test(reg): cover the diag_bending/diag_all corner cross-term bug

[balbasty]

Regression test for the defect fixed in fastfields-kernels#81 (issue fastfields-kernels#48). Test-only: +230 lines across the two test drivers, no production code touched.

The oracle — no reference implementation needed

The boundary-corrected diagonal expanded each corner weight as (fx0*fy0 + fx1*fy0 + fx1*fy0 + fx1*fy1), double-counting fx1*fy0 and dropping fx0*fy1.

On a square/cubic domain with the same boundary condition and voxel size on every axis, relabelling two spatial axes maps the operator onto itself, so its diagonal must be invariant under that relabelling:

case	invariant
field, 2D and 3D	diag(x,y,c) == diag(y,x,c)
flow, bending-only (shears == div == 0)	diag(x,y,c) == diag(y,x,c) — channels uncoupled, isotropic voxel size
flow, diag_all	diag(x,y,c) == diag(y,x,1-c) — the Lamé terms couple the channels, so the axis swap carries a channel swap; shears == div keeps the Lamé part symmetric under that simultaneous relabelling

The buggy corner sum is not symmetric under the fx <-> fy relabelling wherever the two axes' one-sided boundary signs differ. It cancels exactly where they agree (fx0==fx1 and fy0==fy1 make both forms 4*fx0*fy0) — which is precisely why the pre-existing interior-only diagonal checks never caught it.

What this covers beyond the minimum

• 3D as well as 2D. The 3D diagonal carries three independent corner cross-terms (w110/w101/w011) rather than one; the xy and yz swaps exercise two directly and the third by composition. 9 of the 12 fixed terms live in 3D, so 2D-only coverage would leave most of the fix untested.
• Whole-domain sweep rather than a single row/column.
• Three boundary conditions — Zero, DCT2, DST2. DCT2 is a deliberate control: it does not flip signs, so it passes with or without the fix.

Verification — it demonstrably bites

Same tests, same build flags, same binaries; the only thing changed between the two runs is the kernels headers:

kernels	test_reg_field	test_reg_flow
pre-fix (buggy corner term)	19250 checks, 328 failures → FAILED (exit 1)	16347 checks, 1696 failures → FAILED (exit 1)
1df9fd3 (the fix)	19250 checks, 0 failures → PASSED	16347 checks, 0 failures → PASSED

Check counts are identical in both directions, so the only difference is pass/fail. Every one of the 2024 failures is in the new checks — no pre-existing test changes value:

 68 field2d_diag_bending.axis_symmetry
130 field3d_diag_bending.axis_symmetry_xy
130 field3d_diag_bending.axis_symmetry_yz
68 flow2d_diag_bending.axis_symmetry
68 flow2d_diag_all.axis_symmetry
390 flow3d_diag_bending.axis_symmetry_xy 390 flow3d_diag_bending.axis_symmetry_yz
390 flow3d_diag_all.axis_symmetry_xy 390 flow3d_diag_all.axis_symmetry_yz

Discrepancies are large and unambiguous (e.g. got 17 expected 21, got 32.3 expected 36.3) against a 1e-5 tolerance — not a marginal-tolerance test.

Ordering

This depends on the pin chain already reaching the fix, which it now does on main:

cpu-lib bdbe80d -> cpu-impl 5e2c78e -> kernels 1df9fd3

(kernels#81 → cpu-impl#72 → cpu-lib#88, all merged.)

Provenance

An equivalent 2D-only test exists on the teeny branch in 8afcab4. fastfields-cpu-lib#53 was an attempt to port it to main, but it was filed from the claude-fastfields-to-teeny workstream, whose PRs must always target teeny — so it was mis-filed, not wrong. Its oracle is sound and was useful prior art; credit to it. This PR lands equivalent (and broader — 3D, whole-domain, multi-bound) coverage on main properly, re-derived and re-verified from scratch.

🤖 Generated with Claude Code

https://claude.ai/code/session_016AjQcY78NgbagPSbPJRr6Z

---

Generated by Claude Code

[github-actions]

Submodule staleness (non-blocking -- fastfields-lib#15)

submodule	pinned commit	tracks	status	behind by
impl	5e2c78e	fastfields/fastfields-cpu-impl@main	up to date	0