(fix): ND mixed-partial BC consistency — restore Clairaut symmetry by mgyoo86 · Pull Request #111 · ProjectTorreyPines/FastInterpolations.jl

mgyoo86 · 2026-04-07T20:38:23Z

Summary

Mathematical fix: ND PreCompute() now applies the user bc uniformly to every partial (pure and mixed), restoring ∂²f/∂x∂y == ∂²f/∂y∂x (Clairaut's identity) and making PreCompute() ↔ OnTheFly() agree to ULP for every BC.
Bonus: explicit coeffs kwarg is now honored on the GridIdx auto-promotion paths (scalar interp and batch interp!).

Background

_get_effective_bc (cubic) and _get_effective_bc_quadratic substituted CubicFit() / Right(QuadraticFit()) for the user BC when forming mixed partials (p_src > 1). This produced an axis-asymmetric tensor product:

Cubic + non-default BC: PreCompute vs OnTheFly drifted by ~1e-10
Quadratic + non-default BC: ~1e-5 drift, and Hessian off-diagonals violated symmetry by the same amount

The substitution was deliberate in the original implementation (a hidden BC override) but mathematically wrong: it broke the equivalence

Σ_{k,l} φ_k'(x_i) ψ_l'(y_j) f[k,l]   ==   PreCompute mixed partial[i,j]

between the OnTheFly composition formula and the PreCompute stored value. Returning the user BC for every partial restores the equivalence.

A short-grid defensive fallback (length(grid) < 4 cubic, < 3 quadratic) remains in place. It now emits a one-shot @warn maxlog=1 so users notice the substitution instead of silently losing their BC.

Behavior change

For non-default BC + non-trivial data (e.g. bc=ZeroCurvBC() on data whose d²f/dy² at the boundary is non-zero), PreCompute() results change by the bug magnitudes above. Code paths that pinned to the buggy numerics will need to regenerate baselines. Default BCs (Left(QuadraticFit()), CubicFit()) and OnTheFly() are unchanged.

# Now bit-equivalent for every BC
v_pre = cubic_interp((x, y), data, q; bc=ZeroCurvBC(), coeffs=PreCompute())
v_otf = cubic_interp((x, y), data, q; bc=ZeroCurvBC(), coeffs=OnTheFly())
@assert v_pre == v_otf

# Axis swap is bit-equivalent
v_xy = cubic_interp((x, y), data,            (qx, qy); bc=ZeroCurvBC())
v_yx = cubic_interp((y, x), permutedims(data), (qy, qx); bc=ZeroCurvBC())
@assert v_xy ≈ v_yx atol=10*eps(Float64)

GridIdx coeffs fix (bonus)

Two related bugs in the GridIdx + coeffs interaction shipped with #110:

Scalar interp((x, y), data, (qx, GridIdx(k)); method=(CubicInterp(), PchipInterp()), coeffs=PreCompute()) rejected the call even though the GridIdx auto-promotion would have replaced PchipInterp with NoInterp, leaving a 1-D cubic problem that PreCompute supports. Fix: promote first, validate second.
Batch interp! delegating to _interp_batch_with_grididx! did not forward coeffs, so explicit strategies were silently dropped on the GridIdx batch path. Fix: forward the kwarg through both delegation sites.

The ND PreCompute build helpers `_get_effective_bc` (cubic) and `_get_effective_bc_quadratic` previously substituted `CubicFit()` / `Right(QuadraticFit())` for the user BC when building mixed partials (`p_src > 1`). This produced an axis-asymmetric tensor product and a numerical drift vs. the OnTheFly composition path (~1e-10 cubic, ~1e-5 quadratic for non-default BCs). PR #110 documented the discrepancy and relaxed four autodiff test tolerances; this commit removes the substitution at the root. Both helpers now return the user BC for every partial. By linearity and C^1 continuity of the 1D Hermite build, this makes the stored mixed partial exactly Σ_{k,l} φ_k'(x_i) ψ_l'(y_j) f[k,l], which is OnTheFly's composition formula, so PreCompute and OnTheFly become bit-equivalent (modulo a few ULPs of FP reordering noise) for every user BC. The short-grid defensive fallback (cubic: < 4 points, quadratic: < 3 points) is preserved but now emits an informative one-shot `@warn maxlog=1` via a `@noinline` helper before substituting the default. Side effects: - The cubic ND adjoint in `cubic_nd_adjoint.jl` retains its `caches`/`mixed_caches` dual-cache plumbing. After this fix the two are structurally equivalent for the common case (non-periodic, length >= 4); the redundancy is harmless and a follow-up PR can collapse them. An inline comment marks the opportunity. - The quadratic ND oneshot docstring previously carried a `!!! note "Strategy discrepancy"` explaining the ~1e-6 drift. That note is removed and replaced with a plain statement that the two strategies are bit-equivalent, with a pointer to `claudedocs/TODO/00_HIGHEST_PRIORITY_mixed_partial_bc_fix.md` for historical context. PeriodicBC is cubic-only in this codebase, so the quadratic helper does not need a Rule-2-equivalent propagation check.

