[mgyoo86]

Summary

On hardware with FMA, linear and cubic value evaluation now gives the same bits regardless of which search policy or --check-bounds mode compiled it, and runs slightly faster. Nothing changes on hardware without FMA or for non-float carriers.

Why. The shared linear blend α·yR + (1−α)·yL is written as two muladds, but muladd only allows fusion. Depending on the code it gets inlined into, LLVM sometimes fused both operations and sometimes neither, so two search policies could return results 1-2 ULP apart (the flake fixed in #212) and the hot path paid an extra multiply and add.

What. When the blend eltype is a real IEEEFloat and the compilation target has hardware FMA, the blend uses fma, which pins both fused operations. The check is Core.Intrinsics.have_fma(T), the same codegen-time constant Base.fma dispatches on, so there is no runtime branch and no software-emulated fma anywhere. The intrinsic is not public API, so the method sits under @static if isdefined(...) and falls back to today's muladd if it ever disappears.

	before	after
search policies agree bit-for-bit (linear, cubic)	no, 1-2 ULP on ~17 % of queries	yes
cubic 1D, 10k queries	19.2 µs	17.8 µs
linear 1D, 10k queries	13.8 µs	13.5 µs
hardware without FMA, Complex, Dual, Unitful, colorants	unchanged	unchanged

This is a same-machine consistency and performance change, not a cross-machine reproducibility guarantee; other kernels still use muladd, so cross-path tests keep their ULP budget.

Changes

• src/linear/linear_kernels.jl: _linear_value_blend(::_LinearBlendFMA) → _fma2_blend, with a hardware-gated fma method for same-width IEEEFloat and the previous muladd form for everything else.

Not covered

• Results move by at most 2 ULP toward the exact value; no existing test needed a tolerance change.
• The Hermite-family value kernel has a similar, larger opportunity (16 → 12 ops) and is left for its own PR.

Tests

• Linear, cubic, search, node-exactness, colorant, complex, mixed-precision and ND linear test files pass on Julia 1.13; the blend arms and bit-identity were also checked on LTS 1.10 with --check-bounds=yes.

[github-actions]

FastInterpolations.jl Benchmarks

All benchmarks (71 total, click to expand)

