 0) slots[warp] = local;
+    __syncthreads();
+    if (warp == 0) {
+        float value = lane < NWarps ? slots[lane] : 0.0f;
+        value = warp_reduce_max(value);
+        if (lane == 0 && track && global) atomic_max_float(global, value);
+    }
+}
+
+// One thread moves eight BF16 values (16 bytes) via cp.async; the uint4
+// shape keeps source and destination naturally 128-bit aligned.
+__device__ __forceinline__ void cp_async_bf16_8(
+    __nv_bfloat16* destination, const __nv_bfloat16* source, bool valid) {
+    const unsigned shared_address = __cvta_generic_to_shared(destination);
+    const uint4* source_vec = reinterpret_cast<const uint4*>(source);
+    asm volatile("cp.async.cg.shared.global [%0], [%1], 16, %2;"
+                 :: "r"(shared_address), "l"(source_vec),
+                    "r"(valid ? 16 : 0));
+}
+
+// One thread moves sixteen FP8 values (16 bytes) via cp.async.
+template <typename T>
+__device__ __forceinline__ void cp_async_16b(T* destination,
+                                             const T* source, bool valid) {
+    const unsigned shared_address = __cvta_generic_to_shared(destination);
+    const uint4* source_vec = reinterpret_cast<const uint4*>(source);
+    asm volatile("cp.async.cg.shared.global [%0], [%1], 16, %2;"
+                 :: "r"(shared_address), "l"(source_vec),
+                    "r"(valid ? 16 : 0));
+}
+
+// Convert four BF16 values to one 4xFP8 pack, tracking the raw (pre-scale)
+// amax — scaling first would saturate amax at the FP8 max and collapse the
+// scale. Format comes from Traits.
+template <typename Traits, bool TrackAmax = true>
+__device__ __forceinline__ unsigned load_fp8x4_from_bf16(
+    const __nv_bfloat16* source, float scale_inv, float& amax,
+    bool track_amax = true) {
+    float x0 = __bfloat162float(source[0]);
+    float x1 = __bfloat162float(source[1]);
+    float x2 = __bfloat162float(source[2]);
+    float x3 = __bfloat162float(source[3]);
+    if constexpr (TrackAmax) {
+        if (track_amax) {
+            amax = fmaxf(amax, fmaxf(fabsf(x0), fmaxf(fabsf(x1),
+                         fmaxf(fabsf(x2), fabsf(x3)))));
+        }
+    }
+    return pack_fp8x4_vector(x0 * scale_inv, x1 * scale_inv,
+                             x2 * scale_inv, x3 * scale_inv,
+                             Traits::kNvFormat);
+}
+
+// ---------------------------------------------------------------------------
+// Quantize kernel: BF16 -> FP8 (E4M3 or E5M2), fused amax over raw values.
+// ---------------------------------------------------------------------------
+
+template <FP8Format Fmt>
+__global__ void fp8_quantize_kernel(FP8Params p) {
+    const float inv = 1.0f / *p.scale_a;
+    const auto* x = reinterpret_cast<const __nv_bfloat16*>(p.a_ptr);
+    void* x8 = p.out_ptr;
+    float* amax = p.amax_a;
+    float local_amax = 0.0f;
+    const int64_t stride = (int64_t)blockDim.x * gridDim.x;
+    for (int64_t i = blockIdx.x * blockDim.x + threadIdx.x; i < p.total;
+         i += stride) {
+        const float f = __bfloat162float(x[i]);
+        local_amax = fmaxf(local_amax, fabsf(f));
+        const float q = f * inv;
+        if constexpr (Fmt == FP8Format::E5M2) {
+            reinterpret_cast<__nv_fp8_e5m2*>(x8)[i] = __nv_fp8_e5m2(q);
+        } else {
+            reinterpret_cast<__nv_fp8_e4m3*>(x8)[i] = __nv_fp8_e4m3(q);
+        }
+    }
+    if (amax) {
+        local_amax = warp_reduce_max(local_amax);
+        __shared__ float slots[32];
+        if ((threadIdx.x & 31) == 0) slots[threadIdx.x >> 5] = local_amax;
+        __syncthreads();
+        if (threadIdx.x == 0) {
+            float v = 0.0f;
+            for (int w = 0; w < (blockDim.x >> 5); ++w) v = fmaxf(v, slots[w]);
+            atomic_max_float(amax, v);
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------
+// Fused kernel: BF16 A/B -> inline E4M3 quantize -> ldmatrix fragments ->
+// MMA -> BF16 out. 128x64 CTA / 64x16 warp tile / cp.async pipeline.
+// The quantized FP8 tiles live in a separate smem region laid out around
+// ldmatrix's single-address, 128-byte-strided matrices (16-byte rows):
+//   A8: [M/16 block][4 sub-blocks of 8 rows x 16 fp8][...] where sub-block
+//       order is (h0,m0-7), (h0,m8-15), (h1,m0-7), (h1,m8-15) — one
+//       ldmatrix.x4 emits the whole m16n8k32 A fragment (regs 0..3 match).
+//   B8: [N/8 block][2 sub-blocks of 8 rows x 16 fp8][...] with h0 then h1 —
+//       one ldmatrix.x2 emits the m16n8k32 B fragment (regs 0,1).
+// ---------------------------------------------------------------------------
+
+template <typename Traits, bool AddBias, bool TrackAmax>
+__global__ void fp8_fused_gemm_kernel(FP8Params p) {
+    using T8 = __nv_fp8_e4m3;  // fused forward always quantizes to E4M3
+    constexpr int kBlockM = Traits::kBlockM;
+    constexpr int kBlockN = Traits::kBlockN;
+    constexpr int kK = Traits::kK;
+    constexpr int kStages = Traits::kStages;
+    constexpr int kWarpM = 64;  // warp tile rows (BlockM / 2)
+    constexpr int kWarpN = 16;  // warp tile cols (BlockN / 4)
+    constexpr int a_stride = kBlockM * kK;  // bf16 elements per A stage
+    constexpr int b_stride = kBlockN * kK;  // bf16 elements per B stage
+    // A8 block layout: (M/16) blocks x 4 sub-blocks x 128 B = BlockM*32 B.
+    // B8 block layout: (N/8) blocks x 2 sub-blocks x 128 B = BlockN*32 B.
+    constexpr int a8_bytes = kBlockM * 32;
+    constexpr int b8_bytes = kBlockN * 32;
+    // smem layout: [A bf16 stages][B bf16 stages][A8 fp8 tiles][B8 fp8 tiles]
+    constexpr int bf16_bytes = kStages * (a_stride + b_stride) * 2;
+    extern __shared__ char smem[];
+    auto* a_bf16 = reinterpret_cast<__nv_bfloat16*>(smem);
+    auto* b_bf16 = reinterpret_cast<__nv_bfloat16*>(smem + kStages * a_stride * 2);
+    auto* a8 = reinterpret_cast<T8*>(smem + bf16_bytes);
+    auto* b8 = reinterpret_cast<T8*>(smem + bf16_bytes + a8_bytes);
+    __shared__ float warp_amax_a[kWarps];
+    __shared__ float warp_amax_b[kWarps];
+
+    const auto* a = reinterpret_cast<const __nv_bfloat16*>(p.a_ptr);
+    const auto* b = reinterpret_cast<const __nv_bfloat16*>(p.b_ptr);
+    auto* out = reinterpret_cast<__nv_bfloat16*>(p.out_ptr);
+    const auto* bias = p.bias;
+    const float* scale_a = p.scale_a;
+    const float* scale_b = p.scale_b;
+    float* amax_a = p.amax_a;
+    float* amax_b = p.amax_b;
+    const int64_t m = p.m, n = p.n, k = p.k;
+
+    const int tid = threadIdx.x;
+    const int warp = tid >> 5;
+    const int lane = tid & 31;
+    const int group = lane >> 2;
+    const int thread_in_group = lane & 3;
+    constexpr int warps_n = kBlockN / 16;
+    const int warp_m = warp / warps_n;
+    const int warp_n = warp % warps_n;
+    const int64_t row_base = blockIdx.y * kBlockM + warp_m * kWarpM + group;
+    const int64_t output_col =
+        blockIdx.x * kBlockN + warp_n * 16 + thread_in_group * 2;
+    const float sa = *scale_a;
+    const float sb = *scale_b;
+    const float inv_a = 1.0f / sa;
+    const float inv_b = 1.0f / sb;
+    float local_amax_a = 0.0f;
+    float local_amax_b = 0.0f;
+    float acc[4 * 4 * 2] = {};
+
+    const bool track_amax_a = TrackAmax && blockIdx.x == 0;
+    const bool track_amax_b = TrackAmax && blockIdx.y == 0;
+    // Each thread issues 8 A chunks and 4 B chunks of 8 BF16 (16B) per stage.
+    auto load_tile = [&](int stage, int64_t k_base) {
+        const int r0 = tid >> 2;
+        const int c0 = (tid & 3) * 8;
+#pragma unroll
+        for (int j = 0; j < kK / 32; ++j) {
+            const int col = c0 + 32 * j;
+            const bool full_chunk = k_base + col + 7 < k;
+            const int64_t a_row = blockIdx.y * kBlockM + r0;
+            const int64_t b_row = blockIdx.x * kBlockN + r0;
+            auto* a_dst = &a_bf16[stage * a_stride + r0 * kK + col];
+            auto* b_dst = &b_bf16[stage * b_stride + r0 * kK + col];
+            const auto* a_ptr = a + a_row * k + k_base + col;
+            const auto* b_ptr = b + b_row * k + k_base + col;
+            const bool full_a = a_row < m && full_chunk;
+            const bool full_b = b_row < n && full_chunk;
+            const bool aligned_a =
+                (reinterpret_cast<uintptr_t>(a_ptr) & 15) == 0;
+            const bool aligned_b =
+                (reinterpret_cast<uintptr_t>(b_ptr) & 15) == 0;
+            if (full_a && aligned_a) {
+                cp_async_bf16_8(a_dst, a_ptr, true);
+            } else {
+#pragma unroll
+                for (int i = 0; i < 8; ++i) {
+                    a_dst[i] = a_row < m && k_base + col + i < k
+                                   ? a_ptr[i]
+                                   : __float2bfloat16(0.0f);
+                }
+            }
+            if (full_b && aligned_b) {
+                cp_async_bf16_8(b_dst, b_ptr, true);
+            } else {
+#pragma unroll
+                for (int i = 0; i < 8; ++i) {
+                    b_dst[i] = b_row < n && k_base + col + i < k
+                                   ? b_ptr[i]
+                                   : __float2bfloat16(0.0f);
+                }
+            }
+            if (r0 + kWarpM < kBlockM) {
+                const int64_t a_row_hi = blockIdx.y * kBlockM + r0 + kWarpM;
+                auto* a_dst_hi =
+                    &a_bf16[stage * a_stride + (r0 + kWarpM) * kK + col];
+                const auto* a_ptr_hi = a + a_row_hi * k + k_base + col;
+                const bool full_a_hi = a_row_hi < m && full_chunk;
+                const bool aligned_a_hi =
+                    (reinterpret_cast<uintptr_t>(a_ptr_hi) & 15) == 0;
+                if (full_a_hi && aligned_a_hi) {
+                    cp_async_bf16_8(a_dst_hi, a_ptr_hi, true);
+                } else {
+#pragma unroll
+                    for (int i = 0; i < 8; ++i) {
+                        a_dst_hi[i] = a_row_hi < m && k_base + col + i < k
+                                          ? a_ptr_hi[i]
+                                          : __float2bfloat16(0.0f);
+                    }
+                }
+            }
+        }
+    };
+
+    // Quantize the BF16 staging area into the ldmatrix-friendly FP8 tiles.
+    // A8 sub-block for global row `row` and K half `h`:
+    //   (row>>4)*512 + ((h<<1)|((row>>3)&1))*128 + (row&7)*16
+    // B8 sub-block: (row>>3)*256 + h*128 + (row&7)*16.
+    // Each thread emits one 4-FP8 pack at a time (256 threads, kK/4 = 8 packs
+    // per row).
+    auto quantize_tile = [&](int stage) {
+        constexpr int kA_packs = kBlockM * kK / 4;
+        constexpr int kB_packs = kBlockN * kK / 4;
+#pragma unroll
+        for (int i = tid; i < kA_packs; i += 256) {
+            const int row = i >> 3;   // 8 packs per row
+            const int k4 = (i & 7) * 4;
+            const int half = k4 >> 4; // 0: k 0-15, 1: k 16-31
+            const int k16 = k4 & 15;
+            const int a8_idx =
+                (row >> 4) * 512 + (((half << 1) | ((row >> 3) & 1)) * 128) +
+                (row & 7) * 16 + k16;
+            auto* src = &a_bf16[stage * a_stride + row * kK + k4];
+            auto* dst = reinterpret_cast<unsigned*>(&a8[a8_idx]);
+            *dst = load_fp8x4_from_bf16<Traits, TrackAmax>(
+                src, inv_a, local_amax_a, track_amax_a);
+        }
+#pragma unroll
+        for (int i = tid; i < kB_packs; i += 256) {
+            const int row = i >> 3;
+            const int k4 = (i & 7) * 4;
+            const int half = k4 >> 4;
+            const int k16 = k4 & 15;
+            const int b8_idx =
+                (row >> 3) * 256 + half * 128 + (row & 7) * 16 + k16;
+            auto* src = &b_bf16[stage * b_stride + row * kK + k4];
+            auto* dst = reinterpret_cast<unsigned*>(&b8[b8_idx]);
+            *dst = load_fp8x4_from_bf16<Traits, TrackAmax>(
+                src, inv_b, local_amax_b, track_amax_b);
+        }
+    };
+
+    const int64_t tile_count = (k + kK - 1) / kK;
+    load_tile(0, 0);
+    asm volatile("cp.async.commit_group;");
+    if (tile_count > 1) {
+        load_tile(1, kK);
+        asm volatile("cp.async.commit_group;");
+    }
+    if (tile_count > 2) {
+        load_tile(2, 2 * kK);
+        asm volatile("cp.async.commit_group;");
+    }
+    for (int64_t tile_index = 0; tile_index < tile_count; ++tile_index) {
+        const int stage = static_cast<int>(tile_index % kStages);
+        // 3-stage pipeline: at most 2 groups in flight; the tail of the K
+        // loop waits for everything.
+        const int64_t remaining = tile_count - tile_index - 1;
+        if (remaining >= 2) {
+            asm volatile("cp.async.wait_group 2;");
+        } else if (remaining == 1) {
+            asm volatile("cp.async.wait_group 1;");
+        } else {
+            asm volatile("cp.async.wait_group 0;");
+        }
+        // wait_group only waits for this thread's async copies. All threads
+        // must finish loading before the tile is read by the CTA.
+        __syncthreads();
+        quantize_tile(stage);
+        __syncthreads();
+
+        // kK == kMmaK, so one m16n8k32 MMA segment per K stage; fragments
+        // come from the fp8 tiles via ldmatrix.
+#pragma unroll
+        for (int k_seg = 0; k_seg < kK / kMmaK; ++k_seg) {
+#pragma unroll
+            for (int nt = 0; nt < 2; ++nt) {
+                const int b_row0 = warp_n * 16 + nt * 8;
+                unsigned b_frag[2];