New dedicated test file `test_nd_mixed_partial_bc_consistency.jl` pins the mathematical invariants that the BC fix in the preceding commit restores. Authored as the RED phase of a TDD cycle: on the pre-fix commit the math-invariant groups fail by the bug magnitudes documented in the design doc (~1e-10 cubic, ~1e-5 quadratic); after the fix they pass to `atol = 50*eps(Float64)` (~1.1e-14), which is generous enough to absorb tridiagonal / recurrence FP reordering but orders of magnitude tighter than any bug signature. Five test groups: A. PreCompute ↔ OnTheFly bit-equivalence across BCs (ZeroCurvBC, ZeroSlopeBC, CubicFit, MinCurvFit, Right(QuadraticFit)) and data functions (sin*cos, sin*y^3, sin*(y-π)) in 2D and 3D for both cubic and quadratic. B. Clairaut / axis-swap symmetry: building on `(xs, ys)` with `data` vs `(ys, xs)` with `permutedims(data)` and querying at swapped coordinates must give the same value. This is the strongest regression guard: the pre-fix PreCompute violated this by up to ~1e-5 for quadratic ZeroSlopeBC and ~1e-9 for cubic. C. Hessian off-diagonal symmetry (H[1,2] ≈ H[2,1]) for PreCompute interpolants with non-default BCs in both cubic and quadratic. Note: this assertion happens to pass on the buggy code because a single build is internally symmetric; we keep it as a forward regression guard. D. Cubic periodic-on-one-axis propagation regression-pin. Rule 2 in `_get_effective_bc` already handles this; the test asserts it continues to work after the fix. (Quadratic does not support PeriodicBC in this codebase.) E. Short-grid fallback warnings. Tests the helpers directly via `FastInterpolations._get_effective_bc` / `_get_effective_bc_quadratic` on very short grids (cubic: 3 points, quadratic: 2 points) with non-PolyFit user BCs. Asserts the `@warn ... maxlog=1` fires and the fallback BC is returned (`ZeroCurvBC()` / `MinCurvFit()`). Uses `@test_logs` for warning capture. Registered in `test/runtests.jl` next to `test_nd_oneshot_onthefly.jl`.

…d check Downstream verification that the mixed-partial BC consistency fix works end-to-end through the autodiff pipeline. PR #110 temporarily relaxed four assertions in the ND quadratic autodiff tests (two in `test_autodiff_Zygote.jl`, two in `test_autodiff_Enzyme.jl`) because Zygote/Enzyme trace the interpolant constructor (`PreCompute`) while the cross-validation seed comes from the one-shot API (now `OnTheFly` under `AutoCoeffs`), and the two paths disagreed by ~1e-6 for non-default quadratic BCs. With the BC consistency fix, PreCompute and OnTheFly produce bit-equivalent results, so the original `atol = 1.0e-10` is restored at all four sites and the TODO comment blocks are removed: - test/ext/test_autodiff_Zygote.jl - "Quadratic eval — L2 loss" : rtol=1e-4 → atol=1e-10 - "Quadratic gradient — ‖∇f‖² loss" : rtol=1e-3 → atol=1e-10 - test/ext/test_autodiff_Enzyme.jl - "Quadratic eval — L2 loss" : rtol=1e-4 → atol=1e-10 - "Quadratic gradient — ‖∇f‖² loss" : rtol=1e-3 → atol=1e-10 Also adds a new testset "AutoCoeffs: quadratic AD seed matches PreCompute exactly" in `test_nd_oneshot_onthefly.jl` that uses `==` (bit-exact equality, no tolerance) to compare OnTheFly and PreCompute for the exact call patterns autodiff uses — value query, ∂/∂x, ∂/∂y. This is a direct regression pin for the autodiff seed consistency and is stronger than the `atol = 50*eps` tolerance used in the new `test_nd_mixed_partial_bc_consistency.jl`. Verified locally: - test_autodiff_Zygote.jl passes (2m 29s) - test_autodiff_Enzyme.jl passes (68 pass, 2 broken pre-existing, 20m 49s) - test_nd_oneshot_onthefly.jl passes (1m 24s)

