[jtravs]

Summary

Some 2-3-5-smooth grid sizes cost 1.6–1.8× the neighbouring power of two per source evaluation on the native CPU backend. FFTW is not the cause; two size boundaries in our own code are:

• Node-chunk tail (n_t 8640). The node-budget admissions take budget // per_node. At n_to 17280 the four-mode RDW's 33 nodes were cut to a chunk of 32, so every evaluation ran a 32-node pass and then a one-node pass on one thread. _balanced_chunk (translation) now spreads the nodes evenly over the same number of passes (17 + 16). Chunks never exceed the admitted size, planar chunks keep whole rows, and sub-row chunks are left as they are.
• Power-of-two thread thresholds (n_t 4000). The stage threshold (8192 elements) and the modal FFT threshold (32,768 samples) sat just above the RDW's sizes at n_t 4000 (8004 and 32,000). Its stage entry and transforms therefore ran serially: stage entry 708 µs vs 59 µs, D2Z 104 vs 33 µs, Z2D 134 vs 53 µs (kernel timer, one Xeon Gold 6240 socket). On Linux the thresholds are now 4096 and 16,384, chosen from a sweep of stage {8192, 4096, 2048, 1024} × FFT {32768, 16384} over RDW, SSFS and reduced CtC. At 1024 the SSFS case regressed, so it stops at 4096.

Platform split. The lower thresholds apply on Linux only. macOS keeps 8192 and 32,768: on an Apple arm64 laptop the serial stage and transforms are the faster ones at these sizes, so the change made n_t 4000 17 % slower there (see the comments below). A roadmap item asks for a sweep of the Mac crossover. The node-chunk balancing applies on every platform.

Results

Xeon Gold 6240, 18 pinned cores, GCC 16, FFTW 3.3.11, ms per evaluation (native/benchmarks/size_cliffs.py, two rounds each):

n_t	4000	4096	4500	5000	6000	7200	8000	8192	8640
before	2.45–2.47	1.24–1.36	1.49–1.56	1.54–1.57	1.86–1.87	2.21–2.26	2.38–2.39	2.29–2.30	3.52–3.55
after	1.32	1.27–1.36	1.53–1.54	1.57–1.61	1.83–1.87	2.17–2.26	2.38–2.40	2.28–2.31	2.54–2.58

On a loaded 18-core arm64 laptop, RDW at n_t 4000 went from 0.82 to 0.95 ms, level with 4096 (0.98 ms). Thread wake-ups cost more there. SSFS and reduced CtC did not move.

Tests

• GoogleTest CpuThreadPolicy.SmoothGridSizesKeepThePowerOfTwoWidths. The whole native GoogleTest binary passes locally (136); CI does not build it.
• Python: test_budget_chunks_spread_the_nodes_evenly_over_their_passes, test_planar_chunks_stay_whole_rows_when_balanced, and the _even_chunk doctest.
• Targeted runs pass: tests/translate, the held-plasma, memory and multimode backend tests (1821 passed), and native/tests (383 passed). The only failure is test_public_surface_is_exact on the local dirty-tree version suffix.

SEP 30 core A/B (same machine, 18 threads, 3 rounds, candidate/baseline)

case	track	ratio	range
rdw	adaptive-multistep	0.996	0.994–1.025
rdw	adaptive-rk	0.986	0.985–0.995
ctc	adaptive-multistep	1.004	1.001–1.006
ctc	adaptive-rk	1.002	0.998–1.013
kerr_beam_384	fixed-rk4ip	1.005	1.003–1.006
radial_filament_256	adaptive-multistep	1.003	0.992–1.004
radial_filament_256	adaptive-rk	0.974	0.965–0.974

Geometric mean 0.996. Every case did the same work, and the fields agree to rounding (largest difference 5e-15).

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Documentation build overview

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[jtravs]

Mac A/B (18-core arm64 laptop, NEON FFTW, same commit, base/fix/fix/base interleaved, load 2.6–6; ms per evaluation, size_cliffs.py):

n_t	4000	4096	4500	5000	6000	7200	8000	8192	8640
before	0.88–0.89	1.07–1.08	1.07–1.10	1.12	1.19–1.21	1.29–1.32	1.41–1.48	1.50	2.32–2.37
after	1.04	1.04–1.07	0.96–1.06	1.10–1.11	1.03–1.21	1.30–1.31	1.38–1.41	1.48–1.51	1.73

The node-chunk balancing helps on both machines (8640: −26 % here, −28 % on the Xeon). The threshold change does not: here n_t 4000 is 17 % slower (now level with 4096). On this machine the serial stage and FFT were faster at that size; even 4096, threaded under the old thresholds, costs more than 4000 serial. So the stage and FFT crossovers differ between the two hosts by more than a factor of two, and one shared constant cannot suit both.

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[jtravs]

Zen 3 A/B (DMOG node12, dual EPYC 7643, idle node, GCC 16.2, FFTW 3.3.11, OMP_PLACES=cores OMP_PROC_BIND=close, base/fix/fix/base; ms per evaluation, size_cliffs.py):

threads	build	4000	4096	4500	5000	6000	7200	8000	8192	8640
12 (one NUMA domain)	before	2.36–2.42	1.94–1.98	2.05	2.18	2.57	3.02–3.08	3.25–3.36	3.62–3.76	3.75–3.77
12	after	1.74–1.75	2.01	2.02–2.03	2.18–2.19	2.53–2.55	3.01–3.04	3.23–3.27	3.54–3.61	3.60–3.64
24 (two domains)	before	2.36–2.40	2.01–2.06	2.09–2.10	2.25–2.28	2.58–2.60	3.10–3.13	3.32–3.42	3.63–3.73	4.04–4.05
24	after	1.81–1.82	2.04–2.07	2.07–2.11	2.22–2.24	2.61	3.13–3.20	3.39–3.42	3.82–3.84	3.52–3.53

Both Linux x86 hosts gain, at n_t 4000 (Zen 3 −24 to −27 %, Cascade Lake −47 %) and at 8640 (−4 to −13 %, −28 %). The Apple arm64 laptop loses 17 % at 4000. The other sizes move by at most 5 %, within the spread as the node's load rose from 5 to 10 during the 24-thread run. A first attempt on a node shared with other jobs (load ~117 of 128, cores scattered over five NUMA domains) varied 2× between rounds of the same build and was discarded.

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