Threaded leaves-first path for single large power-of-two transforms - #8
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pankgeorg wants to merge 19 commits into
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Threaded leaves-first path for single large power-of-two transforms#8pankgeorg wants to merge 19 commits into
pankgeorg wants to merge 19 commits into
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W butterflies per iteration on SIMD.jl vectors (2 for ComplexF64, 4 for ComplexF32); the twiddle table keeps its compact layout and the triplets are rearranged in registers. Falls back to the scalar loop for strided or non-contiguous output and for other element types.
Above 2^18 elements the depth-first recursion reads each leaf at a stride that uses one element per cache line. Compute the 4096-point sub-transforms first, in input order, gathering one cache line of pencils at a time into a plan-owned buffer, then run the remaining butterfly passes level by level. Same operations, identical output; 2^20 43 -> 21 ms, 2^22 188 -> 101 ms (ComplexF64, Neoverse-N1, with the SIMD pass).
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).
Same structure as the radix-3 kernel, with the 5-/7-point codelets as in-place butterflies; replaces the composite step + O(n^2) leaves for 5^k and 7^k (Float32/Float64). 125-point 1.8 -> 1.2 us, 1000 19 -> 14 us, 10^6 68 -> 55 ms (ComplexF64).
…of two), test for 2^18-2^21 N/B must be a power of 4; with a fixed B = 4096 that failed for odd log2 N (e.g. the 2^19 complex transform inside a 2^20 rfft) and the digit reversal wrote out of bounds.
…py-based packing The even-length real transform's post-processing (and the backward pre-processing) used a per-call twiddle recurrence; the twiddles now live in the workers (Float32 accuracy at 2^20: 8e-6 -> 2.5e-7) and the loops run W values per iteration on SIMD vectors; the real<->complex pair packing is a copy. rfft 16384: 142 -> 131 us (Float64), 136 -> 118 us (Float32).
# Conflicts: # src/FFTA.jl
…56-point block The sibling leaves are computed together, one leaf per complex lane of a SIMD vector (2 for Float64, 4 for Float32), with the twiddle products written to round exactly as the scalar codelets. ComplexF64 2^14 197 -> 168 us (FFTW ESTIMATE 177), ComplexF32 2^14 146 -> 114 us.
Plans with several workers run a 1D transform of >= 2^18 points (and the half-size transform of an even-length real one) as independent sub-transforms on the workers' gather buffers, then butterfly passes split by block or by butterfly range (multiples of 64); same operations, output identical to the serial path. 16 workers, Neoverse-N1: ComplexF64 2^20 20.1 -> 1.87 ms (FFTW MEASURE 1.75 ms), 2^22 105 -> 10.2 ms (9.4 ms), rfft Float64 2^20 11.5 -> 3.2 ms (2.7 ms).
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Stacked on
integration/experiments(all previous branches; needs the leaves-first order of #5 and the per-worker buffers) — new here:src/leaffirst.jl(threaded stages),src/plan.jl(Worker.gathers,_kernel_1d!),test/leaffirst.jl. Plans with several workers run a 1D transform of ≥ 2^18 points — and the half-size transform inside an even-length real one — as independent sub-transforms on the workers' gather buffers, then butterfly passes split by block or by butterfly range (multiples of 64); same operations, output identical to the serial path (tested). Base tasks, not Polyester:@batchcannot pass the vector of per-thread buffers here (cfunction: closures are not supported).16 workers vs 1, Neoverse-N1 (FFTW at 16 threads, MEASURE in brackets): ComplexF64 2^18 3.81→0.47 ms (0.39), 2^20 20.1→1.87 ms (1.75), 2^22 106→10.2 ms (9.4); ComplexF32 2^20 12.3→1.13 ms (1.23); rfft Float64 2^20 11.5→3.2 ms (2.7), 2^21 24.3→7.1 ms (5.4); rfft Float32 2^20 7.0→1.96 ms (2.7).
Tested: full suite green on 4 threads (11 061 tests).