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copy → reg
==========

The ``reg`` variant lowers a synchronous ``copy`` where **exactly one side is a
register** (``local``) buffer and the other is ``shared*`` or ``global``. Unlike
:doc:`gmem_smem`, the partition is **not synthesized** — it is *induced* by the
register operand's layout: that layout's thread-axis iters already say which thread
owns which logical coordinate, so the dispatch drops those axes, leaves each thread
its private bundle of elements, and copies them in a vectorized serial loop. Source:
``python/tvm/backend/cuda/tile_primitive/copy/vec_auto_reg.py``.

What it accepts
---------------

.. code-block:: python

    def _is_reg_copy(op_call, sctx):
        if not sctx.is_target("cuda"):
            return False, "non-cuda target"
        if sctx.scope_kind not in ("thread", "warp", "warpgroup", "cta"):
            return False, f"unsupported exec_scope {sctx.scope_kind}"
        for check in (
            lambda: _all_threads_active(sctx),
            lambda: _is_valid_copy(op_call, sctx),
            lambda: _scope_allowed(op_call, sctx, allowed_pairs=_REG_PAIRS),
            lambda: _r_side_layout_valid(op_call, sctx),   # the register operand
            lambda: _s_side_slice_ok(op_call),             # the other operand
        ):
            ok, msg = check()
            if not ok:
                return False, msg
        return True, None

.. list-table::
   :header-rows: 1
   :widths: 22 78

   * - Property
     - Requirement
   * - target / scope
     - ``cuda``; ``thread`` / ``warp`` / ``warpgroup`` / ``cta`` with all threads
       active
   * - memory pair
     - ``_REG_PAIRS`` = ``(local, shared*)`` / ``(shared*, local)`` /
       ``(local, global)`` / ``(global, local)`` — exactly one side is ``local``
   * - register layout
     - ``_r_side_layout_valid``: the ``local`` operand is a non-swizzle
       ``TileLayout`` whose thread-axis iters have **stride 1**, a register-level
       subscope no wider than the exec scope, and a **zero sliced thread offset**
       (the region doesn't split a thread axis)
   * - other side
     - ``_s_side_slice_ok``: the ``shared*`` / ``global`` operand slices cleanly to
       its region

Demonstration program
----------------------

A warp round-trips a ``32×8`` ``float32`` tile shared → register → shared, with the
register layout ``S[(32,8):(1@laneid, 1)]`` — **lane ``i`` owns row ``i``** (8
contiguous elements). From ``test_reg.py``:

.. code-block:: python

    from tvm.tirx.layout import S, TileLayout, laneid

    shape, dtype = (32, 8), "float32"
    r_layout = TileLayout(S[shape : (1 @ laneid, 1)])   # lane i -> row i, 8 regs
    s_layout = TileLayout(S[shape])
    fs = (slice(0, 32), slice(0, 8))

    @T.prim_func
    def kernel(B_ptr: T.handle):
        B = T.match_buffer(B_ptr, shape, dtype)
        T.device_entry(); T.cta_id([1]); T.lane_id([32]); tid = T.thread_id([32])
        A_smem = T.alloc_buffer(shape, dtype, scope="shared", layout=s_layout)
        for kk in range(8): A_smem[tid, kk] = T.cast(tid * 100 + kk + 1, dtype)
        T.cuda.cta_sync()
        R = T.alloc_buffer(shape, dtype, scope="local", layout=r_layout)
        Tx.warp.copy(R[fs], A_smem[fs])    # shared -> register  (this dispatch)
        # ... clear A_smem, cta_sync ...
        Tx.warp.copy(A_smem[fs], R[fs])    # register -> shared  (this dispatch)
        # ... cta_sync; B[tid, kk] = A_smem[tid, kk] ...

Algorithm
---------

**1. Inherit the partition from R.** The register layout's thread axis (``laneid``)
states that lane ``i`` owns row ``i``; the dispatch aligns the other (shared) side
to that order, then **drops the thread iters** — what remains is each thread's
private memory bundle: here ``8`` contiguous elements per lane.