+                // B8 block = (b_row0>>3), sub-blocks h0 then h1 at +0/+128.
+                // ldmatrix: each thread supplies one matrix-row address —
+                // threads 0-7 feed matrix 0 (h0) rows, 8-15 matrix 1 (h1);
+                // the remaining threads' addresses are ignored.
+                const int b8_base = (b_row0 >> 3) * 256;
+                astrai::ldmatrix_x2<T8>(
+                    b_frag,
+                    &b8[b8_base + ((lane / 8) & 1) * 128 + (lane % 8) * 16]);
+#pragma unroll
+                for (int mt = 0; mt < 4; ++mt) {
+                    const int a_row0 = warp_m * kWarpM + mt * 16;
+                    unsigned a_frag[4];
+                    // A8 block = (a_row0>>4); one x4 emits regs 0..3 in the
+                    // exact mma A-operand order: h0m0-7, h0m8-15, h1m0-7,
+                    // h1m8-15. Each thread supplies matrix (tid/8) row
+                    // (tid%8) — all 32 addresses are used by x4.
+                    const int a8_base = (a_row0 >> 4) * 512;
+                    astrai::ldmatrix_x4<T8>(
+                        a_frag,
+                        &a8[a8_base + (lane / 8) * 128 + (lane % 8) * 16]);
+                    astrai::mma_sync<typename fp8_input<Traits::kFormat>::type>(
+                        acc + (nt * 4 + mt) * 4,
+                        a_frag, b_frag, acc + (nt * 4 + mt) * 4);
+                }
+            }
+        }
+        __syncthreads();
+        if (tile_index + 3 < tile_count) {
+            load_tile(stage, (tile_index + 3) * kK);
+            asm volatile("cp.async.commit_group;");
+        }
+    }
+
+    if constexpr (TrackAmax) {
+        block_reduce_amax<kWarps>(local_amax_a, warp_amax_a, warp, lane,
+                                  track_amax_a, amax_a);
+        block_reduce_amax<kWarps>(local_amax_b, warp_amax_b, warp, lane,
+                                  track_amax_b, amax_b);
+    }
+
+    const float output_scale = sa * sb;
+#pragma unroll
+    for (int nt = 0; nt < 2; ++nt) {
+        const int64_t col = output_col + nt * 8;
+#pragma unroll
+        for (int mt = 0; mt < 4; ++mt) {
+            const int64_t row0 = row_base + mt * 16;
+            const int64_t row1 = row0 + 8;
+            float* tile_acc = acc + (nt * 4 + mt) * 4;
+            if (col < n) {
+                float bias0 = 0.0f;
+                float bias1 = 0.0f;
+                if constexpr (AddBias) {
+                    bias0 = __bfloat162float(bias[col]);
+                    if (col + 1 < n)
+                        bias1 = __bfloat162float(bias[col + 1]);
+                }
+                if (row0 < m) {
+                    out[row0 * n + col] =
+                        __float2bfloat16(tile_acc[0] * output_scale + bias0);
+                    if (col + 1 < n)
+                        out[row0 * n + col + 1] = __float2bfloat16(
+                            tile_acc[1] * output_scale + bias1);
+                }
+                if (row1 < m) {
+                    out[row1 * n + col] =
+                        __float2bfloat16(tile_acc[2] * output_scale + bias0);
+                    if (col + 1 < n)
+                        out[row1 * n + col + 1] = __float2bfloat16(
+                            tile_acc[3] * output_scale + bias1);
+                }
+            }
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------
+// Pre-quantized kernel: FP8 A/B read straight into shared memory, FP32
+// accumulation, BF16 or FP8 output. The input format follows Traits; the
+// tile is compact (row = kK bytes) so MMA fragments read directly.
+// ---------------------------------------------------------------------------
+
+template <typename Traits, bool OutFp8 = false>
+__global__ void fp8_pq_gemm_kernel(FP8Params p) {
+    using T8 = std::conditional_t<Traits::kIsE5M2, __nv_fp8_e5m2, __nv_fp8_e4m3>;
+    constexpr int kBlockM = Traits::kBlockM;
+    constexpr int kBlockN = Traits::kBlockN;
+    constexpr int kK = Traits::kK;
+    constexpr int kStages = Traits::kStages;
+    __shared__ __align__(16) T8 a_tile[kStages][kBlockM][kK];
+    __shared__ __align__(16) T8 b_tile[kStages][kBlockN][kK];
+
+    const auto* a = reinterpret_cast<const T8*>(p.a_ptr);
+    const auto* b = reinterpret_cast<const T8*>(p.b_ptr);
+    auto* out_bf16 = reinterpret_cast<__nv_bfloat16*>(p.out_ptr);
+    auto* out_fp8 = reinterpret_cast<__nv_fp8_e4m3*>(p.out_ptr);
+    const int64_t m = p.m, n = p.n, k = p.k;
+
+    const int tid = threadIdx.x;
+    const int warp = tid >> 5;
+    const int lane = tid & 31;
+    const int group = lane >> 2;
+    const int thread_in_group = lane & 3;
+    constexpr int warps_n = kBlockN / 16;
+    const int warp_m = warp / warps_n;
+    const int warp_n = warp % warps_n;
+    const int64_t row_base = blockIdx.y * kBlockM + warp_m * 64 + group;
+    const int64_t output_col =
+        blockIdx.x * kBlockN + warp_n * 16 + thread_in_group * 2;
+    const float sa = *p.scale_a;
+    const float sb = *p.scale_b;
+    float acc[4 * 4 * 2] = {};
+
+    // One A chunk (16 FP8) per thread covers the 128x32 tile; the first 128
+    // threads issue the 64x32 B chunks.
+    auto load_tile = [&](int stage, int64_t k_base) {
+        const int r0 = tid >> 1;
+        const int c0 = (tid & 1) * 16;
+        const bool full_chunk = k_base + c0 + 15 < k;
+        const int64_t a_row = blockIdx.y * kBlockM + r0;
+        auto* a_dst = &a_tile[stage][r0][c0];
+        const auto* a_ptr = a + a_row * k + k_base + c0;
+        const bool full_a = a_row < m && full_chunk;
+        const bool aligned_a =
+            (reinterpret_cast<uintptr_t>(a_ptr) & 15) == 0;
+        if (full_a && aligned_a) {
+            cp_async_16b(a_dst, a_ptr, true);
+        } else {
+#pragma unroll
+            for (int i = 0; i < 16; ++i) {
+                a_dst[i] = a_row < m && k_base + c0 + i < k
+                               ? a_ptr[i]
+                               : T8(0.0f);
+            }
+        }
+        if (tid < 128) {
+            const int64_t b_row = blockIdx.x * kBlockN + r0;
+            auto* b_dst = &b_tile[stage][r0][c0];
+            const auto* b_ptr = b + b_row * k + k_base + c0;
+            const bool full_b = b_row < n && full_chunk;
+            const bool aligned_b =
+                (reinterpret_cast<uintptr_t>(b_ptr) & 15) == 0;
+            if (full_b && aligned_b) {
+                cp_async_16b(b_dst, b_ptr, true);
+            } else {
+#pragma unroll
+                for (int i = 0; i < 16; ++i) {
+                    b_dst[i] = b_row < n && k_base + c0 + i < k
+                                   ? b_ptr[i]
+                                   : T8(0.0f);
+                }
+            }
+        }
+    };
+
+    const int64_t tile_count = (k + kK - 1) / kK;
+    load_tile(0, 0);
+    asm volatile("cp.async.commit_group;");
+    if (tile_count > 1) {
+        load_tile(1, kK);
+        asm volatile("cp.async.commit_group;");
+    }
+    if (tile_count > 2) {
+        load_tile(2, 2 * kK);
+        asm volatile("cp.async.commit_group;");
+    }
+    for (int64_t tile_index = 0; tile_index < tile_count; ++tile_index) {
+        const int stage = static_cast<int>(tile_index % kStages);
+        const int64_t remaining = tile_count - tile_index - 1;
+        if (remaining >= 2) {
+            asm volatile("cp.async.wait_group 2;");
+        } else if (remaining == 1) {
+            asm volatile("cp.async.wait_group 1;");
+        } else {
+            asm volatile("cp.async.wait_group 0;");
+        }
+        // Barrier 1: every thread's cp.async for this stage is complete
+        // before any thread reads tiles written by other threads.
+        __syncthreads();
+
+#pragma unroll
+        for (int k_seg = 0; k_seg < kK / kMmaK; ++k_seg) {
+            const int frag_col = thread_in_group * 4 + k_seg * 32;
+#pragma unroll
+            for (int nt = 0; nt < 2; ++nt) {
+                const int b_row = warp_n * 16 + nt * 8 + group;
+                unsigned b_frag[2];
+                b_frag[0] = *reinterpret_cast<const unsigned*>(
+                    &b_tile[stage][b_row][frag_col]);
+                b_frag[1] = *reinterpret_cast<const unsigned*>(
+                    &b_tile[stage][b_row][frag_col + 16]);
+#pragma unroll
+                for (int mt = 0; mt < 4; ++mt) {
+                    const int a_row0 = warp_m * 64 + mt * 16 + group;
+                    unsigned a_frag[4];
+                    a_frag[0] = *reinterpret_cast<const unsigned*>(
+                        &a_tile[stage][a_row0][frag_col]);
+                    a_frag[1] = *reinterpret_cast<const unsigned*>(
+                        &a_tile[stage][a_row0 + 8][frag_col]);
+                    a_frag[2] = *reinterpret_cast<const unsigned*>(
+                        &a_tile[stage][a_row0][frag_col + 16]);
+                    a_frag[3] = *reinterpret_cast<const unsigned*>(
+                        &a_tile[stage][a_row0 + 8][frag_col + 16]);
+                    astrai::mma_sync<typename fp8_input<Traits::kFormat>::type>(
+                        acc + (nt * 4 + mt) * 4,
+                        a_frag, b_frag, acc + (nt * 4 + mt) * 4);
+                }
+            }
+        }
+        // Barrier 2: every thread finished reading this stage's tiles before
+        // the prefetch for the (i+3)-th tile overwrites them.
+        __syncthreads();
+        if (tile_index + 3 < tile_count) {
+            load_tile(stage, (tile_index + 3) * kK);
+            asm volatile("cp.async.commit_group;");
+        }
+    }
+
+    const float output_scale = sa * sb;
+    const float o8_scale = OutFp8 ? output_scale * *p.out_scale : 0.0f;
+#pragma unroll
+    for (int nt = 0; nt < 2; ++nt) {
+        const int64_t col = output_col + nt * 8;
+        // Per-row store: FP8 packs two adjacent columns into one 16-bit
+        // write; the BF16 path writes two scalars. Boundary columns fall
+        // back to a scalar convert so the pack never crosses the row edge.
+        auto store_out = [&](int64_t row, float v0, float v1) {
+            if (row >= m) return;
+            if constexpr (OutFp8) {
+                if (col + 1 < n) {
+                    *reinterpret_cast<unsigned short*>(out_fp8 + row * n + col) =
+                        static_cast<unsigned short>(__nv_cvt_float2_to_fp8x2(
+                            make_float2(v0 * o8_scale, v1 * o8_scale),
+                            __NV_SATFINITE, __NV_E4M3));
+                } else {
+                    out_fp8[row * n + col] = __nv_fp8_e4m3(v0 * o8_scale);
+                }
+            } else {
+                out_bf16[row * n + col] = __float2bfloat16(v0 * output_scale);
+                if (col + 1 < n)
+                    out_bf16[row * n + col + 1] =
+                        __float2bfloat16(v1 * output_scale);
+            }
+        };
+#pragma unroll
+        for (int mt = 0; mt < 4; ++mt) {
+            const int64_t row0 = row_base + mt * 16;
+            float* tile_acc = acc + (nt * 4 + mt) * 4;
+            if (col < n) {
+                store_out(row0, tile_acc[0], tile_acc[1]);
+                store_out(row0 + 8, tile_acc[2], tile_acc[3]);
+            }
+        }
+    }
+}
+
+// ---------------------------------------------------------------------------
+// Launchers — pure CUDA (no torch), usable from the binding and pure C tests.
+// ---------------------------------------------------------------------------
+
+// Fused forward tile config: 128x64 CTA, K=32, 3-stage cp.async pipeline,
+// plus the fp8 ldmatrix tile region (A8[2][BlockM][16] + B8[2][BlockN][16]).
+using FusedTraits = Fp8GemmTraits<FP8Format::E4M3, 128, 64, 32, 3>;
+// Pre-quantized tile config: 128x64 CTA, K=32, 3-stage pipeline.
+template <FP8Format Fmt>
+using PqTraits = Fp8GemmTraits<Fmt, 128, 64, 32, 3>;
+
+template <FP8Format Fmt>
+void launch_fp8_quantize(const FP8Params& p, cudaStream_t stream) {
+    constexpr int kThreads = 256;
+    const int64_t blocks = (p.total + kThreads - 1) / kThreads;
+    fp8_quantize_kernel<Fmt><<<blocks, kThreads, 0, stream>>>(p);
+}
+
+template <bool AddBias, bool TrackAmax>
+void launch_fp8_fused(const FP8Params& p, cudaStream_t stream) {
+    // bf16 staging (3 stages) + fp8 ldmatrix tiles (A8[2][M][16] + B8[2][N][16])
+    constexpr int kSmemBytes =
+        FusedTraits::kStages *
+            (FusedTraits::kBlockM * FusedTraits::kK +
+             FusedTraits::kBlockN * FusedTraits::kK) *
+            2 +
+        2 * FusedTraits::kBlockM * 16 + 2 * FusedTraits::kBlockN * 16;
+    dim3 grid((p.n + FusedTraits::kBlockN - 1) / FusedTraits::kBlockN,
+              (p.m + FusedTraits::kBlockM - 1) / FusedTraits::kBlockM);
+    auto kernel = fp8_fused_gemm_kernel<FusedTraits, AddBias, TrackAmax>;
+    static bool attribute_set = false;
+    if (!attribute_set) {
+        cudaFuncSetAttribute(
+            kernel, cudaFuncAttributeMaxDynamicSharedMemorySize, kSmemBytes);
+        attribute_set = true;
+    }
+    kernel<<<grid, kWarps * 32, kSmemBytes, stream>>>(p);
+}
+
+template <FP8Format Fmt, bool OutFp8 = false>
+void launch_fp8_pq(const FP8Params& p, cudaStream_t stream) {
+    using Traits = PqTraits<Fmt>;
+    dim3 grid((p.n + Traits::kBlockN - 1) / Traits::kBlockN,
+              (p.m + Traits::kBlockM - 1) / Traits::kBlockM);
+    fp8_pq_gemm_kernel<Traits, OutFp8><<<grid, kWarps * 32, 0, stream>>>(p);
+}
+
+}  // namespace fp8