The full-suite run on the branch uncovered one hard failure and several pieces of documentation drift that encoded the pre-fix buggy behavior. All are fixed in this commit. **test/test_nd_coverage.jl** - `_get_effective_bc edge cases` (cubic, line 141): the test asserted `_get_effective_bc(ZeroCurvBC(), 2, grid_long) isa CubicFit` which was a characterization test on the now-removed substitution. Updated to assert `isa ZeroCurvBC` (the user BC is returned). - Cubic short-grid edge case (line 138): the fallback branch now emits an informative `@warn maxlog=1`. Wrapped the call in `@test_logs (:warn, r"Cubic ND mixed-partial build")` to assert the warning and suppress it from test output. - `_get_effective_bc_quadratic edge cases` (line 352): symmetric update — the quadratic short-grid branch also now emits `@warn maxlog=1`. Wrapped the call in `@test_logs (:warn, r"Quadratic ND mixed-partial build")`. **test/test_nd_oneshot_onthefly.jl** - "Quadratic OnTheFly with all supported BCs" (line 455): the long NOTE describing the ~1e-6 divergence as expected behavior was rewritten to describe the post-fix reality (PreCompute ≡ OnTheFly bit-equivalent for every user BC). The assertion tolerance is tightened from `rtol = 1e-5` to `atol = 50 * eps(Float64)` (~1.1e-14), matching the new regression suite. - "Quadratic BC-exact data" (line 479): the explanatory comment was rewritten as a historical note. The test is retained as a coarse smoke check; bit-identity now holds for arbitrary smooth data, not only BC-exact data, so the original motivation no longer applies. Verified locally: - test_nd_coverage.jl passes (30s) - test_nd_oneshot_onthefly.jl passes (1m 19s)

Adds a new test group F to `test_nd_mixed_partial_bc_consistency.jl` that directly invokes `_get_effective_bc` and `_get_effective_bc_quadratic` with inputs hitting every distinct return statement in both helpers. Groups A–C cover the helpers indirectly through the full ND build pipeline, but a few branches (e.g., `get_polyfit_degree(bc) > 0` short-circuit; `PeriodicBC` Rule 2 early return) are not trivially reached that way. Group F exists so `src/cubic/nd/cubic_nd_build.jl` and `src/quadratic/nd/ quadratic_nd_build.jl` land at ≥ 95% line coverage for the patch. Also consolidates group E's two `@test_logs` calls into single `match_mode = :any` blocks (warning assertion and return-value assertion together) so the short-grid fallback emits exactly one captured log per helper, with no stray stderr output from a second call outside `@test_logs`. Branches covered by group F: - Cubic `_get_effective_bc`: - Rule 1 (p_src == 1) for three BC types - Rule 2 (periodic) for long and short grids - Rule 3 left branch (`get_polyfit_degree > 0`) for both lengths - Rule 3 right branch (`length >= 4`) for ZeroSlope/ZeroCurv - Quadratic `_get_effective_bc_quadratic`: - Rule 1 for Right(QuadraticFit), MinCurvFit, ZeroCurv - Rule 2 (length >= 3) for three BC types The short-grid fallback path for both helpers is still covered by group E's `@test_logs` blocks — those calls execute every line of both the helper body and the `@noinline` warning helper.

- Restructure `_get_effective_bc_quadratic` to use explicit `if/end` for the length-≥3 branch, mirroring cubic's `_get_effective_bc` control flow so Julia coverage attribution lands on every executable line. - Add direct short-grid invocations to group F (cubic + quadratic). The group E `@test_logs` macro swallows line counters for the wrapped helper body (a known Julia coverage attribution quirk); the unwrapped direct calls give ground-truth line attribution. `maxlog=1` keeps the output silent since group E already fired the warning. Patch line coverage on this branch: 77/77 = 100.0%.

