[Beforerr]

Problem

Evaluating an all-Cardinal, non-periodic HeteroInterpolantND is much slower than its stencil requires. On a 64³ grid, a 3D evaluation takes about 76 ns for
SVector{3,Float64} data and 52 ns for Float64. A hand-written Catmull-Rom takes about 25 ns for SVector{3,Float64}.

Root cause

_collapse_dims runs a full 1D one-shot for each of the 21 fibers in 3D, repeating the search and setup, and acquires pool buffers at each level. A Cardinal fiber is also linear in its stencil values, with coefficients that depend only on the axis and query.

Fix

Add a more specific _collapse_dims method for tuples of two or more CardinalInterp{<:Any, NoBC} axes:

• Resolve the search and the four stencil weights once per axis, for the requested eval op.
• Fold the stencil values recursively as weighted sums, with no pool buffers.

Existing callers need no changes. That includes derivative ops and periodic axes that the wrap-aware path has already stripped to NoBC. PCHIP, Akima, global-solve methods and mixed tuples stay on the existing fiber path, though an all-Cardinal tail of a mixed tuple does use the new method.

Tuples of four or more axes go through a @noinline boundary to limit generated code size.

Extrapolation is not re-applied per fiber. The method relies on callers having already applied it to q_eval, and uses a two-sided clamped search so indices stay in range.

How verified

Benchmarks on an 64³ grid, 3D evaluation:

Data	Before	After
SVector{3,Float64}	76 ns	29 ns
Float64	52 ns	21 ns

Native code for the SVector call drops from about 18.8k to 1.1k instructions.

Results change by rounding only, because weighted sums replace the kernel's secant differences. For example, a constant field of 1.1 now evaluates with an error of about 2e-16 at one test point, where it was exact.

The new test/test_cardinal_cell_fold.jl compares against nested 1D cardinal_interp calls along whole fibers. It covers n = 2, 3, 4, 5, 8, uniform and non-uniform grids, tension, derivatives, SVector data, knots and extrapolated queries. It also checks that a NaN inside the fixed window but outside the end cell's stencil stays out of the result, and that evaluation doesn't allocate.

[github-actions]

FastInterpolations.jl Benchmarks

🚨 Regression baseline is a different CPU

	CPU
This PR run	`znver4
Master baseline (latest commit)	`znver3

The Previous / Imm. Ratio / Grad. Ratio columns compare against master history, but master's most recent commit was benchmarked on a different CPU — so a naive comparison is cross-CPU and unreliable. The ratios below use only same-znver4|4c history and are blank if master has none on this CPU yet.

All benchmarks (71 total, click to expand)