Benchmark	Current: ea58668	Previous	Imm. Ratio	Grad. Ratio
10_nd_construct/bicubic_2d	36848 ns	34525.0 ns	1.067	0.969
10_nd_construct/bilinear_2d	590.52 ns	568.7 ns	1.038	0.949
10_nd_construct/phs_2d	1080527.6 ns	1071600.1 ns	1.008	-
10_nd_construct/phs_3d	17936438.6 ns	17321717.9 ns	1.035	-
10_nd_construct/tricubic_3d	309629 ns	313178.0 ns	0.989	0.865
10_nd_construct/trilinear_3d	1832.62 ns	1648.1 ns	1.112	1.039
11_nd_eval/bicubic_2d_batch	1418.6 ns	1429.7 ns	0.992	1.018
11_nd_eval/bicubic_2d_scalar	15.82 ns	15.8 ns	1.0	0.883
11_nd_eval/bilinear_2d_scalar	8.51 ns	8.5 ns	1.0	0.993
11_nd_eval/phs_2d_batch	38513.1 ns	38945.0 ns	0.989	-
11_nd_eval/phs_2d_scalar	300.36 ns	303.8 ns	0.989	-
11_nd_eval/phs_3d_batch	234966.7 ns	234531.0 ns	1.002	-
11_nd_eval/phs_3d_scalar	2229.18 ns	2224.8 ns	1.002	-
11_nd_eval/tricubic_3d_batch	3066.7 ns	3057.7 ns	1.003	0.939
11_nd_eval/tricubic_3d_scalar	34.76 ns	34.3 ns	1.015	1.019
11_nd_eval/trilinear_3d_scalar	14.02 ns	13.0 ns	1.077	1.004
12_cubic_eval_gridquery/range_random	2853.14 ns	2884.6 ns	0.989	0.673
12_cubic_eval_gridquery/range_sorted	2852.76 ns	2878.0 ns	0.991	0.675
12_cubic_eval_gridquery/vec_random	9848.44 ns	8802.7 ns	1.119	1.068
12_cubic_eval_gridquery/vec_sorted	2381.46 ns	2637.1 ns	0.903	0.738
13_nd_oneshot_gridquery/bicubic_2d_rand_rand	62007 ns	61417.2 ns	1.01	0.952
13_nd_oneshot_gridquery/bicubic_2d_sort_rand	58059.6 ns	57310.5 ns	1.013	0.936
13_nd_oneshot_gridquery/bicubic_2d_sort_sort	56309.3 ns	55603.4 ns	1.013	0.935
13_nd_oneshot_gridquery/bilinear_2d_rand_rand	16800.64 ns	16337.9 ns	1.028	1.012
13_nd_oneshot_gridquery/bilinear_2d_sort_rand	9900.12 ns	9360.0 ns	1.058	1.073
13_nd_oneshot_gridquery/bilinear_2d_sort_sort	5118.96 ns	5596.5 ns	0.915	1.001
14_series_oneshot_batch/constant_inplace_vec_k8_q1000_rand	13572.4 ns	13383.1 ns	1.014	0.937
14_series_oneshot_batch/linear_inplace_vec_k8_q1000_rand	13843.9 ns	14036.3 ns	0.986	0.963
15_gridded_query/cubic_oneshot_2d_40x32	41295.2 ns	41465.7 ns	0.996	0.93
15_gridded_query/cubic_persistent_2d_40x32	8326.5 ns	8331.7 ns	0.999	0.977
15_gridded_query/linear_oneshot_2d_40x32	1661.72 ns	1538.3 ns	1.08	1.077
15_gridded_query/linear_oneshot_3d_12x10x8	2917.06 ns	1932.6 ns	1.509	1.45
15_gridded_query/linear_persistent_2d_40x32	1627.24 ns	1516.6 ns	1.073	1.082
15_gridded_query/linear_persistent_3d_12x10x8	2781.4 ns	1887.5 ns	1.474	1.391
16_phs/construct_g0100	35826.44 ns	34416.5 ns	1.041	-
16_phs/construct_g1000	36138.6 ns	34249.2 ns	1.055	-
16_phs/eval_q00001	112.7 ns	111.6 ns	1.01	-
16_phs/eval_q00100	11879.64 ns	11914.7 ns	0.997	-
16_phs/eval_q10000	1173327.3 ns	1178071.9 ns	0.996	-
16_phs/oneshot_q00001	37321.44 ns	35355.5 ns	1.056	-
16_phs/oneshot_q10000	1770210.3 ns	1763848.5 ns	1.004	-
1_cubic_oneshot/q00001	455.24 ns	457.0 ns	0.996	1.0
1_cubic_oneshot/q10000	29710.6 ns	29532.3 ns	1.006	0.685
2_cubic_construct/g0100	1329.1 ns	1302.4 ns	1.02	1.016
2_cubic_construct/g1000	13555.4 ns	12559.6 ns	1.079	1.075
3_cubic_eval/q00001	9.91 ns	9.9 ns	1.0	0.482
3_cubic_eval/q00100	301.96 ns	304.8 ns	0.991	0.683
3_cubic_eval/q10000	28931.1 ns	29059.5 ns	0.996	0.679
4_linear_oneshot/q00001	27.14 ns	26.7 ns	1.015	1.023
4_linear_oneshot/q10000	18442.5 ns	18657.0 ns	0.989	1.0
5_linear_construct/g0100	40.77 ns	35.5 ns	1.149	1.1
5_linear_construct/g1000	345.94 ns	263.0 ns	1.315	1.263
6_linear_eval/q00001	8.72 ns	9.0 ns	0.968	0.834
6_linear_eval/q00100	197.96 ns	198.4 ns	0.998	1.008
6_linear_eval/q10000	18317.3 ns	18318.3 ns	1.0	1.006
7_cubic_range/scalar_query	5.7 ns	5.7 ns	1.0	0.708
7_cubic_vec/scalar_query	9.11 ns	8.5 ns	1.071	0.832
8_cubic_multi/construct_s001_q100	515.56 ns	511.1 ns	1.009	1.01
8_cubic_multi/construct_s010_q100	4343.74 ns	4240.0 ns	1.024	1.012
8_cubic_multi/construct_s100_q100	40698.1 ns	39579.2 ns	1.028	1.029
8_cubic_multi/eval_s001_q100	428.58 ns	430.4 ns	0.996	0.735
8_cubic_multi/eval_s010_q100	1306.04 ns	1337.3 ns	0.977	0.894
8_cubic_multi/eval_s010_q100_scalar_loop	2210.34 ns	2195.3 ns	1.007	0.951
8_cubic_multi/eval_s100_q100	10030.8 ns	10040.8 ns	0.999	0.982
8_cubic_multi/eval_s100_q100_scalar_loop	3270.1 ns	3338.2 ns	0.98	0.961
9_nd_oneshot/bicubic_2d	34735 ns	34965.6 ns	0.993	0.921
9_nd_oneshot/bilinear_2d	453.46 ns	451.1 ns	1.005	1.004
9_nd_oneshot/phs_2d	1349818.8 ns	1331365.8 ns	1.014	-
9_nd_oneshot/phs_3d	20025410 ns	19856472.4 ns	1.009	-
9_nd_oneshot/tricubic_3d	322088.7 ns	315974.6 ns	1.019	0.874
9_nd_oneshot/trilinear_3d	853.6 ns	837.5 ns	1.019	0.935

