From e9f2a3da598e5f6c748da54f1ccc64c0e707eabc Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 10:30:23 +0000 Subject: [PATCH 01/21] benchmark: compare3.jl, several implementations side by side in separate processes Runs FFTW, a registry FFTA version and any number of FFTA checkouts on the suite.jl case list (moved to cases.jl), one process and environment each, and renders one table with ratios to FFTW, speedups over a reference column, per-class geometric means and thread scaling. --- .gitignore | 2 + benchmark/README.md | 20 +++ benchmark/cases.jl | 132 +++++++++++++++++ benchmark/compare3.jl | 272 +++++++++++++++++++++++++++++++++++ benchmark/compare3_worker.jl | 128 +++++++++++++++++ benchmark/suite.jl | 50 +------ 6 files changed, 557 insertions(+), 47 deletions(-) create mode 100644 benchmark/cases.jl create mode 100644 benchmark/compare3.jl create mode 100644 benchmark/compare3_worker.jl diff --git a/.gitignore b/.gitignore index e624d38..7c275d7 100644 --- a/.gitignore +++ b/.gitignore @@ -2,3 +2,5 @@ docs/build benchmark/Manifest.toml benchmark/*/Manifest.toml +benchmark/envs/ +benchmark/compare3_results/ diff --git a/benchmark/README.md b/benchmark/README.md index 70672b1..9ab2eb3 100644 --- a/benchmark/README.md +++ b/benchmark/README.md @@ -63,6 +63,26 @@ The committed [`REPORT.md`](REPORT.md) was produced on the machine described in its *Environment* section; re-run the suite to obtain numbers for your own hardware. +## Several implementations side by side (`compare3.jl`) + +```bash +cd benchmark +julia --project=. compare3.jl # FFTW vs FFTA 0.3.1 (registry) vs this checkout +julia --project=. compare3.jl --impl fftw=fftw --impl int=/path/to/base --impl new=/path/to/branch --ref int \ + --threads 1,4,16 --only nd,batched +``` + +Each `--impl NAME=SPEC` column runs in its own process and environment +(`envs/NAME/`, git-ignored): `fftw`, `@0.3.1` (an FFTA version from the +registry) or a path to an FFTA checkout / worktree. The same case list as +`suite.jl` (`cases.jl`; the `--only/--kinds/--maxlog2/--sizes/--seconds` +options apply) is run per thread count in `--threads`, and one markdown +table (`compare3_results/COMPARE3.md`) shows the times, each column's ratio +to the first column and its speedup over the `--ref` column, with per-class +geometric means and, for several thread counts, the thread scaling. +Results are checksummed against the first column. `--render-only` +re-renders the table from the JSON files of a previous run. + ## Original 1D suite (`run_benchmarks.jl`) ## Structure diff --git a/benchmark/cases.jl b/benchmark/cases.jl new file mode 100644 index 0000000..8eac367 --- /dev/null +++ b/benchmark/cases.jl @@ -0,0 +1,132 @@ +# Size classes and the case list shared by `suite.jl` and `compare3.jl`. +# +# A case is a NamedTuple (kind, T, sz, dims, shape, nthreads, measure); `T` is +# the *real* element type (complex cases use `Complex{T}`). + +using Primes + +function size_classes(maxlog2) + nmax = 1 << maxlog2 + pow2 = [1 << k for k in 3:maxlog2] + # 2^a 3^b 5^c 7^d, not powers of two, spread log-uniformly + smooth_all = Int[] + for a in 0:maxlog2, b in 0:14, c in 0:9, d in 0:8 + n = 2^a * 3^b * 5^c * 7^d + (n <= nmax && n >= 8 && !ispow2(n)) && push!(smooth_all, n) + end + sort!(unique!(smooth_all)) + smooth = Int[] + for t in exp.(range(log(12), log(nmax), length = 18)) + push!(smooth, smooth_all[argmin(abs.(log.(smooth_all) .- log(t)))]) + end + # explicitly include some "classic" smooth sizes + for n in (12, 60, 120, 360, 720, 1000, 1000_000) + n <= nmax && push!(smooth, n) + end + sort!(unique!(smooth)) + # primes: below (DFT path) and above (Bluestein path) the cutoff + prime = Int[] + for t in exp.(range(log(7), log(nmax), length = 16)) + push!(prime, nextprime(round(Int, t))) + end + # straddle the DFT/Bluestein crossover: the O(n²) leaf is used below the + # cutoff (73 originally, 29 since the twiddle-table work), so sample the + # band 23–46 as well as 61–79 + for n in (23, 29, 31, 37, 43, 61, 71, 73, 79) + push!(prime, n) + end + filter!(<=(nmax), prime); sort!(unique!(prime)) + # awkward: (prime > cutoff) × small factor + awk = Int[] + for p in (101, 1009, 4099, 16411, 65537, 262147), f in (2, 3, 4, 6, 16) + n = p * f + n <= nmax && push!(awk, n) + end + sort!(unique!(awk)) + return (pow2 = pow2, smooth = smooth, prime = prime, awkward = awk) +end + +function class_of(classes, n) + for (k, v) in pairs(classes) + n in v && return String(k) + end + return "other" +end + +""" + case_list(; only, kinds, maxlog2, sizes, nthreads, measure) -> Vector{NamedTuple} + +The sweep of `suite.jl`: 1D classes × {Float64, Float32} × {fft, rfft}, a +FFTW-`MEASURE` column for 1D pow2 ComplexF64, 2D/3D, batched `dims`, and the +threaded subset. `nthreads > 1` selects the threaded subset only when `only` +contains `"threads"`; the other sections are always emitted with `nthreads`. +""" +function case_list(; only = ("1d", "nd", "batched", "threads"), kinds = (:fft, :rfft), + maxlog2 = 22, sizes = Int[], nthreads = 1, measure = true) + classes = size_classes(maxlog2) + nmax = 1 << maxlog2 + cases = NamedTuple[] + add!(kind, T, sz, dims, shape; measure = false, thr = nthreads) = + kind in kinds && push!(cases, (kind = kind, T = T, sz = sz, dims = dims, shape = shape, + nthreads = thr, measure = measure, + class = length(sz) == 1 ? class_of(classes, sz[1]) : "nd")) + if "1d" in only + for cls in (:pow2, :smooth, :prime, :awkward), n in classes[cls] + isempty(sizes) || n in sizes || continue + for T in (Float64, Float32) + add!(:fft, T, (n,), 1, "1d") + add!(:rfft, T, (n,), 1, "1d") + end + end + if measure + for n in classes.pow2 + isempty(sizes) || n in sizes || continue + add!(:fft, Float64, (n,), 1, "1d"; measure = true) + end + end + end + if "nd" in only + nd2 = filter(n -> n * n <= nmax, [8, 16, 32, 64, 128, 256, 512, 1024, 2048]) + for n in nd2, T in (Float64, Float32) + add!(:fft, T, (n, n), (1, 2), "2d") + add!(:rfft, T, (n, n), (1, 2), "2d") + end + for sz in ((1000, 1000), (720, 480), (1009, 64), (64, 1009), (127, 257)) + prod(sz) <= nmax || continue + add!(:fft, Float64, sz, (1, 2), "2d") + add!(:rfft, Float64, sz, (1, 2), "2d") + end + nd3 = filter(n -> n^3 <= nmax, [8, 16, 32, 64, 128]) + for n in nd3, T in (Float64, Float32) + add!(:fft, T, (n, n, n), (1, 2, 3), "3d") + add!(:rfft, T, (n, n, n), (1, 2, 3), "3d") + end + end + if "batched" in only + for n in filter(n -> n * 64 <= nmax, [64, 256, 1024, 4096, 16384, 65536]), T in (Float64, Float32) + add!(:fft, T, (n, 64), 1, "batched_dim1") + add!(:fft, T, (64, n), 2, "batched_dim2") + add!(:rfft, T, (n, 64), 1, "batched_dim1") + add!(:rfft, T, (64, n), 2, "batched_dim2") + end + for (n, m) in ((256, 4096), (1024, 1024), (4096, 256)) + n * m <= nmax || continue + add!(:rfft, Float64, (n, m), 1, "batched_dim1") + end + end + if "threads" in only && nthreads > 1 + for n in filter(n -> n >= 1 << 16, classes.pow2) + add!(:fft, Float64, (n,), 1, "1d") + end + for n in filter(n -> n * n <= nmax && n >= 256, [256, 512, 1024, 2048]) + add!(:fft, Float64, (n, n), (1, 2), "2d") + end + for n in filter(n -> n * 64 <= nmax && n >= 1024, [1024, 4096, 16384, 65536]) + add!(:fft, Float64, (n, 64), 1, "batched_dim1") + end + end + return unique(cases) +end + +casekey(c) = string(c.kind, " ", c.T, " ", join(c.sz, "×"), " dims=", join(c.dims, ","), + c.nthreads > 1 ? " ($(c.nthreads) thr)" : "", c.measure ? " MEASURE" : "") diff --git a/benchmark/compare3.jl b/benchmark/compare3.jl new file mode 100644 index 0000000..7fba606 --- /dev/null +++ b/benchmark/compare3.jl @@ -0,0 +1,272 @@ +#!/usr/bin/env julia +#= +Side-by-side benchmark of several FFT implementations on the `suite.jl` sweep. + +Each implementation runs in its own process and environment (FFTW.jl and +FFTA.jl never share a process), then one markdown table is rendered with +execution times, the ratio of each column to the first (FFTW) and the speedup +of each column over a reference column. + + julia --project=. compare3.jl [--impl NAME=SPEC ...] [--ref NAME] + [--threads 1,4,16] [--out DIR] [--table FILE.md] + [--only 1d,nd,batched,threads] [--kinds fft,rfft] + [--maxlog2 K] [--seconds S] [--sizes a,b,c] + [--no-measure] [--quick] [--render-only] + +`SPEC` is `fftw` (FFTW.jl from the registry), `@VERSION` (FFTA from the +registry, e.g. `@0.3.1`), or a path to an FFTA checkout / worktree. The +defaults reproduce the three-way comparison + + --impl fftw=fftw --impl release=@0.3.1 --impl int=.. (this checkout) + +and `--ref` names the column that later columns are compared with (default: +the second FFTA column if there is one, else the last). A typical experiment +run is therefore + + julia --project=. compare3.jl --impl fftw=fftw --impl int=/path/to/integration \ + --impl new=/path/to/experiment --ref int + +Environments are created under `envs/NAME/` (git-ignored) and re-used; delete +one to rebuild it. Per-run JSON files land in `--out` (default +`compare3_results/`) as `NAME_tN.json`; `--render-only` re-renders the table +from them without benchmarking. +=# +import Pkg; Pkg.instantiate() +using JSON, Printf, Statistics, Dates +include(joinpath(@__DIR__, "cases.jl")) + +function getopt(flag, default) + i = findfirst(==(flag), ARGS) + i === nothing ? default : ARGS[i + 1] +end +getall(flag) = [ARGS[i + 1] for i in findall(==(flag), ARGS)] + +const QUICK = "--quick" in ARGS +const IMPLS = let v = getall("--impl") + isempty(v) && (v = ["fftw=fftw", "release=@0.3.1", "int=" * normpath(joinpath(@__DIR__, ".."))]) + [(name = String(first(split(s, "="; limit = 2))), spec = String(last(split(s, "="; limit = 2)))) for s in v] +end +const THREADS = parse.(Int, split(getopt("--threads", "1"), ",")) +const OUTDIR = getopt("--out", joinpath(@__DIR__, "compare3_results")) +const TABLE = getopt("--table", joinpath(OUTDIR, "COMPARE3.md")) +const REF = let r = getopt("--ref", "") + if isempty(r) + ffta = filter(i -> i.spec != "fftw", IMPLS) + length(ffta) >= 2 ? ffta[2].name : last(IMPLS).name + else + r + end +end +const ENVDIR = joinpath(@__DIR__, "envs") +const PASS = String[] # case options passed through to the workers +for flag in ("--only", "--kinds", "--sizes") + v = getopt(flag, ""); isempty(v) || append!(PASS, [flag, v]) +end +append!(PASS, ["--maxlog2", getopt("--maxlog2", QUICK ? "14" : "22")]) +append!(PASS, ["--seconds", getopt("--seconds", QUICK ? "0.1" : "0.5")]) +"--no-measure" in ARGS && push!(PASS, "--no-measure") + +# --------------------------------------------------------------------------- +# environments +# --------------------------------------------------------------------------- +function ensure_env(impl) + dir = joinpath(ENVDIR, impl.name) + isfile(joinpath(dir, "Project.toml")) && return dir + mkpath(dir) + @info "creating environment" impl.name impl.spec dir + code = if impl.spec == "fftw" + """Pkg.add(["FFTW", "JSON", "Primes"])""" + elseif startswith(impl.spec, "@") + """Pkg.add([Pkg.PackageSpec(name = "FFTA", version = "$(impl.spec[2:end])"), Pkg.PackageSpec(name = "JSON"), Pkg.PackageSpec(name = "Primes")])""" + else + path = abspath(impl.spec) + isfile(joinpath(path, "Project.toml")) || error("$(impl.name): no Project.toml in $path") + """Pkg.develop(path = "$path"); Pkg.add(["JSON", "Primes"])""" + end + run(`$(Base.julia_cmd()) --project=$dir -e "import Pkg; $code; Pkg.precompile()"`) + return dir +end + +function run_worker(impl, nthreads) + dir = ensure_env(impl) + out = joinpath(OUTDIR, "$(impl.name)_t$(nthreads).json") + kind = impl.spec == "fftw" ? "fftw" : "ffta" + cmd = `$(Base.julia_cmd()) -t $nthreads --project=$dir $(joinpath(@__DIR__, "compare3_worker.jl")) --impl $kind --out $out $PASS` + @info "running" impl.name nthreads + run(cmd) + return out +end + +mkpath(OUTDIR) +if !("--render-only" in ARGS) + for nthreads in THREADS, impl in IMPLS + run_worker(impl, nthreads) + end +end + +# --------------------------------------------------------------------------- +# table +# --------------------------------------------------------------------------- +fmt_t(t) = t < 1e-6 ? @sprintf("%.0f ns", t * 1e9) : t < 1e-3 ? @sprintf("%.2f µs", t * 1e6) : + t < 1 ? @sprintf("%.3f ms", t * 1e3) : @sprintf("%.3f s", t) +fmt_r(r) = @sprintf("%.2f×", r) +gmean(v) = exp(mean(log.(v))) +label(e) = (e["kind"] == "fft" ? "Complex" * replace(e["T"], "Float" => "F") : e["T"]) * " " * e["kind"] + +loaded = Dict{Tuple{String,Int},Any}() +for nthreads in THREADS, impl in IMPLS + f = joinpath(OUTDIR, "$(impl.name)_t$(nthreads).json") + isfile(f) || continue + d = JSON.parsefile(f) + loaded[(impl.name, nthreads)] = (meta = d["meta"], res = Dict(e["key"] => e for e in d["results"])) +end +isempty(loaded) && error("no results in $OUTDIR") +names = [i.name for i in IMPLS] +base = first(names) + +open(TABLE, "w") do io + println(io, "# FFT implementations side by side\n") + println(io, "Rendered $(now(UTC)) UTC on $(Sys.CPU_NAME) ($(Sys.ARCH)), Julia $(VERSION).\n") + println(io, "| column | implementation |") + println(io, "|:--|:--|") + for impl in IMPLS + ms = [loaded[k].meta for k in keys(loaded) if k[1] == impl.name] + isempty(ms) && continue + println(io, "| `$(impl.name)` | $(first(ms)["version"]) — `$(impl.spec)` |") + end + println(io, "\nTimes are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). ", + "`/$(base)` is the time divided by the `$(base)` time (lower is better); ", + "`vs $(REF)` is the speedup over the `$(REF)` column (higher is better). ", + "✗ = threw. A checksum mismatch against `$(base)` is flagged with ⚠.\n") + for nthreads in THREADS + cols = [n for n in names if haskey(loaded, (n, nthreads))] + isempty(cols) && continue + length(THREADS) > 1 && println(io, "\n## $nthreads thread$(nthreads > 1 ? "s" : "")\n") + keyset = String[] + for n in cols, k in keys(loaded[(n, nthreads)].res) + k in keyset || push!(keyset, k) + end + # keep the worker's order: sort by the first column that has the key + order(k) = begin + for n in cols + r = loaded[(n, nthreads)].res + haskey(r, k) && return (r[k]["shape"], r[k]["kind"], r[k]["T"], r[k]["measure"], r[k]["n"], k) + end + end + sort!(keyset; by = order) + hdr = "| case | " * join(("`$n`" for n in cols), " | ") + hdr *= " | " * join(("`$n`/`$base`" for n in cols if n != base), " | ") + hdr *= " | " * join(("`$n` vs `$REF`" for n in cols if n != REF && n != base), " | ") * " |" + println(io, hdr) + println(io, "|:--|" * "--:|"^(count(c -> true, cols) + count(!=(base), cols) + count(n -> n != REF && n != base, cols))) + stats = Dict{Any,Vector{Float64}}() # (group, col, :base|:ref) => ratios + for k in keyset + es = Dict(n => get(loaded[(n, nthreads)].res, k, nothing) for n in cols) + t(n) = (e = es[n]; e === nothing || !haskey(e, "exec_min")) ? nothing : e["exec_min"] + cell(n) = begin + e = es[n] + e === nothing && return "—" + haskey(e, "exec_min") || return "✗" + s = fmt_t(e["exec_min"]) + eb = es[base] + if n != base && eb !== nothing && haskey(eb, "norm") && haskey(e, "norm") + tol = (e["T"] == "Float32" ? 1e-3 : 1e-8) * eb["norm"] * sqrt(e["n"]) + (abs(e["norm"] - eb["norm"]) > tol || abs(e["sum_re"] - eb["sum_re"]) > tol || + abs(e["sum_im"] - eb["sum_im"]) > tol) && (s *= " ⚠") + end + s + end + row = "| $k | " * join((cell(n) for n in cols), " | ") + e1 = first(e for e in values(es) if e !== nothing) + grp = (label(e1), e1["shape"] == "1d" ? e1["class"] : e1["shape"], e1["measure"]) + for n in cols + n == base && continue + tb, tn = t(base), t(n) + if tb !== nothing && tn !== nothing + row *= " | " * fmt_r(tn / tb) + push!(get!(stats, (grp, n, :base), Float64[]), tn / tb) + else + row *= " | —" + end + end + for n in cols + (n == REF || n == base) && continue + tr, tn = t(REF), t(n) + if tr !== nothing && tn !== nothing + sp = tr / tn + row *= " | " * (abs(sp - 1) > 0.05 ? "**" * fmt_r(sp) * "**" : fmt_r(sp)) + push!(get!(stats, (grp, n, :ref), Float64[]), sp) + else + row *= " | —" + end + end + println(io, row * " |") + end + # summary + println(io, "\n### Summary ($nthreads thread$(nthreads > 1 ? "s" : ""))\n") + println(io, "Geometric means over the cases of each group; `(min–max)` in brackets.\n") + shdr = "| group | " * join(("`$n`/`$base`" for n in cols if n != base), " | ") + shdr *= " | " * join(("`$n` vs `$REF`" for n in cols if n != REF && n != base), " | ") * " |" + println(io, shdr) + println(io, "|:--|" * "--:|"^(count(!=(base), cols) + count(n -> n != REF && n != base, cols))) + groups = unique(k[1] for k in keys(stats)) + sort!(groups; by = g -> (g[3], g[1], g[2])) + for g in groups + row = "| $(g[1]) $(g[2])$(g[3] ? " (FFTW MEASURE)" : "") |" + for n in cols + n == base && continue + v = get(stats, (g, n, :base), Float64[]) + row *= isempty(v) ? " — |" : @sprintf(" %.2f× (%.2f–%.2f) |", gmean(v), minimum(v), maximum(v)) + end + for n in cols + (n == REF || n == base) && continue + v = get(stats, (g, n, :ref), Float64[]) + row *= isempty(v) ? " — |" : @sprintf(" **%.2f×** (%.2f–%.2f) |", gmean(v), minimum(v), maximum(v)) + end + println(io, row) + end + row = "| **all** |" + for n in cols + n == base && continue + v = vcat((v for (k, v) in stats if k[2] == n && k[3] == :base)...) + row *= isempty(v) ? " — |" : @sprintf(" %.2f× (%.2f–%.2f) |", gmean(v), minimum(v), maximum(v)) + end + for n in cols + (n == REF || n == base) && continue + v = vcat((v for (k, v) in stats if k[2] == n && k[3] == :ref)...) + row *= isempty(v) ? " — |" : @sprintf(" **%.2f×** (%.2f–%.2f), %d cases, %d slower by >5%% |", gmean(v), minimum(v), maximum(v), length(v), count(<(0.95), v)) + end + println(io, row) + end + # thread scaling + if length(THREADS) > 1 + println(io, "\n## Thread scaling (time at 1 thread / time at N threads)\n") + println(io, "| case | " * join(("`$n` ×$t" for n in names for t in THREADS if t > 1 && haskey(loaded, (n, t))), " | ") * " |") + println(io, "|:--|" * "--:|"^count(t -> t > 1, [t for n in names for t in THREADS if haskey(loaded, (n, t))])) + keys1 = String[] + for n in names, t in THREADS + t > 1 && haskey(loaded, (n, t)) || continue + for k in keys(loaded[(n, t)].res) + k1 = replace(k, r" \(\d+ thr\)" => "") + k1 in keys1 || push!(keys1, k1) + end + end + for k1 in keys1 + row = "| $k1 |" + any = false + for n in names, t in THREADS + t > 1 && haskey(loaded, (n, t)) || continue + r1 = haskey(loaded, (n, 1)) ? get(loaded[(n, 1)].res, k1, nothing) : nothing + rt = get(loaded[(n, t)].res, k1 * " ($t thr)", nothing) + if r1 !== nothing && rt !== nothing && haskey(r1, "exec_min") && haskey(rt, "exec_min") + row *= " " * fmt_r(r1["exec_min"] / rt["exec_min"]) * " |"; any = true + else + row *= " — |" + end + end + any && println(io, row) + end + end +end +println("wrote $TABLE") +print(read(TABLE, String)) diff --git a/benchmark/compare3_worker.jl b/benchmark/compare3_worker.jl new file mode 100644 index 0000000..11f93fa --- /dev/null +++ b/benchmark/compare3_worker.jl @@ -0,0 +1,128 @@ +#!/usr/bin/env julia +# One implementation of the `compare3.jl` sweep, run in its own process and +# environment (so that FFTW.jl and FFTA.jl never share a process and dispatch +# is whatever the user of that package would get). +# +# julia -t N --project=ENV compare3_worker.jl --impl fftw|ffta --out FILE.json [case options] +# +# Case options are those of `compare3.jl` (--only, --kinds, --maxlog2, --sizes, +# --seconds, --no-measure). Julia's thread count (-t) is the plan thread count. +using Statistics, LinearAlgebra, Random, Dates +using JSON +include(joinpath(@__DIR__, "cases.jl")) + +function getopt(flag, default) + i = findfirst(==(flag), ARGS) + i === nothing ? default : ARGS[i + 1] +end +const IMPL = getopt("--impl", "ffta") +const OUTFILE = getopt("--out", "compare3_$(IMPL).json") +const ONLY = split(getopt("--only", "1d,nd,batched,threads"), ",") +const KINDS = Tuple(Symbol.(split(getopt("--kinds", "fft,rfft"), ","))) +const SIZES = let v = getopt("--sizes", ""); isempty(v) ? Int[] : parse.(Int, split(v, ",")) end +const MAXLOG2 = parse(Int, getopt("--maxlog2", "22")) +const SECONDS = parse(Float64, getopt("--seconds", "0.5")) +const MEASURE = !("--no-measure" in ARGS) +const NTHREADS = Threads.nthreads() + +if IMPL == "fftw" + using FFTW + FFTW.set_num_threads(NTHREADS) + mkplan(kind, x, dims; measure) = kind === :fft ? + plan_fft(x, dims; flags = measure ? FFTW.MEASURE : FFTW.ESTIMATE) : + plan_rfft(x, dims; flags = measure ? FFTW.MEASURE : FFTW.ESTIMATE) + const VERSION_STR = "FFTW.jl $(pkgversion(FFTW)) / FFTW $(FFTW.version) ($(FFTW.get_provider()))" +else + using FFTA + # `num_threads` is the plan keyword of the threaded FFTA; older versions + # accept and ignore unknown keywords. + function mkplan(kind, x, dims; measure) + try + kind === :fft ? plan_fft(x, dims; num_threads = NTHREADS) : plan_rfft(x, dims; num_threads = NTHREADS) + catch err + # FFTA 0.3.1 accepts a vector region but not a tuple + (err isa MethodError && dims isa Tuple) || rethrow() + kind === :fft ? plan_fft(x, collect(dims); num_threads = NTHREADS) : plan_rfft(x, collect(dims); num_threads = NTHREADS) + end + end + const VERSION_STR = let sha = try + strip(read(`git -C $(pkgdir(FFTA)) rev-parse --short HEAD`, String)) + catch + "" + end + "FFTA.jl $(pkgversion(FFTA))" * (isempty(sha) ? "" : " @ $sha") + end +end + +function timeit(f; seconds = SECONDS) + f(); f() + t0 = time_ns(); f(); t1 = time_ns() + evals = max(1, ceil(Int, 20_000 / max(t1 - t0, 1))) + times = Float64[] + deadline = time_ns() + seconds * 1e9 + while time_ns() < deadline || length(times) < 5 + ts = time_ns() + for _ in 1:evals + f() + end + push!(times, (time_ns() - ts) / evals) + length(times) >= 100_000 && break + end + return (min = minimum(times) * 1e-9, median = median(times) * 1e-9, samples = length(times)) +end + +# deterministic input so that every implementation transforms the same data +function input(c) + rng = Xoshiro(0x5eed) + c.kind === :fft ? randn(rng, Complex{c.T}, c.sz) : randn(rng, c.T, c.sz) +end + +const RESULTS = Dict{String,Any}[] +const META = Dict("impl" => IMPL, "version" => VERSION_STR, "julia" => string(VERSION), + "threads" => NTHREADS, "arch" => String(Sys.ARCH), "cpu" => Sys.CPU_NAME, + "date" => string(now(UTC)), "seconds" => SECONDS) +function flush_results(complete) + open(OUTFILE, "w") do io + JSON.print(io, Dict("meta" => META, "complete" => complete, "results" => RESULTS), 1) + end +end + +cases = case_list(; only = ONLY, kinds = KINDS, maxlog2 = MAXLOG2, sizes = SIZES, + nthreads = NTHREADS, measure = MEASURE && IMPL == "fftw") +println("== compare3 worker: $VERSION_STR, $(length(cases)) cases, $NTHREADS threads") +for c in cases + entry = Dict{String,Any}("key" => casekey(c), "kind" => String(c.kind), "T" => string(c.T), + "size" => collect(c.sz), "dims" => collect(c.dims), "shape" => c.shape, + "class" => c.class, "nthreads" => c.nthreads, "measure" => c.measure, + "n" => prod(c.sz[d] for d in c.dims)) + x = input(c) + try + p = mkplan(c.kind, x, c.dims; measure = c.measure) + y = p * x + # checksum (compared against the reference implementation by the driver) + entry["norm"] = norm(y); entry["sum_re"] = real(sum(y)); entry["sum_im"] = imag(sum(y)) + c.measure || (entry["plan_min"] = timeit(() -> mkplan(c.kind, x, c.dims; measure = false)).min) + has_mul = try + mul!(y, p, x); true + catch err + err isa MethodError || rethrow(); false + end + if has_mul + entry["exec_min"] = timeit(() -> mul!(y, p, x)).min + entry["exec_alloc"] = @allocated mul!(y, p, x) + entry["api"] = "mul!" + else + entry["exec_min"] = timeit(() -> p * x).min + entry["exec_alloc"] = @allocated p * x + entry["api"] = "*" + end + catch err + entry["error"] = sprint(showerror, err)[1:min(end, 200)] + end + push!(RESULTS, entry); flush_results(false) + println(rpad(entry["key"], 52), haskey(entry, "exec_min") ? + string(round(entry["exec_min"] * 1e6; digits = 2), " us") : "✗ " * entry["error"][1:min(end, 60)]) + flush(stdout) +end +flush_results(true) +println("wrote $(length(RESULTS)) results to $OUTFILE") diff --git a/benchmark/suite.jl b/benchmark/suite.jl index 30c62d1..aa75e49 100644 --- a/benchmark/suite.jl +++ b/benchmark/suite.jl @@ -100,48 +100,9 @@ let x = randn(ComplexF64, 8), r = randn(Float64, 8) end # --------------------------------------------------------------------------- -# Size classes +# Size classes (shared with compare3.jl) # --------------------------------------------------------------------------- -function size_classes(maxlog2) - nmax = 1 << maxlog2 - pow2 = [1 << k for k in 3:maxlog2] - # 2^a 3^b 5^c 7^d, not powers of two, spread log-uniformly - smooth_all = Int[] - for a in 0:maxlog2, b in 0:14, c in 0:9, d in 0:8 - n = 2^a * 3^b * 5^c * 7^d - (n <= nmax && n >= 8 && !ispow2(n)) && push!(smooth_all, n) - end - sort!(unique!(smooth_all)) - smooth = Int[] - for t in exp.(range(log(12), log(nmax), length = 18)) - push!(smooth, smooth_all[argmin(abs.(log.(smooth_all) .- log(t)))]) - end - # explicitly include some "classic" smooth sizes - for n in (12, 60, 120, 360, 720, 1000, 1000_000) - n <= nmax && push!(smooth, n) - end - sort!(unique!(smooth)) - # primes: below (DFT path) and above (Bluestein path) the cutoff of 73 - prime = Int[] - for t in exp.(range(log(7), log(nmax), length = 16)) - push!(prime, nextprime(round(Int, t))) - end - # straddle the DFT/Bluestein crossover: the O(n²) leaf is used below the - # cutoff (73 originally, 29 since the twiddle-table work), so sample the - # band 23–46 as well as 61–79 - for n in (23, 29, 31, 37, 43, 61, 71, 73, 79) - push!(prime, n) - end - filter!(<=(nmax), prime); sort!(unique!(prime)) - # awkward: (prime > cutoff) × small factor - awk = Int[] - for p in (101, 1009, 4099, 16411, 65537, 262147), f in (2, 3, 4, 6, 16) - n = p * f - n <= nmax && push!(awk, n) - end - sort!(unique!(awk)) - return (pow2 = pow2, smooth = smooth, prime = prime, awkward = awk) -end +include(joinpath(@__DIR__, "cases.jl")) const CLASSES = size_classes(MAXLOG2) @@ -187,12 +148,7 @@ function record!(entry; complete::Bool = false) end end -function class_of(n) - for (k, v) in pairs(CLASSES) - n in v && return String(k) - end - return "other" -end +class_of(n) = class_of(CLASSES, n) sizestr(sz) = join(sz, "x") From f7190cc21f4f83bc774e55fc2bb5ca41349770a7 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:05:40 +0000 Subject: [PATCH 02/21] compare3: --classes to restrict the 1D size classes, --skip-existing to reuse finished columns --- benchmark/cases.jl | 16 +++++++++------- benchmark/compare3.jl | 14 ++++++++++---- benchmark/compare3_worker.jl | 7 ++++--- 3 files changed, 23 insertions(+), 14 deletions(-) diff --git a/benchmark/cases.jl b/benchmark/cases.jl index 8eac367..69e98aa 100644 --- a/benchmark/cases.jl +++ b/benchmark/cases.jl @@ -56,22 +56,24 @@ end """ case_list(; only, kinds, maxlog2, sizes, nthreads, measure) -> Vector{NamedTuple} -The sweep of `suite.jl`: 1D classes × {Float64, Float32} × {fft, rfft}, a +The sweep of `suite.jl`: 1D classes (restricted with `classes`) × {Float64, Float32} × {fft, rfft}, a FFTW-`MEASURE` column for 1D pow2 ComplexF64, 2D/3D, batched `dims`, and the threaded subset. `nthreads > 1` selects the threaded subset only when `only` contains `"threads"`; the other sections are always emitted with `nthreads`. """ function case_list(; only = ("1d", "nd", "batched", "threads"), kinds = (:fft, :rfft), - maxlog2 = 22, sizes = Int[], nthreads = 1, measure = true) - classes = size_classes(maxlog2) + maxlog2 = 22, sizes = Int[], nthreads = 1, measure = true, + classes = ("pow2", "smooth", "prime", "awkward")) + sizes_by_class = size_classes(maxlog2) nmax = 1 << maxlog2 cases = NamedTuple[] add!(kind, T, sz, dims, shape; measure = false, thr = nthreads) = kind in kinds && push!(cases, (kind = kind, T = T, sz = sz, dims = dims, shape = shape, nthreads = thr, measure = measure, - class = length(sz) == 1 ? class_of(classes, sz[1]) : "nd")) + class = length(sz) == 1 ? class_of(sizes_by_class, sz[1]) : "nd")) if "1d" in only - for cls in (:pow2, :smooth, :prime, :awkward), n in classes[cls] + for cls in (:pow2, :smooth, :prime, :awkward), n in sizes_by_class[cls] + String(cls) in classes || continue isempty(sizes) || n in sizes || continue for T in (Float64, Float32) add!(:fft, T, (n,), 1, "1d") @@ -79,7 +81,7 @@ function case_list(; only = ("1d", "nd", "batched", "threads"), kinds = (:fft, : end end if measure - for n in classes.pow2 + for n in sizes_by_class.pow2 isempty(sizes) || n in sizes || continue add!(:fft, Float64, (n,), 1, "1d"; measure = true) end @@ -115,7 +117,7 @@ function case_list(; only = ("1d", "nd", "batched", "threads"), kinds = (:fft, : end end if "threads" in only && nthreads > 1 - for n in filter(n -> n >= 1 << 16, classes.pow2) + for n in filter(n -> n >= 1 << 16, sizes_by_class.pow2) add!(:fft, Float64, (n,), 1, "1d") end for n in filter(n -> n * n <= nmax && n >= 256, [256, 512, 1024, 2048]) diff --git a/benchmark/compare3.jl b/benchmark/compare3.jl index 7fba606..9582351 100644 --- a/benchmark/compare3.jl +++ b/benchmark/compare3.jl @@ -10,8 +10,9 @@ of each column over a reference column. julia --project=. compare3.jl [--impl NAME=SPEC ...] [--ref NAME] [--threads 1,4,16] [--out DIR] [--table FILE.md] [--only 1d,nd,batched,threads] [--kinds fft,rfft] + [--classes pow2,smooth,prime,awkward] [--maxlog2 K] [--seconds S] [--sizes a,b,c] - [--no-measure] [--quick] [--render-only] + [--no-measure] [--quick] [--render-only] [--skip-existing] `SPEC` is `fftw` (FFTW.jl from the registry), `@VERSION` (FFTA from the registry, e.g. `@0.3.1`), or a path to an FFTA checkout / worktree. The @@ -27,7 +28,8 @@ run is therefore --impl new=/path/to/experiment --ref int Environments are created under `envs/NAME/` (git-ignored) and re-used; delete -one to rebuild it. Per-run JSON files land in `--out` (default +one to rebuild it. `--skip-existing` keeps a column whose complete JSON file +is already in `--out` (e.g. to add one column to a finished run). Per-run JSON files land in `--out` (default `compare3_results/`) as `NAME_tN.json`; `--render-only` re-renders the table from them without benchmarking. =# @@ -59,7 +61,7 @@ const REF = let r = getopt("--ref", "") end const ENVDIR = joinpath(@__DIR__, "envs") const PASS = String[] # case options passed through to the workers -for flag in ("--only", "--kinds", "--sizes") +for flag in ("--only", "--kinds", "--sizes", "--classes") v = getopt(flag, ""); isempty(v) || append!(PASS, [flag, v]) end append!(PASS, ["--maxlog2", getopt("--maxlog2", QUICK ? "14" : "22")]) @@ -88,8 +90,12 @@ function ensure_env(impl) end function run_worker(impl, nthreads) - dir = ensure_env(impl) out = joinpath(OUTDIR, "$(impl.name)_t$(nthreads).json") + if "--skip-existing" in ARGS && isfile(out) && get(JSON.parsefile(out), "complete", false) + @info "keeping existing results" impl.name nthreads out + return out + end + dir = ensure_env(impl) kind = impl.spec == "fftw" ? "fftw" : "ffta" cmd = `$(Base.julia_cmd()) -t $nthreads --project=$dir $(joinpath(@__DIR__, "compare3_worker.jl")) --impl $kind --out $out $PASS` @info "running" impl.name nthreads diff --git a/benchmark/compare3_worker.jl b/benchmark/compare3_worker.jl index 11f93fa..14c76cc 100644 --- a/benchmark/compare3_worker.jl +++ b/benchmark/compare3_worker.jl @@ -5,8 +5,8 @@ # # julia -t N --project=ENV compare3_worker.jl --impl fftw|ffta --out FILE.json [case options] # -# Case options are those of `compare3.jl` (--only, --kinds, --maxlog2, --sizes, -# --seconds, --no-measure). Julia's thread count (-t) is the plan thread count. +# Case options are those of `compare3.jl` (--only, --kinds, --classes, --maxlog2, +# --sizes, --seconds, --no-measure). Julia's thread count (-t) is the plan thread count. using Statistics, LinearAlgebra, Random, Dates using JSON include(joinpath(@__DIR__, "cases.jl")) @@ -23,6 +23,7 @@ const SIZES = let v = getopt("--sizes", ""); isempty(v) ? Int[] : parse.(Int, const MAXLOG2 = parse(Int, getopt("--maxlog2", "22")) const SECONDS = parse(Float64, getopt("--seconds", "0.5")) const MEASURE = !("--no-measure" in ARGS) +const CLASSES = split(getopt("--classes", "pow2,smooth,prime,awkward"), ",") const NTHREADS = Threads.nthreads() if IMPL == "fftw" @@ -88,7 +89,7 @@ function flush_results(complete) end cases = case_list(; only = ONLY, kinds = KINDS, maxlog2 = MAXLOG2, sizes = SIZES, - nthreads = NTHREADS, measure = MEASURE && IMPL == "fftw") + nthreads = NTHREADS, measure = MEASURE && IMPL == "fftw", classes = CLASSES) println("== compare3 worker: $VERSION_STR, $(length(cases)) cases, $NTHREADS threads") for c in cases entry = Dict{String,Any}("key" => casekey(c), "kind" => String(c.kind), "T" => string(c.T), From b410154666abec055a6cff6b74a2561b550c9594 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:05:40 +0000 Subject: [PATCH 03/21] benchmark: kernel_stages.jl, per-stage time breakdown inside the kernels Re-runs the power-of-two, composite and Bluestein kernels with stages removed (leaves / butterfly passes / twiddle pass / sub-transforms) so the stage times add up to the total, next to a memory-pass floor and FFTW. --- benchmark/kernel_stages.jl | 250 +++++++++++++++++++++++++++++++++++++ 1 file changed, 250 insertions(+) create mode 100644 benchmark/kernel_stages.jl diff --git a/benchmark/kernel_stages.jl b/benchmark/kernel_stages.jl new file mode 100644 index 0000000..935b40a --- /dev/null +++ b/benchmark/kernel_stages.jl @@ -0,0 +1,250 @@ +#!/usr/bin/env julia +#= +Where does the time go *inside* FFTA's kernels? + +For a few representative sizes the planned execution is split into its +stages by re-running the kernel with stages left out (the recursion is +copied here with the butterfly pass or the leaves removed), so that the +stage times add up to the measured total. Each stage is put next to the +time a plain memory pass over the same data takes (a `copyto!` of the +array, measured in the same process), which is the bound a stage cannot +beat, and next to FFTW's ESTIMATE/MEASURE totals. + + julia --project=. -t 1 kernel_stages.jl [--sizes 1024,16384,1048576] [--seconds 0.3] + +Reads FFTA from the parent directory (`Pkg.develop`), like `suite.jl`. +=# +import Pkg +Pkg.develop(path = joinpath(@__DIR__, "..")) +Pkg.instantiate() +using FFTA, FFTW, Statistics, Printf, LinearAlgebra +using FFTA: fft_pow2_radix4!, _pow2_codelet!, CODELET_MAX, pow2_twiddles, direction_sign, + FFT_FORWARD, CallGraph, fft_kernel!, COMPOSITE_FFT, BLUESTEIN, POW2RADIX4_FFT + +function getopt(flag, default) + i = findfirst(==(flag), ARGS) + i === nothing ? default : ARGS[i + 1] +end +const SECONDS = parse(Float64, getopt("--seconds", "0.3")) +const SIZES = parse.(Int, split(getopt("--sizes", "1024,16384,262144,4194304,1000,46305,1000000,65537"), ",")) +const T = ComplexF64 + +function timeit(f; seconds = SECONDS) + f(); f() + t0 = time_ns(); f(); t1 = time_ns() + evals = max(1, ceil(Int, 20_000 / max(t1 - t0, 1))) + best = Inf + deadline = time_ns() + seconds * 1e9 + while time_ns() < deadline + ts = time_ns() + for _ in 1:evals; f(); end + best = min(best, (time_ns() - ts) / evals) + end + return best * 1e-9 +end +fmt(t) = t < 1e-6 ? @sprintf("%.0f ns", t * 1e9) : t < 1e-3 ? @sprintf("%.2f µs", t * 1e6) : @sprintf("%.3f ms", t * 1e3) +pct(t, tot) = @sprintf("%.0f%%", 100t / tot) + +# --------------------------------------------------------------------------- +# radix-4 recursion with stages removed (mirrors `fft_pow2_radix4!`) +# --------------------------------------------------------------------------- +# leaves only: the recursion down to the codelet size, no butterfly passes +function pow2_leaves!(out, in, N, so, sto, si, sti, d, tw, toff) + if N <= CODELET_MAX + _pow2_codelet!(out, in, N, so, sto, si, sti, d) && return + fft_pow2_radix4!(out, in, N, so, sto, si, sti, d, tw, toff); return + end + m = N ÷ 4; tn = toff + 3m + pow2_leaves!(out, in, m, so, sto, si, sti * 4, d, tw, tn) + pow2_leaves!(out, in, m, so + m*sto, sto, si + sti, sti * 4, d, tw, tn) + pow2_leaves!(out, in, m, so + 2*m*sto, sto, si + 2*sti, sti * 4, d, tw, tn) + pow2_leaves!(out, in, m, so + 3*m*sto, sto, si + 3*sti, sti * 4, d, tw, tn) +end +# one butterfly pass of the level of size N (data already in `out`) +function pow2_pass!(out, N, so, sto, d, tw, toff) + m = N ÷ 4 + minusi = -direction_sign(d) * im + @inbounds for k in 0:m-1 + wkoe = tw[toff + 3k + 1]; wkeo = tw[toff + 3k + 2]; wkoo = tw[toff + 3k + 3] + kee = so + k * sto; koe = so + (k + m) * sto; keo = so + (k + 2m) * sto; koo = so + (k + 3m) * sto + y_kee, y_koe, y_keo, y_koo = out[kee], out[koe], out[keo], out[koo] + t_koe = y_koe * wkoe; t_keo = y_keo * wkeo; t_koo = y_koo * wkoo + a = y_kee + t_keo; b = y_kee - t_keo + c = t_koe + t_koo; e = -(t_koe - t_koo) * minusi + out[kee] = a + c; out[koe] = b + e; out[keo] = a - c; out[koo] = b - e + end +end +# all butterfly passes of one recursion level (the level whose blocks have size N) +function pow2_level!(out, N, level_size, so, sto, d, tw, toff) + if N == level_size + pow2_pass!(out, N, so, sto, d, tw, toff); return + end + m = N ÷ 4; tn = toff + 3m + for q in 0:3 + pow2_level!(out, m, level_size, so + q*m*sto, sto, d, tw, tn) + end +end +# the same pass with the arithmetic removed: 4 strided read streams, 4 write streams, 3 twiddle reads +function pow2_pass_mem!(out, N, so, sto, d, tw, toff) + m = N ÷ 4 + @inbounds for k in 0:m-1 + wkoe = tw[toff + 3k + 1]; wkeo = tw[toff + 3k + 2]; wkoo = tw[toff + 3k + 3] + kee = so + k * sto; koe = so + (k + m) * sto; keo = so + (k + 2m) * sto; koo = so + (k + 3m) * sto + y_kee, y_koe, y_keo, y_koo = out[kee], out[koe], out[keo], out[koo] + out[kee] = y_kee + wkoe; out[koe] = y_koe + wkeo; out[keo] = y_keo + wkoo; out[koo] = y_koo + end +end +function pow2_level_mem!(out, N, level_size, so, sto, d, tw, toff) + if N == level_size + pow2_pass_mem!(out, N, so, sto, d, tw, toff); return + end + m = N ÷ 4; tn = toff + 3m + for q in 0:3 + pow2_level_mem!(out, m, level_size, so + q*m*sto, sto, d, tw, tn) + end +end + +function stages_pow2(N, io) + x = randn(T, N); y = similar(x); y2 = similar(x) + d = FFT_FORWARD + tw = pow2_twiddles(T, N, d) + t_total = timeit(() -> fft_pow2_radix4!(y, x, N, 1, 1, 1, 1, d, tw, 0)) + t_leaves = timeit(() -> pow2_leaves!(y, x, N, 1, 1, 1, 1, d, tw, 0)) + leaf = let l = N + while l > CODELET_MAX; l ÷= 4; end + l # (a fresh binding: a reassigned local would be boxed in the closures below) + end + levels = Int[]; M = N + while M > leaf; push!(levels, M); M ÷= 4; end + t_copy = timeit(() -> copyto!(y2, y)) + # contiguous codelets of the leaf size on the same data (leaf work without the strided reads) + nleaf = N ÷ leaf + t_leaf_contig = timeit(() -> (for b in 0:nleaf-1; fft_pow2_radix4!(y, x, leaf, 1 + b*leaf, 1, 1 + b*leaf, 1, d, tw, 0); end)) + pw_e = plan_fft(x; flags = FFTW.ESTIMATE); pw_m = plan_fft(x; flags = FFTW.MEASURE) + t_fftw_e = timeit(() -> mul!(y2, pw_e, x)); t_fftw_m = timeit(() -> mul!(y2, pw_m, x)) + println(io, "\n### n = $N = 2^$(round(Int, log2(N))) (radix-4 recursion, $(length(levels)) butterfly levels, $nleaf leaves of $leaf points)\n") + println(io, "| stage | time | share of FFTA total | time of one `copyto!` of the array: $(fmt(t_copy)) |") + println(io, "|:--|--:|--:|--:|") + @printf(io, "| FFTA total | %s | 100%% | %.1f× copy |\n", fmt(t_total), t_total / t_copy) + @printf(io, "| leaves: %d × %d-point codelet, input stride %d | %s | %s | %.1f× copy |\n", nleaf, leaf, N ÷ leaf, fmt(t_leaves), pct(t_leaves, t_total), t_leaves / t_copy) + @printf(io, "| (same codelets on contiguous input) | %s | %s | strided-load penalty %.2f× |\n", fmt(t_leaf_contig), pct(t_leaf_contig, t_total), t_leaves / t_leaf_contig) + sum_levels = 0.0 + for L in levels + t_lvl = timeit(() -> pow2_level!(y, N, L, 1, 1, d, tw, 0)) + t_mem = timeit(() -> pow2_level_mem!(y, N, L, 1, 1, d, tw, 0)) + sum_levels += t_lvl + @printf(io, "| butterfly pass, blocks of %d (stride %d between the 4 legs) | %s | %s | %.1f× copy; memory-only version of the pass %s |\n", + L, L ÷ 4, fmt(t_lvl), pct(t_lvl, t_total), t_lvl / t_copy, fmt(t_mem)) + end + @printf(io, "| leaves + passes (sum of the rows) | %s | %s | recursion/dispatch overhead = total − sum = %s |\n", fmt(t_leaves + sum_levels), pct(t_leaves + sum_levels, t_total), fmt(t_total - t_leaves - sum_levels)) + @printf(io, "| FFTW ESTIMATE / MEASURE | %s / %s | %s / %s | %.1f× / %.1f× copy |\n", fmt(t_fftw_e), fmt(t_fftw_m), pct(t_fftw_e, t_total), pct(t_fftw_m, t_total), t_fftw_e / t_copy, t_fftw_m / t_copy) +end + +# --------------------------------------------------------------------------- +# composite N = N1·N2 (mirrors `fft_composite!`) +# --------------------------------------------------------------------------- +function composite_stages!(out, in, g, idx, d; right = true, twiddle = true, left = true) + root = g[idx]; li = idx + root.left; ri = idx + root.right + N1 = g[li].sz; N2 = g[ri].sz + tmp = g.workspace[idx]; tw = g.twiddles[idx] + for j1 in 0:N1-1 + right && fft_kernel!(tmp, in, 1 + N2*j1, 1 + j1*root.s_in, d, g[ri].type, g, ri) + if twiddle && j1 > 0 + base = (j1 - 1) * (N2 - 1); R = 1 + N2*j1 + @inbounds for k2 in 1:N2-1 + tmp[R + k2] *= tw[base + k2] + end + end + end + left && for k2 in 0:N2-1 + fft_kernel!(out, tmp, 1 + k2*root.s_out, 1 + k2, d, g[li].type, g, li) + end +end +function stages_composite(N, io) + x = randn(T, N); y = similar(x); y2 = similar(x) + d = FFT_FORWARD + g = CallGraph{T}(N, FFTA.DEFAULT_BLUESTEIN_CUTOFF, d) + g[1].type === COMPOSITE_FFT || return + root = g[1]; N1 = g[1 + root.left].sz; N2 = g[1 + root.right].sz + t_total = timeit(() -> fft_kernel!(y, x, 1, 1, d, g[1].type, g, 1)) + t_right = timeit(() -> composite_stages!(y, x, g, 1, d; twiddle = false, left = false)) + t_tw = timeit(() -> composite_stages!(y, x, g, 1, d; right = false, left = false)) + t_left = timeit(() -> composite_stages!(y, x, g, 1, d; right = false, twiddle = false)) + t_copy = timeit(() -> copyto!(y2, y)) + pw_e = plan_fft(x; flags = FFTW.ESTIMATE); pw_m = plan_fft(x; flags = FFTW.MEASURE) + t_fftw_e = timeit(() -> mul!(y2, pw_e, x)); t_fftw_m = timeit(() -> mul!(y2, pw_m, x)) + desc(i) = string(g[i].sz, " ", g[i].type) + println(io, "\n### n = $N = $N1 × $N2 (composite step: right = $(desc(1 + root.right)), left = $(desc(1 + root.left)))\n") + println(io, "| stage | time | share of FFTA total | time of one `copyto!` of the array: $(fmt(t_copy)) |") + println(io, "|:--|--:|--:|--:|") + @printf(io, "| FFTA total | %s | 100%% | %.1f× copy |\n", fmt(t_total), t_total / t_copy) + @printf(io, "| %d right sub-transforms of %d (input stride %d) | %s | %s | %.1f× copy |\n", N1, N2, root.s_in * N1, fmt(t_right), pct(t_right, t_total), t_right / t_copy) + @printf(io, "| twiddle multiply pass | %s | %s | %.1f× copy |\n", fmt(t_tw), pct(t_tw, t_total), t_tw / t_copy) + @printf(io, "| %d left sub-transforms of %d (output stride %d) | %s | %s | %.1f× copy |\n", N2, N1, N2 * root.s_out, fmt(t_left), pct(t_left, t_total), t_left / t_copy) + @printf(io, "| sum of the rows | %s | %s | overhead = %s |\n", fmt(t_right + t_tw + t_left), pct(t_right + t_tw + t_left, t_total), fmt(t_total - t_right - t_tw - t_left)) + @printf(io, "| FFTW ESTIMATE / MEASURE | %s / %s | %s / %s | %.1f× / %.1f× copy |\n", fmt(t_fftw_e), fmt(t_fftw_m), pct(t_fftw_e, t_total), pct(t_fftw_m, t_total), t_fftw_e / t_copy, t_fftw_m / t_copy) +end + +# --------------------------------------------------------------------------- +# Bluestein (mirrors `fft_bluestein!`) +# --------------------------------------------------------------------------- +function blue_fill!(a, x, chirp, N, pad_len) + @inbounds for i in 1:N + a[i] = x[i] * conj(chirp[i]) + end + @inbounds for i in N+1:pad_len + a[i] = zero(eltype(a)) + end +end +function blue_pointwise!(tmp, chirp_fft, pad_len) + @inbounds for i in 1:pad_len + tmp[i] = conj(tmp[i] * chirp_fft[i]) + end +end +function blue_out!(y, a, chirp, N) + @inbounds for i in 1:N + y[i] = conj(chirp[i]) * conj(a[i]) + end +end +function stages_bluestein(N, io) + x = randn(T, N); y = similar(x); y2 = similar(x) + d = FFT_FORWARD + g = CallGraph{T}(N, FFTA.DEFAULT_BLUESTEIN_CUTOFF, d) + g[1].type === BLUESTEIN || return + sc = g.bluestein[1] + (; pad_len, chirp, chirp_fft, a, tmp, graph) = sc + gt = graph[1].type + t_total = timeit(() -> fft_kernel!(y, x, 1, 1, d, g[1].type, g, 1)) + t_fill = timeit(() -> blue_fill!(a, x, chirp, N, pad_len)) + t_fft1 = timeit(() -> fft_kernel!(tmp, a, 1, 1, FFT_FORWARD, gt, graph, 1)) + t_pw = timeit(() -> blue_pointwise!(tmp, chirp_fft, pad_len)) + t_fft2 = timeit(() -> fft_kernel!(a, tmp, 1, 1, FFT_FORWARD, gt, graph, 1)) + t_out = timeit(() -> blue_out!(y, a, chirp, N)) + t_copy = timeit(() -> copyto!(y2, y)) + pw_e = plan_fft(x; flags = FFTW.ESTIMATE); pw_m = plan_fft(x; flags = FFTW.MEASURE) + t_fftw_e = timeit(() -> mul!(y2, pw_e, x)); t_fftw_m = timeit(() -> mul!(y2, pw_m, x)) + println(io, "\n### n = $N (Bluestein, padded to $pad_len)\n") + println(io, "| stage | time | share of FFTA total | time of one `copyto!` of the array: $(fmt(t_copy)) |") + println(io, "|:--|--:|--:|--:|") + @printf(io, "| FFTA total | %s | 100%% | %.1f× copy |\n", fmt(t_total), t_total / t_copy) + @printf(io, "| chirp multiply + zero pad | %s | %s | |\n", fmt(t_fill), pct(t_fill, t_total)) + @printf(io, "| forward FFT of %d | %s | %s | |\n", pad_len, fmt(t_fft1), pct(t_fft1, t_total)) + @printf(io, "| pointwise product | %s | %s | |\n", fmt(t_pw), pct(t_pw, t_total)) + @printf(io, "| second FFT of %d | %s | %s | |\n", pad_len, fmt(t_fft2), pct(t_fft2, t_total)) + @printf(io, "| output chirp multiply | %s | %s | |\n", fmt(t_out), pct(t_out, t_total)) + @printf(io, "| FFTW ESTIMATE / MEASURE | %s / %s | %s / %s | |\n", fmt(t_fftw_e), fmt(t_fftw_m), pct(t_fftw_e, t_total), pct(t_fftw_m, t_total)) +end + +io = stdout +println(io, "# Kernel stage breakdown (ComplexF64, single thread, $(Sys.CPU_NAME), Julia $(VERSION))") +println(io, "\nStage times are minimum times of the kernel re-run with the other stages removed; `copy` is one `copyto!` of the array (the memory-traffic floor of a single pass).") +for N in SIZES + if ispow2(N) + stages_pow2(N, io) + elseif FFTA.Primes.isprime(N) + stages_bluestein(N, io) + else + stages_composite(N, io) + end + flush(io) +end From 564e6447e853e73b8a32300a347c03de2da172e8 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:16:00 +0000 Subject: [PATCH 04/21] benchmark: compare3 results, Polyester @batch vs integration/all (aarch64, 1/4/16 threads) --- .../compare3/aarch64/polyester/COMPARE3.md | 572 ++++ .../compare3/aarch64/polyester/fftw_t1.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/fftw_t16.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/fftw_t4.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/int_t1.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/int_t16.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/int_t4.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/poly_t1.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/poly_t16.json | 2827 +++++++++++++++++ .../compare3/aarch64/polyester/poly_t4.json | 2827 +++++++++++++++++ 10 files changed, 26015 insertions(+) create mode 100644 benchmark/compare3/aarch64/polyester/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/polyester/fftw_t1.json create mode 100644 benchmark/compare3/aarch64/polyester/fftw_t16.json create mode 100644 benchmark/compare3/aarch64/polyester/fftw_t4.json create mode 100644 benchmark/compare3/aarch64/polyester/int_t1.json create mode 100644 benchmark/compare3/aarch64/polyester/int_t16.json create mode 100644 benchmark/compare3/aarch64/polyester/int_t4.json create mode 100644 benchmark/compare3/aarch64/polyester/poly_t1.json create mode 100644 benchmark/compare3/aarch64/polyester/poly_t16.json create mode 100644 benchmark/compare3/aarch64/polyester/poly_t4.json diff --git a/benchmark/compare3/aarch64/polyester/COMPARE3.md b/benchmark/compare3/aarch64/polyester/COMPARE3.md new file mode 100644 index 0000000..4d1cad9 --- /dev/null +++ b/benchmark/compare3/aarch64/polyester/COMPARE3.md @@ -0,0 +1,572 @@ +# FFT implementations side by side + +Rendered 2026-08-30T11:15:03.789 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `poly` | FFTA.jl 0.3.1 @ 94ab080 — `FFTA-poly` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + + +## 1 thread + +| case | `fftw` | `int` | `poly` | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 | 145 ns | 696 ns | 713 ns | 4.79× | 4.91× | 0.98× | +| fft Float32 16×16 dims=1,2 | 569 ns | 2.48 µs | 2.50 µs | 4.35× | 4.40× | 0.99× | +| fft Float32 32×32 dims=1,2 | 2.69 µs | 10.72 µs | 10.72 µs | 3.99× | 3.99× | 1.00× | +| fft Float32 64×64 dims=1,2 | 12.38 µs | 48.76 µs | 48.96 µs | 3.94× | 3.95× | 1.00× | +| fft Float32 128×128 dims=1,2 | 60.76 µs | 250.32 µs | 249.32 µs | 4.12× | 4.10× | 1.00× | +| fft Float32 256×256 dims=1,2 | 739.57 µs | 1.168 ms | 1.171 ms | 1.58× | 1.58× | 1.00× | +| fft Float32 512×512 dims=1,2 | 5.924 ms | 7.105 ms | 7.212 ms | 1.20× | 1.22× | 0.99× | +| fft Float32 1024×1024 dims=1,2 | 26.301 ms | 34.936 ms | 35.220 ms | 1.33× | 1.34× | 0.99× | +| fft Float32 2048×2048 dims=1,2 | 138.018 ms | 159.216 ms | 166.152 ms | 1.15× | 1.20× | 0.96× | +| fft Float64 8×8 dims=1,2 | 174 ns | 715 ns | 731 ns | 4.12× | 4.21× | 0.98× | +| fft Float64 16×16 dims=1,2 | 822 ns | 2.53 µs | 2.58 µs | 3.08× | 3.13× | 0.98× | +| fft Float64 32×32 dims=1,2 | 4.13 µs | 11.36 µs | 11.36 µs | 2.75× | 2.75× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 52.96 µs | 53.24 µs | 2.58× | 2.59× | 0.99× | +| fft Float64 128×128 dims=1,2 | 112.72 µs | 265.76 µs | 267.08 µs | 2.36× | 2.37× | 1.00× | +| fft Float64 127×257 dims=1,2 | 1.800 ms | 4.070 ms | 4.074 ms | 2.26× | 2.26× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 3.687 ms | 3.814 ms | 3.811 ms | 1.03× | 1.03× | 1.00× | +| fft Float64 64×1009 dims=1,2 | 3.872 ms | 3.989 ms | 3.953 ms | 1.03× | 1.02× | 1.01× | +| fft Float64 256×256 dims=1,2 | 1.179 ms | 1.511 ms | 1.520 ms | 1.28× | 1.29× | 0.99× | +| fft Float64 512×512 dims=1,2 | 6.381 ms | 7.593 ms | 7.887 ms | 1.19× | 1.24× | 0.96× | +| fft Float64 720×480 dims=1,2 | 6.656 ms | 19.972 ms | 20.006 ms | 3.00× | 3.01× | 1.00× | +| fft Float64 1000×1000 dims=1,2 | 27.663 ms | 87.046 ms | 87.567 ms | 3.15× | 3.17× | 0.99× | +| fft Float64 1024×1024 dims=1,2 | 32.454 ms | 38.691 ms | 41.713 ms | 1.19× | 1.29× | **0.93×** | +| fft Float64 2048×2048 dims=1,2 | 174.856 ms | 180.159 ms | 191.634 ms | 1.03× | 1.10× | **0.94×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 880 ns | 6.88× | 7.08× | 0.97× | +| rfft Float32 16×16 dims=1,2 | 437 ns | 2.35 µs | 2.41 µs | 5.37× | 5.51× | 0.97× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.01 µs | 8.15 µs | 3.91× | 3.97× | 0.98× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.00 µs | 32.04 µs | 3.25× | 3.26× | 1.00× | +| rfft Float32 128×128 dims=1,2 | 46.72 µs | 140.64 µs | 140.64 µs | 3.01× | 3.01× | 1.00× | +| rfft Float32 256×256 dims=1,2 | 351.44 µs | 620.89 µs | 619.93 µs | 1.77× | 1.76× | 1.00× | +| rfft Float32 512×512 dims=1,2 | 1.463 ms | 2.822 ms | 2.826 ms | 1.93× | 1.93× | 1.00× | +| rfft Float32 1024×1024 dims=1,2 | 6.068 ms | 12.672 ms | 12.707 ms | 2.09× | 2.09× | 1.00× | +| rfft Float32 2048×2048 dims=1,2 | 37.112 ms | 62.733 ms | 62.828 ms | 1.69× | 1.69× | 1.00× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 924 ns | 950 ns | 7.87× | 8.09× | 0.97× | +| rfft Float64 16×16 dims=1,2 | 491 ns | 2.47 µs | 2.49 µs | 5.02× | 5.07× | 0.99× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.47 µs | 8.52 µs | 3.53× | 3.55× | 0.99× | +| rfft Float64 64×64 dims=1,2 | 11.80 µs | 33.60 µs | 33.80 µs | 2.85× | 2.86× | 0.99× | +| rfft Float64 128×128 dims=1,2 | 58.28 µs | 146.52 µs | 146.52 µs | 2.51× | 2.51× | 1.00× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.608 ms | 2.605 ms | 1.72× | 1.72× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.607 ms | 3.427 ms | 3.425 ms | 2.13× | 2.13× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 1.942 ms | 2.053 ms | 2.057 ms | 1.06× | 1.06× | 1.00× | +| rfft Float64 256×256 dims=1,2 | 410.73 µs | 651.45 µs | 653.53 µs | 1.59× | 1.59× | 1.00× | +| rfft Float64 512×512 dims=1,2 | 1.950 ms | 3.033 ms | 3.033 ms | 1.55× | 1.55× | 1.00× | +| rfft Float64 720×480 dims=1,2 | 3.176 ms | 9.686 ms | 9.641 ms | 3.05× | 3.04× | 1.00× | +| rfft Float64 1000×1000 dims=1,2 | 13.416 ms | 42.358 ms | 43.858 ms | 3.16× | 3.27× | 0.97× | +| rfft Float64 1024×1024 dims=1,2 | 9.460 ms | 13.754 ms | 13.898 ms | 1.45× | 1.47× | 0.99× | +| rfft Float64 2048×2048 dims=1,2 | 56.470 ms | 67.545 ms | 68.132 ms | 1.20× | 1.21× | 0.99× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.28 µs | 9.56 µs | 5.98× | 6.16× | 0.97× | +| fft Float32 16×16×16 dims=1,2,3 | 13.42 µs | 64.72 µs | 65.52 µs | 4.82× | 4.88× | 0.99× | +| fft Float32 32×32×32 dims=1,2,3 | 141.16 µs | 586.33 µs | 591.73 µs | 4.15× | 4.19× | 0.99× | +| fft Float32 64×64×64 dims=1,2,3 | 1.534 ms | 5.698 ms | 5.724 ms | 3.71× | 3.73× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 21.421 ms | 65.295 ms | 65.343 ms | 3.05× | 3.05× | 1.00× | +| fft Float64 8×8×8 dims=1,2,3 | 1.91 µs | 9.49 µs | 9.63 µs | 4.98× | 5.05× | 0.99× | +| fft Float64 16×16×16 dims=1,2,3 | 20.00 µs | 66.64 µs | 67.00 µs | 3.33× | 3.35× | 0.99× | +| fft Float64 32×32×32 dims=1,2,3 | 244.72 µs | 641.69 µs | 638.65 µs | 2.62× | 2.61× | 1.00× | +| fft Float64 64×64×64 dims=1,2,3 | 2.549 ms | 6.673 ms | 6.711 ms | 2.62× | 2.63× | 0.99× | +| fft Float64 128×128×128 dims=1,2,3 | 46.029 ms | 81.378 ms | 82.410 ms | 1.77× | 1.79× | 0.99× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.17 µs | 9.29 µs | 7.70× | 7.80× | 0.99× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.92 µs | 52.12 µs | 5.63× | 5.65× | 1.00× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.80 µs | 367.32 µs | 369.24 µs | 4.05× | 4.07× | 0.99× | +| rfft Float32 64×64×64 dims=1,2,3 | 962.65 µs | 3.098 ms | 3.138 ms | 3.22× | 3.26× | 0.99× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.939 ms | 28.947 ms | 29.452 ms | 2.91× | 2.96× | 0.98× | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.72 µs | 9.88 µs | 8.12× | 8.25× | 0.98× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.36 µs | 53.16 µs | 53.96 µs | 4.68× | 4.75× | 0.99× | +| rfft Float64 32×32×32 dims=1,2,3 | 117.20 µs | 387.52 µs | 388.76 µs | 3.31× | 3.32× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.387 ms | 3.478 ms | 3.501 ms | 2.51× | 2.52× | 0.99× | +| rfft Float64 128×128×128 dims=1,2,3 | 20.650 ms | 35.542 ms | 36.969 ms | 1.72× | 1.79× | 0.96× | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.32 µs | 3.61× | 3.58× | 1.01× | +| fft Float32 256×64 dims=1 | 52.40 µs | 123.56 µs | 123.36 µs | 2.36× | 2.35× | 1.00× | +| fft Float32 1024×64 dims=1 | 246.04 µs | 639.65 µs | 637.65 µs | 2.60× | 2.59× | 1.00× | +| fft Float32 4096×64 dims=1 | 1.294 ms | 3.263 ms | 3.270 ms | 2.52× | 2.53× | 1.00× | +| fft Float32 16384×64 dims=1 | 7.996 ms | 17.115 ms | 17.219 ms | 2.14× | 2.15× | 0.99× | +| fft Float32 65536×64 dims=1 | 46.349 ms | 88.718 ms | 88.734 ms | 1.91× | 1.91× | 1.00× | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.84 µs | 23.72 µs | 2.31× | 2.30× | 1.01× | +| fft Float64 256×64 dims=1 | 87.16 µs | 129.80 µs | 129.44 µs | 1.49× | 1.49× | 1.00× | +| fft Float64 1024×64 dims=1 | 433.05 µs | 690.57 µs | 697.81 µs | 1.59× | 1.61× | 0.99× | +| fft Float64 4096×64 dims=1 | 2.187 ms | 3.721 ms | 3.705 ms | 1.70× | 1.69× | 1.00× | +| fft Float64 16384×64 dims=1 | 15.622 ms | 21.157 ms | 21.236 ms | 1.35× | 1.36× | 1.00× | +| fft Float64 65536×64 dims=1 | 91.439 ms | 110.940 ms | 112.056 ms | 1.21× | 1.23× | 0.99× | +| rfft Float32 64×64 dims=1 | 6.59 µs | 18.78 µs | 18.88 µs | 2.85× | 2.87× | 0.99× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.76 µs | 84.76 µs | 2.08× | 2.08× | 1.00× | +| rfft Float32 1024×64 dims=1 | 143.64 µs | 398.76 µs | 398.80 µs | 2.78× | 2.78× | 1.00× | +| rfft Float32 4096×64 dims=1 | 694.21 µs | 1.877 ms | 1.880 ms | 2.70× | 2.71× | 1.00× | +| rfft Float32 16384×64 dims=1 | 3.764 ms | 8.859 ms | 8.903 ms | 2.35× | 2.37× | 1.00× | +| rfft Float32 65536×64 dims=1 | 19.901 ms | 43.060 ms | 43.281 ms | 2.16× | 2.17× | 0.99× | +| rfft Float64 64×64 dims=1 | 6.67 µs | 19.86 µs | 20.04 µs | 2.98× | 3.01× | 0.99× | +| rfft Float64 256×4096 dims=1 | 3.306 ms | 5.801 ms | 5.759 ms | 1.75× | 1.74× | 1.01× | +| rfft Float64 256×64 dims=1 | 44.52 µs | 87.64 µs | 87.44 µs | 1.97× | 1.96× | 1.00× | +| rfft Float64 1024×1024 dims=1 | 3.756 ms | 6.880 ms | 6.816 ms | 1.83× | 1.81× | 1.01× | +| rfft Float64 1024×64 dims=1 | 214.60 µs | 414.48 µs | 413.29 µs | 1.93× | 1.93× | 1.00× | +| rfft Float64 4096×256 dims=1 | 4.365 ms | 7.991 ms | 8.075 ms | 1.83× | 1.85× | 0.99× | +| rfft Float64 4096×64 dims=1 | 1.061 ms | 1.970 ms | 1.972 ms | 1.86× | 1.86× | 1.00× | +| rfft Float64 16384×64 dims=1 | 6.438 ms | 9.891 ms | 9.858 ms | 1.54× | 1.53× | 1.00× | +| rfft Float64 65536×64 dims=1 | 38.798 ms | 50.306 ms | 50.903 ms | 1.30× | 1.31× | 0.99× | +| fft Float32 64×64 dims=2 | 6.16 µs | 27.16 µs | 27.20 µs | 4.41× | 4.42× | 1.00× | +| fft Float32 64×256 dims=2 | 88.28 µs | 152.56 µs | 153.12 µs | 1.73× | 1.73× | 1.00× | +| fft Float32 64×1024 dims=2 | 632.21 µs | 823.97 µs | 831.57 µs | 1.30× | 1.32× | 0.99× | +| fft Float32 64×4096 dims=2 | 4.579 ms | 5.773 ms | 5.937 ms | 1.26× | 1.30× | 0.97× | +| fft Float32 64×16384 dims=2 | 28.500 ms | 32.989 ms | 31.739 ms | 1.16× | 1.11× | 1.04× | +| fft Float32 64×65536 dims=2 | 181.140 ms | 218.277 ms | 219.986 ms | 1.21× | 1.21× | 0.99× | +| fft Float64 64×64 dims=2 | 10.80 µs | 28.52 µs | 28.76 µs | 2.64× | 2.66× | 0.99× | +| fft Float64 64×256 dims=2 | 107.76 µs | 161.68 µs | 162.88 µs | 1.50× | 1.51× | 0.99× | +| fft Float64 64×1024 dims=2 | 882.53 µs | 1.147 ms | 1.250 ms | 1.30× | 1.42× | **0.92×** | +| fft Float64 64×4096 dims=2 | 5.598 ms | 6.868 ms | 6.988 ms | 1.23× | 1.25× | 0.98× | +| fft Float64 64×16384 dims=2 | 36.820 ms | 46.079 ms | 44.972 ms | 1.25× | 1.22× | 1.02× | +| fft Float64 64×65536 dims=2 | 257.156 ms | 269.652 ms | 272.116 ms | 1.05× | 1.06× | 0.99× | +| rfft Float32 64×64 dims=2 | 6.61 µs | 22.24 µs | 22.16 µs | 3.36× | 3.35× | 1.00× | +| rfft Float32 64×256 dims=2 | 57.40 µs | 107.28 µs | 108.08 µs | 1.87× | 1.88× | 0.99× | +| rfft Float32 64×1024 dims=2 | 280.80 µs | 538.89 µs | 538.17 µs | 1.92× | 1.92× | 1.00× | +| rfft Float32 64×4096 dims=2 | 1.874 ms | 2.805 ms | 2.815 ms | 1.50× | 1.50× | 1.00× | +| rfft Float32 64×16384 dims=2 | 11.949 ms | 14.174 ms | 14.144 ms | 1.19× | 1.18× | 1.00× | +| rfft Float32 64×65536 dims=2 | 73.559 ms | 70.004 ms | 71.932 ms | 0.95× | 0.98× | 0.97× | +| rfft Float64 64×64 dims=2 | 6.57 µs | 23.68 µs | 23.60 µs | 3.60× | 3.59× | 1.00× | +| rfft Float64 64×256 dims=2 | 71.40 µs | 123.52 µs | 122.92 µs | 1.73× | 1.72× | 1.00× | +| rfft Float64 64×1024 dims=2 | 353.68 µs | 571.29 µs | 577.73 µs | 1.62× | 1.63× | 0.99× | +| rfft Float64 64×4096 dims=2 | 2.850 ms | 3.242 ms | 3.269 ms | 1.14× | 1.15× | 0.99× | +| rfft Float64 64×16384 dims=2 | 15.428 ms | 15.071 ms | 15.056 ms | 0.98× | 0.98× | 1.00× | +| rfft Float64 64×65536 dims=2 | 111.346 ms | 88.785 ms | 89.940 ms | 0.80× | 0.81× | 0.99× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.51× (1.15–4.79) | 2.54× (1.20–4.91) | **0.99×** (0.96–1.00) | +| ComplexF32 fft 3d | 4.23× (3.05–5.98) | 4.28× (3.05–6.16) | **0.99×** (0.97–1.00) | +| ComplexF32 fft batched_dim1 | 2.47× (1.91–3.61) | 2.47× (1.91–3.58) | **1.00×** (0.99–1.01) | +| ComplexF32 fft batched_dim2 | 1.61× (1.16–4.41) | 1.61× (1.11–4.42) | **1.00×** (0.97–1.04) | +| ComplexF64 fft 2d | 1.92× (1.03–4.12) | 1.95× (1.02–4.21) | **0.98×** (0.93–1.01) | +| ComplexF64 fft 3d | 2.89× (1.77–4.98) | 2.91× (1.79–5.05) | **0.99×** (0.99–1.00) | +| ComplexF64 fft batched_dim1 | 1.58× (1.21–2.31) | 1.58× (1.23–2.30) | **1.00×** (0.99–1.01) | +| ComplexF64 fft batched_dim2 | 1.42× (1.05–2.64) | 1.45× (1.06–2.66) | **0.98×** (0.92–1.02) | +| Float32 rfft 2d | 2.95× (1.69–6.88) | 2.98× (1.69–7.08) | **0.99×** (0.97–1.00) | +| Float32 rfft 3d | 4.40× (2.91–7.70) | 4.44× (2.96–7.80) | **0.99×** (0.98–1.00) | +| Float32 rfft batched_dim1 | 2.47× (2.08–2.85) | 2.48× (2.08–2.87) | **1.00×** (0.99–1.00) | +| Float32 rfft batched_dim2 | 1.65× (0.95–3.36) | 1.66× (0.98–3.35) | **0.99×** (0.97–1.00) | +| Float64 rfft 2d | 2.35× (1.06–7.87) | 2.37× (1.06–8.09) | **0.99×** (0.97–1.00) | +| Float64 rfft 3d | 3.52× (1.72–8.12) | 3.58× (1.79–8.25) | **0.98×** (0.96–1.00) | +| Float64 rfft batched_dim1 | 1.84× (1.30–2.98) | 1.85× (1.31–3.01) | **1.00×** (0.99–1.01) | +| Float64 rfft batched_dim2 | 1.44× (0.80–3.60) | 1.45× (0.81–3.59) | **1.00×** (0.99–1.00) | +| **all** | 2.24× (0.80–8.12) | 2.26× (0.81–8.25) | **0.99×** (0.92–1.04), 117 cases, 3 slower by >5% | + +## 4 threads + +| case | `fftw` | `int` | `poly` | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 (4 thr) | 8.12 µs | 741 ns | 717 ns | 0.09× | 0.09× | 1.03× | +| fft Float32 16×16 dims=1,2 (4 thr) | 10.96 µs | 2.50 µs | 2.48 µs | 0.23× | 0.23× | 1.01× | +| fft Float32 32×32 dims=1,2 (4 thr) | 12.00 µs | 10.78 µs | 10.76 µs | 0.90× | 0.90× | 1.00× | +| fft Float32 64×64 dims=1,2 (4 thr) | 22.04 µs | 48.92 µs | 48.96 µs | 2.22× | 2.22× | 1.00× | +| fft Float32 128×128 dims=1,2 (4 thr) | 46.76 µs | 249.92 µs | 249.08 µs | 5.34× | 5.33× | 1.00× | +| fft Float32 256×256 dims=1,2 (4 thr) | 272.32 µs | 409.93 µs | 362.00 µs | 1.51× | 1.33× | **1.13×** | +| fft Float32 512×512 dims=1,2 (4 thr) | 1.552 ms | 2.165 ms | 2.065 ms | 1.39× | 1.33× | 1.05× | +| fft Float32 1024×1024 dims=1,2 (4 thr) | 6.759 ms | 10.641 ms | 9.759 ms | 1.57× | 1.44× | **1.09×** | +| fft Float32 2048×2048 dims=1,2 (4 thr) | 35.866 ms | 46.145 ms | 44.005 ms | 1.29× | 1.23× | 1.05× | +| fft Float64 8×8 dims=1,2 (4 thr) | 6.56 µs | 749 ns | 720 ns | 0.11× | 0.11× | 1.04× | +| fft Float64 16×16 dims=1,2 (4 thr) | 8.56 µs | 2.56 µs | 2.53 µs | 0.30× | 0.30× | 1.01× | +| fft Float64 32×32 dims=1,2 (4 thr) | 12.28 µs | 11.38 µs | 11.38 µs | 0.93× | 0.93× | 1.00× | +| fft Float64 64×64 dims=1,2 (4 thr) | 27.56 µs | 53.00 µs | 53.16 µs | 1.92× | 1.93× | 1.00× | +| fft Float64 128×128 dims=1,2 (4 thr) | 66.44 µs | 268.32 µs | 264.84 µs | 4.04× | 3.99× | 1.01× | +| fft Float64 127×257 dims=1,2 (4 thr) | 518.13 µs | 4.065 ms | 4.072 ms | 7.84× | 7.86× | 1.00× | +| fft Float64 1009×64 dims=1,2 (4 thr) | 990.73 µs | 1.188 ms | 1.058 ms | 1.20× | 1.07× | **1.12×** | +| fft Float64 64×1009 dims=1,2 (4 thr) | 1.066 ms | 1.200 ms | 1.116 ms | 1.13× | 1.05× | **1.08×** | +| fft Float64 256×256 dims=1,2 (4 thr) | 368.28 µs | 573.73 µs | 502.72 µs | 1.56× | 1.37× | **1.14×** | +| fft Float64 512×512 dims=1,2 (4 thr) | 1.700 ms | 2.608 ms | 2.365 ms | 1.53× | 1.39× | **1.10×** | +| fft Float64 720×480 dims=1,2 (4 thr) | 1.839 ms | 5.793 ms | 5.688 ms | 3.15× | 3.09× | 1.02× | +| fft Float64 1000×1000 dims=1,2 (4 thr) | 7.247 ms | 25.438 ms | 23.011 ms | 3.51× | 3.18× | **1.11×** | +| fft Float64 1024×1024 dims=1,2 (4 thr) | 8.171 ms | 13.385 ms | 11.911 ms | 1.64× | 1.46× | **1.12×** | +| fft Float64 2048×2048 dims=1,2 (4 thr) | 45.493 ms | 56.509 ms | 53.844 ms | 1.24× | 1.18× | 1.05× | +| rfft Float32 8×8 dims=1,2 (4 thr) | 12.60 µs | 855 ns | 890 ns | 0.07× | 0.07× | 0.96× | +| rfft Float32 16×16 dims=1,2 (4 thr) | 16.84 µs | 2.36 µs | 2.41 µs | 0.14× | 0.14× | 0.98× | +| rfft Float32 32×32 dims=1,2 (4 thr) | 11.80 µs | 8.04 µs | 8.09 µs | 0.68× | 0.69× | 0.99× | +| rfft Float32 64×64 dims=1,2 (4 thr) | 22.08 µs | 32.00 µs | 32.00 µs | 1.45× | 1.45× | 1.00× | +| rfft Float32 128×128 dims=1,2 (4 thr) | 39.16 µs | 140.48 µs | 140.68 µs | 3.59× | 3.59× | 1.00× | +| rfft Float32 256×256 dims=1,2 (4 thr) | 130.52 µs | 216.64 µs | 188.52 µs | 1.66× | 1.44× | **1.15×** | +| rfft Float32 512×512 dims=1,2 (4 thr) | 471.53 µs | 845.77 µs | 836.53 µs | 1.79× | 1.77× | 1.01× | +| rfft Float32 1024×1024 dims=1,2 (4 thr) | 1.652 ms | 3.454 ms | 3.487 ms | 2.09× | 2.11× | 0.99× | +| rfft Float32 2048×2048 dims=1,2 (4 thr) | 8.433 ms | 16.652 ms | 16.232 ms | 1.97× | 1.92× | 1.03× | +| rfft Float64 8×8 dims=1,2 (4 thr) | 12.32 µs | 920 ns | 952 ns | 0.07× | 0.08× | 0.97× | +| rfft Float64 16×16 dims=1,2 (4 thr) | 16.84 µs | 2.44 µs | 2.51 µs | 0.14× | 0.15× | 0.97× | +| rfft Float64 32×32 dims=1,2 (4 thr) | 12.52 µs | 8.41 µs | 8.53 µs | 0.67× | 0.68× | 0.99× | +| rfft Float64 64×64 dims=1,2 (4 thr) | 18.40 µs | 33.60 µs | 33.80 µs | 1.83× | 1.84× | 0.99× | +| rfft Float64 128×128 dims=1,2 (4 thr) | 44.24 µs | 147.12 µs | 146.88 µs | 3.33× | 3.32× | 1.00× | +| rfft Float64 127×257 dims=1,2 (4 thr) | 1.393 ms | 2.604 ms | 2.605 ms | 1.87× | 1.87× | 1.00× | +| rfft Float64 1009×64 dims=1,2 (4 thr) | 445.13 µs | 1.433 ms | 1.140 ms | 3.22× | 2.56× | **1.26×** | +| rfft Float64 64×1009 dims=1,2 (4 thr) | 614.01 µs | 673.25 µs | 639.89 µs | 1.10× | 1.04× | **1.05×** | +| rfft Float64 256×256 dims=1,2 (4 thr) | 162.76 µs | 251.08 µs | 215.84 µs | 1.54× | 1.33× | **1.16×** | +| rfft Float64 512×512 dims=1,2 (4 thr) | 576.93 µs | 978.69 µs | 964.93 µs | 1.70× | 1.67× | 1.01× | +| rfft Float64 720×480 dims=1,2 (4 thr) | 947.77 µs | 2.608 ms | 2.577 ms | 2.75× | 2.72× | 1.01× | +| rfft Float64 1000×1000 dims=1,2 (4 thr) | 3.509 ms | 10.887 ms | 10.853 ms | 3.10× | 3.09× | 1.00× | +| rfft Float64 1024×1024 dims=1,2 (4 thr) | 2.389 ms | 3.975 ms | 3.775 ms | 1.66× | 1.58× | **1.05×** | +| rfft Float64 2048×2048 dims=1,2 (4 thr) | 13.961 ms | 17.797 ms | 17.251 ms | 1.27× | 1.24× | 1.03× | +| fft Float32 8×8×8 dims=1,2,3 (4 thr) | 10.88 µs | 9.41 µs | 9.40 µs | 0.87× | 0.86× | 1.00× | +| fft Float32 16×16×16 dims=1,2,3 (4 thr) | 21.32 µs | 64.96 µs | 65.40 µs | 3.05× | 3.07× | 0.99× | +| fft Float32 32×32×32 dims=1,2,3 (4 thr) | 76.24 µs | 218.40 µs | 182.92 µs | 2.86× | 2.40× | **1.19×** | +| fft Float32 64×64×64 dims=1,2,3 (4 thr) | 495.17 µs | 1.856 ms | 1.682 ms | 3.75× | 3.40× | **1.10×** | +| fft Float32 128×128×128 dims=1,2,3 (4 thr) | 4.909 ms | 20.646 ms | 17.775 ms | 4.21× | 3.62× | **1.16×** | +| fft Float64 8×8×8 dims=1,2,3 (4 thr) | 10.28 µs | 9.59 µs | 9.72 µs | 0.93× | 0.95× | 0.99× | +| fft Float64 16×16×16 dims=1,2,3 (4 thr) | 27.80 µs | 66.28 µs | 66.36 µs | 2.38× | 2.39× | 1.00× | +| fft Float64 32×32×32 dims=1,2,3 (4 thr) | 113.64 µs | 266.12 µs | 224.76 µs | 2.34× | 1.98× | **1.18×** | +| fft Float64 64×64×64 dims=1,2,3 (4 thr) | 780.49 µs | 2.477 ms | 2.143 ms | 3.17× | 2.75× | **1.16×** | +| fft Float64 128×128×128 dims=1,2,3 (4 thr) | 10.214 ms | 24.623 ms | 23.078 ms | 2.41× | 2.26× | **1.07×** | +| rfft Float32 8×8×8 dims=1,2,3 (4 thr) | 8.92 µs | 9.17 µs | 9.32 µs | 1.03× | 1.04× | 0.98× | +| rfft Float32 16×16×16 dims=1,2,3 (4 thr) | 14.20 µs | 51.64 µs | 52.28 µs | 3.64× | 3.68× | 0.99× | +| rfft Float32 32×32×32 dims=1,2,3 (4 thr) | 54.48 µs | 316.00 µs | 274.12 µs | 5.80× | 5.03× | **1.15×** | +| rfft Float32 64×64×64 dims=1,2,3 (4 thr) | 344.20 µs | 948.21 µs | 867.25 µs | 2.75× | 2.52× | **1.09×** | +| rfft Float32 128×128×128 dims=1,2,3 (4 thr) | 2.545 ms | 7.717 ms | 7.756 ms | 3.03× | 3.05× | 1.00× | +| rfft Float64 8×8×8 dims=1,2,3 (4 thr) | 11.56 µs | 9.82 µs | 9.87 µs | 0.85× | 0.85× | 1.00× | +| rfft Float64 16×16×16 dims=1,2,3 (4 thr) | 16.04 µs | 53.88 µs | 54.00 µs | 3.36× | 3.37× | 1.00× | +| rfft Float64 32×32×32 dims=1,2,3 (4 thr) | 70.08 µs | 371.12 µs | 309.08 µs | 5.30× | 4.41× | **1.20×** | +| rfft Float64 64×64×64 dims=1,2,3 (4 thr) | 450.25 µs | 1.081 ms | 1.015 ms | 2.40× | 2.25× | **1.06×** | +| rfft Float64 128×128×128 dims=1,2,3 (4 thr) | 3.989 ms | 9.282 ms | 9.020 ms | 2.33× | 2.26× | 1.03× | +| fft Float32 64×64 dims=1 (4 thr) | 6.60 µs | 22.44 µs | 22.48 µs | 3.40× | 3.41× | 1.00× | +| fft Float32 256×64 dims=1 (4 thr) | 24.88 µs | 123.80 µs | 123.92 µs | 4.98× | 4.98× | 1.00× | +| fft Float32 1024×64 dims=1 (4 thr) | 75.28 µs | 175.64 µs | 158.52 µs | 2.33× | 2.11× | **1.11×** | +| fft Float32 4096×64 dims=1 (4 thr) | 335.52 µs | 927.17 µs | 801.29 µs | 2.76× | 2.39× | **1.16×** | +| fft Float32 16384×64 dims=1 (4 thr) | 2.026 ms | 4.442 ms | 4.404 ms | 2.19× | 2.17× | 1.01× | +| fft Float32 65536×64 dims=1 (4 thr) | 13.130 ms | 23.345 ms | 23.207 ms | 1.78× | 1.77× | 1.01× | +| fft Float64 64×64 dims=1 (4 thr) | 7.88 µs | 23.84 µs | 23.80 µs | 3.03× | 3.02× | 1.00× | +| fft Float64 256×64 dims=1 (4 thr) | 34.64 µs | 129.56 µs | 130.00 µs | 3.74× | 3.75× | 1.00× | +| fft Float64 1024×64 dims=1 (4 thr) | 122.56 µs | 201.72 µs | 165.84 µs | 1.65× | 1.35× | **1.22×** | +| fft Float64 4096×64 dims=1 (4 thr) | 604.41 µs | 1.071 ms | 947.41 µs | 1.77× | 1.57× | **1.13×** | +| fft Float64 16384×64 dims=1 (4 thr) | 4.058 ms | 5.895 ms | 5.595 ms | 1.45× | 1.38× | **1.05×** | +| fft Float64 65536×64 dims=1 (4 thr) | 24.343 ms | 29.335 ms | 30.215 ms | 1.21× | 1.24× | 0.97× | +| rfft Float32 64×64 dims=1 (4 thr) | 6.80 µs | 18.80 µs | 18.86 µs | 2.76× | 2.77× | 1.00× | +| rfft Float32 256×64 dims=1 (4 thr) | 22.44 µs | 84.28 µs | 84.32 µs | 3.76× | 3.76× | 1.00× | +| rfft Float32 1024×64 dims=1 (4 thr) | 51.20 µs | 115.40 µs | 99.92 µs | 2.25× | 1.95× | **1.15×** | +| rfft Float32 4096×64 dims=1 (4 thr) | 173.36 µs | 495.85 µs | 468.17 µs | 2.86× | 2.70× | **1.06×** | +| rfft Float32 16384×64 dims=1 (4 thr) | 960.37 µs | 2.356 ms | 2.239 ms | 2.45× | 2.33× | **1.05×** | +| rfft Float32 65536×64 dims=1 (4 thr) | 4.945 ms | 11.572 ms | 10.898 ms | 2.34× | 2.20× | **1.06×** | +| rfft Float64 64×64 dims=1 (4 thr) | 5.84 µs | 19.90 µs | 20.00 µs | 3.41× | 3.42× | 0.99× | +| rfft Float64 256×4096 dims=1 (4 thr) | 859.49 µs | 1.712 ms | 1.435 ms | 1.99× | 1.67× | **1.19×** | +| rfft Float64 256×64 dims=1 (4 thr) | 21.96 µs | 87.44 µs | 87.76 µs | 3.98× | 4.00× | 1.00× | +| rfft Float64 1024×1024 dims=1 (4 thr) | 1.033 ms | 1.885 ms | 1.722 ms | 1.82× | 1.67× | **1.09×** | +| rfft Float64 1024×64 dims=1 (4 thr) | 67.96 µs | 119.92 µs | 103.40 µs | 1.76× | 1.52× | **1.16×** | +| rfft Float64 4096×256 dims=1 (4 thr) | 1.192 ms | 2.265 ms | 2.006 ms | 1.90× | 1.68× | **1.13×** | +| rfft Float64 4096×64 dims=1 (4 thr) | 292.48 µs | 521.56 µs | 490.73 µs | 1.78× | 1.68× | **1.06×** | +| rfft Float64 16384×64 dims=1 (4 thr) | 1.641 ms | 2.640 ms | 2.497 ms | 1.61× | 1.52× | **1.06×** | +| rfft Float64 65536×64 dims=1 (4 thr) | 9.900 ms | 13.358 ms | 13.112 ms | 1.35× | 1.32× | 1.02× | +| fft Float32 64×64 dims=2 (4 thr) | 6.76 µs | 27.12 µs | 27.16 µs | 4.01× | 4.02× | 1.00× | +| fft Float32 64×256 dims=2 (4 thr) | 32.72 µs | 153.04 µs | 153.00 µs | 4.68× | 4.68× | 1.00× | +| fft Float32 64×1024 dims=2 (4 thr) | 117.80 µs | 232.48 µs | 204.44 µs | 1.97× | 1.74× | **1.14×** | +| fft Float32 64×4096 dims=2 (4 thr) | 1.287 ms | 1.808 ms | 1.611 ms | 1.40× | 1.25× | **1.12×** | +| fft Float32 64×16384 dims=2 (4 thr) | 6.708 ms | 8.385 ms | 8.527 ms | 1.25× | 1.27× | 0.98× | +| fft Float32 64×65536 dims=2 (4 thr) | 47.260 ms | 60.523 ms | 61.079 ms | 1.28× | 1.29× | 0.99× | +| fft Float64 64×64 dims=2 (4 thr) | 10.12 µs | 28.56 µs | 29.48 µs | 2.82× | 2.91× | 0.97× | +| fft Float64 64×256 dims=2 (4 thr) | 40.56 µs | 162.88 µs | 161.24 µs | 4.02× | 3.98× | 1.01× | +| fft Float64 64×1024 dims=2 (4 thr) | 248.64 µs | 386.72 µs | 329.72 µs | 1.56× | 1.33× | **1.17×** | +| fft Float64 64×4096 dims=2 (4 thr) | 1.551 ms | 2.073 ms | 1.984 ms | 1.34× | 1.28× | 1.04× | +| fft Float64 64×16384 dims=2 (4 thr) | 8.758 ms | 12.547 ms | 12.725 ms | 1.43× | 1.45× | 0.99× | +| fft Float64 64×65536 dims=2 (4 thr) | 66.738 ms | 72.188 ms | 74.128 ms | 1.08× | 1.11× | 0.97× | +| rfft Float32 64×64 dims=2 (4 thr) | 6.84 µs | 22.24 µs | 22.24 µs | 3.25× | 3.25× | 1.00× | +| rfft Float32 64×256 dims=2 (4 thr) | 26.20 µs | 107.08 µs | 108.44 µs | 4.09× | 4.14× | 0.99× | +| rfft Float32 64×1024 dims=2 (4 thr) | 85.68 µs | 149.88 µs | 135.20 µs | 1.75× | 1.58× | **1.11×** | +| rfft Float32 64×4096 dims=2 (4 thr) | 556.49 µs | 838.01 µs | 734.89 µs | 1.51× | 1.32× | **1.14×** | +| rfft Float32 64×16384 dims=2 (4 thr) | 3.282 ms | 3.758 ms | 3.593 ms | 1.15× | 1.09× | 1.05× | +| rfft Float32 64×65536 dims=2 (4 thr) | 20.677 ms | 19.754 ms | 19.442 ms | 0.96× | 0.94× | 1.02× | +| rfft Float64 64×64 dims=2 (4 thr) | 5.88 µs | 23.76 µs | 23.48 µs | 4.04× | 3.99× | 1.01× | +| rfft Float64 64×256 dims=2 (4 thr) | 30.60 µs | 122.92 µs | 123.36 µs | 4.02× | 4.03× | 1.00× | +| rfft Float64 64×1024 dims=2 (4 thr) | 109.96 µs | 164.48 µs | 159.52 µs | 1.50× | 1.45× | 1.03× | +| rfft Float64 64×4096 dims=2 (4 thr) | 850.13 µs | 949.77 µs | 915.21 µs | 1.12× | 1.08× | 1.04× | +| rfft Float64 64×16384 dims=2 (4 thr) | 4.106 ms | 4.109 ms | 4.156 ms | 1.00× | 1.01× | 0.99× | +| rfft Float64 64×65536 dims=2 (4 thr) | 30.907 ms | 24.999 ms | 25.190 ms | 0.81× | 0.82× | 0.99× | + +### Summary (4 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 0.99× (0.09–5.34) | 0.96× (0.09–5.33) | **1.04×** (1.00–1.13) | +| ComplexF32 fft 3d | 2.60× (0.87–4.21) | 2.39× (0.86–3.62) | **1.09×** (0.99–1.19) | +| ComplexF32 fft batched_dim1 | 2.74× (1.78–4.98) | 2.63× (1.77–4.98) | **1.04×** (1.00–1.16) | +| ComplexF32 fft batched_dim2 | 2.09× (1.25–4.68) | 2.02× (1.25–4.68) | **1.04×** (0.98–1.14) | +| ComplexF64 fft 2d | 1.42× (0.11–7.84) | 1.35× (0.11–7.86) | **1.06×** (1.00–1.14) | +| ComplexF64 fft 3d | 2.09× (0.93–3.17) | 1.94× (0.95–2.75) | **1.08×** (0.99–1.18) | +| ComplexF64 fft batched_dim1 | 1.97× (1.21–3.74) | 1.86× (1.24–3.75) | **1.06×** (0.97–1.22) | +| ComplexF64 fft batched_dim2 | 1.82× (1.08–4.02) | 1.78× (1.11–3.98) | **1.02×** (0.97–1.17) | +| Float32 rfft 2d | 0.91× (0.07–3.59) | 0.90× (0.07–3.59) | **1.01×** (0.96–1.15) | +| Float32 rfft 3d | 2.83× (1.03–5.80) | 2.72× (1.04–5.03) | **1.04×** (0.98–1.15) | +| Float32 rfft batched_dim1 | 2.70× (2.25–3.76) | 2.56× (1.95–3.76) | **1.05×** (1.00–1.15) | +| Float32 rfft batched_dim2 | 1.84× (0.96–4.09) | 1.75× (0.94–4.14) | **1.05×** (0.99–1.14) | +| Float64 rfft 2d | 1.21× (0.07–3.33) | 1.17× (0.08–3.32) | **1.03×** (0.97–1.26) | +| Float64 rfft 3d | 2.43× (0.85–5.30) | 2.30× (0.85–4.41) | **1.05×** (1.00–1.20) | +| Float64 rfft batched_dim1 | 2.05× (1.35–3.98) | 1.90× (1.32–4.00) | **1.08×** (0.99–1.19) | +| Float64 rfft batched_dim2 | 1.67× (0.81–4.04) | 1.66× (0.82–4.03) | **1.01×** (0.99–1.04) | +| **all** | 1.70× (0.07–7.84) | 1.63× (0.07–7.86) | **1.05×** (0.96–1.26), 117 cases, 0 slower by >5% | + +## 16 threads + +| case | `fftw` | `int` | `poly` | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 (16 thr) | 15.48 µs | 704 ns | 720 ns | 0.05× | 0.05× | 0.98× | +| fft Float32 16×16 dims=1,2 (16 thr) | 29.24 µs | 2.51 µs | 2.47 µs | 0.09× | 0.08× | 1.02× | +| fft Float32 32×32 dims=1,2 (16 thr) | 29.92 µs | 10.80 µs | 10.76 µs | 0.36× | 0.36× | 1.00× | +| fft Float32 64×64 dims=1,2 (16 thr) | 33.04 µs | 48.60 µs | 48.92 µs | 1.47× | 1.48× | 0.99× | +| fft Float32 128×128 dims=1,2 (16 thr) | 38.00 µs | 250.28 µs | 250.08 µs | 6.59× | 6.58× | 1.00× | +| fft Float32 256×256 dims=1,2 (16 thr) | 94.24 µs | 155.32 µs | 115.84 µs | 1.65× | 1.23× | **1.34×** | +| fft Float32 512×512 dims=1,2 (16 thr) | 463.97 µs | 800.33 µs | 672.33 µs | 1.72× | 1.45× | **1.19×** | +| fft Float32 1024×1024 dims=1,2 (16 thr) | 2.072 ms | 3.605 ms | 3.024 ms | 1.74× | 1.46× | **1.19×** | +| fft Float32 2048×2048 dims=1,2 (16 thr) | 10.643 ms | 19.557 ms | 13.288 ms | 1.84× | 1.25× | **1.47×** | +| fft Float64 8×8 dims=1,2 (16 thr) | 14.88 µs | 739 ns | 720 ns | 0.05× | 0.05× | 1.03× | +| fft Float64 16×16 dims=1,2 (16 thr) | 29.00 µs | 2.54 µs | 2.52 µs | 0.09× | 0.09× | 1.01× | +| fft Float64 32×32 dims=1,2 (16 thr) | 30.12 µs | 11.28 µs | 11.38 µs | 0.37× | 0.38× | 0.99× | +| fft Float64 64×64 dims=1,2 (16 thr) | 32.72 µs | 53.08 µs | 53.04 µs | 1.62× | 1.62× | 1.00× | +| fft Float64 128×128 dims=1,2 (16 thr) | 43.28 µs | 266.24 µs | 267.60 µs | 6.15× | 6.18× | 0.99× | +| fft Float64 127×257 dims=1,2 (16 thr) | 159.12 µs | 4.083 ms | 4.086 ms | 25.66× | 25.68× | 1.00× | +| fft Float64 1009×64 dims=1,2 (16 thr) | 280.68 µs | 478.21 µs | 323.36 µs | 1.70× | 1.15× | **1.48×** | +| fft Float64 64×1009 dims=1,2 (16 thr) | 303.56 µs | 470.21 µs | 347.12 µs | 1.55× | 1.14× | **1.35×** | +| fft Float64 256×256 dims=1,2 (16 thr) | 3.199 ms | 232.96 µs | 184.72 µs | 0.07× | 0.06× | **1.26×** | +| fft Float64 512×512 dims=1,2 (16 thr) | 504.41 µs | 1.058 ms | 905.73 µs | 2.10× | 1.80× | **1.17×** | +| fft Float64 720×480 dims=1,2 (16 thr) | 573.53 µs | 2.206 ms | 1.824 ms | 3.85× | 3.18× | **1.21×** | +| fft Float64 1000×1000 dims=1,2 (16 thr) | 7.122 ms | 10.365 ms | 6.827 ms | 1.46× | 0.96× | **1.52×** | +| fft Float64 1024×1024 dims=1,2 (16 thr) | 2.305 ms | 4.465 ms | 3.916 ms | 1.94× | 1.70× | **1.14×** | +| fft Float64 2048×2048 dims=1,2 (16 thr) | 13.913 ms | 23.948 ms | 19.576 ms | 1.72× | 1.41× | **1.22×** | +| rfft Float32 8×8 dims=1,2 (16 thr) | 13.16 µs | 855 ns | 888 ns | 0.06× | 0.07× | 0.96× | +| rfft Float32 16×16 dims=1,2 (16 thr) | 23.32 µs | 2.36 µs | 2.41 µs | 0.10× | 0.10× | 0.98× | +| rfft Float32 32×32 dims=1,2 (16 thr) | 31.92 µs | 8.00 µs | 8.15 µs | 0.25× | 0.26× | 0.98× | +| rfft Float32 64×64 dims=1,2 (16 thr) | 29.56 µs | 32.00 µs | 32.12 µs | 1.08× | 1.09× | 1.00× | +| rfft Float32 128×128 dims=1,2 (16 thr) | 45.40 µs | 140.24 µs | 141.20 µs | 3.09× | 3.11× | 0.99× | +| rfft Float32 256×256 dims=1,2 (16 thr) | 102.80 µs | 87.16 µs | 57.56 µs | 0.85× | 0.56× | **1.51×** | +| rfft Float32 512×512 dims=1,2 (16 thr) | 171.00 µs | 263.32 µs | 233.24 µs | 1.54× | 1.36× | **1.13×** | +| rfft Float32 1024×1024 dims=1,2 (16 thr) | 554.09 µs | 1.146 ms | 1.048 ms | 2.07× | 1.89× | **1.09×** | +| rfft Float32 2048×2048 dims=1,2 (16 thr) | 2.640 ms | 4.522 ms | 4.088 ms | 1.71× | 1.55× | **1.11×** | +| rfft Float64 8×8 dims=1,2 (16 thr) | 14.04 µs | 926 ns | 954 ns | 0.07× | 0.07× | 0.97× | +| rfft Float64 16×16 dims=1,2 (16 thr) | 24.52 µs | 2.47 µs | 2.50 µs | 0.10× | 0.10× | 0.99× | +| rfft Float64 32×32 dims=1,2 (16 thr) | 32.48 µs | 8.48 µs | 8.56 µs | 0.26× | 0.26× | 0.99× | +| rfft Float64 64×64 dims=1,2 (16 thr) | 29.48 µs | 33.64 µs | 33.68 µs | 1.14× | 1.14× | 1.00× | +| rfft Float64 128×128 dims=1,2 (16 thr) | 46.24 µs | 146.56 µs | 146.52 µs | 3.17× | 3.17× | 1.00× | +| rfft Float64 127×257 dims=1,2 (16 thr) | 1.278 ms | 2.609 ms | 2.605 ms | 2.04× | 2.04× | 1.00× | +| rfft Float64 1009×64 dims=1,2 (16 thr) | 8.566 ms | 781.09 µs | 556.85 µs | 0.09× | 0.07× | **1.40×** | +| rfft Float64 64×1009 dims=1,2 (16 thr) | 260.40 µs | 301.32 µs | 229.84 µs | 1.16× | 0.88× | **1.31×** | +| rfft Float64 256×256 dims=1,2 (16 thr) | 4.431 ms | 95.40 µs | 65.16 µs | 0.02× | 0.01× | **1.46×** | +| rfft Float64 512×512 dims=1,2 (16 thr) | 2.825 ms | 325.12 µs | 273.64 µs | 0.12× | 0.10× | **1.19×** | +| rfft Float64 720×480 dims=1,2 (16 thr) | 307.32 µs | 819.61 µs | 701.49 µs | 2.67× | 2.28× | **1.17×** | +| rfft Float64 1000×1000 dims=1,2 (16 thr) | 1.177 ms | 3.459 ms | 2.832 ms | 2.94× | 2.41× | **1.22×** | +| rfft Float64 1024×1024 dims=1,2 (16 thr) | 2.767 ms | 1.218 ms | 1.095 ms | 0.44× | 0.40× | **1.11×** | +| rfft Float64 2048×2048 dims=1,2 (16 thr) | 4.453 ms | 5.407 ms | 4.476 ms | 1.21× | 1.01× | **1.21×** | +| fft Float32 8×8×8 dims=1,2,3 (16 thr) | 40.64 µs | 9.48 µs | 9.59 µs | 0.23× | 0.24× | 0.99× | +| fft Float32 16×16×16 dims=1,2,3 (16 thr) | 30.72 µs | 65.12 µs | 65.04 µs | 2.12× | 2.12× | 1.00× | +| fft Float32 32×32×32 dims=1,2,3 (16 thr) | 46.52 µs | 105.16 µs | 57.60 µs | 2.26× | 1.24× | **1.83×** | +| fft Float32 64×64×64 dims=1,2,3 (16 thr) | 166.00 µs | 723.21 µs | 555.85 µs | 4.36× | 3.35× | **1.30×** | +| fft Float32 128×128×128 dims=1,2,3 (16 thr) | 1.353 ms | 9.109 ms | 5.579 ms | 6.73× | 4.12× | **1.63×** | +| fft Float64 8×8×8 dims=1,2,3 (16 thr) | 40.36 µs | 9.68 µs | 9.61 µs | 0.24× | 0.24× | 1.01× | +| fft Float64 16×16×16 dims=1,2,3 (16 thr) | 33.08 µs | 66.92 µs | 66.72 µs | 2.02× | 2.02× | 1.00× | +| fft Float64 32×32×32 dims=1,2,3 (16 thr) | 53.56 µs | 134.20 µs | 72.96 µs | 2.51× | 1.36× | **1.84×** | +| fft Float64 64×64×64 dims=1,2,3 (16 thr) | 272.44 µs | 1.102 ms | 834.17 µs | 4.04× | 3.06× | **1.32×** | +| fft Float64 128×128×128 dims=1,2,3 (16 thr) | 3.038 ms | 11.653 ms | 7.884 ms | 3.84× | 2.60× | **1.48×** | +| rfft Float32 8×8×8 dims=1,2,3 (16 thr) | 54.36 µs | 9.09 µs | 9.43 µs | 0.17× | 0.17× | 0.96× | +| rfft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.92 µs | 51.56 µs | 52.32 µs | 1.72× | 1.75× | 0.99× | +| rfft Float32 32×32×32 dims=1,2,3 (16 thr) | 39.72 µs | 284.32 µs | 242.88 µs | 7.16× | 6.11× | **1.17×** | +| rfft Float32 64×64×64 dims=1,2,3 (16 thr) | 116.32 µs | 291.36 µs | 230.04 µs | 2.50× | 1.98× | **1.27×** | +| rfft Float32 128×128×128 dims=1,2,3 (16 thr) | 900.21 µs | 2.283 ms | 2.110 ms | 2.54× | 2.34× | **1.08×** | +| rfft Float64 8×8×8 dims=1,2,3 (16 thr) | 47.16 µs | 9.64 µs | 9.88 µs | 0.20× | 0.21× | 0.98× | +| rfft Float64 16×16×16 dims=1,2,3 (16 thr) | 31.04 µs | 53.20 µs | 53.96 µs | 1.71× | 1.74× | 0.99× | +| rfft Float64 32×32×32 dims=1,2,3 (16 thr) | 45.20 µs | 329.56 µs | 279.28 µs | 7.29× | 6.18× | **1.18×** | +| rfft Float64 64×64×64 dims=1,2,3 (16 thr) | 148.24 µs | 351.64 µs | 268.84 µs | 2.37× | 1.81× | **1.31×** | +| rfft Float64 128×128×128 dims=1,2,3 (16 thr) | 1.086 ms | 2.705 ms | 2.335 ms | 2.49× | 2.15× | **1.16×** | +| fft Float32 64×64 dims=1 (16 thr) | 14.64 µs | 22.48 µs | 22.44 µs | 1.54× | 1.53× | 1.00× | +| fft Float32 256×64 dims=1 (16 thr) | 21.00 µs | 123.64 µs | 123.68 µs | 5.89× | 5.89× | 1.00× | +| fft Float32 1024×64 dims=1 (16 thr) | 35.96 µs | 67.52 µs | 41.00 µs | 1.88× | 1.14× | **1.65×** | +| fft Float32 4096×64 dims=1 (16 thr) | 120.56 µs | 281.20 µs | 198.40 µs | 2.33× | 1.65× | **1.42×** | +| fft Float32 16384×64 dims=1 (16 thr) | 571.33 µs | 1.243 ms | 1.004 ms | 2.18× | 1.76× | **1.24×** | +| fft Float32 65536×64 dims=1 (16 thr) | 3.642 ms | 6.612 ms | 5.820 ms | 1.82× | 1.60× | **1.14×** | +| fft Float64 64×64 dims=1 (16 thr) | 14.40 µs | 23.80 µs | 23.80 µs | 1.65× | 1.65× | 1.00× | +| fft Float64 256×64 dims=1 (16 thr) | 21.56 µs | 129.48 µs | 129.28 µs | 6.01× | 6.00× | 1.00× | +| fft Float64 1024×64 dims=1 (16 thr) | 48.24 µs | 81.36 µs | 42.56 µs | 1.69× | 0.88× | **1.91×** | +| fft Float64 4096×64 dims=1 (16 thr) | 205.48 µs | 400.16 µs | 216.28 µs | 1.95× | 1.05× | **1.85×** | +| fft Float64 16384×64 dims=1 (16 thr) | 1.092 ms | 1.698 ms | 1.183 ms | 1.56× | 1.08× | **1.43×** | +| fft Float64 65536×64 dims=1 (16 thr) | 7.095 ms | 8.164 ms | 7.973 ms | 1.15× | 1.12× | 1.02× | +| rfft Float32 64×64 dims=1 (16 thr) | 14.84 µs | 18.78 µs | 18.86 µs | 1.27× | 1.27× | 1.00× | +| rfft Float32 256×64 dims=1 (16 thr) | 18.36 µs | 84.36 µs | 84.56 µs | 4.59× | 4.61× | 1.00× | +| rfft Float32 1024×64 dims=1 (16 thr) | 25.64 µs | 42.68 µs | 26.32 µs | 1.66× | 1.03× | **1.62×** | +| rfft Float32 4096×64 dims=1 (16 thr) | 65.68 µs | 151.44 µs | 118.40 µs | 2.31× | 1.80× | **1.28×** | +| rfft Float32 16384×64 dims=1 (16 thr) | 289.40 µs | 737.29 µs | 551.21 µs | 2.55× | 1.90× | **1.34×** | +| rfft Float32 65536×64 dims=1 (16 thr) | 1.566 ms | 3.299 ms | 2.755 ms | 2.11× | 1.76× | **1.20×** | +| rfft Float64 64×64 dims=1 (16 thr) | 14.12 µs | 19.92 µs | 19.96 µs | 1.41× | 1.41× | 1.00× | +| rfft Float64 256×4096 dims=1 (16 thr) | 277.44 µs | 573.17 µs | 355.40 µs | 2.07× | 1.28× | **1.61×** | +| rfft Float64 256×64 dims=1 (16 thr) | 18.56 µs | 87.60 µs | 87.48 µs | 4.72× | 4.71× | 1.00× | +| rfft Float64 1024×1024 dims=1 (16 thr) | 311.96 µs | 556.33 µs | 416.77 µs | 1.78× | 1.34× | **1.33×** | +| rfft Float64 1024×64 dims=1 (16 thr) | 31.44 µs | 48.12 µs | 27.28 µs | 1.53× | 0.87× | **1.76×** | +| rfft Float64 4096×256 dims=1 (16 thr) | 389.16 µs | 643.57 µs | 492.61 µs | 1.65× | 1.27× | **1.31×** | +| rfft Float64 4096×64 dims=1 (16 thr) | 104.52 µs | 173.32 µs | 122.92 µs | 1.66× | 1.18× | **1.41×** | +| rfft Float64 16384×64 dims=1 (16 thr) | 567.33 µs | 712.29 µs | 617.09 µs | 1.26× | 1.09× | **1.15×** | +| rfft Float64 65536×64 dims=1 (16 thr) | 2.782 ms | 3.843 ms | 3.347 ms | 1.38× | 1.20× | **1.15×** | +| fft Float32 64×64 dims=2 (16 thr) | 15.12 µs | 27.36 µs | 27.12 µs | 1.81× | 1.79× | 1.01× | +| fft Float32 64×256 dims=2 (16 thr) | 37.40 µs | 152.60 µs | 153.24 µs | 4.08× | 4.10× | 1.00× | +| fft Float32 64×1024 dims=2 (16 thr) | 113.12 µs | 143.16 µs | 117.00 µs | 1.27× | 1.03× | **1.22×** | +| fft Float32 64×4096 dims=2 (16 thr) | 587.65 µs | 830.81 µs | 636.49 µs | 1.41× | 1.08× | **1.31×** | +| fft Float32 64×16384 dims=2 (16 thr) | 2.501 ms | 3.213 ms | 2.793 ms | 1.28× | 1.12× | **1.15×** | +| fft Float32 64×65536 dims=2 (16 thr) | 16.053 ms | 20.963 ms | 20.586 ms | 1.31× | 1.28× | 1.02× | +| fft Float64 64×64 dims=2 (16 thr) | 14.64 µs | 28.60 µs | 28.60 µs | 1.95× | 1.95× | 1.00× | +| fft Float64 64×256 dims=2 (16 thr) | 23.48 µs | 161.36 µs | 169.84 µs | 6.87× | 7.23× | 0.95× | +| fft Float64 64×1024 dims=2 (16 thr) | 91.36 µs | 121.72 µs | 78.56 µs | 1.33× | 0.86× | **1.55×** | +| fft Float64 64×4096 dims=2 (16 thr) | 438.81 µs | 586.37 µs | 508.49 µs | 1.34× | 1.16× | **1.15×** | +| fft Float64 64×16384 dims=2 (16 thr) | 2.477 ms | 3.235 ms | 2.955 ms | 1.31× | 1.19× | **1.09×** | +| fft Float64 64×65536 dims=2 (16 thr) | 22.281 ms | 21.062 ms | 20.927 ms | 0.95× | 0.94× | 1.01× | +| rfft Float32 64×64 dims=2 (16 thr) | 14.32 µs | 22.08 µs | 22.20 µs | 1.54× | 1.55× | 0.99× | +| rfft Float32 64×256 dims=2 (16 thr) | 28.60 µs | 108.16 µs | 108.32 µs | 3.78× | 3.79× | 1.00× | +| rfft Float32 64×1024 dims=2 (16 thr) | 71.08 µs | 68.96 µs | 52.76 µs | 0.97× | 0.74× | **1.31×** | +| rfft Float32 64×4096 dims=2 (16 thr) | 278.20 µs | 298.20 µs | 252.32 µs | 1.07× | 0.91× | **1.18×** | +| rfft Float32 64×16384 dims=2 (16 thr) | 1.232 ms | 1.247 ms | 1.108 ms | 1.01× | 0.90× | **1.13×** | +| rfft Float32 64×65536 dims=2 (16 thr) | 6.437 ms | 5.765 ms | 5.527 ms | 0.90× | 0.86× | 1.04× | +| rfft Float64 64×64 dims=2 (16 thr) | 14.56 µs | 23.60 µs | 23.56 µs | 1.62× | 1.62× | 1.00× | +| rfft Float64 64×256 dims=2 (16 thr) | 20.04 µs | 123.04 µs | 123.36 µs | 6.14× | 6.16× | 1.00× | +| rfft Float64 64×1024 dims=2 (16 thr) | 45.32 µs | 59.64 µs | 40.96 µs | 1.32× | 0.90× | **1.46×** | +| rfft Float64 64×4096 dims=2 (16 thr) | 269.84 µs | 305.44 µs | 257.36 µs | 1.13× | 0.95× | **1.19×** | +| rfft Float64 64×16384 dims=2 (16 thr) | 1.282 ms | 1.261 ms | 1.131 ms | 0.98× | 0.88× | **1.12×** | +| rfft Float64 64×65536 dims=2 (16 thr) | 9.983 ms | 7.672 ms | 7.468 ms | 0.77× | 0.75× | 1.03× | + +### Summary (16 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `poly`/`fftw` | `poly` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 0.79× (0.05–6.59) | 0.71× (0.05–6.58) | **1.12×** (0.98–1.47) | +| ComplexF32 fft 3d | 2.01× (0.23–6.73) | 1.54× (0.24–4.12) | **1.31×** (0.99–1.83) | +| ComplexF32 fft batched_dim1 | 2.32× (1.54–5.89) | 1.90× (1.14–5.89) | **1.22×** (1.00–1.65) | +| ComplexF32 fft batched_dim2 | 1.68× (1.27–4.08) | 1.51× (1.03–4.10) | **1.11×** (1.00–1.31) | +| ComplexF64 fft 2d | 1.09× (0.05–25.66) | 0.94× (0.05–25.68) | **1.16×** (0.99–1.52) | +| ComplexF64 fft 3d | 1.80× (0.24–4.04) | 1.39× (0.24–3.06) | **1.29×** (1.00–1.84) | +| ComplexF64 fft batched_dim1 | 1.97× (1.15–6.01) | 1.50× (0.88–6.00) | **1.32×** (1.00–1.91) | +| ComplexF64 fft batched_dim2 | 1.76× (0.95–6.87) | 1.58× (0.86–7.23) | **1.11×** (0.95–1.55) | +| Float32 rfft 2d | 0.67× (0.06–3.09) | 0.62× (0.07–3.11) | **1.07×** (0.96–1.51) | +| Float32 rfft 3d | 1.67× (0.17–7.16) | 1.54× (0.17–6.11) | **1.09×** (0.96–1.27) | +| Float32 rfft batched_dim1 | 2.22× (1.27–4.59) | 1.82× (1.03–4.61) | **1.22×** (1.00–1.62) | +| Float32 rfft batched_dim2 | 1.33× (0.90–3.78) | 1.20× (0.74–3.79) | **1.10×** (0.99–1.31) | +| Float64 rfft 2d | 0.45× (0.02–3.17) | 0.40× (0.01–3.17) | **1.13×** (0.97–1.46) | +| Float64 rfft 3d | 1.72× (0.20–7.29) | 1.54× (0.21–6.18) | **1.11×** (0.98–1.31) | +| Float64 rfft batched_dim1 | 1.78× (1.26–4.72) | 1.39× (0.87–4.71) | **1.28×** (1.00–1.76) | +| Float64 rfft batched_dim2 | 1.50× (0.77–6.14) | 1.34× (0.75–6.16) | **1.12×** (1.00–1.46) | +| **all** | 1.24× (0.02–25.66) | 1.07× (0.01–25.68) | **1.16×** (0.95–1.91), 117 cases, 0 slower by >5% | + +## Thread scaling (time at 1 thread / time at N threads) + +| case | `fftw` ×4 | `fftw` ×16 | `int` ×4 | `int` ×16 | `poly` ×4 | `poly` ×16 | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 16×16×16 dims=1,2,3 | 0.63× | 0.44× | 1.00× | 0.99× | 1.00× | 1.01× | +| fft Float64 127×257 dims=1,2 | 3.47× | 11.31× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float64 4096×256 dims=1 | 3.66× | 11.22× | 3.53× | 12.42× | 4.03× | 16.39× | +| rfft Float64 128×128×128 dims=1,2,3 | 5.18× | 19.02× | 3.83× | 13.14× | 4.10× | 15.83× | +| rfft Float64 64×64 dims=1,2 | 0.64× | 0.40× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float32 8×8 dims=1,2 | 0.02× | 0.01× | 0.94× | 0.99× | 0.99× | 0.99× | +| fft Float64 2048×2048 dims=1,2 | 3.84× | 12.57× | 3.19× | 7.52× | 3.56× | 9.79× | +| fft Float64 64×64×64 dims=1,2,3 | 3.27× | 9.36× | 2.69× | 6.06× | 3.13× | 8.05× | +| rfft Float64 64×1024 dims=2 | 3.22× | 7.80× | 3.47× | 9.58× | 3.62× | 14.10× | +| rfft Float32 32×32 dims=1,2 | 0.17× | 0.06× | 1.00× | 1.00× | 1.01× | 1.00× | +| fft Float64 64×1024 dims=2 | 3.55× | 9.66× | 2.97× | 9.43× | 3.79× | 15.92× | +| rfft Float32 128×128×128 dims=1,2,3 | 3.91× | 11.04× | 3.75× | 12.68× | 3.80× | 13.96× | +| fft Float32 64×65536 dims=2 | 3.83× | 11.28× | 3.61× | 10.41× | 3.60× | 10.69× | +| rfft Float32 64×4096 dims=2 | 3.37× | 6.74× | 3.35× | 9.40× | 3.83× | 11.16× | +| fft Float64 64×64 dims=2 | 1.07× | 0.74× | 1.00× | 1.00× | 0.98× | 1.01× | +| fft Float64 64×64 dims=1 | 1.31× | 0.72× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float32 256×256 dims=1,2 | 2.72× | 7.85× | 2.85× | 7.52× | 3.23× | 10.11× | +| fft Float32 64×64×64 dims=1,2,3 | 3.10× | 9.24× | 3.07× | 7.88× | 3.40× | 10.30× | +| rfft Float32 64×64×64 dims=1,2,3 | 2.80× | 8.28× | 3.27× | 10.63× | 3.62× | 13.64× | +| fft Float32 4096×64 dims=1 | 3.86× | 10.73× | 3.52× | 11.60× | 4.08× | 16.48× | +| fft Float32 64×64 dims=1 | 0.94× | 0.43× | 1.00× | 1.00× | 0.99× | 0.99× | +| fft Float32 1024×1024 dims=1,2 | 3.89× | 12.70× | 3.28× | 9.69× | 3.61× | 11.64× | +| rfft Float32 16×16 dims=1,2 | 0.03× | 0.02× | 0.99× | 1.00× | 1.00× | 1.00× | +| fft Float32 512×512 dims=1,2 | 3.82× | 12.77× | 3.28× | 8.88× | 3.49× | 10.73× | +| rfft Float64 2048×2048 dims=1,2 | 4.04× | 12.68× | 3.80× | 12.49× | 3.95× | 15.22× | +| rfft Float64 128×128 dims=1,2 | 1.32× | 1.26× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float32 8×8×8 dims=1,2,3 | 0.14× | 0.04× | 0.99× | 0.98× | 1.02× | 1.00× | +| fft Float64 256×256 dims=1,2 | 3.20× | 0.37× | 2.63× | 6.49× | 3.02× | 8.23× | +| fft Float64 64×64 dims=1,2 | 0.75× | 0.63× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float64 256×64 dims=1 | 2.03× | 2.40× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float32 64×1024 dims=2 | 3.28× | 3.95× | 3.60× | 7.81× | 3.98× | 10.20× | +| rfft Float64 8×8 dims=1,2 | 0.01× | 0.01× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float64 64×1009 dims=1,2 | 3.63× | 12.76× | 3.32× | 8.48× | 3.54× | 11.39× | +| fft Float32 32×32 dims=1,2 | 0.22× | 0.09× | 0.99× | 0.99× | 1.00× | 1.00× | +| fft Float32 1024×64 dims=1 | 3.27× | 6.84× | 3.64× | 9.47× | 4.02× | 15.55× | +| fft Float32 64×16384 dims=2 | 4.25× | 11.40× | 3.93× | 10.27× | 3.72× | 11.36× | +| rfft Float32 8×8×8 dims=1,2,3 | 0.13× | 0.02× | 1.00× | 1.01× | 1.00× | 0.99× | +| fft Float64 1024×1024 dims=1,2 | 3.97× | 14.08× | 2.89× | 8.67× | 3.50× | 10.65× | +| rfft Float64 256×256 dims=1,2 | 2.52× | 0.09× | 2.59× | 6.83× | 3.03× | 10.03× | +| fft Float64 32×32 dims=1,2 | 0.34× | 0.14× | 1.00× | 1.01× | 1.00× | 1.00× | +| rfft Float64 16×16×16 dims=1,2,3 | 0.71× | 0.37× | 0.99× | 1.00× | 1.00× | 1.00× | +| rfft Float64 65536×64 dims=1 | 3.92× | 13.95× | 3.77× | 13.09× | 3.88× | 15.21× | +| fft Float32 128×128×128 dims=1,2,3 | 4.36× | 15.83× | 3.16× | 7.17× | 3.68× | 11.71× | +| fft Float32 64×64 dims=2 | 0.91× | 0.41× | 1.00× | 0.99× | 1.00× | 1.00× | +| rfft Float64 512×512 dims=1,2 | 3.38× | 0.69× | 3.10× | 9.33× | 3.14× | 11.08× | +| rfft Float32 64×64 dims=1,2 | 0.45× | 0.33× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float64 128×128 dims=1,2 | 1.70× | 2.60× | 0.99× | 1.00× | 1.01× | 1.00× | +| fft Float64 64×256 dims=2 | 2.66× | 4.59× | 0.99× | 1.00× | 1.01× | 0.96× | +| fft Float32 64×1024 dims=2 | 5.37× | 5.59× | 3.54× | 5.76× | 4.07× | 7.11× | +| rfft Float64 64×64 dims=1 | 1.14× | 0.47× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float64 1000×1000 dims=1,2 | 3.82× | 11.40× | 3.89× | 12.24× | 4.04× | 15.48× | +| fft Float32 65536×64 dims=1 | 3.53× | 12.73× | 3.80× | 13.42× | 3.82× | 15.25× | +| rfft Float32 64×256 dims=2 | 2.19× | 2.01× | 1.00× | 0.99× | 1.00× | 1.00× | +| fft Float32 128×128 dims=1,2 | 1.30× | 1.60× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float32 8×8 dims=1,2 | 0.01× | 0.01× | 1.00× | 1.00× | 0.99× | 0.99× | +| rfft Float32 512×512 dims=1,2 | 3.10× | 8.55× | 3.34× | 10.72× | 3.38× | 12.12× | +| rfft Float32 256×256 dims=1,2 | 2.69× | 3.42× | 2.87× | 7.12× | 3.29× | 10.77× | +| fft Float32 64×4096 dims=2 | 3.56× | 7.79× | 3.19× | 6.95× | 3.69× | 9.33× | +| rfft Float64 127×257 dims=1,2 | 1.09× | 1.18× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float32 32×32×32 dims=1,2,3 | 1.67× | 2.29× | 1.16× | 1.29× | 1.35× | 1.52× | +| rfft Float64 1024×64 dims=1 | 3.16× | 6.83× | 3.46× | 8.61× | 4.00× | 15.15× | +| rfft Float32 65536×64 dims=1 | 4.02× | 12.71× | 3.72× | 13.05× | 3.97× | 15.71× | +| rfft Float32 64×65536 dims=2 | 3.56× | 11.43× | 3.54× | 12.14× | 3.70× | 13.01× | +| rfft Float64 16384×64 dims=1 | 3.92× | 11.35× | 3.75× | 13.89× | 3.95× | 15.97× | +| rfft Float32 16384×64 dims=1 | 3.92× | 13.01× | 3.76× | 12.02× | 3.98× | 16.15× | +| rfft Float64 256×4096 dims=1 | 3.85× | 11.92× | 3.39× | 10.12× | 4.01× | 16.20× | +| rfft Float64 32×32 dims=1,2 | 0.19× | 0.07× | 1.01× | 1.00× | 1.00× | 1.00× | +| fft Float32 64×256 dims=2 | 2.70× | 2.36× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float32 64×16384 dims=2 | 3.64× | 9.70× | 3.77× | 11.37× | 3.94× | 12.77× | +| fft Float64 1024×64 dims=1 | 3.53× | 8.98× | 3.42× | 8.49× | 4.21× | 16.40× | +| fft Float64 720×480 dims=1,2 | 3.62× | 11.61× | 3.45× | 9.05× | 3.52× | 10.97× | +| fft Float64 512×512 dims=1,2 | 3.75× | 12.65× | 2.91× | 7.18× | 3.33× | 8.71× | +| fft Float64 256×64 dims=1 | 2.52× | 4.04× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float64 16×16 dims=1,2 | 0.03× | 0.02× | 1.01× | 1.00× | 0.99× | 1.00× | +| fft Float32 2048×2048 dims=1,2 | 3.85× | 12.97× | 3.45× | 8.14× | 3.78× | 12.50× | +| rfft Float64 1024×1024 dims=1 | 3.63× | 12.04× | 3.65× | 12.37× | 3.96× | 16.35× | +| fft Float64 8×8 dims=1,2 | 0.03× | 0.01× | 0.96× | 0.97× | 1.02× | 1.02× | +| fft Float64 64×4096 dims=2 | 3.61× | 12.76× | 3.31× | 11.71× | 3.52× | 13.74× | +| rfft Float64 64×65536 dims=2 | 3.60× | 11.15× | 3.55× | 11.57× | 3.57× | 12.04× | +| fft Float64 32×32×32 dims=1,2,3 | 2.15× | 4.57× | 2.41× | 4.78× | 2.84× | 8.75× | +| fft Float32 32×32×32 dims=1,2,3 | 1.85× | 3.03× | 2.68× | 5.58× | 3.23× | 10.27× | +| fft Float64 128×128×128 dims=1,2,3 | 4.51× | 15.15× | 3.30× | 6.98× | 3.57× | 10.45× | +| rfft Float32 128×128 dims=1,2 | 1.19× | 1.03× | 1.00× | 1.00× | 1.00× | 1.00× | +| rfft Float32 16×16×16 dims=1,2,3 | 0.65× | 0.31× | 1.01× | 1.01× | 1.00× | 1.00× | +| rfft Float64 64×64 dims=2 | 1.12× | 0.45× | 1.00× | 1.00× | 1.01× | 1.00× | +| rfft Float64 64×4096 dims=2 | 3.35× | 10.56× | 3.41× | 10.62× | 3.57× | 12.70× | +| rfft Float32 1024×64 dims=1 | 2.81× | 5.60× | 3.46× | 9.34× | 3.99× | 15.15× | +| rfft Float32 64×64 dims=2 | 0.97× | 0.46× | 1.00× | 1.01× | 1.00× | 1.00× | +| fft Float64 16×16×16 dims=1,2,3 | 0.72× | 0.60× | 1.01× | 1.00× | 1.01× | 1.00× | +| rfft Float64 1024×1024 dims=1,2 | 3.96× | 3.42× | 3.46× | 11.29× | 3.68× | 12.69× | +| fft Float64 1000×1000 dims=1,2 | 3.82× | 3.88× | 3.42× | 8.40× | 3.81× | 12.83× | +| rfft Float32 4096×64 dims=1 | 4.00× | 10.57× | 3.79× | 12.40× | 4.01× | 15.88× | +| rfft Float32 256×64 dims=1 | 1.82× | 2.22× | 1.01× | 1.00× | 1.01× | 1.00× | +| fft Float64 64×65536 dims=2 | 3.85× | 11.54× | 3.74× | 12.80× | 3.67× | 13.00× | +| fft Float64 65536×64 dims=1 | 3.76× | 12.89× | 3.78× | 13.59× | 3.71× | 14.05× | +| fft Float64 16384×64 dims=1 | 3.85× | 14.31× | 3.59× | 12.46× | 3.80× | 17.94× | +| fft Float32 16384×64 dims=1 | 3.95× | 14.00× | 3.85× | 13.77× | 3.91× | 17.15× | +| rfft Float64 64×16384 dims=2 | 3.76× | 12.04× | 3.67× | 11.95× | 3.62× | 13.31× | +| fft Float32 256×64 dims=1 | 2.11× | 2.50× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float64 8×8×8 dims=1,2,3 | 0.19× | 0.05× | 0.99× | 0.98× | 0.99× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 3.08× | 9.36× | 3.22× | 9.89× | 3.45× | 13.02× | +| rfft 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], + "sum_im": 439989.97, + "sum_re": -183525.03 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 80, + "exec_min": 0.0014351370000000002, + "key": "rfft Float64 256×4096 dims=1 (4 thr)", + "kind": "rfft", + "measure": false, + "n": 256, + "norm": 11640.925722730331, + "nthreads": 4, + "plan_min": 5.22e-6, + "shape": "batched_dim1", + "size": [ + 256, + 4096 + ], + "sum_im": 4845.767554722023, + "sum_re": 347.8471366990625 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 80, + "exec_min": 0.00172178, + "key": "rfft Float64 1024×1024 dims=1 (4 thr)", + "kind": "rfft", + "measure": false, + "n": 1024, + "norm": 23213.335828584088, + "nthreads": 4, + "plan_min": 7.180000000000001e-6, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790562, + "sum_re": -8799.055444945061 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 80, + "exec_min": 0.0020058230000000003, + "key": "rfft Float64 4096×256 dims=1 (4 thr)", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113902925, + "nthreads": 4, + "plan_min": 1.4201e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255915, + "sum_re": -2384.3887021656665 + } + ] +} \ No newline at end of file From 7061654c51bf486f21824ebb76372f99870f313e Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:16:58 +0000 Subject: [PATCH 05/21] benchmark: KERNEL_STAGES.md, stage breakdown on aarch64 for integration/all --- benchmark/KERNEL_STAGES.md | 108 +++++++++++++++++++++++++++++++++++++ 1 file changed, 108 insertions(+) create mode 100644 benchmark/KERNEL_STAGES.md diff --git a/benchmark/KERNEL_STAGES.md b/benchmark/KERNEL_STAGES.md new file mode 100644 index 0000000..5f8dc23 --- /dev/null +++ b/benchmark/KERNEL_STAGES.md @@ -0,0 +1,108 @@ +# Kernel stage breakdown (ComplexF64, single thread, neoverse-n1, Julia 1.12.6) + +Stage times are minimum times of the kernel re-run with the other stages removed; `copy` is one `copyto!` of the array (the memory-traffic floor of a single pass). + +Branch `integration/all` @ 901692b (before the SIMD-pass / leaves-first / codelet branches). Each block re-runs the kernel with stages removed, so the stage rows add up to the total; the last column relates each stage to one `copyto!` of the array (the memory-traffic floor of a single pass). Hardware counters were not available on this host. +### n = 1024 = 2^10 (radix-4 recursion, 2 butterfly levels, 16 leaves of 64 points) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 346 ns | +|:--|--:|--:|--:| +| FFTA total | 9.52 µs | 100% | 27.5× copy | +| leaves: 16 × 64-point codelet, input stride 16 | 5.32 µs | 56% | 15.4× copy | +| (same codelets on contiguous input) | 5.28 µs | 55% | strided-load penalty 1.01× | +| butterfly pass, blocks of 1024 (stride 256 between the 4 legs) | 2.11 µs | 22% | 6.1× copy; memory-only version of the pass 620 ns | +| butterfly pass, blocks of 256 (stride 64 between the 4 legs) | 2.14 µs | 22% | 6.2× copy; memory-only version of the pass 631 ns | +| leaves + passes (sum of the rows) | 9.56 µs | 100% | recursion/dispatch overhead = total − sum = -43 ns | +| FFTW ESTIMATE / MEASURE | 6.32 µs / 5.28 µs | 66% / 55% | 18.2× / 15.2× copy | + +### n = 16384 = 2^14 (radix-4 recursion, 4 butterfly levels, 256 leaves of 64 points) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 6.04 µs | +|:--|--:|--:|--:| +| FFTA total | 244.68 µs | 100% | 40.5× copy | +| leaves: 256 × 64-point codelet, input stride 256 | 97.64 µs | 40% | 16.2× copy | +| (same codelets on contiguous input) | 86.64 µs | 35% | strided-load penalty 1.13× | +| butterfly pass, blocks of 16384 (stride 4096 between the 4 legs) | 34.16 µs | 14% | 5.7× copy; memory-only version of the pass 14.08 µs | +| butterfly pass, blocks of 4096 (stride 1024 between the 4 legs) | 34.40 µs | 14% | 5.7× copy; memory-only version of the pass 14.14 µs | +| butterfly pass, blocks of 1024 (stride 256 between the 4 legs) | 33.84 µs | 14% | 5.6× copy; memory-only version of the pass 12.52 µs | +| butterfly pass, blocks of 256 (stride 64 between the 4 legs) | 34.72 µs | 14% | 5.7× copy; memory-only version of the pass 12.86 µs | +| leaves + passes (sum of the rows) | 234.76 µs | 96% | recursion/dispatch overhead = total − sum = 9.92 µs | +| FFTW ESTIMATE / MEASURE | 176.64 µs / 157.64 µs | 72% / 64% | 29.2× / 26.1× copy | + +### n = 262144 = 2^18 (radix-4 recursion, 6 butterfly levels, 4096 leaves of 64 points) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 334.44 µs | +|:--|--:|--:|--:| +| FFTA total | 6.733 ms | 100% | 20.1× copy | +| leaves: 4096 × 64-point codelet, input stride 4096 | 3.198 ms | 47% | 9.6× copy | +| (same codelets on contiguous input) | 1.465 ms | 22% | strided-load penalty 2.18× | +| butterfly pass, blocks of 262144 (stride 65536 between the 4 legs) | 560.61 µs | 8% | 1.7× copy; memory-only version of the pass 241.20 µs | +| butterfly pass, blocks of 65536 (stride 16384 between the 4 legs) | 557.29 µs | 8% | 1.7× copy; memory-only version of the pass 237.44 µs | +| butterfly pass, blocks of 16384 (stride 4096 between the 4 legs) | 553.53 µs | 8% | 1.7× copy; memory-only version of the pass 232.48 µs | +| butterfly pass, blocks of 4096 (stride 1024 between the 4 legs) | 556.89 µs | 8% | 1.7× copy; memory-only version of the pass 233.80 µs | +| butterfly pass, blocks of 1024 (stride 256 between the 4 legs) | 561.65 µs | 8% | 1.7× copy; memory-only version of the pass 219.52 µs | +| butterfly pass, blocks of 256 (stride 64 between the 4 legs) | 600.41 µs | 9% | 1.8× copy; memory-only version of the pass 245.24 µs | +| leaves + passes (sum of the rows) | 6.588 ms | 98% | recursion/dispatch overhead = total − sum = 145.52 µs | +| FFTW ESTIMATE / MEASURE | 8.897 ms / 4.631 ms | 132% / 69% | 26.6× / 13.8× copy | + +### n = 4194304 = 2^22 (radix-4 recursion, 8 butterfly levels, 65536 leaves of 64 points) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 6.120 ms | +|:--|--:|--:|--:| +| FFTA total | 210.500 ms | 100% | 34.4× copy | +| leaves: 65536 × 64-point codelet, input stride 65536 | 124.993 ms | 59% | 20.4× copy | +| (same codelets on contiguous input) | 33.230 ms | 16% | strided-load penalty 3.76× | +| butterfly pass, blocks of 4194304 (stride 1048576 between the 4 legs) | 9.916 ms | 5% | 1.6× copy; memory-only version of the pass 7.003 ms | +| butterfly pass, blocks of 1048576 (stride 262144 between the 4 legs) | 9.250 ms | 4% | 1.5× copy; memory-only version of the pass 4.768 ms | +| butterfly pass, blocks of 262144 (stride 65536 between the 4 legs) | 9.076 ms | 4% | 1.5× copy; memory-only version of the pass 4.336 ms | +| butterfly pass, blocks of 65536 (stride 16384 between the 4 legs) | 9.051 ms | 4% | 1.5× copy; memory-only version of the pass 4.255 ms | +| butterfly pass, blocks of 16384 (stride 4096 between the 4 legs) | 9.064 ms | 4% | 1.5× copy; memory-only version of the pass 4.171 ms | +| butterfly pass, blocks of 4096 (stride 1024 between the 4 legs) | 9.362 ms | 4% | 1.5× copy; memory-only version of the pass 4.570 ms | +| butterfly pass, blocks of 1024 (stride 256 between the 4 legs) | 10.913 ms | 5% | 1.8× copy; memory-only version of the pass 5.828 ms | +| butterfly pass, blocks of 256 (stride 64 between the 4 legs) | 11.518 ms | 5% | 1.9× copy; memory-only version of the pass 6.324 ms | +| leaves + passes (sum of the rows) | 203.144 ms | 97% | recursion/dispatch overhead = total − sum = 7.357 ms | +| FFTW ESTIMATE / MEASURE | 242.198 ms / 104.928 ms | 115% / 50% | 39.6× / 17.1× copy | +### n = 1000 = 8 × 125 (composite step: right = 125 COMPOSITE_FFT, left = 8 POW2RADIX4_FFT) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 338 ns | +|:--|--:|--:|--:| +| FFTA total | 35.32 µs | 100% | 104.4× copy | +| 8 right sub-transforms of 125 (input stride 8) | 30.80 µs | 87% | 91.0× copy | +| twiddle multiply pass | 1.27 µs | 4% | 3.7× copy | +| 125 left sub-transforms of 8 (output stride 125) | 3.09 µs | 9% | 9.1× copy | +| sum of the rows | 35.15 µs | 100% | overhead = 169 ns | +| FFTW ESTIMATE / MEASURE | 10.28 µs / 7.36 µs | 29% / 21% | 30.4× / 21.7× copy | + +### n = 46305 = 27 × 1715 (composite step: right = 1715 COMPOSITE_FFT, left = 27 POW3_FFT) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 27.56 µs | +|:--|--:|--:|--:| +| FFTA total | 3.326 ms | 100% | 120.7× copy | +| 27 right sub-transforms of 1715 (input stride 27) | 2.521 ms | 76% | 91.5× copy | +| twiddle multiply pass | 68.76 µs | 2% | 2.5× copy | +| 1715 left sub-transforms of 27 (output stride 1715) | 693.69 µs | 21% | 25.2× copy | +| sum of the rows | 3.284 ms | 99% | overhead = 42.32 µs | +| FFTW ESTIMATE / MEASURE | 1.052 ms / 865.49 µs | 32% / 26% | 38.2× / 31.4× copy | + +### n = 1000000 = 64 × 15625 (composite step: right = 15625 COMPOSITE_FFT, left = 64 POW2RADIX4_FFT) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 1.274 ms | +|:--|--:|--:|--:| +| FFTA total | 100.257 ms | 100% | 78.7× copy | +| 64 right sub-transforms of 15625 (input stride 64) | 83.168 ms | 83% | 65.3× copy | +| twiddle multiply pass | 2.005 ms | 2% | 1.6× copy | +| 15625 left sub-transforms of 64 (output stride 15625) | 11.154 ms | 11% | 8.8× copy | +| sum of the rows | 96.327 ms | 96% | overhead = 3.930 ms | +| FFTW ESTIMATE / MEASURE | 55.945 ms / 24.771 ms | 56% / 25% | 43.9× / 19.4× copy | + +### n = 65537 (Bluestein, padded to 262144) + +| stage | time | share of FFTA total | time of one `copyto!` of the array: 60.56 µs | +|:--|--:|--:|--:| +| FFTA total | 15.552 ms | 100% | 256.8× copy | +| chirp multiply + zero pad | 191.36 µs | 1% | | +| forward FFT of 262144 | 6.390 ms | 41% | | +| pointwise product | 540.45 µs | 3% | | +| second FFT of 262144 | 6.401 ms | 41% | | +| output chirp multiply | 131.68 µs | 1% | | +| FFTW ESTIMATE / MEASURE | 3.362 ms / 2.660 ms | 22% / 17% | | From 9ba2f16a4c661ca5b522d1a4fa5c1fc039d03a01 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:24:22 +0000 Subject: [PATCH 06/21] benchmark: compare3 baseline, FFTW vs FFTA 0.3.1 vs integration/all (aarch64, 1 thread) --- .../compare3/aarch64/baseline/COMPARE3.md | 623 + .../compare3/aarch64/baseline/fftw_t1.json | 11375 ++++++++++++++++ .../compare3/aarch64/baseline/int_t1.json | 10975 +++++++++++++++ .../compare3/aarch64/baseline/release_t1.json | 9008 ++++++++++++ 4 files changed, 31981 insertions(+) create mode 100644 benchmark/compare3/aarch64/baseline/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/baseline/fftw_t1.json create mode 100644 benchmark/compare3/aarch64/baseline/int_t1.json create mode 100644 benchmark/compare3/aarch64/baseline/release_t1.json diff --git a/benchmark/compare3/aarch64/baseline/COMPARE3.md b/benchmark/compare3/aarch64/baseline/COMPARE3.md new file mode 100644 index 0000000..82772f8 --- /dev/null +++ b/benchmark/compare3/aarch64/baseline/COMPARE3.md @@ -0,0 +1,623 @@ +# FFT implementations side by side + +Rendered 2026-08-30T11:19:30.199 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `release` | FFTA.jl 0.3.1 — `@0.3.1` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA-bench/` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `release` | `int` | `release`/`fftw` | `int`/`fftw` | `release` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 211 ns | 120 ns | 5.61× | 3.19× | **0.57×** | +| fft Float32 8 dims=1 | 37 ns | 66 ns | 24 ns | 1.77× | 0.65× | **0.37×** | +| fft Float32 11 dims=1 | — | 589 ns | — | — | — | — | +| fft Float32 12 dims=1 | 43 ns | 154 ns | 153 ns | 3.55× | 3.52× | 0.99× | +| fft Float32 16 dims=1 | 55 ns | 104 ns | 54 ns | 1.89× | 0.97× | **0.52×** | +| fft Float32 17 dims=1 | 136 ns | 1.50 µs | 805 ns | 11.02× | 5.92× | **0.54×** | +| fft Float32 23 dims=1 | 230 ns | 2.82 µs | 1.50 µs | 12.26× | 6.55× | **0.53×** | +| fft Float32 25 dims=1 | 126 ns | 1.04 µs | 667 ns | 8.25× | 5.29× | **0.64×** | +| fft Float32 29 dims=1 | 342 ns | 4.54 µs | 814 ns | 13.27× | 2.38× | **0.18×** | +| fft Float32 31 dims=1 | 387 ns | 5.22 µs | 820 ns | 13.49× | 2.12× | **0.16×** | +| fft Float32 32 dims=1 | 105 ns | 349 ns | 132 ns | 3.33× | 1.26× | **0.38×** | +| fft Float32 37 dims=1 | 836 ns | 7.52 µs | 1.81 µs | 8.99× | 2.16× | **0.24×** | +| fft Float32 41 dims=1 | 817 ns | 9.29 µs | 1.81 µs | 11.37× | 2.22× | **0.20×** | +| fft Float32 43 dims=1 | 699 ns | 10.24 µs | 1.82 µs | 14.64× | 2.60× | **0.18×** | +| fft Float32 54 dims=1 | 325 ns | 1.10 µs | 910 ns | 3.39× | 2.80× | **0.83×** | +| fft Float32 59 dims=1 | — | 19.52 µs | — | — | — | — | +| fft Float32 60 dims=1 | 217 ns | 2.11 µs | 1.52 µs | 9.75× | 7.03× | **0.72×** | +| fft Float32 61 dims=1 | 1.19 µs | 20.88 µs | 1.87 µs | 17.55× | 1.57× | **0.09×** | +| fft Float32 64 dims=1 | 194 ns | 592 ns | 328 ns | 3.05× | 1.69× | **0.55×** | +| fft Float32 71 dims=1 | 2.40 µs | 28.40 µs | 4.09 µs | 11.81× | 1.70× | **0.14×** | +| fft Float32 73 dims=1 | 1.34 µs | 30.04 µs | 4.11 µs | 22.37× | 3.06× | **0.14×** | +| fft Float32 79 dims=1 | 1.76 µs | 35.20 µs | 4.13 µs | 19.96× | 2.34× | **0.12×** | +| fft Float32 97 dims=1 | — | 53.28 µs | — | — | — | — | +| fft Float32 101 dims=1 | 1.94 µs | — | 4.18 µs | — | 2.16× | — | +| fft Float32 112 dims=1 | 360 ns | 4.42 µs | 2.51 µs | 12.27× | 6.97× | **0.57×** | +| fft Float32 120 dims=1 | 392 ns | 4.74 µs | 2.94 µs | 12.09× | 7.50× | **0.62×** | +| fft Float32 128 dims=1 | 390 ns | 1.79 µs | 790 ns | 4.58× | 2.03× | **0.44×** | +| fft Float32 137 dims=1 | — | 106.76 µs | — | — | — | — | +| fft Float32 202 dims=1 | 4.13 µs | 117.20 µs | 9.57 µs | 28.39× | 2.32× | **0.08×** | +| fft Float32 211 dims=1 | — | 254.28 µs | — | — | — | — | +| fft Float32 243 dims=1 | 1.90 µs | 4.54 µs | 3.83 µs | 2.39× | 2.02× | **0.84×** | +| fft Float32 251 dims=1 | 5.99 µs | — | 9.57 µs | — | 1.60× | — | +| fft Float32 256 dims=1 | 807 ns | 3.13 µs | 1.83 µs | 3.87× | 2.27× | **0.59×** | +| fft Float32 303 dims=1 | 6.36 µs | 175.84 µs | 14.40 µs | 27.65× | 2.26× | **0.08×** | +| fft Float32 331 dims=1 | — | 627.49 µs | — | — | — | — | +| fft Float32 360 dims=1 | 2.37 µs | 15.24 µs | 9.40 µs | 6.42× | 3.96× | **0.62×** | +| fft Float32 404 dims=1 | 8.45 µs | 233.92 µs | 18.48 µs | 27.67× | 2.19× | **0.08×** | +| fft Float32 491 dims=1 | — | 1.385 ms | — | — | — | — | +| fft Float32 504 dims=1 | 2.69 µs | 26.72 µs | 15.58 µs | 9.95× | 5.80× | **0.58×** | +| fft Float32 512 dims=1 | 1.69 µs | 8.63 µs | 4.22 µs | 5.11× | 2.50× | **0.49×** | +| fft Float32 593 dims=1 | 15.24 µs | — | 45.76 µs | — | 3.00× | — | +| fft Float32 606 dims=1 | 12.82 µs | 357.08 µs | 32.40 µs | 27.85× | 2.53× | **0.09×** | +| fft Float32 720 dims=1 | 5.25 µs | 29.00 µs | 18.74 µs | 5.52× | 3.57× | **0.65×** | +| fft Float32 751 dims=1 | — | 3.247 ms | — | — | — | — | +| fft Float32 1000 dims=1 | 6.69 µs | 75.64 µs | 43.56 µs | 11.30× | 6.51× | **0.58×** | +| fft Float32 1024 dims=1 | 3.64 µs | 15.56 µs | 9.44 µs | 4.27× | 2.59× | **0.61×** | +| fft Float32 1080 dims=1 | 8.77 µs | 48.92 µs | 30.40 µs | 5.58× | 3.47× | **0.62×** | +| fft Float32 1151 dims=1 | — | 7.631 ms | — | — | — | — | +| fft Float32 1433 dims=1 | 57.64 µs | — | 100.76 µs | — | 1.75× | — | +| fft Float32 1616 dims=1 | 36.12 µs | 941.25 µs | 73.60 µs | 26.06× | 2.04× | **0.08×** | +| fft Float32 1753 dims=1 | — | 17.721 ms | — | — | — | — | +| fft Float32 2018 dims=1 | 73.28 µs | 11.745 ms | 106.24 µs | 160.28× | 1.45× | **0.01×** | +| fft Float32 2048 dims=1 | 7.68 µs | 40.60 µs | 21.04 µs | 5.29× | 2.74× | **0.52×** | +| fft Float32 2304 dims=1 | 12.42 µs | 55.04 µs | 37.04 µs | 4.43× | 2.98× | **0.67×** | +| fft Float32 2683 dims=1 | — | 41.536 ms | — | — | — | — | +| fft Float32 3027 dims=1 | 112.08 µs | 17.621 ms | 160.12 µs | 157.22× | 1.43× | **0.01×** | +| fft Float32 3491 dims=1 | 158.56 µs | — | 224.96 µs | — | 1.42× | — | +| fft Float32 4036 dims=1 | 149.00 µs | 23.492 ms | 206.28 µs | 157.66× | 1.38× | **0.01×** | +| fft Float32 4096 dims=1 | 16.88 µs | 74.32 µs | 46.68 µs | 4.40× | 2.77× | **0.63×** | +| fft Float32 4860 dims=1 | 49.84 µs | 230.12 µs | 164.92 µs | 4.62× | 3.31× | **0.72×** | +| fft Float32 6054 dims=1 | 225.88 µs | — | 355.84 µs | — | 1.58× | — | +| fft Float32 8192 dims=1 | 48.72 µs | 190.04 µs | 104.04 µs | 3.90× | 2.14× | **0.55×** | +| fft Float32 8198 dims=1 | 411.25 µs | — | 1.025 ms | — | 2.49× | — | +| fft Float32 8443 dims=1 | 413.05 µs | — | 1.066 ms | — | 2.58× | — | +| fft Float32 10290 dims=1 | 97.28 µs | 1.398 ms | 842.69 µs | 14.37× | 8.66× | **0.60×** | +| fft Float32 12297 dims=1 | 624.25 µs | — | 1.540 ms | — | 2.47× | — | +| fft Float32 16144 dims=1 | 629.25 µs | — | 824.97 µs | — | 1.31× | — | +| fft Float32 16384 dims=1 | 109.16 µs | 357.96 µs | 228.16 µs | 3.28× | 2.09× | **0.64×** | +| fft Float32 16396 dims=1 | 831.89 µs | — | 2.028 ms | — | 2.44× | — | +| fft Float32 20507 dims=1 | 1.290 ms | — | 2.677 ms | — | 2.08× | — | +| fft Float32 21875 dims=1 | 264.12 µs | 3.144 ms | 1.885 ms | 11.90× | 7.14× | **0.60×** | +| fft Float32 24594 dims=1 | 1.260 ms | — | 3.246 ms | — | 2.58× | — | +| fft Float32 32768 dims=1 | 278.20 µs | 886.37 µs | 513.45 µs | 3.19× | 1.85× | **0.58×** | +| fft Float32 32822 dims=1 | 2.015 ms | — | 5.448 ms | — | 2.70× | — | +| fft Float32 46305 dims=1 | 560.49 µs | 6.413 ms | 3.942 ms | 11.44× | 7.03× | **0.61×** | +| fft Float32 49233 dims=1 | 3.073 ms | — | 8.161 ms | — | 2.66× | — | +| fft Float32 49757 dims=1 | 2.680 ms | — | 6.136 ms | — | 2.29× | — | +| fft Float32 65536 dims=1 | 563.53 µs | 1.809 ms | 1.239 ms | 3.21× | 2.20× | **0.69×** | +| fft Float32 65584 dims=1 | 3.557 ms | — | 8.304 ms | — | 2.33× | — | +| fft Float32 65644 dims=1 | 4.107 ms | — | 10.813 ms | — | 2.63× | — | +| fft Float32 98304 dims=1 | 1.126 ms | 4.007 ms | 2.676 ms | 3.56× | 2.38× | **0.67×** | +| fft Float32 98466 dims=1 | 6.367 ms | — | 17.251 ms | — | 2.71× | — | +| fft Float32 120779 dims=1 | 9.432 ms | — | 13.839 ms | — | 1.47× | — | +| fft Float32 131072 dims=1 | 1.322 ms | 4.839 ms | 2.828 ms | 3.66× | 2.14× | **0.58×** | +| fft Float32 131074 dims=1 | 4.394 ms | — | 28.158 ms | — | 6.41× | — | +| fft Float32 196611 dims=1 | 6.678 ms | — | 42.398 ms | — | 6.35× | — | +| fft Float32 207360 dims=1 | 3.276 ms | 14.310 ms | 9.246 ms | 4.37× | 2.82× | **0.65×** | +| fft Float32 262144 dims=1 | 3.482 ms | 8.984 ms | 6.358 ms | 2.58× | 1.83× | **0.71×** | +| fft Float32 262148 dims=1 | 8.965 ms | — | 58.332 ms | — | 6.51× | — | +| fft Float32 262576 dims=1 | 18.216 ms | — | 46.404 ms | — | 2.55× | — | +| fft Float32 293201 dims=1 | 30.534 ms | — | 69.516 ms | — | 2.28× | — | +| fft Float32 393222 dims=1 | 13.552 ms | — | 90.905 ms | — | 6.71× | — | +| fft Float32 441000 dims=1 | 6.625 ms | 75.261 ms | 44.051 ms | 11.36× | 6.65× | **0.59×** | +| fft Float32 524288 dims=1 | 11.364 ms | 22.417 ms | 12.639 ms | 1.97× | 1.11× | **0.56×** | +| fft Float32 524294 dims=1 | 47.952 ms | — | 138.558 ms | — | 2.89× | — | +| fft Float32 711749 dims=1 | 76.629 ms | — | 166.553 ms | — | 2.17× | — | +| fft Float32 786441 dims=1 | 72.471 ms | — | 197.644 ms | — | 2.73× | — | +| fft Float32 933120 dims=1 | 18.504 ms | 75.834 ms | 50.926 ms | 4.10× | 2.75× | **0.67×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 164.884 ms | 104.327 ms | 6.75× | 4.27× | **0.63×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 46.496 ms | 40.752 ms | 1.93× | 1.69× | **0.88×** | +| fft Float32 1048588 dims=1 | 97.647 ms | — | 265.431 ms | — | 2.72× | — | +| fft Float32 1048592 dims=1 | 37.789 ms | — | 233.614 ms | — | 6.18× | — | +| fft Float32 1572882 dims=1 | 150.252 ms | — | 404.776 ms | — | 2.69× | — | +| fft Float32 1727797 dims=1 | 174.941 ms | — | 381.490 ms | — | 2.18× | — | +| fft Float32 1975680 dims=1 | 40.474 ms | 354.833 ms | 203.408 ms | 8.77× | 5.03× | **0.57×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 135.851 ms | 82.298 ms | 1.73× | 1.05× | **0.61×** | +| fft Float32 4167450 dims=1 | 126.844 ms | 887.725 ms | 582.126 ms | 7.00× | 4.59× | **0.66×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 244.540 ms | 184.687 ms | 1.48× | 1.12× | **0.76×** | +| fft Float64 7 dims=1 | 26 ns | 135 ns | 82 ns | 5.21× | 3.19× | **0.61×** | +| fft Float64 8 dims=1 | 25 ns | 66 ns | 24 ns | 2.63× | 0.96× | **0.37×** | +| fft Float64 11 dims=1 | — | 361 ns | — | — | — | — | +| fft Float64 12 dims=1 | 33 ns | 153 ns | 154 ns | 4.59× | 4.63× | 1.01× | +| fft Float64 16 dims=1 | 41 ns | 104 ns | 54 ns | 2.54× | 1.33× | **0.52×** | +| fft Float64 17 dims=1 | 136 ns | 920 ns | 488 ns | 6.78× | 3.59× | **0.53×** | +| fft Float64 23 dims=1 | 230 ns | 1.72 µs | 899 ns | 7.48× | 3.91× | **0.52×** | +| fft Float64 25 dims=1 | 139 ns | 720 ns | 514 ns | 5.20× | 3.71× | **0.71×** | +| fft Float64 29 dims=1 | 343 ns | 2.72 µs | 884 ns | 7.93× | 2.57× | **0.32×** | +| fft Float64 31 dims=1 | 385 ns | 3.19 µs | 888 ns | 8.28× | 2.31× | **0.28×** | +| fft Float64 32 dims=1 | 80 ns | 351 ns | 137 ns | 4.41× | 1.72× | **0.39×** | +| fft Float64 37 dims=1 | 771 ns | 4.50 µs | 1.96 µs | 5.84× | 2.54× | **0.43×** | +| fft Float64 41 dims=1 | 910 ns | 5.53 µs | 1.96 µs | 6.07× | 2.16× | **0.36×** | +| fft Float64 43 dims=1 | 699 ns | 6.16 µs | 1.97 µs | 8.81× | 2.81× | **0.32×** | +| fft Float64 54 dims=1 | 274 ns | 1.10 µs | 922 ns | 4.01× | 3.37× | **0.84×** | +| fft Float64 59 dims=1 | — | 11.76 µs | — | — | — | — | +| fft Float64 60 dims=1 | 311 ns | 1.71 µs | 1.37 µs | 5.49× | 4.40× | **0.80×** | +| fft Float64 61 dims=1 | 1.39 µs | 12.20 µs | 2.02 µs | 8.80× | 1.46× | **0.17×** | +| fft Float64 64 dims=1 | 310 ns | 588 ns | 338 ns | 1.90× | 1.09× | **0.58×** | +| fft Float64 71 dims=1 | 3.06 µs | 16.94 µs | 4.39 µs | 5.54× | 1.44× | **0.26×** | +| fft Float64 73 dims=1 | 1.74 µs | 18.08 µs | 4.39 µs | 10.38× | 2.52× | **0.24×** | +| fft Float64 79 dims=1 | 2.50 µs | 20.84 µs | 4.42 µs | 8.35× | 1.77× | **0.21×** | +| fft Float64 97 dims=1 | — | 32.64 µs | — | — | — | — | +| fft Float64 101 dims=1 | 2.37 µs | — | 4.46 µs | — | 1.88× | — | +| fft Float64 112 dims=1 | 591 ns | 3.19 µs | 1.90 µs | 5.40× | 3.21× | **0.59×** | +| fft Float64 120 dims=1 | 634 ns | 3.98 µs | 2.60 µs | 6.27× | 4.11× | **0.66×** | +| fft Float64 128 dims=1 | 647 ns | 1.75 µs | 803 ns | 2.71× | 1.24× | **0.46×** | +| fft Float64 137 dims=1 | — | 63.96 µs | — | — | — | — | +| fft Float64 202 dims=1 | 4.97 µs | 72.56 µs | 10.18 µs | 14.60× | 2.05× | **0.14×** | +| fft Float64 211 dims=1 | — | 152.00 µs | — | — | — | — | +| fft Float64 243 dims=1 | 1.94 µs | 4.55 µs | 3.84 µs | 2.34× | 1.98× | **0.84×** | +| fft Float64 251 dims=1 | 6.73 µs | — | 10.12 µs | — | 1.50× | — | +| fft Float64 256 dims=1 | 1.32 µs | 3.07 µs | 1.86 µs | 2.33× | 1.41× | **0.60×** | +| fft Float64 303 dims=1 | 7.79 µs | 107.24 µs | 15.52 µs | 13.77× | 1.99× | **0.14×** | +| fft Float64 331 dims=1 | — | 365.16 µs | — | — | — | — | +| fft Float64 360 dims=1 | 2.83 µs | 12.88 µs | 8.45 µs | 4.54× | 2.98× | **0.66×** | +| fft Float64 404 dims=1 | 10.46 µs | 143.00 µs | 19.92 µs | 13.67× | 1.90× | **0.14×** | +| fft Float64 491 dims=1 | — | 763.69 µs | — | — | — | — | +| fft Float64 504 dims=1 | 4.30 µs | 21.20 µs | 12.92 µs | 4.93× | 3.01× | **0.61×** | +| fft Float64 512 dims=1 | 2.83 µs | 8.47 µs | 4.25 µs | 2.99× | 1.50× | **0.50×** | +| fft Float64 593 dims=1 | 27.48 µs | — | 48.80 µs | — | 1.78× | — | +| fft Float64 606 dims=1 | 15.84 µs | 221.40 µs | 34.72 µs | 13.98× | 2.19× | **0.16×** | +| fft Float64 720 dims=1 | 5.64 µs | 24.56 µs | 17.02 µs | 4.35× | 3.02× | **0.69×** | +| fft Float64 751 dims=1 | — | 1.901 ms | — | — | — | — | +| fft Float64 1000 dims=1 | 10.26 µs | 56.56 µs | 35.12 µs | 5.51× | 3.42× | **0.62×** | +| fft Float64 1024 dims=1 | 6.30 µs | 15.20 µs | 9.55 µs | 2.41× | 1.52× | **0.63×** | +| fft Float64 1080 dims=1 | 9.27 µs | 41.96 µs | 27.52 µs | 4.53× | 2.97× | **0.66×** | +| fft Float64 1151 dims=1 | — | 4.593 ms | — | — | — | — | +| fft Float64 1433 dims=1 | 77.40 µs | — | 109.44 µs | — | 1.41× | — | +| fft Float64 1616 dims=1 | 44.28 µs | 578.49 µs | 79.76 µs | 13.06× | 1.80× | **0.14×** | +| fft Float64 1753 dims=1 | — | 10.932 ms | — | — | — | — | +| fft Float64 2018 dims=1 | 109.44 µs | 7.253 ms | 112.88 µs | 66.28× | 1.03× | **0.02×** | +| fft Float64 2048 dims=1 | 13.52 µs | 39.64 µs | 21.72 µs | 2.93× | 1.61× | **0.55×** | +| fft Float64 2304 dims=1 | 22.48 µs | 55.84 µs | 39.88 µs | 2.48× | 1.77× | **0.71×** | +| fft Float64 2683 dims=1 | — | 25.516 ms | — | — | — | — | +| fft Float64 3027 dims=1 | 168.20 µs | 10.878 ms | 170.24 µs | 64.67× | 1.01× | **0.02×** | +| fft Float64 3491 dims=1 | 222.48 µs | — | 240.96 µs | — | 1.08× | — | +| fft Float64 4036 dims=1 | 223.80 µs | 14.491 ms | 221.20 µs | 64.75× | 0.99× | **0.02×** | +| fft Float64 4096 dims=1 | 29.80 µs | 74.24 µs | 49.32 µs | 2.49× | 1.66× | **0.66×** | +| fft Float64 4860 dims=1 | 57.56 µs | 199.92 µs | 156.28 µs | 3.47× | 2.72× | **0.78×** | +| fft Float64 6054 dims=1 | 340.04 µs | — | 380.88 µs | — | 1.12× | — | +| fft Float64 8192 dims=1 | 84.76 µs | 189.36 µs | 107.36 µs | 2.23× | 1.27× | **0.57×** | +| fft Float64 8198 dims=1 | 506.65 µs | — | 1.145 ms | — | 2.26× | — | +| fft Float64 8443 dims=1 | 554.85 µs | — | 1.354 ms | — | 2.44× | — | +| fft Float64 10290 dims=1 | 149.96 µs | 1.002 ms | 662.53 µs | 6.68× | 4.42× | **0.66×** | +| fft Float64 12297 dims=1 | 777.05 µs | — | 1.769 ms | — | 2.28× | — | +| fft Float64 16144 dims=1 | 922.45 µs | — | 899.77 µs | — | 0.98× | — | +| fft Float64 16384 dims=1 | 180.40 µs | 354.28 µs | 249.84 µs | 1.96× | 1.38× | **0.71×** | +| fft Float64 16396 dims=1 | 1.036 ms | — | 2.281 ms | — | 2.20× | — | +| fft Float64 20507 dims=1 | 1.694 ms | — | 3.312 ms | — | 1.95× | — | +| fft Float64 21875 dims=1 | 384.44 µs | 2.263 ms | 1.573 ms | 5.89× | 4.09× | **0.70×** | +| fft Float64 24594 dims=1 | 1.613 ms | — | 3.763 ms | — | 2.33× | — | +| fft Float64 32768 dims=1 | 444.61 µs | 1.007 ms | 605.73 µs | 2.26× | 1.36× | **0.60×** | +| fft Float64 32822 dims=1 | 2.985 ms | — | 6.732 ms | — | 2.26× | — | +| fft Float64 46305 dims=1 | 1.031 ms | 4.877 ms | 3.311 ms | 4.73× | 3.21× | **0.68×** | +| fft Float64 49233 dims=1 | 4.545 ms | — | 10.122 ms | — | 2.23× | — | +| fft Float64 49757 dims=1 | 4.565 ms | — | 7.187 ms | — | 1.57× | — | +| fft Float64 65536 dims=1 | 1.088 ms | 1.930 ms | 1.433 ms | 1.77× | 1.32× | **0.74×** | +| fft Float64 65584 dims=1 | 4.401 ms | — | 9.489 ms | — | 2.16× | — | +| fft Float64 65644 dims=1 | 6.122 ms | — | 13.423 ms | — | 2.19× | — | +| fft Float64 98304 dims=1 | 1.926 ms | 4.160 ms | 2.854 ms | 2.16× | 1.48× | **0.69×** | +| fft Float64 98466 dims=1 | 9.391 ms | — | 21.008 ms | — | 2.24× | — | +| fft Float64 120779 dims=1 | 12.568 ms | — | 16.292 ms | — | 1.30× | — | +| fft Float64 131072 dims=1 | 2.406 ms | 4.918 ms | 3.018 ms | 2.04× | 1.25× | **0.61×** | +| fft Float64 131074 dims=1 | 6.943 ms | — | 32.213 ms | — | 4.64× | — | +| fft Float64 196611 dims=1 | 10.356 ms | — | 48.757 ms | — | 4.71× | — | +| fft Float64 207360 dims=1 | 4.519 ms | 14.918 ms | 9.456 ms | 3.30× | 2.09× | **0.63×** | +| fft Float64 262144 dims=1 | 5.670 ms | 8.754 ms | 6.419 ms | 1.54× | 1.13× | **0.73×** | +| fft Float64 262148 dims=1 | 13.759 ms | — | 64.921 