[jorgensd]

With sum_factorization=True, FFCx tabulates each tensor product element both as 1D factors and as a full table on the whole tensor product rule. Kernels only read the 1D factors; the full table is used only for its shape and its type (zeros, ones, piecewise, ...). Tabulating it costs O(Q^d N^2d) time and O(Q^d N^d) memory, which dominates code generation at high degree.

For a P=80 mass matrix on a quadrilateral, the full table is 6724 points × 6561 dofs = 353 MB, and Basix takes 13.6 s to build it, once for the trial and once for the test function. Code generation took 33 s, almost all of it in this tabulation and in scanning the table. With this change it takes 0.7 s, with a peak of 2 MB.

Changes

• For cell integrals without permutations or averages, when an element has tensor factors on a tensor product rule, build_optimized_tables no longer forms the full table:
  • analyse_tensor_product_table_type derives its type from the 1D factors.
  • Its values are a TensorProductTablePlaceholder, which has the table's shape but raises if its values are read. Tables that reach code generation are asserted to be formed.
  • Offset and stride come from get_component_element.
• The 1D factors are clamped like full tables (clamp_table_small_numbers). A table is "zeros" when every product of its factors clamps to zero, as the clamped full table would be.

Generated code

Kernels without sum factorisation are unchanged. Of the 66 sum-factorised kernels I compared (11 forms, quadrilateral and hexahedron, P = 1–3), 8 differ, only where clamping the factors now writes round-off such as -5.55e-17 as 0.0.

Tests

• test_tensor_product_table_type: the type derived from the factors matches analyse_table_type on the full table, for quadrilaterals and hexahedra, P = 1–3, several 1D rules including collocated GLL points (quadrature tables), and derivatives up to second order, including vanishing ones.
• test_tensor_product_table_type_clamped_to_zero: factors whose products all clamp to zero give a zero table, as the full table does.
• test_tensor_product_table_placeholder: reading the placeholder's values raises.

🤖 Generated with Claude Code

I have reviewed the contribution and stand by the implementation

[IgorBaratta]

LGTM.
One minor comment,sub_tbl is clamped before the tensor product is formed, which I don't think is equivalent to clamping the full table. With atol=1e-9, factors containing 1e-10 and 1e2 become 0 and 1e2 -> 0, whereas the full product would 1e-8.