einsum: delegate nesting-preserving products to the expression layer; drop per-tile reference kernels

src/CMakeLists.txt

@@ -110,7 +110,6 @@ TiledArray/expressions/binary_expr.h
 TiledArray/expressions/blk_tsr_engine.h
 TiledArray/expressions/blk_tsr_expr.h
 TiledArray/expressions/cont_engine.h
-TiledArray/expressions/contraction_helpers.h
 TiledArray/expressions/expr.h
 TiledArray/expressions/expr_engine.h
 TiledArray/expressions/expr_trace.h

src/TiledArray/einsum/tiledarray.h

@@ -673,23 +673,38 @@ auto einsum(expressions::TsrExpr<ArrayA_> A, expressions::TsrExpr<ArrayB_> B,
     auto range_map =
         (RangeMap(a, A.array().trange()) | RangeMap(b, B.array().trange()));
 
-    // special Hadamard
+    // Fused broadcast: one operand is ENTIRELY fused (h == its index set) and
+    // there is no contraction -- C(h,e) = A * B, a per-fused-block scale. The
+    // general-product expression engine evaluates this natively when the
+    // fully-fused operand LEADS (it folds to a rank-0 left tile, restored by a
+    // synthetic unit left-external mode; see ContEngine::
+    // synthetic_unit_left_external). Order the fully-fused operand first and
+    // delegate -- no physical replication needed.
     if (h.size() == a.size() || h.size() == b.size()) {
       TA_ASSERT(!i && e);
-      bool const small_a = h.size() == a.size();
-      auto const delta_trng = make_trange(range_map, e);
+      _ein_call.branch = "fused-broadcast-expression";
+      const bool a_leads = (h.size() == a.size());  // A entirely fused?
+      // the engine produces the result in its canonical inner layout
+      // (inner fused, then left-then-right inner externals, in the order the
+      // operands are handed to it) and rejects a non-identity inner result
+      // permutation; evaluate canonically, then apply the inner permutation
+      // (cf. the generalized-inner-perm-recurse path below). The canonical
+      // inner-external order tracks the operand order, so mirror the swap.
+      std::string canon_inner;
+      if constexpr (IsArrayToT<ArrayC>) {
+        auto inner_e = a_leads ? (inner.A ^ inner.B) : (inner.B ^ inner.A);
+        canon_inner = ";" + (std::string)(inner.h + inner_e);
+      }
+      std::string canon_layout = std::string(c) + canon_inner;
+      ArrayC C0;
+      if (a_leads)  // A fully fused -> already leads
+        C0(canon_layout) = A * B;
+      else  // B fully fused -> put it first (multiplication commutes)
+        C0(canon_layout) = B * A;
       std::string target_layout = std::string(c) + inner.c;
+      if (target_layout == canon_layout) return C0;
       ArrayC C;
-      if (small_a) {
-        auto temp = replicate_array(A.array(), delta_trng);
-        std::string temp_layout = std::string(e) + "," + A.annotation();
-        C(target_layout) = temp(temp_layout) * B;
-      } else {
-        auto temp = replicate_array(B.array(), delta_trng);
-        std::string temp_layout = std::string(e) + "," + B.annotation();
-        C(target_layout) = A * temp(temp_layout);
-      }
-
+      C(target_layout) = C0(canon_layout);  // inner-permute to requested layout
       return C;
     }
 
@@ -791,7 +806,28 @@ auto einsum(expressions::TsrExpr<ArrayA_> A, expressions::TsrExpr<ArrayB_> B,
       }
     }
 
-    if (!e) {  // hadamard reduction
+    if (!e) {  // no external outer index (fused + contracted): a nesting-
+               // preserving reduction. By default the expression layer handles
+               // it natively (synthetic unit left-external mode, see
+               // ContEngine::synthetic_unit_left_external); the legacy local
+               // kernel below is retained only as the opt-in legacy
+               // cross-check oracle (cf. the generalized-subworld path).
+      if (!detail::einsum_legacy_subworld()) {
+        _ein_call.branch = "no-external-expression";
+        // evaluate in the engine's canonical inner layout, then apply any
+        // inner result permutation (cf. the broadcast / inner-perm-recurse)
+        std::string canon_inner;
+        if constexpr (IsArrayToT<ArrayC>)
+          canon_inner = ";" + (std::string)(inner.h + inner.e);
+        std::string canon_layout = std::string(c) + canon_inner;
+        ArrayC C0;
+        C0(canon_layout) = A * B;
+        std::string target_layout = std::string(c) + inner.c;
+        if (target_layout == canon_layout) return C0;
+        ArrayC C;
+        C(target_layout) = C0(canon_layout);
+        return C;
+      }
 
       _ein_call.branch = "hadamard-reduction-local";
       const auto _ein_he_t0 = _ein_call.active ? now() : time_point{};

src/TiledArray/expressions/cont_engine.h

@@ -677,18 +677,20 @@ class ContEngine : public BinaryEngine<Derived> {
     this->init_perm(target_indices);
     general_repermute_ = (outer(target_indices) != outer(indices_));
 