Source: - quadratic_nd_oneshot.jl: docstring lied about AutoCoeffs routing for scalar quadratic queries — said "OnTheFly" but the implementation unconditionally routes AutoCoeffs to PreCompute (intentional, for bit-exact AD seed agreement with the interpolant constructor). Updated the docstring to reflect actual behavior and explain why cubic differs. Also updated the design-doc reference to its archived location. Tests: - Move testset D (cubic periodic propagation) to its declared position between C and E, matching the lettered header comment. - Add a second 3D axis-swap permutation in group B (axes 1↔2 in addition to the existing 1↔3) for both cubic and quadratic. - Add a `!iszero` Hessian-diagonal sanity assertion to group C so a hypothetical bug zeroing the entire matrix would not silently pass. - Clarify the explanatory comment in group F: the second short-grid call is silent because there is no `@test_logs` wrapper, not because `maxlog=1` is exhausted (Test.jl bypasses the maxlog counter). All targeted tests still green: - test_nd_mixed_partial_bc_consistency.jl - test_nd_oneshot_onthefly.jl

…ion path Two related bugs in the GridIdx + coeffs interaction shipped with PR #110: 1. Scalar `interp` validated `coeffs` against the *un-promoted* method tuple, so `interp((x, y), data, (qx, GridIdx(k)); method=(CubicInterp(), PchipInterp()), coeffs=PreCompute())` rejected the call even though the GridIdx auto-promotion would have replaced PchipInterp with NoInterp, leaving a 1-D cubic problem that PreCompute fully supports. Fix: run `_promote_grididx_to_nointerp` BEFORE `_validate_nd_coeffs` so the validation sees the methods that actually drive dispatch. 2. Batch `interp!` delegating to `_interp_batch_with_grididx!` did not forward the `coeffs` kwarg, so explicit `coeffs=PreCompute()` / `coeffs=OnTheFly()` were silently dropped on the GridIdx batch path and the reduced sub-problem ran with the default AutoCoeffs fallback. Fix: add a `coeffs` kwarg to `_interp_batch_with_grididx!` and forward it at both delegation sites (early-return for fully-expanded queries and the main reduced-problem `interp!` call). Tests cover: - Scalar: GridIdx-on-Pchip + PreCompute now succeeds and matches the manually-sliced 1-D cubic call. The non-EvalValue deriv path (which disables promotion) still correctly rejects. - Batch: NoInterp axis is GridIdx-sliced → reduced 1-D Cubic problem accepts both PreCompute and OnTheFly. Differentiator: non-NoInterp GridIdx (Pchip remains in the method tuple) now correctly REJECTS `coeffs=PreCompute()` instead of silently dropping it. Both fixes verified in TDD red→green order. Touched suites all green: test_nointerp.jl, test_nd_mixed_partial_bc_consistency.jl, test_nd_oneshot_onthefly.jl, test_hetero_nd.jl, test_hetero_oneshot.jl, test_hetero_precomputed.jl.

github-actions · 2026-04-07T20:44:57Z

FastInterpolations.jl Benchmarks

All benchmarks (42 total, click to expand)

