[mgyoo86]

Follow-up to #224.

Summary

Problem: on Metal, linear interpolation on a Float32 range grid ran at 74 % of copy bandwidth (a hand-written kernel reaches 100 %).

• Cause: the cell's left edge lo + (idx − 1)·h is rebuilt from an Int64 index, and 64-bit integer ↔ float conversions are costly on Metal. In isolation, an Int64 round trip measured 10× an Int32 one.

Fix: on Float32/Float16 grids the left edge is rebuilt from (idx − 1) % Int32. The index itself, the clamps, the loads and the returned Int are unchanged, and results are bit-identical to master.

Metal (M1 Pro), 1D range grid, 1e8 Float32 queries, share of copy	master	this PR
InBounds(), ClampExtrap()	74 %	99 %
FillExtrap, ExtendExtrap(), NoExtrap()	74 %	100 %
inside a KernelAbstractions kernel	69 %	97 %

Changes

• _idx_type(T): Int32 for Float32/Float16 grids, Int otherwise. It is used at the 8 left-edge rebuild sites of the range searches: muladd((idx - 1) % _idx_type(T), h, lo).
• Float32/Float16 range grids are limited to typemax(Int32) ÷ 2 (≈ 1.07e9) points (ArgumentError), so the narrowing is always exact.

Performance

• CUDA (V100S): no difference observed. Master, this PR and an all-Int32 index all reach 85 % of copy.
• CPU (M1 Pro, Julia 1.13.2):
  • Float64: LLVM IR identical to master.
  • Float32: native code identical apart from the 32-bit conversion operand.
  • ABAB against master: within noise (±0.8 %).

Not covered

• The float → Int64 truncation stays 64-bit. It is hidden by memory latency here; revisit when compute-heavier families reach the GPU.

Tests

• test/test_range_cell_index.jl:
  • 32-bit conversion in the IR, and the length guard (both fail on master);
  • bit identity with the all-Int chain (Float32/Float16 grids, Float64/Dual queries, at the length limit);
  • end cells for far out-of-domain queries.
• The JLArrays GPU tests and the real-GPU suite on Metal pass.

[github-actions]

FastInterpolations.jl Benchmarks

🚨 Regression baseline is a different CPU

	CPU
This PR run	`znver5
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-znver5|4c history and are blank if master has none on this CPU yet.

All benchmarks (71 total, click to expand)