csrc/kernels/fp8/mm.cu

@@ -0,0 +1,369 @@
+// FP8 GEMM torch binding: tensor validation, FP8Params packing, template
+// dispatch and pybind. Device code lives in gemm.cuh (pure CUDA) —
+// mirroring the attn_*.cu / attn_*_mma.cuh split of the attention kernels.
+
+#include <torch/extension.h>
+#include <ATen/cuda/CUDAContext.h>
+#include <c10/cuda/CUDAGuard.h>
+#include <cuda_bf16.h>
+#include <cstdint>
+#include <mutex>
+#include <tuple>
+#include <unordered_map>
+
+#include "gemm.cuh"
+#include "../common/device.cuh"
+
+namespace {
+
+// FP8Format / FP8Params live in the global namespace (common.h); the
+// launchers live in fp8:: (gemm.cuh).
+
+void check_fp8_device(const torch::Tensor& tensor) {
+    static std::mutex mutex;
+    static std::unordered_map<int, bool> supported;
+    const int device = tensor.device().index();
+    {
+        std::lock_guard<std::mutex> lock(mutex);
+        auto cached = supported.find(device);
+        if (cached != supported.end()) {
+            TORCH_CHECK(cached->second,
+                        "fused FP8 MMA requires compute capability 8.9 or newer");
+            return;
+        }
+    }
+
+    const auto* properties = at::cuda::getDeviceProperties(device);
+    const bool is_supported =
+        astrai::sm_at_least(properties->major, properties->minor,
+                            astrai::kMinSmForFp8Major,
+                            astrai::kMinSmForFp8Minor);
+    {
+        std::lock_guard<std::mutex> lock(mutex);
+        supported.emplace(device, is_supported);
+    }
+    TORCH_CHECK(is_supported,
+                "fused FP8 MMA requires compute capability 8.9 or newer");
+}
+
+void check_scale(const torch::Tensor& scale, const torch::Tensor& input,
+                 const char* name) {
+    TORCH_CHECK(scale.is_cuda() && scale.device() == input.device() &&
+                    scale.scalar_type() == torch::kFloat32 && scale.numel() == 1,
+                name, " must be a CUDA float32 scalar on the input device");
+}
+
+// ---- FP8Params packing (mirrors attention/entry_utils.cuh pack_* helpers) ----
+
+void pack_gemm_params(FP8Params& p, const void* a, const void* b, void* out,
+                      const torch::Tensor& sa, const torch::Tensor& sb,
+                      const torch::Tensor* out_scale, int64_t m, int64_t n,
+                      int64_t k) {
+    p.a_ptr = a;
+    p.b_ptr = b;
+    p.out_ptr = out;
+    p.scale_a = sa.data_ptr<float>();
+    p.scale_b = sb.data_ptr<float>();
+    p.out_scale = out_scale ? out_scale->data_ptr<float>() : nullptr;
+    p.bias = nullptr;
+    p.amax_a = nullptr;
+    p.amax_b = nullptr;
+    p.m = m;
+    p.n = n;
+    p.k = k;
+    p.total = 0;
+}
+
+void pack_quantize_params(FP8Params& p, const void* x, void* x8,
+                          const torch::Tensor& scale, torch::Tensor* amax,
+                          int64_t total) {
+    p.a_ptr = x;
+    p.b_ptr = nullptr;
+    p.out_ptr = x8;
+    p.scale_a = scale.data_ptr<float>();
+    p.scale_b = nullptr;
+    p.out_scale = nullptr;
+    p.bias = nullptr;
+    p.amax_a = amax ? amax->data_ptr<float>() : nullptr;
+    p.amax_b = nullptr;
+    p.m = p.n = p.k = 0;
+    p.total = total;
+}
+
+}  // namespace
+
+// ---------------------------------------------------------------------------
+// Entry points
+// ---------------------------------------------------------------------------
+
+std::tuple<torch::Tensor, torch::Tensor> quantize_bf16(torch::Tensor x,
+                                                       torch::Tensor scale,
+                                                       int64_t fmt) {
+    // BF16 -> FP8 quantize with fused amax. fmt: 0 = E4M3, 1 = E5M2.
+    // Returns (x8, amax); the caller never clears amax (zero-initialized here).
+    TORCH_CHECK(x.is_cuda() && scale.is_cuda(), "CUDA tensors required");
+    TORCH_CHECK(x.scalar_type() == torch::kBFloat16, "x must be bf16");
+    check_scale(scale, x, "scale");
+    check_fp8_device(x);
+    const at::cuda::OptionalCUDAGuard guard(x.device());
+    auto stream = at::cuda::getCurrentCUDAStream();
+
+    auto x_c = x.contiguous();
+    auto x8 = torch::empty_like(
+        x_c, x_c.options().dtype(fmt ? torch::kFloat8_e5m2
+                                     : torch::kFloat8_e4m3fn));
+    auto amax = torch::zeros({1}, x_c.options().dtype(torch::kFloat32));
+    FP8Params p;
+    pack_quantize_params(p, x_c.data_ptr(), x8.data_ptr(), scale, &amax,
+                         x_c.numel());
+    if (fmt) {
+        fp8::launch_fp8_quantize<FP8Format::E5M2>(p, stream.stream());
+    } else {
+        fp8::launch_fp8_quantize<FP8Format::E4M3>(p, stream.stream());
+    }
+    C10_CUDA_CHECK(cudaGetLastError());
+    return {x8, amax};
+}
+
+torch::Tensor mm_fp8(torch::Tensor a, torch::Tensor b, torch::Tensor sa,
+                     torch::Tensor sb, int64_t out_dtype,
+                     c10::optional<torch::Tensor> out_scale) {
+    // Pre-quantized FP8 GEMM: out = a @ b^T * (sa * sb), FP32 accumulation.
+    // out_dtype: 0 = BF16 (default), 1 = FP8 E4M3 (requires out_scale, the
+    // quantization step for the output — mirrors torch._scaled_mm's
+    // out_dtype / scale_result). Both operands share the same FP8 format.
+    TORCH_CHECK(a.is_cuda() && b.is_cuda(), "CUDA tensors required");
+    TORCH_CHECK(a.scalar_type() == torch::kFloat8_e4m3fn ||
+                    a.scalar_type() == torch::kFloat8_e5m2,
+                "a and b must be fp8 (e4m3fn or e5m2)");
+    TORCH_CHECK(a.scalar_type() == b.scalar_type(),
+                "a and b must share the same fp8 format");
+    TORCH_CHECK(a.dim() == 2 && b.dim() == 2, "a and b must be 2D");
+    TORCH_CHECK(a.device() == b.device(), "a and b must be on the same device");
+    TORCH_CHECK(a.size(1) == b.size(1), "inner dim mismatch");
+    check_scale(sa, a, "sa");
+    check_scale(sb, a, "sb");
+    check_fp8_device(a);
+    const at::cuda::OptionalCUDAGuard guard(a.device());
+    auto stream = at::cuda::getCurrentCUDAStream();
+
+    auto a_c = a.contiguous();
+    auto b_c = b.contiguous();
+    int64_t m = a_c.size(0), k = a_c.size(1), n = b_c.size(0);
+    const bool out_fp8 = (out_dtype == 1);
+    TORCH_CHECK(out_dtype == 0 || out_fp8,
+                "out_dtype must be 0 (bf16) or 1 (fp8 e4m3)");
+    torch::Tensor os;
+    if (out_fp8) {
+        TORCH_CHECK(out_scale.has_value(), "fp8 output requires out_scale");
+        os = out_scale.value();
+        check_scale(os, a, "out_scale");
+    }
+    auto out = torch::empty(
+        {m, n},
+        out_fp8 ? a_c.options().dtype(torch::kFloat8_e4m3fn)
+                : a_c.options().dtype(torch::kBFloat16));
+    FP8Params p;
+    pack_gemm_params(p, a_c.data_ptr(), b_c.data_ptr(), out.data_ptr(), sa, sb,
+                     out_fp8 ? &os : nullptr, m, n, k);
+    if (a.scalar_type() == torch::kFloat8_e4m3fn) {
+        if (out_fp8) {
+            fp8::launch_fp8_pq<FP8Format::E4M3, true>(p, stream.stream());
+        } else {
+            fp8::launch_fp8_pq<FP8Format::E4M3>(p, stream.stream());
+        }
+    } else {
+        if (out_fp8) {
+            fp8::launch_fp8_pq<FP8Format::E5M2, true>(p, stream.stream());
+        } else {
+            fp8::launch_fp8_pq<FP8Format::E5M2>(p, stream.stream());
+        }
+    }
+    C10_CUDA_CHECK(cudaGetLastError());
+    return out;
+}
+
+std::tuple<torch::Tensor, torch::Tensor, torch::Tensor> linear_forward_fp8(
+    torch::Tensor x, torch::Tensor w, torch::Tensor bias, torch::Tensor sx,
+    torch::Tensor sw) {
+    // Fused BF16 -> E4M3 -> MMA -> BF16 linear forward. amax_x / amax_w are
+    // zero-initialized here and returned (caller does not clear them).
+    TORCH_CHECK(x.is_cuda() && w.is_cuda(), "CUDA tensors required");
+    TORCH_CHECK(x.scalar_type() == torch::kBFloat16 &&
+                    w.scalar_type() == torch::kBFloat16,
+                "x and w must be bf16");
+    TORCH_CHECK(x.device() == w.device(), "x and w must be on the same device");
+    check_scale(sx, x, "sx");
+    check_scale(sw, x, "sw");
+    check_fp8_device(x);
+    const at::cuda::OptionalCUDAGuard guard(x.device());
+    auto stream = at::cuda::getCurrentCUDAStream();
+
+    auto x_c = x.reshape({-1, w.size(1)}).contiguous();
+    auto w_c = w.contiguous();
+    int64_t m = x_c.size(0), k = x_c.size(1), n = w_c.size(0);
+    TORCH_CHECK(w_c.dim() == 2 && w_c.size(1) == k, "inner dim mismatch");
+    // amax slots are zero-initialized here; the kernel atomically maxes in.
+    auto amax_x = torch::zeros({1}, x.options().dtype(torch::kFloat32));
+    auto amax_w = torch::zeros({1}, x.options().dtype(torch::kFloat32));
+    auto out = torch::empty({m, n}, x_c.options());
+    const bool has_bias = bias.defined() && bias.numel() > 0;
+    if (has_bias) {
+        TORCH_CHECK(bias.is_cuda() && bias.device() == x.device() &&
+                        bias.scalar_type() == torch::kBFloat16 &&
+                        bias.numel() == n,
+                    "bias must be CUDA bf16 with shape [N]");
+    }
+    FP8Params p;
+    pack_gemm_params(p, x_c.data_ptr(), w_c.data_ptr(), out.data_ptr(), sx, sw,
+                     nullptr, m, n, k);
+    p.bias = has_bias ? reinterpret_cast<const __nv_bfloat16*>(bias.data_ptr())
+                      : nullptr;
+    p.amax_a = amax_x.data_ptr<float>();
+    p.amax_b = amax_w.data_ptr<float>();
+    if (has_bias) {
+        fp8::launch_fp8_fused<true, true>(p, stream.stream());
+    } else {
+        fp8::launch_fp8_fused<false, true>(p, stream.stream());
+    }
+    C10_CUDA_CHECK(cudaGetLastError());
+
+    std::vector<int64_t> shape(x.sizes().begin(), x.sizes().end() - 1);
+    shape.push_back(n);
+    return {out.reshape(shape), amax_x, amax_w};
+}
+
+std::tuple<torch::Tensor, torch::Tensor, torch::Tensor, torch::Tensor>
+linear_backward_fp8(torch::Tensor g, torch::Tensor x, torch::Tensor w,
+                    std::vector<int64_t> masks, torch::Tensor sg,
+                    torch::Tensor sw, torch::Tensor sx, int64_t fmt) {
+    // Pre-quantized FP8 backward: grad is quantized once (E4M3 or E5M2 per
+    // `fmt`), then dX / dW run as FP8 tensor-core GEMMs sharing g8.
+    // Returns (grad_input, grad_weight, grad_bias, amax_g).
+    TORCH_CHECK(g.is_cuda() && x.is_cuda() && w.is_cuda(), "CUDA tensors required");
+    TORCH_CHECK(g.scalar_type() == torch::kBFloat16 &&
+                    x.scalar_type() == torch::kBFloat16 &&
+                    w.scalar_type() == torch::kBFloat16,
+                "g, x, and w must be bf16");
+    TORCH_CHECK(g.device() == x.device() && g.device() == w.device(),
+                "g, x, and w must be on the same device");
+    TORCH_CHECK(masks.size() == 3, "masks must contain three values");
+    check_fp8_device(g);
+    const at::cuda::OptionalCUDAGuard guard(g.device());
+    auto stream = at::cuda::getCurrentCUDAStream();
+
+    auto g_c = g.reshape({-1, w.size(0)}).contiguous();   // [M, N]
+    auto x_c = x.reshape({-1, x.size(-1)}).contiguous();  // [M, K]
+    auto w_c = w.contiguous();                            // [N, K]
+    int64_t m = g_c.size(0), n = w_c.size(0), k = w_c.size(1);
+    TORCH_CHECK(x_c.size(0) == m && x_c.size(1) == k && g_c.size(1) == n,
+                "backward shape mismatch");
+
+    auto grad_input = torch::empty_like(x);
+    auto grad_weight = torch::empty_like(w);
+    auto grad_bias = torch::empty({0}, g.options());
+    auto amax_g = torch::zeros({1}, g.options().dtype(torch::kFloat32));
+    auto f8opt = fmt ? g.options().dtype(torch::kFloat8_e5m2)
+                     : g.options().dtype(torch::kFloat8_e4m3fn);
+    const auto q_fmt = fmt ? FP8Format::E5M2 : FP8Format::E4M3;
+
+    auto quantize = [&](const torch::Tensor& src, torch::Tensor& dst,
+                        const torch::Tensor& scale, torch::Tensor* amax) {
+        FP8Params qp;
+        pack_quantize_params(qp, src.data_ptr(), dst.data_ptr(), scale, amax,
+                             src.numel());
+        if (fmt) {
+            fp8::launch_fp8_quantize<FP8Format::E5M2>(qp, stream.stream());
+        } else {
+            fp8::launch_fp8_quantize<FP8Format::E4M3>(qp, stream.stream());
+        }
+    };
+    auto pq = [&](const torch::Tensor& a8, const torch::Tensor& b8,
+                  torch::Tensor& out, const torch::Tensor& sa,
+                  const torch::Tensor& sb, int64_t mm, int64_t nn, int64_t kk) {
+        FP8Params gp;
+        pack_gemm_params(gp, a8.data_ptr(), b8.data_ptr(), out.data_ptr(), sa,
+                         sb, nullptr, mm, nn, kk);
+        if (fmt) {
+            fp8::launch_fp8_pq<FP8Format::E5M2>(gp, stream.stream());
+        } else {
+            fp8::launch_fp8_pq<FP8Format::E4M3>(gp, stream.stream());
+        }
+    };
+
+    // dX = g @ W: quantize g once, then g8 @ w8^T.
+    if (masks[0]) {
+        auto g8 = torch::empty({m, n}, f8opt);
+        quantize(g_c, g8, sg, &amax_g);
+        auto w_t = w_c.transpose(0, 1).contiguous();  // [K, N]
+        auto w8_t = torch::empty({k, n}, f8opt);
+        quantize(w_t, w8_t, sw, nullptr);
+        auto grad_input_2d = grad_input.reshape({m, k});
+        pq(g8, w8_t, grad_input_2d, sg, sw, m, k, n);
+    }
+    // dW = g^T @ x: transposed layouts for both operands.
+    if (masks[1]) {
+        auto g_t = g_c.transpose(0, 1).contiguous();  // [N, M]
+        auto x_t = x_c.transpose(0, 1).contiguous();  // [K, M]
+        auto g8_t = torch::empty({n, m}, f8opt);
+        auto x8_t = torch::empty({k, m}, f8opt);
+        quantize(g_t, g8_t, sg, nullptr);
+        quantize(x_t, x8_t, sx, nullptr);
+        pq(g8_t, x8_t, grad_weight, sg, sx, n, k, m);
+    }
+    if (!masks[0] && !masks[1]) {
+        amax_g.copy_(g_c.abs().amax().to(torch::kFloat32));
+    }
+    C10_CUDA_CHECK(cudaGetLastError());
+    if (masks[2]) grad_bias = g_c.sum(0).to(g.scalar_type());
+    return {grad_input, grad_weight, grad_bias, amax_g};
+}
+
+torch::Tensor fp8_mm(torch::Tensor a, torch::Tensor b, torch::Tensor sx,
+                     torch::Tensor sw) {
+    // BF16-in fused FP8 GEMM primitive (no bias, no amax): a @ b^T.
+    TORCH_CHECK(a.is_cuda() && b.is_cuda(), "CUDA tensors required");
+    TORCH_CHECK(a.scalar_type() == torch::kBFloat16 &&
+                    b.scalar_type() == torch::kBFloat16,
+                "a and b must be bf16");
+    TORCH_CHECK(a.dim() == 2 && b.dim() == 2, "a and b must be 2D");
+    TORCH_CHECK(a.device() == b.device(), "a and b must be on the same device");
+    TORCH_CHECK(a.size(1) == b.size(1), "inner dim mismatch");
+    check_scale(sx, a, "sx");
+    check_scale(sw, a, "sw");
+    check_fp8_device(a);
+    const at::cuda::OptionalCUDAGuard guard(a.device());
+    auto stream = at::cuda::getCurrentCUDAStream();
+
+    auto a_c = a.contiguous();
+    auto b_c = b.contiguous();
+    int64_t m = a_c.size(0), n = b_c.size(0), k = a_c.size(1);
+    auto out = torch::empty({m, n}, a_c.options());
+    FP8Params p;
+    pack_gemm_params(p, a_c.data_ptr(), b_c.data_ptr(), out.data_ptr(), sx, sw,
+                     nullptr, m, n, k);
+    fp8::launch_fp8_fused<false, false>(p, stream.stream());
+    C10_CUDA_CHECK(cudaGetLastError());
+    return out;
+}
+
+PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
+    m.def("fp8_mm", &fp8_mm, py::arg("a"), py::arg("b"), py::arg("sx"),
+          py::arg("sw"),
+          "Fused BF16 input, E4M3 MMA, FP32 accumulation, BF16 output GEMM");
+    m.def("quantize_bf16", &quantize_bf16, py::arg("x"), py::arg("scale"),
+          py::arg("fmt"),
+          "BF16 to FP8 (E4M3/E5M2) quantize with fused amax; returns (x8, amax)");
+    m.def("mm_fp8", &mm_fp8, py::arg("a"), py::arg("b"), py::arg("sa"),
+          py::arg("sb"), py::arg("out_dtype") = 0,
+          py::arg("out_scale") = py::none(),
+          "Pre-quantized FP8 GEMM: a @ b^T * (sa * sb); out_dtype 0=bf16, "
+          "1=fp8 e4m3 (requires out_scale)");
+    m.def("linear_forward_fp8", &linear_forward_fp8, py::arg("x"),
+          py::arg("w"), py::arg("bias"), py::arg("sx"), py::arg("sw"),
+          "Fused BF16-to-FP8 linear forward; returns (out, amax_x, amax_w)");
+    m.def("linear_backward_fp8", &linear_backward_fp8, py::arg("g"),
+          py::arg("x"), py::arg("w"), py::arg("masks"), py::arg("sg"),
+          py::arg("sw"), py::arg("sx"), py::arg("fmt"),
+          "FP8 linear backward; returns (grad_input, grad_weight, grad_bias, amax_g)");
+}