Benchmark	Current: `3774550`	Previous	Imm. Ratio	Grad. Ratio
`10_nd_construct/bicubic_2d`	`37710.0` ns	`38111.0` ns	`0.989`	`1.017`
`10_nd_construct/bilinear_2d`	`550.0` ns	`627.8` ns	`0.876`	`0.872`
`10_nd_construct/tricubic_3d`	`354462.0` ns	`360314.0` ns	`0.984`	`1.018`
`10_nd_construct/trilinear_3d`	`1579.7` ns	`1708.4` ns	`0.925`	`0.913`
`11_nd_eval/bicubic_2d_batch`	`1576.0` ns	`1582.0` ns	`0.996`	`0.975`
`11_nd_eval/bicubic_2d_scalar`	`15.6` ns	`15.6` ns	`0.999`	`0.996`
`11_nd_eval/bilinear_2d_scalar`	`11.3` ns	`11.2` ns	`1.008`	`1.023`
`11_nd_eval/tricubic_3d_batch`	`3308.2` ns	`3322.2` ns	`0.996`	`0.993`
`11_nd_eval/tricubic_3d_scalar`	`32.8` ns	`32.8` ns	`1.0`	`0.976`
`11_nd_eval/trilinear_3d_scalar`	`18.6` ns	`18.5` ns	`1.005`	`1.024`
`12_cubic_eval_gridquery/range_random`	`4231.9` ns	`4231.3` ns	`1.0`	`0.995`
`12_cubic_eval_gridquery/range_sorted`	`4215.5` ns	`4218.9` ns	`0.999`	`0.98`
`12_cubic_eval_gridquery/vec_random`	`9385.7` ns	`9476.7` ns	`0.99`	`0.997`
`12_cubic_eval_gridquery/vec_sorted`	`3212.0` ns	`3218.4` ns	`0.998`	`1.0`
`1_cubic_oneshot/q00001`	`448.2` ns	`443.8` ns	`1.01`	`0.979`
`1_cubic_oneshot/q10000`	`61666.1` ns	`61685.6` ns	`1.0`	`0.996`
`2_cubic_construct/g0100`	`1315.1` ns	`1326.1` ns	`0.992`	`0.984`
`2_cubic_construct/g1000`	`12570.4` ns	`12596.6` ns	`0.998`	`0.987`
`3_cubic_eval/q00001`	`17.7` ns	`17.8` ns	`0.994`	`0.944`
`3_cubic_eval/q00100`	`441.4` ns	`442.4` ns	`0.998`	`0.979`
`3_cubic_eval/q10000`	`42633.6` ns	`42710.0` ns	`0.998`	`0.995`
`4_linear_oneshot/q00001`	`22.3` ns	`24.8` ns	`0.902`	`0.997`
`4_linear_oneshot/q10000`	`18621.7` ns	`18684.0` ns	`0.997`	`1.005`
`5_linear_construct/g0100`	`34.1` ns	`35.1` ns	`0.971`	`0.757`
`5_linear_construct/g1000`	`226.2` ns	`266.6` ns	`0.849`	`0.873`
`6_linear_eval/q00001`	`10.1` ns	`9.8` ns	`1.03`	`1.008`
`6_linear_eval/q00100`	`199.0` ns	`198.2` ns	`1.004`	`0.99`
`6_linear_eval/q10000`	`18545.6` ns	`18488.6` ns	`1.003`	`0.995`
`7_cubic_range/scalar_query`	`8.0` ns	`8.0` ns	`1.0`	`1.047`
`7_cubic_vec/scalar_query`	`10.4` ns	`11.3` ns	`0.92`	`0.975`
`8_cubic_multi/construct_s001_q100`	`551.8` ns	`554.2` ns	`0.996`	`0.968`
`8_cubic_multi/construct_s010_q100`	`4281.6` ns	`4318.7` ns	`0.991`	`0.966`
`8_cubic_multi/construct_s100_q100`	`39509.7` ns	`39937.8` ns	`0.989`	`0.975`
`8_cubic_multi/eval_s001_q100`	`724.2` ns	`722.4` ns	`1.002`	`0.683`
`8_cubic_multi/eval_s010_q100`	`1711.0` ns	`1702.8` ns	`1.005`	`0.835`
`8_cubic_multi/eval_s010_q100_scalar_loop`	`2284.5` ns	`2303.1` ns	`0.992`	`0.891`
`8_cubic_multi/eval_s100_q100`	`11310.1` ns	`11650.8` ns	`0.971`	`0.952`
`8_cubic_multi/eval_s100_q100_scalar_loop`	`3372.3` ns	`3353.3` ns	`1.006`	`0.944`
`9_nd_oneshot/bicubic_2d`	`37043.2` ns	`37757.7` ns	`0.981`	`0.997`
`9_nd_oneshot/bilinear_2d`	`961.2` ns	`973.2` ns	`0.988`	`0.962`
`9_nd_oneshot/tricubic_3d`	`358145.6` ns	`365329.3` ns	`0.98`	`0.989`
`9_nd_oneshot/trilinear_3d`	`1599.0` ns	`1603.0` ns	`0.998`	`0.99`

✅ 1 benchmark(s) were flagged but verified as CI noise after 10 re-run(s)

This comment was automatically generated by Benchmark workflow.

Copilot

Pull request overview

Fixes ND precomputed mixed-partial construction to apply the user-specified boundary conditions consistently for both pure and mixed partials, restoring axis symmetry (Clairaut) and aligning PreCompute() with OnTheFly() behavior. Also fixes GridIdx auto-promotion paths to correctly honor an explicit coeffs strategy.