Benchmark	Current: 009ef6c	Previous	Imm. Ratio	Grad. Ratio
10_nd_construct/bicubic_2d	34011 ns	35262.0 ns	0.965	0.87
10_nd_construct/bilinear_2d	579.28 ns	691.0 ns	0.838	0.79
10_nd_construct/phs_2d	1051949.8 ns	1164076.4 ns	0.904	-
10_nd_construct/phs_3d	15605470.5 ns	18671391.9 ns	0.836	-
10_nd_construct/tricubic_3d	269366 ns	289847.0 ns	0.929	0.817
10_nd_construct/trilinear_3d	1559.74 ns	1955.9 ns	0.797	0.764
11_nd_eval/bicubic_2d_batch	1256.9 ns	1500.2 ns	0.838	0.815
11_nd_eval/bicubic_2d_scalar	15.12 ns	16.5 ns	0.915	0.851
11_nd_eval/bilinear_2d_scalar	7.31 ns	7.6 ns	0.961	0.948
11_nd_eval/phs_2d_batch	26664.1 ns	35060.6 ns	0.761	-
11_nd_eval/phs_2d_scalar	220.72 ns	291.4 ns	0.757	-
11_nd_eval/phs_3d_batch	157316.9 ns	206960.8 ns	0.76	-
11_nd_eval/phs_3d_scalar	1484.82 ns	2001.0 ns	0.742	-
11_nd_eval/tricubic_3d_batch	2557.8 ns	3268.8 ns	0.782	0.724
11_nd_eval/tricubic_3d_scalar	25.73 ns	36.6 ns	0.704	0.686
11_nd_eval/trilinear_3d_scalar	11.41 ns	12.1 ns	0.942	0.841
12_cubic_eval_gridquery/range_random	2422.06 ns	3002.0 ns	0.807	0.521
12_cubic_eval_gridquery/range_sorted	2416.24 ns	2993.0 ns	0.807	0.52
12_cubic_eval_gridquery/vec_random	7491.08 ns	9557.3 ns	0.784	0.749
12_cubic_eval_gridquery/vec_sorted	2022.66 ns	2538.5 ns	0.797	0.636
13_nd_oneshot_gridquery/bicubic_2d_rand_rand	53997.3 ns	62970.7 ns	0.857	0.835
13_nd_oneshot_gridquery/bicubic_2d_sort_rand	50815.5 ns	57671.9 ns	0.881	0.833
13_nd_oneshot_gridquery/bicubic_2d_sort_sort	49679.8 ns	55947.3 ns	0.888	0.841
13_nd_oneshot_gridquery/bilinear_2d_rand_rand	13950 ns	16910.3 ns	0.825	0.812
13_nd_oneshot_gridquery/bilinear_2d_sort_rand	8414.06 ns	9601.5 ns	0.876	0.89
13_nd_oneshot_gridquery/bilinear_2d_sort_sort	3891.24 ns	4748.6 ns	0.819	0.844
14_series_oneshot_batch/constant_inplace_vec_k8_q1000_rand	10690.1 ns	13677.2 ns	0.782	0.59
14_series_oneshot_batch/linear_inplace_vec_k8_q1000_rand	12517.8 ns	16030.6 ns	0.781	0.732
15_gridded_query/cubic_oneshot_2d_40x32	39366.3 ns	41303.9 ns	0.953	0.881
15_gridded_query/cubic_persistent_2d_40x32	6543.9 ns	7886.6 ns	0.83	0.805
15_gridded_query/linear_oneshot_2d_40x32	1253.28 ns	1558.5 ns	0.804	0.789
15_gridded_query/linear_oneshot_3d_12x10x8	1449.78 ns	1833.5 ns	0.791	0.719
15_gridded_query/linear_persistent_2d_40x32	1213.62 ns	1526.8 ns	0.795	0.78
15_gridded_query/linear_persistent_3d_12x10x8	1447.58 ns	1800.1 ns	0.804	0.741
16_phs/construct_g0100	30298.4 ns	37382.7 ns	0.81	-
16_phs/construct_g1000	30173.4 ns	37214.8 ns	0.811	-
16_phs/eval_q00001	77.41 ns	98.9 ns	0.782	-
16_phs/eval_q00100	8068.74 ns	10330.6 ns	0.781	-
16_phs/eval_q10000	807106.1 ns	1034718.9 ns	0.78	-
16_phs/oneshot_q00001	31040.54 ns	38354.5 ns	0.809	-
16_phs/oneshot_q10000	1274782.2 ns	1629214.3 ns	0.782	-
1_cubic_oneshot/q00001	414.82 ns	499.5 ns	0.83	0.776
1_cubic_oneshot/q10000	25343.1 ns	31012.7 ns	0.817	0.53
2_cubic_construct/g0100	1088.64 ns	1366.4 ns	0.797	0.729
2_cubic_construct/g1000	10364.6 ns	13238.5 ns	0.783	0.734
3_cubic_eval/q00001	6.91 ns	9.0 ns	0.767	0.289
3_cubic_eval/q00100	275.4 ns	314.9 ns	0.875	0.569
3_cubic_eval/q10000	24744.3 ns	30292.6 ns	0.817	0.526
4_linear_oneshot/q00001	22.63 ns	29.1 ns	0.777	0.789
4_linear_oneshot/q10000	16176.4 ns	19335.5 ns	0.837	0.829
5_linear_construct/g0100	27.24 ns	33.4 ns	0.814	0.718
5_linear_construct/g1000	216.03 ns	254.6 ns	0.849	0.791
6_linear_eval/q00001	6.1 ns	7.9 ns	0.771	0.599
6_linear_eval/q00100	186.88 ns	200.7 ns	0.931	0.939
6_linear_eval/q10000	15857.9 ns	19192.3 ns	0.826	0.822
7_cubic_range/scalar_query	4.6 ns	5.4 ns	0.852	0.494
7_cubic_vec/scalar_query	7.01 ns	8.6 ns	0.814	0.67
8_cubic_multi/construct_s001_q100	450.88 ns	553.4 ns	0.815	0.716
8_cubic_multi/construct_s010_q100	3663.72 ns	4675.7 ns	0.784	0.755
8_cubic_multi/construct_s100_q100	33726.8 ns	43932.7 ns	0.768	0.759
8_cubic_multi/eval_s001_q100	361.54 ns	461.1 ns	0.784	0.499
8_cubic_multi/eval_s010_q100	1147.12 ns	1384.2 ns	0.829	0.678
8_cubic_multi/eval_s010_q100_scalar_loop	1978.18 ns	2366.5 ns	0.836	0.785
8_cubic_multi/eval_s100_q100	8414.6 ns	10703.8 ns	0.786	0.748
8_cubic_multi/eval_s100_q100_scalar_loop	3215.9 ns	3680.4 ns	0.874	0.886
9_nd_oneshot/bicubic_2d	34091.3 ns	35423.2 ns	0.962	0.792
9_nd_oneshot/bilinear_2d	430.86 ns	459.7 ns	0.937	0.921
9_nd_oneshot/phs_2d	1285733.5 ns	1409314.6 ns	0.912	-
9_nd_oneshot/phs_3d	18596539.4 ns	21174592.9 ns	0.878	-
9_nd_oneshot/tricubic_3d	272859.8 ns	301679.3 ns	0.904	0.746
9_nd_oneshot/trilinear_3d	731.1 ns	802.2 ns	0.911	0.817

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

Runner: znver4|4c — AMD EPYC 9V74 80-Core Processor, julia 1.13.3. Times are min-merged and compared only against this same machine's history.

This comment was automatically generated by Benchmark workflow.