csrc/kernels/fp8_mm.cu

@@ -1,817 +0,0 @@
-// Fused BF16 -> E4M3 MMA -> BF16 matrix multiplication
-
-#include <torch/extension.h>
-#include <ATen/cuda/CUDAContext.h>
-#include <c10/cuda/CUDAGuard.h>
-#include <cuda_fp8.h>
-#include <cuda_runtime.h>
-#include <cstdint>
-#include <mutex>
-#include <unordered_map>
-
-namespace {
-
-constexpr int kMmaK = 32;
-constexpr int kWarps = 8;
-// Fast forward path: 128x64 CTA, 64x16 warp tile, 2-stage pipeline, dynamic
-// shared memory. Mirrors the CUTLASS 58_ada_fp8_gemm threadblock geometry
-// while keeping the fused BF16->FP8 quantize path. The FP8 tile overwrites
-// the BF16 staging area in place. L20 opts in to only 101376 B shared per
-// block; K=32 keeps the footprint at 24576 B so four CTAs/SM stay resident.
-constexpr int kFastBlockM = 128;
-constexpr int kFastBlockN = 64;
-constexpr int kFastK = 32;
-constexpr int kFastStages = 2;
-constexpr int kFastSmemBytes =
-    kFastStages * (kFastBlockM * kFastK * 2 + kFastBlockN * kFastK * 2);
-
-__device__ __forceinline__ unsigned pack_fp8x4_vector(float x0, float x1,
-                                                       float x2, float x3) {
-    const auto low = __nv_cvt_float2_to_fp8x2(
-        make_float2(x0, x1), __NV_SATFINITE, __NV_E4M3);
-    const auto high = __nv_cvt_float2_to_fp8x2(
-        make_float2(x2, x3), __NV_SATFINITE, __NV_E4M3);
-    return static_cast<unsigned>(low) | (static_cast<unsigned>(high) << 16);
-}
-
-
-__device__ __forceinline__ void mma_fp8_16832(float d[4],
-                                               const unsigned a[4],
-                                               const unsigned b[2]) {
-#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 890
-    asm volatile(
-        "mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32 "
-        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%0,%1,%2,%3};"
-        : "+f"(d[0]), "+f"(d[1]), "+f"(d[2]), "+f"(d[3])
-        : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]),
-          "r"(b[0]), "r"(b[1]));
-#endif
-}
-
-__device__ __forceinline__ void atomic_max_float(float* destination,
-                                                  float value) {
-    if (destination)
-        atomicMax(reinterpret_cast<unsigned*>(destination), __float_as_uint(value));
-}
-
-__device__ __forceinline__ float warp_reduce_max(float value) {
-#pragma unroll
-    for (int offset = 16; offset; offset >>= 1) {
-        value = fmaxf(value, __shfl_xor_sync(0xffffffffu, value, offset));
-    }
-    return value;
-}
-
-// Block-wide max reduction of a per-warp tracked value, then an atomic
-// update of the global amax slot when `track` is set.
-template <int NWarps>
-__device__ __forceinline__ void block_reduce_amax(float& local, float* slots,
-                                                  int warp, int lane,
-                                                  bool track, float* global) {
-    local = warp_reduce_max(local);
-    if (lane == 0) slots[warp] = local;
-    __syncthreads();
-    if (warp == 0) {
-        float value = lane < NWarps ? slots[lane] : 0.0f;
-        value = warp_reduce_max(value);
-        if (lane == 0 && track && global) atomic_max_float(global, value);
-    }
-}
-
-// One thread moves eight BF16 values (16 bytes). The async copy is issued
-// through a uint4-shaped pointer so the source and destination are both
-// naturally 128-bit aligned for contiguous forward GEMMs.
-__device__ __forceinline__ void cp_async_bf16_8(
-    __nv_bfloat16* destination, const __nv_bfloat16* source, bool valid) {
-    const unsigned shared_address = __cvta_generic_to_shared(destination);
-    const uint4* source_vec = reinterpret_cast<const uint4*>(source);
-    asm volatile("cp.async.cg.shared.global [%0], [%1], 16, %2;"
-                 :: "r"(shared_address), "l"(source_vec),
-                    "r"(valid ? 16 : 0));
-}
-
-template <bool TrackAmax = true>
-__device__ __forceinline__ unsigned load_fp8x4_from_bf16(
-    const __nv_bfloat16* source, float scale_inv, float& amax,
-    bool track_amax = true) {
-    float x0 = __bfloat162float(source[0]);
-    float x1 = __bfloat162float(source[1]);
-    float x2 = __bfloat162float(source[2]);
-    float x3 = __bfloat162float(source[3]);
-    if constexpr (TrackAmax) {
-        if (track_amax) {
-        amax = fmaxf(amax, fmaxf(fabsf(x0), fmaxf(fabsf(x1),
-                             fmaxf(fabsf(x2), fabsf(x3)))));
-        }
-    }
-    return pack_fp8x4_vector(x0 * scale_inv, x1 * scale_inv,
-                             x2 * scale_inv, x3 * scale_inv);
-}
-
-
-template <bool AddBias, bool TrackAmax>
-__global__ void fused_fp8_gemm_fast_kernel(
-    const __nv_bfloat16* __restrict__ a,
-    const __nv_bfloat16* __restrict__ b,
-    __nv_bfloat16* __restrict__ out,
-    const __nv_bfloat16* __restrict__ bias,
-    const float* __restrict__ scale_a,
-    const float* __restrict__ scale_b,
-    float* __restrict__ amax_a,
-    float* __restrict__ amax_b,
-    int64_t m, int64_t n, int64_t k) {
-    extern __shared__ char smem[];
-    constexpr int a_stride = kFastBlockM * kFastK;
-    constexpr int b_stride = kFastBlockN * kFastK;
-    constexpr int b_bf16_offset = kFastStages * a_stride;
-    auto* a_bf16 = reinterpret_cast<__nv_bfloat16*>(smem);
-    auto* b_bf16 =
-        reinterpret_cast<__nv_bfloat16*>(smem + b_bf16_offset * 2);
-    __shared__ float warp_amax_a[kWarps];
-    __shared__ float warp_amax_b[kWarps];
-
-    const int tid = threadIdx.x;
-    const int warp = tid >> 5;
-    const int lane = tid & 31;
-    const int group = lane >> 2;
-    const int thread_in_group = lane & 3;
-    constexpr int warps_n = kFastBlockN / 16;
-    const int warp_m = warp / warps_n;
-    const int warp_n = warp % warps_n;
-    const int64_t row_base =
-        blockIdx.y * kFastBlockM + warp_m * 64 + group;
-    const int64_t output_col =
-        blockIdx.x * kFastBlockN + warp_n * 16 + thread_in_group * 2;
-    const float sa = *scale_a;
-    const float sb = *scale_b;
-    const float inv_a = 1.0f / sa;
-    const float inv_b = 1.0f / sb;
-    float local_amax_a = 0.0f;
-    float local_amax_b = 0.0f;
-    float acc[4 * 4 * 2] = {};
-
-    const bool track_amax_a = TrackAmax && blockIdx.x == 0;
-    const bool track_amax_b = TrackAmax && blockIdx.y == 0;
-    // Each thread issues 8 A chunks and 4 B chunks of 8 BF16 (16B) per stage.
-    auto load_tile = [&](int stage, int64_t k_base) {
-        const int r0 = tid >> 2;
-        const int c0 = (tid & 3) * 8;
-#pragma unroll
-        for (int j = 0; j < kFastK / 32; ++j) {
-            const int col = c0 + 32 * j;
-            const bool full_chunk = k_base + col + 7 < k;
-            const int64_t a_row = blockIdx.y * kFastBlockM + r0;
-            const int64_t b_row = blockIdx.x * kFastBlockN + r0;
-            auto* a_dst = &a_bf16[stage * a_stride + r0 * kFastK + col];
-            auto* b_dst = &b_bf16[stage * b_stride + r0 * kFastK + col];
-            const auto* a_ptr = a + a_row * k + k_base + col;
-            const auto* b_ptr = b + b_row * k + k_base + col;
-            const bool full_a = a_row < m && full_chunk;
-            const bool full_b = b_row < n && full_chunk;
-            const bool aligned_a =
-                (reinterpret_cast<uintptr_t>(a_ptr) & 15) == 0;
-            const bool aligned_b =
-                (reinterpret_cast<uintptr_t>(b_ptr) & 15) == 0;
-            if (full_a && aligned_a) {
-                cp_async_bf16_8(a_dst, a_ptr, true);
-            } else {
-#pragma unroll
-                for (int i = 0; i < 8; ++i) {
-                    a_dst[i] = a_row < m && k_base + col + i < k
-                                   ? a_ptr[i]
-                                   : __float2bfloat16(0.0f);
-                }
-            }
-            if (full_b && aligned_b) {
-                cp_async_bf16_8(b_dst, b_ptr, true);
-            } else {
-#pragma unroll
-                for (int i = 0; i < 8; ++i) {
-                    b_dst[i] = b_row < n && k_base + col + i < k
-                                   ? b_ptr[i]
-                                   : __float2bfloat16(0.0f);
-                }
-            }
-            if (r0 + 64 < kFastBlockM) {
-                const int64_t a_row_hi = blockIdx.y * kFastBlockM + r0 + 64;
-                auto* a_dst_hi =
-                    &a_bf16[stage * a_stride + (r0 + 64) * kFastK + col];
-                const auto* a_ptr_hi = a + a_row_hi * k + k_base + col;
-                const bool full_a_hi = a_row_hi < m && full_chunk;
-                const bool aligned_a_hi =
-                    (reinterpret_cast<uintptr_t>(a_ptr_hi) & 15) == 0;
-                if (full_a_hi && aligned_a_hi) {
-                    cp_async_bf16_8(a_dst_hi, a_ptr_hi, true);
-                } else {
-#pragma unroll
-                    for (int i = 0; i < 8; ++i) {
-                        a_dst_hi[i] = a_row_hi < m && k_base + col + i < k
-                                          ? a_ptr_hi[i]
-                                          : __float2bfloat16(0.0f);
-                    }
-                }
-            }
-        }
-    };
-
-    // Quantize must place each 4-BP8 group at the byte offset the MMA
-    // fragment reads: 8*(lane&3) + 64*k_seg for a row. With in-place storage
-    // (fp8 element k lives at byte 2k), the BF16 column of a group is
-    // 4*(tid&7) + 32*j, so partition by 4-element groups instead of the
-    // 8-element cp.async chunks.
-    auto quantize_tile = [&](int stage) {
-        const int r0 = tid >> 3;
-        const int c0 = (tid & 7) * 4;
-#pragma unroll
-        for (int s = 0; s < 4; ++s) {
-            const int row = r0 + 32 * s;
-            auto* a_src = &a_bf16[stage * a_stride + row * kFastK + c0];
-            auto* a_dst = reinterpret_cast<unsigned*>(a_src);
-#pragma unroll
-            for (int j = 0; j < kFastK / 32; ++j) {
-                a_dst[16 * j] = load_fp8x4_from_bf16<TrackAmax>(
-                    a_src + 32 * j, inv_a, local_amax_a, track_amax_a);
-            }
-        }
-#pragma unroll
-        for (int s = 0; s < 2; ++s) {
-            const int row = r0 + 32 * s;
-            auto* b_src = &b_bf16[stage * b_stride + row * kFastK + c0];
-            auto* b_dst = reinterpret_cast<unsigned*>(b_src);
-#pragma unroll
-            for (int j = 0; j < kFastK / 32; ++j) {
-                b_dst[16 * j] = load_fp8x4_from_bf16<TrackAmax>(
-                    b_src + 32 * j, inv_b, local_amax_b, track_amax_b);
-            }
-        }
-    };
-
-    const int64_t tile_count = (k + kFastK - 1) / kFastK;
-    load_tile(0, 0);
-    asm volatile("cp.async.commit_group;");
-    if (tile_count > 1) {
-        load_tile(1, kFastK);
-        asm volatile("cp.async.commit_group;");
-    }
-    for (int64_t tile_index = 0; tile_index < tile_count; ++tile_index) {
-        const int stage = static_cast<int>(tile_index % kFastStages);
-        if (tile_index + 1 == tile_count) {
-            asm volatile("cp.async.wait_group 0;");
-        } else {
-            asm volatile("cp.async.wait_group 1;");
-        }
-        // wait_group only waits for this thread's async copies. All threads
-        // must finish loading before the tile is read by the CTA.
-        __syncthreads();
-        quantize_tile(stage);
-        __syncthreads();
-
-        // Four m16n8k32 MMA segments per 128-K stage.
-#pragma unroll
-        for (int k_seg = 0; k_seg < kFastK / kMmaK; ++k_seg) {
-            const int frag_col = thread_in_group * 4 + k_seg * 32;
-#pragma unroll
-            for (int nt = 0; nt < 2; ++nt) {
-                const int b_row = warp_n * 16 + nt * 8 + group;
-                unsigned b_frag[2];
-                b_frag[0] = *reinterpret_cast<const unsigned*>(
-                    &b_bf16[stage * b_stride + b_row * kFastK + frag_col]);
-                b_frag[1] = *reinterpret_cast<const unsigned*>(
-                    &b_bf16[stage * b_stride + b_row * kFastK + frag_col + 16]);
-#pragma unroll
-                for (int mt = 0; mt < 4; ++mt) {
