Straight-line codelets for the 5-, 7-, 11- and 13-point leaves - #4
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pankgeorg wants to merge 2 commits into
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Straight-line codelets for the 5-, 7-, 11- and 13-point leaves#4pankgeorg wants to merge 2 commits into
pankgeorg wants to merge 2 commits into
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Symmetric odd-length DFT (cosine and sine sums over x_j ± x_{N-j}) with
folded constants, (N-1)^2 real multiplications instead of 4(N-1)^2 from a
twiddle table. Real input is accepted. Composite sizes with factors 5/7:
1000 35 -> 19 us, 46305 3.3 -> 1.9 ms, 10^6 100 -> 68 ms (ComplexF64).
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src/odd_codelets.jl:@generatedsymmetric odd-length DFTs (cosine/sine sums over x_j ± x_{N-j}, folded constants, explicit fma) replace the O(N²) twiddle-table loop for the DFT leaves 5/7/11/13 (Float32/Float64, real input accepted); other sizes and types keepfft_dft!.compare3 vs
integration/all, aarch64, 1 thread, 505 cases: 1.08× geomean; smooth class 1.33× ComplexF64 / 1.61× ComplexF32 / 1.27–1.51× rfft (n=1000 35→20 µs, 46305 3.3→2.0 ms, 10^6 100→66 ms), 5–13-point primes up to 5×; everything without factors 5–13 unchanged (the sub-0.95× cells of the first run were noise: a quiet back-to-back re-run of the N-d/batched cases,benchmark/compare3/aarch64/recheck-nd-batched/, has ≤2 of 117 cells below 0.95×, min 0.93×). Table:benchmark/compare3/aarch64/odd/COMPARE3.mdonbench/compare3.Tested: full suite green on 4 threads (
muladd→ explicitfmaneeded for the exact-equality batched-vs-mapslicestests).x86-64 (companion session,
benchmark/x86-64/compare3/odd/): 1.08× geomean; smooth 1.46× ComplexF64 / 1.79× ComplexF32.