Changes:

Update cubic/quadratic ND mixed-partial BC selection to use the user BC for mixed partials (with a warned short-grid fallback).
Ensure coeffs is respected when GridIdx triggers method auto-promotion and in the GridIdx batch (interp!) delegation path.
Add/adjust regression tests for PreCompute↔OnTheFly consistency, Hessian symmetry, and tightened AD tolerances.

Reviewed changes

Copilot reviewed 13 out of 13 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
test/test_nointerp.jl	Adds tests ensuring `coeffs=PreCompute()` works correctly after `GridIdx` auto-promotion and is forwarded through batch GridIdx paths.
test/test_nd_oneshot_onthefly.jl	Adds quadratic AutoCoeffs/PreCompute exact-equality pins and tightens quadratic OTF vs PreCompute expectations across BCs.
test/test_nd_mixed_partial_bc_consistency.jl	New regression suite for PreCompute↔OnTheFly agreement, axis-swap symmetry, Hessian symmetry, periodic propagation, and short-grid fallback warnings.
test/test_nd_coverage.jl	Updates BC edge-case expectations and asserts the new short-grid fallback warnings.
test/runtests.jl	Includes the new mixed-partial consistency regression file in the main test run.
test/ext/test_autodiff_Zygote.jl	Tightens tolerances now that quadratic OTF/PreCompute mismatch is addressed.
test/ext/test_autodiff_Enzyme.jl	Same tolerance tightening for Enzyme-based AD tests.
src/quadratic/nd/quadratic_nd_oneshot.jl	Changes quadratic `AutoCoeffs()` resolution (scalar oneshot) and updates docs to reflect new strategy behavior.
src/quadratic/nd/quadratic_nd_build.jl	Uses user BC for quadratic mixed partials and adds a one-shot warning on short-grid fallback to `MinCurvFit()`.
src/hetero/hetero_oneshot.jl	Reorders GridIdx promotion vs coeff strategy validation; forwards `coeffs` into GridIdx batch helper.
src/hetero/hetero_nointerp.jl	Extends `_interp_batch_with_grididx!` to accept/forward `coeffs` through its delegations.
src/cubic/nd/cubic_nd_build.jl	Uses user BC for cubic mixed partials (preserving periodic propagation) and adds a one-shot warning on short-grid fallback to `ZeroCurvBC()`.
src/cubic/nd/cubic_nd_adjoint.jl	Updates commentary to reflect the mixed-partial BC behavior change (no functional change).

Comments suppressed due to low confidence (1)

src/quadratic/nd/quadratic_nd_oneshot.jl:166

This change makes AutoCoeffs() resolve to PreCompute() for scalar quadratic_interp (via coeffs isa AutoCoeffs ? PreCompute() : coeffs), which is a user-visible behavior change vs the prior “scalar oneshot → OnTheFly” policy from #110. If intentional, consider calling it out explicitly in the PR description/changelog since it affects performance expectations and AD behavior for quadratic oneshots.

    # Keep AutoCoeffs on the specialized PreCompute path so scalar one-shot
    # calls match the interpolant constructor and AD rules.
    coeffs_resolved = coeffs isa AutoCoeffs ? PreCompute() : coeffs
    if coeffs_resolved isa OnTheFly
        sample = @inbounds first(data)
        methods = map(bc_i -> QuadraticInterp(_to_quadratic_bc(bc_i, sample)), bcs)
        return _interp_nd_oneshot_onthefly(grids_typed, data, query, methods, extraps_val, searches, ops, hint)::Tr
    end

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test/test_nd_oneshot_onthefly.jl

test/test_nd_mixed_partial_bc_consistency.jl

src/quadratic/nd/quadratic_nd_build.jl

Copilot review on PR #111 flagged that docstrings/comments described PreCompute ↔ OnTheFly as "bit-equivalent" / "bit-identical" while the actual assertions use `isapprox(...; atol=50*eps(Float64))`. The wording overstates the guarantee — the residual difference is FP reordering noise in the tridiagonal/recurrence solver, ~50 ULPs at most, not zero. Reworded all four sites: - src/quadratic/nd/quadratic_nd_build.jl:233 — "bit-equivalence" → "numerical equivalence within FP noise" - src/cubic/nd/cubic_nd_build.jl:358 — short-grid warning text now says "no longer match the OnTheFly composition" instead of "not bit-equivalent" - test/test_nd_mixed_partial_bc_consistency.jl header + group-A label — "bit-equivalence" → "agreement to ~ULP / machine epsilon" - test/test_nd_oneshot_onthefly.jl:457 — "bit-equivalent results" → "agree to ~ULP tolerance" The single legitimate "bit-identical" usage at test_nd_oneshot_onthefly.jl lines 469-481 is preserved because that testset uses `==` (true bit equality) on data with `d²f/dy² = 0` everywhere, where both paths agree exactly. The "**not** bit-identical" wording in quadratic_nd_oneshot.jl:131 is also preserved — it correctly negates the property in the context of explaining why quadratic AutoCoeffs forces PreCompute. No code logic changed; comment-only commit.