-                    const int a_row0 = warp_m * 64 + mt * 16 + group;
-                    unsigned a_frag[4];
-                    a_frag[0] = *reinterpret_cast<const unsigned*>(
-                        &a_bf16[stage * a_stride + a_row0 * kFastK + frag_col]);
-                    a_frag[1] = *reinterpret_cast<const unsigned*>(
-                        &a_bf16[stage * a_stride + (a_row0 + 8) * kFastK + frag_col]);
-                    a_frag[2] = *reinterpret_cast<const unsigned*>(
-                        &a_bf16[stage * a_stride + a_row0 * kFastK + frag_col + 16]);
-                    a_frag[3] = *reinterpret_cast<const unsigned*>(
-                        &a_bf16[stage * a_stride + (a_row0 + 8) * kFastK + frag_col + 16]);
-                    mma_fp8_16832(acc + (nt * 4 + mt) * 4, a_frag, b_frag);
-                }
-            }
-        }
-        __syncthreads();
-        if (tile_index + 2 < tile_count) {
-            load_tile(stage, (tile_index + 2) * kFastK);
-            asm volatile("cp.async.commit_group;");
-        }
-    }
-
-    if constexpr (TrackAmax) {
-    block_reduce_amax<kWarps>(local_amax_a, warp_amax_a, warp, lane,
-                              track_amax_a, amax_a);
-    block_reduce_amax<kWarps>(local_amax_b, warp_amax_b, warp, lane,
-                              track_amax_b, amax_b);
-    }
-
-    const float output_scale = sa * sb;
-#pragma unroll
-    for (int nt = 0; nt < 2; ++nt) {
-        const int64_t col = output_col + nt * 8;
-#pragma unroll
-        for (int mt = 0; mt < 4; ++mt) {
-            const int64_t row0 = row_base + mt * 16;
-            const int64_t row1 = row0 + 8;
-            float* tile_acc = acc + (nt * 4 + mt) * 4;
-            if (col < n) {
-                float bias0 = 0.0f;
-                float bias1 = 0.0f;
-                if constexpr (AddBias) {
-                    bias0 = __bfloat162float(bias[col]);
-                    if (col + 1 < n)
-                        bias1 = __bfloat162float(bias[col + 1]);
-                }
-                if (row0 < m) {
-                    out[row0 * n + col] =
-                        __float2bfloat16(tile_acc[0] * output_scale + bias0);
-                    if (col + 1 < n)
-                        out[row0 * n + col + 1] = __float2bfloat16(
-                            tile_acc[1] * output_scale + bias1);
-                }
-                if (row1 < m) {
-                    out[row1 * n + col] =
-                        __float2bfloat16(tile_acc[2] * output_scale + bias0);
-                    if (col + 1 < n)
-                        out[row1 * n + col + 1] = __float2bfloat16(
-                            tile_acc[3] * output_scale + bias1);
-                }
-            }
-        }
-    }
-}
-
-// Pre-quantized FP8-in path: FP8 A/B read straight into shared memory (no
-// BF16 staging, no inline quantization), FP32 accumulation, BF16 output.
-// Same 128x64 CTA / 64x16 warp tile geometry as the fused kernel; the fp8
-// tile is compact (row = kFastK bytes) so MMA fragments read directly.
-constexpr int kPqBlockM = 128;
-constexpr int kPqBlockN = 64;
-constexpr int kPqK = 32;
-constexpr int kPqStages = 3;
-
-template <typename T>
-__device__ __forceinline__ void cp_async_16b(T* destination,
-                                             const T* source, bool valid) {
-    const unsigned shared_address = __cvta_generic_to_shared(destination);
-    const uint4* source_vec = reinterpret_cast<const uint4*>(source);
-    asm volatile("cp.async.cg.shared.global [%0], [%1], 16, %2;"
-                 :: "r"(shared_address), "l"(source_vec),
-                    "r"(valid ? 16 : 0));
-}
-
-template <bool OutFp8>
-__global__ void fp8_mm_pq_kernel(
-    const __nv_fp8_e4m3* __restrict__ a,
-    const __nv_fp8_e4m3* __restrict__ b,
-    __nv_bfloat16* __restrict__ out_bf16,
-    __nv_fp8_e4m3* __restrict__ out_fp8,
-    const float scale, const float out_scale,
-    int64_t m, int64_t n, int64_t k) {
-    __shared__ __align__(16) __nv_fp8_e4m3 a_tile[kPqStages][kPqBlockM][kPqK];
-    __shared__ __align__(16) __nv_fp8_e4m3 b_tile[kPqStages][kPqBlockN][kPqK];
-
-    const int tid = threadIdx.x;
-    const int warp = tid >> 5;
-    const int lane = tid & 31;
-    const int group = lane >> 2;
-    const int thread_in_group = lane & 3;
-    constexpr int warps_n = kPqBlockN / 16;
-    const int warp_m = warp / warps_n;
-    const int warp_n = warp % warps_n;
-    const int64_t row_base = blockIdx.y * kPqBlockM + warp_m * 64 + group;
-    const int64_t output_col =
-        blockIdx.x * kPqBlockN + warp_n * 16 + thread_in_group * 2;
-    float acc[4 * 4 * 2] = {};
-
-    // One A chunk (16 FP8) per thread covers the 128x32 tile; the first 128
-    // threads issue the 64x32 B chunks.
-    auto load_tile = [&](int stage, int64_t k_base) {
-        const int r0 = tid >> 1;
-        const int c0 = (tid & 1) * 16;
-        const bool full_chunk = k_base + c0 + 15 < k;
-        const int64_t a_row = blockIdx.y * kPqBlockM + r0;
-        auto* a_dst = &a_tile[stage][r0][c0];
-        const auto* a_ptr = a + a_row * k + k_base + c0;
-        const bool full_a = a_row < m && full_chunk;
-        const bool aligned_a =
-            (reinterpret_cast<uintptr_t>(a_ptr) & 15) == 0;
-        if (full_a && aligned_a) {
-            cp_async_16b(a_dst, a_ptr, true);
-        } else {
-#pragma unroll
-            for (int i = 0; i < 16; ++i) {
-                a_dst[i] = a_row < m && k_base + c0 + i < k
-                               ? a_ptr[i]
-                               : __nv_fp8_e4m3(0.0f);
-            }
-        }
-        if (tid < 128) {
-            const int64_t b_row = blockIdx.x * kPqBlockN + r0;
-            auto* b_dst = &b_tile[stage][r0][c0];
-            const auto* b_ptr = b + b_row * k + k_base + c0;
-            const bool full_b = b_row < n && full_chunk;
-            const bool aligned_b =
-                (reinterpret_cast<uintptr_t>(b_ptr) & 15) == 0;
-            if (full_b && aligned_b) {
-                cp_async_16b(b_dst, b_ptr, true);
-            } else {
-#pragma unroll
-                for (int i = 0; i < 16; ++i) {
-                    b_dst[i] = b_row < n && k_base + c0 + i < k
-                                   ? b_ptr[i]
-                                   : __nv_fp8_e4m3(0.0f);
-                }
-            }
-        }
-    };
-
-    const int64_t tile_count = (k + kPqK - 1) / kPqK;
-    load_tile(0, 0);
-    asm volatile("cp.async.commit_group;");
-    if (tile_count > 1) {
-        load_tile(1, kPqK);
-        asm volatile("cp.async.commit_group;");
-    }
-    if (tile_count > 2) {
-        load_tile(2, 2 * kPqK);
-        asm volatile("cp.async.commit_group;");
-    }
-    for (int64_t tile_index = 0; tile_index < tile_count; ++tile_index) {
-        const int stage = static_cast<int>(tile_index % kPqStages);
-        const int64_t remaining = tile_count - tile_index - 1;
-        if (remaining >= 2) {
-            asm volatile("cp.async.wait_group 2;");
-        } else if (remaining == 1) {
-            asm volatile("cp.async.wait_group 1;");
-        } else {
-            asm volatile("cp.async.wait_group 0;");
-        }
-        // Barrier 1: every thread's cp.async for this stage is complete
-        // before any thread reads tiles written by other threads.
-        __syncthreads();
-
-#pragma unroll
-        for (int k_seg = 0; k_seg < kPqK / kMmaK; ++k_seg) {
-            const int frag_col = thread_in_group * 4 + k_seg * 32;
-#pragma unroll
-            for (int nt = 0; nt < 2; ++nt) {
-                const int b_row = warp_n * 16 + nt * 8 + group;
-                unsigned b_frag[2];
-                b_frag[0] = *reinterpret_cast<const unsigned*>(
-                    &b_tile[stage][b_row][frag_col]);
-                b_frag[1] = *reinterpret_cast<const unsigned*>(
-                    &b_tile[stage][b_row][frag_col + 16]);
-#pragma unroll
-                for (int mt = 0; mt < 4; ++mt) {
-                    const int a_row0 = warp_m * 64 + mt * 16 + group;
-                    unsigned a_frag[4];
-                    a_frag[0] = *reinterpret_cast<const unsigned*>(
-                        &a_tile[stage][a_row0][frag_col]);
-                    a_frag[1] = *reinterpret_cast<const unsigned*>(
-                        &a_tile[stage][a_row0 + 8][frag_col]);
-                    a_frag[2] = *reinterpret_cast<const unsigned*>(
-                        &a_tile[stage][a_row0][frag_col + 16]);
-                    a_frag[3] = *reinterpret_cast<const unsigned*>(
-                        &a_tile[stage][a_row0 + 8][frag_col + 16]);
-                    mma_fp8_16832(acc + (nt * 4 + mt) * 4, a_frag, b_frag);
-                }
-            }
-        }
-        // Barrier 2: every thread finished reading this stage's tiles before
-        // the prefetch for the (i+3)-th tile overwrites them.
-        __syncthreads();
-        if (tile_index + 3 < tile_count) {
-            load_tile(stage, (tile_index + 3) * kPqK);
-            asm volatile("cp.async.commit_group;");
-        }
-    }
-
-    const float output_scale = scale * out_scale;
-#pragma unroll
-    for (int nt = 0; nt < 2; ++nt) {
-        const int64_t col = output_col + nt * 8;
-        // Per-row store: FP8 packs two adjacent columns into one 16-bit
-        // write; the BF16 path writes two scalars. Boundary columns fall
-        // back to a scalar convert so the pack never crosses the row edge.
-        auto store_out = [&](int64_t row, float v0, float v1) {
-            if (row >= m) return;
-            if constexpr (OutFp8) {
-                if (col + 1 < n) {
-                    *reinterpret_cast<unsigned short*>(
-                        out_fp8 + row * n + col) =
-                        static_cast<unsigned short>(__nv_cvt_float2_to_fp8x2(
-                            make_float2(v0 * output_scale, v1 * output_scale),
-                            __NV_SATFINITE, __NV_E4M3));
-                } else {
-                    out_fp8[row * n + col] = __nv_fp8_e4m3(v0 * output_scale);
-                }
-            } else {
-                out_bf16[row * n + col] = __float2bfloat16(v0 * scale);
-                if (col + 1 < n)
-                    out_bf16[row * n + col + 1] = __float2bfloat16(v1 * scale);
-            }
-        };
-#pragma unroll
-        for (int mt = 0; mt < 4; ++mt) {
-            const int64_t row0 = row_base + mt * 16;
-            float* tile_acc = acc + (nt * 4 + mt) * 4;
-            if (col < n) {
-                store_out(row0, tile_acc[0], tile_acc[1]);
-                store_out(row0 + 8, tile_acc[2], tile_acc[3]);
-            }
-        }
-    }
-}
-
-template <bool AddBias = false, bool TrackAmax = true>
-void launch_fused_fp8_gemm_fast(
-    const torch::Tensor& a, const torch::Tensor& b, torch::Tensor& out,
-    const torch::Tensor& bias, const torch::Tensor& scale_a,
-    const torch::Tensor& scale_b, torch::Tensor* amax_a,
-    torch::Tensor* amax_b, int64_t m, int64_t n, int64_t k,
-    cudaStream_t stream) {
-    dim3 grid((n + kFastBlockN - 1) / kFastBlockN,
-              (m + kFastBlockM - 1) / kFastBlockM);
-    const auto* bias_ptr = AddBias
-        ? reinterpret_cast<const __nv_bfloat16*>(bias.data_ptr())
-        : nullptr;
-    auto kernel = fused_fp8_gemm_fast_kernel<AddBias, TrackAmax>;
-    static bool attribute_set = false;
-    if (!attribute_set) {
-        C10_CUDA_CHECK(cudaFuncSetAttribute(
-            kernel, cudaFuncAttributeMaxDynamicSharedMemorySize,
-            kFastSmemBytes));
-        attribute_set = true;
-    }
-    kernel<<<grid, kWarps * 32, kFastSmemBytes, stream>>>(
-        reinterpret_cast<const __nv_bfloat16*>(a.data_ptr()),
-        reinterpret_cast<const __nv_bfloat16*>(b.data_ptr()),
-        reinterpret_cast<__nv_bfloat16*>(out.data_ptr()), bias_ptr,
-        scale_a.data_ptr<float>(), scale_b.data_ptr<float>(),
-        amax_a ? amax_a->data_ptr<float>() : nullptr,
-        amax_b ? amax_b->data_ptr<float>() : nullptr, m, n, k);
-}
-
-void check_fp8_device(const torch::Tensor& tensor) {