ms | — | 4.72× | — | +| fft Float64 262576 dims=1 | 25.621 ms | — | 57.019 ms | — | 2.23× | — | +| fft Float64 293201 dims=1 | 41.017 ms | — | 90.478 ms | — | 2.21× | — | +| fft Float64 393222 dims=1 | 21.186 ms | — | 103.449 ms | — | 4.88× | — | +| fft Float64 441000 dims=1 | 10.759 ms | 61.016 ms | 42.476 ms | 5.67× | 3.95× | **0.70×** | +| fft Float64 524288 dims=1 | 16.863 ms | 28.178 ms | 17.631 ms | 1.67× | 1.05× | **0.63×** | +| fft Float64 524294 dims=1 | 69.443 ms | — | 180.370 ms | — | 2.60× | — | +| fft Float64 711749 dims=1 | 103.554 ms | — | 187.621 ms | — | 1.81× | — | +| fft Float64 786441 dims=1 | 104.363 ms | — | 266.104 ms | — | 2.55× | — | +| fft Float64 933120 dims=1 | 32.838 ms | 74.899 ms | 57.812 ms | 2.28× | 1.76× | **0.77×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 135.522 ms | 100.410 ms | 2.69× | 1.99× | **0.74×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 55.759 ms | 44.533 ms | 1.06× | 0.85× | **0.80×** | +| fft Float64 1048588 dims=1 | 141.957 ms | — | 370.972 ms | — | 2.61× | — | +| fft Float64 1048592 dims=1 | 64.157 ms | — | 267.025 ms | — | 4.16× | — | +| fft Float64 1572882 dims=1 | 218.031 ms | — | 548.306 ms | — | 2.51× | — | +| fft Float64 1727797 dims=1 | 263.816 ms | — | 397.133 ms | — | 1.51× | — | +| fft Float64 1975680 dims=1 | 76.790 ms | 297.188 ms | 192.282 ms | 3.87× | 2.50× | **0.65×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 136.512 ms | 91.048 ms | 1.14× | 0.76× | **0.67×** | +| fft Float64 4167450 dims=1 | 214.097 ms | 747.426 ms | 555.303 ms | 3.49× | 2.59× | **0.74×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 238.521 ms | 192.556 ms | 1.00× | 0.81× | **0.81×** | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 288 ns | 52 ns | 11.99× | 2.15× | **0.18×** | +| rfft Float32 8 dims=1 | 22 ns | 81 ns | 76 ns | 3.74× | 3.50× | **0.94×** | +| rfft Float32 11 dims=1 | — | 673 ns | — | — | — | — | +| rfft Float32 12 dims=1 | 27 ns | 194 ns | 178 ns | 7.16× | 6.56× | **0.92×** | +| rfft Float32 16 dims=1 | 33 ns | 158 ns | 100 ns | 4.82× | 3.06× | **0.64×** | +| rfft Float32 17 dims=1 | 134 ns | 1.58 µs | 178 ns | 11.82× | 1.33× | **0.11×** | +| rfft Float32 23 dims=1 | 202 ns | 2.90 µs | 314 ns | 14.35× | 1.55× | **0.11×** | +| rfft Float32 25 dims=1 | 76 ns | 1.11 µs | 501 ns | 14.57× | 6.56× | **0.45×** | +| rfft Float32 29 dims=1 | 288 ns | 4.63 µs | 812 ns | 16.08× | 2.82× | **0.18×** | +| rfft Float32 31 dims=1 | 319 ns | 5.31 µs | 811 ns | 16.64× | 2.54× | **0.15×** | +| rfft Float32 32 dims=1 | 101 ns | 216 ns | 159 ns | 2.13× | 1.56× | **0.73×** | +| rfft Float32 37 dims=1 | 428 ns | 7.61 µs | 1.80 µs | 17.80× | 4.21× | **0.24×** | +| rfft Float32 41 dims=1 | 508 ns | 9.39 µs | 1.81 µs | 18.49× | 3.57× | **0.19×** | +| rfft Float32 43 dims=1 | 553 ns | 10.34 µs | 1.81 µs | 18.70× | 3.28× | **0.18×** | +| rfft Float32 54 dims=1 | 213 ns | 585 ns | 461 ns | 2.74× | 2.16× | **0.79×** | +| rfft Float32 59 dims=1 | — | 19.62 µs | — | — | — | — | +| rfft Float32 60 dims=1 | 219 ns | 1.33 µs | 1.06 µs | 6.08× | 4.81× | **0.79×** | +| rfft Float32 61 dims=1 | 1.04 µs | 21.00 µs | 1.85 µs | 20.28× | 1.79× | **0.09×** | +| rfft Float32 64 dims=1 | 183 ns | 571 ns | 296 ns | 3.13× | 1.62× | **0.52×** | +| rfft Float32 71 dims=1 | 1.37 µs | 28.48 µs | 4.06 µs | 20.72× | 2.95× | **0.14×** | +| rfft Float32 73 dims=1 | 1.45 µs | 30.12 µs | 4.07 µs | 20.79× | 2.81× | **0.14×** | +| rfft Float32 79 dims=1 | 1.68 µs | 35.28 µs | 4.09 µs | 20.96× | 2.43× | **0.12×** | +| rfft Float32 97 dims=1 | — | 53.40 µs | — | — | — | — | +| rfft Float32 101 dims=1 | 2.69 µs | — | 4.14 µs | — | 1.53× | — | +| rfft Float32 112 dims=1 | 288 ns | 2.67 µs | 1.52 µs | 9.28× | 5.28× | **0.57×** | +| rfft Float32 120 dims=1 | 287 ns | 2.44 µs | 1.84 µs | 8.48× | 6.42× | **0.76×** | +| rfft Float32 128 dims=1 | 265 ns | 902 ns | 606 ns | 3.41× | 2.29× | **0.67×** | +| rfft Float32 137 dims=1 | — | 106.92 µs | — | — | — | — | +| rfft Float32 202 dims=1 | 2.12 µs | 58.12 µs | 4.58 µs | 27.36× | 2.15× | **0.08×** | +| rfft Float32 211 dims=1 | — | 254.52 µs | — | — | — | — | +| rfft Float32 243 dims=1 | 1.18 µs | 4.77 µs | 3.82 µs | 4.05× | 3.24× | **0.80×** | +| rfft Float32 251 dims=1 | 5.48 µs | — | 9.39 µs | — | 1.71× | — | +| rfft Float32 256 dims=1 | 636 ns | 2.52 µs | 1.30 µs | 3.96× | 2.05× | **0.52×** | +| rfft Float32 303 dims=1 | 8.39 µs | 176.72 µs | 14.22 µs | 21.07× | 1.70× | **0.08×** | +| rfft Float32 331 dims=1 | — | 628.45 µs | — | — | — | — | +| rfft Float32 360 dims=1 | 1.31 µs | 7.67 µs | 5.65 µs | 5.83× | 4.30× | **0.74×** | +| rfft Float32 404 dims=1 | 4.31 µs | 118.00 µs | 10.94 µs | 27.37× | 2.54× | **0.09×** | +| rfft Float32 491 dims=1 | — | 1.386 ms | — | — | — | — | +| rfft Float32 504 dims=1 | 1.53 µs | 13.64 µs | 9.19 µs | 8.90× | 6.00× | **0.67×** | +| rfft Float32 512 dims=1 | 1.14 µs | 4.34 µs | 2.81 µs | 3.82× | 2.48× | **0.65×** | +| rfft Float32 593 dims=1 | 21.96 µs | — | 45.40 µs | — | 2.07× | — | +| rfft Float32 606 dims=1 | 6.52 µs | 177.04 µs | 16.06 µs | 27.15× | 2.46× | **0.09×** | +| rfft Float32 720 dims=1 | 2.87 µs | 17.42 µs | 10.76 µs | 6.06× | 3.74× | **0.62×** | +| rfft Float32 751 dims=1 | — | 3.249 ms | — | — | — | — | +| rfft Float32 1000 dims=1 | 3.13 µs | 37.96 µs | 24.40 µs | 12.14× | 7.81× | **0.64×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 11.62 µs | 6.14 µs | 5.28× | 2.79× | **0.53×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 24.48 µs | 17.94 µs | 5.28× | 3.87× | **0.73×** | +| rfft Float32 1151 dims=1 | — | 7.636 ms | — | — | — | — | +| rfft Float32 1433 dims=1 | 54.24 µs | — | 99.76 µs | — | 1.84× | — | +| rfft Float32 1616 dims=1 | 17.54 µs | 475.61 µs | 39.84 µs | 27.12× | 2.27× | **0.08×** | +| rfft Float32 1753 dims=1 | — | 17.724 ms | — | — | — | — | +| rfft Float32 2018 dims=1 | 37.16 µs | 5.864 ms | 50.64 µs | 157.80× | 1.36× | **0.01×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 19.80 µs | 13.30 µs | 4.45× | 2.99× | **0.67×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 38.48 µs | 21.52 µs | 5.63× | 3.15× | **0.56×** | +| rfft Float32 2683 dims=1 | — | 41.545 ms | — | — | — | — | +| rfft Float32 3027 dims=1 | 71.52 µs | 17.626 ms | 157.40 µs | 246.45× | 2.20× | **0.01×** | +| rfft Float32 3491 dims=1 | 149.84 µs | — | 222.76 µs | — | 1.49× | — | +| rfft Float32 4036 dims=1 | 75.00 µs | 11.758 ms | 119.44 µs | 156.77× | 1.59× | **0.01×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 51.84 µs | 28.84 µs | 5.52× | 3.07× | **0.56×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 130.84 µs | 103.00 µs | 5.14× | 4.04× | **0.79×** | +| rfft Float32 6054 dims=1 | 113.60 µs | — | 175.92 µs | — | 1.55× | — | +| rfft Float32 8192 dims=1 | 25.56 µs | 91.48 µs | 62.00 µs | 3.58× | 2.43× | **0.68×** | +| rfft Float32 8198 dims=1 | 207.04 µs | — | 499.61 µs | — | 2.41× | — | +| rfft Float32 8443 dims=1 | 345.44 µs | — | 1.060 ms | — | 3.07× | — | +| rfft Float32 10290 dims=1 | 62.92 µs | 681.21 µs | 415.88 µs | 10.83× | 6.61× | **0.61×** | +| rfft Float32 12297 dims=1 | 522.37 µs | — | 1.532 ms | — | 2.93× | — | +| rfft Float32 16144 dims=1 | 307.68 µs | — | 441.89 µs | — | 1.44× | — | +| rfft Float32 16384 dims=1 | 54.04 µs | 234.60 µs | 135.84 µs | 4.34× | 2.51× | **0.58×** | +| rfft Float32 16396 dims=1 | 418.08 µs | — | 1.079 ms | — | 2.58× | — | +| rfft Float32 20507 dims=1 | 962.05 µs | — | 2.609 ms | — | 2.71× | — | +| rfft Float32 21875 dims=1 | 197.00 µs | 3.214 ms | 1.615 ms | 16.31× | 8.20× | **0.50×** | +| rfft Float32 24594 dims=1 | 631.01 µs | — | 1.610 ms | — | 2.55× | — | +| rfft Float32 32768 dims=1 | 117.04 µs | 421.21 µs | 291.12 µs | 3.60× | 2.49× | **0.69×** | +| rfft Float32 32822 dims=1 | 1.010 ms | — | 2.663 ms | — | 2.64× | — | +| rfft Float32 46305 dims=1 | 453.65 µs | 6.744 ms | 3.355 ms | 14.87× | 7.40× | **0.50×** | +| rfft Float32 49233 dims=1 | 2.572 ms | — | 8.145 ms | — | 3.17× | — | +| rfft Float32 49757 dims=1 | 2.717 ms | — | 6.098 ms | — | 2.24× | — | +| rfft Float32 65536 dims=1 | 244.00 µs | 1.061 ms | 645.89 µs | 4.35× | 2.65× | **0.61×** | +| rfft Float32 65584 dims=1 | 1.708 ms | — | 4.237 ms | — | 2.48× | — | +| rfft Float32 65644 dims=1 | 2.032 ms | — | 5.754 ms | — | 2.83× | — | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.877 ms | 1.402 ms | 3.65× | 2.72× | **0.75×** | +| rfft Float32 98466 dims=1 | 3.089 ms | — | 8.583 ms | — | 2.78× | — | +| rfft Float32 120779 dims=1 | 10.598 ms | — | 13.816 ms | — | 1.30× | — | +| rfft Float32 131072 dims=1 | 614.25 µs | 2.049 ms | 1.492 ms | 3.34× | 2.43× | **0.73×** | +| rfft Float32 131074 dims=1 | 2.210 ms | — | 13.789 ms | — | 6.24× | — | +| rfft Float32 196611 dims=1 | 6.210 ms | — | 42.160 ms | — | 6.79× | — | +| rfft Float32 207360 dims=1 | 1.700 ms | 6.965 ms | 4.635 ms | 4.10× | 2.73× | **0.67×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 5.665 ms | 3.428 ms | 3.39× | 2.05× | **0.61×** | +| rfft Float32 262148 dims=1 | 4.534 ms | — | 30.091 ms | — | 6.64× | — | +| rfft Float32 262576 dims=1 | 8.653 ms | — | 23.147 ms | — | 2.68× | — | +| rfft Float32 293201 dims=1 | 31.617 ms | — | 75.204 ms | — | 2.38× | — | +| rfft Float32 393222 dims=1 | 6.798 ms | — | 44.980 ms | — | 6.62× | — | +| rfft Float32 441000 dims=1 | 3.804 ms | 37.207 ms | 22.935 ms | 9.78× | 6.03× | **0.62×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 10.446 ms | 7.534 ms | 2.76× | 1.99× | **0.72×** | +| rfft Float32 524294 dims=1 | 23.932 ms | — | 72.213 ms | — | 3.02× | — | +| rfft Float32 711749 dims=1 | 91.203 ms | — | 168.063 ms | — | 1.84× | — | +| rfft Float32 786441 dims=1 | 89.117 ms | — | 205.696 ms | — | 2.31× | — | +| rfft Float32 933120 dims=1 | 9.020 ms | 40.413 ms | 26.508 ms | 4.48× | 2.94× | **0.66×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 88.934 ms | 53.061 ms | 10.23× | 6.10× | **0.60×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 24.874 ms | 16.583 ms | 3.17× | 2.12× | **0.67×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | — | 138.800 ms | — | 2.90× | — | +| rfft Float32 1048592 dims=1 | 18.670 ms | — | 117.241 ms | — | 6.28× | — | +| rfft Float32 1572882 dims=1 | 73.534 ms | — | 198.825 ms | — | 2.70× | — | +| rfft Float32 1727797 dims=1 | 251.742 ms | — | 377.923 ms | — | 1.50× | — | +| rfft Float32 1975680 dims=1 | 16.948 ms | 172.736 ms | 105.066 ms | 10.19× | 6.20× | **0.61×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 61.345 ms | 45.389 ms | 3.74× | 2.77× | **0.74×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 423.884 ms | 283.209 ms | 5.07× | 3.39× | **0.67×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 162.361 ms | 92.203 ms | 3.15× | 1.79× | **0.57×** | +| rfft Float64 7 dims=1 | 24 ns | 205 ns | 52 ns | 8.54× | 2.17× | **0.25×** | +| rfft Float64 8 dims=1 | 22 ns | 85 ns | 82 ns | 3.91× | 3.79× | 0.97× | +| rfft Float64 11 dims=1 | — | 438 ns | — | — | — | — | +| rfft Float64 12 dims=1 | 28 ns | 203 ns | 187 ns | 7.36× | 6.78× | **0.92×** | +| rfft Float64 16 dims=1 | 32 ns | 165 ns | 106 ns | 5.14× | 3.30× | **0.64×** | +| rfft Float64 17 dims=1 | 137 ns | 989 ns | 191 ns | 7.23× | 1.40× | **0.19×** | +| rfft Float64 23 dims=1 | 205 ns | 1.81 µs | 339 ns | 8.82× | 1.65× | **0.19×** | +| rfft Float64 25 dims=1 | 75 ns | 824 ns | 427 ns | 10.96× | 5.67× | **0.52×** | +| rfft Float64 29 dims=1 | 290 ns | 2.75 µs | 886 ns | 9.48× | 3.05× | **0.32×** | +| rfft Float64 31 dims=1 | 323 ns | 3.24 µs | 888 ns | 10.02× | 2.75× | **0.27×** | +| rfft Float64 32 dims=1 | 89 ns | 225 ns | 166 ns | 2.53× | 1.86× | **0.74×** | +| rfft Float64 37 dims=1 | 431 ns | 4.47 µs | 1.96 µs | 10.39× | 4.55× | **0.44×** | +| rfft Float64 41 dims=1 | 512 ns | 5.50 µs | 1.96 µs | 10.74× | 3.83× | **0.36×** | +| rfft Float64 43 dims=1 | 556 ns | 6.21 µs | 1.97 µs | 11.17× | 3.54× | **0.32×** | +| rfft Float64 54 dims=1 | 167 ns | 601 ns | 474 ns | 3.60× | 2.83× | **0.79×** | +| rfft Float64 59 dims=1 | — | 11.72 µs | — | — | — | — | +| rfft Float64 60 dims=1 | 171 ns | 1.13 µs | 982 ns | 6.59× | 5.75× | **0.87×** | +| rfft Float64 61 dims=1 | 1.04 µs | 12.24 µs | 2.01 µs | 11.72× | 1.93× | **0.16×** | +| rfft Float64 64 dims=1 | 166 ns | 582 ns | 310 ns | 3.50× | 1.87× | **0.53×** | +| rfft Float64 71 dims=1 | 1.39 µs | 16.96 µs | 4.38 µs | 12.24× | 3.16× | **0.26×** | +| rfft Float64 73 dims=1 | 1.46 µs | 17.54 µs | 4.39 µs | 12.04× | 3.01× | **0.25×** | +| rfft Float64 79 dims=1 | 1.69 µs | 21.00 µs | 4.39 µs | 12.40× | 2.59× | **0.21×** | +| rfft Float64 97 dims=1 | — | 31.04 µs | — | — | — | — | +| rfft Float64 101 dims=1 | 2.71 µs | — | 4.45 µs | — | 1.64× | — | +| rfft Float64 112 dims=1 | 297 ns | 2.06 µs | 1.22 µs | 6.93× | 4.11× | **0.59×** | +| rfft Float64 120 dims=1 | 334 ns | 2.05 µs | 1.70 µs | 6.14× | 5.09× | **0.83×** | +| rfft Float64 128 dims=1 | 327 ns | 916 ns | 637 ns | 2.80× | 1.95× | **0.70×** | +| rfft Float64 137 dims=1 | — | 62.36 µs | — | — | — | — | +| rfft Float64 202 dims=1 | 2.60 µs | 37.16 µs | 4.90 µs | 14.29× | 1.88× | **0.13×** | +| rfft Float64 211 dims=1 | — | 149.28 µs | — | — | — | — | +| rfft Float64 243 dims=1 | 1.26 µs | 5.20 µs | 3.85 µs | 4.12× | 3.05× | **0.74×** | +| rfft Float64 251 dims=1 | 5.71 µs | — | 10.10 µs | — | 1.77× | — | +| rfft Float64 256 dims=1 | 693 ns | 2.65 µs | 1.35 µs | 3.83× | 1.95× | **0.51×** | +| rfft Float64 303 dims=1 | 8.40 µs | 108.92 µs | 15.50 µs | 12.97× | 1.85× | **0.14×** | +| rfft Float64 331 dims=1 | — | 366.96 µs | — | — | — | — | +| rfft Float64 360 dims=1 | 1.40 µs | 6.75 µs | 5.25 µs | 4.81× | 3.74× | **0.78×** | +| rfft Float64 404 dims=1 | 5.36 µs | 76.84 µs | 11.70 µs | 14.34× | 2.18× | **0.15×** | +| rfft Float64 491 dims=1 | — | 804.37 µs | — | — | — | — | +| rfft Float64 504 dims=1 | 2.03 µs | 10.88 µs | 7.92 µs | 5.35× | 3.90× | **0.73×** | +| rfft Float64 512 dims=1 | 1.46 µs | 4.38 µs | 2.92 µs | 2.99× | 2.00× | **0.67×** | +| rfft Float64 593 dims=1 | 22.36 µs | — | 48.68 µs | — | 2.18× | — | +| rfft Float64 606 dims=1 | 8.15 µs | 114.96 µs | 17.06 µs | 14.11× | 2.09× | **0.15×** | +| rfft Float64 720 dims=1 | 2.88 µs | 15.12 µs | 9.92 µs | 5.25× | 3.44× | **0.66×** | +| rfft Float64 751 dims=1 | — | 1.918 ms | — | — | — | — | +| rfft Float64 1000 dims=1 | 4.49 µs | 28.72 µs | 20.40 µs | 6.40× | 4.55× | **0.71×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 11.86 µs | 6.30 µs | 3.79× | 2.02× | **0.53×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 21.56 µs | 16.82 µs | 4.58× | 3.57× | **0.78×** | +| rfft Float64 1151 dims=1 | — | 4.593 ms | — | — | — | — | +| rfft Float64 1433 dims=1 | 56.12 µs | — | 109.24 µs | — | 1.95× | — | +| rfft Float64 1616 dims=1 | 22.28 µs | 310.04 µs | 43.16 µs | 13.92× | 1.94× | **0.14×** | +| rfft Float64 1753 dims=1 | — | 10.939 ms | — | — | — | — | +| rfft Float64 2018 dims=1 | 55.68 µs | 3.748 ms | 53.72 µs | 67.32× | 0.96× | **0.01×** | +| rfft Float64 2048 dims=1 | 6.68 µs | 20.12 µs | 13.80 µs | 3.01× | 2.07× | **0.69×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 40.04 µs | 23.32 µs | 4.10× | 2.39× | **0.58×** | +| rfft Float64 2683 dims=1 | — | 25.468 ms | — | — | — | — | +| rfft Float64 3027 dims=1 | 73.56 µs | 10.890 ms | 169.48 µs | 148.04× | 2.30× | **0.02×** | +| rfft Float64 3491 dims=1 | 156.80 µs | — | 240.52 µs | — | 1.53× | — | +| rfft Float64 4036 dims=1 | 113.44 µs | 7.566 ms | 126.84 µs | 66.70× | 1.12× | **0.02×** | +| rfft Float64 4096 dims=1 | 14.52 µs | 52.60 µs | 30.08 µs | 3.62× | 2.07× | **0.57×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 115.96 µs | 97.36 µs | 3.99× | 3.35× | **0.84×** | +| rfft Float64 6054 dims=1 | 171.84 µs | — | 186.92 µs | — | 1.09× | — | +| rfft Float64 8192 dims=1 | 39.12 µs | 93.80 µs | 66.20 µs | 2.40× | 1.69× | **0.71×** | +| rfft Float64 8198 dims=1 | 258.64 µs | — | 550.57 µs | — | 2.13× | — | +| rfft Float64 8443 dims=1 | 364.37 µs | — | 1.326 ms | — | 3.64× | — | +| rfft Float64 10290 dims=1 | 74.76 µs | 477.85 µs | 322.36 µs | 6.39× | 4.31× | **0.67×** | +| rfft Float64 12297 dims=1 | 549.53 µs | — | 1.727 ms | — | 3.14× | — | +| rfft Float64 16144 dims=1 | 460.81 µs | — | 478.77 µs | — | 1.04× | — | +| rfft Float64 16384 dims=1 | 86.72 µs | 240.56 µs | 142.44 µs | 2.77× | 1.64× | **0.59×** | +| rfft Float64 16396 dims=1 | 523.69 µs | — | 1.234 ms | — | 2.36× | — | +| rfft Float64 20507 dims=1 | 1.134 ms | — | 3.309 ms | — | 2.92× | — | +| rfft Float64 21875 dims=1 | 200.92 µs | 2.375 ms | 1.386 ms | 11.82× | 6.90× | **0.58×** | +| rfft Float64 24594 dims=1 | 794.97 µs | — | 1.783 ms | — | 2.24× | — | +| rfft Float64 32768 dims=1 | 195.60 µs | 443.89 µs | 323.20 µs | 2.27× | 1.65× | **0.73×** | +| rfft Float64 32822 dims=1 | 1.488 ms | — | 3.316 ms | — | 2.23× | — | +| rfft Float64 46305 dims=1 | 482.65 µs | 5.368 ms | 3.111 ms | 11.12× | 6.45× | **0.58×** | +| rfft Float64 49233 dims=1 | 2.796 ms | — | 10.107 ms | — | 3.62× | — | +| rfft Float64 49757 dims=1 | 2.906 ms | — | 7.156 ms | — | 2.46× | — | +| rfft Float64 65536 dims=1 | 468.09 µs | 1.214 ms | 777.21 µs | 2.59× | 1.66× | **0.64×** | +| rfft Float64 65584 dims=1 | 2.195 ms | — | 4.947 ms | — | 2.25× | — | +| rfft Float64 65644 dims=1 | 3.025 ms | — | 7.010 ms | — | 2.32× | — | +| rfft Float64 98304 dims=1 | 928.13 µs | 2.083 ms | 1.612 ms | 2.24× | 1.74× | **0.77×** | +| rfft Float64 98466 dims=1 | 4.623 ms | — | 10.431 ms | — | 2.26× | — | +| rfft Float64 120779 dims=1 | 11.377 ms | — | 15.972 ms | — | 1.40× | — | +| rfft Float64 131072 dims=1 | 1.139 ms | 2.404 ms | 1.788 ms | 2.11× | 1.57× | **0.74×** | +| rfft Float64 131074 dims=1 | 3.508 ms | — | 15.799 ms | — | 4.50× | — | +| rfft Float64 196611 dims=1 | 7.590 ms | — | 48.616 ms | — | 6.41× | — | +| rfft Float64 207360 dims=1 | 2.319 ms | 6.521 ms | 4.971 ms | 2.81× | 2.14× | **0.76×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 5.926 ms | 3.886 ms | 2.27× | 1.49× | **0.66×** | +| rfft Float64 262148 dims=1 | 7.006 ms | — | 33.701 ms | — | 4.81× | — | +| rfft Float64 262576 dims=1 | 12.798 ms | — | 29.094 ms | — | 2.27× | — | +| rfft Float64 293201 dims=1 | 36.020 ms | — | 89.305 ms | — | 2.48× | — | +| rfft Float64 393222 dims=1 | 10.518 ms | — | 50.481 ms | — | 4.80× | — | +| rfft Float64 441000 dims=1 | 5.855 ms | 27.779 ms | 21.021 ms | 4.74× | 3.59× | **0.76×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 11.151 ms | 9.322 ms | 1.94× | 1.62× | **0.84×** | +| rfft Float64 524294 dims=1 | 34.813 ms | — | 87.086 ms | — | 2.50× | — | +| rfft Float64 711749 dims=1 | 110.585 ms | — | 188.235 ms | — | 1.70× | — | +| rfft Float64 786441 dims=1 | 98.952 ms | — | 279.184 ms | — | 2.82× | — | +| rfft Float64 933120 dims=1 | 11.815 ms | 39.195 ms | 30.104 ms | 3.32× | 2.55× | **0.77×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 71.973 ms | 49.824 ms | 3.37× | 2.33× | **0.69×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 34.374 ms | 22.659 ms | 2.55× | 1.68× | **0.66×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | — | 202.002 ms | — | 2.89× | — | +| rfft Float64 1048592 dims=1 | 30.247 ms | — | 136.732 ms | — | 4.52× | — | +| rfft Float64 1572882 dims=1 | 107.501 ms | — | 263.714 ms | — | 2.45× | — | +| rfft Float64 1727797 dims=1 | 329.992 ms | — | 399.009 ms | — | 1.21× | — | +| rfft Float64 1975680 dims=1 | 38.541 ms | 140.202 ms | 97.390 ms | 3.64× | 2.53× | **0.69×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 71.504 ms | 50.658 ms | 1.28× | 0.91× | **0.71×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 364.338 ms | 276.903 ms | 3.23× | 2.45× | **0.76×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 172.528 ms | 100.592 ms | 1.45× | 0.85× | **0.58×** | +| fft Float32 8×8 dims=1,2 | 144 ns | 5.12 µs | 695 ns | 35.56× | 4.83× | **0.14×** | +| fft Float32 16×16 dims=1,2 | 570 ns | 8.16 µs | 2.49 µs | 14.32× | 4.36× | **0.30×** | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 33.04 µs | 10.72 µs | 12.35× | 4.01× | **0.32×** | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 93.76 µs | 48.76 µs | 7.60× | 3.95× | **0.52×** | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 589.73 µs | 249.20 µs | 9.80× | 4.14× | **0.42×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 2.140 ms | 1.174 ms | 2.80× | 1.54× | **0.55×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 17.206 ms | 7.114 ms | 3.06× | 1.27× | **0.41×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 71.614 ms | 33.975 ms | 2.84× | 1.35× | **0.47×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 452.656 ms | 159.402 ms | 3.39× | 1.19× | **0.35×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 5.12 µs | 720 ns | 29.54× | 4.15× | **0.14×** | +| fft Float64 16×16 dims=1,2 | 819 ns | 8.19 µs | 2.52 µs | 9.99× | 3.08× | **0.31×** | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 33.52 µs | 11.34 µs | 8.15× | 2.76× | **0.34×** | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 96.28 µs | 53.04 µs | 4.68× | 2.58× | **0.55×** | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 639.65 µs | 279.08 µs | 5.80× | 2.53× | **0.44×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 46.229 ms | 4.074 ms | 25.76× | 2.27× | **0.09×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 243.873 ms | 3.820 ms | 66.40× | 1.04× | **0.02×** | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 245.441 ms | 3.978 ms | 63.71× | 1.03× | **0.02×** | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 2.923 ms | 1.476 ms | 2.56× | 1.29× | **0.51×** | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 18.764 ms | 7.519 ms | 3.07× | 1.23× | **0.40×** | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 31.742 ms | 19.637 ms | 4.80× | 2.97× | **0.62×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 139.656 ms | 87.006 ms | 5.02× | 3.13× | **0.62×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 80.880 ms | 37.090 ms | 2.69× | 1.23× | **0.46×** | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 536.406 ms | 181.709 ms | 3.27× | 1.11× | **0.34×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 5.92 µs | 855 ns | 47.91× | 6.92× | **0.14×** | +| rfft Float32 16×16 dims=1,2 | 438 ns | 9.60 µs | 2.36 µs | 21.93× | 5.38× | **0.25×** | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 35.56 µs | 8.03 µs | 17.36× | 3.92× | **0.23×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 99.72 µs | 32.04 µs | 10.13× | 3.26× | **0.32×** | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 628.61 µs | 140.80 µs | 13.47× | 3.02× | **0.22×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 2.175 ms | 626.61 µs | 6.24× | 1.80× | **0.29×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 16.948 ms | 2.827 ms | 11.74× | 1.96× | **0.17×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 72.126 ms | 12.647 ms | 12.00× | 2.10× | **0.18×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 493.419 ms | 62.300 ms | 14.21× | 1.79× | **0.13×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 5.96 µs | 918 ns | 50.88× | 7.84× | **0.15×** | +| rfft Float64 16×16 dims=1,2 | 490 ns | 9.74 µs | 2.47 µs | 19.88× | 5.03× | **0.25×** | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 36.64 µs | 8.43 µs | 15.27× | 3.51× | **0.23×** | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 103.24 µs | 33.56 µs | 8.78× | 2.85× | **0.33×** | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 677.17 µs | 147.56 µs | 11.63× | 2.53× | **0.22×** | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 46.354 ms | 2.621 ms | 30.64× | 1.73× | **0.06×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 243.997 ms | 3.435 ms | 151.11× | 2.13× | **0.01×** | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 245.381 ms | 2.061 ms | 126.57× | 1.06× | **0.01×** | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 3.116 ms | 655.81 µs | 7.64× | 1.61× | **0.21×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 19.180 ms | 3.023 ms | 10.02× | 1.58× | **0.16×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 32.163 ms | 9.706 ms | 10.21× | 3.08× | **0.30×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 142.463 ms | 41.844 ms | 10.91× | 3.21× | **0.29×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 82.443 ms | 13.501 ms | 9.43× | 1.54× | **0.16×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 610.292 ms | 66.415 ms | 11.23× | 1.22× | **0.11×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | ✗ | 9.43 µs | — | 6.09× | — | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | ✗ | 64.72 µs | — | 4.81× | — | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | ✗ | 586.89 µs | — | 4.14× | — | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | ✗ | 5.730 ms | — | 3.84× | — | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | ✗ | 63.521 ms | — | 3.44× | — | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | ✗ | 9.51 µs | — | 4.99× | — | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | ✗ | 66.48 µs | — | 3.33× | — | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | ✗ | 635.97 µs | — | 2.63× | — | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | ✗ | 6.546 ms | — | 2.63× | — | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | ✗ | 79.089 ms | — | 2.03× | — | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | ✗ | 9.15 µs | — | 7.70× | — | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | ✗ | 51.52 µs | — | 5.58× | — | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | ✗ | 367.28 µs | — | 4.04× | — | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | ✗ | 3.117 ms | — | 3.27× | — | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | ✗ | 28.825 ms | — | 3.08× | — | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | ✗ | 9.68 µs | — | 8.09× | — | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | ✗ | 53.44 µs | — | 4.70× | — | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | ✗ | 389.12 µs | — | 3.33× | — | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | ✗ | 3.502 ms | — | 2.59× | — | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | ✗ | 32.189 ms | — | 2.18× | — | +| fft Float32 64×64 dims=1 | 6.23 µs | 131.28 µs | 22.52 µs | 21.07× | 3.61× | **0.17×** | +| fft Float32 256×64 dims=1 | 52.20 µs | 311.44 µs | 123.72 µs | 5.97× | 2.37× | **0.40×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 1.192 ms | 641.05 µs | 4.87× | 2.62× | **0.54×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 5.519 ms | 3.274 ms | 4.32× | 2.56× | **0.59×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 28.367 ms | 16.238 ms | 3.66× | 2.09× | **0.57×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 137.092 ms | 89.441 ms | 3.08× | 2.01× | **0.65×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 150.44 µs | 23.80 µs | 14.58× | 2.31× | **0.16×** | +| fft Float64 256×64 dims=1 | 87.04 µs | 340.00 µs | 128.96 µs | 3.91× | 1.48× | **0.38×** | +| fft Float64 1024×64 dims=1 | 434.17 µs | 1.269 ms | 692.65 µs | 2.92× | 1.60× | **0.55×** | +| fft Float64 4096×64 dims=1 | 2.162 ms | 7.087 ms | 3.704 ms | 3.28× | 1.71× | **0.52×** | +| fft Float64 16384×64 dims=1 | 14.861 ms | 33.913 ms | 20.696 ms | 2.28× | 1.39× | **0.61×** | +| fft Float64 65536×64 dims=1 | 88.463 ms | 183.380 ms | 114.295 ms | 2.07× | 1.29× | **0.62×** | +| rfft Float32 64×64 dims=1 | 6.61 µs | 45.16 µs | 18.84 µs | 6.83× | 2.85× | **0.42×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 179.08 µs | 84.84 µs | 4.38× | 2.08× | **0.47×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 813.77 µs | 398.04 µs | 5.65× | 2.77× | **0.49×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 3.573 ms | 1.883 ms | 5.19× | 2.73× | **0.53×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 16.151 ms | 8.886 ms | 4.33× | 2.38× | **0.55×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 72.975 ms | 43.449 ms | 3.83× | 2.28× | **0.60×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 47.28 µs | 19.88 µs | 7.08× | 2.98× | **0.42×** | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 14.722 ms | 5.795 ms | 4.73× | 1.86× | **0.39×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 202.24 µs | 87.40 µs | 4.54× | 1.96× | **0.43×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 14.213 ms | 6.792 ms | 3.87× | 1.85× | **0.48×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 862.81 µs | 414.57 µs | 4.03× | 1.94× | **0.48×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 15.294 ms | 8.002 ms | 3.60× | 1.89× | **0.52×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 3.743 ms | 1.974 ms | 3.60× | 1.90× | **0.53×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 18.009 ms | 9.841 ms | 2.93× | 1.60× | **0.55×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 96.680 ms | 51.373 ms | 2.54× | 1.35× | **0.53×** | +| fft Float32 64×64 dims=2 | 6.13 µs | 151.44 µs | 27.16 µs | 24.71× | 4.43× | **0.18×** | +| fft Float32 64×256 dims=2 | 79.52 µs | 350.88 µs | 152.72 µs | 4.41× | 1.92× | **0.44×** | +| fft Float32 64×1024 dims=2 | 433.65 µs | 1.443 ms | 855.77 µs | 3.33× | 1.97× | **0.59×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 8.549 ms | 5.921 ms | 1.82× | 1.26× | **0.69×** | +| fft Float32 64×16384 dims=2 | 24.311 ms | 47.582 ms | 33.530 ms | 1.96× | 1.38× | **0.70×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 277.223 ms | 204.301 ms | 1.61× | 1.19× | **0.74×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 148.56 µs | 28.56 µs | 13.68× | 2.63× | **0.19×** | +| fft Float64 64×256 dims=2 | 108.96 µs | 361.00 µs | 166.52 µs | 3.31× | 1.53× | **0.46×** | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.884 ms | 1.189 ms | 2.13× | 1.35× | **0.63×** | +| fft Float64 64×4096 dims=2 | 5.347 ms | 9.816 ms | 6.816 ms | 1.84× | 1.27× | **0.69×** | +| fft Float64 64×16384 dims=2 | 34.143 ms | 62.892 ms | 44.409 ms | 1.84× | 1.30× | **0.71×** | +| fft Float64 64×65536 dims=2 | 247.287 ms | 340.856 ms | 270.970 ms | 1.38× | 1.10× | **0.79×** | +| rfft Float32 64×64 dims=2 | 6.60 µs | 47.56 µs | 22.20 µs | 7.21× | 3.36× | **0.47×** | +| rfft Float32 64×256 dims=2 | 57.92 µs | 205.92 µs | 108.84 µs | 3.56× | 1.88× | **0.53×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 953.49 µs | 542.45 µs | 3.30× | 1.88× | **0.57×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 4.541 ms | 2.858 ms | 2.55× | 1.60× | **0.63×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 22.360 ms | 14.192 ms | 1.92× | 1.22× | **0.63×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 112.089 ms | 71.405 ms | 1.63× | 1.04× | **0.64×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 49.60 µs | 23.48 µs | 7.50× | 3.55× | **0.47×** | +| rfft Float64 64×256 dims=2 | 71.64 µs | 237.80 µs | 122.84 µs | 3.32× | 1.71× | **0.52×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 1.075 ms | 579.85 µs | 3.09× | 1.67× | **0.54×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 5.281 ms | 3.269 ms | 1.94× | 1.20× | **0.62×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 25.091 ms | 15.739 ms | 1.77× | 1.11× | **0.63×** | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 149.756 ms | 89.091 ms | 1.34× | 0.80× | **0.59×** | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `release`/`fftw` | `int`/`fftw` | `release` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 6.97× (2.80–35.56) | 2.53× (1.19–4.83) | **0.36×** (0.14–0.55) | +| ComplexF32 fft 3d | — | 4.38× (3.44–6.09) | — | +| ComplexF32 fft awkward | 53.04× (26.06–160.28) | 2.68× (1.31–6.71) | **0.04×** (0.01–0.09) | +| ComplexF32 fft batched_dim1 | 5.57× (3.08–21.07) | 2.50× (2.01–3.61) | **0.45×** (0.17–0.65) | +| ComplexF32 fft batched_dim2 | 3.57× (1.61–24.71) | 1.81× (1.19–4.43) | **0.51×** (0.18–0.74) | +| ComplexF32 fft pow2 | 3.01× (1.48–5.29) | 1.71× (0.65–2.77) | **0.57×** (0.37–0.88) | +| ComplexF32 fft prime | 12.77× (5.61–22.37) | 2.34× (1.42–6.55) | **0.21×** (0.09–0.57) | +| ComplexF32 fft smooth | 6.79× (2.39–14.37) | 4.45× (2.02–8.66) | **0.66×** (0.57–0.99) | +| ComplexF64 fft 2d | 8.59× (2.56–66.40) | 1.95× (1.03–4.15) | **0.23×** (0.02–0.62) | +| ComplexF64 fft 3d | — | 2.98× (2.03–4.99) | — | +| ComplexF64 fft awkward | 24.72× (13.06–66.28) | 2.21× (0.98–4.88) | **0.06×** (0.02–0.16) | +| ComplexF64 fft batched_dim1 | 3.70× (2.07–14.58) | 1.60× (1.29–2.31) | **0.43×** (0.16–0.62) | +| ComplexF64 fft batched_dim2 | 2.77× (1.38–13.68) | 1.46× (1.10–2.63) | **0.53×** (0.19–0.79) | +| ComplexF64 fft pow2 | 2.07× (1.00–4.41) | 1.23× (0.76–1.72) | **0.59×** (0.37–0.81) | +| ComplexF64 fft prime | 7.30× (5.21–10.38) | 2.00× (1.08–3.91) | **0.33×** (0.17–0.61) | +| ComplexF64 fft smooth | 4.11× (2.16–6.68) | 2.92× (1.48–4.63) | **0.71×** (0.59–1.01) | +| Float32 rfft 2d | 14.65× (6.24–47.91) | 2.99× (1.79–6.92) | **0.20×** (0.13–0.32) | +| Float32 rfft 3d | — | 4.45× (3.08–7.70) | — | +| Float32 rfft awkward | 53.86× (21.07–246.45) | 2.77× (1.36–6.79) | **0.04×** (0.01–0.09) | +| Float32 rfft batched_dim1 | 4.94× (3.83–6.83) | 2.50× (2.08–2.85) | **0.51×** (0.42–0.60) | +| Float32 rfft batched_dim2 | 2.96× (1.63–7.21) | 1.70× (1.04–3.36) | **0.57×** (0.47–0.64) | +| Float32 rfft pow2 | 3.70× (2.13–5.52) | 2.38× (1.56–3.50) | **0.64×** (0.52–0.94) | +| Float32 rfft prime | 17.07× (11.82–20.96) | 2.18× (1.30–4.21) | **0.15×** (0.09–0.24) | +| Float32 rfft smooth | 7.12× (2.74–16.31) | 4.68× (2.16–8.20) | **0.66×** (0.45–0.92) | +| Float64 rfft 2d | 19.06× (7.64–151.11) | 2.38× (1.06–7.84) | **0.12×** (0.01–0.33) | +| Float64 rfft 3d | — | 3.72× (2.18–8.09) | — | +| Float64 rfft awkward | 27.70× (12.97–148.04) | 2.39× (0.96–6.41) | **0.06×** (0.01–0.15) | +| Float64 rfft batched_dim1 | 3.94× (2.54–7.08) | 1.89× (1.35–2.98) | **0.48×** (0.39–0.55) | +| Float64 rfft batched_dim2 | 2.66× (1.34–7.50) | 1.49× (0.80–3.55) | **0.56×** (0.47–0.63) | +| Float64 rfft pow2 | 2.70× (1.28–5.14) | 1.78× (0.85–3.79) | **0.66×** (0.51–0.97) | +| Float64 rfft prime | 10.27× (7.23–12.40) | 2.29× (1.21–4.55) | **0.26×** (0.16–0.44) | +| Float64 rfft smooth | 5.04× (2.24–11.82) | 3.61× (1.74–6.90) | **0.72×** (0.52–0.92) | +| **all** | 6.49× (1.00–246.45) | 2.45× (0.65–8.66) | **0.37×** (0.01–1.01), 353 cases, 350 slower by >5% | diff --git a/benchmark/compare3/aarch64/baseline/fftw_t1.json b/benchmark/compare3/aarch64/baseline/fftw_t1.json new file mode 100644 index 0000000..82da41b --- /dev/null +++ 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0.015294058000000001, + "key": "rfft Float64 4096\u00d7256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113903044, + "nthreads": 1, + "plan_min": 1.3652173913043478e-07, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853256748, + "sum_re": -2384.388702165721 + } + ] +} \ No newline at end of file From a501433ac44725c9acce2511c8b3362709ef39e5 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 11:35:07 +0000 Subject: [PATCH 07/21] benchmark: compare3 results for the SIMD butterfly pass and the odd codelets (aarch64, 1 thread) --- benchmark/compare3/aarch64/odd/COMPARE3.md | 579 + benchmark/compare3/aarch64/odd/odd_t1.json | 10975 +++++++++++++++++ benchmark/compare3/aarch64/simd/COMPARE3.md | 579 + benchmark/compare3/aarch64/simd/simd_t1.json | 10975 +++++++++++++++++ 4 files changed, 23108 insertions(+) create mode 100644 benchmark/compare3/aarch64/odd/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/odd/odd_t1.json create mode 100644 benchmark/compare3/aarch64/simd/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/simd/simd_t1.json diff --git a/benchmark/compare3/aarch64/odd/COMPARE3.md b/benchmark/compare3/aarch64/odd/COMPARE3.md new file mode 100644 index 0000000..cfbd691 --- /dev/null +++ b/benchmark/compare3/aarch64/odd/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T11:34:15.986 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `odd` | FFTA.jl 0.3.1 @ e73dac4 — `FFTA-odd` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `odd` | `int`/`fftw` | `odd`/`fftw` | `odd` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 22 ns | 3.19× | 0.60× | **5.36×** | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 25 ns | 0.65× | 0.68× | 0.96× | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 158 ns | 3.52× | 3.65× | 0.97× | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 54 ns | 0.97× | 0.97× | 1.00× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 805 ns | 5.92× | 5.92× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.51 µs | 6.55× | 6.56× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 243 ns | 5.29× | 1.93× | **2.74×** | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 812 ns | 2.38× | 2.37× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 817 ns | 2.12× | 2.11× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 134 ns | 1.26× | 1.28× | 0.98× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.81 µs | 2.16× | 2.16× | 1.00× | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.83 µs | 2.22× | 2.23× | 0.99× | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.83 µs | 2.60× | 2.62× | 0.99× | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 938 ns | 2.80× | 2.89× | 0.97× | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.08 µs | 7.03× | 4.97× | **1.41×** | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.87 µs | 1.57× | 1.57× | 1.00× | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 328 ns | 1.69× | 1.69× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 4.10 µs | 1.70× | 1.71× | 1.00× | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 4.11 µs | 3.06× | 3.06× | 1.00× | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 4.13 µs | 2.34× | 2.34× | 1.00× | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 4.18 µs | 2.16× | 2.16× | 1.00× | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 948 ns | 6.97× | 2.63× | **2.65×** | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 2.01 µs | 7.50× | 5.13× | **1.46×** | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 790 ns | 2.03× | 2.03× | 1.00× | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 9.65 µs | 2.32× | 2.34× | 0.99× | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.84 µs | 2.02× | 2.02× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 9.53 µs | 1.60× | 1.59× | 1.00× | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 1.82 µs | 2.27× | 2.26× | 1.01× | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 14.54 µs | 2.26× | 2.29× | 0.99× | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 6.38 µs | 3.96× | 2.69× | **1.47×** | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 18.64 µs | 2.19× | 2.21× | 0.99× | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 8.65 µs | 5.80× | 3.22× | **1.80×** | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 4.21 µs | 2.50× | 2.49× | 1.00× | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 45.72 µs | 3.00× | 3.00× | 1.00× | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 32.84 µs | 2.53× | 2.56× | 0.99× | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 12.84 µs | 3.57× | 2.45× | **1.46×** | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 18.22 µs | 6.51× | 2.72× | **2.39×** | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 9.44 µs | 2.59× | 2.59× | 1.00× | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 21.32 µs | 3.47× | 2.43× | **1.43×** | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 100.64 µs | 1.75× | 1.75× | 1.00× | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 73.76 µs | 2.04× | 2.04× | 1.00× | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 107.12 µs | 1.45× | 1.46× | 0.99× | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 21.08 µs | 2.74× | 2.74× | 1.00× | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 37.44 µs | 2.98× | 3.01× | 0.99× | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 160.92 µs | 1.43× | 1.44× | 1.00× | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 225.24 µs | 1.42× | 1.42× | 1.00× | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 207.12 µs | 1.38× | 1.39× | 1.00× | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 46.60 µs | 2.77× | 2.76× | 1.00× | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 126.24 µs | 3.31× | 2.53× | **1.31×** | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 360.48 µs | 1.58× | 1.60× | 0.99× | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 103.92 µs | 2.14× | 2.13× | 1.00× | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 1.030 ms | 2.49× | 2.50× | 0.99× | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 1.060 ms | 2.58× | 2.57× | 1.01× | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 327.48 µs | 8.66× | 3.37× | **2.57×** | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 1.540 ms | 2.47× | 2.47× | 1.00× | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 824.69 µs | 1.31× | 1.31× | 1.00× | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 227.60 µs | 2.09× | 2.09× | 1.00× | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 2.032 ms | 2.44× | 2.44× | 1.00× | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 2.646 ms | 2.08× | 2.05× | 1.01× | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 666.01 µs | 7.14× | 2.52× | **2.83×** | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 3.253 ms | 2.58× | 2.58× | 1.00× | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 497.45 µs | 1.85× | 1.79× | 1.03× | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 5.473 ms | 2.70× | 2.72× | 1.00× | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 1.620 ms | 7.03× | 2.89× | **2.43×** | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 8.047 ms | 2.66× | 2.62× | 1.01× | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 6.114 ms | 2.29× | 2.28× | 1.00× | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 1.195 ms | 2.20× | 2.12× | 1.04× | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 8.277 ms | 2.33× | 2.33× | 1.00× | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 10.798 ms | 2.63× | 2.63× | 1.00× | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.661 ms | 2.38× | 2.36× | 1.01× | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 17.056 ms | 2.71× | 2.68× | 1.01× | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 13.869 ms | 1.47× | 1.47× | 1.00× | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 2.803 ms | 2.14× | 2.12× | 1.01× | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 28.296 ms | 6.41× | 6.44× | 1.00× | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 42.611 ms | 6.35× | 6.38× | 1.00× | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 7.596 ms | 2.82× | 2.32× | **1.22×** | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 6.331 ms | 1.83× | 1.82× | 1.00× | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 56.501 ms | 6.51× | 6.30× | 1.03× | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 44.470 ms | 2.55× | 2.44× | 1.04× | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 71.656 ms | 2.28× | 2.35× | 0.97× | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 88.786 ms | 6.71× | 6.55× | 1.02× | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 19.525 ms | 6.65× | 2.95× | **2.26×** | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 12.576 ms | 1.11× | 1.11× | 1.00× | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 143.378 ms | 2.89× | 2.99× | 0.97× | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 168.097 ms | 2.17× | 2.19× | 0.99× | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 205.023 ms | 2.73× | 2.83× | 0.96× | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 43.713 ms | 2.75× | 2.36× | **1.17×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 55.463 ms | 4.27× | 2.27× | **1.88×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 36.096 ms | 1.69× | 1.49× | **1.13×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 270.462 ms | 2.72× | 2.77× | 0.98× | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 234.816 ms | 6.18× | 6.21× | 0.99× | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 413.068 ms | 2.69× | 2.75× | 0.98× | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 381.309 ms | 2.18× | 2.18× | 1.00× | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 100.254 ms | 5.03× | 2.48× | **2.03×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 81.610 ms | 1.05× | 1.04× | 1.01× | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 328.222 ms | 4.59× | 2.59× | **1.77×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 185.124 ms | 1.12× | 1.12× | 1.00× | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 26 ns | 3.19× | 1.02× | **3.12×** | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 24 ns | 0.96× | 0.97× | 0.99× | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 156 ns | 4.63× | 4.68× | 0.99× | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 54 ns | 1.33× | 1.34× | 1.00× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 491 ns | 3.59× | 3.62× | 0.99× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 903 ns | 3.91× | 3.93× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 241 ns | 3.71× | 1.74× | **2.13×** | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 884 ns | 2.57× | 2.58× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 887 ns | 2.31× | 2.31× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 137 ns | 1.72× | 1.72× | 1.00× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.96 µs | 2.54× | 2.54× | 1.00× | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.97 µs | 2.16× | 2.16× | 1.00× | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.97 µs | 2.81× | 2.82× | 1.00× | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 960 ns | 3.37× | 3.51× | 0.96× | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.09 µs | 4.40× | 3.50× | **1.26×** | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 2.02 µs | 1.46× | 1.46× | 1.00× | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 337 ns | 1.09× | 1.09× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 4.38 µs | 1.44× | 1.43× | 1.00× | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 4.38 µs | 2.52× | 2.52× | 1.00× | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 4.40 µs | 1.77× | 1.76× | 1.00× | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 4.45 µs | 1.88× | 1.88× | 1.00× | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.02 µs | 3.21× | 1.73× | **1.85×** | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.06 µs | 4.11× | 3.24× | **1.27×** | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 809 ns | 1.24× | 1.25× | 0.99× | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 10.32 µs | 2.05× | 2.08× | 0.99× | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.85 µs | 1.98× | 1.98× | 1.00× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 10.16 µs | 1.50× | 1.51× | 1.00× | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.86 µs | 1.41× | 1.41× | 1.00× | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 15.48 µs | 1.99× | 1.99× | 1.00× | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 6.55 µs | 2.98× | 2.31× | **1.29×** | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 20.04 µs | 1.90× | 1.92× | 0.99× | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 9.13 µs | 3.01× | 2.13× | **1.41×** | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 4.27 µs | 1.50× | 1.51× | 0.99× | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 48.76 µs | 1.78× | 1.77× | 1.00× | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 35.56 µs | 2.19× | 2.24× | 0.98× | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 13.58 µs | 3.02× | 2.41× | **1.25×** | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 19.92 µs | 3.42× | 1.94× | **1.76×** | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 9.56 µs | 1.52× | 1.52× | 1.00× | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 22.16 µs | 2.97× | 2.39× | **1.24×** | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 109.60 µs | 1.41× | 1.42× | 1.00× | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 80.80 µs | 1.80× | 1.82× | 0.99× | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 113.60 µs | 1.03× | 1.04× | 0.99× | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 21.76 µs | 1.61× | 1.61× | 1.00× | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 40.52 µs | 1.77× | 1.80× | 0.98× | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 171.00 µs | 1.01× | 1.02× | 1.00× | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 240.24 µs | 1.08× | 1.08× | 1.00× | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 222.76 µs | 0.99× | 1.00× | 0.99× | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 49.04 µs | 1.66× | 1.65× | 1.01× | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 132.08 µs | 2.72× | 2.29× | **1.18×** | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 385.88 µs | 1.12× | 1.13× | 0.99× | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 107.20 µs | 1.27× | 1.26× | 1.00× | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 1.139 ms | 2.26× | 2.25× | 1.01× | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 1.355 ms | 2.44× | 2.44× | 1.00× | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 376.20 µs | 4.42× | 2.51× | **1.76×** | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.716 ms | 2.28× | 2.21× | 1.03× | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 898.57 µs | 0.98× | 0.97× | 1.00× | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 241.32 µs | 1.38× | 1.34× | 1.04× | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 2.368 ms | 2.20× | 2.29× | 0.96× | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 3.291 ms | 1.95× | 1.94× | 1.01× | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 828.81 µs | 4.09× | 2.16× | **1.90×** | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 3.715 ms | 2.33× | 2.30× | 1.01× | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 589.57 µs | 1.36× | 1.33× | 1.03× | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 6.806 ms | 2.26× | 2.28× | 0.99× | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 2.036 ms | 3.21× | 1.98× | **1.63×** | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 10.302 ms | 2.23× | 2.27× | 0.98× | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 7.051 ms | 1.57× | 1.54× | 1.02× | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 1.431 ms | 1.32× | 1.32× | 1.00× | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 9.137 ms | 2.16× | 2.08× | 1.04× | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 13.420 ms | 2.19× | 2.19× | 1.00× | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.918 ms | 1.48× | 1.51× | 0.98× | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 21.231 ms | 2.24× | 2.26× | 0.99× | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 15.948 ms | 1.30× | 1.27× | 1.02× | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 3.012 ms | 1.25× | 1.25× | 1.00× | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 32.698 ms | 4.64× | 4.71× | 0.99× | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 49.086 ms | 4.71× | 4.74× | 0.99× | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 8.284 ms | 2.09× | 1.83× | **1.14×** | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 6.395 ms | 1.13× | 1.13× | 1.00× | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 74.934 ms | 4.72× | 5.45× | **0.87×** | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 55.126 ms | 2.23× | 2.15× | 1.03× | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 90.708 ms | 2.21× | 2.21× | 1.00× | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 105.891 ms | 4.88× | 5.00× | 0.98× | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 25.302 ms | 3.95× | 2.35× | **1.68×** | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 14.627 ms | 1.05× | 0.87× | **1.21×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 186.380 ms | 2.60× | 2.68× | 0.97× | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 190.223 ms | 1.81× | 1.84× | 0.99× | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 280.368 ms | 2.55× | 2.69× | **0.95×** | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 53.290 ms | 1.76× | 1.62× | **1.08×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 66.356 ms | 1.99× | 1.32× | **1.51×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 43.672 ms | 0.85× | 0.83× | 1.02× | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 365.179 ms | 2.61× | 2.57× | 1.02× | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 262.796 ms | 4.16× | 4.10× | 1.02× | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 581.981 ms | 2.51× | 2.67× | **0.94×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 403.993 ms | 1.51× | 1.53× | 0.98× | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 145.968 ms | 2.50× | 1.90× | **1.32×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 90.742 ms | 0.76× | 0.76× | 1.00× | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 419.503 ms | 2.59× | 1.96× | **1.32×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 191.310 ms | 0.81× | 0.80× | 1.01× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 35 ns | 2.15× | 1.46× | **1.47×** | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 75 ns | 3.50× | 3.45× | 1.02× | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 186 ns | 6.56× | 6.88× | 0.95× | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 101 ns | 3.06× | 3.07× | 1.00× | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 180 ns | 1.33× | 1.34× | 0.99× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 315 ns | 1.55× | 1.56× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 233 ns | 6.56× | 3.05× | **2.15×** | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 815 ns | 2.82× | 2.83× | 1.00× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 814 ns | 2.54× | 2.55× | 1.00× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 159 ns | 1.56× | 1.57× | 1.00× | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.80 µs | 4.21× | 4.20× | 1.00× | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.81 µs | 3.57× | 3.57× | 1.00× | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.81 µs | 3.28× | 3.28× | 1.00× | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 462 ns | 2.16× | 2.16× | 1.00× | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 847 ns | 4.81× | 3.86× | **1.25×** | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.84 µs | 1.79× | 1.78× | 1.01× | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 298 ns | 1.62× | 1.63× | 0.99× | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 4.07 µs | 2.95× | 2.96× | 1.00× | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 4.08 µs | 2.81× | 2.82× | 1.00× | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 4.08 µs | 2.43× | 2.42× | 1.00× | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 4.13 µs | 1.53× | 1.53× | 1.00× | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 762 ns | 5.28× | 2.65× | **2.00×** | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.39 µs | 6.42× | 4.86× | **1.32×** | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 607 ns | 2.29× | 2.29× | 1.00× | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 4.58 µs | 2.15× | 2.15× | 1.00× | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.82 µs | 3.24× | 3.24× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 9.37 µs | 1.71× | 1.71× | 1.00× | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.31 µs | 2.05× | 2.06× | 1.00× | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 14.30 µs | 1.70× | 1.71× | 0.99× | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 4.26 µs | 4.30× | 3.24× | **1.33×** | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 11.14 µs | 2.54× | 2.58× | 0.98× | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 5.77 µs | 6.00× | 3.77× | **1.59×** | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.82 µs | 2.48× | 2.49× | 1.00× | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 45.36 µs | 2.07× | 2.07× | 1.00× | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 16.18 µs | 2.46× | 2.48× | 0.99× | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 7.95 µs | 3.74× | 2.76× | **1.35×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 11.94 µs | 7.81× | 3.82× | **2.04×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 6.16 µs | 2.79× | 2.80× | 1.00× | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 13.78 µs | 3.87× | 2.97× | **1.30×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 99.92 µs | 1.84× | 1.84× | 1.00× | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 40.12 µs | 2.27× | 2.29× | 0.99× | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 50.76 µs | 1.36× | 1.37× | 1.00× | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 13.22 µs | 2.99× | 2.97× | 1.01× | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 21.72 µs | 3.15× | 3.18× | 0.99× | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 158.44 µs | 2.20× | 2.22× | 0.99× | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 222.96 µs | 1.49× | 1.49× | 1.00× | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 121.28 µs | 1.59× | 1.62× | 0.98× | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 28.88 µs | 3.07× | 3.07× | 1.00× | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 85.64 µs | 4.04× | 3.36× | **1.20×** | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 177.28 µs | 1.55× | 1.56× | 0.99× | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 62.04 µs | 2.43× | 2.43× | 1.00× | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 501.61 µs | 2.41× | 2.42× | 1.00× | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 1.079 ms | 3.07× | 3.12× | 0.98× | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 157.48 µs | 6.61× | 2.50× | **2.64×** | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.535 ms | 2.93× | 2.94× | 1.00× | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 443.13 µs | 1.44× | 1.44× | 1.00× | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 135.96 µs | 2.51× | 2.52× | 1.00× | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 1.090 ms | 2.58× | 2.61× | 0.99× | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 2.632 ms | 2.71× | 2.74× | 0.99× | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 648.37 µs | 8.20× | 3.29× | **2.49×** | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.611 ms | 2.55× | 2.55× | 1.00× | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 291.08 µs | 2.49× | 2.49× | 1.00× | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 2.722 ms | 2.64× | 2.70× | 0.98× | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 1.577 ms | 7.40× | 3.48× | **2.13×** | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 8.036 ms | 3.17× | 3.12× | 1.01× | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 6.090 ms | 2.24× | 2.24× | 1.00× | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 649.45 µs | 2.65× | 2.66× | 0.99× | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 4.225 ms | 2.48× | 2.47× | 1.00× | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 5.732 ms | 2.83× | 2.82× | 1.00× | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.422 ms | 2.72× | 2.76× | 0.99× | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 8.421 ms | 2.78× | 2.73× | 1.02× | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 13.950 ms | 1.30× | 1.32× | 0.99× | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.488 ms | 2.43× | 2.42× | 1.00× | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 13.868 ms | 6.24× | 6.28× | 0.99× | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 42.309 ms | 6.79× | 6.81× | 1.00× | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 3.846 ms | 2.73× | 2.26× | **1.21×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 3.413 ms | 2.05× | 2.04× | 1.00× | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 29.249 ms | 6.64× | 6.45× | 1.03× | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 22.644 ms | 2.68× | 2.62× | 1.02× | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 74.471 ms | 2.38× | 2.36× | 1.01× | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 43.296 ms | 6.62× | 6.37× | 1.04× | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 11.420 ms | 6.03× | 3.00× | **2.01×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 7.489 ms | 1.99× | 1.98× | 1.01× | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 71.308 ms | 3.02× | 2.98× | 1.01× | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 167.986 ms | 1.84× | 1.84× | 1.00× | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 217.416 ms | 2.31× | 2.44× | **0.95×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 21.198 ms | 2.94× | 2.35× | **1.25×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 26.943 ms | 6.10× | 3.10× | **1.97×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 15.682 ms | 2.12× | 2.00× | **1.06×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 134.902 ms | 2.90× | 2.82× | 1.03× | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 117.246 ms | 6.28× | 6.28× | 1.00× | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 214.157 ms | 2.70× | 2.91× | **0.93×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 380.658 ms | 1.50× | 1.51× | 0.99× | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 52.184 ms | 6.20× | 3.08× | **2.01×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 36.665 ms | 2.77× | 2.24× | **1.24×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 154.594 ms | 3.39× | 1.85× | **1.83×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 88.333 ms | 1.79× | 1.71× | 1.04× | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 35 ns | 2.17× | 1.46× | **1.48×** | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 85 ns | 3.79× | 3.92× | 0.97× | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 197 ns | 6.78× | 7.16× | **0.95×** | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 109 ns | 3.30× | 3.40× | 0.97× | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 193 ns | 1.40× | 1.41× | 0.99× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 342 ns | 1.65× | 1.67× | 0.99× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 239 ns | 5.67× | 3.18× | **1.78×** | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 