-    // A product with NO external (free) outer indices (every outer index
-    // fused or contracted, e.g. C("i,j;a,b") = A("x,i,j;a") * B("x,i,j;b"))
-    // folds to a GEMM with no free modes, i.e. rank-0 tensors, which the
-    // tile kernels do not support. Evaluate it with a SYNTHETIC UNIT
-    // left-external mode instead: the folded product becomes
-    // (1,K) x (K) -> (1), the exact shape of the (supported) one-sided
-    // neB == 0 case. The unit mode lives only in the tile op's GemmHelper;
-    // tranges, shapes and tiles carry the true (external-free) ranks, and
-    // BatchedContractReduce / SparseShape::gemm_batched detect the
-    // synthetic mode from the one-rank mismatch and pad their folded views
+    // Some degenerate folded shapes would carry a rank-0 tensor, which the
+    // tile kernels do not support (see synthetic_unit_left_external()):
+    //  - a NO-EXTERNAL product (every outer index fused or contracted, e.g.
+    //    C("i,j;a,b") = A("x,i,j;a") * B("x,i,j;b")) folds to a rank-0 RESULT;
+    //  - a FUSED BROADCAST (the left operand is entirely fused, no contraction,
+    //    e.g. C("b,k") = A("b") * B("b,k")) folds to a rank-0 LEFT operand.
+    // Evaluate both with a SYNTHETIC UNIT left-external mode: the folded
+    // product becomes (1,K) x (K,N) -> (1,N), a supported shape (the no-
+    // external case has N == 1, the broadcast has K == 1). The unit mode lives
+    // only in the tile op's GemmHelper; tranges, shapes and tiles carry the
+    // true ranks, and BatchedContractReduce / SparseShape::gemm_batched detect
+    // the synthetic mode from the one-rank mismatch and pad their folded views
     // with a unit extent.
-    const unsigned int u = (outer_size(indices_) == nh) ? 1u : 0u;
+    const unsigned int u = synthetic_unit_left_external();
 
     // the tile op operates on the folded (fused-mode-free) shapes; the
     // synthetic unit mode leads the folded left operand, so it is NoTrans
@@ -749,17 +751,34 @@ class ContEngine : public BinaryEngine<Derived> {
     }
   }
 
+  /// \return 1 if the folded general product needs a SYNTHETIC unit
+  /// left-external mode, else 0. The folded (fused-mode-free) GEMM cannot host
+  /// a rank-0 tensor, which arises in two degenerate cases:
+  ///  - rank-0 RESULT: every outer index is fused or contracted (no external),
+  ///    i.e. outer_size(indices_) == n_fused_modes_;
+  ///  - rank-0 LEFT operand: the left argument is entirely fused with no
+  ///    contraction (a fused broadcast / per-fused-block scale), i.e.
+  ///    outer_size(left_indices_) == n_fused_modes_.
+  /// A unit left-external mode (carried only in the GemmHelper) restores a
+  /// supported (1,K) x (K,N) -> (1,N) shape in both cases.
+  unsigned int synthetic_unit_left_external() const {
+    return (outer_size(indices_) == n_fused_modes_ ||
+            outer_size(left_indices_) == n_fused_modes_)
+               ? 1u
+               : 0u;
+  }
+
   /// Tiled range factory function for a general product
 
   /// \return The result tiled range: the fused mode ranges followed by the
   /// left- and right-external mode ranges
   trange_type make_trange_general() const {
     const unsigned int nh = n_fused_modes_;
     const unsigned int nc = op_.gemm_helper().num_contract_ranks();
-    // the no-external case carries a synthetic unit left-external mode in
-    // the GemmHelper only (see init_struct_general); the actual tranges do
-    // not have it
-    const unsigned int u = (outer_size(indices_) == n_fused_modes_) ? 1u : 0u;
+    // degenerate folds carry a synthetic unit left-external mode in the
+    // GemmHelper only (see synthetic_unit_left_external()); the actual tranges
+    // do not have it
+    const unsigned int u = synthetic_unit_left_external();
     const unsigned int neA = op_.gemm_helper().left_rank() - nc - u;
     const unsigned int neB = op_.gemm_helper().right_rank() - nc;
 
@@ -812,10 +831,10 @@ class ContEngine : public BinaryEngine<Derived> {
                                  std::shared_ptr<const pmap_interface> pmap) {
     const unsigned int nh = n_fused_modes_;
     const unsigned int nc = op_.gemm_helper().num_contract_ranks();
-    // the no-external case carries a synthetic unit left-external mode in
-    // the GemmHelper only (see init_struct_general); the actual tranges do
-    // not have it
-    const unsigned int u = (outer_size(indices_) == nh) ? 1u : 0u;
+    // degenerate folds carry a synthetic unit left-external mode in the
+    // GemmHelper only (see synthetic_unit_left_external()); the actual tranges
+    // do not have it
+    const unsigned int u = synthetic_unit_left_external();
     const unsigned int neA = op_.gemm_helper().left_rank() - nc - u;
     const unsigned int neB = op_.gemm_helper().right_rank() - nc;