-    static std::mutex mutex;
-    static std::unordered_map<int, bool> supported;
-    const int device = tensor.device().index();
-    {
-        std::lock_guard<std::mutex> lock(mutex);
-        auto cached = supported.find(device);
-        if (cached != supported.end()) {
-            TORCH_CHECK(cached->second,
-                        "fused FP8 MMA requires compute capability 8.9 or newer");
-            return;
-        }
-    }
-
-    const auto* properties = at::cuda::getDeviceProperties(device);
-    const bool is_supported = properties->major > 8 ||
-                              (properties->major == 8 && properties->minor >= 9);
-    {
-        std::lock_guard<std::mutex> lock(mutex);
-        supported.emplace(device, is_supported);
-    }
-    TORCH_CHECK(is_supported,
-                "fused FP8 MMA requires compute capability 8.9 or newer");
-}
-
-void check_scale(const torch::Tensor& scale, const torch::Tensor& input,
-                 const char* name) {
-    TORCH_CHECK(scale.is_cuda() && scale.device() == input.device() &&
-                    scale.scalar_type() == torch::kFloat32 && scale.numel() == 1,
-                name, " must be a CUDA float32 scalar on the input device");
-}
-
-}  // namespace
-
-torch::Tensor fp8_mm(torch::Tensor a, torch::Tensor b, torch::Tensor sx,
-                     torch::Tensor sw) {
-    TORCH_CHECK(a.is_cuda() && b.is_cuda(), "CUDA tensors required");
-    TORCH_CHECK(a.scalar_type() == torch::kBFloat16 &&
-                    b.scalar_type() == torch::kBFloat16,
-                "a and b must be bf16");
-    TORCH_CHECK(a.dim() == 2 && b.dim() == 2, "a and b must be 2D");
-    TORCH_CHECK(a.device() == b.device(), "a and b must be on the same device");
-    TORCH_CHECK(a.size(1) == b.size(1), "inner dim mismatch");
-    check_scale(sx, a, "sx");
-    check_scale(sw, a, "sw");
-    check_fp8_device(a);
-    const at::cuda::OptionalCUDAGuard guard(a.device());
-    auto stream = at::cuda::getCurrentCUDAStream();
-
-    auto a_c = a.contiguous();
-    auto b_c = b.contiguous();
-    auto out = torch::empty({a_c.size(0), b_c.size(0)}, a_c.options());
-    torch::Tensor no_bias;
-    launch_fused_fp8_gemm_fast<false, false>(
-        a_c, b_c, out, no_bias, sx, sw, nullptr, nullptr,
-        a_c.size(0), b_c.size(0), a_c.size(1), stream.stream());
-    C10_CUDA_CHECK(cudaGetLastError());
-    return out;
-}
-
-torch::Tensor fp8_linear_forward_scaled(
-    torch::Tensor x, torch::Tensor w, torch::Tensor bias, torch::Tensor sx,
-    torch::Tensor sw, torch::Tensor sx_inv, torch::Tensor sw_inv,
-    torch::Tensor amax_x, torch::Tensor amax_w) {
-    TORCH_CHECK(x.is_cuda() && w.is_cuda(), "CUDA tensors required");
-    TORCH_CHECK(x.scalar_type() == torch::kBFloat16 &&
-                    w.scalar_type() == torch::kBFloat16,
-                "x and w must be bf16");
-    TORCH_CHECK(x.device() == w.device(), "x and w must be on the same device");
-    check_scale(sx, x, "sx");
-    check_scale(sw, x, "sw");
-    check_fp8_device(x);
-    const at::cuda::OptionalCUDAGuard guard(x.device());
-    auto stream = at::cuda::getCurrentCUDAStream();
-
-    auto x_c = x.reshape({-1, w.size(1)}).contiguous();
-    auto w_c = w.contiguous();
-    int64_t m = x_c.size(0), k = x_c.size(1), n = w_c.size(0);
-    TORCH_CHECK(w_c.dim() == 2 && w_c.size(1) == k, "inner dim mismatch");
-    C10_CUDA_CHECK(cudaMemsetAsync(amax_x.data_ptr<float>(), 0, sizeof(float),
-                                   stream.stream()));
-    C10_CUDA_CHECK(cudaMemsetAsync(amax_w.data_ptr<float>(), 0, sizeof(float),
-                                   stream.stream()));
-    auto out = torch::empty({m, n}, x_c.options());
-    if (bias.defined() && bias.numel() > 0) {
-        TORCH_CHECK(bias.is_cuda() && bias.device() == x.device() &&
-                        bias.scalar_type() == torch::kBFloat16 &&
-                        bias.numel() == n,
-                    "bias must be CUDA bf16 with shape [N]");
-        launch_fused_fp8_gemm_fast<true, true>(
-            x_c, w_c, out, bias, sx, sw, &amax_x, &amax_w,
-            m, n, k, stream.stream());
-    } else {
-        launch_fused_fp8_gemm_fast<false, true>(
-            x_c, w_c, out, bias, sx, sw, &amax_x, &amax_w,
-            m, n, k, stream.stream());
-    }
-    C10_CUDA_CHECK(cudaGetLastError());
-
-    (void)sx_inv;
-    (void)sw_inv;
-    std::vector<int64_t> shape(x.sizes().begin(), x.sizes().end() - 1);
-    shape.push_back(n);
-    return out.reshape(shape);
-}
-
-std::tuple<torch::Tensor, torch::Tensor, torch::Tensor> fp8_linear_backward_scaled(
-    torch::Tensor g, torch::Tensor x, torch::Tensor w,
-    std::vector<int64_t> masks, torch::Tensor sg, torch::Tensor sw,
-    torch::Tensor sx, torch::Tensor sg_inv, torch::Tensor sw_inv,
-    torch::Tensor sx_inv, torch::Tensor amax_g) {
-    TORCH_CHECK(g.is_cuda() && x.is_cuda() && w.is_cuda(), "CUDA tensors required");
-    TORCH_CHECK(g.scalar_type() == torch::kBFloat16 &&
-                    x.scalar_type() == torch::kBFloat16 &&
-                    w.scalar_type() == torch::kBFloat16,
-                "g, x, and w must be bf16");
-    TORCH_CHECK(g.device() == x.device() && g.device() == w.device(),
-                "g, x, and w must be on the same device");
-    TORCH_CHECK(masks.size() == 3, "masks must contain three values");
-    check_fp8_device(g);
-    const at::cuda::OptionalCUDAGuard guard(g.device());
-    auto stream = at::cuda::getCurrentCUDAStream();
-
-    auto g_c = g.reshape({-1, w.size(0)}).contiguous();
-    auto x_c = x.reshape({-1, x.size(-1)}).contiguous();
-    auto w_c = w.contiguous();
-    int64_t m = g_c.size(0), n = w_c.size(0), k = w_c.size(1);
-    TORCH_CHECK(x_c.size(0) == m && x_c.size(1) == k && g_c.size(1) == n,
-                "backward shape mismatch");
-
-    auto grad_input = torch::empty_like(x);
-    auto grad_weight = torch::empty_like(w);
-    auto grad_bias = torch::empty({0}, g.options());
-    C10_CUDA_CHECK(cudaMemsetAsync(amax_g.data_ptr<float>(), 0, sizeof(float),
-                                   stream.stream()));
-    torch::Tensor no_bias;
-    bool recorded_amax = false;
-    if (masks[0]) {
-        auto grad_input_2d = grad_input.reshape({m, k});
-        // The fast kernel computes A @ B^T. A contiguous W^T makes dX use
-        // the same coalesced forward tile path instead of scalar fragments.
-        auto w_t = w_c.transpose(0, 1).contiguous();
-        launch_fused_fp8_gemm_fast<false, true>(
-            g_c, w_t, grad_input_2d, no_bias, sg, sw, &amax_g, nullptr,
-            m, k, n, stream.stream());
-        recorded_amax = true;
-    }
-    if (masks[1]) {
-        // dW = G^T @ X, expressed as (G^T) @ (X^T)^T for the same kernel.
-        auto g_t = g_c.transpose(0, 1).contiguous();
-        auto x_t = x_c.transpose(0, 1).contiguous();
-        if (recorded_amax) {
-            launch_fused_fp8_gemm_fast<false, false>(
-                g_t, x_t, grad_weight, no_bias, sg, sx, nullptr, nullptr,
-                n, k, m, stream.stream());
-        } else {
-            launch_fused_fp8_gemm_fast<false, true>(
-                g_t, x_t, grad_weight, no_bias, sg, sx, &amax_g, nullptr,
-                n, k, m, stream.stream());
-        }
-        recorded_amax = true;
-    }
-    if (!recorded_amax) {
-        amax_g.copy_(g_c.abs().amax().to(torch::kFloat32));
-    }
-    C10_CUDA_CHECK(cudaGetLastError());
-    if (masks[2]) grad_bias = g_c.sum(0).to(g.scalar_type());
-
-    (void)sg_inv;
-    (void)sw_inv;
-    (void)sx_inv;
-    return {grad_input, grad_weight, grad_bias};
-}
-
-torch::Tensor fp8_mm_prequant(torch::Tensor a, torch::Tensor b,
-                              torch::Tensor scale) {
-    TORCH_CHECK(a.is_cuda() && b.is_cuda(), "CUDA tensors required");
-    TORCH_CHECK(a.scalar_type() == torch::kFloat8_e4m3fn &&
-                    b.scalar_type() == torch::kFloat8_e4m3fn,
-                "a and b must be fp8_e4m3fn");
-    TORCH_CHECK(a.dim() == 2 && b.dim() == 2, "a and b must be 2D");
-    TORCH_CHECK(a.device() == b.device(), "a and b must be on the same device");
-    TORCH_CHECK(a.size(1) == b.size(1), "inner dim mismatch");
-    check_scale(scale, a, "scale");
-    check_fp8_device(a);
-    const at::cuda::OptionalCUDAGuard guard(a.device());
-    auto stream = at::cuda::getCurrentCUDAStream();
-
-    auto a_c = a.contiguous();
-    auto b_c = b.contiguous();
-    int64_t m = a_c.size(0), k = a_c.size(1), n = b_c.size(0);
-    auto out = torch::empty({m, n},
-                            a_c.options().dtype(torch::kBFloat16));
-    const float scale_value = scale.item<float>();
-    dim3 grid((n + kPqBlockN - 1) / kPqBlockN,
-              (m + kPqBlockM - 1) / kPqBlockM);
-    fp8_mm_pq_kernel<false><<<grid, kWarps * 32, 0, stream>>>(
-        reinterpret_cast<const __nv_fp8_e4m3*>(a_c.data_ptr()),
-        reinterpret_cast<const __nv_fp8_e4m3*>(b_c.data_ptr()),
-        reinterpret_cast<__nv_bfloat16*>(out.data_ptr()), nullptr,
-        scale_value, 1.0f, m, n, k);
-    C10_CUDA_CHECK(cudaGetLastError());
-    return out;
-}
-
-torch::Tensor fp8_mm_prequant_fp8(torch::Tensor a, torch::Tensor b,
-                                  torch::Tensor scale,
-                                  torch::Tensor out_scale) {
-    TORCH_CHECK(a.is_cuda() && b.is_cuda(), "CUDA tensors required");
-    TORCH_CHECK(a.scalar_type() == torch::kFloat8_e4m3fn &&
-                    b.scalar_type() == torch::kFloat8_e4m3fn,
-                "a and b must be fp8_e4m3fn");
-    TORCH_CHECK(a.dim() == 2 && b.dim() == 2, "a and b must be 2D");
-    TORCH_CHECK(a.device() == b.device(), "a and b must be on the same device");
-    TORCH_CHECK(a.size(1) == b.size(1), "inner dim mismatch");
-    check_scale(scale, a, "scale");
-    check_scale(out_scale, a, "out_scale");
-    check_fp8_device(a);
-    const at::cuda::OptionalCUDAGuard guard(a.device());
-    auto stream = at::cuda::getCurrentCUDAStream();
-
-    auto a_c = a.contiguous();
-    auto b_c = b.contiguous();
-    int64_t m = a_c.size(0), k = a_c.size(1), n = b_c.size(0);
-    auto out = torch::empty({m, n}, a_c.options());
-    const float scale_value = scale.item<float>();
-    const float out_scale_value = out_scale.item<float>();
-    dim3 grid((n + kPqBlockN - 1) / kPqBlockN,
-              (m + kPqBlockM - 1) / kPqBlockM);
-    fp8_mm_pq_kernel<true><<<grid, kWarps * 32, 0, stream>>>(
-        reinterpret_cast<const __nv_fp8_e4m3*>(a_c.data_ptr()),
-        reinterpret_cast<const __nv_fp8_e4m3*>(b_c.data_ptr()), nullptr,
-        reinterpret_cast<__nv_fp8_e4m3*>(out.data_ptr()),
-        scale_value, out_scale_value, m, n, k);
-    C10_CUDA_CHECK(cudaGetLastError());
-    return out;
-}
-
-PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
-    m.def("fp8_mm", &fp8_mm, py::arg("a"), py::arg("b"), py::arg("sx"),
-          py::arg("sw"),
-          "Fused BF16 input, E4M3 MMA, FP32 accumulation, BF16 output GEMM");
-    m.def("fp8_mm_prequant", &fp8_mm_prequant, py::arg("a"), py::arg("b"),
-          py::arg("scale"),
-          "Pre-quantized FP8 GEMM with FP32 accumulation and BF16 output");
-    m.def("fp8_mm_prequant_fp8", &fp8_mm_prequant_fp8, py::arg("a"),
-          py::arg("b"), py::arg("scale"), py::arg("out_scale"),
-          "Pre-quantized FP8 GEMM with FP32 accumulation and FP8 output");
-    m.def("fp8_linear_forward_scaled", &fp8_linear_forward_scaled,
-          py::arg("x"), py::arg("w"), py::arg("bias"), py::arg("sx"),
-          py::arg("sw"), py::arg("sx_inv"), py::arg("sw_inv"),
-          py::arg("amax_x"), py::arg("amax_w"),
-          "Fused BF16-to-FP8 linear forward with FP32 accumulation");
-    m.def("fp8_linear_backward_scaled", &fp8_linear_backward_scaled,
-          py::arg("g"), py::arg("x"), py::arg("w"), py::arg("masks"),
-          py::arg("sg"), py::arg("sw"), py::arg("sx"), py::arg("sg_inv"),
-          py::arg("sw_inv"), py::arg("sx_inv"), py::arg("amax_g"),
-          "Fused BF16-to-FP8 linear backward with FP32 accumulation");
-}