885 ns | 3.05× | 3.05× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 890 ns | 2.75× | 2.75× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 167 ns | 1.86× | 1.88× | 0.99× | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.96 µs | 4.55× | 4.55× | 1.00× | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.96 µs | 3.83× | 3.83× | 1.00× | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.97 µs | 3.54× | 3.55× | 1.00× | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 474 ns | 2.83× | 2.83× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 876 ns | 5.75× | 5.12× | **1.12×** | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 2.00 µs | 1.93× | 1.92× | 1.00× | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 311 ns | 1.87× | 1.87× | 1.00× | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 4.37 µs | 3.16× | 3.15× | 1.00× | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 4.38 µs | 3.01× | 3.00× | 1.00× | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.40 µs | 2.59× | 2.60× | 1.00× | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.43 µs | 1.64× | 1.64× | 1.00× | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 826 ns | 4.11× | 2.78× | **1.48×** | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.45 µs | 5.09× | 4.34× | **1.17×** | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 640 ns | 1.95× | 1.96× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.90 µs | 1.88× | 1.88× | 1.00× | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.85 µs | 3.05× | 3.05× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 10.02 µs | 1.77× | 1.75× | 1.01× | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.35 µs | 1.95× | 1.95× | 1.00× | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 15.38 µs | 1.85× | 1.83× | 1.01× | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 4.40 µs | 3.74× | 3.14× | **1.19×** | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 11.84 µs | 2.18× | 2.21× | 0.99× | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 6.08 µs | 3.90× | 2.99× | **1.30×** | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.93 µs | 2.00× | 2.00× | 1.00× | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 48.40 µs | 2.18× | 2.16× | 1.01× | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 17.24 µs | 2.09× | 2.12× | 0.99× | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 8.21 µs | 3.44× | 2.85× | **1.21×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 12.78 µs | 4.55× | 2.85× | **1.60×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 6.28 µs | 2.02× | 2.01× | 1.00× | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 14.24 µs | 3.57× | 3.02× | **1.18×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 109.04 µs | 1.95× | 1.94× | 1.00× | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 43.48 µs | 1.94× | 1.95× | 0.99× | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 54.00 µs | 0.96× | 0.97× | 0.99× | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 13.84 µs | 2.07× | 2.07× | 1.00× | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 23.40 µs | 2.39× | 2.40× | 1.00× | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 169.64 µs | 2.30× | 2.31× | 1.00× | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 238.76 µs | 1.53× | 1.52× | 1.01× | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 129.12 µs | 1.12× | 1.14× | 0.98× | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 30.16 µs | 2.07× | 2.08× | 1.00× | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 87.88 µs | 3.35× | 3.03× | **1.11×** | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 189.28 µs | 1.09× | 1.10× | 0.99× | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 66.60 µs | 1.69× | 1.70× | 0.99× | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 561.97 µs | 2.13× | 2.17× | 0.98× | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.365 ms | 3.64× | 3.75× | 0.97× | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 179.24 µs | 4.31× | 2.40× | **1.80×** | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.709 ms | 3.14× | 3.11× | 1.01× | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 481.21 µs | 1.04× | 1.04× | 0.99× | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 142.32 µs | 1.64× | 1.64× | 1.00× | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.236 ms | 2.36× | 2.36× | 1.00× | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 3.268 ms | 2.92× | 2.88× | 1.01× | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 755.97 µs | 6.90× | 3.76× | **1.83×** | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.807 ms | 2.24× | 2.27× | 0.99× | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 328.12 µs | 1.65× | 1.68× | 0.99× | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 3.342 ms | 2.23× | 2.25× | 0.99× | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 2.028 ms | 6.45× | 4.20× | **1.53×** | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 10.260 ms | 3.62× | 3.67× | 0.99× | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 7.101 ms | 2.46× | 2.44× | 1.01× | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 771.81 µs | 1.66× | 1.65× | 1.01× | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 4.846 ms | 2.25× | 2.21× | 1.02× | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 7.023 ms | 2.32× | 2.32× | 1.00× | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.628 ms | 1.74× | 1.75× | 0.99× | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 10.396 ms | 2.26× | 2.25× | 1.00× | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 15.865 ms | 1.40× | 1.39× | 1.01× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.787 ms | 1.57× | 1.57× | 1.00× | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 16.195 ms | 4.50× | 4.62× | 0.98× | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 49.359 ms | 6.41× | 6.50× | 0.98× | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.536 ms | 2.14× | 1.96× | **1.10×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.731 ms | 1.49× | 1.43× | 1.04× | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 34.733 ms | 4.81× | 4.96× | 0.97× | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 28.186 ms | 2.27× | 2.20× | 1.03× | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 92.487 ms | 2.48× | 2.57× | 0.97× | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 53.269 ms | 4.80× | 5.06× | **0.95×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 13.915 ms | 3.59× | 2.38× | **1.51×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 8.780 ms | 1.62× | 1.52× | **1.06×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 92.917 ms | 2.50× | 2.67× | **0.94×** | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 189.891 ms | 1.70× | 1.72× | 0.99× | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 280.101 ms | 2.82× | 2.83× | 1.00× | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 27.163 ms | 2.55× | 2.30× | **1.11×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 32.872 ms | 2.33× | 1.54× | **1.52×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 19.408 ms | 1.68× | 1.44× | **1.17×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 188.284 ms | 2.89× | 2.70× | **1.07×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 134.551 ms | 4.52× | 4.45× | 1.02× | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 284.353 ms | 2.45× | 2.65× | **0.93×** | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 400.919 ms | 1.21× | 1.21× | 1.00× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 70.590 ms | 2.53× | 1.83× | **1.38×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 50.090 ms | 0.91× | 0.90× | 1.01× | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 200.788 ms | 2.45× | 1.78× | **1.38×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 99.200 ms | 0.85× | 0.84× | 1.01× | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 723 ns | 4.83× | 5.02× | 0.96× | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.51 µs | 4.36× | 4.40× | 0.99× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.88 µs | 4.01× | 4.07× | 0.99× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 49.12 µs | 3.95× | 3.98× | 0.99× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 249.04 µs | 4.14× | 4.14× | 1.00× | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 1.195 ms | 1.54× | 1.56× | 0.98× | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 7.533 ms | 1.27× | 1.34× | **0.94×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 36.047 ms | 1.35× | 1.43× | **0.94×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 166.207 ms | 1.19× | 1.25× | 0.96× | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 749 ns | 4.15× | 4.32× | 0.96× | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.60 µs | 3.08× | 3.17× | 0.97× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.50 µs | 2.76× | 2.80× | 0.99× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.40 µs | 2.58× | 2.60× | 0.99× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 267.48 µs | 2.53× | 2.42× | 1.04× | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 4.082 ms | 2.27× | 2.27× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 3.855 ms | 1.04× | 1.05× | 0.99× | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 4.005 ms | 1.03× | 1.04× | 0.99× | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.506 ms | 1.29× | 1.32× | 0.98× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 7.729 ms | 1.23× | 1.26× | 0.97× | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 17.506 ms | 2.97× | 2.65× | **1.12×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 58.201 ms | 3.13× | 2.09× | **1.49×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 42.205 ms | 1.23× | 1.40× | **0.88×** | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 226.361 ms | 1.11× | 1.38× | **0.80×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 884 ns | 6.92× | 7.15× | 0.97× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.41 µs | 5.38× | 5.49× | 0.98× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 8.17 µs | 3.92× | 3.99× | 0.98× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 32.20 µs | 3.26× | 3.27× | 1.00× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 141.08 µs | 3.02× | 3.02× | 1.00× | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 619.73 µs | 1.80× | 1.78× | 1.01× | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.845 ms | 1.96× | 1.97× | 0.99× | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 12.855 ms | 2.10× | 2.14× | 0.98× | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 63.328 ms | 1.79× | 1.82× | 0.98× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 946 ns | 7.84× | 8.08× | 0.97× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.48 µs | 5.03× | 5.06× | 0.99× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 8.61 µs | 3.51× | 3.59× | 0.98× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 33.88 µs | 2.85× | 2.88× | 0.99× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 147.28 µs | 2.53× | 2.53× | 1.00× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.610 ms | 1.73× | 1.73× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 3.447 ms | 2.13× | 2.13× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 2.077 ms | 1.06× | 1.07× | 0.99× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 653.17 µs | 1.61× | 1.60× | 1.00× | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 3.043 ms | 1.58× | 1.59× | 0.99× | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 8.188 ms | 3.08× | 2.60× | **1.19×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 28.833 ms | 3.21× | 2.21× | **1.45×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 14.377 ms | 1.54× | 1.64× | **0.94×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 68.857 ms | 1.22× | 1.27× | 0.96× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 9.64 µs | 6.09× | 6.23× | 0.98× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 66.12 µs | 4.81× | 4.91× | 0.98× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 596.29 µs | 4.14× | 4.21× | 0.98× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.782 ms | 3.84× | 3.88× | 0.99× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 67.520 ms | 3.44× | 3.66× | **0.94×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.88 µs | 4.99× | 5.19× | 0.96× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 68.12 µs | 3.33× | 3.41× | 0.98× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 645.13 µs | 2.63× | 2.67× | 0.99× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.862 ms | 2.63× | 2.76× | 0.95× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 83.599 ms | 2.03× | 2.15× | **0.95×** | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 9.45 µs | 7.70× | 7.96× | 0.97× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 52.88 µs | 5.58× | 5.73× | 0.97× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 373.84 µs | 4.04× | 4.11× | 0.98× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 3.158 ms | 3.27× | 3.31× | 0.99× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 29.400 ms | 3.08× | 3.14× | 0.98× | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 9.92 µs | 8.09× | 8.29× | 0.98× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 54.40 µs | 4.70× | 4.78× | 0.98× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 391.64 µs | 3.33× | 3.35× | 0.99× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.583 ms | 2.59× | 2.65× | 0.98× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 35.492 ms | 2.18× | 2.40× | **0.91×** | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.68 µs | 3.61× | 3.64× | 0.99× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 123.92 µs | 2.37× | 2.37× | 1.00× | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 642.73 µs | 2.62× | 2.63× | 1.00× | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 3.270 ms | 2.56× | 2.56× | 1.00× | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 17.972 ms | 2.09× | 2.32× | **0.90×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 89.643 ms | 2.01× | 2.01× | 1.00× | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 24.00 µs | 2.31× | 2.33× | 0.99× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 129.32 µs | 1.48× | 1.49× | 1.00× | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 698.69 µs | 1.60× | 1.61× | 0.99× | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 3.813 ms | 1.71× | 1.76× | 0.97× | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 21.647 ms | 1.39× | 1.46× | 0.96× | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 111.198 ms | 1.29× | 1.26× | 1.03× | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 18.98 µs | 2.85× | 2.87× | 0.99× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 84.76 µs | 2.08× | 2.08× | 1.00× | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 399.32 µs | 2.77× | 2.77× | 1.00× | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.881 ms | 2.73× | 2.73× | 1.00× | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 9.020 ms | 2.38× | 2.42× | 0.99× | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 43.229 ms | 2.28× | 2.27× | 1.01× | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 19.96 µs | 2.98× | 2.99× | 1.00× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.711 ms | 1.86× | 1.83× | 1.01× | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 87.80 µs | 1.96× | 1.97× | 1.00× | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.772 ms | 1.85× | 1.84× | 1.00× | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 415.33 µs | 1.94× | 1.94× | 1.00× | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 7.955 ms | 1.89× | 1.87× | 1.01× | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.978 ms | 1.90× | 1.90× | 1.00× | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 9.854 ms | 1.60× | 1.61× | 1.00× | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 50.098 ms | 1.35× | 1.32× | 1.03× | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.60 µs | 4.43× | 4.50× | 0.98× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 153.04 µs | 1.92× | 1.92× | 1.00× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 906.97 µs | 1.97× | 2.09× | **0.94×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 5.785 ms | 1.26× | 1.23× | 1.02× | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 32.820 ms | 1.38× | 1.35× | 1.02× | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 218.993 ms | 1.19× | 1.27× | **0.93×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 28.84 µs | 2.63× | 2.66× | 0.99× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 162.36 µs | 1.53× | 1.49× | 1.03× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.284 ms | 1.35× | 1.45× | **0.93×** | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 7.582 ms | 1.27× | 1.42× | **0.90×** | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 46.676 ms | 1.30× | 1.37× | 0.95× | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 274.541 ms | 1.10× | 1.11× | 0.99× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 22.40 µs | 3.36× | 3.39× | 0.99× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 108.68 µs | 1.88× | 1.88× | 1.00× | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 539.61 µs | 1.88× | 1.87× | 1.01× | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.837 ms | 1.60× | 1.59× | 1.01× | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 14.179 ms | 1.22× | 1.22× | 1.00× | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 71.088 ms | 1.04× | 1.04× | 1.00× | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 23.68 µs | 3.55× | 3.58× | 0.99× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 122.96 µs | 1.71× | 1.72× | 1.00× | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 580.69 µs | 1.67× | 1.67× | 1.00× | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 3.251 ms | 1.20× | 1.19× | 1.01× | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 15.110 ms | 1.11× | 1.07× | 1.04× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 88.975 ms | 0.80× | 0.80× | 1.00× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `odd`/`fftw` | `odd` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 2.61× (1.25–5.02) | **0.97×** (0.94–1.00) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.49× (3.66–6.23) | **0.97×** (0.94–0.99) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 2.69× (1.31–6.55) | **1.00×** (0.96–1.04) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 2.54× (2.01–3.64) | **0.98×** (0.90–1.00) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.84× (1.23–4.50) | **0.98×** (0.93–1.02) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 1.70× (0.68–2.76) | **1.01×** (0.96–1.13) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 2.19× (0.60–6.56) | **1.07×** (0.97–5.36) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 2.77× (1.93–5.13) | **1.61×** (0.97–2.83) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.94× (1.04–4.32) | **1.00×** (0.80–1.49) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 3.09× (2.15–5.19) | **0.96×** (0.95–0.99) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 2.24× (0.97–5.45) | **0.99×** (0.87–1.04) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.62× (1.26–2.33) | **0.99×** (0.96–1.03) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.52× (1.11–2.66) | **0.96×** (0.90–1.03) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 1.21× (0.76–1.72) | **1.01×** (0.99–1.21) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.91× (1.02–3.93) | **1.05×** (0.98–3.12) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.18× (1.32–4.68) | **1.33×** (0.96–2.13) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 3.02× (1.78–7.15) | **0.99×** (0.97–1.01) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 4.55× (3.14–7.96) | **0.98×** (0.97–0.99) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 2.78× (1.37–6.81) | **1.00×** (0.93–1.04) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 2.51× (2.08–2.87) | **1.00×** (0.99–1.01) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.70× (1.04–3.39) | **1.00×** (0.99–1.01) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 2.34× (1.57–3.45) | **1.02×** (0.99–1.24) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 2.15× (1.32–4.20) | **1.01×** (0.98–1.47) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 3.11× (1.85–6.88) | **1.51×** (0.95–2.64) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.32× (1.07–8.08) | **1.03×** (0.94–1.45) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.85× (2.40–8.29) | **0.97×** (0.91–0.99) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 2.41× (0.97–6.50) | **0.99×** (0.93–1.07) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.88× (1.32–2.99) | **1.00×** (1.00–1.03) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.48× (0.80–3.58) | **1.01×** (0.99–1.04) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.77× (0.84–3.92) | **1.01×** (0.97–1.17) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 2.26× (1.21–4.55) | **1.02×** (0.97–1.48) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 2.83× (1.54–7.16) | **1.27×** (0.95–1.83) | +| **all** | 2.45× (0.65–8.66) | 2.28× (0.60–8.29) | **1.08×** (0.80–5.36), 505 cases, 22 slower by >5% | diff --git a/benchmark/compare3/aarch64/odd/odd_t1.json b/benchmark/compare3/aarch64/odd/odd_t1.json new file mode 100644 index 0000000..e2e19b4 --- /dev/null +++ b/benchmark/compare3/aarch64/odd/odd_t1.json @@ -0,0 +1,10975 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T11:20:30.088", + "impl": "ffta", + "julia": "1.12.6", + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ e73dac4" + }, + "results": [ + { + "T": "Float64", + "api": 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"T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.043228970000000005, + "key": "rfft Float32 65536×64 dims=1", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369855.16, + "nthreads": 1, + "plan_min": 0.00012088100000000001, + "shape": "batched_dim1", + "size": [ + 65536, + 64 + ], + "sum_im": -665970.94, + "sum_re": 12625.094 + }, + { + "T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 2, + "exec_alloc": 0, + "exec_min": 0.07108840500000001, + "key": "rfft Float32 64×65536 dims=2", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369917.0, + "nthreads": 1, + "plan_min": 0.000124282, + "shape": "batched_dim2", + "size": [ + 64, + 65536 + ], + "sum_im": 439989.97, + "sum_re": -183525.03 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.005711425, + "key": "rfft Float64 256×4096 dims=1", + "kind": "rfft", + "measure": false, + "n": 256, + "norm": 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-2384.3887021656665 + } + ] +} \ No newline at end of file diff --git a/benchmark/compare3/aarch64/simd/COMPARE3.md b/benchmark/compare3/aarch64/simd/COMPARE3.md new file mode 100644 index 0000000..c0e6b5d --- /dev/null +++ b/benchmark/compare3/aarch64/simd/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T11:33:27.611 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `simd` | FFTA.jl 0.3.1 @ 4419199 — `FFTA-simd` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `simd` | `int`/`fftw` | `simd`/`fftw` | `simd` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 121 ns | 3.19× | 3.21× | 0.99× | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 25 ns | 0.65× | 0.68× | 0.97× | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 152 ns | 3.52× | 3.50× | 1.01× | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 53 ns | 0.97× | 0.96× | 1.01× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 809 ns | 5.92× | 5.95× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.50 µs | 6.55× | 6.55× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 667 ns | 5.29× | 5.29× | 1.00× | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 814 ns | 2.38× | 2.38× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 817 ns | 2.12× | 2.11× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 133 ns | 1.26× | 1.27× | 0.99× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.49 µs | 2.16× | 1.78× | **1.21×** | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.50 µs | 2.22× | 1.83× | **1.21×** | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.50 µs | 2.60× | 2.15× | **1.21×** | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 904 ns | 2.80× | 2.78× | 1.01× | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.54 µs | 7.03× | 7.09× | 0.99× | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.55 µs | 1.57× | 1.31× | **1.20×** | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 329 ns | 1.69× | 1.69× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 3.46 µs | 1.70× | 1.44× | **1.18×** | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 3.49 µs | 3.06× | 2.60× | **1.18×** | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 3.48 µs | 2.34× | 1.97× | **1.19×** | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 3.55 µs | 2.16× | 1.84× | **1.18×** | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 2.51 µs | 6.97× | 6.96× | 1.00× | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 2.92 µs | 7.50× | 7.44× | 1.01× | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 628 ns | 2.03× | 1.61× | **1.26×** | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 8.31 µs | 2.32× | 2.01× | **1.15×** | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.83 µs | 2.02× | 2.02× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 7.03 µs | 1.60× | 1.17× | **1.36×** | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 1.51 µs | 2.27× | 1.88× | **1.21×** | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 12.52 µs | 2.26× | 1.97× | **1.15×** | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 9.27 µs | 3.96× | 3.90× | 1.01× | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 15.98 µs | 2.19× | 1.89× | **1.16×** | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 15.58 µs | 5.80× | 5.80× | 1.00× | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 2.93 µs | 2.50× | 1.74× | **1.44×** | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 30.56 µs | 3.00× | 2.01× | **1.50×** | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 28.72 µs | 2.53× | 2.24× | **1.13×** | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 18.64 µs | 3.57× | 3.55× | 1.01× | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 43.52 µs | 6.51× | 6.50× | 1.00× | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 6.89 µs | 2.59× | 1.89× | **1.37×** | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 30.08 µs | 3.47× | 3.43× | 1.01× | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 70.32 µs | 1.75× | 1.22× | **1.43×** | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 63.40 µs | 2.04× | 1.76× | **1.16×** | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 75.80 µs | 1.45× | 1.03× | **1.40×** | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 13.48 µs | 2.74× | 1.76× | **1.56×** | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 37.08 µs | 2.98× | 2.99× | 1.00× | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 114.36 µs | 1.43× | 1.02× | **1.40×** | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 143.72 µs | 1.42× | 0.91× | **1.57×** | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 145.20 µs | 1.38× | 0.97× | **1.42×** | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 31.40 µs | 2.77× | 1.86× | **1.49×** | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 165.12 µs | 3.31× | 3.31× | 1.00× | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 265.24 µs | 1.58× | 1.17× | **1.34×** | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 63.72 µs | 2.14× | 1.31× | **1.63×** | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 695.05 µs | 2.49× | 1.69× | **1.47×** | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 662.33 µs | 2.58× | 1.60× | **1.61×** | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 839.69 µs | 8.66× | 8.63× | 1.00× | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 1.060 ms | 2.47× | 1.70× | **1.45×** | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 580.21 µs | 1.31× | 0.92× | **1.42×** | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 147.28 µs | 2.09× | 1.35× | **1.55×** | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 1.373 ms | 2.44× | 1.65× | **1.48×** | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 1.787 ms | 2.08× | 1.39× | **1.50×** | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 1.888 ms | 7.14× | 7.15× | 1.00× | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 2.262 ms | 2.58× | 1.80× | **1.44×** | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 296.84 µs | 1.85× | 1.07× | **1.73×** | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 3.718 ms | 2.70× | 1.85× | **1.47×** | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 3.964 ms | 7.03× | 7.07× | 0.99× | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 5.683 ms | 2.66× | 1.85× | **1.44×** | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 4.109 ms | 2.29× | 1.53× | **1.49×** | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 771.09 µs | 2.20× | 1.37× | **1.61×** | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 5.636 ms | 2.33× | 1.58× | **1.47×** | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 7.754 ms | 2.63× | 1.89× | **1.39×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.658 ms | 2.38× | 2.36× | 1.01× | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 11.910 ms | 2.71× | 1.87× | **1.45×** | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 9.728 ms | 1.47× | 1.03× | **1.42×** | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 1.792 ms | 2.14× | 1.36× | **1.58×** | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 19.870 ms | 6.41× | 4.52× | **1.42×** | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 30.480 ms | 6.35× | 4.56× | **1.39×** | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 9.219 ms | 2.82× | 2.81× | 1.00× | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 4.222 ms | 1.83× | 1.21× | **1.51×** | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 40.266 ms | 6.51× | 4.49× | **1.45×** | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 30.400 ms | 2.55× | 1.67× | **1.53×** | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 48.638 ms | 2.28× | 1.59× | **1.43×** | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 69.006 ms | 6.71× | 5.09× | **1.32×** | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 43.130 ms | 6.65× | 6.51× | 1.02× | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 7.826 ms | 1.11× | 0.69× | **1.62×** | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 124.812 ms | 2.89× | 2.60× | **1.11×** | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 126.684 ms | 2.17× | 1.65× | **1.31×** | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 163.002 ms | 2.73× | 2.25× | **1.21×** | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 52.194 ms | 2.75× | 2.82× | 0.98× | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 103.377 ms | 4.27× | 4.23× | 1.01× | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 21.439 ms | 1.69× | 0.89× | **1.90×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 200.423 ms | 2.72× | 2.05× | **1.32×** | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 178.674 ms | 6.18× | 4.73× | **1.31×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 346.260 ms | 2.69× | 2.30× | **1.17×** | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 299.519 ms | 2.18× | 1.71× | **1.27×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 200.694 ms | 5.03× | 4.96× | 1.01× | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 55.239 ms | 1.05× | 0.70× | **1.49×** | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 569.895 ms | 4.59× | 4.49× | 1.02× | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 142.038 ms | 1.12× | 0.86× | **1.30×** | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 82 ns | 3.19× | 3.18× | 1.00× | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 24 ns | 0.96× | 0.95× | 1.01× | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 152 ns | 4.63× | 4.56× | 1.01× | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 56 ns | 1.33× | 1.38× | 0.97× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 489 ns | 3.59× | 3.61× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 900 ns | 3.91× | 3.92× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 512 ns | 3.71× | 3.69× | 1.00× | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 886 ns | 2.57× | 2.58× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 888 ns | 2.31× | 2.31× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 138 ns | 1.72× | 1.73× | 1.00× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.77 µs | 2.54× | 2.30× | **1.10×** | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.77 µs | 2.16× | 1.95× | **1.11×** | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.80 µs | 2.81× | 2.57× | **1.09×** | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 934 ns | 3.37× | 3.41× | 0.99× | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.36 µs | 4.40× | 4.38× | 1.01× | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 1.82 µs | 1.46× | 1.31× | **1.11×** | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 339 ns | 1.09× | 1.09× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 4.00 µs | 1.44× | 1.31× | **1.10×** | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 4.00 µs | 2.52× | 2.30× | **1.10×** | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 4.02 µs | 1.77× | 1.61× | **1.10×** | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 4.07 µs | 1.88× | 1.72× | **1.09×** | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.89 µs | 3.21× | 3.21× | 1.00× | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.60 µs | 4.11× | 4.11× | 1.00× | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 705 ns | 1.24× | 1.09× | **1.14×** | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 9.45 µs | 2.05× | 1.90× | **1.08×** | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.85 µs | 1.98× | 1.98× | 1.00× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 8.52 µs | 1.50× | 1.27× | **1.19×** | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.67 µs | 1.41× | 1.27× | **1.11×** | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 14.22 µs | 1.99× | 1.83× | **1.09×** | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 8.35 µs | 2.98× | 2.94× | 1.01× | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 18.34 µs | 1.90× | 1.75× | **1.09×** | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 13.08 µs | 3.01× | 3.04× | 0.99× | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 3.48 µs | 1.50× | 1.23× | **1.22×** | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 39.00 µs | 1.78× | 1.42× | **1.25×** | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 32.40 µs | 2.19× | 2.05× | **1.07×** | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 17.02 µs | 3.02× | 3.02× | 1.00× | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 35.04 µs | 3.42× | 3.42× | 1.00× | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 8.00 µs | 1.52× | 1.27× | **1.19×** | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 27.52 µs | 2.97× | 2.97× | 1.00× | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 90.20 µs | 1.41× | 1.17× | **1.21×** | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 73.96 µs | 1.80× | 1.67× | **1.08×** | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 93.88 µs | 1.03× | 0.86× | **1.20×** | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 16.98 µs | 1.61× | 1.26× | **1.28×** | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 40.32 µs | 1.77× | 1.79× | 0.99× | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 141.08 µs | 1.01× | 0.84× | **1.21×** | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 188.08 µs | 1.08× | 0.85× | **1.28×** | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 182.24 µs | 0.99× | 0.81× | **1.21×** | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 39.32 µs | 1.66× | 1.32× | **1.25×** | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 155.72 µs | 2.72× | 2.71× | 1.00× | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 324.20 µs | 1.12× | 0.95× | **1.17×** | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 81.52 µs | 1.27× | 0.96× | **1.32×** | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 952.97 µs | 2.26× | 1.88× | **1.20×** | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 1.120 ms | 2.44× | 2.02× | **1.21×** | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 665.45 µs | 4.42× | 4.44× | 1.00× | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.393 ms | 2.28× | 1.79× | **1.27×** | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 739.05 µs | 0.98× | 0.80× | **1.22×** | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 186.20 µs | 1.38× | 1.03× | **1.34×** | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 1.836 ms | 2.20× | 1.77× | **1.24×** | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 2.735 ms | 1.95× | 1.61× | **1.21×** | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 1.563 ms | 4.09× | 4.07× | 1.01× | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 3.012 ms | 2.33× | 1.87× | **1.25×** | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 470.61 µs | 1.36× | 1.06× | **1.29×** | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 5.685 ms | 2.26× | 1.90× | **1.18×** | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 3.361 ms | 3.21× | 3.26× | 0.98× | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 8.656 ms | 2.23× | 1.90× | **1.17×** | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 5.760 ms | 1.57× | 1.26× | **1.25×** | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 1.143 ms | 1.32× | 1.05× | **1.25×** | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 7.602 ms | 2.16× | 1.73× | **1.25×** | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 11.309 ms | 2.19× | 1.85× | **1.19×** | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.915 ms | 1.48× | 1.51× | 0.98× | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 18.016 ms | 2.24× | 1.92× | **1.17×** | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 13.539 ms | 1.30× | 1.08× | **1.20×** | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 2.336 ms | 1.25× | 0.97× | **1.29×** | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 27.796 ms | 4.64× | 4.00× | **1.16×** | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 42.720 ms | 4.71× | 4.12× | **1.14×** | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 9.330 ms | 2.09× | 2.06× | 1.01× | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 5.029 ms | 1.13× | 0.89× | **1.28×** | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 55.182 ms | 4.72× | 4.01× | **1.18×** | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 47.054 ms | 2.23× | 1.84× | **1.21×** | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 79.792 ms | 2.21× | 1.95× | **1.13×** | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 91.452 ms | 4.88× | 4.32× | **1.13×** | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 38.222 ms | 3.95× | 3.55× | **1.11×** | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 11.321 ms | 1.05× | 0.67× | **1.56×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 167.425 ms | 2.60× | 2.41× | **1.08×** | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 161.365 ms | 1.81× | 1.56× | **1.16×** | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 253.398 ms | 2.55× | 2.43× | **1.05×** | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 56.883 ms | 1.76× | 1.73× | 1.02× | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 99.982 ms | 1.99× | 1.98× | 1.00× | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 37.555 ms | 0.85× | 0.71× | **1.19×** | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 333.714 ms | 2.61× | 2.35× | **1.11×** | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 237.754 ms | 4.16× | 3.71× | **1.12×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 509.187 ms | 2.51× | 2.34× | **1.08×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 346.183 ms | 1.51× | 1.31× | **1.15×** | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 188.658 ms | 2.50× | 2.46× | 1.02× | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 76.687 ms | 0.76× | 0.64× | **1.19×** | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 531.960 ms | 2.59× | 2.48× | 1.04× | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 166.529 ms | 0.81× | 0.70× | **1.16×** | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 50 ns | 2.15× | 2.08× | 1.03× | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 75 ns | 3.50× | 3.48× | 1.01× | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 180 ns | 6.56× | 6.67× | 0.98× | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 100 ns | 3.06× | 3.03× | 1.01× | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 178 ns | 1.33× | 1.33× | 1.00× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 315 ns | 1.55× | 1.56× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 500 ns | 6.56× | 6.54× | 1.00× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 807 ns | 2.82× | 2.80× | 1.01× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 812 ns | 2.54× | 2.54× | 1.00× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 158 ns | 1.56× | 1.56× | 1.01× | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.48 µs | 4.21× | 3.47× | **1.21×** | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.49 µs | 3.57× | 2.94× | **1.22×** | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.50 µs | 3.28× | 2.71× | **1.21×** | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 459 ns | 2.16× | 2.15× | 1.00× | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 1.08 µs | 4.81× | 4.91× | 0.98× | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.53 µs | 1.79× | 1.48× | **1.21×** | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 295 ns | 1.62× | 1.61× | 1.00× | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 3.43 µs | 2.95× | 2.50× | **1.18×** | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 3.45 µs | 2.81× | 2.38× | **1.18×** | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 3.45 µs | 2.43× | 2.05× | **1.18×** | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 3.49 µs | 1.53× | 1.30× | **1.18×** | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 1.52 µs | 5.28× | 5.29× | 1.00× | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.84 µs | 6.42× | 6.42× | 1.00× | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 605 ns | 2.29× | 2.29× | 1.00× | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 3.94 µs | 2.15× | 1.86× | **1.16×** | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.81 µs | 3.24× | 3.23× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 6.84 µs | 1.71× | 1.25× | **1.37×** | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.15 µs | 2.05× | 1.81× | **1.14×** | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 12.30 µs | 1.70× | 1.47× | **1.16×** | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 5.65 µs | 4.30× | 4.30× | 1.00× | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 9.77 µs | 2.54× | 2.27× | **1.12×** | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 9.24 µs | 6.00× | 6.03× | 0.99× | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.50 µs | 2.48× | 2.20× | **1.13×** | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 30.16 µs | 2.07× | 1.37× | **1.51×** | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 14.18 µs | 2.46× | 2.17× | **1.13×** | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 10.80 µs | 3.74× | 3.76× | 1.00× | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 24.32 µs | 7.81× | 7.78× | 1.00× | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 4.88 µs | 2.79× | 2.22× | **1.26×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 18.20 µs | 3.87× | 3.92× | 0.99× | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 69.24 µs | 1.84× | 1.28× | **1.44×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 34.92 µs | 2.27× | 1.99× | **1.14×** | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 35.44 µs | 1.36× | 0.95× | **1.43×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 10.72 µs | 2.99× | 2.41× | **1.24×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 21.56 µs | 3.15× | 3.15× | 1.00× | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 112.20 µs | 2.20× | 1.57× | **1.40×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 141.96 µs | 1.49× | 0.95× | **1.57×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 90.20 µs | 1.59× | 1.20× | **1.32×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 21.16 µs | 3.07× | 2.25× | **1.36×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 103.68 µs | 4.04× | 4.07× | 0.99× | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 130.60 µs | 1.55× | 1.15× | **1.35×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 46.64 µs | 2.43× | 1.82× | **1.33×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 335.20 µs | 2.41× | 1.62× | **1.49×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 648.89 µs | 3.07× | 1.88× | **1.63×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 417.05 µs | 6.61× | 6.63× | 1.00× | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.046 ms | 2.93× | 2.00× | **1.46×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 321.72 µs | 1.44× | 1.05× | **1.37×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 94.00 µs | 2.51× | 1.74× | **1.45×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 755.25 µs | 2.58× | 1.81× | **1.43×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 1.765 ms | 2.71× | 1.83× | **1.48×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 1.615 ms | 8.20× | 8.20× | 1.00× | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.117 ms | 2.55× | 1.77× | **1.44×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 208.24 µs | 2.49× | 1.78× | **1.40×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 1.893 ms | 2.64× | 1.88× | **1.41×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 3.379 ms | 7.40× | 7.45× | 0.99× | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 5.590 ms | 3.17× | 2.17× | **1.46×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 4.053 ms | 2.24× | 1.49× | **1.50×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 439.16 µs | 2.65× | 1.80× | **1.47×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 2.911 ms | 2.48× | 1.70× | **1.46×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 3.950 ms | 2.83× | 1.94× | **1.46×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.407 ms | 2.72× | 2.73× | 1.00× | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 6.021 ms | 2.78× | 1.95× | **1.43×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 9.665 ms | 1.30× | 0.91× | **1.43×** | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.069 ms | 2.43× | 1.74× | **1.40×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 9.836 ms | 6.24× | 4.45× | **1.40×** | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 30.277 ms | 6.79× | 4.88× | **1.39×** | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 4.667 ms | 2.73× | 2.75× | 0.99× | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 2.371 ms | 2.05× | 1.42× | **1.45×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 21.527 ms | 6.64× | 4.75× | **1.40×** | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 15.814 ms | 2.68× | 1.83× | **1.46×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 47.643 ms | 2.38× | 1.51× | **1.58×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 33.210 ms | 6.62× | 4.89× | **1.35×** | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 22.934 ms | 6.03× | 6.03× | 1.00× | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 5.345 ms | 1.99× | 1.41× | **1.41×** | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 56.952 ms | 3.02× | 2.38× | **1.27×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 126.089 ms | 1.84× | 1.38× | **1.33×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 161.155 ms | 2.31× | 1.81× | **1.28×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 27.197 ms | 2.94× | 3.02× | 0.97× | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 52.606 ms | 6.10× | 6.05× | 1.01× | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 10.854 ms | 2.12× | 1.38× | **1.53×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 104.043 ms | 2.90× | 2.17× | **1.33×** | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 89.463 ms | 6.28× | 4.79× | **1.31×** | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 160.356 ms | 2.70× | 2.18× | **1.24×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 294.102 ms | 1.50× | 1.17× | **1.29×** | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 102.808 ms | 6.20× | 6.07× | 1.02× | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 26.620 ms | 2.77× | 1.62× | **1.71×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 276.928 ms | 3.39× | 3.31× | 1.02× | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 70.106 ms | 1.79× | 1.36× | **1.32×** | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 52 ns | 2.17× | 2.17× | 1.00× | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 82 ns | 3.79× | 3.80× | 1.00× | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 189 ns | 6.78× | 6.85× | 0.99× | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 107 ns | 3.30× | 3.31× | 0.99× | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 192 ns | 1.40× | 1.40× | 1.00× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 339 ns | 1.65× | 1.66× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 428 ns | 5.67× | 5.69× | 1.00× | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 888 ns | 3.05× | 3.06× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 895 ns | 2.75× | 2.77× | 0.99× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 166 ns | 1.86× | 1.87× | 1.00× | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.76 µs | 4.55× | 4.10× | **1.11×** | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.77 µs | 3.83× | 3.46× | **1.11×** | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.77 µs | 3.54× | 3.19× | **1.11×** | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 472 ns | 2.83× | 2.82× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 991 ns | 5.75× | 5.80× | 0.99× | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 1.82 µs | 1.93× | 1.74× | **1.11×** | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 310 ns | 1.87× | 1.87× | 1.00× | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 3.98 µs | 3.16× | 2.87× | **1.10×** | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 3.98 µs | 3.01× | 2.73× | **1.10×** | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.00 µs | 2.59× | 2.36× | **1.10×** | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.05 µs | 1.64× | 1.49× | **1.10×** | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 1.22 µs | 4.11× | 4.10× | 1.00× | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.70 µs | 5.09× | 5.10× | 1.00× | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 640 ns | 1.95× | 1.96× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.50 µs | 1.88× | 1.73× | **1.09×** | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.85 µs | 3.05× | 3.05× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 8.48 µs | 1.77× | 1.49× | **1.19×** | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.25 µs | 1.95× | 1.80× | **1.08×** | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 14.14 µs | 1.85× | 1.68× | **1.10×** | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 5.26 µs | 3.74× | 3.75× | 1.00× | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 10.90 µs | 2.18× | 2.03× | **1.07×** | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 7.93 µs | 3.90× | 3.90× | 1.00× | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.73 µs | 2.00× | 1.87× | **1.07×** | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 38.96 µs | 2.18× | 1.74× | **1.25×** | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 15.90 µs | 2.09× | 1.95× | **1.07×** | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 9.90 µs | 3.44× | 3.44× | 1.00× | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 20.40 µs | 4.55× | 4.55× | 1.00× | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 5.47 µs | 2.02× | 1.75× | **1.15×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 16.76 µs | 3.57× | 3.56× | 1.00× | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 89.84 µs | 1.95× | 1.60× | **1.22×** | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 40.16 µs | 1.94× | 1.80× | **1.07×** | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 44.16 µs | 0.96× | 0.79× | **1.22×** | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 12.14 µs | 2.07× | 1.82× | **1.14×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 23.28 µs | 2.39× | 2.39× | 1.00× | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 139.68 µs | 2.30× | 1.90× | **1.21×** | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 188.88 µs | 1.53× | 1.20× | **1.27×** | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 107.28 µs | 1.12× | 0.95× | **1.18×** | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 25.08 µs | 2.07× | 1.73× | **1.20×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 97.00 µs | 3.35× | 3.34× | 1.00× | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 157.80 µs | 1.09× | 0.92× | **1.18×** | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 55.92 µs | 1.69× | 1.43× | **1.18×** | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 460.09 µs | 2.13× | 1.78× | **1.20×** | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.084 ms | 3.64× | 2.98× | **1.22×** | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 322.52 µs | 4.31× | 4.31× | 1.00× | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.402 ms | 3.14× | 2.55× | **1.23×** | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 400.36 µs | 1.04× | 0.87× | **1.20×** | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 115.16 µs | 1.64× | 1.33× | **1.24×** | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.063 ms | 2.36× | 2.03× | **1.16×** | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 2.740 ms | 2.92× | 2.42× | **1.21×** | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 1.385 ms | 6.90× | 6.89× | 1.00× | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.528 ms | 2.24× | 1.92× | **1.17×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 277.72 µs | 1.65× | 1.42× | **1.16×** | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 2.782 ms | 2.23× | 1.87× | **1.19×** | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 3.073 ms | 6.45× | 6.37× | 1.01× | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 8.673 ms | 3.62× | 3.10× | **1.17×** | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 5.954 ms | 2.46× | 2.05× | **1.20×** | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 606.13 µs | 1.66× | 1.29× | **1.28×** | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 4.075 ms | 2.25× | 1.86× | **1.21×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 6.009 ms | 2.32× | 1.99× | **1.17×** | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.623 ms | 1.74× | 1.75× | 0.99× | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 8.877 ms | 2.26× | 1.92× | **1.18×** | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 13.621 ms | 1.40× | 1.20× | **1.17×** | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.481 ms | 1.57× | 1.30× | **1.21×** | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 13.546 ms | 4.50× | 3.86× | **1.17×** | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 41.249 ms | 6.41× | 5.43× | **1.18×** | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.988 ms | 2.14× | 2.15× | 1.00× | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.051 ms | 1.49× | 1.17× | **1.27×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 29.140 ms | 4.81× | 4.16× | **1.16×** | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 24.243 ms | 2.27× | 1.89× | **1.20×** | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 81.374 ms | 2.48× | 2.26× | **1.10×** | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 45.987 ms | 4.80× | 4.37× | **1.10×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 20.098 ms | 3.59× | 3.43× | 1.05× | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 7.440 ms | 1.62× | 1.29× | **1.25×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 84.320 ms | 2.50× | 2.42× | 1.03× | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 166.058 ms | 1.70× | 1.50× | **1.13×** | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 255.817 ms | 2.82× | 2.59× | **1.09×** | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 28.833 ms | 2.55× | 2.44× | 1.04× | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 48.545 ms | 2.33× | 2.27× | 1.03× | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 16.891 ms | 1.68× | 1.25× | **1.34×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 173.680 ms | 2.89× | 2.49× | **1.16×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 120.732 ms | 4.52× | 3.99× | **1.13×** | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 260.489 ms | 2.45× | 2.42× | 1.01× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 346.666 ms | 1.21× | 1.05× | **1.15×** | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 93.477 ms | 2.53× | 2.43× | 1.04× | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 42.492 ms | 0.91× | 0.76× | **1.19×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 263.108 ms | 2.45× | 2.33× | **1.05×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 86.476 ms | 0.85× | 0.73× | **1.16×** | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 741 ns | 4.83× | 5.14× | **0.94×** | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.49 µs | 4.36× | 4.37× | 1.00× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.76 µs | 4.01× | 4.02× | 1.00× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 48.72 µs | 3.95× | 3.95× | 1.00× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 209.36 µs | 4.14× | 3.48× | **1.19×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 1.009 ms | 1.54× | 1.32× | **1.16×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 5.778 ms | 1.27× | 1.03× | **1.23×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 29.008 ms | 1.35× | 1.15× | **1.17×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 133.520 ms | 1.19× | 1.00× | **1.19×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 758 ns | 4.15× | 4.38× | **0.95×** | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.56 µs | 3.08× | 3.13× | 0.98× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.38 µs | 2.76× | 2.77× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.12 µs | 2.58× | 2.58× | 1.00× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 242.52 µs | 2.53× | 2.20× | **1.15×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 3.566 ms | 2.27× | 1.99× | **1.14×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 3.193 ms | 1.04× | 0.87× | **1.20×** | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 3.346 ms | 1.03× | 0.87× | **1.19×** | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.389 ms | 1.29× | 1.22× | **1.06×** | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 6.840 ms | 1.23× | 1.12× | **1.10×** | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 20.813 ms | 2.97× | 3.14× | **0.94×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 87.657 ms | 3.13× | 3.15× | 0.99× | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 36.158 ms | 1.23× | 1.20× | 1.03× | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 167.828 ms | 1.11× | 1.02× | **1.08×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 864 ns | 6.92× | 6.99× | 0.99× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.36 µs | 5.38× | 5.40× | 1.00× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 8.04 µs | 3.92× | 3.93× | 1.00× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 31.92 µs | 3.26× | 3.24× | 1.00× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 130.60 µs | 3.02× | 2.80× | **1.08×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 538.69 µs | 1.80× | 1.55× | **1.16×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.322 ms | 1.96× | 1.61× | **1.22×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 10.039 ms | 2.10× | 1.67× | **1.26×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 49.653 ms | 1.79× | 1.43× | **1.25×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 920 ns | 7.84× | 7.85× | 1.00× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.44 µs | 5.03× | 4.98× | 1.01× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 8.40 µs | 3.51× | 3.50× | 1.00× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 33.68 µs | 2.85× | 2.86× | 1.00× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 140.40 µs | 2.53× | 2.41× | **1.05×** | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.301 ms | 1.73× | 1.52× | **1.14×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 2.804 ms | 2.13× | 1.74× | **1.23×** | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 1.725 ms | 1.06× | 0.89× | **1.19×** | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 601.09 µs | 1.61× | 1.47× | **1.09×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 2.701 ms | 1.58× | 1.41× | **1.12×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 9.765 ms | 3.08× | 3.10× | 0.99× | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 45.111 ms | 3.21× | 3.46× | **0.93×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 11.881 ms | 1.54× | 1.36× | **1.14×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 59.270 ms | 1.22× | 1.09× | **1.12×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 9.43 µs | 6.09× | 6.09× | 1.00× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 64.96 µs | 4.81× | 