[teeny] Phase B2: posdef entry points take teeny carriers — delete the _any shared-size reconstruction

[balbasty]

Agent: claude-fastfields-to-teeny

Part of the tensor-native-boundaries umbrella (fastfields-lib#57), Phase B. One coordinated PR-set with the cpu-lib half (fastfields-cpu-lib "Phase B2" issue); this issue covers the impl repo (posdef.h). Convention: TEENY-MIGRATION.md §9 — R2 spellings at.ndim / at.size(at.ndim - 1).

Tier-1 status confirmed (no kernel work here): kernels/posdef/matrix.h is already tensor-native — matvec(Ov&& o, const Hv& h, const Xv& x) per packed layout, matvec_backward(Hv&&, const Xv&, const Yv&), solve_/solve_w_/invert_w_ all take teeny views. This issue is the impl-entry re-skin ONLY, the same shape distance_l1/euclidean went through in Phase A.

Current signatures (exact; 8 entry points)

matvec / addmatvec_ / submatvec_ (via _matvec), sym_matvec_backward, solve, solve_, sym_invert, sym_invert_:

template <type Ty, int C, typename reduce_t, typename scalar_t, typename offset_t>
void matvec(offset_t nbatch, offset_t nchannel, scalar_t* out,
 const scalar_t* hes, const scalar_t* inp, const offset_t* size,
 const offset_t* stride_out, const offset_t* stride_hes, const offset_t* stride_inp);

template <type Ty, typename reduce_t, typename scalar_t, typename offset_t>
void solve(offset_t nbatch, offset_t nchannel, scalar_t* out, const scalar_t* inp,
 const scalar_t* hes, const scalar_t* wgt, const offset_t* size,
 const offset_t* stride_out, const offset_t* stride_inp,
 const offset_t* stride_hes, const offset_t* stride_wgt); // wgt may be nullptr

Every body opens with the _any helper — the textbook R3 hazard instance §9.2 cites: ONE shared size[] for all operands, each carrier rebuilt from the shared batch dims + a per-tensor trailing extent (nchannel vs CC), because vectors trail C while the packed hessian trails C(C+1)/2:

template <typename T, typename offset_t>
static inline auto _any(T* p, const offset_t* size, offset_t nbatch,
 offset_t trailing, const offset_t* stride)
{
 std::vector<offset_t> sz(size, size + nbatch);
 sz.push_back(trailing);
 return tny::as_anyrank(p, sz.data(), stride, static_cast<int>(nbatch + 1), tny::copy_meta);
}

With carriers built lib-side from each DLTensor's OWN shape (from_dlpack), the reconstruction — including its per-call std::vector allocation — disappears entirely. (The lib's CHECK_SAME_BATCH/CHECK_RANK/CHECK_SAME validation already guarantees the geometry _any was re-deriving.)

Target

template <type Ty, wr W, int C, typename reduce_t, class AO, class AH, class AI>
static void _matvec(AO ao, const AH ah, const AI ai)
// offset_t = decltype(ao.size(0)); nchannel = ao.size(ao.ndim - 1) (R2)
// static_assert the three carriers' element types agree (Phase A's one-line
// mismatch report, instead of a template error inside the kernel)

template <type Ty, typename reduce_t, class AO, class AI, class AH>
void solve(AO ao, const AI ai, const AH ah); // no weight
template <type Ty, typename reduce_t, class AO, class AI, class AH, class AW>
void solve(AO ao, const AI ai, const AH ah, const AW aw); // with weight

• nbatch, nchannel, size[], and every stride_*[] argument disappear (R2/R3). CC for validation/recast still comes from _packed/_packed_s (kept — the C > 0 static recast(tny::shape<C>{}) fast path is untouched).
• The optional weight becomes overloads, not a null carrier: _dispatch_solve already has exactly these two arities; the lib's has_wgt branch picks the overload. A "null-data carrier" sentinel would smuggle the pointer-era convention through the tensor boundary.
• Read-only operands (ah, ai, aw, ag) are const-element carriers (R4).
• The per-thread Cholesky workspace (std::vector<reduce_t> b + tny::wrap(b.data(), shape<-1,-1>{nc,nc})) and the peel_front_at<-1> voxel loop are unchanged — only the prologue moves out.

Scope

posdef.h only, all 8 entry points (matvec, addmatvec_, submatvec_, sym_matvec_backward, solve, solve_, sym_invert, sym_invert_). NOT kernels/posdef/* (already tier-1 tensor-native). NOT cuda-impl (its own Phase B issue — the cuda twin keeps its signature until then; separate files, nothing breaks). Old signatures deleted, not deprecated — cpu-lib is the only caller and converts in the same PR-set.

Gate (Phase A's, restated — the PR-set merges only if ALL hold)

1. Untouched kernel-layer instantiations (kernels/posdef/matrix.h: eye/diag/estatics/sym/full::matvec, sym::matvec_backward, solve_/solve_w_/invert_w_) byte-identical at -O2 wherever they exist as standalone symbols in cpu-lib's posdef.o, both compilers.
2. Re-skinned driver loops (parallel_for bodies): no new instructions inside the per-voxel loop; anything added is explained or eliminated before merge. Note one expected prologue-side improvement: _any's heap std::vector construction per entry disappears — that is outside the loop and is the point.
3. Oracle: test_posdef 5092 checks (clang make test baseline, 2026-08-04), identical counts clang++ AND g++, true make clean between; whole suite green, unchanged counts; asan/ubsan on touched paths.
4. g++ nuance (Phase A finding): whole-TU inlining jitter in untouched neighboring symbols under g++ is acceptable; the g++ bar is kernels + driver loops + oracles.

Judgment call to document in the PR

Whether _matvec's if constexpr (C > 0) static-recast arms keep nchannel folded from C (as today) — they should; the dynamic arm alone reads the carrier. Confirm the recast still folds to the same code (gate 1 covers the kernels; the recast itself is driver-side, gate 2).