csrc/tests/attn_paged_test.cu

@@ -7,7 +7,7 @@
 #include <cstring>
 #include <vector>
 #include "test_utils.cuh"
-#include "../kernels/attn_dispatchers.cuh"
+#include "../kernels/attention/dispatchers.cuh"
 
 struct PagedDecodeDispatch { AttentionParams<bf16>& p; template<int H> void operator()() { dispatch_paged_decode<H>(p, 0); } };
 struct PagedPrefillDispatch { AttentionParams<bf16>& p; template<int H> void operator()() { dispatch_paged_prefill<H>(p, 0); } };

csrc/tests/attn_test.cu

@@ -7,7 +7,7 @@ nvcc -I csrc -arch=sm_89 -O3 \
 */
 
 #include "test_utils.cuh"
-#include "../kernels/attn_dispatchers.cuh"
+#include "../kernels/attention/dispatchers.cuh"
 
 struct DecodeDispatch { AttentionParams<bf16>& p; template<int H> void operator()() { dispatch_decode<H>(p, 0); } };
 struct PrefillDispatch { AttentionParams<bf16>& p; template<int H> void operator()() { dispatch_prefill<H>(p, 0); } };

csrc/tests/fp8_mma_test.cu

@@ -10,6 +10,8 @@ nvcc -I csrc -arch=sm_89 -std=c++17 -O3 --use_fast_math \
 
 #include <cuda_fp8.h>
 
+#include "../kernels/common/mma.cuh"
+
 #include <algorithm>
 #include <vector>
 
@@ -37,17 +39,6 @@ __device__ __forceinline__ unsigned load_quantize_fp8x4(
                       __bfloat162float(src[3]) * scale_inv);
 }
 
-__device__ __forceinline__ void mma_fp8_16832(float d[4],
-                                               const unsigned a[4],
-                                               const unsigned b[2]) {
-    asm volatile(
-        "mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32 "
-        "{%0,%1,%2,%3}, {%4,%5,%6,%7}, {%8,%9}, {%0,%1,%2,%3};"
-        : "+f"(d[0]), "+f"(d[1]), "+f"(d[2]), "+f"(d[3])
-        : "r"(a[0]), "r"(a[1]), "r"(a[2]), "r"(a[3]),
-          "r"(b[0]), "r"(b[1]));
-}
-
 __global__ void fused_bf16_fp8_mma_kernel(
     const bf16* __restrict__ a, const bf16* __restrict__ b,
     bf16* __restrict__ out, float scale_a, float scale_b) {
@@ -71,7 +62,7 @@ __global__ void fused_bf16_fp8_mma_kernel(
     b_frag[1] = load_quantize_fp8x4(&b[group * K + k0 + 16], 1.0f / scale_b);
 
     float acc[4] = {0.0f, 0.0f, 0.0f, 0.0f};
-    mma_fp8_16832(acc, a_frag, b_frag);
+    astrai::mma_sync<__nv_fp8_e4m3>(acc, a_frag, b_frag, acc);
 
     const int col = thread_in_group * 2;
     const float output_scale = scale_a * scale_b;

tests/extension/test_fp8_mma.py

@@ -1,11 +1,30 @@
-"""Fused BF16-boundary FP8 MMA kernel tests."""
+"""FP8 primitives: kernel-level (CUDA) and policy-level (CPU-verifiable) tests.
+
+The kernel-level tests exercise the fused and pre-quantized CUDA paths; the
+policy-level tests (recipes, autocast context, per-tensor meta, CPU fallbacks
+of the custom ops) run without a GPU.
+"""
 
 import pytest
 import torch
 
+from astrai.extension.fp8 import (
+    DelayedScaling,
+    DynamicScaling,
+    FP8Format,
+    FP8TensorMeta,
+    fp8_autocast,
+    fp8_state,
+)
 from astrai.extension.loader import get_module, is_available
+from astrai.extension.ops.fp8 import (
+    linear_backward_fp8,
+    linear_forward_fp8,
+    mm_fp8,
+    quantize_bf16,
+)
 
-pytestmark = pytest.mark.skipif(
+_GPU = pytest.mark.skipif(
     not torch.cuda.is_available()
     or torch.cuda.get_device_capability() < (8, 9)
     or not is_available("fp8_mm"),
@@ -21,6 +40,12 @@ def _quantize(tensor, scale):
     return (tensor.float() / scale).to(torch.float8_e4m3fn).float()
 
 
+# --------------------------------------------------------------------------
+# Kernel-level (CUDA)
+# --------------------------------------------------------------------------
+
+
+@_GPU
 @pytest.mark.parametrize(
     ("m", "n", "k"),
     [(16, 8, 32), (17, 9, 33), (31, 15, 64), (32, 48, 96)],
@@ -42,6 +67,31 @@ def test_fused_fp8_mma_matches_explicit_quantization(m, n, k):
     torch.testing.assert_close(out, expected, atol=0.125, rtol=0.01)
 