4.83× | 1.00× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 587.57 µs | 4.14× | 4.15× | 1.00× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.728 ms | 3.84× | 3.84× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 58.158 ms | 3.44× | 3.15× | **1.09×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.57 µs | 4.99× | 5.03× | 0.99× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 66.52 µs | 3.33× | 3.33× | 1.00× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 645.41 µs | 2.63× | 2.67× | 0.99× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.798 ms | 2.63× | 2.73× | 0.96× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 77.964 ms | 2.03× | 2.00× | 1.01× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 9.12 µs | 7.70× | 7.68× | 1.00× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 51.76 µs | 5.58× | 5.61× | 1.00× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 367.00 µs | 4.04× | 4.04× | 1.00× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 3.118 ms | 3.27× | 3.27× | 1.00× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 28.336 ms | 3.08× | 3.02× | 1.02× | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 9.83 µs | 8.09× | 8.21× | 0.99× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 53.20 µs | 4.70× | 4.67× | 1.00× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 387.32 µs | 3.33× | 3.31× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.527 ms | 2.59× | 2.60× | 0.99× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 35.921 ms | 2.18× | 2.43× | **0.90×** | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.44 µs | 3.61× | 3.60× | 1.00× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 103.72 µs | 2.37× | 1.99× | **1.19×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 475.13 µs | 2.62× | 1.94× | **1.35×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 2.312 ms | 2.56× | 1.81× | **1.42×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 12.734 ms | 2.09× | 1.64× | **1.28×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 64.408 ms | 2.01× | 1.45× | **1.39×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 23.80 µs | 2.31× | 2.31× | 1.00× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 115.96 µs | 1.48× | 1.33× | **1.11×** | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 585.17 µs | 1.60× | 1.35× | **1.18×** | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 3.093 ms | 1.71× | 1.43× | **1.20×** | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 19.009 ms | 1.39× | 1.28× | **1.09×** | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 98.086 ms | 1.29× | 1.11× | **1.17×** | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 18.72 µs | 2.85× | 2.83× | 1.01× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 74.24 µs | 2.08× | 1.82× | **1.14×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 315.76 µs | 2.77× | 2.19× | **1.26×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.386 ms | 2.73× | 2.01× | **1.36×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 6.219 ms | 2.38× | 1.67× | **1.43×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 30.263 ms | 2.28× | 1.59× | **1.44×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 19.92 µs | 2.98× | 2.98× | 1.00× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.449 ms | 1.86× | 1.75× | **1.06×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 80.68 µs | 1.96× | 1.81× | **1.08×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.140 ms | 1.85× | 1.67× | **1.11×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 359.56 µs | 1.94× | 1.68× | **1.15×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 7.025 ms | 1.89× | 1.66× | **1.14×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.652 ms | 1.90× | 1.59× | **1.20×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 8.264 ms | 1.60× | 1.35× | **1.19×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 43.139 ms | 1.35× | 1.14× | **1.19×** | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.52 µs | 4.43× | 4.49× | 0.99× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 153.68 µs | 1.92× | 1.93× | 0.99× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 847.09 µs | 1.97× | 1.95× | 1.01× | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 6.194 ms | 1.26× | 1.32× | 0.96× | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 36.951 ms | 1.38× | 1.52× | **0.91×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 233.291 ms | 1.19× | 1.35× | **0.88×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 28.56 µs | 2.63× | 2.63× | 1.00× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 165.72 µs | 1.53× | 1.52× | 1.00× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.193 ms | 1.35× | 1.35× | 1.00× | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 6.908 ms | 1.27× | 1.29× | 0.99× | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 51.216 ms | 1.30× | 1.50× | **0.87×** | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 287.702 ms | 1.10× | 1.16× | **0.94×** | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 22.20 µs | 3.36× | 3.36× | 1.00× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 96.92 µs | 1.88× | 1.67× | **1.12×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 459.61 µs | 1.88× | 1.59× | **1.18×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.377 ms | 1.60× | 1.33× | **1.20×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 11.724 ms | 1.22× | 1.01× | **1.21×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 63.221 ms | 1.04× | 0.92× | **1.13×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 23.60 µs | 3.55× | 3.57× | 0.99× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 115.80 µs | 1.71× | 1.62× | **1.06×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 521.89 µs | 1.67× | 1.50× | **1.11×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 2.972 ms | 1.20× | 1.09× | **1.10×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 13.831 ms | 1.11× | 0.98× | **1.14×** | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 84.638 ms | 0.80× | 0.76× | **1.05×** | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `simd`/`fftw` | `simd` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 2.32× (1.00–5.14) | **1.09×** (0.94–1.23) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.30× (3.15–6.09) | **1.02×** (1.00–1.09) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 2.00× (0.92–5.09) | **1.34×** (1.11–1.53) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 1.98× (1.45–3.60) | **1.26×** (1.00–1.42) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.89× (1.32–4.49) | **0.95×** (0.88–1.01) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 1.24× (0.68–1.89) | **1.38×** (0.97–1.90) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 1.87× (0.91–6.55) | **1.25×** (0.99–1.61) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 4.44× (2.02–8.63) | **1.00×** (0.98–1.02) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.85× (0.87–4.38) | **1.05×** (0.94–1.20) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 3.00× (2.00–5.03) | **0.99×** (0.96–1.01) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 1.91× (0.80–4.32) | **1.16×** (1.05–1.27) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.43× (1.11–2.31) | **1.12×** (1.00–1.20) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.52× (1.16–2.63) | **0.96×** (0.87–1.00) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 1.03× (0.64–1.73) | **1.19×** (0.97–1.56) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.78× (0.85–3.92) | **1.12×** (1.00–1.28) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.89× (1.51–4.56) | **1.01×** (0.98–1.11) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 2.71× (1.43–6.99) | **1.10×** (0.99–1.26) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 4.44× (3.02–7.68) | **1.00×** (1.00–1.02) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 2.07× (0.95–4.89) | **1.34×** (1.12–1.49) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 1.98× (1.59–2.83) | **1.26×** (1.01–1.44) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.49× (0.92–3.36) | **1.14×** (1.00–1.21) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 1.88× (1.36–3.48) | **1.26×** (1.00–1.71) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 1.72× (0.91–3.47) | **1.27×** (1.00–1.63) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 4.69× (2.15–8.20) | **1.00×** (0.97–1.02) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.23× (0.89–7.85) | **1.07×** (0.93–1.23) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.81× (2.43–8.21) | **0.98×** (0.90–1.00) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 2.09× (0.79–5.43) | **1.15×** (1.01–1.23) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.68× (1.14–2.98) | **1.12×** (1.00–1.20) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.38× (0.76–3.57) | **1.08×** (0.99–1.14) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.56× (0.73–3.80) | **1.14×** (0.99–1.34) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 2.05× (1.05–4.10) | **1.12×** (0.99–1.27) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 3.58× (1.75–6.89) | **1.01×** (0.99–1.05) | +| **all** | 2.45× (0.65–8.66) | 2.14× (0.64–8.63) | **1.14×** (0.87–1.90), 505 cases, 9 slower by >5% | diff --git a/benchmark/compare3/aarch64/simd/simd_t1.json b/benchmark/compare3/aarch64/simd/simd_t1.json new file mode 100644 index 0000000..c2b81eb --- /dev/null +++ b/benchmark/compare3/aarch64/simd/simd_t1.json @@ -0,0 +1,10975 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T11:20:30.330", + "impl": "ffta", + "julia": "1.12.6", + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ 4419199" + }, + "results": [ + { + "T": "Float64", + "api": "mul!", + "class": "pow2", + "dims": 1, + "exec_alloc": 0, + "exec_min": 2.384e-8, + "key": "fft Float64 8 dims=1", + "kind": "fft", + "measure": false, + "n": 8, + 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benchmark: compare3 results for the leaves-first order (aarch64, 1 thread) --- benchmark/compare3/aarch64/large/COMPARE3.md | 579 + .../compare3/aarch64/large/large_t1.json | 10975 ++++++++++++++++ 2 files changed, 11554 insertions(+) create mode 100644 benchmark/compare3/aarch64/large/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/large/large_t1.json diff --git a/benchmark/compare3/aarch64/large/COMPARE3.md b/benchmark/compare3/aarch64/large/COMPARE3.md new file mode 100644 index 0000000..04d7aeb --- /dev/null +++ b/benchmark/compare3/aarch64/large/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T11:46:51.213 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `large` | FFTA.jl 0.3.1 @ 605c9c3 — `FFTA-large` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `large` | `int`/`fftw` | `large`/`fftw` | `large` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 118 ns | 3.19× | 3.15× | 1.01× | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 26 ns | 0.65× | 0.70× | **0.94×** | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 157 ns | 3.52× | 3.61× | 0.98× | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 54 ns | 0.97× | 0.97× | 1.00× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 807 ns | 5.92× | 5.94× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.51 µs | 6.55× | 6.57× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 667 ns | 5.29× | 5.29× | 1.00× | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 816 ns | 2.38× | 2.38× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 818 ns | 2.12× | 2.11× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 134 ns | 1.26× | 1.28× | 0.98× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.48 µs | 2.16× | 1.77× | **1.22×** | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.50 µs | 2.22× | 1.83× | **1.21×** | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.50 µs | 2.60× | 2.14× | **1.21×** | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 962 ns | 2.80× | 2.96× | **0.95×** | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.56 µs | 7.03× | 7.20× | 0.98× | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.55 µs | 1.57× | 1.30× | **1.21×** | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 327 ns | 1.69× | 1.68× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 3.45 µs | 1.70× | 1.44× | **1.18×** | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 3.47 µs | 3.06× | 2.58× | **1.19×** | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 3.47 µs | 2.34× | 1.97× | **1.19×** | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 3.53 µs | 2.16× | 1.83× | **1.18×** | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 2.53 µs | 6.97× | 7.03× | 0.99× | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 3.01 µs | 7.50× | 7.67× | 0.98× | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 625 ns | 2.03× | 1.60× | **1.26×** | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 8.44 µs | 2.32× | 2.04× | **1.13×** | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.83 µs | 2.02× | 2.02× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 7.01 µs | 1.60× | 1.17× | **1.37×** | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 1.51 µs | 2.27× | 1.87× | **1.21×** | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 12.54 µs | 2.26× | 1.97× | **1.15×** | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 9.45 µs | 3.96× | 3.98× | 0.99× | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 16.08 µs | 2.19× | 1.90× | **1.15×** | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 15.72 µs | 5.80× | 5.85× | 0.99× | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 2.93 µs | 2.50× | 1.74× | **1.44×** | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 30.44 µs | 3.00× | 2.00× | **1.50×** | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 29.12 µs | 2.53× | 2.27× | **1.11×** | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 18.82 µs | 3.57× | 3.58× | 1.00× | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 43.20 µs | 6.51× | 6.45× | 1.01× | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 6.91 µs | 2.59× | 1.90× | **1.37×** | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 30.68 µs | 3.47× | 3.50× | 0.99× | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 70.16 µs | 1.75× | 1.22× | **1.44×** | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 63.40 µs | 2.04× | 1.76× | **1.16×** | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 77.08 µs | 1.45× | 1.05× | **1.38×** | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 13.42 µs | 2.74× | 1.75× | **1.57×** | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 37.16 µs | 2.98× | 2.99× | 1.00× | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 114.04 µs | 1.43× | 1.02× | **1.40×** | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 143.64 µs | 1.42× | 0.91× | **1.57×** | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 146.24 µs | 1.38× | 0.98× | **1.41×** | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 31.32 µs | 2.77× | 1.86× | **1.49×** | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 167.20 µs | 3.31× | 3.35× | 0.99× | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 269.12 µs | 1.58× | 1.19× | **1.32×** | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 63.60 µs | 2.14× | 1.31× | **1.64×** | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 699.01 µs | 2.49× | 1.70× | **1.47×** | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 657.41 µs | 2.58× | 1.59× | **1.62×** | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 849.05 µs | 8.66× | 8.73× | 0.99× | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 1.044 ms | 2.47× | 1.67× | **1.47×** | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 581.25 µs | 1.31× | 0.92× | **1.42×** | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 146.72 µs | 2.09× | 1.34× | **1.56×** | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 1.365 ms | 2.44× | 1.64× | **1.49×** | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 1.834 ms | 2.08× | 1.42× | **1.46×** | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 1.886 ms | 7.14× | 7.14× | 1.00× | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 2.281 ms | 2.58× | 1.81× | **1.42×** | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 292.96 µs | 1.85× | 1.05× | **1.75×** | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 3.884 ms | 2.70× | 1.93× | **1.40×** | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 3.988 ms | 7.03× | 7.11× | 0.99× | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 5.872 ms | 2.66× | 1.91× | **1.39×** | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 4.063 ms | 2.29× | 1.52× | **1.51×** | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 838.09 µs | 2.20× | 1.49× | **1.48×** | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 5.644 ms | 2.33× | 1.59× | **1.47×** | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 7.601 ms | 2.63× | 1.85× | **1.42×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.612 ms | 2.38× | 2.32× | 1.02× | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 12.305 ms | 2.71× | 1.93× | **1.40×** | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 6.872 ms | 1.47× | 0.73× | **2.01×** | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 1.867 ms | 2.14× | 1.41× | **1.51×** | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 14.580 ms | 6.41× | 3.32× | **1.93×** | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 21.757 ms | 6.35× | 3.26× | **1.95×** | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 9.168 ms | 2.82× | 2.80× | 1.01× | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 2.995 ms | 1.83× | 0.86× | **2.12×** | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 28.633 ms | 6.51× | 3.19× | **2.04×** | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 30.738 ms | 2.55× | 1.69× | **1.51×** | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 31.362 ms | 2.28× | 1.03× | **2.22×** | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 47.219 ms | 6.71× | 3.48× | **1.93×** | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 43.330 ms | 6.65× | 6.54× | 1.02× | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 6.105 ms | 1.11× | 0.54× | **2.07×** | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 66.269 ms | 2.89× | 1.38× | **2.09×** | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 66.578 ms | 2.17× | 0.87× | **2.50×** | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 99.818 ms | 2.73× | 1.38× | **1.98×** | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 53.268 ms | 2.75× | 2.88× | 0.96× | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 103.887 ms | 4.27× | 4.25× | 1.00× | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 14.397 ms | 1.69× | 0.60× | **2.83×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 134.785 ms | 2.72× | 1.38× | **1.97×** | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 122.301 ms | 6.18× | 3.24× | **1.91×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 212.281 ms | 2.69× | 1.41× | **1.91×** | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 146.465 ms | 2.18× | 0.84× | **2.60×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 200.447 ms | 5.03× | 4.95× | 1.01× | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 31.041 ms | 1.05× | 0.40× | **2.65×** | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 581.606 ms | 4.59× | 4.59× | 1.00× | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 67.705 ms | 1.12× | 0.41× | **2.73×** | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 83 ns | 3.19× | 3.21× | 0.99× | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 26 ns | 0.96× | 1.06× | **0.91×** | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 162 ns | 4.63× | 4.88× | **0.95×** | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 56 ns | 1.33× | 1.36× | 0.98× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 489 ns | 3.59× | 3.60× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 901 ns | 3.91× | 3.92× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 518 ns | 3.71× | 3.74× | 0.99× | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 890 ns | 2.57× | 2.59× | 0.99× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 896 ns | 2.31× | 2.33× | 0.99× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 139 ns | 1.72× | 1.75× | 0.99× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.76 µs | 2.54× | 2.29× | **1.11×** | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.77 µs | 2.16× | 1.95× | **1.11×** | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.77 µs | 2.81× | 2.54× | **1.11×** | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 979 ns | 3.37× | 3.58× | **0.94×** | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.40 µs | 4.40× | 4.49× | 0.98× | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 1.84 µs | 1.46× | 1.33× | **1.10×** | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 339 ns | 1.09× | 1.09× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 4.01 µs | 1.44× | 1.31× | **1.10×** | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 4.02 µs | 2.52× | 2.31× | **1.09×** | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 4.03 µs | 1.77× | 1.62× | **1.10×** | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 4.09 µs | 1.88× | 1.73× | **1.09×** | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.91 µs | 3.21× | 3.24× | 0.99× | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.68 µs | 4.11× | 4.23× | 0.97× | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 707 ns | 1.24× | 1.09× | **1.14×** | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 9.68 µs | 2.05× | 1.95× | **1.05×** | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.85 µs | 1.98× | 1.98× | 1.00× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 8.56 µs | 1.50× | 1.27× | **1.18×** | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.67 µs | 1.41× | 1.27× | **1.11×** | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 14.30 µs | 1.99× | 1.84× | **1.09×** | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 8.63 µs | 2.98× | 3.04× | 0.98× | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 18.54 µs | 1.90× | 1.77× | **1.07×** | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 13.28 µs | 3.01× | 3.09× | 0.97× | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 3.48 µs | 1.50× | 1.23× | **1.22×** | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 39.24 µs | 1.78× | 1.43× | **1.24×** | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 33.40 µs | 2.19× | 2.11× | 1.04× | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 17.44 µs | 3.02× | 3.09× | 0.98× | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 36.44 µs | 3.42× | 3.55× | 0.96× | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 8.01 µs | 1.52× | 1.27× | **1.19×** | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 27.92 µs | 2.97× | 3.01× | 0.99× | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 90.12 µs | 1.41× | 1.16× | **1.21×** | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 73.96 µs | 1.80× | 1.67× | **1.08×** | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 95.76 µs | 1.03× | 0.88× | **1.18×** | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 16.98 µs | 1.61× | 1.26× | **1.28×** | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 40.64 µs | 1.77× | 1.81× | 0.98× | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 141.80 µs | 1.01× | 0.84× | **1.20×** | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 189.28 µs | 1.08× | 0.85× | **1.27×** | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 184.88 µs | 0.99× | 0.83× | **1.20×** | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 39.48 µs | 1.66× | 1.32× | **1.25×** | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 158.76 µs | 2.72× | 2.76× | 0.98× | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 334.20 µs | 1.12× | 0.98× | **1.14×** | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 83.20 µs | 1.27× | 0.98× | **1.29×** | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 928.41 µs | 2.26× | 1.83× | **1.23×** | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 1.070 ms | 2.44× | 1.93× | **1.27×** | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 679.13 µs | 4.42× | 4.53× | 0.98× | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.428 ms | 2.28× | 1.84× | **1.24×** | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 743.29 µs | 0.98× | 0.81× | **1.21×** | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 194.36 µs | 1.38× | 1.08× | **1.29×** | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 1.941 ms | 2.20× | 1.87× | **1.18×** | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 2.732 ms | 1.95× | 1.61× | **1.21×** | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 1.574 ms | 4.09× | 4.09× | 1.00× | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 3.127 ms | 2.33× | 1.94× | **1.20×** | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 465.17 µs | 1.36× | 1.05× | **1.30×** | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 5.795 ms | 2.26× | 1.94× | **1.16×** | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 3.327 ms | 3.21× | 3.23× | 1.00× | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 8.696 ms | 2.23× | 1.91× | **1.16×** | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 5.775 ms | 1.57× | 1.27× | **1.24×** | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 1.200 ms | 1.32× | 1.10× | **1.19×** | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 7.562 ms | 2.16× | 1.72× | **1.25×** | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 11.625 ms | 2.19× | 1.90× | **1.15×** | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.887 ms | 1.48× | 1.50× | 0.99× | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 18.345 ms | 2.24× | 1.95× | **1.15×** | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 9.881 ms | 1.30× | 0.79× | **1.65×** | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 2.429 ms | 1.25× | 1.01× | **1.24×** | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 20.828 ms | 4.64× | 3.00× | **1.55×** | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 31.026 ms | 4.71× | 3.00× | **1.57×** | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 9.094 ms | 2.09× | 2.01× | 1.04× | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 4.137 ms | 1.13× | 0.73× | **1.55×** | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 42.473 ms | 4.72× | 3.09× | **1.53×** | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 48.003 ms | 2.23× | 1.87× | **1.19×** | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 46.918 ms | 2.21× | 1.14× | **1.93×** | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 67.695 ms | 4.88× | 3.20× | **1.53×** | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 44.293 ms | 3.95× | 4.12× | 0.96× | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 9.028 ms | 1.05× | 0.54× | **1.95×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 97.086 ms | 2.60× | 1.40× | **1.86×** | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 97.797 ms | 1.81× | 0.94× | **1.92×** | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 144.177 ms | 2.55× | 1.38× | **1.85×** | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 55.192 ms | 1.76× | 1.68× | 1.05× | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 99.366 ms | 1.99× | 1.97× | 1.01× | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 21.139 ms | 0.85× | 0.40× | **2.11×** | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 194.454 ms | 2.61× | 1.37× | **1.91×** | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 173.606 ms | 4.16× | 2.71× | **1.54×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 316.420 ms | 2.51× | 1.45× | **1.73×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 221.722 ms | 1.51× | 0.84× | **1.79×** | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 189.719 ms | 2.50× | 2.47× | 1.01× | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 45.008 ms | 0.76× | 0.38× | **2.02×** | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 537.830 ms | 2.59× | 2.51× | 1.03× | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 102.910 ms | 0.81× | 0.43× | **1.87×** | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 51 ns | 2.15× | 2.13× | 1.01× | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 77 ns | 3.50× | 3.55× | 0.99× | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 183 ns | 6.56× | 6.76× | 0.97× | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 101 ns | 3.06× | 3.09× | 0.99× | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 178 ns | 1.33× | 1.33× | 1.00× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 314 ns | 1.55× | 1.55× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 502 ns | 6.56× | 6.57× | 1.00× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 810 ns | 2.82× | 2.81× | 1.00× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 816 ns | 2.54× | 2.56× | 0.99× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 160 ns | 1.56× | 1.58× | 0.99× | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.48 µs | 4.21× | 3.45× | **1.22×** | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.49 µs | 3.57× | 2.93× | **1.22×** | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.49 µs | 3.28× | 2.70× | **1.22×** | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 457 ns | 2.16× | 2.14× | 1.01× | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 1.09 µs | 4.81× | 4.98× | 0.97× | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.53 µs | 1.79× | 1.47× | **1.22×** | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 297 ns | 1.62× | 1.62× | 1.00× | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 3.43 µs | 2.95× | 2.50× | **1.18×** | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 3.43 µs | 2.81× | 2.37× | **1.19×** | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 3.44 µs | 2.43× | 2.04× | **1.19×** | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 3.49 µs | 1.53× | 1.29× | **1.19×** | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 1.54 µs | 5.28× | 5.34× | 0.99× | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.87 µs | 6.42× | 6.51× | 0.99× | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 609 ns | 2.29× | 2.30× | 1.00× | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 3.94 µs | 2.15× | 1.85× | **1.16×** | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.82 µs | 3.24× | 3.24× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 6.83 µs | 1.71× | 1.25× | **1.37×** | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.15 µs | 2.05× | 1.81× | **1.13×** | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 12.32 µs | 1.70× | 1.47× | **1.15×** | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 5.77 µs | 4.30× | 4.39× | 0.98× | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 9.89 µs | 2.54× | 2.29× | **1.11×** | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 9.29 µs | 6.00× | 6.06× | 0.99× | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.50 µs | 2.48× | 2.20× | **1.13×** | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 30.20 µs | 2.07× | 1.38× | **1.50×** | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 14.16 µs | 2.46× | 2.17× | **1.13×** | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 10.94 µs | 3.74× | 3.81× | 0.98× | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 24.40 µs | 7.81× | 7.81× | 1.00× | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 4.95 µs | 2.79× | 2.25× | **1.24×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 18.26 µs | 3.87× | 3.94× | 0.98× | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 69.20 µs | 1.84× | 1.28× | **1.44×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 34.92 µs | 2.27× | 1.99× | **1.14×** | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 35.24 µs | 1.36× | 0.95× | **1.44×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 10.80 µs | 2.99× | 2.43× | **1.23×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 21.60 µs | 3.15× | 3.16× | 1.00× | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 112.16 µs | 2.20× | 1.57× | **1.40×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 141.48 µs | 1.49× | 0.94× | **1.57×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 91.40 µs | 1.59× | 1.22× | **1.31×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 21.52 µs | 3.07× | 2.29× | **1.34×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 105.52 µs | 4.04× | 4.14× | 0.98× | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 130.08 µs | 1.55× | 1.15× | **1.35×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 47.12 µs | 2.43× | 1.84× | **1.32×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 336.28 µs | 2.41× | 1.62× | **1.49×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 645.65 µs | 3.07× | 1.87× | **1.64×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 416.13 µs | 6.61× | 6.61× | 1.00× | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.046 ms | 2.93× | 2.00× | **1.46×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 322.84 µs | 1.44× | 1.05× | **1.37×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 96.16 µs | 2.51× | 1.78× | **1.41×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 760.37 µs | 2.58× | 1.82× | **1.42×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 1.773 ms | 2.71× | 1.84× | **1.47×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 1.613 ms | 8.20× | 8.19× | 1.00× | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.122 ms | 2.55× | 1.78× | **1.44×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 211.80 µs | 2.49× | 1.81× | **1.37×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 1.902 ms | 2.64× | 1.88× | **1.40×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 3.368 ms | 7.40× | 7.42× | 1.00× | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 5.734 ms | 3.17× | 2.23× | **1.42×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 4.048 ms | 2.24× | 1.49× | **1.51×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 443.05 µs | 2.65× | 1.82× | **1.46×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 2.911 ms | 2.48× | 1.70× | **1.46×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 4.095 ms | 2.83× | 2.02× | **1.41×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.387 ms | 2.72× | 2.70× | 1.01× | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 5.943 ms | 2.78× | 1.92× | **1.44×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 6.774 ms | 1.30× | 0.64× | **2.04×** | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.102 ms | 2.43× | 1.79× | **1.35×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 6.991 ms | 6.24× | 3.16× | **1.97×** | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 21.424 ms | 6.79× | 3.45× | **1.97×** | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 4.643 ms | 2.73× | 2.73× | 1.00× | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 2.476 ms | 2.05× | 1.48× | **1.38×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 15.511 ms | 6.64× | 3.42× | **1.94×** | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 15.935 ms | 2.68× | 1.84× | **1.45×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 30.729 ms | 2.38× | 0.97× | **2.45×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 23.064 ms | 6.62× | 3.39× | **1.95×** | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 22.762 ms | 6.03× | 5.98× | 1.01× | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 4.288 ms | 1.99× | 1.13× | **1.76×** | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 31.973 ms | 3.02× | 1.34× | **2.26×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 66.725 ms | 1.84× | 0.73× | **2.52×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 99.016 ms | 2.31× | 1.11× | **2.08×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 25.799 ms | 2.94× | 2.86× | 1.03× | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 52.316 ms | 6.10× | 6.02× | 1.01× | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 8.849 ms | 2.12× | 1.13× | **1.87×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 71.242 ms | 2.90× | 1.49× | **1.95×** | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 60.931 ms | 6.28× | 3.26× | **1.92×** | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 104.629 ms | 2.70× | 1.42× | **1.90×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 145.533 ms | 1.50× | 0.58× | **2.60×** | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 102.246 ms | 6.20× | 6.03× | 1.03× | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 19.301 ms | 2.77× | 1.18× | **2.35×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 278.293 ms | 3.39× | 3.33× | 1.02× | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 40.668 ms | 1.79× | 0.79× | **2.27×** | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 53 ns | 2.17× | 2.20× | 0.99× | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 84 ns | 3.79× | 3.88× | 0.98× | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 194 ns | 6.78× | 7.07× | 0.96× | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 109 ns | 3.30× | 3.38× | 0.98× | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 192 ns | 1.40× | 1.41× | 1.00× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 341 ns | 1.65× | 1.66× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 435 ns | 5.67× | 5.79× | 0.98× | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 889 ns | 3.05× | 3.07× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 891 ns | 2.75× | 2.76× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 167 ns | 1.86× | 1.87× | 0.99× | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.76 µs | 4.55× | 4.10× | **1.11×** | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.77 µs | 3.83× | 3.46× | **1.11×** | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.77 µs | 3.54× | 3.19× | **1.11×** | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 472 ns | 2.83× | 2.82× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 1.01 µs | 5.75× | 5.91× | 0.97× | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 1.82 µs | 1.93× | 1.74× | **1.11×** | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 310 ns | 1.87× | 1.86× | 1.00× | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 3.99 µs | 3.16× | 2.88× | **1.10×** | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 4.00 µs | 3.01× | 2.75× | **1.10×** | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.00 µs | 2.59× | 2.36× | **1.10×** | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.05 µs | 1.64× | 1.49× | **1.10×** | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 1.25 µs | 4.11× | 4.22× | 0.98× | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.73 µs | 5.09× | 5.20× | 0.98× | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 637 ns | 1.95× | 1.95× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.50 µs | 1.88× | 1.73× | **1.09×** | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.86 µs | 3.05× | 3.06× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 8.52 µs | 1.77× | 1.49× | **1.19×** | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.25 µs | 1.95× | 1.80× | **1.09×** | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 14.20 µs | 1.85× | 1.69× | **1.09×** | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 5.33 µs | 3.74× | 3.80× | 0.98× | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 11.08 µs | 2.18× | 2.07× | **1.06×** | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 8.08 µs | 3.90× | 3.98× | 0.98× | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.72 µs | 2.00× | 1.86× | **1.07×** | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 39.04 µs | 2.18× | 1.75× | **1.25×** | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 16.02 µs | 2.09× | 1.97× | **1.06×** | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 10.18 µs | 3.44× | 3.53× | 0.97× | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 20.68 µs | 4.55× | 4.61× | 0.99× | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 5.62 µs | 2.02× | 1.80× | **1.12×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 17.14 µs | 3.57× | 3.64× | 0.98× | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 89.52 µs | 1.95× | 1.60× | **1.22×** | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 40.28 µs | 1.94× | 1.81× | **1.07×** | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 44.28 µs | 0.96× | 0.80× | **1.21×** | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 12.22 µs | 2.07× | 1.83× | **1.13×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 23.44 µs | 2.39× | 2.40× | 0.99× | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 140.56 µs | 2.30× | 1.91× | **1.21×** | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 187.60 µs | 1.53× | 1.20× | **1.28×** | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 109.08 µs | 1.12× | 0.96× | **1.16×** | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 25.52 µs | 2.07× | 1.76× | **1.18×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 99.24 µs | 3.35× | 3.42× | 0.98× | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 158.32 µs | 1.09× | 0.92× | **1.18×** | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 56.52 µs | 1.69× | 1.44× | **1.17×** | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 454.45 µs | 2.13× | 1.76× | **1.21×** | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.086 ms | 3.64× | 2.98× | **1.22×** | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 324.32 µs | 4.31× | 4.34× | 0.99× | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.414 ms | 3.14× | 2.57× | **1.22×** | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 404.28 µs | 1.04× | 0.88× | **1.18×** | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 118.04 µs | 1.64× | 1.36× | **1.21×** | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.035 ms | 2.36× | 1.98× | **1.19×** | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 2.723 ms | 2.92× | 2.40× | **1.22×** | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 1.396 ms | 6.90× | 6.95× | 0.99× | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.477 ms | 2.24× | 1.86× | **1.21×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 280.88 µs | 1.65× | 1.44× | **1.15×** | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 2.838 ms | 2.23× | 1.91× | **1.17×** | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 3.128 ms | 6.45× | 6.48× | 0.99× | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 8.647 ms | 3.62× | 3.09× | **1.17×** | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 5.769 ms | 2.46× | 1.98× | **1.24×** | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 652.85 µs | 1.66× | 1.39× | **1.19×** | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 4.028 ms | 2.25× | 1.84× | **1.23×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 6.065 ms | 2.32× | 2.01× | **1.16×** | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.635 ms | 1.74× | 1.76× | 0.99× | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 9.032 ms | 2.26× | 1.95× | **1.15×** | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 9.859 ms | 1.40× | 0.87× | **1.62×** | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.531 ms | 1.57× | 1.34× | **1.17×** | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 9.946 ms | 4.50× | 2.84× | **1.59×** | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 31.072 ms | 6.41× | 4.09× | **1.56×** | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.928 ms | 2.14× | 2.12× | 1.01× | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.241 ms | 1.49× | 1.24× | **1.20×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 21.958 ms | 4.81× | 3.13× | **1.53×** | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 24.793 ms | 2.27× | 1.94× | **1.17×** | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 46.883 ms | 2.48× | 1.30× | **1.90×** | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 32.988 ms | 4.80× | 3.14× | **1.53×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 20.360 ms | 3.59× | 3.48× | 1.03× | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 6.033 ms | 1.62× | 1.05× | **1.55×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 46.377 ms | 2.50× | 1.33× | **1.88×** | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 98.196 ms | 1.70× | 0.89× | **1.92×** | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 145.379 ms | 2.82× | 1.47× | **1.92×** | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 27.975 ms | 2.55× | 2.37× | **1.08×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 49.028 ms | 2.33× | 2.29× | 1.02× | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 11.979 ms | 1.68× | 0.89× | **1.89×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 101.951 ms | 2.89× | 1.46× | **1.98×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 89.558 ms | 4.52× | 2.96× | **1.53×** | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 151.590 ms | 2.45× | 1.41× | **1.74×** | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 221.737 ms | 1.21× | 0.67× | **1.80×** | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 94.130 ms | 2.53× | 2.44× | 1.03× | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 27.672 ms | 0.91× | 0.50× | **1.83×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 269.150 ms | 2.45× | 2.39× | 1.03× | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 57.082 ms | 0.85× | 0.48× | **1.76×** | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 752 ns | 4.83× | 5.22× | **0.92×** | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.50 µs | 4.36× | 4.39× | 0.99× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.78 µs | 4.01× | 4.03× | 0.99× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 48.88 µs | 3.95× | 3.96× | 1.00× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 208.96 µs | 4.14× | 3.47× | **1.19×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 1.025 ms | 1.54× | 1.34× | **1.15×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 6.109 ms | 1.27× | 1.09× | **1.16×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 29.823 ms | 1.35× | 1.18× | **1.14×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 133.918 ms | 1.19× | 1.00× | **1.19×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 773 ns | 4.15× | 4.46× | **0.93×** | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.60 µs | 3.08× | 3.17× | 0.97× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.40 µs | 2.76× | 2.77× | 0.99× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.24 µs | 2.58× | 2.59× | 1.00× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 244.08 µs | 2.53× | 2.21× | **1.14×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 3.573 ms | 2.27× | 1.99× | **1.14×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 3.220 ms | 1.04× | 0.88× | **1.19×** | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 3.354 ms | 1.03× | 0.87× | **1.19×** | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.444 ms | 1.29× | 1.26× | 1.02× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 7.001 ms | 1.23× | 1.15× | **1.07×** | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 19.915 ms | 2.97× | 3.01× | 0.99× | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 88.217 ms | 3.13× | 3.17× | 0.99× | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 37.334 ms | 1.23× | 1.24× | 0.99× | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 165.449 ms | 1.11× | 1.01× | **1.10×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 871 ns | 6.92× | 7.05× | 0.98× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.40 µs | 5.38× | 5.47× | 0.98× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 8.09 µs | 3.92× | 3.95× | 0.99× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 32.08 µs | 3.26× | 3.26× | 1.00× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 130.20 µs | 3.02× | 2.79× | **1.08×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 542.21 µs | 1.80× | 1.56× | **1.16×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.363 ms | 1.96× | 1.64× | **1.20×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 10.225 ms | 2.10× | 1.70× | **1.24×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 50.539 ms | 1.79× | 1.46× | **1.23×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 944 ns | 7.84× | 8.06× | 0.97× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.52 µs | 5.03× | 5.15× | 0.98× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 8.55 µs | 3.51× | 3.56× | 0.99× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 33.76 µs | 2.85× | 2.87× | 0.99× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 141.16 µs | 2.53× | 2.42× | 1.05× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.305 ms | 1.73× | 1.52× | **1.14×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 2.818 ms | 2.13× | 1.75× | **1.22×** | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 1.737 ms | 1.06× | 0.90× | **1.19×** | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 605.85 µs | 1.61× | 1.49× | **1.08×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 2.759 ms | 1.58× | 1.44× | **1.10×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 9.852 ms | 3.08× | 3.13× | 0.99× | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 43.475 ms | 3.21× | 3.33× | 0.96× | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 12.105 ms | 1.54× | 1.38× | **1.12×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 60.038 ms | 1.22× | 1.10× | **1.11×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 9.69 µs | 6.09× | 6.27× | 0.97× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 65.96 µs | 4.81× | 4.90× | 0.98× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 590.61 µs | 4.14× | 4.17× | 0.99× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.718 ms | 3.84× | 3.84× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 57.589 ms | 3.44× | 3.12× | **1.10×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.88 µs | 4.99× | 5.19× | 0.96× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 67.64 µs | 3.33× | 3.39× | 0.98× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 637.93 µs | 2.63× | 2.64× | 1.00× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.585 ms | 2.63× | 2.65× | 0.99× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 76.217 ms | 2.03× | 1.96× | 1.04× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 9.65 µs | 7.70× | 8.13× | **0.95×** | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 53.44 µs | 5.58× | 5.79× | 0.96× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 373.72 µs | 4.04× | 4.11× | 0.98× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 3.135 ms | 3.27× | 3.29× | 0.99× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 26.271 ms | 3.08× | 2.80× | **1.10×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 10.00 µs | 8.09× | 8.35× | 0.97× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 54.32 µs | 4.70× | 4.77× | 0.98× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 390.81 µs | 3.33× | 3.34× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.473 ms | 2.59× | 2.56× | 1.01× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 31.401 ms | 2.18× | 2.12× | 1.03× | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.64 µs | 3.61× | 3.63× | 0.99× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 103.56 µs | 2.37× | 1.98× | **1.19×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 479.57 µs | 2.62× | 1.96× | **1.34×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 2.288 ms | 2.56× | 1.79× | **1.43×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 11.169 ms | 2.09× | 1.44× | **1.45×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 63.243 ms | 2.01× | 1.42× | **1.41×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 23.92 µs | 2.31× | 2.32× | 0.99× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 116.64 µs | 1.48× | 1.34× | **1.11×** | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 589.89 µs | 1.60× | 1.36× | **1.17×** | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 3.145 ms | 1.71× | 1.45× | **1.18×** | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 18.186 ms | 1.39× | 1.22× | **1.14×** | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 95.441 ms | 1.29× | 1.08× | **1.20×** | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 18.96 µs | 2.85× | 2.87× | 0.99× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 74.52 µs | 2.08× | 1.82× | **1.14×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 323.64 µs | 2.77× | 2.25× | **1.23×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.416 ms | 2.73× | 2.06× | **1.33×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 6.331 ms | 2.38× | 1.70× | **1.40×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 30.490 ms | 2.28× | 1.60× | **1.43×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 20.00 µs | 2.98× | 2.99× | 0.99× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.333 ms | 1.86× | 1.71× | **1.09×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 80.84 µs | 1.96× | 1.81× | **1.08×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.023 ms | 1.85× | 1.64× | **1.13×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 367.56 µs | 1.94× | 1.72× | **1.13×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 6.786 ms | 1.89× | 1.60× | **1.18×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.675 ms | 1.90× | 1.61× | **1.18×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 8.351 ms | 1.60× | 1.36× | **1.18×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 42.129 ms | 1.35× | 1.11× | **1.22×** | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.32 µs | 4.43× | 4.46× | 0.99× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 152.96 µs | 1.92× | 1.92× | 1.00× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 837.25 µs | 1.97× | 1.93× | 1.02× | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 5.970 ms | 1.26× | 1.27× | 0.99× | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 31.999 ms | 1.38× | 1.32× | 1.05× | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 211.237 ms | 1.19× | 1.23× | 0.97× | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 29.00 µs | 2.63× | 2.67× | 0.98× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 165.52 µs | 1.53× | 1.52× | 1.01× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.230 ms | 1.35× | 1.39× | 0.97× | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 7.142 ms | 1.27× | 1.34× | 0.95× | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 47.666 ms | 1.30× | 1.40× | **0.93×** | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 275.226 ms | 1.10× | 1.11× | 0.98× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 22.32 µs | 3.36× | 3.38× | 0.99× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 97.64 µs | 1.88× | 1.69× | **1.11×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 460.77 µs | 1.88× | 1.59× | **1.18×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.444 ms | 1.60× | 1.37× | **1.17×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 11.673 ms | 1.22× | 1.00× | **1.22×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 57.642 ms | 1.04× | 0.84× | **1.24×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 23.56 µs | 3.55× | 3.56× | 1.00× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 115.84 µs | 1.71× | 1.62× | **1.06×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 530.09 µs | 1.67× | 1.52× | **1.09×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 2.956 ms | 1.20× | 1.09× | **1.11×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 13.532 ms | 1.11× | 0.96× | **1.16×** | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 79.682 ms | 0.80× | 0.71× | **1.12×** | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `large`/`fftw` | `large` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 2.35× (1.00–5.22) | **1.08×** (0.92–1.19) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.34× (3.12–6.27) | **1.01×** (0.97–1.10) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 1.77× (0.92–3.48) | **1.52×** (1.11–2.09) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 1.93× (1.42–3.63) | **1.29×** (0.99–1.45) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.80× (1.23–4.46) | **1.00×** (0.97–1.05) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 1.11× (0.40–1.90) | **1.54×** (0.94–2.83) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 1.70× (0.73–6.57) | **1.37×** (1.00–2.60) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 4.49× (2.02–8.73) | **0.99×** (0.95–1.02) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.86× (0.87–4.46) | **1.05×** (0.93–1.19) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 2.99× (1.96–5.19) | **0.99×** (0.96–1.04) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 1.71× (0.81–3.20) | **1.30×** (1.04–1.91) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.42× (1.08–2.32) | **1.13×** (0.99–1.20) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.51× (1.11–2.67) | **0.97×** (0.93–1.01) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 0.94× (0.38–1.75) | **1.30×** (0.91–2.11) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.65× (0.79–3.92) | **1.21×** (0.99–1.93) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.95× (1.50–4.88) | **0.99×** (0.94–1.05) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 2.74× (1.46–7.05) | **1.09×** (0.98–1.24) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 4.47× (2.80–8.13) | **1.00×** (0.95–1.10) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 1.83× (0.95–3.45) | **1.52×** (1.11–2.26) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 2.01× (1.60–2.87) | **1.24×** (0.99–1.43) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.48× (0.84–3.38) | **1.15×** (0.99–1.24) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 1.79× (0.79–3.55) | **1.33×** (0.99–2.35) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 1.58× (0.58–3.45) | **1.38×** (0.99–2.60) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 4.70× (2.14–8.19) | **1.00×** (0.97–1.03) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.25× (0.90–8.06) | **1.06×** (0.96–1.22) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.73× (2.12–8.35) | **1.00×** (0.97–1.03) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 1.84× (0.80–4.09) | **1.30×** (1.06–1.98) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.67× (1.11–2.99) | **1.13×** (0.99–1.22) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.37× (0.71–3.56) | **1.09×** (1.00–1.16) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.48× (0.48–3.88) | **1.21×** (0.98–1.89) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 1.89× (0.67–4.10) | **1.21×** (0.99–1.92) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 3.63× (1.76–7.07) | **1.00×** (0.96–1.08) | +| **all** | 2.45× (0.65–8.66) | 2.03× (0.38–8.73) | **1.21×** (0.91–2.83), 505 cases, 9 slower by >5% | diff --git a/benchmark/compare3/aarch64/large/large_t1.json b/benchmark/compare3/aarch64/large/large_t1.json new file mode 100644 index 0000000..5313ea2 --- /dev/null +++ b/benchmark/compare3/aarch64/large/large_t1.json @@ -0,0 +1,10975 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T11:34:30.349", + "impl": "ffta", + "julia": "1.12.6", + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ 605c9c3" + }, + "results": [ + { + "T": "Float64", + "api": "mul!", + "class": "pow2", + "dims": 1, + "exec_alloc": 0, + "exec_min": 2.64e-8, + "key": "fft Float64 8 dims=1", + "kind": "fft", + "measure": false, + "n": 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Georgakopoulos Date: Sun, 30 Aug 2026 12:06:47 +0000 Subject: [PATCH 09/21] benchmark: compare3 results for the radix-5/7 kernels (aarch64, 1 thread) --- .../compare3/aarch64/radix57/COMPARE3.md | 579 + .../compare3/aarch64/radix57/r57_t1.json | 10975 ++++++++++++++++ 2 files changed, 11554 insertions(+) create mode 100644 benchmark/compare3/aarch64/radix57/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/radix57/r57_t1.json diff --git a/benchmark/compare3/aarch64/radix57/COMPARE3.md b/benchmark/compare3/aarch64/radix57/COMPARE3.md new file mode 100644 index 0000000..b10e8ff --- /dev/null +++ b/benchmark/compare3/aarch64/radix57/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T12:02:50.059 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `r57` | FFTA.jl 0.3.1 @ d93eb1d — `FFTA-r57` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `r57` | `int`/`fftw` | `r57`/`fftw` | `r57` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 25 ns | 3.19× | 0.66× | **4.87×** | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 24 ns | 0.65× | 0.66× | 0.99× | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 156 ns | 3.52× | 3.60× | 0.98× | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 54 ns | 0.97× | 0.97× | 1.00× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 807 ns | 5.92× | 5.94× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.50 µs | 6.55× | 6.55× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 160 ns | 5.29× | 1.27× | **4.18×** | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 815 ns | 2.38× | 2.38× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 819 ns | 2.12× | 2.12× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 132 ns | 1.26× | 1.26× | 1.00× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.81 µs | 2.16× | 2.16× | 1.00× | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.81 µs | 2.22× | 2.22× | 1.00× | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.83 µs | 2.60× | 2.61× | 1.00× | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 935 ns | 2.80× | 2.88× | 0.97× | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.10 µs | 7.03× | 5.07× | **1.39×** | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.87 µs | 1.57× | 1.57× | 1.00× | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 327 ns | 1.69× | 1.68× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 4.10 µs | 1.70× | 1.71× | 1.00× | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 