**2. Linearize and choose the vector width.** The per-thread elements are
flattened into ``(extent, stride)`` atoms; the vector width is chosen widest-first
(``128 → … → 8`` bits) so the contiguous tail divides it and the outer atom
strides + base offsets are aligned. Crucially the **thread-axis strides are
excluded** from this alignment check (they live in *partition-coordinate* space —
which thread owns which element — and never appear in a single thread's physical
address). For ``8`` contiguous ``float32`` that is ``vec = 4``, so ``outer = 2``.

**3. Per-thread base offset + serial loop.** The shared-side base offset is built
from thread-axis placeholders (substituted with the real ``T.lane_id()`` etc.),
and the register side is a flat per-thread ``local`` buffer. The emit is a serial
loop (not ``T.unroll`` — same flooding rationale as :doc:`gmem_smem`):

.. code-block:: python

    r_local = r_buf.local()                      # raw per-thread physical span
    for f in range(total_outer):
        ds, dr = _outer_const_offsets(outer, f)               # shared / reg deltas
        s_ptr = _ptr_off(s_buf.ptr_to(s_zero_indices), _s_iter_off(f, ds, s_off))
        r_ptr = _ptr_off(r_local.ptr_to([0]), r_off_base + dr)
        if r_is_src:
            copy_op(s_ptr, r_ptr)     # register -> shared/global
        else:
            copy_op(r_ptr, s_ptr)     # shared/global -> register

``dr`` and ``r_off_base`` are physical storage offsets, so the register alias
must use the raw-span ``local()`` view.  This remains correct when storage
iterators are permuted or leave gaps; every physical slot through
``layout.storage().span()`` is directly addressable.

Generated TIRx IR
-----------------

``LowerTIRx`` turns the shared → register copy into a per-thread loop over the
8-element register bundle (trimmed):

.. code-block:: python

    r_local = T.decl_buffer((8,), data=R.data, scope="local")   # 8 regs / lane
    for f in range(2):                                           # outer = 8 / vec 4
        s_ptr = pointer_offset(A_smem, ...)                      # this lane's row
        r_ptr = pointer_offset(r_local, dr)
        T.cuda.copy_bytes(r_ptr, s_ptr, 16)                      # 16 B = vec 4 × 4 B

(The register → shared copy is the mirror: ``copy_bytes(s_ptr, r_ptr, 16)``.)

Generated CUDA
--------------

.. code-block:: c++

    alignas(64) float r_local_ptr[8];          // 8 registers, private to the lane
    for (int f = 0; f < 2; ++f) {
      void* r_ptr = tvm_builtin_pointer_offset(&r_local_ptr[0], dr);
      void* s_ptr = tvm_builtin_pointer_offset(&A_smem_ptr[0], /* lane row + f*4 */);
      tvm_builtin_copy_128b(r_ptr, s_ptr);     // shared -> register
    }
    // ... register -> shared mirror writes A_smem back ...

Each lane copies its own 8 elements as 2 × 128-bit transfers; no cross-lane
addressing appears because the thread partition was resolved away at lowering.

How inputs change the algorithm
-------------------------------

The register layout's **per-thread element count** (the non-thread extents — here
``k``) and the **dtype** set the register count, vector width, and round count:

.. list-table::
   :header-rows: 1
   :widths: 18 18 22 22 20

   * - dtype
     - ``k``
     - regs / lane
     - ``vec``
     - ``outer = k / vec``
   * - ``float32``
     - 8
     - 8
     - 4
     - 2
   * - ``float32``
     - 16
     - 16
     - 4
     - 4
   * - ``float16``
     - 8
     - 8
     - 8
     - 1
   * - ``float16``
     - 16
     - 16
     - 8
     - 2

The copy is always a 128-bit transfer (``copy_bytes = 16``) when the contiguous
tail allows. The **scope** sets the thread axis (``warp`` → ``laneid``, ``cta`` →
``tx``, …) the register layout must use; a different R layout (e.g. a strided or
multi-row ownership) changes which elements each lane holds and therefore the atom
list and ``outer``.