 
+@_GPU
+def test_quantize_bf16_returns_amax():
+    """quantize_bf16 returns (x8, amax); amax tracks the *raw* values and the
+    caller never clears it (zero-initialized inside the kernel entry)."""
+    torch.manual_seed(3)
+    x = torch.randn(64, 128, device="cuda", dtype=torch.bfloat16)
+    scale = torch.tensor([0.5], device="cuda")
+    x8, amax = quantize_bf16(x, scale, "e4m3")
+    assert x8.dtype == torch.float8_e4m3fn
+    assert x8.shape == x.shape
+    assert amax.shape == (1,)
+    torch.testing.assert_close(amax, x.abs().amax().float().reshape(1))
+    ref = (x.float() / 0.5).to(torch.float8_e4m3fn)
+    assert torch.equal(x8, ref)
+
+
+@_GPU
+def test_quantize_bf16_e5m2_format():
+    x = torch.randn(32, 64, device="cuda", dtype=torch.bfloat16)
+    x8, amax = quantize_bf16(x, torch.tensor([0.1], device="cuda"), "e5m2")
+    assert x8.dtype == torch.float8_e5m2
+    torch.testing.assert_close(amax, x.abs().amax().float().reshape(1))
+
+
+@_GPU
 def test_fused_fp8_linear_forward_and_backward():
     torch.manual_seed(7)
     m, n, k = 19, 13, 37
@@ -50,34 +100,10 @@ def test_fused_fp8_linear_forward_and_backward():
     grad = torch.randn(m, n, device="cuda", dtype=torch.bfloat16)
     bias = torch.randn(n, device="cuda", dtype=torch.bfloat16)
     scale_x, scale_w, scale_g = _scale(x), _scale(weight), _scale(grad)
-    amax_x = torch.empty(1, device="cuda", dtype=torch.float32)
-    amax_w = torch.empty(1, device="cuda", dtype=torch.float32)
-    amax_g = torch.empty(1, device="cuda", dtype=torch.float32)
-    module = get_module("fp8_mm")
 
-    out = module.fp8_linear_forward_scaled(
+    out, amax_x, amax_w = linear_forward_fp8(x, weight, bias, scale_x, scale_w)
-        x,
+    grad_x, grad_w, grad_b, amax_g = linear_backward_fp8(
-        weight,
+        grad, x, weight, [1, 1, 1], scale_g, scale_w, scale_x, "e4m3"
-        bias,
-        scale_x,
-        scale_w,
-        scale_x.reciprocal(),
-        scale_w.reciprocal(),
-        amax_x,
-        amax_w,
-    )
-    grad_x, grad_w, grad_b = module.fp8_linear_backward_scaled(
-        grad,
-        x,
-        weight,
-        [1, 1, 1],
-        scale_g,
-        scale_w,
-        scale_x,
-        scale_g.reciprocal(),
-        scale_w.reciprocal(),
-        scale_x.reciprocal(),
-        amax_g,
     )
 
     qx = _quantize(x, scale_x)
@@ -96,61 +122,178 @@ def test_fused_fp8_linear_forward_and_backward():
     torch.testing.assert_close(amax_g, grad.abs().amax().float().reshape(1))
 
 
-def test_fp8_mm_prequant_matches_scaled_mm():
+@_GPU
+def test_linear_backward_e5m2_gradients():
+    """Hybrid backward: gradient GEMMs run in E5M2 (larger dynamic range)."""
+    torch.manual_seed(5)
+    m, n, k = 32, 16, 64
+    x = torch.randn(m, k, device="cuda", dtype=torch.bfloat16) * 3.0
+    weight = torch.randn(n, k, device="cuda", dtype=torch.bfloat16)
+    grad = torch.randn(m, n, device="cuda", dtype=torch.bfloat16) * 10.0
+    sg = _scale(grad) * 0.5
+    sw = _scale(weight)
+    sx = _scale(x)
+
+    grad_x, grad_w, grad_b, amax_g = linear_backward_fp8(
+        grad, x, weight, [1, 1, 1], sg, sw, sx, "e5m2"
+    )
+
+    def q5(t, s):
+        return (t.float() / s).to(torch.float8_e5m2).float()
+
+    qg = q5(grad, sg)
+    qw = q5(weight, sw)
+    qx = q5(x, sx)
+    expected_grad_x = (qg @ qw * sg * sw).to(torch.bfloat16)
+    expected_grad_w = (qg.t() @ qx * sg * sx).to(torch.bfloat16)
+    torch.testing.assert_close(grad_x, expected_grad_x, atol=0.5, rtol=0.05)
+    torch.testing.assert_close(grad_w, expected_grad_w, atol=0.5, rtol=0.05)
+    torch.testing.assert_close(amax_g, grad.abs().amax().float().reshape(1))
+
+
+@_GPU
+def test_mm_fp8_matches_scaled_mm():
     torch.manual_seed(11)
     m, n, k = 512, 4096, 4096
     a = torch.randn(m, k, device="cuda", dtype=torch.bfloat16)
-    weight = torch.randn(n, k, device="cuda", dtype=torch.bfloat16)
+    b = torch.randn(n, k, device="cuda", dtype=torch.bfloat16)
-    a8 = a.to(torch.float8_e4m3fn)
+    sa = torch.tensor([2.5], device="cuda")
-    w8 = weight.to(torch.float8_e4m3fn)
+    sb = torch.tensor([1.5], device="cuda")
-    scale = torch.tensor([2.5], device="cuda")
+    a8, _ = quantize_bf16(a, sa, "e4m3")
-
+    b8, _ = quantize_bf16(b, sb, "e4m3")
-    out = get_module("fp8_mm").fp8_mm_prequant(a8, w8, scale)
+    out = mm_fp8(a8, b8, sa, sb)
-
-    # Reference via fp64: FP8 quantization error is dominated by the 3-bit
-    # mantissa, so the tolerance must track the input quantization scale.
-    ref = (a8.float().double() @ w8.float().double().t() * 2.5).to(torch.bfloat16)
     assert out.dtype == torch.bfloat16
     assert out.shape == (m, n)
+
+    ref = (a8.float().double() @ b8.float().double().t() * 2.5 * 1.5).to(torch.bfloat16)
     torch.testing.assert_close(out, ref, atol=6.0, rtol=0.05)
 
-    # Cross-check against torch's native FP8 GEMM on identical inputs.
     try:
-        torch._scaled_mm(
+        torch._scaled_mm(a8, b8.t(), sa, sb, out_dtype=torch.bfloat16)
-            a8,
-            w8.t(),
-            torch.full((m, 1), 2.5, device="cuda"),
-            torch.ones((1, n), device="cuda"),
-            out_dtype=torch.bfloat16,
-        )
     except (RuntimeError, NotImplementedError):
         return
     torch.testing.assert_close(
         out,
-        torch._scaled_mm(
+        torch._scaled_mm(a8, b8.t(), sa, sb, out_dtype=torch.bfloat16),
-            a8,
-            w8.t(),
-            torch.full((m, 1), 2.5, device="cuda"),
-            torch.ones((1, n), device="cuda"),
-            out_dtype=torch.bfloat16,
-        ),
         atol=2.0,
         rtol=0.01,
     )
 
 
-def test_fp8_mm_prequant_fp8_output():
+@_GPU
-    torch.manual_seed(13)
+def test_mm_fp8_fp8_output():
-    m, n, k = 512, 4096, 4096
+    """mm_fp8 with out_dtype='e4m3' produces an FP8 output (layer-to-layer)."""
+    torch.manual_seed(12)
+    m, n, k = 256, 128, 64
     a = torch.randn(m, k, device="cuda", dtype=torch.bfloat16)
-    weight = torch.randn(n, k, device="cuda", dtype=torch.bfloat16)
+    b = torch.randn(n, k, device="cuda", dtype=torch.bfloat16)
-    a8 = a.to(torch.float8_e4m3fn)
+    sa = torch.tensor([2.0], device="cuda")
-    w8 = weight.to(torch.float8_e4m3fn)
+    sb = torch.tensor([1.0], device="cuda")
-    scale = torch.tensor([2.5], device="cuda")
+    os_ = torch.tensor([0.5], device="cuda")
-    out_scale = torch.tensor([0.1], device="cuda")
+    a8, _ = quantize_bf16(a, sa, "e4m3")
+    b8, _ = quantize_bf16(b, sb, "e4m3")
+    out8 = mm_fp8(a8, b8, sa, sb, out_dtype="e4m3", out_scale=os_)
+    assert out8.dtype == torch.float8_e4m3fn
+    assert out8.shape == (m, n)
 
-    out = get_module("fp8_mm").fp8_mm_prequant_fp8(a8, w8, scale, out_scale)
+    ref = (a8.float().double() @ b8.float().double().t() * 2.0 * 1.0 * 0.5).to(
-    assert out.dtype == torch.float8_e4m3fn
+        torch.bfloat16
-    assert out.shape == (m, n)
+    )
-    ref = (a8.float().double() @ w8.float().double().t() * 2.5 * 0.1).to(torch.bfloat16)
+    torch.testing.assert_close(
-    torch.testing.assert_close(out.float().to(torch.bfloat16), ref, atol=1.0, rtol=0.05)
+        out8.float().to(torch.bfloat16), ref, atol=6.0, rtol=0.05
+    )
+
+
+# --------------------------------------------------------------------------
+# Policy-level (CPU-verifiable)
+# --------------------------------------------------------------------------
+
+
+def test_recipe_scale_from_history():
+    """Delayed: max over the window + margin; dynamic: current amax."""
+    hist = torch.tensor([1.0, 2.0, 0.5])
+    d = DelayedScaling(history_len=3, margin=0)
+    assert torch.allclose(d.scale_from_history(hist, "e4m3"), torch.tensor(2.0 / 448.0))
+    d_m = DelayedScaling(history_len=3, margin=2)
+    assert torch.allclose(
+        d_m.scale_from_history(hist, "e4m3"), torch.tensor(2.0 / 448.0 / 4.0)
+    )
+    dyn = DynamicScaling()
+    amax = torch.tensor([0.25])
+    assert torch.allclose(
+        dyn.scale_from_history(amax, "e4m3"), torch.tensor(0.25 / 448.0)
+    )
+    assert torch.allclose(
+        dyn.scale_from_history(amax, "e5m2"), torch.tensor(0.25 / 57344.0)
+    )
+
+
+def test_fp8_format_enum():
+    assert FP8Format.HYBRID.fwd() == "e4m3"
+    assert FP8Format.HYBRID.bwd() == "e5m2"
+    assert FP8Format.E4M3.fwd() == FP8Format.E4M3.bwd() == "e4m3"
+    assert FP8Format.E5M2.fwd() == FP8Format.E5M2.bwd() == "e5m2"
+
+
+def test_fp8_autocast_context():
+    """fp8_autocast sets and restores recipe + format on the global state."""
+    state = fp8_state()
+    prev = (state.enabled, state.recipe, state.fp8_format)
+    try:
+        with fp8_autocast(enabled=True, fp8_format="hybrid", update_interval=8):
+            assert state.enabled
+            assert isinstance(state.recipe, DelayedScaling)
+            assert state.recipe.history_len == 8
+            assert state.fp8_format is FP8Format.HYBRID
+            with fp8_autocast(enabled=True, recipe=DynamicScaling(), fp8_format="e4m3"):
+                assert isinstance(state.recipe, DynamicScaling)
+                assert state.fp8_format is FP8Format.E4M3
+            assert state.fp8_format is FP8Format.HYBRID  # restored on exit
+        assert not state.enabled
+    finally:
+        state.enabled, state.recipe, state.fp8_format = prev
+
+
+def test_fp8_tensor_meta_delayed_update():
+    """Meta seeds from data and refreshes the scale from the amax ring."""
+    meta = FP8TensorMeta(torch.device("cpu"), DelayedScaling(history_len=4, margin=0))
+    w = torch.randn(8, 8)
+    meta.init_w(w, "e4m3")
+    assert meta.w_init
+    torch.testing.assert_close(meta.w_scale, (w.abs().amax() / 448.0).reshape(1))
+    meta.update_w(torch.tensor([4.0]), "e4m3")
+    torch.testing.assert_close(meta.w_scale, torch.tensor(4.0 / 448.0).reshape(1))
+
+
+def test_quantize_bf16_cpu_fallback():
+    """CPU fallback of the quantize primitive (scale semantics + amax)."""
+    x = torch.randn(16, 32, dtype=torch.bfloat16)
+    scale = torch.tensor([0.5])
+    x8, amax = quantize_bf16(x, scale, "e4m3")
+    assert x8.dtype == torch.float8_e4m3fn
+    ref = (x.float() / 0.5).to(torch.float8_e4m3fn)
+    assert torch.equal(x8, ref)
+    torch.testing.assert_close(amax, x.abs().amax().float().reshape(1))
+
+
+def test_mm_fp8_cpu_fallback():
+    a8 = torch.tensor([[1.0, 2.0]], dtype=torch.float8_e4m3fn)
+    b8 = torch.tensor([[3.0, 4.0]], dtype=torch.float8_e4m3fn)
+    sa = torch.tensor([2.0])
+    sb = torch.tensor([0.5])
+    out = mm_fp8(a8, b8, sa, sb)
+    ref = (a8.float() @ b8.float().t() * 2.0 * 0.5).to(torch.bfloat16)
+    torch.testing.assert_close(out, ref)
+
+
+def test_mm_fp8_fp8_output_cpu():
+    """CPU fallback with an FP8 output (out_dtype='e4m3' + out_scale)."""
+    a8 = torch.tensor([[1.0, 2.0]], dtype=torch.float8_e4m3fn)
+    b8 = torch.tensor([[3.0, 4.0]], dtype=torch.float8_e4m3fn)
+    sa = torch.tensor([2.0])
+    sb = torch.tensor([0.5])
+    os_ = torch.tensor([0.25])
+    out8 = mm_fp8(a8, b8, sa, sb, out_dtype="e4m3", out_scale=os_)
+    assert out8.dtype == torch.float8_e4m3fn
+    ref = (a8.float() @ b8.float().t() * 2.0 * 0.5 * 0.25).to(torch.float8_e4m3fn)
+    assert torch.equal(out8, ref)