4.11 µs | 3.06× | 3.06× | 1.00× | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 4.13 µs | 2.34× | 2.34× | 1.00× | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 4.18 µs | 2.16× | 2.16× | 1.00× | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 992 ns | 6.97× | 2.76× | **2.53×** | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 2.05 µs | 7.50× | 5.23× | **1.43×** | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 785 ns | 2.03× | 2.02× | 1.01× | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 9.65 µs | 2.32× | 2.34× | 0.99× | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.84 µs | 2.02× | 2.02× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 9.53 µs | 1.60× | 1.59× | 1.00× | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 1.83 µs | 2.27× | 2.26× | 1.00× | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 14.54 µs | 2.26× | 2.29× | 0.99× | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 6.51 µs | 3.96× | 2.74× | **1.44×** | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 18.60 µs | 2.19× | 2.20× | 0.99× | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 8.75 µs | 5.80× | 3.26× | **1.78×** | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 4.20 µs | 2.50× | 2.49× | 1.00× | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 45.72 µs | 3.00× | 3.00× | 1.00× | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 33.00 µs | 2.53× | 2.57× | 0.98× | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 13.20 µs | 3.57× | 2.51× | **1.42×** | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 13.60 µs | 6.51× | 2.03× | **3.20×** | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 9.41 µs | 2.59× | 2.59× | 1.00× | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 21.72 µs | 3.47× | 2.48× | **1.40×** | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 100.72 µs | 1.75× | 1.75× | 1.00× | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 73.60 µs | 2.04× | 2.04× | 1.00× | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 107.08 µs | 1.45× | 1.46× | 0.99× | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 21.00 µs | 2.74× | 2.73× | 1.00× | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 37.40 µs | 2.98× | 3.01× | 0.99× | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 160.76 µs | 1.43× | 1.43× | 1.00× | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 226.00 µs | 1.42× | 1.43× | 1.00× | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 207.32 µs | 1.38× | 1.39× | 0.99× | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 46.60 µs | 2.77× | 2.76× | 1.00× | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 129.12 µs | 3.31× | 2.59× | **1.28×** | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 361.32 µs | 1.58× | 1.60× | 0.98× | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 104.12 µs | 2.14× | 2.14× | 1.00× | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 1.028 ms | 2.49× | 2.50× | 1.00× | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 1.066 ms | 2.58× | 2.58× | 1.00× | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 313.28 µs | 8.66× | 3.22× | **2.69×** | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 1.551 ms | 2.47× | 2.48× | 0.99× | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 827.29 µs | 1.31× | 1.31× | 1.00× | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 228.80 µs | 2.09× | 2.10× | 1.00× | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 2.037 ms | 2.44× | 2.45× | 1.00× | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 2.649 ms | 2.08× | 2.05× | 1.01× | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 579.85 µs | 7.14× | 2.20× | **3.25×** | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 3.293 ms | 2.58× | 2.61× | 0.99× | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 502.13 µs | 1.85× | 1.80× | 1.02× | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 5.538 ms | 2.70× | 2.75× | 0.98× | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 1.543 ms | 7.03× | 2.75× | **2.55×** | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 8.570 ms | 2.66× | 2.79× | 0.95× | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 6.210 ms | 2.29× | 2.32× | 0.99× | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 1.229 ms | 2.20× | 2.18× | 1.01× | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 8.290 ms | 2.33× | 2.33× | 1.00× | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 10.909 ms | 2.63× | 2.66× | 0.99× | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.684 ms | 2.38× | 2.38× | 1.00× | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 17.246 ms | 2.71× | 2.71× | 1.00× | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 13.967 ms | 1.47× | 1.48× | 0.99× | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 2.859 ms | 2.14× | 2.16× | 0.99× | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 28.974 ms | 6.41× | 6.59× | 0.97× | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 43.759 ms | 6.35× | 6.55× | 0.97× | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 7.829 ms | 2.82× | 2.39× | **1.18×** | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 6.386 ms | 1.83× | 1.83× | 1.00× | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 58.357 ms | 6.51× | 6.51× | 1.00× | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 44.700 ms | 2.55× | 2.45× | 1.04× | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 65.586 ms | 2.28× | 2.15× | **1.06×** | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 91.195 ms | 6.71× | 6.73× | 1.00× | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 16.668 ms | 6.65× | 2.52× | **2.64×** | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 12.737 ms | 1.11× | 1.12× | 0.99× | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 134.231 ms | 2.89× | 2.80× | 1.03× | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 157.583 ms | 2.17× | 2.06× | **1.06×** | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 201.448 ms | 2.73× | 2.78× | 0.98× | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 42.642 ms | 2.75× | 2.30× | **1.19×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 42.587 ms | 4.27× | 1.74× | **2.45×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 29.591 ms | 1.69× | 1.23× | **1.38×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 267.155 ms | 2.72× | 2.74× | 0.99× | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 239.547 ms | 6.18× | 6.34× | 0.98× | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 418.015 ms | 2.69× | 2.78× | 0.97× | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 376.361 ms | 2.18× | 2.15× | 1.01× | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 99.410 ms | 5.03× | 2.46× | **2.05×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 78.630 ms | 1.05× | 1.00× | 1.05× | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 306.534 ms | 4.59× | 2.42× | **1.90×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 181.506 ms | 1.12× | 1.10× | 1.02× | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 29 ns | 3.19× | 1.11× | **2.86×** | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 26 ns | 0.96× | 1.04× | **0.93×** | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 158 ns | 4.63× | 4.74× | 0.98× | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 55 ns | 1.33× | 1.36× | 0.98× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 491 ns | 3.59× | 3.62× | 0.99× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 900 ns | 3.91× | 3.92× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 159 ns | 3.71× | 1.14× | **3.24×** | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 884 ns | 2.57× | 2.58× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 886 ns | 2.31× | 2.30× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 137 ns | 1.72× | 1.72× | 1.00× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.95 µs | 2.54× | 2.53× | 1.00× | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.96 µs | 2.16× | 2.16× | 1.00× | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.97 µs | 2.81× | 2.82× | 1.00× | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 956 ns | 3.37× | 3.49× | 0.96× | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.12 µs | 4.40× | 3.58× | **1.23×** | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 2.01 µs | 1.46× | 1.45× | 1.00× | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 338 ns | 1.09× | 1.09× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 4.43 µs | 1.44× | 1.45× | 0.99× | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 4.38 µs | 2.52× | 2.52× | 1.00× | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 4.40 µs | 1.77× | 1.76× | 1.00× | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 4.45 µs | 1.88× | 1.88× | 1.00× | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.05 µs | 3.21× | 1.78× | **1.80×** | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.09 µs | 4.11× | 3.30× | **1.24×** | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 805 ns | 1.24× | 1.24× | 1.00× | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 10.42 µs | 2.05× | 2.10× | 0.98× | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.85 µs | 1.98× | 1.98× | 1.00× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 10.18 µs | 1.50× | 1.51× | 0.99× | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.86 µs | 1.41× | 1.41× | 1.00× | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 15.50 µs | 1.99× | 1.99× | 1.00× | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 6.75 µs | 2.98× | 2.38× | **1.25×** | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 20.24 µs | 1.90× | 1.93× | 0.98× | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 9.31 µs | 3.01× | 2.17× | **1.39×** | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 4.26 µs | 1.50× | 1.50× | 1.00× | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 48.76 µs | 1.78× | 1.77× | 1.00× | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 35.24 µs | 2.19× | 2.22× | 0.99× | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 13.74 µs | 3.02× | 2.44× | **1.24×** | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 14.40 µs | 3.42× | 1.40× | **2.44×** | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 9.55 µs | 1.52× | 1.52× | 1.00× | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 22.88 µs | 2.97× | 2.47× | **1.20×** | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 109.44 µs | 1.41× | 1.41× | 1.00× | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 80.24 µs | 1.80× | 1.81× | 0.99× | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 113.60 µs | 1.03× | 1.04× | 0.99× | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 21.68 µs | 1.61× | 1.60× | 1.00× | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 40.32 µs | 1.77× | 1.79× | 0.99× | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 170.92 µs | 1.01× | 1.02× | 1.00× | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 239.76 µs | 1.08× | 1.08× | 1.01× | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 221.84 µs | 0.99× | 0.99× | 1.00× | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 49.12 µs | 1.66× | 1.65× | 1.00× | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 135.00 µs | 2.72× | 2.35× | **1.16×** | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 387.00 µs | 1.12× | 1.14× | 0.98× | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 107.28 µs | 1.27× | 1.27× | 1.00× | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 1.160 ms | 2.26× | 2.29× | 0.99× | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 1.342 ms | 2.44× | 2.42× | 1.01× | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 358.48 µs | 4.42× | 2.39× | **1.85×** | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.727 ms | 2.28× | 2.22× | 1.02× | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 898.85 µs | 0.98× | 0.97× | 1.00× | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 245.12 µs | 1.38× | 1.36× | 1.02× | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 2.376 ms | 2.20× | 2.29× | 0.96× | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 3.344 ms | 1.95× | 1.97× | 0.99× | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 740.61 µs | 4.09× | 1.93× | **2.12×** | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 3.755 ms | 2.33× | 2.33× | 1.00× | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 602.45 µs | 1.36× | 1.36× | 1.01× | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 6.953 ms | 2.26× | 2.33× | 0.97× | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 1.946 ms | 3.21× | 1.89× | **1.70×** | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 10.493 ms | 2.23× | 2.31× | 0.96× | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 7.208 ms | 1.57× | 1.58× | 1.00× | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 1.456 ms | 1.32× | 1.34× | 0.98× | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 9.486 ms | 2.16× | 2.16× | 1.00× | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 13.941 ms | 2.19× | 2.28× | 0.96× | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.939 ms | 1.48× | 1.53× | 0.97× | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 21.851 ms | 2.24× | 2.33× | 0.96× | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 15.870 ms | 1.30× | 1.26× | 1.03× | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 3.060 ms | 1.25× | 1.27× | 0.99× | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 32.580 ms | 4.64× | 4.69× | 0.99× | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 48.853 ms | 4.71× | 4.72× | 1.00× | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 8.422 ms | 2.09× | 1.86× | **1.12×** | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 6.454 ms | 1.13× | 1.14× | 0.99× | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 65.887 ms | 4.72× | 4.79× | 0.99× | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 57.165 ms | 2.23× | 2.23× | 1.00× | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 90.173 ms | 2.21× | 2.20× | 1.00× | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 103.809 ms | 4.88× | 4.90× | 1.00× | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 22.309 ms | 3.95× | 2.07× | **1.90×** | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 14.581 ms | 1.05× | 0.86× | **1.21×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 181.750 ms | 2.60× | 2.62× | 0.99× | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 188.763 ms | 1.81× | 1.82× | 0.99× | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 274.287 ms | 2.55× | 2.63× | 0.97× | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 51.682 ms | 1.76× | 1.57× | **1.12×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 54.511 ms | 1.99× | 1.08× | **1.84×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 41.966 ms | 0.85× | 0.80× | **1.06×** | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 365.584 ms | 2.61× | 2.58× | 1.01× | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 271.404 ms | 4.16× | 4.23× | 0.98× | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 578.413 ms | 2.51× | 2.65× | **0.95×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 401.398 ms | 1.51× | 1.52× | 0.99× | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 142.295 ms | 2.50× | 1.85× | **1.35×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 90.034 ms | 0.76× | 0.75× | 1.01× | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 409.612 ms | 2.59× | 1.91× | **1.36×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 188.587 ms | 0.81× | 0.79× | 1.02× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 37 ns | 2.15× | 1.53× | **1.40×** | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 78 ns | 3.50× | 3.58× | 0.98× | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 189 ns | 6.56× | 6.97× | **0.94×** | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 102 ns | 3.06× | 3.10× | 0.99× | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 179 ns | 1.33× | 1.34× | 0.99× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 313 ns | 1.55× | 1.55× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 161 ns | 6.56× | 2.10× | **3.12×** | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 805 ns | 2.82× | 2.80× | 1.01× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 815 ns | 2.54× | 2.55× | 1.00× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 160 ns | 1.56× | 1.58× | 0.99× | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.80 µs | 4.21× | 4.20× | 1.00× | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.81 µs | 3.57× | 3.56× | 1.00× | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.81 µs | 3.28× | 3.28× | 1.00× | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 462 ns | 2.16× | 2.16× | 1.00× | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 876 ns | 4.81× | 3.99× | **1.20×** | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.84 µs | 1.79× | 1.78× | 1.01× | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 298 ns | 1.62× | 1.63× | 0.99× | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 4.07 µs | 2.95× | 2.96× | 1.00× | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 4.07 µs | 2.81× | 2.81× | 1.00× | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 4.09 µs | 2.43× | 2.43× | 1.00× | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 4.13 µs | 1.53× | 1.53× | 1.00× | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 779 ns | 5.28× | 2.71× | **1.95×** | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.43 µs | 6.42× | 4.99× | **1.29×** | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 614 ns | 2.29× | 2.32× | 0.99× | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 4.56 µs | 2.15× | 2.15× | 1.00× | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.83 µs | 3.24× | 3.25× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 9.36 µs | 1.71× | 1.71× | 1.00× | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.31 µs | 2.05× | 2.07× | 0.99× | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 14.32 µs | 1.70× | 1.71× | 0.99× | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 4.34 µs | 4.30× | 3.30× | **1.30×** | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 11.16 µs | 2.54× | 2.59× | 0.98× | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 5.87 µs | 6.00× | 3.83× | **1.57×** | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.82 µs | 2.48× | 2.48× | 1.00× | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 45.32 µs | 2.07× | 2.06× | 1.00× | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 16.18 µs | 2.46× | 2.48× | 0.99× | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 8.16 µs | 3.74× | 2.84× | **1.32×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 9.79 µs | 7.81× | 3.13× | **2.49×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 6.16 µs | 2.79× | 2.80× | 1.00× | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 14.02 µs | 3.87× | 3.02× | **1.28×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 99.84 µs | 1.84× | 1.84× | 1.00× | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 40.12 µs | 2.27× | 2.29× | 0.99× | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 50.52 µs | 1.36× | 1.36× | 1.00× | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 13.22 µs | 2.99× | 2.97× | 1.01× | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 21.80 µs | 3.15× | 3.19× | 0.99× | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 158.92 µs | 2.20× | 2.22× | 0.99× | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 223.08 µs | 1.49× | 1.49× | 1.00× | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 122.56 µs | 1.59× | 1.63× | 0.97× | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 28.80 µs | 3.07× | 3.06× | 1.00× | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 86.36 µs | 4.04× | 3.39× | **1.19×** | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 177.64 µs | 1.55× | 1.56× | 0.99× | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 61.92 µs | 2.43× | 2.42× | 1.00× | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 500.97 µs | 2.41× | 2.42× | 1.00× | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 1.062 ms | 3.07× | 3.08× | 1.00× | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 150.68 µs | 6.61× | 2.39× | **2.76×** | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.536 ms | 2.93× | 2.94× | 1.00× | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 444.44 µs | 1.44× | 1.44× | 0.99× | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 135.64 µs | 2.51× | 2.51× | 1.00× | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 1.089 ms | 2.58× | 2.61× | 0.99× | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 2.664 ms | 2.71× | 2.77× | 0.98× | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 569.37 µs | 8.20× | 2.89× | **2.84×** | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.621 ms | 2.55× | 2.57× | 0.99× | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 292.84 µs | 2.49× | 2.50× | 0.99× | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 2.706 ms | 2.64× | 2.68× | 0.98× | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 1.474 ms | 7.40× | 3.25× | **2.28×** | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 8.194 ms | 3.17× | 3.19× | 0.99× | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 6.186 ms | 2.24× | 2.28× | 0.99× | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 643.13 µs | 2.65× | 2.64× | 1.00× | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 4.250 ms | 2.48× | 2.49× | 1.00× | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 5.877 ms | 2.83× | 2.89× | 0.98× | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.424 ms | 2.72× | 2.77× | 0.98× | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 8.755 ms | 2.78× | 2.83× | 0.98× | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 13.962 ms | 1.30× | 1.32× | 0.99× | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.481 ms | 2.43× | 2.41× | 1.01× | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 14.412 ms | 6.24× | 6.52× | 0.96× | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 43.716 ms | 6.79× | 7.04× | 0.96× | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 3.909 ms | 2.73× | 2.30× | **1.19×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 3.463 ms | 2.05× | 2.07× | 0.99× | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 30.132 ms | 6.64× | 6.65× | 1.00× | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 23.372 ms | 2.68× | 2.70× | 0.99× | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 64.793 ms | 2.38× | 2.05× | **1.16×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 44.936 ms | 6.62× | 6.61× | 1.00× | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 9.560 ms | 6.03× | 2.51× | **2.40×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 7.602 ms | 1.99× | 2.01× | 0.99× | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 66.074 ms | 3.02× | 2.76× | **1.09×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 153.389 ms | 1.84× | 1.68× | **1.10×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 202.836 ms | 2.31× | 2.28× | 1.01× | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 20.667 ms | 2.94× | 2.29× | **1.28×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 21.584 ms | 6.10× | 2.48× | **2.46×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 15.787 ms | 2.12× | 2.01× | **1.05×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 138.772 ms | 2.90× | 2.90× | 1.00× | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 119.991 ms | 6.28× | 6.43× | 0.98× | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 206.986 ms | 2.70× | 2.81× | 0.96× | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 379.007 ms | 1.50× | 1.51× | 1.00× | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 51.722 ms | 6.20× | 3.05× | **2.03×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 35.019 ms | 2.77× | 2.14× | **1.30×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 145.252 ms | 3.39× | 1.74× | **1.95×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 88.121 ms | 1.79× | 1.71× | 1.05× | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 36 ns | 2.17× | 1.50× | **1.44×** | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 84 ns | 3.79× | 3.90× | 0.97× | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 198 ns | 6.78× | 7.21× | **0.94×** | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 108 ns | 3.30× | 3.34× | 0.99× | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 193 ns | 1.40× | 1.41× | 0.99× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 341 ns | 1.65× | 1.66× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 161 ns | 5.67× | 2.14× | **2.65×** | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 886 ns | 3.05× | 3.05× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 891 ns | 2.75× | 2.76× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 168 ns | 1.86× | 1.89× | 0.99× | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.96 µs | 4.55× | 4.55× | 1.00× | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.97 µs | 3.83× | 3.84× | 1.00× | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.97 µs | 3.54× | 3.55× | 1.00× | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 476 ns | 2.83× | 2.84× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 891 ns | 5.75× | 5.21× | **1.10×** | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 2.01 µs | 1.93× | 1.93× | 1.00× | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 310 ns | 1.87× | 1.87× | 1.00× | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 4.38 µs | 3.16× | 3.16× | 1.00× | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 4.38 µs | 3.01× | 3.01× | 1.00× | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.40 µs | 2.59× | 2.60× | 1.00× | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.52 µs | 1.64× | 1.67× | 0.98× | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 819 ns | 4.11× | 2.76× | **1.49×** | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.47 µs | 5.09× | 4.40× | **1.16×** | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 640 ns | 1.95× | 1.96× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.88 µs | 1.88× | 1.88× | 1.00× | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.85 µs | 3.05× | 3.05× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 10.06 µs | 1.77× | 1.76× | 1.00× | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.35 µs | 1.95× | 1.95× | 1.00× | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 15.42 µs | 1.85× | 1.84× | 1.01× | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 4.49 µs | 3.74× | 3.20× | **1.17×** | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 11.90 µs | 2.18× | 2.22× | 0.98× | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 6.20 µs | 3.90× | 3.05× | **1.28×** | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.93 µs | 2.00× | 2.00× | 1.00× | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 48.64 µs | 2.18× | 2.18× | 1.00× | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 17.28 µs | 2.09× | 2.12× | 0.99× | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 8.41 µs | 3.44× | 2.92× | **1.18×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 10.18 µs | 4.55× | 2.27× | **2.00×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 6.30 µs | 2.02× | 2.02× | 1.00× | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 14.60 µs | 3.57× | 3.10× | **1.15×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 110.12 µs | 1.95× | 1.96× | 0.99× | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 43.36 µs | 1.94× | 1.95× | 1.00× | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 53.68 µs | 0.96× | 0.96× | 1.00× | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 13.84 µs | 2.07× | 2.07× | 1.00× | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 23.48 µs | 2.39× | 2.41× | 0.99× | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 169.96 µs | 2.30× | 2.31× | 1.00× | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 240.88 µs | 1.53× | 1.54× | 1.00× | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 128.48 µs | 1.12× | 1.13× | 0.99× | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 30.12 µs | 2.07× | 2.07× | 1.00× | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 88.80 µs | 3.35× | 3.06× | **1.10×** | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 189.12 µs | 1.09× | 1.10× | 0.99× | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 66.68 µs | 1.69× | 1.70× | 0.99× | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 561.97 µs | 2.13× | 2.17× | 0.98× | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.362 ms | 3.64× | 3.74× | 0.97× | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 166.36 µs | 4.31× | 2.23× | **1.94×** | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.733 ms | 3.14× | 3.15× | 1.00× | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 481.13 µs | 1.04× | 1.04× | 1.00× | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 142.04 µs | 1.64× | 1.64× | 1.00× | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.245 ms | 2.36× | 2.38× | 0.99× | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 3.342 ms | 2.92× | 2.95× | 0.99× | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 687.25 µs | 6.90× | 3.42× | **2.02×** | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.823 ms | 2.24× | 2.29× | 0.98× | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 333.04 µs | 1.65× | 1.70× | 0.97× | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 3.429 ms | 2.23× | 2.30× | 0.97× | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 1.928 ms | 6.45× | 3.99× | **1.61×** | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 10.424 ms | 3.62× | 3.73× | 0.97× | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 7.120 ms | 2.46× | 2.45× | 1.01× | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 771.89 µs | 1.66× | 1.65× | 1.01× | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 4.899 ms | 2.25× | 2.23× | 1.01× | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 7.268 ms | 2.32× | 2.40× | 0.96× | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.650 ms | 1.74× | 1.78× | 0.98× | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 10.830 ms | 2.26× | 2.34× | 0.96× | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 15.987 ms | 1.40× | 1.41× | 1.00× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.803 ms | 1.57× | 1.58× | 0.99× | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 15.982 ms | 4.50× | 4.56× | 0.99× | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 49.237 ms | 6.41× | 6.49× | 0.99× | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.639 ms | 2.14× | 2.00× | **1.07×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.743 ms | 1.49× | 1.44× | 1.04× | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 34.375 ms | 4.81× | 4.91× | 0.98× | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 29.143 ms | 2.27× | 2.28× | 1.00× | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 89.083 ms | 2.48× | 2.47× | 1.00× | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 50.643 ms | 4.80× | 4.81× | 1.00× | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 12.403 ms | 3.59× | 2.12× | **1.69×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 8.790 ms | 1.62× | 1.53× | **1.06×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 89.239 ms | 2.50× | 2.56× | 0.98× | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 189.034 ms | 1.70× | 1.71× | 1.00× | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 274.229 ms | 2.82× | 2.77× | 1.02× | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 26.392 ms | 2.55× | 2.23× | **1.14×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 26.451 ms | 2.33× | 1.24× | **1.88×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 19.014 ms | 1.68× | 1.41× | **1.19×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 188.425 ms | 2.89× | 2.70× | **1.07×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 138.114 ms | 4.52× | 4.57× | 0.99× | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 274.504 ms | 2.45× | 2.55× | 0.96× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 400.910 ms | 1.21× | 1.21× | 1.00× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 68.037 ms | 2.53× | 1.77× | **1.43×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 51.356 ms | 0.91× | 0.92× | 0.99× | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 188.357 ms | 2.45× | 1.67× | **1.47×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 99.228 ms | 0.85× | 0.84× | 1.01× | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 749 ns | 4.83× | 5.20× | **0.93×** | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.59 µs | 4.36× | 4.54× | 0.96× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.88 µs | 4.01× | 4.07× | 0.99× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 49.16 µs | 3.95× | 3.98× | 0.99× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 250.96 µs | 4.14× | 4.17× | 0.99× | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 1.199 ms | 1.54× | 1.57× | 0.98× | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 7.401 ms | 1.27× | 1.32× | 0.96× | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 35.628 ms | 1.35× | 1.41× | 0.95× | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 165.109 ms | 1.19× | 1.24× | 0.97× | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 772 ns | 4.15× | 4.45× | **0.93×** | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.63 µs | 3.08× | 3.21× | 0.96× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.46 µs | 2.76× | 2.79× | 0.99× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.40 µs | 2.58× | 2.60× | 0.99× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 265.44 µs | 2.53× | 2.41× | **1.05×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 4.072 ms | 2.27× | 2.27× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 3.843 ms | 1.04× | 1.05× | 0.99× | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 3.990 ms | 1.03× | 1.04× | 1.00× | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.530 ms | 1.29× | 1.34× | 0.96× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 7.871 ms | 1.23× | 1.29× | 0.96× | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 17.656 ms | 2.97× | 2.67× | **1.11×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 43.744 ms | 3.13× | 1.57× | **1.99×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 40.395 ms | 1.23× | 1.34× | **0.92×** | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 185.993 ms | 1.11× | 1.13× | 0.98× | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 880 ns | 6.92× | 7.12× | 0.97× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.41 µs | 5.38× | 5.50× | 0.98× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 8.08 µs | 3.92× | 3.95× | 0.99× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 32.28 µs | 3.26× | 3.28× | 0.99× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 141.48 µs | 3.02× | 3.03× | 1.00× | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 619.89 µs | 1.80× | 1.78× | 1.01× | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.845 ms | 1.96× | 1.97× | 0.99× | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 12.712 ms | 2.10× | 2.11× | 0.99× | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 63.138 ms | 1.79× | 1.82× | 0.99× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 970 ns | 7.84× | 8.28× | **0.95×** | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.52 µs | 5.03× | 5.15× | 0.98× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 8.61 µs | 3.51× | 3.59× | 0.98× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 33.84 µs | 2.85× | 2.88× | 0.99× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 147.20 µs | 2.53× | 2.53× | 1.00× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.610 ms | 1.73× | 1.73× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 3.439 ms | 2.13× | 2.13× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 2.065 ms | 1.06× | 1.07× | 1.00× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 658.73 µs | 1.61× | 1.61× | 1.00× | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 3.076 ms | 1.58× | 1.61× | 0.98× | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 8.360 ms | 3.08× | 2.65× | **1.16×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 21.653 ms | 3.21× | 1.66× | **1.93×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 13.772 ms | 1.54× | 1.58× | 0.98× | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 68.589 ms | 1.22× | 1.26× | 0.97× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 9.80 µs | 6.09× | 6.34× | 0.96× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 66.04 µs | 4.81× | 4.91× | 0.98× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 595.21 µs | 4.14× | 4.20× | 0.99× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.721 ms | 3.84× | 3.84× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 64.408 ms | 3.44× | 3.49× | 0.99× | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 10.00 µs | 4.99× | 5.25× | 0.95× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 68.56 µs | 3.33× | 3.43× | 0.97× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 643.73 µs | 2.63× | 2.66× | 0.99× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.658 ms | 2.63× | 2.68× | 0.98× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 79.581 ms | 2.03× | 2.04× | 0.99× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 9.59 µs | 7.70× | 8.07× | 0.95× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 53.24 µs | 5.58× | 5.77× | 0.97× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 373.64 µs | 4.04× | 4.11× | 0.98× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 3.136 ms | 3.27× | 3.29× | 0.99× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 28.840 ms | 3.08× | 3.08× | 1.00× | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 10.06 µs | 8.09× | 8.40× | 0.96× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 54.68 µs | 4.70× | 4.80× | 0.98× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 390.92 µs | 3.33× | 3.34× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.495 ms | 2.59× | 2.58× | 1.00× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 34.547 ms | 2.18× | 2.34× | **0.93×** | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.80 µs | 3.61× | 3.66× | 0.99× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 123.72 µs | 2.37× | 2.37× | 1.00× | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 640.21 µs | 2.62× | 2.62× | 1.00× | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 3.281 ms | 2.56× | 2.57× | 1.00× | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 17.058 ms | 2.09× | 2.20× | 0.95× | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 91.071 ms | 2.01× | 2.04× | 0.98× | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 24.00 µs | 2.31× | 2.33× | 0.99× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 129.24 µs | 1.48× | 1.48× | 1.00× | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 692.05 µs | 1.60× | 1.59× | 1.00× | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 3.747 ms | 1.71× | 1.73× | 0.99× | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 21.672 ms | 1.39× | 1.46× | 0.95× | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 114.984 ms | 1.29× | 1.30× | 0.99× | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 19.08 µs | 2.85× | 2.89× | 0.99× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 85.00 µs | 2.08× | 2.08× | 1.00× | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 399.00 µs | 2.77× | 2.77× | 1.00× | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.882 ms | 2.73× | 2.73× | 1.00× | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 8.916 ms | 2.38× | 2.39× | 1.00× | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 43.816 ms | 2.28× | 2.30× | 0.99× | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 20.00 µs | 2.98× | 2.99× | 0.99× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.762 ms | 1.86× | 1.85× | 1.01× | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 87.64 µs | 1.96× | 1.97× | 1.00× | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.783 ms | 1.85× | 1.85× | 1.00× | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 415.01 µs | 1.94× | 1.94× | 1.00× | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 8.032 ms | 1.89× | 1.89× | 1.00× | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.983 ms | 1.90× | 1.91× | 1.00× | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 9.846 ms | 1.60× | 1.60× | 1.00× | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 51.477 ms | 1.35× | 1.35× | 1.00× | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.48 µs | 4.43× | 4.48× | 0.99× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 153.20 µs | 1.92× | 1.93× | 1.00× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 865.09 µs | 1.97× | 1.99× | 0.99× | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 6.166 ms | 1.26× | 1.31× | 0.96× | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 32.223 ms | 1.38× | 1.33× | 1.04× | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 212.267 ms | 1.19× | 1.23× | 0.96× | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 28.96 µs | 2.63× | 2.67× | 0.99× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 163.20 µs | 1.53× | 1.50× | 1.02× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.279 ms | 1.35× | 1.45× | **0.93×** | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 7.478 ms | 1.27× | 1.40× | **0.91×** | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 46.626 ms | 1.30× | 1.37× | 0.95× | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 281.150 ms | 1.10× | 1.14× | 0.96× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 22.60 µs | 3.36× | 3.42× | 0.98× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 107.84 µs | 1.88× | 1.86× | 1.01× | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 540.37 µs | 1.88× | 1.87× | 1.00× | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.891 ms | 1.60× | 1.62× | 0.99× | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 14.294 ms | 1.22× | 1.23× | 0.99× | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 73.154 ms | 1.04× | 1.07× | 0.98× | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 23.68 µs | 3.55× | 3.58× | 0.99× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 122.68 µs | 1.71× | 1.71× | 1.00× | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 577.65 µs | 1.67× | 1.66× | 1.00× | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 3.315 ms | 1.20× | 1.22× | 0.99× | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 15.250 ms | 1.11× | 1.08× | 1.03× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 92.379 ms | 0.80× | 0.83× | 0.96× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `r57`/`fftw` | `r57` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 2.62× (1.24–5.20) | **0.97×** (0.93–0.99) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.45× (3.49–6.34) | **0.98×** (0.96–1.00) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 2.70× (1.31–6.73) | **0.99×** (0.95–1.04) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 2.53× (2.04–3.66) | **0.99×** (0.95–1.00) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.82× (1.23–4.48) | **0.99×** (0.96–1.04) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 1.68× (0.66–2.76) | **1.02×** (0.99–1.38) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 2.18× (0.66–6.55) | **1.07×** (0.99–4.87) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 2.62× (1.27–5.23) | **1.70×** (0.97–4.18) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.88× (1.04–4.45) | **1.04×** (0.92–1.99) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 3.05× (2.04–5.25) | **0.98×** (0.95–0.99) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 2.24× (0.97–4.90) | **0.99×** (0.95–1.02) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.62× (1.30–2.33) | **0.99×** (0.95–1.00) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.52× (1.14–2.67) | **0.96×** (0.91–1.02) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 1.22× (0.75–1.72) | **1.01×** (0.93–1.21) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.92× (1.08–3.92) | **1.05×** (0.99–2.86) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.08× (1.08–4.74) | **1.40×** (0.96–3.24) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 3.02× (1.78–7.12) | **0.99×** (0.97–1.01) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 4.54× (3.08–8.07) | **0.98×** (0.95–1.00) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 2.80× (1.36–7.04) | **0.99×** (0.96–1.09) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 2.51× (2.08–2.89) | **1.00×** (0.99–1.00) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.71× (1.07–3.42) | **0.99×** (0.98–1.01) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 2.35× (1.58–3.58) | **1.01×** (0.98–1.30) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 2.13× (1.32–4.20) | **1.02×** (0.98–1.40) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 2.97× (1.74–6.97) | **1.58×** (0.94–3.12) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.27× (1.07–8.28) | **1.05×** (0.95–1.93) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.82× (2.34–8.40) | **0.97×** (0.93–1.00) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 2.42× (0.96–6.49) | **0.99×** (0.96–1.07) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.89× (1.35–2.99) | **1.00×** (0.99–1.01) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.49× (0.83–3.58) | **1.00×** (0.96–1.03) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.77× (0.84–3.90) | **1.01×** (0.97–1.19) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 2.26× (1.21–4.55) | **1.01×** (0.97–1.44) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 2.70× (1.24–7.21) | **1.34×** (0.94–2.65) | +| **all** | 2.45× (0.65–8.66) | 2.26× (0.66–8.40) | **1.09×** (0.91–4.87), 505 cases, 11 slower by >5% | diff --git a/benchmark/compare3/aarch64/radix57/r57_t1.json b/benchmark/compare3/aarch64/radix57/r57_t1.json new file mode 100644 index 0000000..b3bbbf2 --- /dev/null +++ b/benchmark/compare3/aarch64/radix57/r57_t1.json @@ -0,0 +1,10975 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T11:49:04.653", + "impl": "ffta", + "julia": "1.12.6", + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ d93eb1d" + }, + "results": [ + { + "T": "Float64", + "api": "mul!", + "class": "pow2", + 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"kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369855.16, + "nthreads": 1, + "plan_min": 0.000121281, + "shape": "batched_dim1", + "size": [ + 65536, + 64 + ], + "sum_im": -665970.94, + "sum_re": 12625.094 + }, + { + "T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 2, + "exec_alloc": 0, + "exec_min": 0.073153707, + "key": "rfft Float32 64×65536 dims=2", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369917.0, + "nthreads": 1, + "plan_min": 0.00012156200000000001, + "shape": "batched_dim2", + "size": [ + 64, + 65536 + ], + "sum_im": 439989.97, + "sum_re": -183525.03 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.005762425000000001, + "key": "rfft Float64 256×4096 dims=1", + "kind": "rfft", + "measure": false, + "n": 256, + "norm": 11640.925722730331, + "nthreads": 1, + "plan_min": 1.6933333333333334e-6, + "shape": "batched_dim1", + "size": [ + 256, + 4096 + ], + "sum_im": 4845.767554722023, + "sum_re": 347.8471366990625 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.006782797, + "key": "rfft Float64 1024×1024 dims=1", + "kind": "rfft", + "measure": false, + "n": 1024, + "norm": 23213.335828584088, + "nthreads": 1, + "plan_min": 3.27e-6, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790562, + "sum_re": -8799.055444945061 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.008031651, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113902925, + "nthreads": 1, + "plan_min": 9.88e-6, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255915, + "sum_re": -2384.3887021656665 + } + ] +} \ No newline at end of file From e593a7d288da1616aa1b7e46d372dd69b9712feb Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 12:35:41 +0000 Subject: [PATCH 10/21] benchmark: quiet back-to-back re-run of the N-d/batched cases for all experiment columns (aarch64, 1 thread) --- .../aarch64/recheck-nd-batched/COMPARE3.md | 159 + .../aarch64/recheck-nd-batched/fftw_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/int_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/large_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/odd_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/r57_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/rpost_t1.json | 2827 +++++++++++++++++ .../aarch64/recheck-nd-batched/simd_t1.json | 2827 +++++++++++++++++ 8 files changed, 19948 insertions(+) create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/fftw_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/int_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/large_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/odd_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/r57_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/rpost_t1.json create mode 100644 benchmark/compare3/aarch64/recheck-nd-batched/simd_t1.json diff --git a/benchmark/compare3/aarch64/recheck-nd-batched/COMPARE3.md b/benchmark/compare3/aarch64/recheck-nd-batched/COMPARE3.md new file mode 100644 index 0000000..3859cc6 --- /dev/null +++ b/benchmark/compare3/aarch64/recheck-nd-batched/COMPARE3.md @@ -0,0 +1,159 @@ +# FFT implementations side by side + +Rendered 2026-08-30T12:35:21.887 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `simd` | FFTA.jl 0.3.1 @ 4419199 — `FFTA-simd` | +| `large` | FFTA.jl 0.3.1 @ 605c9c3 — `FFTA-large` | +| `odd` | FFTA.jl 0.3.1 @ e73dac4 — `FFTA-odd` | +| `r57` | FFTA.jl 0.3.1 @ d93eb1d — `FFTA-r57` | +| `rpost` | FFTA.jl 0.3.1 @ a919b4f — `FFTA-rpost` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `simd` | `large` | `odd` | `r57` | `rpost` | `int`/`fftw` | `simd`/`fftw` | `large`/`fftw` | `odd`/`fftw` | `r57`/`fftw` | `rpost`/`fftw` | `simd` vs `int` | `large` vs `int` | `odd` vs `int` | `r57` vs `int` | `rpost` vs `int` | +|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 | 144 ns | 693 ns | 701 ns | 716 ns | 731 ns | 758 ns | 742 ns | 4.83× | 4.88× | 4.98× | 5.09× | 5.28× | 5.17× | 0.99× | 0.97× | **0.95×** | **0.91×** | **0.93×** | +| fft Float32 16×16 dims=1,2 | 571 ns | 2.46 µs | 2.49 µs | 2.51 µs | 2.56 µs | 2.53 µs | 2.51 µs | 4.30× | 4.35× | 4.39× | 4.48× | 4.43× | 4.39× | 0.99× | 0.98× | 0.96× | 0.97× | 0.98× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.76 µs | 10.74 µs | 10.78 µs | 10.82 µs | 10.82 µs | 4.00× | 4.01× | 4.01× | 4.02× | 4.04× | 4.04× | 1.00× | 1.00× | 0.99× | 0.99× | 0.99× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 49.40 µs | 48.76 µs | 48.76 µs | 49.00 µs | 49.20 µs | 49.08 µs | 4.00× | 3.95× | 3.95× | 3.97× | 3.99× | 3.98× | 1.01× | 1.01× | 1.01× | 1.00× | 1.01× | +| fft Float32 128×128 dims=1,2 | 60.04 µs | 250.16 µs | 208.92 µs | 209.68 µs | 251.80 µs | 250.92 µs | 250.48 µs | 4.17× | 3.48× | 3.49× | 4.19× | 4.18× | 4.17× | **1.20×** | **1.19×** | 0.99× | 1.00× | 1.00× | +| fft Float32 256×256 dims=1,2 | 793.77 µs | 1.173 ms | 1.014 ms | 1.033 ms | 1.203 ms | 1.196 ms | 1.203 ms | 1.48× | 1.28× | 1.30× | 1.52× | 1.51× | 1.52× | **1.16×** | **1.14×** | 0.98× | 0.98× | 0.98× | +| fft Float32 512×512 dims=1,2 | 5.898 ms | 7.205 ms | 5.949 ms | 6.007 ms | 7.456 ms | 7.125 ms | 7.322 ms | 1.22× | 1.01× | 1.02× | 1.26× | 1.21× | 1.24× | **1.21×** | **1.20×** | 0.97× | 1.01× | 0.98× | +| fft Float32 1024×1024 dims=1,2 | 26.145 ms | 36.418 ms | 28.997 ms | 29.858 ms | 35.784 ms | 34.149 ms | 35.008 ms | 1.39× | 1.11× | 1.14× | 1.37× | 1.31× | 1.34× | **1.26×** | **1.22×** | 1.02× | **1.07×** | 1.04× | +| fft Float32 2048×2048 dims=1,2 | 134.730 ms | 164.479 ms | 128.252 ms | 130.603 ms | 165.264 ms | 159.202 ms | 159.886 ms | 1.22× | 0.95× | 0.97× | 1.23× | 1.18× | 1.19× | **1.28×** | **1.26×** | 1.00× | 1.03× | 1.03× | +| fft Float64 8×8 dims=1,2 | 173 ns | 730 ns | 733 ns | 728 ns | 755 ns | 760 ns | 763 ns | 4.23× | 4.24× | 4.21× | 4.37× | 4.40× | 4.42× | 1.00× | 1.00× | 0.97× | 0.96× | 0.96× | +| fft Float64 16×16 dims=1,2 | 823 ns | 2.54 µs | 2.53 µs | 2.56 µs | 2.59 µs | 2.62 µs | 2.56 µs | 3.08× | 3.08× | 3.11× | 3.15× | 3.18× | 3.11× | 1.00× | 0.99× | 0.98× | 0.97× | 0.99× | +| fft Float64 32×32 dims=1,2 | 4.12 µs | 11.34 µs | 11.30 µs | 11.44 µs | 11.42 µs | 11.44 µs | 11.34 µs | 2.75× | 2.74× | 2.78× | 2.77× | 2.78× | 2.75× | 1.00× | 0.99× | 0.99× | 0.99× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.48 µs | 53.12 µs | 53.04 µs | 53.28 µs | 53.32 µs | 53.28 µs | 53.24 µs | 2.59× | 2.59× | 2.60× | 2.60× | 2.60× | 2.60× | 1.00× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float64 128×128 dims=1,2 | 113.12 µs | 266.28 µs | 241.52 µs | 240.96 µs | 268.12 µs | 268.64 µs | 266.16 µs | 2.35× | 2.14× | 2.13× | 2.37× | 2.37× | 2.35× | **1.10×** | **1.11×** | 0.99× | 0.99× | 1.00× | +| fft Float64 127×257 dims=1,2 | 1.798 ms | 4.099 ms | 3.572 ms | 3.579 ms | 4.066 ms | 4.071 ms | 4.084 ms | 2.28× | 1.99× | 1.99× | 2.26× | 2.26× | 2.27× | **1.15×** | **1.15×** | 1.01× | 1.01× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 3.680 ms | 3.863 ms | 3.203 ms | 3.223 ms | 3.842 ms | 3.834 ms | 3.836 ms | 1.05× | 0.87× | 0.88× | 1.04× | 1.04× | 1.04× | **1.21×** | **1.20×** | 1.01× | 1.01× | 1.01× | +| fft Float64 64×1009 dims=1,2 | 3.870 ms | 4.015 ms | 3.361 ms | 3.354 ms | 3.985 ms | 3.953 ms | 3.984 ms | 1.04× | 0.87× | 0.87× | 1.03× | 1.02× | 1.03× | **1.19×** | **1.20×** | 1.01× | 1.02× | 1.01× | +| fft Float64 256×256 dims=1,2 | 1.174 ms | 1.532 ms | 1.417 ms | 1.421 ms | 1.586 ms | 1.479 ms | 1.523 ms | 1.31× | 1.21× | 1.21× | 1.35× | 1.26× | 1.30× | **1.08×** | **1.08×** | 0.97× | 1.04× | 1.01× | +| fft Float64 512×512 dims=1,2 | 6.346 ms | 7.640 ms | 6.870 ms | 6.942 ms | 7.901 ms | 7.544 ms | 7.781 ms | 1.20× | 1.08× | 1.09× | 1.25× | 1.19× | 1.23× | **1.11×** | **1.10×** | 0.97× | 1.01× | 0.98× | +| fft Float64 720×480 dims=1,2 | 6.712 ms | 19.849 ms | 20.159 ms | 19.941 ms | 16.798 ms | 17.474 ms | 20.272 ms | 2.96× | 3.00× | 2.97× | 2.50× | 2.60× | 3.02× | 0.98× | 1.00× | **1.18×** | **1.14×** | 0.98× | +| fft Float64 1000×1000 dims=1,2 | 27.715 ms | 88.268 ms | 87.477 ms | 88.094 ms | 56.015 ms | 43.255 ms | 87.413 ms | 3.18× | 3.16× | 3.18× | 2.02× | 1.56× | 3.15× | 1.01× | 1.00× | **1.58×** | **2.04×** | 1.01× | +| fft Float64 1024×1024 dims=1,2 | 32.025 ms | 40.034 ms | 34.405 ms | 36.077 ms | 39.800 ms | 37.756 ms | 38.165 ms | 1.25× | 1.07× | 1.13× | 1.24× | 1.18× | 1.19× | **1.16×** | **1.11×** | 1.01× | **1.06×** | 1.05× | +| fft Float64 2048×2048 dims=1,2 | 171.997 ms | 188.864 ms | 161.464 ms | 163.010 ms | 188.864 ms | 181.128 ms | 184.851 ms | 1.10× | 0.94× | 0.95× | 1.10× | 1.05× | 1.07× | **1.17×** | **1.16×** | 1.00× | 1.04× | 1.02× | +| rfft Float32 8×8 dims=1,2 | 124 ns | 861 ns | 857 ns | 874 ns | 884 ns | 888 ns | 679 ns | 6.92× | 6.89× | 7.03× | 7.11× | 7.14× | 5.46× | 1.00× | 0.98× | 0.97× | 0.97× | **1.27×** | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.37 µs | 2.36 µs | 2.43 µs | 2.43 µs | 2.40 µs | 1.97 µs | 5.42× | 5.38× | 5.54× | 5.55× | 5.48× | 4.50× | 1.01× | 0.98× | 0.98× | 0.99× | **1.20×** | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.00 µs | 8.00 µs | 8.13 µs | 8.11 µs | 8.04 µs | 6.80 µs | 3.90× | 3.90× | 3.96× | 3.95× | 3.92× | 3.31× | 1.00× | 0.98× | 0.99× | 1.00× | **1.18×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.00 µs | 31.88 µs | 32.16 µs | 32.20 µs | 32.24 µs | 27.56 µs | 3.25× | 3.24× | 3.27× | 3.27× | 3.28× | 2.80× | 1.00× | 1.00× | 0.99× | 0.99× | **1.16×** | +| rfft Float32 128×128 dims=1,2 | 46.56 µs | 140.56 µs | 130.60 µs | 130.32 µs | 141.12 µs | 140.80 µs | 122.88 µs | 3.02× | 2.81× | 2.80× | 3.03× | 3.02× | 2.64× | **1.08×** | **1.08×** | 1.00× | 1.00× | **1.14×** | +| rfft Float32 256×256 dims=1,2 | 347.84 µs | 619.73 µs | 536.49 µs | 538.01 µs | 624.17 µs | 620.89 µs | 549.89 µs | 1.78× | 1.54× | 1.55× | 1.79× | 1.78× | 1.58× | **1.16×** | **1.15×** | 0.99× | 1.00× | **1.13×** | +| rfft Float32 512×512 dims=1,2 | 1.457 ms | 2.830 ms | 2.348 ms | 2.347 ms | 2.846 ms | 2.818 ms | 2.555 ms | 1.94× | 1.61× | 1.61× | 1.95× | 1.93× | 1.75× | **1.21×** | **1.21×** | 0.99× | 1.00× | **1.11×** | +| rfft Float32 1024×1024 dims=1,2 | 6.055 ms | 12.833 ms | 10.025 ms | 10.190 ms | 12.763 ms | 12.623 ms | 11.599 ms | 2.12× | 1.66× | 1.68× | 2.11× | 2.08× | 1.92× | **1.28×** | **1.26×** | 1.01× | 1.02× | **1.11×** | +| rfft Float32 2048×2048 dims=1,2 | 34.888 ms | 63.494 ms | 49.221 ms | 49.840 ms | 63.077 ms | 62.671 ms | 57.777 ms | 1.82× | 1.41× | 1.43× | 1.81× | 1.80× | 1.66× | **1.29×** | **1.27×** | 1.01× | 1.01× | **1.10×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 930 ns | 944 ns | 952 ns | 934 ns | 948 ns | 681 ns | 7.92× | 8.04× | 8.11× | 7.96× | 8.08× | 5.81× | 0.99× | 0.98× | 1.00× | 0.98× | **1.36×** | +| rfft Float64 16×16 dims=1,2 | 489 ns | 2.47 µs | 2.47 µs | 2.50 µs | 2.50 µs | 2.50 µs | 1.93 µs | 5.04× | 5.04× | 5.10× | 5.11× | 5.11× | 3.94× | 1.00× | 0.99× | 0.99× | 0.99× | **1.28×** | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.44 µs | 8.44 µs | 8.55 µs | 8.53 µs | 8.60 µs | 6.97 µs | 3.52× | 3.52× | 3.56× | 3.56× | 3.58× | 2.91× | 1.00× | 0.99× | 0.99× | 0.98× | **1.21×** | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.60 µs | 33.68 µs | 33.76 µs | 33.80 µs | 33.88 µs | 29.36 µs | 2.86× | 2.86× | 2.87× | 2.87× | 2.88× | 2.50× | 1.00× | 1.00× | 0.99× | 0.99× | **1.14×** | +| rfft Float64 128×128 dims=1,2 | 58.16 µs | 146.44 µs | 140.60 µs | 140.84 µs | 147.92 µs | 146.80 µs | 131.96 µs | 2.52× | 2.42× | 2.42× | 2.54× | 2.52× | 2.27× | 1.04× | 1.04× | 0.99× | 1.00× | **1.11×** | +| rfft Float64 127×257 dims=1,2 | 1.517 ms | 2.606 ms | 2.301 ms | 2.307 ms | 2.604 ms | 2.617 ms | 2.615 ms | 1.72× | 1.52× | 1.52× | 1.72× | 1.72× | 1.72× | **1.13×** | **1.13×** | 1.00× | 1.00× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.610 ms | 3.465 ms | 2.802 ms | 2.815 ms | 3.432 ms | 3.421 ms | 3.426 ms | 2.15× | 1.74× | 1.75× | 2.13× | 2.12× | 2.13× | **1.24×** | **1.23×** | 1.01× | 1.01× | 1.01× | +| rfft Float64 64×1009 dims=1,2 | 1.943 ms | 2.067 ms | 1.735 ms | 1.733 ms | 2.058 ms | 2.049 ms | 2.008 ms | 1.06× | 0.89× | 0.89× | 1.06× | 1.05× | 1.03× | **1.19×** | **1.19×** | 1.00× | 1.01× | 1.03× | +| rfft Float64 256×256 dims=1,2 | 415.05 µs | 660.25 µs | 606.21 µs | 608.37 µs | 650.57 µs | 652.81 µs | 609.33 µs | 1.59× | 1.46× | 1.47× | 1.57× | 1.57× | 1.47× | **1.09×** | **1.09×** | 1.01× | 1.01× | **1.08×** | +| rfft Float64 512×512 dims=1,2 | 1.950 ms | 3.031 ms | 2.709 ms | 2.736 ms | 3.075 ms | 3.031 ms | 2.837 ms | 1.55× | 1.39× | 1.40× | 1.58× | 1.55× | 1.45× | **1.12×** | **1.11×** | 0.99× | 1.00× | **1.07×** | +| rfft Float64 720×480 dims=1,2 | 3.184 ms | 9.761 ms | 9.677 ms | 9.888 ms | 8.215 ms | 8.337 ms | 9.528 ms | 3.07× | 3.04× | 3.11× | 2.58× | 2.62× | 2.99× | 1.01× | 0.99× | **1.19×** | **1.17×** | 1.02× | +| rfft Float64 1000×1000 dims=1,2 | 13.247 ms | 43.068 ms | 43.258 ms | 42.708 ms | 26.843 ms | 20.648 ms | 42.212 ms | 3.25× | 3.27× | 3.22× | 2.03× | 1.56× | 3.19× | 1.00× | 1.01× | **1.60×** | **2.09×** | 1.02× | +| rfft Float64 1024×1024 dims=1,2 | 8.961 ms | 13.835 ms | 11.825 ms | 12.116 ms | 13.910 ms | 13.626 ms | 12.820 ms | 1.54× | 1.32× | 1.35× | 1.55× | 1.52× | 1.43× | **1.17×** | **1.14×** | 0.99× | 1.02× | **1.08×** | +| rfft Float64 2048×2048 dims=1,2 | 55.705 ms | 68.549 ms | 59.182 ms | 59.563 ms | 68.729 ms | 68.506 ms | 64.620 ms | 1.23× | 1.06× | 1.07× | 1.23× | 1.23× | 1.16× | **1.16×** | **1.15×** | 1.00× | 1.00× | **1.06×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.49 µs | 9.36 µs | 9.71 µs | 9.68 µs | 9.84 µs | 9.47 µs | 6.12× | 6.04× | 6.26× | 6.25× | 6.35× | 6.11× | 1.01× | 0.98× | 0.98× | 0.96× | 1.00× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 65.20 µs | 64.60 µs | 66.08 µs | 65.92 µs | 66.48 µs | 65.24 µs | 4.84× | 4.80× | 4.91× | 4.90× | 4.94× | 4.85× | 1.01× | 0.99× | 0.99× | 0.98× | 1.00× | +| fft Float32 32×32×32 dims=1,2,3 | 141.28 µs | 591.05 µs | 585.09 µs | 592.21 µs | 591.73 µs | 593.57 µs | 591.25 µs | 4.18× | 4.14× | 4.19× | 4.19× | 4.20× | 4.18× | 1.01× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float32 64×64×64 dims=1,2,3 | 1.508 ms | 5.730 ms | 5.763 ms | 5.793 ms | 5.793 ms | 5.706 ms | 5.742 ms | 3.80× | 3.82× | 3.84× | 3.84× | 3.78× | 3.81× | 0.99× | 0.99× | 0.99× | 1.00× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 18.039 ms | 65.003 ms | 57.365 ms | 56.018 ms | 63.401 ms | 62.863 ms | 63.858 ms | 3.60× | 3.18× | 3.11× | 3.51× | 3.48× | 3.54× | **1.13×** | **1.16×** | 1.03× | 1.03× | 1.02× | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.64 µs | 9.61 µs | 9.98 µs | 10.06 µs | 10.06 µs | 9.57 µs | 5.06× | 5.05× | 5.24× | 5.28× | 5.28× | 5.03× | 1.00× | 0.97× | 0.96× | 0.96× | 1.01× | +| fft Float64 16×16×16 dims=1,2,3 | 20.08 µs | 67.20 µs | 66.88 µs | 67.76 µs | 69.16 µs | 68.52 µs | 66.72 µs | 3.35× | 3.33× | 3.37× | 3.44× | 3.41× | 3.32× | 1.00× | 0.99× | 0.97× | 0.98× | 1.01× | +| fft Float64 32×32×32 dims=1,2,3 | 244.84 µs | 635.85 µs | 638.61 µs | 645.53 µs | 655.41 µs | 661.17 µs | 643.17 µs | 2.60× | 2.61× | 2.64× | 2.68× | 2.70× | 2.63× | 1.00× | 0.99× | 0.97× | 0.96× | 0.99× | +| fft Float64 64×64×64 dims=1,2,3 | 2.512 ms | 6.550 ms | 6.665 ms | 6.543 ms | 6.707 ms | 6.531 ms | 6.688 ms | 2.61× | 2.65× | 2.60× | 2.67× | 2.60× | 2.66× | 0.98× | 1.00× | 0.98× | 1.00× | 0.98× | +| fft Float64 128×128×128 dims=1,2,3 | 40.280 ms | 82.290 ms | 76.959 ms | 77.098 ms | 82.554 ms | 80.907 ms | 79.602 ms | 2.04× | 1.91× | 1.91× | 2.05× | 2.01× | 1.98× | **1.07×** | **1.07×** | 1.00× | 1.02× | 1.03× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.18 µs | 9.07 µs | 9.17 µs | 9.33 µs | 9.41 µs | 9.52 µs | 7.73 µs | 