⚠️ Performance Regression Confirmed ⚠️

After re-running 6 flagged benchmark(s) 10 time(s), 6 regression(s) confirmed.

Benchmark	Current	Previous	Imm. Ratio	Grad. Ratio	Tier
10_nd_construct/trilinear_3d	1832.62 ns	1648.1 ns	1.112	1.039	immediate
12_cubic_eval_gridquery/vec_random	9848.44 ns	8802.7 ns	1.119	1.068	immediate
15_gridded_query/linear_oneshot_3d_12x10x8	2917.06 ns	1932.6 ns	1.509	1.45	both
15_gridded_query/linear_persistent_3d_12x10x8	2781.4 ns	1887.5 ns	1.474	1.391	both
5_linear_construct/g0100	40.77 ns	35.5 ns	1.149	1.1	immediate
5_linear_construct/g1000	345.94 ns	263.0 ns	1.315	1.263	both

Thresholds: immediate > 1.1x (vs latest master), gradual > 1.1x (vs sliding window)

Runner: znver3|4c — AMD EPYC 7763 64-Core Processor, julia 1.13.1. Times are min-merged and compared only against this same machine's history.

This comment was automatically generated by Benchmark workflow.

[Copilot]

🟢 Approval recommended

The focused implementation correctly preserves fallback behavior while enforcing deterministic fused evaluation where supported.

0 open findings

What changed in this PR

Pins real IEEE-float interpolation blends to hardware FMA while preserving existing fallbacks.

Changes:

• Adds hardware-gated two-FMA evaluation.
• Retains muladd for unsupported hardware and other carriers.

File	Description
src/​linear/​linear_kernels.jl	Introduces the guarded _fma2_blend implementation.

🧠 Review effort: Balanced

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.26%. Comparing base (5901fbe) to head (ea58668).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #215   +/-   ##
=======================================
  Coverage   96.26%   96.26%           
=======================================
  Files         171      171           
  Lines       15417    15420    +3     
=======================================
+ Hits        14841    14844    +3     
  Misses        576      576           

Files with missing lines	Coverage Δ
src/linear/linear_kernels.jl	100.00% <100.00%> (ø)

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[mgyoo86]

Closing: premature optimization.

The CI benchmark regressions on linear ND / gridded paths (+4…+19 %) are real and reproduce locally. Pinning fma removes the freedom LLVM used to pack the independent blends of an ND cell into vector instructions, so forcing fusion loses more than it gains there. Even on cubic 1D the effect is a wash (sorted batches −3 %, random queries with LinearBinarySearch +8 %).

The cross-path consistency issue that motivated this is already handled on the test side by #212. Keeping muladd as the repo-wide default stands.