Benchmark	Current: 02923b0	Previous	Imm. Ratio	Grad. Ratio
10_nd_construct/bicubic_2d	23655 ns	25138.0 ns	0.941	0.935
10_nd_construct/bilinear_2d	228.94 ns	271.4 ns	0.843	0.926
10_nd_construct/phs_2d	680786.6 ns	660962.5 ns	1.03	1.067
10_nd_construct/phs_3d	10172485.9 ns	10901033.3 ns	0.933	0.902
10_nd_construct/tricubic_3d	187613 ns	194822.0 ns	0.963	0.903
10_nd_construct/trilinear_3d	575.66 ns	652.8 ns	0.882	0.91
11_nd_eval/bicubic_2d_batch	973.5 ns	1063.6 ns	0.915	0.941
11_nd_eval/bicubic_2d_scalar	12.91 ns	13.7 ns	0.941	0.969
11_nd_eval/bilinear_2d_scalar	5.5 ns	5.9 ns	0.932	0.971
11_nd_eval/phs_2d_batch	20072.3 ns	19812.7 ns	1.013	0.957
11_nd_eval/phs_2d_scalar	149.42 ns	154.4 ns	0.967	0.909
11_nd_eval/phs_3d_batch	103017.3 ns	104308.6 ns	0.988	0.962
11_nd_eval/phs_3d_scalar	938.42 ns	972.5 ns	0.965	0.975
11_nd_eval/tricubic_3d_batch	1981 ns	2103.2 ns	0.942	0.954
11_nd_eval/tricubic_3d_scalar	20.13 ns	21.2 ns	0.948	0.919
11_nd_eval/trilinear_3d_scalar	8.91 ns	9.5 ns	0.937	0.937
12_cubic_eval_gridquery/range_random	1817.54 ns	1967.1 ns	0.924	0.707
12_cubic_eval_gridquery/range_sorted	1812.74 ns	1947.9 ns	0.931	0.707
12_cubic_eval_gridquery/vec_random	2946.86 ns	3203.0 ns	0.92	0.837
12_cubic_eval_gridquery/vec_sorted	1453.18 ns	1602.8 ns	0.907	0.812
13_nd_oneshot_gridquery/bicubic_2d_rand_rand	36204.6 ns	36808.3 ns	0.984	0.913
13_nd_oneshot_gridquery/bicubic_2d_sort_rand	34819.5 ns	35405.2 ns	0.983	0.925
13_nd_oneshot_gridquery/bicubic_2d_sort_sort	34153.5 ns	35279.9 ns	0.968	0.922
13_nd_oneshot_gridquery/bilinear_2d_rand_rand	6107.2 ns	6404.6 ns	0.954	0.999
13_nd_oneshot_gridquery/bilinear_2d_sort_rand	3958.76 ns	4268.8 ns	0.927	0.999
13_nd_oneshot_gridquery/bilinear_2d_sort_sort	3080.24 ns	3415.9 ns	0.902	0.975
14_series_oneshot_batch/constant_inplace_vec_k8_q1000_rand	5582.4 ns	5878.8 ns	0.95	0.782
14_series_oneshot_batch/linear_inplace_vec_k8_q1000_rand	6380.6 ns	7229.8 ns	0.883	0.868
15_gridded_query/cubic_oneshot_2d_40x32	27151 ns	27955.0 ns	0.971	0.933
15_gridded_query/cubic_persistent_2d_40x32	4243.4 ns	4381.6 ns	0.968	0.923
15_gridded_query/linear_oneshot_2d_40x32	828.86 ns	860.5 ns	0.963	0.923
15_gridded_query/linear_oneshot_3d_12x10x8	980.48 ns	992.5 ns	0.988	0.922
15_gridded_query/linear_persistent_2d_40x32	813.22 ns	827.3 ns	0.983	0.924
15_gridded_query/linear_persistent_3d_12x10x8	961.26 ns	989.1 ns	0.972	0.921
16_phs/construct_g0100	21000.68 ns	24034.5 ns	0.874	0.94
16_phs/construct_g1000	20992.7 ns	23845.8 ns	0.88	0.95
16_phs/eval_q00001	53.78 ns	54.4 ns	0.989	0.928
16_phs/eval_q00100	5569.8 ns	5846.8 ns	0.953	0.923
16_phs/eval_q10000	543125.6 ns	557251.5 ns	0.975	0.906
16_phs/oneshot_q00001	21517.22 ns	24148.7 ns	0.891	0.952
16_phs/oneshot_q10000	874791.2 ns	877198.8 ns	0.997	0.888
1_cubic_oneshot/q00001	312.26 ns	316.9 ns	0.985	0.917
1_cubic_oneshot/q10000	18760.3 ns	19522.3 ns	0.961	0.666
2_cubic_construct/g0100	823.64 ns	899.7 ns	0.915	0.888
2_cubic_construct/g1000	7986.1 ns	9259.9 ns	0.862	0.921
3_cubic_eval/q00001	4.8 ns	5.0 ns	0.96	0.568
3_cubic_eval/q00100	200.3 ns	213.5 ns	0.938	0.755
3_cubic_eval/q10000	18235.5 ns	19421.2 ns	0.939	0.711
4_linear_oneshot/q00001	13.42 ns	14.1 ns	0.95	0.993
4_linear_oneshot/q10000	11543.4 ns	12369.5 ns	0.933	0.984
5_linear_construct/g0100	17.93 ns	19.2 ns	0.932	0.661
5_linear_construct/g1000	128.19 ns	154.6 ns	0.829	0.896
6_linear_eval/q00001	4.1 ns	4.4 ns	0.932	0.854
6_linear_eval/q00100	138.4 ns	143.2 ns	0.966	1.058
6_linear_eval/q10000	11416.2 ns	12518.8 ns	0.912	0.985
7_cubic_range/scalar_query	3.5 ns	3.7 ns	0.946	0.648
7_cubic_vec/scalar_query	5.1 ns	5.0 ns	1.018	0.927
8_cubic_multi/construct_s001_q100	333.1 ns	353.9 ns	0.941	0.894
8_cubic_multi/construct_s010_q100	2816.46 ns	3165.8 ns	0.89	0.94
8_cubic_multi/construct_s100_q100	26680.3 ns	29990.0 ns	0.89	0.952
8_cubic_multi/eval_s001_q100	234.14 ns	244.4 ns	0.958	0.655
8_cubic_multi/eval_s010_q100	738.5 ns	767.6 ns	0.962	0.799
8_cubic_multi/eval_s010_q100_scalar_loop	1663.9 ns	1695.3 ns	0.981	0.996
8_cubic_multi/eval_s100_q100	5774.7 ns	6069.2 ns	0.951	0.881
8_cubic_multi/eval_s100_q100_scalar_loop	2127.2 ns	2251.3 ns	0.945	0.892
9_nd_oneshot/bicubic_2d	23817.9 ns	24432.7 ns	0.975	0.863
9_nd_oneshot/bilinear_2d	300.64 ns	319.1 ns	0.942	1.04
9_nd_oneshot/phs_2d	805489.8 ns	795733.0 ns	1.012	0.977
9_nd_oneshot/phs_3d	11444296.7 ns	12385423.6 ns	0.924	0.896
9_nd_oneshot/tricubic_3d	186919.9 ns	187544.6 ns	0.997	0.849
9_nd_oneshot/trilinear_3d	490.7 ns	527.8 ns	0.93	0.949

✅ No regressions detected

Runner: znver5|4c — AMD EPYC 9V45 96-Core Processor, julia 1.13.2. Times are min-merged and compared only against this same machine's history.

This comment was automatically generated by Benchmark workflow.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.38%. Comparing base (920df35) to head (02923b0).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #226   +/-   ##
=======================================
  Coverage   96.38%   96.38%           
=======================================
  Files         176      176           
  Lines       15810    15816    +6     
=======================================
+ Hits        15239    15245    +6     
  Misses        571      571           

Files with missing lines	Coverage Δ
src/core/axis_types.jl	92.45% <100.00%> (+0.96%)	⬆️
src/core/search.jl	98.58% <100.00%> (ø)

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