7.66× | 7.75× | 7.88× | 7.95× | 8.04× | 6.53× | 0.99× | 0.97× | 0.96× | 0.95× | **1.17×** | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.28 µs | 51.44 µs | 52.92 µs | 52.68 µs | 53.28 µs | 45.64 µs | 5.56× | 5.58× | 5.74× | 5.71× | 5.77× | 4.95× | 1.00× | 0.97× | 0.97× | 0.96× | **1.12×** | +| rfft Float32 32×32×32 dims=1,2,3 | 90.96 µs | 367.80 µs | 367.04 µs | 369.08 µs | 372.85 µs | 373.68 µs | 331.72 µs | 4.04× | 4.04× | 4.06× | 4.10× | 4.11× | 3.65× | 1.00× | 1.00× | 0.99× | 0.98× | **1.11×** | +| rfft Float32 64×64×64 dims=1,2,3 | 966.25 µs | 3.121 ms | 3.128 ms | 3.127 ms | 3.157 ms | 3.134 ms | 2.861 ms | 3.23× | 3.24× | 3.24× | 3.27× | 3.24× | 2.96× | 1.00× | 1.00× | 0.99× | 1.00× | **1.09×** | +| rfft Float32 128×128×128 dims=1,2,3 | 9.530 ms | 28.822 ms | 26.415 ms | 26.193 ms | 29.174 ms | 28.862 ms | 26.998 ms | 3.02× | 2.77× | 2.75× | 3.06× | 3.03× | 2.83× | **1.09×** | **1.10×** | 0.99× | 1.00× | **1.07×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 9.64 µs | 10.02 µs | 9.98 µs | 10.14 µs | 7.83 µs | 8.09× | 8.05× | 8.37× | 8.34× | 8.47× | 6.54× | 1.00× | 0.97× | 0.97× | 0.95× | **1.24×** | +| rfft Float64 16×16×16 dims=1,2,3 | 11.40 µs | 53.24 µs | 53.28 µs | 54.60 µs | 54.44 µs | 54.88 µs | 44.88 µs | 4.67× | 4.67× | 4.79× | 4.78× | 4.81× | 3.94× | 1.00× | 0.98× | 0.98× | 0.97× | **1.19×** | +| rfft Float64 32×32×32 dims=1,2,3 | 116.88 µs | 387.84 µs | 387.13 µs | 393.40 µs | 392.84 µs | 392.92 µs | 345.48 µs | 3.32× | 3.31× | 3.37× | 3.36× | 3.36× | 2.96× | 1.00× | 0.99× | 0.99× | 0.99× | **1.12×** | +| rfft Float64 64×64×64 dims=1,2,3 | 1.388 ms | 3.491 ms | 3.483 ms | 3.514 ms | 3.569 ms | 3.502 ms | 3.246 ms | 2.52× | 2.51× | 2.53× | 2.57× | 2.52× | 2.34× | 1.00× | 0.99× | 0.98× | 1.00× | **1.08×** | +| rfft Float64 128×128×128 dims=1,2,3 | 14.920 ms | 34.148 ms | 33.087 ms | 31.945 ms | 33.613 ms | 33.800 ms | 30.643 ms | 2.29× | 2.22× | 2.14× | 2.25× | 2.27× | 2.05× | 1.03× | **1.07×** | 1.02× | 1.01× | **1.11×** | +| fft Float32 64×64 dims=1 | 6.21 µs | 22.40 µs | 22.48 µs | 22.68 µs | 22.72 µs | 22.76 µs | 22.44 µs | 3.61× | 3.62× | 3.65× | 3.66× | 3.67× | 3.61× | 1.00× | 0.99× | 0.99× | 0.98× | 1.00× | +| fft Float32 256×64 dims=1 | 52.52 µs | 124.08 µs | 103.36 µs | 103.68 µs | 123.52 µs | 124.84 µs | 123.60 µs | 2.36× | 1.97× | 1.97× | 2.35× | 2.38× | 2.35× | **1.20×** | **1.20×** | 1.00× | 0.99× | 1.00× | +| fft Float32 1024×64 dims=1 | 248.08 µs | 639.49 µs | 473.41 µs | 478.97 µs | 637.17 µs | 638.73 µs | 641.89 µs | 2.58× | 1.91× | 1.93× | 2.57× | 2.57× | 2.59× | **1.35×** | **1.34×** | 1.00× | 1.00× | 1.00× | +| fft Float32 4096×64 dims=1 | 1.289 ms | 3.267 ms | 2.253 ms | 2.287 ms | 3.259 ms | 3.272 ms | 3.293 ms | 2.53× | 1.75× | 1.77× | 2.53× | 2.54× | 2.55× | **1.45×** | **1.43×** | 1.00× | 1.00× | 0.99× | +| fft Float32 16384×64 dims=1 | 7.891 ms | 17.273 ms | 10.894 ms | 11.082 ms | 17.023 ms | 17.254 ms | 16.434 ms | 2.19× | 1.38× | 1.40× | 2.16× | 2.19× | 2.08× | **1.59×** | **1.56×** | 1.01× | 1.00× | **1.05×** | +| fft Float32 65536×64 dims=1 | 44.779 ms | 88.834 ms | 61.404 ms | 62.121 ms | 89.266 ms | 87.996 ms | 90.203 ms | 1.98× | 1.37× | 1.39× | 1.99× | 1.97× | 2.01× | **1.45×** | **1.43×** | 1.00× | 1.01× | 0.98× | +| fft Float64 64×64 dims=1 | 10.34 µs | 23.80 µs | 23.80 µs | 23.96 µs | 23.92 µs | 24.04 µs | 23.84 µs | 2.30× | 2.30× | 2.32× | 2.31× | 2.32× | 2.31× | 1.00× | 0.99× | 0.99× | 0.99× | 1.00× | +| fft Float64 256×64 dims=1 | 87.20 µs | 129.80 µs | 116.48 µs | 116.60 µs | 129.36 µs | 129.52 µs | 130.00 µs | 1.49× | 1.34× | 1.34× | 1.48× | 1.49× | 1.49× | **1.11×** | **1.11×** | 1.00× | 1.00× | 1.00× | +| fft Float64 1024×64 dims=1 | 433.88 µs | 695.45 µs | 581.33 µs | 606.49 µs | 696.69 µs | 688.85 µs | 694.25 µs | 1.60× | 1.34× | 1.40× | 1.61× | 1.59× | 1.60× | **1.20×** | **1.15×** | 1.00× | 1.01× | 1.00× | +| fft Float64 4096×64 dims=1 | 2.187 ms | 3.757 ms | 3.023 ms | 3.092 ms | 3.695 ms | 3.716 ms | 3.749 ms | 1.72× | 1.38× | 1.41× | 1.69× | 1.70× | 1.71× | **1.24×** | **1.21×** | 1.02× | 1.01× | 1.00× | +| fft Float64 16384×64 dims=1 | 15.523 ms | 21.802 ms | 17.731 ms | 17.841 ms | 21.628 ms | 21.314 ms | 20.862 ms | 1.40× | 1.14× | 1.15× | 1.39× | 1.37× | 1.34× | **1.23×** | **1.22×** | 1.01× | 1.02× | 1.05× | +| fft Float64 65536×64 dims=1 | 91.276 ms | 112.336 ms | 93.428 ms | 96.681 ms | 111.990 ms | 110.847 ms | 113.786 ms | 1.23× | 1.02× | 1.06× | 1.23× | 1.21× | 1.25× | **1.20×** | **1.16×** | 1.00× | 1.01× | 0.99× | +| rfft Float32 64×64 dims=1 | 6.59 µs | 18.68 µs | 18.80 µs | 18.96 µs | 19.04 µs | 19.08 µs | 14.24 µs | 2.84× | 2.85× | 2.88× | 2.89× | 2.90× | 2.16× | 0.99× | 0.99× | 0.98× | 0.98× | **1.31×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.60 µs | 74.16 µs | 74.20 µs | 84.80 µs | 84.76 µs | 66.24 µs | 2.07× | 1.82× | 1.82× | 2.08× | 2.08× | 1.62× | **1.14×** | **1.14×** | 1.00× | 1.00× | **1.28×** | +| rfft Float32 1024×64 dims=1 | 143.60 µs | 398.72 µs | 315.84 µs | 321.44 µs | 397.44 µs | 397.56 µs | 326.60 µs | 2.78× | 2.20× | 2.24× | 2.77× | 2.77× | 2.27× | **1.26×** | **1.24×** | 1.00× | 1.00× | **1.22×** | +| rfft Float32 4096×64 dims=1 | 684.57 µs | 1.879 ms | 1.380 ms | 1.418 ms | 1.883 ms | 1.879 ms | 1.600 ms | 2.74× | 2.02× | 2.07× | 2.75× | 2.74× | 2.34× | **1.36×** | **1.33×** | 1.00× | 1.00× | **1.17×** | +| rfft Float32 16384×64 dims=1 | 3.765 ms | 8.875 ms | 6.151 ms | 6.307 ms | 8.909 ms | 8.895 ms | 7.791 ms | 2.36× | 1.63× | 1.67× | 2.37× | 2.36× | 2.07× | **1.44×** | **1.41×** | 1.00× | 1.00× | **1.14×** | +| rfft Float32 65536×64 dims=1 | 19.560 ms | 43.038 ms | 29.525 ms | 30.403 ms | 43.069 ms | 42.952 ms | 39.199 ms | 2.20× | 1.51× | 1.55× | 2.20× | 2.20× | 2.00× | **1.46×** | **1.42×** | 1.00× | 1.00× | **1.10×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.84 µs | 19.88 µs | 20.00 µs | 19.96 µs | 20.00 µs | 15.52 µs | 2.97× | 2.98× | 2.99× | 2.99× | 2.99× | 2.32× | 1.00× | 0.99× | 0.99× | 0.99× | **1.28×** | +| rfft Float64 256×4096 dims=1 | 3.138 ms | 5.820 ms | 5.442 ms | 5.387 ms | 5.786 ms | 5.744 ms | 4.909 ms | 1.85× | 1.73× | 1.72× | 1.84× | 1.83× | 1.56× | **1.07×** | **1.08×** | 1.01× | 1.01× | **1.19×** | +| rfft Float64 256×64 dims=1 | 44.48 µs | 87.56 µs | 80.80 µs | 80.96 µs | 87.56 µs | 87.56 µs | 73.76 µs | 1.97× | 1.82× | 1.82× | 1.97× | 1.97× | 1.66× | **1.08×** | **1.08×** | 1.00× | 1.00× | **1.19×** | +| rfft Float64 1024×1024 dims=1 | 3.742 ms | 6.797 ms | 6.187 ms | 5.996 ms | 6.792 ms | 6.763 ms | 5.971 ms | 1.82× | 1.65× | 1.60× | 1.81× | 1.81× | 1.60× | **1.10×** | **1.13×** | 1.00× | 1.01× | **1.14×** | +| rfft Float64 1024×64 dims=1 | 215.88 µs | 414.08 µs | 361.16 µs | 366.24 µs | 415.12 µs | 414.08 µs | 365.28 µs | 1.92× | 1.67× | 1.70× | 1.92× | 1.92× | 1.69× | **1.15×** | **1.13×** | 1.00× | 1.00× | **1.13×** | +| rfft Float64 4096×256 dims=1 | 4.298 ms | 7.999 ms | 6.753 ms | 6.811 ms | 8.034 ms | 8.007 ms | 7.199 ms | 1.86× | 1.57× | 1.58× | 1.87× | 1.86× | 1.67× | **1.18×** | **1.17×** | 1.00× | 1.00× | **1.11×** | +| rfft Float64 4096×64 dims=1 | 1.058 ms | 1.970 ms | 1.643 ms | 1.682 ms | 1.981 ms | 1.977 ms | 1.782 ms | 1.86× | 1.55× | 1.59× | 1.87× | 1.87× | 1.68× | **1.20×** | **1.17×** | 0.99× | 1.00× | **1.11×** | +| rfft Float64 16384×64 dims=1 | 6.258 ms | 9.837 ms | 8.103 ms | 8.218 ms | 9.816 ms | 9.796 ms | 9.103 ms | 1.57× | 1.29× | 1.31× | 1.57× | 1.57× | 1.45× | **1.21×** | **1.20×** | 1.00× | 1.00× | **1.08×** | +| rfft Float64 65536×64 dims=1 | 37.190 ms | 50.758 ms | 41.556 ms | 42.949 ms | 50.654 ms | 50.278 ms | 47.832 ms | 1.36× | 1.12× | 1.15× | 1.36× | 1.35× | 1.29× | **1.22×** | **1.18×** | 1.00× | 1.01× | **1.06×** | +| fft Float32 64×64 dims=2 | 6.16 µs | 27.12 µs | 27.12 µs | 27.24 µs | 27.36 µs | 27.72 µs | 27.28 µs | 4.40× | 4.40× | 4.42× | 4.44× | 4.50× | 4.43× | 1.00× | 1.00× | 0.99× | 0.98× | 0.99× | +| fft Float32 64×256 dims=2 | 78.52 µs | 153.08 µs | 152.88 µs | 153.36 µs | 153.00 µs | 153.00 µs | 152.72 µs | 1.95× | 1.95× | 1.95× | 1.95× | 1.95× | 1.94× | 1.00× | 1.00× | 1.00× | 1.00× | 1.00× | +| fft Float32 64×1024 dims=2 | 458.65 µs | 1.099 ms | 826.73 µs | 847.37 µs | 863.01 µs | 864.17 µs | 867.17 µs | 2.40× | 1.80× | 1.85× | 1.88× | 1.88× | 1.89× | **1.33×** | **1.30×** | **1.27×** | **1.27×** | **1.27×** | +| fft Float32 64×4096 dims=2 | 4.705 ms | 5.975 ms | 5.872 ms | 6.111 ms | 5.944 ms | 5.776 ms | 6.084 ms | 1.27× | 1.25× | 1.30× | 1.26× | 1.23× | 1.29× | 1.02× | 0.98× | 1.01× | 1.03× | 0.98× | +| fft Float32 64×16384 dims=2 | 25.171 ms | 31.383 ms | 35.049 ms | 32.288 ms | 32.213 ms | 31.408 ms | 30.978 ms | 1.25× | 1.39× | 1.28× | 1.28× | 1.25× | 1.23× | **0.90×** | 0.97× | 0.97× | 1.00× | 1.01× | +| fft Float32 64×65536 dims=2 | 171.759 ms | 203.539 ms | 218.787 ms | 224.539 ms | 218.811 ms | 216.582 ms | 219.715 ms | 1.19× | 1.27× | 1.31× | 1.27× | 1.26× | 1.28× | **0.93×** | **0.91×** | **0.93×** | **0.94×** | **0.93×** | +| fft Float64 64×64 dims=2 | 10.84 µs | 28.52 µs | 28.52 µs | 28.76 µs | 28.76 µs | 28.80 µs | 28.56 µs | 2.63× | 2.63× | 2.65× | 2.65× | 2.66× | 2.63× | 1.00× | 0.99× | 0.99× | 0.99× | 1.00× | +| fft Float64 64×256 dims=2 | 119.04 µs | 166.60 µs | 160.88 µs | 169.68 µs | 161.00 µs | 162.52 µs | 163.56 µs | 1.40× | 1.35× | 1.43× | 1.35× | 1.37× | 1.37× | 1.04× | 0.98× | 1.03× | 1.03× | 1.02× | +| fft Float64 64×1024 dims=2 | 893.05 µs | 1.215 ms | 1.180 ms | 1.238 ms | 1.163 ms | 1.178 ms | 1.247 ms | 1.36× | 1.32× | 1.39× | 1.30× | 1.32× | 1.40× | 1.03× | 0.98× | 1.05× | 1.03× | 0.97× | +| fft Float64 64×4096 dims=2 | 5.692 ms | 7.130 ms | 6.915 ms | 7.221 ms | 7.014 ms | 6.860 ms | 7.183 ms | 1.25× | 1.21× | 1.27× | 1.23× | 1.21× | 1.26× | 1.03× | 0.99× | 1.02× | 1.04× | 0.99× | +| fft Float64 64×16384 dims=2 | 34.085 ms | 47.918 ms | 46.249 ms | 47.684 ms | 46.860 ms | 45.161 ms | 45.429 ms | 1.41× | 1.36× | 1.40× | 1.37× | 1.32× | 1.33× | 1.04× | 1.00× | 1.02× | **1.06×** | **1.05×** | +| fft Float64 64×65536 dims=2 | 253.345 ms | 276.062 ms | 270.961 ms | 276.236 ms | 270.325 ms | 268.369 ms | 272.732 ms | 1.09× | 1.07× | 1.09× | 1.07× | 1.06× | 1.08× | 1.02× | 1.00× | 1.02× | 1.03× | 1.01× | +| rfft Float32 64×64 dims=2 | 6.61 µs | 22.32 µs | 22.44 µs | 22.48 µs | 22.36 µs | 22.56 µs | 17.34 µs | 3.38× | 3.39× | 3.40× | 3.38× | 3.41× | 2.62× | 0.99× | 0.99× | 1.00× | 0.99× | **1.29×** | +| rfft Float32 64×256 dims=2 | 58.16 µs | 108.84 µs | 96.36 µs | 96.20 µs | 106.88 µs | 107.40 µs | 89.04 µs | 1.87× | 1.66× | 1.65× | 1.84× | 1.85× | 1.53× | **1.13×** | **1.13×** | 1.02× | 1.01× | **1.22×** | +| rfft Float32 64×1024 dims=2 | 285.60 µs | 541.01 µs | 455.44 µs | 461.09 µs | 537.25 µs | 540.01 µs | 468.32 µs | 1.89× | 1.59× | 1.61× | 1.88× | 1.89× | 1.64× | **1.19×** | **1.17×** | 1.01× | 1.00× | **1.16×** | +| rfft Float32 64×4096 dims=2 | 1.834 ms | 2.863 ms | 2.367 ms | 2.398 ms | 2.814 ms | 2.842 ms | 2.606 ms | 1.56× | 1.29× | 1.31× | 1.53× | 1.55× | 1.42× | **1.21×** | **1.19×** | 1.02× | 1.01× | **1.10×** | +| rfft Float32 64×16384 dims=2 | 11.931 ms | 14.247 ms | 11.445 ms | 11.700 ms | 14.217 ms | 14.163 ms | 13.090 ms | 1.19× | 0.96× | 0.98× | 1.19× | 1.19× | 1.10× | **1.24×** | **1.22×** | 1.00× | 1.01× | **1.09×** | +| rfft Float32 64×65536 dims=2 | 74.106 ms | 70.805 ms | 59.170 ms | 58.749 ms | 71.647 ms | 71.884 ms | 66.763 ms | 0.96× | 0.80× | 0.79× | 0.97× | 0.97× | 0.90× | **1.20×** | **1.21×** | 0.99× | 0.98× | **1.06×** | +| rfft Float64 64×64 dims=2 | 6.59 µs | 23.68 µs | 23.84 µs | 23.60 µs | 23.68 µs | 23.76 µs | 19.02 µs | 3.60× | 3.62× | 3.58× | 3.60× | 3.61× | 2.89× | 0.99× | 1.00× | 1.00× | 1.00× | **1.25×** | +| rfft Float64 64×256 dims=2 | 71.24 µs | 122.72 µs | 115.80 µs | 115.72 µs | 122.68 µs | 122.96 µs | 108.52 µs | 1.72× | 1.63× | 1.62× | 1.72× | 1.73× | 1.52× | **1.06×** | **1.06×** | 1.00× | 1.00× | **1.13×** | +| rfft Float64 64×1024 dims=2 | 344.08 µs | 584.21 µs | 521.21 µs | 525.17 µs | 581.41 µs | 580.41 µs | 524.41 µs | 1.70× | 1.51× | 1.53× | 1.69× | 1.69× | 1.52× | **1.12×** | **1.11×** | 1.00× | 1.01× | **1.11×** | +| rfft Float64 64×4096 dims=2 | 2.844 ms | 3.409 ms | 2.900 ms | 2.979 ms | 3.252 ms | 3.229 ms | 3.178 ms | 1.20× | 1.02× | 1.05× | 1.14× | 1.14× | 1.12× | **1.18×** | **1.14×** | 1.05× | **1.06×** | **1.07×** | +| rfft Float64 64×16384 dims=2 | 14.476 ms | 15.495 ms | 13.164 ms | 13.565 ms | 15.195 ms | 15.030 ms | 15.131 ms | 1.07× | 0.91× | 0.94× | 1.05× | 1.04× | 1.05× | **1.18×** | **1.14×** | 1.02× | 1.03× | 1.02× | +| rfft Float64 64×65536 dims=2 | 112.823 ms | 89.254 ms | 80.816 ms | 84.407 ms | 90.000 ms | 86.841 ms | 85.863 ms | 0.79× | 0.72× | 0.75× | 0.80× | 0.77× | 0.76× | **1.10×** | **1.06×** | 0.99× | 1.03× | 1.04× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `simd`/`fftw` | `large`/`fftw` | `odd`/`fftw` | `r57`/`fftw` | `rpost`/`fftw` | `simd` vs `int` | `large` vs `int` | `odd` vs `int` | `r57` vs `int` | `rpost` vs `int` | +|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.22–4.83) | 2.27× (0.95–4.88) | 2.30× (0.97–4.98) | 2.57× (1.23–5.09) | 2.54× (1.18–5.28) | 2.55× (1.19–5.17) | **1.12×** (0.99–1.28) | **1.10×** (0.97–1.26) | **0.98×** (0.95–1.02) | **1.00×** (0.91–1.07) | **0.99×** (0.93–1.04) | +| ComplexF32 fft 3d | 4.43× (3.60–6.12) | 4.29× (3.18–6.04) | 4.34× (3.11–6.26) | 4.44× (3.51–6.25) | 4.45× (3.48–6.35) | 4.41× (3.54–6.11) | **1.03×** (0.99–1.13) | **1.02×** (0.98–1.16) | **1.00×** (0.98–1.03) | **1.00×** (0.96–1.03) | **1.00×** (1.00–1.02) | +| ComplexF32 fft batched_dim1 | 2.50× (1.98–3.61) | 1.89× (1.37–3.62) | 1.91× (1.39–3.65) | 2.49× (1.99–3.66) | 2.50× (1.97–3.67) | 2.49× (2.01–3.61) | **1.32×** (1.00–1.59) | **1.31×** (0.99–1.56) | **1.00×** (0.99–1.01) | **1.00×** (0.98–1.01) | **1.00×** (0.98–1.05) | +| ComplexF32 fft batched_dim2 | 1.84× (1.19–4.40) | 1.80× (1.25–4.40) | 1.81× (1.28–4.42) | 1.80× (1.26–4.44) | 1.78× (1.23–4.50) | 1.79× (1.23–4.43) | **1.02×** (0.90–1.33) | **1.02×** (0.91–1.30) | **1.02×** (0.93–1.27) | **1.03×** (0.94–1.27) | **1.03×** (0.93–1.27) | +| ComplexF64 fft 2d | 1.94× (1.04–4.23) | 1.80× (0.87–4.24) | 1.81× (0.87–4.21) | 1.88× (1.03–4.37) | 1.82× (1.02–4.40) | 1.94× (1.03–4.42) | **1.08×** (0.98–1.21) | **1.07×** (0.99–1.20) | **1.04×** (0.97–1.58) | **1.07×** (0.96–2.04) | **1.00×** (0.96–1.05) | +| ComplexF64 fft 3d | 2.98× (2.04–5.06) | 2.95× (1.91–5.05) | 2.97× (1.91–5.24) | 3.06× (2.05–5.28) | 3.03× (2.01–5.28) | 2.97× (1.98–5.03) | **1.01×** (0.98–1.07) | **1.00×** (0.97–1.07) | **0.97×** (0.96–1.00) | **0.98×** (0.96–1.02) | **1.00×** (0.98–1.03) | +| ComplexF64 fft batched_dim1 | 1.59× (1.23–2.30) | 1.37× (1.02–2.30) | 1.40× (1.06–2.32) | 1.59× (1.23–2.31) | 1.58× (1.21–2.32) | 1.58× (1.25–2.31) | **1.16×** (1.00–1.24) | **1.14×** (0.99–1.22) | **1.00×** (0.99–1.02) | **1.01×** (0.99–1.02) | **1.01×** (0.99–1.05) | +| ComplexF64 fft batched_dim2 | 1.46× (1.09–2.63) | 1.42× (1.07–2.63) | 1.47× (1.09–2.65) | 1.43× (1.07–2.65) | 1.42× (1.06–2.66) | 1.45× (1.08–2.63) | **1.03×** (1.00–1.04) | **0.99×** (0.98–1.00) | **1.02×** (0.99–1.05) | **1.03×** (0.99–1.06) | **1.01×** (0.97–1.05) | +| Float32 rfft 2d | 2.99× (1.78–6.92) | 2.70× (1.41–6.89) | 2.73× (1.43–7.03) | 3.02× (1.79–7.11) | 3.00× (1.78–7.14) | 2.59× (1.58–5.46) | **1.11×** (1.00–1.29) | **1.10×** (0.98–1.27) | **0.99×** (0.97–1.01) | **1.00×** (0.97–1.02) | **1.15×** (1.10–1.27) | +| Float32 rfft 3d | 4.42× (3.02–7.66) | 4.35× (2.77–7.75) | 4.39× (2.75–7.88) | 4.51× (3.06–7.95) | 4.51× (3.03–8.04) | 3.97× (2.83–6.53) | **1.01×** (0.99–1.09) | **1.01×** (0.97–1.10) | **0.98×** (0.96–0.99) | **0.98×** (0.95–1.00) | **1.11×** (1.07–1.17) | +| Float32 rfft batched_dim1 | 2.48× (2.07–2.84) | 1.96× (1.51–2.85) | 2.00× (1.55–2.88) | 2.49× (2.08–2.89) | 2.49× (2.08–2.90) | 2.06× (1.62–2.34) | **1.26×** (0.99–1.46) | **1.24×** (0.99–1.42) | **1.00×** (0.98–1.00) | **1.00×** (0.98–1.00) | **1.20×** (1.10–1.31) | +| Float32 rfft batched_dim2 | 1.67× (0.96–3.38) | 1.44× (0.80–3.39) | 1.45× (0.79–3.40) | 1.66× (0.97–3.38) | 1.66× (0.97–3.41) | 1.45× (0.90–2.62) | **1.16×** (0.99–1.24) | **1.15×** (0.99–1.22) | **1.01×** (0.99–1.02) | **1.00×** (0.98–1.01) | **1.15×** (1.06–1.29) | +| Float64 rfft 2d | 2.38× (1.06–7.92) | 2.21× (0.89–8.04) | 2.22× (0.89–8.11) | 2.28× (1.06–7.96) | 2.23× (1.05–8.08) | 2.16× (1.03–5.81) | **1.08×** (0.99–1.24) | **1.07×** (0.98–1.23) | **1.04×** (0.99–1.60) | **1.06×** (0.98–2.09) | **1.10×** (1.00–1.36) | +| Float64 rfft 3d | 3.73× (2.29–8.09) | 3.70× (2.22–8.05) | 3.74× (2.14–8.37) | 3.78× (2.25–8.34) | 3.79× (2.27–8.47) | 3.26× (2.05–6.54) | **1.01×** (1.00–1.03) | **1.00×** (0.97–1.07) | **0.99×** (0.97–1.02) | **0.98×** (0.95–1.01) | **1.15×** (1.08–1.24) | +| Float64 rfft batched_dim1 | 1.87× (1.36–2.97) | 1.65× (1.12–2.98) | 1.66× (1.15–2.99) | 1.87× (1.36–2.99) | 1.87× (1.35–2.99) | 1.64× (1.29–2.32) | **1.13×** (1.00–1.22) | **1.13×** (0.99–1.20) | **1.00×** (0.99–1.01) | **1.00×** (0.99–1.01) | **1.14×** (1.06–1.28) | +| Float64 rfft batched_dim2 | 1.48× (0.79–3.60) | 1.34× (0.72–3.62) | 1.37× (0.75–3.58) | 1.47× (0.80–3.60) | 1.46× (0.77–3.61) | 1.35× (0.76–2.89) | **1.10×** (0.99–1.18) | **1.09×** (1.00–1.14) | **1.01×** (0.99–1.05) | **1.02×** (1.00–1.06) | **1.10×** (1.02–1.25) | +| **all** | 2.30× (0.79–8.09) | 2.09× (0.72–8.05) | 2.11× (0.75–8.37) | 2.28× (0.80–8.34) | 2.26× (0.77–8.47) | 2.15× (0.76–6.54) | **1.10×** (0.90–1.59), 117 cases, 2 slower by >5% | **1.09×** (0.91–1.56), 117 cases, 1 slower by >5% | **1.01×** (0.93–1.60), 117 cases, 2 slower by >5% | **1.02×** (0.91–2.09), 117 cases, 2 slower by >5% | **1.07×** (0.93–1.36), 117 cases, 2 slower by >5% | diff --git a/benchmark/compare3/aarch64/recheck-nd-batched/fftw_t1.json b/benchmark/compare3/aarch64/recheck-nd-batched/fftw_t1.json new file mode 100644 index 0000000..df7f245 --- 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"sum_im": -665970.94, + "sum_re": 12625.125 + }, + { + "T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 2, + "exec_alloc": 0, + "exec_min": 0.059170110000000005, + "key": "rfft Float32 64×65536 dims=2", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369917.0, + "nthreads": 1, + "plan_min": 0.00012244100000000002, + "shape": "batched_dim2", + "size": [ + 64, + 65536 + ], + "sum_im": 439990.06, + "sum_re": -183525.22 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.005442462, + "key": "rfft Float64 256×4096 dims=1", + "kind": "rfft", + "measure": false, + "n": 256, + "norm": 11640.925722730331, + "nthreads": 1, + "plan_min": 1.8533333333333333e-6, + "shape": "batched_dim1", + "size": [ + 256, + 4096 + ], + "sum_im": 4845.767554722018, + "sum_re": 347.8471366990625 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.00618667, + "key": "rfft Float64 1024×1024 dims=1", + "kind": "rfft", + "measure": false, + "n": 1024, + "norm": 23213.335828584084, + "nthreads": 1, + "plan_min": 3.2666666666666666e-6, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790577, + "sum_re": -8799.055444945076 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.006752916, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113902924, + "nthreads": 1, + "plan_min": 9.820000000000001e-6, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255893, + "sum_re": -2384.3887021656265 + } + ] +} \ No newline at end of file From f14eff4af310ed33c689a486db98773e671f5860 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 12:58:07 +0000 Subject: [PATCH 11/21] benchmark: final compare3 table (FFTW vs integration/all vs integration/experiments), FFTW MEASURE sweeps, DSP.jl workloads (aarch64) --- benchmark/compare3/aarch64/final/COMPARE3.md | 579 + .../compare3/aarch64/final/DSP_WORKLOADS.md | 24 + .../compare3/aarch64/final/MEASURE_t1.md | 23 + .../compare3/aarch64/final/MEASURE_t16.md | 23 + benchmark/compare3/aarch64/final/all_t1.json | 10975 ++++++++++++++++ 5 files changed, 11624 insertions(+) create mode 100644 benchmark/compare3/aarch64/final/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/final/DSP_WORKLOADS.md create mode 100644 benchmark/compare3/aarch64/final/MEASURE_t1.md create mode 100644 benchmark/compare3/aarch64/final/MEASURE_t16.md create mode 100644 benchmark/compare3/aarch64/final/all_t1.json diff --git a/benchmark/compare3/aarch64/final/COMPARE3.md b/benchmark/compare3/aarch64/final/COMPARE3.md new file mode 100644 index 0000000..353648c --- /dev/null +++ b/benchmark/compare3/aarch64/final/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T12:50:13.269 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `all` | FFTA.jl 0.3.1 @ 2940713 — `FFTA-all` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `all` | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 24 ns | 3.19× | 0.65× | **4.93×** | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 26 ns | 0.65× | 0.71× | **0.92×** | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 161 ns | 3.52× | 3.71× | **0.95×** | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 55 ns | 0.97× | 0.99× | 0.98× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 805 ns | 5.92× | 5.92× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.51 µs | 6.55× | 6.59× | 0.99× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 160 ns | 5.29× | 1.27× | **4.16×** | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 815 ns | 2.38× | 2.38× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 820 ns | 2.12× | 2.12× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 136 ns | 1.26× | 1.30× | 0.97× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.05 µs | 2.16× | 1.25× | **1.72×** | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.06 µs | 2.22× | 1.30× | **1.71×** | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.07 µs | 2.60× | 1.53× | **1.70×** | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 989 ns | 2.80× | 3.05× | **0.92×** | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.11 µs | 7.03× | 5.13× | **1.37×** | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.11 µs | 1.57× | 0.93× | **1.68×** | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 329 ns | 1.69× | 1.69× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 2.36 µs | 1.70× | 0.98× | **1.73×** | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 2.37 µs | 3.06× | 1.77× | **1.73×** | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 2.39 µs | 2.34× | 1.35× | **1.73×** | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 2.45 µs | 2.16× | 1.26× | **1.71×** | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 1.01 µs | 6.97× | 2.80× | **2.49×** | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 2.08 µs | 7.50× | 5.30× | **1.41×** | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 408 ns | 2.03× | 1.05× | **1.94×** | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 6.39 µs | 2.32× | 1.55× | **1.50×** | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.83 µs | 2.02× | 2.02× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 5.21 µs | 1.60× | 0.87× | **1.84×** | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 964 ns | 2.27× | 1.19× | **1.90×** | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 9.39 µs | 2.26× | 1.48× | **1.53×** | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 6.60 µs | 3.96× | 2.78× | **1.42×** | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 11.82 µs | 2.19× | 1.40× | **1.56×** | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 8.93 µs | 5.80× | 3.33× | **1.74×** | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 2.04 µs | 2.50× | 1.21× | **2.07×** | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 23.40 µs | 3.00× | 1.54× | **1.96×** | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 23.12 µs | 2.53× | 1.80× | **1.40×** | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 13.38 µs | 3.57× | 2.55× | **1.40×** | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 13.88 µs | 6.51× | 2.07× | **3.14×** | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 4.69 µs | 2.59× | 1.29× | **2.01×** | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 22.04 µs | 3.47× | 2.51× | **1.38×** | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 52.36 µs | 1.75× | 0.91× | **1.92×** | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 46.08 µs | 2.04× | 1.28× | **1.60×** | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 64.08 µs | 1.45× | 0.87× | **1.66×** | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 9.89 µs | 2.74× | 1.29× | **2.13×** | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 32.48 µs | 2.98× | 2.62× | **1.14×** | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 93.96 µs | 1.43× | 0.84× | **1.70×** | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 117.08 µs | 1.42× | 0.74× | **1.92×** | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 119.36 µs | 1.38× | 0.80× | **1.73×** | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 22.72 µs | 2.77× | 1.35× | **2.05×** | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 131.00 µs | 3.31× | 2.63× | **1.26×** | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 232.80 µs | 1.58× | 1.03× | **1.53×** | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 49.92 µs | 2.14× | 1.02× | **2.08×** | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 575.53 µs | 2.49× | 1.40× | **1.78×** | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 550.85 µs | 2.58× | 1.33× | **1.93×** | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 321.60 µs | 8.66× | 3.31× | **2.62×** | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 854.01 µs | 2.47× | 1.37× | **1.80×** | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 469.85 µs | 1.31× | 0.75× | **1.76×** | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 114.48 µs | 2.09× | 1.05× | **1.99×** | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 1.121 ms | 2.44× | 1.35× | **1.81×** | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 1.290 ms | 2.08× | 1.00× | **2.08×** | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 590.45 µs | 7.14× | 2.24× | **3.19×** | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 1.904 ms | 2.58× | 1.51× | **1.70×** | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 243.00 µs | 1.85× | 0.87× | **2.11×** | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 2.845 ms | 2.70× | 1.41× | **1.91×** | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 1.560 ms | 7.03× | 2.78× | **2.53×** | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 4.274 ms | 2.66× | 1.39× | **1.91×** | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 3.132 ms | 2.29× | 1.17× | **1.96×** | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 565.97 µs | 2.20× | 1.00× | **2.19×** | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 4.593 ms | 2.33× | 1.29× | **1.81×** | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 5.588 ms | 2.63× | 1.36× | **1.93×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.352 ms | 2.38× | 2.09× | **1.14×** | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 9.496 ms | 2.71× | 1.49× | **1.82×** | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 5.691 ms | 1.47× | 0.60× | **2.43×** | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 1.362 ms | 2.14× | 1.03× | **2.08×** | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 12.194 ms | 6.41× | 2.77× | **2.31×** | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 18.240 ms | 6.35× | 2.73× | **2.32×** | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 7.239 ms | 2.82× | 2.21× | **1.28×** | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 2.423 ms | 1.83× | 0.70× | **2.62×** | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 24.069 ms | 6.51× | 2.68× | **2.42×** | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 22.735 ms | 2.55× | 1.25× | **2.04×** | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 27.105 ms | 2.28× | 0.89× | **2.56×** | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 39.925 ms | 6.71× | 2.95× | **2.28×** | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 16.376 ms | 6.65× | 2.47× | **2.69×** | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 5.105 ms | 1.11× | 0.45× | **2.48×** | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 59.323 ms | 2.89× | 1.24× | **2.34×** | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 61.693 ms | 2.17× | 0.81× | **2.70×** | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 88.704 ms | 2.73× | 1.22× | **2.23×** | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 37.645 ms | 2.75× | 2.03× | **1.35×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 39.329 ms | 4.27× | 1.61× | **2.65×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 11.260 ms | 1.69× | 0.47× | **3.62×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 119.504 ms | 2.72× | 1.22× | **2.22×** | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 103.481 ms | 6.18× | 2.74× | **2.26×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 193.346 ms | 2.69× | 1.29× | **2.09×** | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 137.259 ms | 2.18× | 0.78× | **2.78×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 91.003 ms | 5.03× | 2.25× | **2.24×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 26.972 ms | 1.05× | 0.34× | **3.05×** | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 307.184 ms | 4.59× | 2.42× | **1.90×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 60.992 ms | 1.12× | 0.37× | **3.03×** | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 28 ns | 3.19× | 1.09× | **2.91×** | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 27 ns | 0.96× | 1.07× | **0.90×** | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 164 ns | 4.63× | 4.94× | **0.94×** | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 56 ns | 1.33× | 1.38× | 0.96× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 489 ns | 3.59× | 3.60× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 901 ns | 3.91× | 3.92× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 161 ns | 3.71× | 1.16× | **3.19×** | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 884 ns | 2.57× | 2.57× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 893 ns | 2.31× | 2.32× | 0.99× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 141 ns | 1.72× | 1.77× | 0.97× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.51 µs | 2.54× | 1.95× | **1.30×** | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.51 µs | 2.16× | 1.66× | **1.30×** | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.51 µs | 2.81× | 2.17× | **1.30×** | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 1.02 µs | 3.37× | 3.71× | **0.91×** | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.16 µs | 4.40× | 3.72× | **1.18×** | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 1.56 µs | 1.46× | 1.12× | **1.30×** | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 340 ns | 1.09× | 1.10× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 3.47 µs | 1.44× | 1.14× | **1.26×** | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 3.48 µs | 2.52× | 2.00× | **1.26×** | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 3.51 µs | 1.77× | 1.41× | **1.26×** | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 3.57 µs | 1.88× | 1.51× | **1.25×** | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.08 µs | 3.21× | 1.83× | **1.76×** | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.17 µs | 4.11× | 3.42× | **1.20×** | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 575 ns | 1.24× | 0.89× | **1.40×** | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 8.72 µs | 2.05× | 1.75× | **1.17×** | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.86 µs | 1.98× | 1.99× | 0.99× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 7.51 µs | 1.50× | 1.11× | **1.35×** | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.41 µs | 1.41× | 1.07× | **1.32×** | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 12.80 µs | 1.99× | 1.64× | **1.21×** | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 7.00 µs | 2.98× | 2.47× | **1.21×** | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 16.60 µs | 1.90× | 1.59× | **1.20×** | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 9.53 µs | 3.01× | 2.22× | **1.36×** | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 2.95 µs | 1.50× | 1.04× | **1.44×** | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 34.80 µs | 1.78× | 1.27× | **1.40×** | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 30.72 µs | 2.19× | 1.94× | **1.13×** | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 14.06 µs | 3.02× | 2.49× | **1.21×** | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 14.70 µs | 3.42× | 1.43× | **2.39×** | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 6.97 µs | 1.52× | 1.11× | **1.37×** | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 23.20 µs | 2.97× | 2.50× | **1.19×** | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 81.32 µs | 1.41× | 1.05× | **1.35×** | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 65.68 µs | 1.80× | 1.48× | **1.21×** | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 88.36 µs | 1.03× | 0.81× | **1.28×** | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 14.88 µs | 1.61× | 1.10× | **1.46×** | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 38.36 µs | 1.77× | 1.71× | 1.04× | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 129.92 µs | 1.01× | 0.77× | **1.31×** | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 173.92 µs | 1.08× | 0.78× | **1.39×** | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 168.96 µs | 0.99× | 0.75× | **1.31×** | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 34.84 µs | 1.66× | 1.17× | **1.42×** | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 137.88 µs | 2.72× | 2.40× | **1.13×** | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 311.68 µs | 1.12× | 0.92× | **1.22×** | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 74.04 µs | 1.27× | 0.87× | **1.45×** | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 871.37 µs | 2.26× | 1.72× | **1.31×** | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 966.85 µs | 2.44× | 1.74× | **1.40×** | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 374.08 µs | 4.42× | 2.49× | **1.77×** | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.287 ms | 2.28× | 1.66× | **1.37×** | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 676.49 µs | 0.98× | 0.73× | **1.33×** | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 177.84 µs | 1.38× | 0.99× | **1.40×** | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 1.692 ms | 2.20× | 1.63× | **1.35×** | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 2.366 ms | 1.95× | 1.40× | **1.40×** | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 744.65 µs | 4.09× | 1.94× | **2.11×** | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 2.971 ms | 2.33× | 1.84× | **1.27×** | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 399.25 µs | 1.36× | 0.90× | **1.52×** | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 4.990 ms | 2.26× | 1.67× | **1.35×** | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 1.942 ms | 3.21× | 1.88× | **1.71×** | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 7.484 ms | 2.23× | 1.65× | **1.35×** | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 4.940 ms | 1.57× | 1.08× | **1.45×** | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 969.09 µs | 1.32× | 0.89× | **1.48×** | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 7.169 ms | 2.16× | 1.63× | **1.32×** | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 9.980 ms | 2.19× | 1.63× | **1.35×** | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.679 ms | 1.48× | 1.39× | **1.07×** | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 15.866 ms | 2.24× | 1.69× | **1.32×** | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 9.279 ms | 1.30× | 0.74× | **1.76×** | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 2.023 ms | 1.25× | 0.84× | **1.49×** | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 19.375 ms | 4.64× | 2.79× | **1.66×** | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 28.878 ms | 4.71× | 2.79× | **1.69×** | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 7.934 ms | 2.09× | 1.76× | **1.19×** | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 3.815 ms | 1.13× | 0.67× | **1.68×** | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 38.473 ms | 4.72× | 2.80× | **1.69×** | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 40.363 ms | 2.23× | 1.58× | **1.41×** | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 47.189 ms | 2.21× | 1.15× | **1.92×** | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 62.567 ms | 4.88× | 2.95× | **1.65×** | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 21.020 ms | 3.95× | 1.95× | **2.02×** | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 7.985 ms | 1.05× | 0.47× | **2.21×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 95.122 ms | 2.60× | 1.37× | **1.90×** | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 102.110 ms | 1.81× | 0.99× | **1.84×** | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 143.920 ms | 2.55× | 1.38× | **1.85×** | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 48.617 ms | 1.76× | 1.48× | **1.19×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 47.709 ms | 1.99× | 0.95× | **2.10×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 19.607 ms | 0.85× | 0.37× | **2.27×** | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 187.101 ms | 2.61× | 1.32× | **1.98×** | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 160.478 ms | 4.16× | 2.50× | **1.66×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 308.790 ms | 2.51× | 1.42× | **1.78×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 225.309 ms | 1.51× | 0.85× | **1.76×** | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 139.081 ms | 2.50× | 1.81× | **1.38×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 45.513 ms | 0.76× | 0.38× | **2.00×** | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 405.118 ms | 2.59× | 1.89× | **1.37×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 102.964 ms | 0.81× | 0.43× | **1.87×** | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 38 ns | 2.15× | 1.57× | **1.36×** | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 53 ns | 3.50× | 2.43× | **1.44×** | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 170 ns | 6.56× | 6.30× | 1.04× | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 76 ns | 3.06× | 2.32× | **1.32×** | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 180 ns | 1.33× | 1.34× | 0.99× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 316 ns | 1.55× | 1.56× | 0.99× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 162 ns | 6.56× | 2.13× | **3.09×** | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 815 ns | 2.82× | 2.83× | 1.00× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 817 ns | 2.54× | 2.56× | 0.99× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 120 ns | 1.56× | 1.18× | **1.33×** | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.04 µs | 4.21× | 2.44× | **1.73×** | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.05 µs | 3.57× | 2.07× | **1.72×** | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.06 µs | 3.28× | 1.91× | **1.72×** | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 387 ns | 2.16× | 1.81× | **1.19×** | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 844 ns | 4.81× | 3.84× | **1.25×** | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.09 µs | 1.79× | 1.05× | **1.70×** | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 221 ns | 1.62× | 1.21× | **1.34×** | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 2.33 µs | 2.95× | 1.70× | **1.74×** | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 2.34 µs | 2.81× | 1.61× | **1.74×** | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 2.36 µs | 2.43× | 1.40× | **1.73×** | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 2.39 µs | 1.53× | 0.89× | **1.73×** | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 676 ns | 5.28× | 2.35× | **2.25×** | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.32 µs | 6.42× | 4.61× | **1.39×** | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 463 ns | 2.29× | 1.75× | **1.31×** | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 2.60 µs | 2.15× | 1.23× | **1.76×** | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.83 µs | 3.24× | 3.25× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 5.08 µs | 1.71× | 0.93× | **1.85×** | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 616 ns | 2.05× | 0.97× | **2.12×** | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 9.13 µs | 1.70× | 1.09× | **1.56×** | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 4.04 µs | 4.30× | 3.07× | **1.40×** | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 7.49 µs | 2.54× | 1.74× | **1.46×** | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 5.47 µs | 6.00× | 3.57× | **1.68×** | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 1.34 µs | 2.48× | 1.18× | **2.10×** | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 23.00 µs | 2.07× | 1.05× | **1.97×** | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 10.40 µs | 2.46× | 1.60× | **1.54×** | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 7.51 µs | 3.74× | 2.61× | **1.43×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 8.96 µs | 7.81× | 2.87× | **2.72×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 2.77 µs | 2.79× | 1.26× | **2.21×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 13.16 µs | 3.87× | 2.84× | **1.36×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 51.76 µs | 1.84× | 0.95× | **1.93×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 24.80 µs | 2.27× | 1.41× | **1.61×** | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 25.96 µs | 1.36× | 0.70× | **1.95×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 6.10 µs | 2.99× | 1.37× | **2.18×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 17.20 µs | 3.15× | 2.51× | **1.25×** | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 91.96 µs | 2.20× | 1.29× | **1.71×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 114.28 µs | 1.49× | 0.76× | **1.95×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 75.08 µs | 1.59× | 1.00× | **1.59×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 12.96 µs | 3.07× | 1.38× | **2.23×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 83.96 µs | 4.04× | 3.30× | **1.23×** | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 103.96 µs | 1.55× | 0.92× | **1.69×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 28.40 µs | 2.43× | 1.11× | **2.18×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 262.20 µs | 2.41× | 1.27× | **1.91×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 539.25 µs | 3.07× | 1.56× | **1.96×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 138.76 µs | 6.61× | 2.21× | **3.00×** | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 845.97 µs | 2.93× | 1.62× | **1.81×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 251.16 µs | 1.44× | 0.82× | **1.76×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 62.12 µs | 2.51× | 1.15× | **2.19×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 620.97 µs | 2.58× | 1.49× | **1.74×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 1.297 ms | 2.71× | 1.35× | **2.01×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 572.85 µs | 8.20× | 2.91× | **2.82×** | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 899.49 µs | 2.55× | 1.43× | **1.79×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 138.56 µs | 2.49× | 1.18× | **2.10×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 1.301 ms | 2.64× | 1.29× | **2.05×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 1.482 ms | 7.40× | 3.27× | **2.26×** | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 4.196 ms | 3.17× | 1.63× | **1.94×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 3.122 ms | 2.24× | 1.15× | **1.95×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 312.68 µs | 2.65× | 1.28× | **2.07×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 2.322 ms | 2.48× | 1.36× | **1.82×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 3.047 ms | 2.83× | 1.50× | **1.89×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.158 ms | 2.72× | 2.25× | **1.21×** | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 4.436 ms | 2.78× | 1.44× | **1.93×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 5.643 ms | 1.30× | 0.53× | **2.45×** | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 718.69 µs | 2.43× | 1.17× | **2.08×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 5.685 ms | 6.24× | 2.57× | **2.43×** | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 18.076 ms | 6.79× | 2.91× | **2.33×** | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 3.414 ms | 2.73× | 2.01× | **1.36×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 1.676 ms | 2.05× | 1.00× | **2.05×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 12.973 ms | 6.64× | 2.86× | **2.32×** | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 11.504 ms | 2.68× | 1.33× | **2.01×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 26.984 ms | 2.38× | 0.85× | **2.79×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 18.945 ms | 6.62× | 2.79× | **2.37×** | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 9.137 ms | 6.03× | 2.40× | **2.51×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 3.253 ms | 1.99× | 0.86× | **2.32×** | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 27.557 ms | 3.02× | 1.15× | **2.62×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 62.354 ms | 1.84× | 0.68× | **2.70×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 89.326 ms | 2.31× | 1.00× | **2.30×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 18.739 ms | 2.94× | 2.08× | **1.41×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 20.179 ms | 6.10× | 2.32× | **2.63×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 6.895 ms | 2.12× | 0.88× | **2.41×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 62.808 ms | 2.90× | 1.31× | **2.21×** | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 50.355 ms | 6.28× | 2.70× | **2.33×** | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 91.880 ms | 2.70× | 1.25× | **2.16×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 136.412 ms | 1.50× | 0.54× | **2.77×** | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 46.286 ms | 6.20× | 2.73× | **2.27×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 15.133 ms | 2.77× | 0.92× | **3.00×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 140.623 ms | 3.39× | 1.68× | **2.01×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 32.625 ms | 1.79× | 0.63× | **2.83×** | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 37 ns | 2.17× | 1.53× | **1.41×** | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 55 ns | 3.79× | 2.56× | **1.48×** | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 169 ns | 6.78× | 6.14× | **1.10×** | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 74 ns | 3.30× | 2.29× | **1.44×** | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 195 ns | 1.40× | 1.43× | 0.98× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 342 ns | 1.65× | 1.67× | 0.99× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 165 ns | 5.67× | 2.19× | **2.59×** | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 891 ns | 3.05× | 3.07× | 0.99× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 890 ns | 2.75× | 2.75× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 124 ns | 1.86× | 1.40× | **1.33×** | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.50 µs | 4.55× | 3.49× | **1.31×** | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.50 µs | 3.83× | 2.93× | **1.31×** | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.51 µs | 3.54× | 2.71× | **1.31×** | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 402 ns | 2.83× | 2.40× | **1.18×** | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 876 ns | 5.75× | 5.13× | **1.12×** | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 1.54 µs | 1.93× | 1.47× | **1.31×** | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 240 ns | 1.87× | 1.44× | **1.29×** | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 3.45 µs | 3.16× | 2.49× | **1.27×** | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 3.46 µs | 3.01× | 2.37× | **1.27×** | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 3.50 µs | 2.59× | 2.07× | **1.25×** | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 3.53 µs | 1.64× | 1.30× | **1.26×** | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 738 ns | 4.11× | 2.48× | **1.66×** | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.42 µs | 5.09× | 4.25× | **1.20×** | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 527 ns | 1.95× | 1.61× | **1.21×** | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 3.80 µs | 1.88× | 1.46× | **1.29×** | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.85 µs | 3.05× | 3.05× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 7.44 µs | 1.77× | 1.30× | **1.36×** | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 888 ns | 1.95× | 1.28× | **1.52×** | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 12.68 µs | 1.85× | 1.51× | **1.22×** | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 4.37 µs | 3.74× | 3.11× | **1.20×** | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 10.06 µs | 2.18× | 1.88× | **1.16×** | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 5.98 µs | 3.90× | 2.94× | **1.32×** | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.00 µs | 2.00× | 1.37× | **1.46×** | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 34.52 µs | 2.18× | 1.54× | **1.41×** | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 14.24 µs | 2.09× | 1.75× | **1.20×** | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 8.08 µs | 3.44× | 2.81× | **1.23×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 9.71 µs | 4.55× | 2.16× | **2.10×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 4.14 µs | 2.02× | 1.32× | **1.52×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 14.20 µs | 3.57× | 3.01× | **1.18×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 80.48 µs | 1.95× | 1.43× | **1.36×** | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 35.20 µs | 1.94× | 1.58× | **1.23×** | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 38.28 µs | 0.96× | 0.69× | **1.40×** | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 9.39 µs | 2.07× | 1.41× | **1.47×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 20.56 µs | 2.39× | 2.11× | **1.13×** | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 128.28 µs | 2.30× | 1.74× | **1.32×** | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 171.20 µs | 1.53× | 1.09× | **1.40×** | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 101.12 µs | 1.12× | 0.89× | **1.25×** | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 19.72 µs | 2.07× | 1.36× | **1.53×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 89.04 µs | 3.35× | 3.07× | **1.09×** | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 143.28 µs | 1.09× | 0.83× | **1.30×** | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 44.48 µs | 1.69× | 1.14× | **1.49×** | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 410.85 µs | 2.13× | 1.59× | **1.34×** | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 954.85 µs | 3.64× | 2.62× | **1.39×** | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 162.56 µs | 4.31× | 2.17× | **1.98×** | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.314 ms | 3.14× | 2.39× | **1.31×** | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 362.08 µs | 1.04× | 0.79× | **1.32×** | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 96.04 µs | 1.64× | 1.11× | **1.48×** | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 934.85 µs | 2.36× | 1.79× | **1.32×** | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 2.356 ms | 2.92× | 2.08× | **1.40×** | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 677.05 µs | 6.90× | 3.37× | **2.05×** | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.323 ms | 2.24× | 1.66× | **1.35×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 231.68 µs | 1.65× | 1.18× | **1.40×** | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 2.363 ms | 2.23× | 1.59× | **1.40×** | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 1.919 ms | 6.45× | 3.98× | **1.62×** | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 7.445 ms | 3.62× | 2.66× | **1.36×** | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 4.929 ms | 2.46× | 1.70× | **1.45×** | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 546.01 µs | 1.66× | 1.17× | **1.42×** | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 3.822 ms | 2.25× | 1.74× | **1.29×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 5.278 ms | 2.32× | 1.74× | **1.33×** | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.430 ms | 1.74× | 1.54× | **1.13×** | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 7.701 ms | 2.26× | 1.67× | **1.35×** | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 9.210 ms | 1.40× | 0.81× | **1.73×** | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.318 ms | 1.57× | 1.16× | **1.36×** | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 9.242 ms | 4.50× | 2.63× | **1.71×** | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 28.900 ms | 6.41× | 3.81× | **1.68×** | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.317 ms | 2.14× | 1.86× | **1.15×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 2.643 ms | 1.49× | 1.01× | **1.47×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 20.519 ms | 4.81× | 2.93× | **1.64×** | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 20.602 ms | 2.27× | 1.61× | **1.41×** | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 44.642 ms | 2.48× | 1.24× | **2.00×** | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 29.820 ms | 4.80× | 2.84× | **1.69×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 12.021 ms | 3.59× | 2.05× | **1.75×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 5.371 ms | 1.62× | 0.93× | **1.74×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 45.525 ms | 2.50× | 1.31× | **1.91×** | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 104.894 ms | 1.70× | 0.95× | **1.79×** | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 148.470 ms | 2.82× | 1.50× | **1.88×** | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 23.443 ms | 2.55× | 1.98× | **1.28×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 24.879 ms | 2.33× | 1.16× | **2.00×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 11.621 ms | 1.68× | 0.86× | **1.95×** | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 102.950 ms | 2.89× | 1.47× | **1.96×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 81.731 ms | 4.52× | 2.70× | **1.67×** | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 143.648 ms | 2.45× | 1.34× | **1.84×** | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 226.326 ms | 1.21× | 0.69× | **1.76×** | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 67.111 ms | 2.53× | 1.74× | **1.45×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 24.613 ms | 0.91× | 0.44× | **2.06×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 186.429 ms | 2.45× | 1.65× | **1.49×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 52.493 ms | 0.85× | 0.44× | **1.92×** | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 792 ns | 4.83× | 5.50× | **0.88×** | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.63 µs | 4.36× | 4.61× | **0.95×** | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 11.02 µs | 4.01× | 4.12× | 0.97× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 49.36 µs | 3.95× | 4.00× | 0.99× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 152.96 µs | 4.14× | 2.54× | **1.63×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 753.09 µs | 1.54× | 0.98× | **1.56×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 4.416 ms | 1.27× | 0.79× | **1.61×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 20.301 ms | 1.35× | 0.81× | **1.67×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 95.217 ms | 1.19× | 0.71× | **1.67×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 808 ns | 4.15× | 4.66× | **0.89×** | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.70 µs | 3.08× | 3.30× | **0.93×** | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.60 µs | 2.76× | 2.82× | 0.98× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.76 µs | 2.58× | 2.61× | 0.99× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 200.76 µs | 2.53× | 1.82× | **1.39×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 3.157 ms | 2.27× | 1.76× | **1.29×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 2.945 ms | 1.04× | 0.80× | **1.30×** | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 3.105 ms | 1.03× | 0.81× | **1.28×** | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.215 ms | 1.29× | 1.06× | **1.21×** | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 5.815 ms | 1.23× | 0.95× | **1.29×** | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 17.498 ms | 2.97× | 2.64× | **1.12×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 42.763 ms | 3.13× | 1.54× | **2.03×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 29.031 ms | 1.23× | 0.97× | **1.28×** | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 135.133 ms | 1.11× | 0.82× | **1.34×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 757 ns | 6.92× | 6.12× | **1.13×** | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.14 µs | 5.38× | 4.89× | **1.10×** | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 7.23 µs | 3.92× | 3.53× | **1.11×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 28.16 µs | 3.26× | 2.86× | **1.14×** | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 100.68 µs | 3.02× | 2.16× | **1.40×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 339.16 µs | 1.80× | 0.97× | **1.85×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 1.483 ms | 1.96× | 1.03× | **1.91×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 6.513 ms | 2.10× | 1.08× | **1.94×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 33.685 ms | 1.79× | 0.97× | **1.85×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 760 ns | 7.84× | 6.49× | **1.21×** | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.10 µs | 5.03× | 4.28× | **1.18×** | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 7.39 µs | 3.51× | 3.08× | **1.14×** | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 29.92 µs | 2.85× | 2.54× | **1.12×** | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 115.08 µs | 2.53× | 1.98× | **1.28×** | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.034 ms | 1.73× | 1.34× | **1.29×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 2.540 ms | 2.13× | 1.57× | **1.35×** | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 1.543 ms | 1.06× | 0.80× | **1.34×** | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 470.73 µs | 1.61× | 1.15× | **1.39×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 2.109 ms | 1.58× | 1.10× | **1.43×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 8.248 ms | 3.08× | 2.62× | **1.18×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 20.513 ms | 3.21× | 1.57× | **2.04×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 9.582 ms | 1.54× | 1.10× | **1.41×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 47.947 ms | 1.22× | 0.88× | **1.39×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 10.56 µs | 6.09× | 6.83× | **0.89×** | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 69.68 µs | 4.81× | 5.18× | **0.93×** | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 603.77 µs | 4.14× | 4.26× | 0.97× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.787 ms | 3.84× | 3.88× | 0.99× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 40.267 ms | 3.44× | 2.18× | **1.58×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 10.70 µs | 4.99× | 5.62× | **0.89×** | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 70.76 µs | 3.33× | 3.55× | **0.94×** | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 652.69 µs | 2.63× | 2.70× | 0.97× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.783 ms | 2.63× | 2.73× | 0.97× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 64.011 ms | 2.03× | 1.64× | **1.24×** | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 8.65 µs | 7.70× | 7.29× | **1.06×** | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 49.24 µs | 5.58× | 5.34× | 1.05× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 345.28 µs | 4.04× | 3.80× | **1.06×** | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 2.907 ms | 3.27× | 3.05× | **1.07×** | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 20.366 ms | 3.08× | 2.17× | **1.42×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 8.72 µs | 8.09× | 7.28× | **1.11×** | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 49.36 µs | 4.70× | 4.34× | **1.08×** | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 358.56 µs | 3.33× | 3.07× | **1.09×** | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.297 ms | 2.59× | 2.43× | **1.06×** | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 25.365 ms | 2.18× | 1.71× | **1.27×** | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 23.08 µs | 3.61× | 3.70× | 0.98× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 64.40 µs | 2.37× | 1.23× | **1.92×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 320.76 µs | 2.62× | 1.31× | **2.00×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 1.582 ms | 2.56× | 1.24× | **2.07×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 8.029 ms | 2.09× | 1.03× | **2.02×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 