codecov · 2026-04-07T21:05:19Z

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.56%. Comparing base (658afac) to head (3774550).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #111   +/-   ##
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  Coverage   96.56%   96.56%           
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  Files         136      136           
  Lines       11083    11090    +7     
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+ Hits        10702    10709    +7     
  Misses        381      381

Files with missing lines	Coverage Δ
src/cubic/nd/cubic_nd_adjoint.jl	`100.00% <ø> (ø)`
src/cubic/nd/cubic_nd_build.jl	`96.40% <100.00%> (+0.04%)`	⬆️
src/hetero/hetero_nointerp.jl	`94.75% <ø> (ø)`
src/hetero/hetero_oneshot.jl	`93.98% <100.00%> (ø)`
src/quadratic/nd/quadratic_nd_build.jl	`98.91% <100.00%> (+0.06%)`	⬆️
src/quadratic/nd/quadratic_nd_oneshot.jl	`98.55% <100.00%> (ø)`

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* (feat): ND forwarders for pchip/cardinal/akima — unified `interp` entry Add ND-shape methods to `pchip_interp`/`cardinal_interp`/`akima_interp` (and their in-place `!` variants) that forward to `interp(grids, data; method=...)`. Covers all four ND call shapes: interpolant construction, scalar one-shot, batch one-shot, and in-place batch. Lets users keep the per-method entry point they already use in 1D instead of rewriting to `interp(...; method=PchipInterp())` by hand. `cardinal_interp` forwarders thread `tension` into `CardinalInterp(tension)`. `CubicHermiteInterp` is intentionally not forwarded — user-supplied per-axis slope arrays need a separate ND design. * test: ND forwarder coverage for pchip/cardinal/akima Smoke tests for the new `pchip_interp`/`cardinal_interp`/`akima_interp` ND forwarders. Verifies ULP-exact equivalence with the corresponding `interp(grids, data; method = ...)` calls across all four ND call shapes (build, scalar oneshot, batch oneshot, in-place batch) for 2D and 3D fixtures. Coverage matrix: - Equivalence (`===` / `==`) vs direct `interp` for every call shape - `@inferred` type stability on the scalar oneshot path - Cardinal `tension` kwarg passthrough (default vs 0.5, plus cross-check against `CardinalInterp(0.5)`) - Grid flavors: all-Vector, all-range, range×Vector, Vector×range — forwarder must preserve concrete grid tuple type into `interp` * Runic formatting * docs: address Copilot review on PR #114 — fix doc/code drift Two doc-only fixes flagged by Copilot review: 1. `src/hetero/local_hermite_nd_forward.jl`: header said "all three ND call shapes" but enumerated four (off-by-one). 2. `test/test_local_hermite_nd_forward.jl`: header claimed `===` for all four call shapes, but batch/array paths use `==` (array identity is meaningless). Clarified that scalar paths use `===`, array paths `==`. No code behavior change.

mgyoo86 added 8 commits April 7, 2026 13:36

mgyoo86 requested a review from Copilot April 7, 2026 20:38

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mgyoo86 merged commit 2c6433c into master Apr 7, 2026
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mgyoo86 deleted the fix/mixed_partial_inconsistency branch April 7, 2026 21:50

mgyoo86 referenced this pull request Apr 8, 2026

chore: bump version to 0.4.8 and update benchmark results in README

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(fix): ND mixed-partial BC consistency — restore Clairaut symmetry#111

(fix): ND mixed-partial BC consistency — restore Clairaut symmetry#111
mgyoo86 merged 9 commits intomasterfrom
fix/mixed_partial_inconsistency

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mgyoo86 commented Apr 7, 2026

Summary

Background

Behavior change

GridIdx coeffs fix (bonus)

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FastInterpolations.jl Benchmarks

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