47.743 ms | 2.01× | 1.07× | **1.87×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 24.32 µs | 2.31× | 2.36× | 0.98× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 94.84 µs | 1.48× | 1.09× | **1.36×** | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 518.85 µs | 1.60× | 1.20× | **1.33×** | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 2.552 ms | 1.71× | 1.18× | **1.45×** | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 14.141 ms | 1.39× | 0.95× | **1.46×** | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 87.591 ms | 1.29× | 0.99× | **1.30×** | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 15.00 µs | 2.85× | 2.27× | **1.26×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 40.88 µs | 2.08× | 1.00× | **2.08×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 180.96 µs | 2.77× | 1.26× | **2.20×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 846.29 µs | 2.73× | 1.23× | **2.22×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 4.074 ms | 2.38× | 1.09× | **2.18×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 20.999 ms | 2.28× | 1.10× | **2.07×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 15.96 µs | 2.98× | 2.39× | **1.25×** | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 3.964 ms | 1.86× | 1.27× | **1.46×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 58.00 µs | 1.96× | 1.30× | **1.51×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 4.607 ms | 1.85× | 1.25× | **1.47×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 275.88 µs | 1.94× | 1.29× | **1.50×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 5.327 ms | 1.89× | 1.26× | **1.50×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.322 ms | 1.90× | 1.27× | **1.49×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 6.991 ms | 1.60× | 1.14× | **1.41×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 36.664 ms | 1.35× | 0.96× | **1.40×** | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.72 µs | 4.43× | 4.52× | 0.98× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 123.60 µs | 1.92× | 1.55× | **1.24×** | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 789.29 µs | 1.97× | 1.82× | **1.08×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 4.742 ms | 1.26× | 1.01× | **1.25×** | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 24.530 ms | 1.38× | 1.01× | **1.37×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 148.931 ms | 1.19× | 0.86× | **1.37×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 29.20 µs | 2.63× | 2.69× | 0.98× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 138.84 µs | 1.53× | 1.27× | **1.20×** | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.045 ms | 1.35× | 1.18× | **1.14×** | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 6.254 ms | 1.27× | 1.17× | **1.09×** | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 38.841 ms | 1.30× | 1.14× | **1.14×** | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 234.811 ms | 1.10× | 0.95× | **1.15×** | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 17.60 µs | 3.36× | 2.67× | **1.26×** | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 62.84 µs | 1.88× | 1.08× | **1.73×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 320.92 µs | 1.88× | 1.11× | **1.69×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 1.820 ms | 1.60× | 1.02× | **1.57×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 9.391 ms | 1.22× | 0.81× | **1.51×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 50.507 ms | 1.04× | 0.74× | **1.41×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 19.36 µs | 3.55× | 2.93× | **1.21×** | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 92.80 µs | 1.71× | 1.30× | **1.32×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 438.45 µs | 1.67× | 1.26× | **1.32×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 2.579 ms | 1.20× | 0.95× | **1.27×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 11.756 ms | 1.11× | 0.83× | **1.34×** | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 74.571 ms | 0.80× | 0.67× | **1.19×** | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 1.98× (0.71–5.50) | **1.28×** (0.88–1.67) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.18× (2.18–6.83) | **1.05×** (0.89–1.58) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 1.43× (0.75–2.95) | **1.87×** (1.40–2.42) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 1.42× (1.03–3.70) | **1.76×** (0.98–2.07) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.50× (0.86–4.52) | **1.21×** (0.98–1.37) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 0.89× (0.34–1.69) | **1.93×** (0.92–3.62) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 1.29× (0.60–6.59) | **1.82×** (0.99–4.93) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 2.58× (1.27–5.30) | **1.72×** (0.92–4.16) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.61× (0.80–4.66) | **1.21×** (0.89–2.03) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 2.99× (1.64–5.62) | **0.99×** (0.89–1.24) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 1.56× (0.73–2.95) | **1.42×** (1.13–1.98) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.23× (0.95–2.36) | **1.30×** (0.98–1.46) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.31× (0.95–2.69) | **1.11×** (0.98–1.20) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 0.86× (0.37–1.77) | **1.43×** (0.90–2.27) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.45× (0.74–3.92) | **1.38×** (0.99–2.91) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.08× (0.95–4.94) | **1.40×** (0.91–3.19) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 2.07× (0.97–6.12) | **1.45×** (1.10–1.94) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 3.96× (2.17–7.29) | **1.12×** (1.05–1.42) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 1.44× (0.70–2.91) | **1.93×** (1.46–2.62) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 1.27× (1.00–2.27) | **1.96×** (1.26–2.22) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.12× (0.74–2.67) | **1.52×** (1.26–1.73) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 1.20× (0.63–2.43) | **1.98×** (1.31–3.00) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 1.26× (0.53–2.83) | **1.74×** (0.99–2.79) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 2.74× (1.68–6.30) | **1.71×** (1.00–3.09) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 1.80× (0.80–6.49) | **1.32×** (1.12–2.04) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.32× (1.71–7.28) | **1.12×** (1.06–1.27) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 1.67× (0.69–3.81) | **1.44×** (1.16–1.96) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.31× (0.96–2.39) | **1.44×** (1.25–1.51) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.17× (0.67–2.93) | **1.28×** (1.19–1.34) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.18× (0.44–2.56) | **1.51×** (1.21–2.06) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 1.71× (0.69–3.49) | **1.34×** (0.98–2.00) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 2.57× (1.16–6.14) | **1.41×** (1.00–2.59) | +| **all** | 2.45× (0.65–8.66) | 1.60× (0.34–7.29) | **1.54×** (0.88–4.93), 505 cases, 14 slower by >5% | diff --git a/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md new file mode 100644 index 0000000..a2ab3d6 --- /dev/null +++ b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md @@ -0,0 +1,24 @@ +# DSP.jl workloads, FFTW vs FFTA integration/experiments (aarch64, 1 thread, DSP.jl ffta-eval branch) + +``` +== FFTW +welch_pgram(x,1024,512) n=2^18 1.981 ms +periodogram(x) n=2^16 0.826 ms +conv(a,b) 2^16*2^12 3.507 ms +conv(512x512, 16x16) 5.062 ms +conv(64^3, 8^3) 10.857 ms +fftfilt(b257, x) n=2^18 2.589 ms +stft(x,512,256) n=2^17 1.052 ms +mt_pgram(x) n=2^14 40.45 ms +hilbert(x) n=2^17 3.735 ms +== FFTA integration/experiments +welch_pgram(x,1024,512) n=2^18 2.516 ms +periodogram(x) n=2^16 1.449 ms +conv(a,b) 2^16*2^12 4.014 ms +conv(512x512, 16x16) 7.774 ms +conv(64^3, 8^3) 26.035 ms +fftfilt(b257, x) n=2^18 3.251 ms +stft(x,512,256) n=2^17 1.343 ms +mt_pgram(x) n=2^14 40.652 ms +hilbert(x) n=2^17 6.112 ms +``` diff --git a/benchmark/compare3/aarch64/final/MEASURE_t1.md b/benchmark/compare3/aarch64/final/MEASURE_t1.md new file mode 100644 index 0000000..2003339 --- /dev/null +++ b/benchmark/compare3/aarch64/final/MEASURE_t1.md @@ -0,0 +1,23 @@ +| case (1 thread) | FFTW ESTIMATE | FFTW MEASURE | FFTA (all) | FFTA / MEASURE | +|:--|--:|--:|--:|--:| +| fft ComplexF64 1024 dims=1 | 6.30 µs | 5.30 µs | **6.95 µs** | 1.31× | +| fft ComplexF64 65536 dims=1 | 1.138 ms | 844.05 µs | **1.015 ms** | 1.20× | +| fft ComplexF64 1048576 dims=1 | 47.243 ms | 21.186 ms | **19.172 ms** | 0.90× | +| fft ComplexF32 65536 dims=1 | 576.65 µs | 463.93 µs | **563.93 µs** | 1.22× | +| fft ComplexF32 1048576 dims=1 | 25.148 ms | 14.385 ms | **11.271 ms** | 0.78× | +| fft ComplexF64 1000 dims=1 | 10.26 µs | 7.37 µs | **14.66 µs** | 1.99× | +| fft ComplexF64 1000000 dims=1 | 46.157 ms | 24.658 ms | **47.349 ms** | 1.92× | +| fft ComplexF64 65537 dims=1 | 3.358 ms | 2.679 ms | **8.967 ms** | 3.35× | +| fft ComplexF64 12297 dims=1 | 790.81 µs | 617.29 µs | **1.305 ms** | 2.11× | +| rfft Float64 4096 dims=1 | 14.54 µs | 14.48 µs | **19.76 µs** | 1.36× | +| rfft Float64 65536 dims=1 | 475.21 µs | 414.61 µs | **535.53 µs** | 1.29× | +| rfft Float64 1048576 dims=1 | 12.448 ms | 9.858 ms | **11.380 ms** | 1.15× | +| rfft Float32 65536 dims=1 | 246.76 µs | 211.00 µs | **305.04 µs** | 1.45× | +| fft ComplexF64 256×256 dims=(1, 2) | 1.281 ms | 764.05 µs | **1.227 ms** | 1.61× | +| fft ComplexF64 1024×1024 dims=(1, 2) | 31.142 ms | 17.783 ms | **30.049 ms** | 1.69× | +| rfft Float64 1024×1024 dims=(1, 2) | 8.935 ms | 7.862 ms | **9.620 ms** | 1.22× | +| fft ComplexF64 64×64×64 dims=(1, 2, 3) | 2.525 ms | 2.452 ms | **6.754 ms** | 2.75× | +| fft ComplexF64 4096×64 dims=1 | 2.182 ms | 2.046 ms | **2.614 ms** | 1.28× | +| rfft Float64 4096×64 dims=1 | 1.068 ms | 1.064 ms | **1.325 ms** | 1.24× | +| fft ComplexF64 64×4096 dims=2 | 5.692 ms | 5.170 ms | **6.366 ms** | 1.23× | +| rfft Float64 1024×1024 dims=1 | 3.540 ms | 3.533 ms | **4.604 ms** | 1.30× | diff --git a/benchmark/compare3/aarch64/final/MEASURE_t16.md b/benchmark/compare3/aarch64/final/MEASURE_t16.md new file mode 100644 index 0000000..23574c0 --- /dev/null +++ b/benchmark/compare3/aarch64/final/MEASURE_t16.md @@ -0,0 +1,23 @@ +| case (16 threads) | FFTW ESTIMATE | FFTW MEASURE | FFTA (all) | FFTA / MEASURE | +|:--|--:|--:|--:|--:| +| fft ComplexF64 1024 dims=1 | 29.20 µs | 23.32 µs | **6.95 µs** | 0.30× | +| fft ComplexF64 65536 dims=1 | 135.20 µs | 106.80 µs | **1.089 ms** | 10.19× | +| fft ComplexF64 1048576 dims=1 | 3.265 ms | 1.889 ms | **19.815 ms** | 10.49× | +| fft ComplexF32 65536 dims=1 | 77.32 µs | 85.48 µs | **583.45 µs** | 6.83× | +| fft ComplexF32 1048576 dims=1 | 1.911 ms | 1.406 ms | **11.219 ms** | 7.98× | +| fft ComplexF64 1000 dims=1 | 42.68 µs | 33.68 µs | **14.70 µs** | 0.44× | +| fft ComplexF64 1000000 dims=1 | 3.043 ms | 2.593 ms | **48.243 ms** | 18.60× | +| fft ComplexF64 65537 dims=1 | 1.540 ms | 1.611 ms | **9.102 ms** | 5.65× | +| fft ComplexF64 12297 dims=1 | 261.72 µs | 213.96 µs | **1.321 ms** | 6.17× | +| rfft Float64 4096 dims=1 | 14.52 µs | 32.08 µs | **19.80 µs** | 0.62× | +| rfft Float64 65536 dims=1 | 336.80 µs | 165.88 µs | **513.89 µs** | 3.10× | +| rfft Float64 1048576 dims=1 | 5.139 ms | 2.427 ms | **11.567 ms** | 4.77× | +| rfft Float32 65536 dims=1 | 235.88 µs | 215.84 µs | **302.52 µs** | 1.40× | +| fft ComplexF64 256×256 dims=(1, 2) | 3.116 ms | 88.28 µs | **158.72 µs** | 1.80× | +| fft ComplexF64 1024×1024 dims=(1, 2) | 2.309 ms | 1.638 ms | **3.317 ms** | 2.02× | +| rfft Float64 1024×1024 dims=(1, 2) | 2.649 ms | 715.05 µs | **771.21 µs** | 1.08× | +| fft ComplexF64 64×64×64 dims=(1, 2, 3) | 252.68 µs | 252.72 µs | **813.57 µs** | 3.22× | +| fft ComplexF64 4096×64 dims=1 | 196.28 µs | 185.60 µs | **149.20 µs** | 0.80× | +| rfft Float64 4096×64 dims=1 | 99.96 µs | 105.48 µs | **81.80 µs** | 0.78× | +| fft ComplexF64 64×4096 dims=2 | 413.01 µs | 410.72 µs | **483.93 µs** | 1.18× | +| rfft Float64 1024×1024 dims=1 | 274.04 µs | 318.36 µs | **278.72 µs** | 0.88× | diff --git a/benchmark/compare3/aarch64/final/all_t1.json 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"batched_dim1", + "size": [ + 256, + 4096 + ], + "sum_im": 4845.767554722028, + "sum_re": 347.84713669905796 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.004607414000000001, + "key": "rfft Float64 1024×1024 dims=1", + "kind": "rfft", + "measure": false, + "n": 1024, + "norm": 23213.33582858409, + "nthreads": 1, + "plan_min": 7.92e-6, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790575, + "sum_re": -8799.055444945056 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.005326982, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.401139029265, + "nthreads": 1, + "plan_min": 2.784e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255871, + "sum_re": -2384.3887021657065 + } + ] +} \ No newline at end of file From f0253bc1613b0f663a1131209bede4c108c707e1 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 13:12:31 +0000 Subject: [PATCH 12/21] benchmark: final compare3 table at 4 and 16 threads (N-d/batched) --- .../aarch64/final/COMPARE3_threads.md | 309 ++ benchmark/compare3/aarch64/final/all_t16.json | 2827 +++++++++++++++++ benchmark/compare3/aarch64/final/all_t4.json | 2827 +++++++++++++++++ 3 files changed, 5963 insertions(+) create mode 100644 benchmark/compare3/aarch64/final/COMPARE3_threads.md create mode 100644 benchmark/compare3/aarch64/final/all_t16.json create mode 100644 benchmark/compare3/aarch64/final/all_t4.json diff --git a/benchmark/compare3/aarch64/final/COMPARE3_threads.md b/benchmark/compare3/aarch64/final/COMPARE3_threads.md new file mode 100644 index 0000000..c51b318 --- /dev/null +++ b/benchmark/compare3/aarch64/final/COMPARE3_threads.md @@ -0,0 +1,309 @@ +# FFT implementations side by side + +Rendered 2026-08-30T13:09:35.311 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `all` | FFTA.jl 0.3.1 @ 2940713 — `FFTA-all` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + + +## 4 threads + +| case | `fftw` | `int` | `all` | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 (4 thr) | 8.12 µs | 741 ns | 795 ns | 0.09× | 0.10× | **0.93×** | +| fft Float32 16×16 dims=1,2 (4 thr) | 10.96 µs | 2.50 µs | 2.60 µs | 0.23× | 0.24× | 0.96× | +| fft Float32 32×32 dims=1,2 (4 thr) | 12.00 µs | 10.78 µs | 11.00 µs | 0.90× | 0.92× | 0.98× | +| fft Float32 64×64 dims=1,2 (4 thr) | 22.04 µs | 48.92 µs | 49.40 µs | 2.22× | 2.24× | 0.99× | +| fft Float32 128×128 dims=1,2 (4 thr) | 46.76 µs | 249.92 µs | 153.88 µs | 5.34× | 3.29× | **1.62×** | +| fft Float32 256×256 dims=1,2 (4 thr) | 272.32 µs | 409.93 µs | 233.52 µs | 1.51× | 0.86× | **1.76×** | +| fft Float32 512×512 dims=1,2 (4 thr) | 1.552 ms | 2.165 ms | 1.342 ms | 1.39× | 0.86× | **1.61×** | +| fft Float32 1024×1024 dims=1,2 (4 thr) | 6.759 ms | 10.641 ms | 5.999 ms | 1.57× | 0.89× | **1.77×** | +| fft Float32 2048×2048 dims=1,2 (4 thr) | 35.866 ms | 46.145 ms | 27.540 ms | 1.29× | 0.77× | **1.68×** | +| fft Float64 8×8 dims=1,2 (4 thr) | 6.56 µs | 749 ns | 803 ns | 0.11× | 0.12× | **0.93×** | +| fft Float64 16×16 dims=1,2 (4 thr) | 8.56 µs | 2.56 µs | 2.69 µs | 0.30× | 0.31× | 0.95× | +| fft Float64 32×32 dims=1,2 (4 thr) | 12.28 µs | 11.38 µs | 11.60 µs | 0.93× | 0.94× | 0.98× | +| fft Float64 64×64 dims=1,2 (4 thr) | 27.56 µs | 53.00 µs | 53.72 µs | 1.92× | 1.95× | 0.99× | +| fft Float64 128×128 dims=1,2 (4 thr) | 66.44 µs | 268.32 µs | 200.44 µs | 4.04× | 3.02× | **1.34×** | +| fft Float64 127×257 dims=1,2 (4 thr) | 518.13 µs | 4.065 ms | 3.154 ms | 7.84× | 6.09× | **1.29×** | +| fft Float64 1009×64 dims=1,2 (4 thr) | 990.73 µs | 1.188 ms | 843.05 µs | 1.20× | 0.85× | **1.41×** | +| fft Float64 64×1009 dims=1,2 (4 thr) | 1.066 ms | 1.200 ms | 889.17 µs | 1.13× | 0.83× | **1.35×** | +| fft Float64 256×256 dims=1,2 (4 thr) | 368.28 µs | 573.73 µs | 423.28 µs | 1.56× | 1.15× | **1.36×** | +| fft Float64 512×512 dims=1,2 (4 thr) | 1.700 ms | 2.608 ms | 1.847 ms | 1.53× | 1.09× | **1.41×** | +| fft Float64 720×480 dims=1,2 (4 thr) | 1.839 ms | 5.793 ms | 5.025 ms | 3.15× | 2.73× | **1.15×** | +| fft Float64 1000×1000 dims=1,2 (4 thr) | 7.247 ms | 25.438 ms | 11.782 ms | 3.51× | 1.63× | **2.16×** | +| fft Float64 1024×1024 dims=1,2 (4 thr) | 8.171 ms | 13.385 ms | 8.820 ms | 1.64× | 1.08× | **1.52×** | +| fft Float64 2048×2048 dims=1,2 (4 thr) | 45.493 ms | 56.509 ms | 41.912 ms | 1.24× | 0.92× | **1.35×** | +| rfft Float32 8×8 dims=1,2 (4 thr) | 12.60 µs | 855 ns | 738 ns | 0.07× | 0.06× | **1.16×** | +| rfft Float32 16×16 dims=1,2 (4 thr) | 16.84 µs | 2.36 µs | 2.18 µs | 0.14× | 0.13× | **1.08×** | +| rfft Float32 32×32 dims=1,2 (4 thr) | 11.80 µs | 8.04 µs | 7.16 µs | 0.68× | 0.61× | **1.12×** | +| rfft Float32 64×64 dims=1,2 (4 thr) | 22.08 µs | 32.00 µs | 28.00 µs | 1.45× | 1.27× | **1.14×** | +| rfft Float32 128×128 dims=1,2 (4 thr) | 39.16 µs | 140.48 µs | 100.44 µs | 3.59× | 2.56× | **1.40×** | +| rfft Float32 256×256 dims=1,2 (4 thr) | 130.52 µs | 216.64 µs | 105.04 µs | 1.66× | 0.80× | **2.06×** | +| rfft Float32 512×512 dims=1,2 (4 thr) | 471.53 µs | 845.77 µs | 447.29 µs | 1.79× | 0.95× | **1.89×** | +| rfft Float32 1024×1024 dims=1,2 (4 thr) | 1.652 ms | 3.454 ms | 1.778 ms | 2.09× | 1.08× | **1.94×** | +| rfft Float32 2048×2048 dims=1,2 (4 thr) | 8.433 ms | 16.652 ms | 8.446 ms | 1.97× | 1.00× | **1.97×** | +| rfft Float64 8×8 dims=1,2 (4 thr) | 12.32 µs | 920 ns | 758 ns | 0.07× | 0.06× | **1.21×** | +| rfft Float64 16×16 dims=1,2 (4 thr) | 16.84 µs | 2.44 µs | 2.09 µs | 0.14× | 0.12× | **1.16×** | +| rfft Float64 32×32 dims=1,2 (4 thr) | 12.52 µs | 8.41 µs | 7.36 µs | 0.67× | 0.59× | **1.14×** | +| rfft Float64 64×64 dims=1,2 (4 thr) | 18.40 µs | 33.60 µs | 29.92 µs | 1.83× | 1.63× | **1.12×** | +| rfft Float64 128×128 dims=1,2 (4 thr) | 44.24 µs | 147.12 µs | 114.32 µs | 3.33× | 2.58× | **1.29×** | +| rfft Float64 127×257 dims=1,2 (4 thr) | 1.393 ms | 2.604 ms | 2.029 ms | 1.87× | 1.46× | **1.28×** | +| rfft Float64 1009×64 dims=1,2 (4 thr) | 445.13 µs | 1.433 ms | 911.09 µs | 3.22× | 2.05× | **1.57×** | +| rfft Float64 64×1009 dims=1,2 (4 thr) | 614.01 µs | 673.25 µs | 512.25 µs | 1.10× | 0.83× | **1.31×** | +| rfft Float64 256×256 dims=1,2 (4 thr) | 162.76 µs | 251.08 µs | 152.84 µs | 1.54× | 0.94× | **1.64×** | +| rfft Float64 512×512 dims=1,2 (4 thr) | 576.93 µs | 978.69 µs | 629.89 µs | 1.70× | 1.09× | **1.55×** | +| rfft Float64 720×480 dims=1,2 (4 thr) | 947.77 µs | 2.608 ms | 2.263 ms | 2.75× | 2.39× | **1.15×** | +| rfft Float64 1000×1000 dims=1,2 (4 thr) | 3.509 ms | 10.887 ms | 5.432 ms | 3.10× | 1.55× | **2.00×** | +| rfft Float64 1024×1024 dims=1,2 (4 thr) | 2.389 ms | 3.975 ms | 2.559 ms | 1.66× | 1.07× | **1.55×** | +| rfft Float64 2048×2048 dims=1,2 (4 thr) | 13.961 ms | 17.797 ms | 12.450 ms | 1.27× | 0.89× | **1.43×** | +| fft Float32 8×8×8 dims=1,2,3 (4 thr) | 10.88 µs | 9.41 µs | 10.52 µs | 0.87× | 0.97× | **0.89×** | +| fft Float32 16×16×16 dims=1,2,3 (4 thr) | 21.32 µs | 64.96 µs | 69.04 µs | 3.05× | 3.24× | **0.94×** | +| fft Float32 32×32×32 dims=1,2,3 (4 thr) | 76.24 µs | 218.40 µs | 186.44 µs | 2.86× | 2.45× | **1.17×** | +| fft Float32 64×64×64 dims=1,2,3 (4 thr) | 495.17 µs | 1.856 ms | 1.699 ms | 3.75× | 3.43× | **1.09×** | +| fft Float32 128×128×128 dims=1,2,3 (4 thr) | 4.909 ms | 20.646 ms | 11.682 ms | 4.21× | 2.38× | **1.77×** | +| fft Float64 8×8×8 dims=1,2,3 (4 thr) | 10.28 µs | 9.59 µs | 10.72 µs | 0.93× | 1.04× | **0.89×** | +| fft Float64 16×16×16 dims=1,2,3 (4 thr) | 27.80 µs | 66.28 µs | 71.00 µs | 2.38× | 2.55× | **0.93×** | +| fft Float64 32×32×32 dims=1,2,3 (4 thr) | 113.64 µs | 266.12 µs | 230.36 µs | 2.34× | 2.03× | **1.16×** | +| fft Float64 64×64×64 dims=1,2,3 (4 thr) | 780.49 µs | 2.477 ms | 2.168 ms | 3.17× | 2.78× | **1.14×** | +| fft Float64 128×128×128 dims=1,2,3 (4 thr) | 10.214 ms | 24.623 ms | 17.919 ms | 2.41× | 1.75× | **1.37×** | +| rfft Float32 8×8×8 dims=1,2,3 (4 thr) | 8.92 µs | 9.17 µs | 8.56 µs | 1.03× | 0.96× | **1.07×** | +| rfft Float32 16×16×16 dims=1,2,3 (4 thr) | 14.20 µs | 51.64 µs | 48.76 µs | 3.64× | 3.43× | **1.06×** | +| rfft Float32 32×32×32 dims=1,2,3 (4 thr) | 54.48 µs | 316.00 µs | 273.76 µs | 5.80× | 5.03× | **1.15×** | +| rfft Float32 64×64×64 dims=1,2,3 (4 thr) | 344.20 µs | 948.21 µs | 820.13 µs | 2.75× | 2.38× | **1.16×** | +| rfft Float32 128×128×128 dims=1,2,3 (4 thr) | 2.545 ms | 7.717 ms | 5.423 ms | 3.03× | 2.13× | **1.42×** | +| rfft Float64 8×8×8 dims=1,2,3 (4 thr) | 11.56 µs | 9.82 µs | 8.76 µs | 0.85× | 0.76× | **1.12×** | +| rfft Float64 16×16×16 dims=1,2,3 (4 thr) | 16.04 µs | 53.88 µs | 48.44 µs | 3.36× | 3.02× | **1.11×** | +| rfft Float64 32×32×32 dims=1,2,3 (4 thr) | 70.08 µs | 371.12 µs | 305.16 µs | 5.30× | 4.35× | **1.22×** | +| rfft Float64 64×64×64 dims=1,2,3 (4 thr) | 450.25 µs | 1.081 ms | 958.77 µs | 2.40× | 2.13× | **1.13×** | +| rfft Float64 128×128×128 dims=1,2,3 (4 thr) | 3.989 ms | 9.282 ms | 7.041 ms | 2.33× | 1.76× | **1.32×** | +| fft Float32 64×64 dims=1 (4 thr) | 6.60 µs | 22.44 µs | 22.96 µs | 3.40× | 3.48× | 0.98× | +| fft Float32 256×64 dims=1 (4 thr) | 24.88 µs | 123.80 µs | 64.40 µs | 4.98× | 2.59× | **1.92×** | +| fft Float32 1024×64 dims=1 (4 thr) | 75.28 µs | 175.64 µs | 79.24 µs | 2.33× | 1.05× | **2.22×** | +| fft Float32 4096×64 dims=1 (4 thr) | 335.52 µs | 927.17 µs | 386.84 µs | 2.76× | 1.15× | **2.40×** | +| fft Float32 16384×64 dims=1 (4 thr) | 2.026 ms | 4.442 ms | 2.026 ms | 2.19× | 1.00× | **2.19×** | +| fft Float32 65536×64 dims=1 (4 thr) | 13.130 ms | 23.345 ms | 12.265 ms | 1.78× | 0.93× | **1.90×** | +| fft Float64 64×64 dims=1 (4 thr) | 7.88 µs | 23.84 µs | 24.36 µs | 3.03× | 3.09× | 0.98× | +| fft Float64 256×64 dims=1 (4 thr) | 34.64 µs | 129.56 µs | 93.88 µs | 3.74× | 2.71× | **1.38×** | +| fft Float64 1024×64 dims=1 (4 thr) | 122.56 µs | 201.72 µs | 115.28 µs | 1.65× | 0.94× | **1.75×** | +| fft Float64 4096×64 dims=1 (4 thr) | 604.41 µs | 1.071 ms | 643.05 µs | 1.77× | 1.06× | **1.67×** | +| fft Float64 16384×64 dims=1 (4 thr) | 4.058 ms | 5.895 ms | 3.562 ms | 1.45× | 0.88× | **1.65×** | +| fft Float64 65536×64 dims=1 (4 thr) | 24.343 ms | 29.335 ms | 23.072 ms | 1.21× | 0.95× | **1.27×** | +| rfft Float32 64×64 dims=1 (4 thr) | 6.80 µs | 18.80 µs | 14.76 µs | 2.76× | 2.17× | **1.27×** | +| rfft Float32 256×64 dims=1 (4 thr) | 22.44 µs | 84.28 µs | 40.44 µs | 3.76× | 1.80× | **2.08×** | +| rfft Float32 1024×64 dims=1 (4 thr) | 51.20 µs | 115.40 µs | 45.76 µs | 2.25× | 0.89× | **2.52×** | +| rfft Float32 4096×64 dims=1 (4 thr) | 173.36 µs | 495.85 µs | 210.72 µs | 2.86× | 1.22× | **2.35×** | +| rfft Float32 16384×64 dims=1 (4 thr) | 960.37 µs | 2.356 ms | 1.019 ms | 2.45× | 1.06× | **2.31×** | +| rfft Float32 65536×64 dims=1 (4 thr) | 4.945 ms | 11.572 ms | 5.188 ms | 2.34× | 1.05× | **2.23×** | +| rfft Float64 64×64 dims=1 (4 thr) | 5.84 µs | 19.90 µs | 16.00 µs | 3.41× | 2.74× | **1.24×** | +| rfft Float64 256×4096 dims=1 (4 thr) | 859.49 µs | 1.712 ms | 1.001 ms | 1.99× | 1.16× | **1.71×** | +| rfft Float64 256×64 dims=1 (4 thr) | 21.96 µs | 87.44 µs | 58.24 µs | 3.98× | 2.65× | **1.50×** | +| rfft Float64 1024×1024 dims=1 (4 thr) | 1.033 ms | 1.885 ms | 1.151 ms | 1.82× | 1.11× | **1.64×** | +| rfft Float64 1024×64 dims=1 (4 thr) | 67.96 µs | 119.92 µs | 67.96 µs | 1.76× | 1.00× | **1.76×** | +| rfft Float64 4096×256 dims=1 (4 thr) | 1.192 ms | 2.265 ms | 1.333 ms | 1.90× | 1.12× | **1.70×** | +| rfft Float64 4096×64 dims=1 (4 thr) | 292.48 µs | 521.56 µs | 325.08 µs | 1.78× | 1.11× | **1.60×** | +| rfft Float64 16384×64 dims=1 (4 thr) | 1.641 ms | 2.640 ms | 1.771 ms | 1.61× | 1.08× | **1.49×** | +| rfft Float64 65536×64 dims=1 (4 thr) | 9.900 ms | 13.358 ms | 9.252 ms | 1.35× | 0.93× | **1.44×** | +| fft Float32 64×64 dims=2 (4 thr) | 6.76 µs | 27.12 µs | 27.72 µs | 4.01× | 4.10× | 0.98× | +| fft Float32 64×256 dims=2 (4 thr) | 32.72 µs | 153.04 µs | 123.68 µs | 4.68× | 3.78× | **1.24×** | +| fft Float32 64×1024 dims=2 (4 thr) | 117.80 µs | 232.48 µs | 170.28 µs | 1.97× | 1.45× | **1.37×** | +| fft Float32 64×4096 dims=2 (4 thr) | 1.287 ms | 1.808 ms | 1.234 ms | 1.40× | 0.96× | **1.47×** | +| fft Float32 64×16384 dims=2 (4 thr) | 6.708 ms | 8.385 ms | 6.298 ms | 1.25× | 0.94× | **1.33×** | +| fft Float32 64×65536 dims=2 (4 thr) | 47.260 ms | 60.523 ms | 42.827 ms | 1.28× | 0.91× | **1.41×** | +| fft Float64 64×64 dims=2 (4 thr) | 10.12 µs | 28.56 µs | 29.16 µs | 2.82× | 2.88× | 0.98× | +| fft Float64 64×256 dims=2 (4 thr) | 40.56 µs | 162.88 µs | 141.40 µs | 4.02× | 3.49× | **1.15×** | +| fft Float64 64×1024 dims=2 (4 thr) | 248.64 µs | 386.72 µs | 258.76 µs | 1.56× | 1.04× | **1.49×** | +| fft Float64 64×4096 dims=2 (4 thr) | 1.551 ms | 2.073 ms | 1.688 ms | 1.34× | 1.09× | **1.23×** | +| fft Float64 64×16384 dims=2 (4 thr) | 8.758 ms | 12.547 ms | 9.805 ms | 1.43× | 1.12× | **1.28×** | +| fft Float64 64×65536 dims=2 (4 thr) | 66.738 ms | 72.188 ms | 63.082 ms | 1.08× | 0.95× | **1.14×** | +| rfft Float32 64×64 dims=2 (4 thr) | 6.84 µs | 22.24 µs | 17.62 µs | 3.25× | 2.58× | **1.26×** | +| rfft Float32 64×256 dims=2 (4 thr) | 26.20 µs | 107.08 µs | 63.08 µs | 4.09× | 2.41× | **1.70×** | +| rfft Float32 64×1024 dims=2 (4 thr) | 85.68 µs | 149.88 µs | 80.92 µs | 1.75× | 0.94× | **1.85×** | +| rfft Float32 64×4096 dims=2 (4 thr) | 556.49 µs | 838.01 µs | 464.97 µs | 1.51× | 0.84× | **1.80×** | +| rfft Float32 64×16384 dims=2 (4 thr) | 3.282 ms | 3.758 ms | 2.353 ms | 1.15× | 0.72× | **1.60×** | +| rfft Float32 64×65536 dims=2 (4 thr) | 20.677 ms | 19.754 ms | 12.139 ms | 0.96× | 0.59× | **1.63×** | +| rfft Float64 64×64 dims=2 (4 thr) | 5.88 µs | 23.76 µs | 19.24 µs | 4.04× | 3.27× | **1.23×** | +| rfft Float64 64×256 dims=2 (4 thr) | 30.60 µs | 122.92 µs | 93.12 µs | 4.02× | 3.04× | **1.32×** | +| rfft Float64 64×1024 dims=2 (4 thr) | 109.96 µs | 164.48 µs | 107.40 µs | 1.50× | 0.98× | **1.53×** | +| rfft Float64 64×4096 dims=2 (4 thr) | 850.13 µs | 949.77 µs | 661.85 µs | 1.12× | 0.78× | **1.44×** | +| rfft Float64 64×16384 dims=2 (4 thr) | 4.106 ms | 4.109 ms | 2.985 ms | 1.00× | 0.73× | **1.38×** | +| rfft Float64 64×65536 dims=2 (4 thr) | 30.907 ms | 24.999 ms | 20.437 ms | 0.81× | 0.66× | **1.22×** | + +### Summary (4 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 0.99× (0.09–5.34) | 0.75× (0.10–3.29) | **1.32×** (0.93–1.77) | +| ComplexF32 fft 3d | 2.60× (0.87–4.21) | 2.29× (0.97–3.43) | **1.14×** (0.89–1.77) | +| ComplexF32 fft batched_dim1 | 2.74× (1.78–4.98) | 1.47× (0.93–3.48) | **1.86×** (0.98–2.40) | +| ComplexF32 fft batched_dim2 | 2.09× (1.25–4.68) | 1.62× (0.91–4.10) | **1.29×** (0.98–1.47) | +| ComplexF64 fft 2d | 1.42× (0.11–7.84) | 1.12× (0.12–6.09) | **1.27×** (0.93–2.16) | +| ComplexF64 fft 3d | 2.09× (0.93–3.17) | 1.92× (1.04–2.78) | **1.09×** (0.89–1.37) | +| ComplexF64 fft batched_dim1 | 1.97× (1.21–3.74) | 1.38× (0.88–3.09) | **1.42×** (0.98–1.75) | +| ComplexF64 fft batched_dim2 | 1.82× (1.08–4.02) | 1.51× (0.95–3.49) | **1.20×** (0.98–1.49) | +| Float32 rfft 2d | 0.91× (0.07–3.59) | 0.61× (0.06–2.56) | **1.48×** (1.08–2.06) | +| Float32 rfft 3d | 2.83× (1.03–5.80) | 2.43× (0.96–5.03) | **1.17×** (1.06–1.42) | +| Float32 rfft batched_dim1 | 2.70× (2.25–3.76) | 1.30× (0.89–2.17) | **2.08×** (1.27–2.52) | +| Float32 rfft batched_dim2 | 1.84× (0.96–4.09) | 1.13× (0.59–2.58) | **1.63×** (1.26–1.85) | +| Float64 rfft 2d | 1.21× (0.07–3.33) | 0.88× (0.06–2.58) | **1.37×** (1.12–2.00) | +| Float64 rfft 3d | 2.43× (0.85–5.30) | 2.06× (0.76–4.35) | **1.18×** (1.11–1.32) | +| Float64 rfft batched_dim1 | 2.05× (1.35–3.98) | 1.32× (0.93–2.74) | **1.56×** (1.24–1.76) | +| Float64 rfft batched_dim2 | 1.67× (0.81–4.04) | 1.24× (0.66–3.27) | **1.35×** (1.22–1.53) | +| **all** | 1.70× (0.07–7.84) | 1.23× (0.06–6.09) | **1.38×** (0.89–2.52), 117 cases, 6 slower by >5% | + +## 16 threads + +| case | `fftw` | `int` | `all` | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 8×8 dims=1,2 (16 thr) | 15.48 µs | 704 ns | 787 ns | 0.05× | 0.05× | **0.89×** | +| fft Float32 16×16 dims=1,2 (16 thr) | 29.24 µs | 2.51 µs | 2.64 µs | 0.09× | 0.09× | **0.95×** | +| fft Float32 32×32 dims=1,2 (16 thr) | 29.92 µs | 10.80 µs | 11.00 µs | 0.36× | 0.37× | 0.98× | +| fft Float32 64×64 dims=1,2 (16 thr) | 33.04 µs | 48.60 µs | 49.40 µs | 1.47× | 1.50× | 0.98× | +| fft Float32 128×128 dims=1,2 (16 thr) | 38.00 µs | 250.28 µs | 153.88 µs | 6.59× | 4.05× | **1.63×** | +| fft Float32 256×256 dims=1,2 (16 thr) | 94.24 µs | 155.32 µs | 79.92 µs | 1.65× | 0.85× | **1.94×** | +| fft Float32 512×512 dims=1,2 (16 thr) | 463.97 µs | 800.33 µs | 476.93 µs | 1.72× | 1.03× | **1.68×** | +| fft Float32 1024×1024 dims=1,2 (16 thr) | 2.072 ms | 3.605 ms | 2.079 ms | 1.74× | 1.00× | **1.73×** | +| fft Float32 2048×2048 dims=1,2 (16 thr) | 10.643 ms | 19.557 ms | 9.454 ms | 1.84× | 0.89× | **2.07×** | +| fft Float64 8×8 dims=1,2 (16 thr) | 14.88 µs | 739 ns | 800 ns | 0.05× | 0.05× | **0.92×** | +| fft Float64 16×16 dims=1,2 (16 thr) | 29.00 µs | 2.54 µs | 2.72 µs | 0.09× | 0.09× | **0.93×** | +| fft Float64 32×32 dims=1,2 (16 thr) | 30.12 µs | 11.28 µs | 11.58 µs | 0.37× | 0.38× | 0.97× | +| fft Float64 64×64 dims=1,2 (16 thr) | 32.72 µs | 53.08 µs | 53.72 µs | 1.62× | 1.64× | 0.99× | +| fft Float64 128×128 dims=1,2 (16 thr) | 43.28 µs | 266.24 µs | 200.64 µs | 6.15× | 4.64× | **1.33×** | +| fft Float64 127×257 dims=1,2 (16 thr) | 159.12 µs | 4.083 ms | 3.157 ms | 25.66× | 19.84× | **1.29×** | +| fft Float64 1009×64 dims=1,2 (16 thr) | 280.68 µs | 478.21 µs | 267.32 µs | 1.70× | 0.95× | **1.79×** | +| fft Float64 64×1009 dims=1,2 (16 thr) | 303.56 µs | 470.21 µs | 286.92 µs | 1.55× | 0.95× | **1.64×** | +| fft Float64 256×256 dims=1,2 (16 thr) | 3.199 ms | 232.96 µs | 156.04 µs | 0.07× | 0.05× | **1.49×** | +| fft Float64 512×512 dims=1,2 (16 thr) | 504.41 µs | 1.058 ms | 773.61 µs | 2.10× | 1.53× | **1.37×** | +| fft Float64 720×480 dims=1,2 (16 thr) | 573.53 µs | 2.206 ms | 1.726 ms | 3.85× | 3.01× | **1.28×** | +| fft Float64 1000×1000 dims=1,2 (16 thr) | 7.122 ms | 10.365 ms | 4.186 ms | 1.46× | 0.59× | **2.48×** | +| fft Float64 1024×1024 dims=1,2 (16 thr) | 2.305 ms | 4.465 ms | 3.429 ms | 1.94× | 1.49× | **1.30×** | +| fft Float64 2048×2048 dims=1,2 (16 thr) | 13.913 ms | 23.948 ms | 16.851 ms | 1.72× | 1.21× | **1.42×** | +| rfft Float32 8×8 dims=1,2 (16 thr) | 13.16 µs | 855 ns | 767 ns | 0.06× | 0.06× | **1.12×** | +| rfft Float32 16×16 dims=1,2 (16 thr) | 23.32 µs | 2.36 µs | 2.14 µs | 0.10× | 0.09× | **1.10×** | +| rfft Float32 32×32 dims=1,2 (16 thr) | 31.92 µs | 8.00 µs | 7.17 µs | 0.25× | 0.22× | **1.12×** | +| rfft Float32 64×64 dims=1,2 (16 thr) | 29.56 µs | 32.00 µs | 28.08 µs | 1.08× | 0.95× | **1.14×** | +| rfft Float32 128×128 dims=1,2 (16 thr) | 45.40 µs | 140.24 µs | 100.60 µs | 3.09× | 2.22× | **1.39×** | +| rfft Float32 256×256 dims=1,2 (16 thr) | 102.80 µs | 87.16 µs | 34.36 µs | 0.85× | 0.33× | **2.54×** | +| rfft Float32 512×512 dims=1,2 (16 thr) | 171.00 µs | 263.32 µs | 130.00 µs | 1.54× | 0.76× | **2.03×** | +| rfft Float32 1024×1024 dims=1,2 (16 thr) | 554.09 µs | 1.146 ms | 566.73 µs | 2.07× | 1.02× | **2.02×** | +| rfft Float32 2048×2048 dims=1,2 (16 thr) | 2.640 ms | 4.522 ms | 2.218 ms | 1.71× | 0.84× | **2.04×** | +| rfft Float64 8×8 dims=1,2 (16 thr) | 14.04 µs | 926 ns | 758 ns | 0.07× | 0.05× | **1.22×** | +| rfft Float64 16×16 dims=1,2 (16 thr) | 24.52 µs | 2.47 µs | 2.10 µs | 0.10× | 0.09× | **1.17×** | +| rfft Float64 32×32 dims=1,2 (16 thr) | 32.48 µs | 8.48 µs | 7.29 µs | 0.26× | 0.22× | **1.16×** | +| rfft Float64 64×64 dims=1,2 (16 thr) | 29.48 µs | 33.64 µs | 29.92 µs | 1.14× | 1.01× | **1.12×** | +| rfft Float64 128×128 dims=1,2 (16 thr) | 46.24 µs | 146.56 µs | 114.64 µs | 3.17× | 2.48× | **1.28×** | +| rfft Float64 127×257 dims=1,2 (16 thr) | 1.278 ms | 2.609 ms | 2.030 ms | 2.04× | 1.59× | **1.29×** | +| rfft Float64 1009×64 dims=1,2 (16 thr) | 8.566 ms | 781.09 µs | 505.13 µs | 0.09× | 0.06× | **1.55×** | +| rfft Float64 64×1009 dims=1,2 (16 thr) | 260.40 µs | 301.32 µs | 183.36 µs | 1.16× | 0.70× | **1.64×** | +| rfft Float64 256×256 dims=1,2 (16 thr) | 4.431 ms | 95.40 µs | 48.84 µs | 0.02× | 0.01× | **1.95×** | +| rfft Float64 512×512 dims=1,2 (16 thr) | 2.825 ms | 325.12 µs | 191.48 µs | 0.12× | 0.07× | **1.70×** | +| rfft Float64 720×480 dims=1,2 (16 thr) | 307.32 µs | 819.61 µs | 590.01 µs | 2.67× | 1.92× | **1.39×** | +| rfft Float64 1000×1000 dims=1,2 (16 thr) | 1.177 ms | 3.459 ms | 1.445 ms | 2.94× | 1.23× | **2.39×** | +| rfft Float64 1024×1024 dims=1,2 (16 thr) | 2.767 ms | 1.218 ms | 771.09 µs | 0.44× | 0.28× | **1.58×** | +| rfft Float64 2048×2048 dims=1,2 (16 thr) | 4.453 ms | 5.407 ms | 3.196 ms | 1.21× | 0.72× | **1.69×** | +| fft Float32 8×8×8 dims=1,2,3 (16 thr) | 40.64 µs | 9.48 µs | 10.46 µs | 0.23× | 0.26× | **0.91×** | +| fft Float32 16×16×16 dims=1,2,3 (16 thr) | 30.72 µs | 65.12 µs | 69.24 µs | 2.12× | 2.25× | **0.94×** | +| fft Float32 32×32×32 dims=1,2,3 (16 thr) | 46.52 µs | 105.16 µs | 58.24 µs | 2.26× | 1.25× | **1.81×** | +| fft Float32 64×64×64 dims=1,2,3 (16 thr) | 166.00 µs | 723.21 µs | 559.49 µs | 4.36× | 3.37× | **1.29×** | +| fft Float32 128×128×128 dims=1,2,3 (16 thr) | 1.353 ms | 9.109 ms | 4.225 ms | 6.73× | 3.12× | **2.16×** | +| fft Float64 8×8×8 dims=1,2,3 (16 thr) | 40.36 µs | 9.68 µs | 10.76 µs | 0.24× | 0.27× | **0.90×** | +| fft Float64 16×16×16 dims=1,2,3 (16 thr) | 33.08 µs | 66.92 µs | 70.68 µs | 2.02× | 2.14× | **0.95×** | +| fft Float64 32×32×32 dims=1,2,3 (16 thr) | 53.56 µs | 134.20 µs | 73.04 µs | 2.51× | 1.36× | **1.84×** | +| fft Float64 64×64×64 dims=1,2,3 (16 thr) | 272.44 µs | 1.102 ms | 841.37 µs | 4.04× | 3.09× | **1.31×** | +| fft Float64 128×128×128 dims=1,2,3 (16 thr) | 3.038 ms | 11.653 ms | 6.828 ms | 3.84× | 2.25× | **1.71×** | +| rfft Float32 8×8×8 dims=1,2,3 (16 thr) | 54.36 µs | 9.09 µs | 8.57 µs | 0.17× | 0.16× | **1.06×** | +| rfft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.92 µs | 51.56 µs | 48.44 µs | 1.72× | 1.62× | **1.06×** | +| rfft Float32 32×32×32 dims=1,2,3 (16 thr) | 39.72 µs | 284.32 µs | 243.32 µs | 7.16× | 6.13× | **1.17×** | +| rfft Float32 64×64×64 dims=1,2,3 (16 thr) | 116.32 µs | 291.36 µs | 216.28 µs | 2.50× | 1.86× | **1.35×** | +| rfft Float32 128×128×128 dims=1,2,3 (16 thr) | 900.21 µs | 2.283 ms | 1.500 ms | 2.54× | 1.67× | **1.52×** | +| rfft Float64 8×8×8 dims=1,2,3 (16 thr) | 47.16 µs | 9.64 µs | 8.69 µs | 0.20× | 0.18× | **1.11×** | +| rfft Float64 16×16×16 dims=1,2,3 (16 thr) | 31.04 µs | 53.20 µs | 48.28 µs | 1.71× | 1.56× | **1.10×** | +| rfft Float64 32×32×32 dims=1,2,3 (16 thr) | 45.20 µs | 329.56 µs | 285.68 µs | 7.29× | 6.32× | **1.15×** | +| rfft Float64 64×64×64 dims=1,2,3 (16 thr) | 148.24 µs | 351.64 µs | 259.36 µs | 2.37× | 1.75× | **1.36×** | +| rfft Float64 128×128×128 dims=1,2,3 (16 thr) | 1.086 ms | 2.705 ms | 1.872 ms | 2.49× | 1.72× | **1.44×** | +| fft Float32 64×64 dims=1 (16 thr) | 14.64 µs | 22.48 µs | 23.04 µs | 1.54× | 1.57× | 0.98× | +| fft Float32 256×64 dims=1 (16 thr) | 21.00 µs | 123.64 µs | 64.44 µs | 5.89× | 3.07× | **1.92×** | +| fft Float32 1024×64 dims=1 (16 thr) | 35.96 µs | 67.52 µs | 21.04 µs | 1.88× | 0.59× | **3.21×** | +| fft Float32 4096×64 dims=1 (16 thr) | 120.56 µs | 281.20 µs | 95.80 µs | 2.33× | 0.79× | **2.94×** | +| fft Float32 16384×64 dims=1 (16 thr) | 571.33 µs | 1.243 ms | 489.81 µs | 2.18× | 0.86× | **2.54×** | +| fft Float32 65536×64 dims=1 (16 thr) | 3.642 ms | 6.612 ms | 3.207 ms | 1.82× | 0.88× | **2.06×** | +| fft Float64 64×64 dims=1 (16 thr) | 14.40 µs | 23.80 µs | 24.40 µs | 1.65× | 1.69× | 0.98× | +| fft Float64 256×64 dims=1 (16 thr) | 21.56 µs | 129.48 µs | 94.16 µs | 6.01× | 4.37× | **1.38×** | +| fft Float64 1024×64 dims=1 (16 thr) | 48.24 µs | 81.36 µs | 30.24 µs | 1.69× | 0.63× | **2.69×** | +| fft Float64 4096×64 dims=1 (16 thr) | 205.48 µs | 400.16 µs | 147.80 µs | 1.95× | 0.72× | **2.71×** | +| fft Float64 16384×64 dims=1 (16 thr) | 1.092 ms | 1.698 ms | 806.57 µs | 1.56× | 0.74× | **2.10×** | +| fft Float64 65536×64 dims=1 (16 thr) | 7.095 ms | 8.164 ms | 6.536 ms | 1.15× | 0.92× | **1.25×** | +| rfft Float32 64×64 dims=1 (16 thr) | 14.84 µs | 18.78 µs | 14.66 µs | 1.27× | 0.99× | **1.28×** | +| rfft Float32 256×64 dims=1 (16 thr) | 18.36 µs | 84.36 µs | 40.52 µs | 4.59× | 2.21× | **2.08×** | +| rfft Float32 1024×64 dims=1 (16 thr) | 25.64 µs | 42.68 µs | 12.80 µs | 1.66× | 0.50× | **3.33×** | +| rfft Float32 4096×64 dims=1 (16 thr) | 65.68 µs | 151.44 µs | 54.16 µs | 2.31× | 0.82× | **2.80×** | +| rfft Float32 16384×64 dims=1 (16 thr) | 289.40 µs | 737.29 µs | 253.32 µs | 2.55× | 0.88× | **2.91×** | +| rfft Float32 65536×64 dims=1 (16 thr) | 1.566 ms | 3.299 ms | 1.338 ms | 2.11× | 0.85× | **2.47×** | +| rfft Float64 64×64 dims=1 (16 thr) | 14.12 µs | 19.92 µs | 16.16 µs | 1.41× | 1.14× | **1.23×** | +| rfft Float64 256×4096 dims=1 (16 thr) | 277.44 µs | 573.17 µs | 239.84 µs | 2.07× | 0.86× | **2.39×** | +| rfft Float64 256×64 dims=1 (16 thr) | 18.56 µs | 87.60 µs | 58.04 µs | 4.72× | 3.13× | **1.51×** | +| rfft Float64 1024×1024 dims=1 (16 thr) | 311.96 µs | 556.33 µs | 278.40 µs | 1.78× | 0.89× | **2.00×** | +| rfft Float64 1024×64 dims=1 (16 thr) | 31.44 µs | 48.12 µs | 18.56 µs | 1.53× | 0.59× | **2.59×** | +| rfft Float64 4096×256 dims=1 (16 thr) | 389.16 µs | 643.57 µs | 327.20 µs | 1.65× | 0.84× | **1.97×** | +| rfft Float64 4096×64 dims=1 (16 thr) | 104.52 µs | 173.32 µs | 80.88 µs | 1.66× | 0.77× | **2.14×** | +| rfft Float64 16384×64 dims=1 (16 thr) | 567.33 µs | 712.29 µs | 435.44 µs | 1.26× | 0.77× | **1.64×** | +| rfft Float64 65536×64 dims=1 (16 thr) | 2.782 ms | 3.843 ms | 2.547 ms | 1.38× | 0.92× | **1.51×** | +| fft Float32 64×64 dims=2 (16 thr) | 15.12 µs | 27.36 µs | 27.76 µs | 1.81× | 1.84× | 0.99× | +| fft Float32 64×256 dims=2 (16 thr) | 37.40 µs | 152.60 µs | 122.80 µs | 4.08× | 3.28× | **1.24×** | +| fft Float32 64×1024 dims=2 (16 thr) | 113.12 µs | 143.16 µs | 125.08 µs | 1.27× | 1.11× | **1.14×** | +| fft Float32 64×4096 dims=2 (16 thr) | 587.65 µs | 830.81 µs | 534.41 µs | 1.41× | 0.91× | **1.55×** | +| fft Float32 64×16384 dims=2 (16 thr) | 2.501 ms | 3.213 ms | 2.456 ms | 1.28× | 0.98× | **1.31×** | +| fft Float32 64×65536 dims=2 (16 thr) | 16.053 ms | 20.963 ms | 14.848 ms | 1.31× | 0.92× | **1.41×** | +| fft Float64 64×64 dims=2 (16 thr) | 14.64 µs | 28.60 µs | 29.08 µs | 1.95× | 1.99× | 0.98× | +| fft Float64 64×256 dims=2 (16 thr) | 23.48 µs | 161.36 µs | 138.44 µs | 6.87× | 5.90× | **1.17×** | +| fft Float64 64×1024 dims=2 (16 thr) | 91.36 µs | 121.72 µs | 72.80 µs | 1.33× | 0.80× | **1.67×** | +| fft Float64 64×4096 dims=2 (16 thr) | 438.81 µs | 586.37 µs | 427.96 µs | 1.34× | 0.98× | **1.37×** | +| fft Float64 64×16384 dims=2 (16 thr) | 2.477 ms | 3.235 ms | 2.529 ms | 1.31× | 1.02× | **1.28×** | +| fft Float64 64×65536 dims=2 (16 thr) | 22.281 ms | 21.062 ms | 18.385 ms | 0.95× | 0.83× | **1.15×** | +| rfft Float32 64×64 dims=2 (16 thr) | 14.32 µs | 22.08 µs | 17.44 µs | 1.54× | 1.22× | **1.27×** | +| rfft Float32 64×256 dims=2 (16 thr) | 28.60 µs | 108.16 µs | 63.52 µs | 3.78× | 2.22× | **1.70×** | +| rfft Float32 64×1024 dims=2 (16 thr) | 71.08 µs | 68.96 µs | 38.76 µs | 0.97× | 0.55× | **1.78×** | +| rfft Float32 64×4096 dims=2 (16 thr) | 278.20 µs | 298.20 µs | 187.24 µs | 1.07× | 0.67× | **1.59×** | +| rfft Float32 64×16384 dims=2 (16 thr) | 1.232 ms | 1.247 ms | 741.77 µs | 1.01× | 0.60× | **1.68×** | +| rfft Float32 64×65536 dims=2 (16 thr) | 6.437 ms | 5.765 ms | 3.948 ms | 0.90× | 0.61× | **1.46×** | +| rfft Float64 64×64 dims=2 (16 thr) | 14.56 µs | 23.60 µs | 19.22 µs | 1.62× | 1.32× | **1.23×** | +| rfft Float64 64×256 dims=2 (16 thr) | 20.04 µs | 123.04 µs | 92.96 µs | 6.14× | 4.64× | **1.32×** | +| rfft Float64 64×1024 dims=2 (16 thr) | 45.32 µs | 59.64 µs | 31.36 µs | 1.32× | 0.69× | **1.90×** | +| rfft Float64 64×4096 dims=2 (16 thr) | 269.84 µs | 305.44 µs | 170.84 µs | 1.13× | 0.63× | **1.79×** | +| rfft Float64 64×16384 dims=2 (16 thr) | 1.282 ms | 1.261 ms | 789.33 µs | 0.98× | 0.62× | **1.60×** | +| rfft Float64 64×65536 dims=2 (16 thr) | 9.983 ms | 7.672 ms | 6.311 ms | 0.77× | 0.63× | **1.22×** | + +### Summary (16 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `all`/`fftw` | `all` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 0.79× (0.05–6.59) | 0.58× (0.05–4.05) | **1.36×** (0.89–2.07) | +| ComplexF32 fft 3d | 2.01× (0.23–6.73) | 1.50× (0.26–3.37) | **1.34×** (0.91–2.16) | +| ComplexF32 fft batched_dim1 | 2.32× (1.54–5.89) | 1.09× (0.59–3.07) | **2.13×** (0.98–3.21) | +| ComplexF32 fft batched_dim2 | 1.68× (1.27–4.08) | 1.33× (0.91–3.28) | **1.26×** (0.99–1.55) | +| ComplexF64 fft 2d | 1.09× (0.05–25.66) | 0.82× (0.05–19.84) | **1.32×** (0.92–2.48) | +| ComplexF64 fft 3d | 1.80× (0.24–4.04) | 1.40× (0.27–3.09) | **1.28×** (0.90–1.84) | +| ComplexF64 fft batched_dim1 | 1.97× (1.15–6.01) | 1.15× (0.63–4.37) | **1.72×** (0.98–2.71) | +| ComplexF64 fft batched_dim2 | 1.76× (0.95–6.87) | 1.40× (0.80–5.90) | **1.25×** (0.98–1.67) | +| Float32 rfft 2d | 0.67× (0.06–3.09) | 0.43× (0.06–2.22) | **1.53×** (1.10–2.54) | +| Float32 rfft 3d | 1.67× (0.17–7.16) | 1.37× (0.16–6.13) | **1.22×** (1.06–1.52) | +| Float32 rfft batched_dim1 | 2.22× (1.27–4.59) | 0.94× (0.50–2.21) | **2.37×** (1.28–3.33) | +| Float32 rfft batched_dim2 | 1.33× (0.90–3.78) | 0.85× (0.55–2.22) | **1.57×** (1.27–1.78) | +| Float64 rfft 2d | 0.45× (0.02–3.17) | 0.31× (0.01–2.48) | **1.48×** (1.12–2.39) | +| Float64 rfft 3d | 1.72× (0.20–7.29) | 1.40× (0.18–6.32) | **1.23×** (1.10–1.44) | +| Float64 rfft batched_dim1 | 1.78× (1.26–4.72) | 0.97× (0.59–3.13) | **1.84×** (1.23–2.59) | +| 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"measure": false, + "n": 1024, + "norm": 23213.33582858409, + "nthreads": 4, + "plan_min": 1.1200000000000001e-5, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790575, + "sum_re": -8799.055444945056 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 80, + "exec_min": 0.0013329350000000002, + "key": "rfft Float64 4096×256 dims=1 (4 thr)", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.401139029265, + "nthreads": 4, + "plan_min": 3.1641000000000004e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255871, + "sum_re": -2384.3887021657065 + } + ] +} \ No newline at end of file From 901d9e1f2a107934840196846291efef605baec3 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 13:17:39 +0000 Subject: [PATCH 13/21] benchmark: compare3 results for the real-transform pre/post-processing branch (aarch64, 1 thread, rfft cases) --- .../compare3/aarch64/rfft-post/COMPARE3.md | 579 ++ .../compare3/aarch64/rfft-post/rpost_t1.json | 5528 +++++++++++++++++ 2 files changed, 6107 insertions(+) create mode 100644 benchmark/compare3/aarch64/rfft-post/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/rfft-post/rpost_t1.json diff --git a/benchmark/compare3/aarch64/rfft-post/COMPARE3.md b/benchmark/compare3/aarch64/rfft-post/COMPARE3.md new file mode 100644 index 0000000..55de703 --- /dev/null +++ b/benchmark/compare3/aarch64/rfft-post/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T13:17:11.030 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `rpost` | FFTA.jl 0.3.1 @ a919b4f — `FFTA-rpost` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs int` is the speedup over the `int` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `rpost` | `int`/`fftw` | `rpost`/`fftw` | `rpost` vs `int` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | — | 3.19× | — | — | +| fft Float32 8 dims=1 | 37 ns | 24 ns | — | 0.65× | — | — | +| fft Float32 12 dims=1 | 43 ns | 153 ns | — | 3.52× | — | — | +| fft Float32 16 dims=1 | 55 ns | 54 ns | — | 0.97× | — | — | +| fft Float32 17 dims=1 | 136 ns | 805 ns | — | 5.92× | — | — | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | — | 6.55× | — | — | +| fft Float32 25 dims=1 | 126 ns | 667 ns | — | 5.29× | — | — | +| fft Float32 29 dims=1 | 342 ns | 814 ns | — | 2.38× | — | — | +| fft Float32 31 dims=1 | 387 ns | 820 ns | — | 2.12× | — | — | +| fft Float32 32 dims=1 | 105 ns | 132 ns | — | 1.26× | — | — | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | — | 2.16× | — | — | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | — | 2.22× | — | — | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | — | 2.60× | — | — | +| fft Float32 54 dims=1 | 325 ns | 910 ns | — | 2.80× | — | — | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | — | 7.03× | — | — | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | — | 1.57× | — | — | +| fft Float32 64 dims=1 | 194 ns | 328 ns | — | 1.69× | — | — | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | — | 1.70× | — | — | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | — | 3.06× | — | — | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | — | 2.34× | — | — | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | — | 2.16× | — | — | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | — | 6.97× | — | — | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | — | 7.50× | — | — | +| fft Float32 128 dims=1 | 390 ns | 790 ns | — | 2.03× | — | — | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | — | 2.32× | — | — | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | — | 2.02× | — | — | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | — | 1.60× | — | — | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | — | 2.27× | — | — | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | — | 2.26× | — | — | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | — | 3.96× | — | — | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | — | 2.19× | — | — | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | — | 5.80× | — | — | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | — | 2.50× | — | — | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | — | 3.00× | — | — | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | — | 2.53× | — | — | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | — | 3.57× | — | — | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | — | 6.51× | — | — | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | — | 2.59× | — | — | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | — | 3.47× | — | — | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | — | 1.75× | — | — | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | — | 2.04× | — | — | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | — | 1.45× | — | — | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | — | 2.74× | — | — | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | — | 2.98× | — | — | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | — | 1.43× | — | — | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | — | 1.42× | — | — | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | — | 1.38× | — | — | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | — | 2.77× | — | — | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | — | 3.31× | — | — | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | — | 1.58× | — | — | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | — | 2.14× | — | — | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | — | 2.49× | — | — | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | — | 2.58× | — | — | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | — | 8.66× | — | — | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | — | 2.47× | — | — | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | — | 1.31× | — | — | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | — | 2.09× | — | — | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | — | 2.44× | — | — | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | — | 2.08× | — | — | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | — | 7.14× | — | — | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | — | 2.58× | — | — | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | — | 1.85× | — | — | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | — | 2.70× | — | — | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | — | 7.03× | — | — | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | — | 2.66× | — | — | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | — | 2.29× | — | — | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | — | 2.20× | — | — | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | — | 2.33× | — | — | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | — | 2.63× | — | — | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | — | 2.38× | — | — | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | — | 2.71× | — | — | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | — | 1.47× | — | — | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | — | 2.14× | — | — | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | — | 6.41× | — | — | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | — | 6.35× | — | — | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | — | 2.82× | — | — | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | — | 1.83× | — | — | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | — | 6.51× | — | — | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | — | 2.55× | — | — | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | — | 2.28× | — | — | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | — | 6.71× | — | — | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | — | 6.65× | — | — | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | — | 1.11× | — | — | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | — | 2.89× | — | — | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | — | 2.17× | — | — | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | — | 2.73× | — | — | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | — | 2.75× | — | — | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | — | 4.27× | — | — | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | — | 1.69× | — | — | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | — | 2.72× | — | — | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | — | 6.18× | — | — | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | — | 2.69× | — | — | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | — | 2.18× | — | — | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | — | 5.03× | — | — | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | — | 1.05× | — | — | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | — | 4.59× | — | — | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | — | 1.12× | — | — | +| fft Float64 7 dims=1 | 26 ns | 82 ns | — | 3.19× | — | — | +| fft Float64 8 dims=1 | 25 ns | 24 ns | — | 0.96× | — | — | +| fft Float64 12 dims=1 | 33 ns | 154 ns | — | 4.63× | — | — | +| fft Float64 16 dims=1 | 41 ns | 54 ns | — | 1.33× | — | — | +| fft Float64 17 dims=1 | 136 ns | 488 ns | — | 3.59× | — | — | +| fft Float64 23 dims=1 | 230 ns | 899 ns | — | 3.91× | — | — | +| fft Float64 25 dims=1 | 139 ns | 514 ns | — | 3.71× | — | — | +| fft Float64 29 dims=1 | 343 ns | 884 ns | — | 2.57× | — | — | +| fft Float64 31 dims=1 | 385 ns | 888 ns | — | 2.31× | — | — | +| fft Float64 32 dims=1 | 80 ns | 137 ns | — | 1.72× | — | — | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | — | 2.54× | — | — | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | — | 2.16× | — | — | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | — | 2.81× | — | — | +| fft Float64 54 dims=1 | 274 ns | 922 ns | — | 3.37× | — | — | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | — | 4.40× | — | — | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | — | 1.46× | — | — | +| fft Float64 64 dims=1 | 310 ns | 338 ns | — | 1.09× | — | — | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | — | 1.44× | — | — | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | — | 2.52× | — | — | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | — | 1.77× | — | — | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | — | 1.88× | — | — | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | — | 3.21× | — | — | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | — | 4.11× | — | — | +| fft Float64 128 dims=1 | 647 ns | 803 ns | — | 1.24× | — | — | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | — | 2.05× | — | — | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | — | 1.98× | — | — | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | — | 1.50× | — | — | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | — | 1.41× | — | — | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | — | 1.99× | — | — | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | — | 2.98× | — | — | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | — | 1.90× | — | — | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | — | 3.01× | — | — | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | — | 1.50× | — | — | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | — | 1.78× | — | — | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | — | 2.19× | — | — | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | — | 3.02× | — | — | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | — | 3.42× | — | — | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | — | 1.52× | — | — | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | — | 2.97× | — | — | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | — | 1.41× | — | — | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | — | 1.80× | — | — | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | — | 1.03× | — | — | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | — | 1.61× | — | — | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | — | 1.77× | — | — | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | — | 1.01× | — | — | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | — | 1.08× | — | — | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | — | 0.99× | — | — | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | — | 1.66× | — | — | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | — | 2.72× | — | — | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | — | 1.12× | — | — | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | — | 1.27× | — | — | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | — | 2.26× | — | — | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | — | 2.44× | — | — | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | — | 4.42× | — | — | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | — | 2.28× | — | — | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | — | 0.98× | — | — | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | — | 1.38× | — | — | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | — | 2.20× | — | — | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | — | 1.95× | — | — | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | — | 4.09× | — | — | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | — | 2.33× | — | — | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | — | 1.36× | — | — | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | — | 2.26× | — | — | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | — | 3.21× | — | — | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | — | 2.23× | — | — | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | — | 1.57× | — | — | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | — | 1.32× | — | — | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | — | 2.16× | — | — | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | — | 2.19× | — | — | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | — | 1.48× | — | — | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | — | 2.24× | — | — | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | — | 1.30× | — | — | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | — | 1.25× | — | — | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | — | 4.64× | — | — | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | — | 4.71× | — | — | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | — | 2.09× | — | — | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | — | 1.13× | — | — | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | — | 4.72× | — | — | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | — | 2.23× | — | — | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | — | 2.21× | — | — | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | — | 4.88× | — | — | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | — | 3.95× | — | — | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | — | 1.05× | — | — | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | — | 2.60× | — | — | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | — | 1.81× | — | — | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | — | 2.55× | — | — | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | — | 1.76× | — | — | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | — | 1.99× | — | — | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | — | 0.85× | — | — | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | — | 2.61× | — | — | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | — | 4.16× | — | — | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | — | 2.51× | — | — | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | — | 1.51× | — | — | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | — | 2.50× | — | — | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | — | 0.76× | — | — | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | — | 2.59× | — | — | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | — | 0.81× | — | — | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 50 ns | 2.15× | 2.10× | 1.02× | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 48 ns | 3.50× | 2.23× | **1.57×** | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 151 ns | 6.56× | 5.59× | **1.17×** | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 71 ns | 3.06× | 2.15× | **1.42×** | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 178 ns | 1.33× | 1.33× | 1.00× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 314 ns | 1.55× | 1.55× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 501 ns | 6.56× | 6.56× | 1.00× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 808 ns | 2.82× | 2.81× | 1.00× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 811 ns | 2.54× | 2.54× | 1.00× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 116 ns | 1.56× | 1.15× | **1.36×** | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.80 µs | 4.21× | 4.21× | 1.00× | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.81 µs | 3.57× | 3.56× | 1.00× | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.81 µs | 3.28× | 3.28× | 1.00× | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 387 ns | 2.16× | 1.81× | **1.19×** | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 981 ns | 4.81× | 4.47× | **1.08×** | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.85 µs | 1.79× | 1.78× | 1.00× | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 219 ns | 1.62× | 1.20× | **1.35×** | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 4.06 µs | 2.95× | 2.95× | 1.00× | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 4.07 µs | 2.81× | 2.81× | 1.00× | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 4.07 µs | 2.43× | 2.42× | 1.00× | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 4.11 µs | 1.53× | 1.53× | 1.01× | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 1.39 µs | 5.28× | 4.83× | **1.09×** | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.71 µs | 6.42× | 5.97× | **1.08×** | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 457 ns | 2.29× | 1.73× | **1.32×** | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 4.36 µs | 2.15× | 2.05× | 1.05× | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.83 µs | 3.24× | 3.25× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 9.40 µs | 1.71× | 1.72× | 1.00× | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.02 µs | 2.05× | 1.61× | **1.28×** | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 14.22 µs | 1.70× | 1.70× | 1.00× | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 5.29 µs | 4.30× | 4.02× | **1.07×** | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 10.48 µs | 2.54× | 2.43× | 1.04× | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 8.67 µs | 6.00× | 5.66× | **1.06×** | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.24 µs | 2.48× | 1.97× | **1.26×** | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 45.44 µs | 2.07× | 2.07× | 1.00× | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 15.42 µs | 2.46× | 2.37× | 1.04× | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 9.98 µs | 3.74× | 3.47× | **1.08×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 23.12 µs | 7.81× | 7.40× | **1.06×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 5.03 µs | 2.79× | 2.29× | **1.22×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 16.80 µs | 3.87× | 3.62× | **1.07×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 99.72 µs | 1.84× | 1.84× | 1.00× | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 37.96 µs | 2.27× | 2.16× | 1.05× | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 48.40 µs | 1.36× | 1.30× | 1.05× | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 11.00 µs | 2.99× | 2.47× | **1.21×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 19.16 µs | 3.15× | 2.80× | **1.12×** | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 157.84 µs | 2.20× | 2.21× | 1.00× | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 225.68 µs | 1.49× | 1.51× | 0.99× | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 115.20 µs | 1.59× | 1.54× | 1.04× | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 24.44 µs | 3.07× | 2.60× | **1.18×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 98.24 µs | 4.04× | 3.86× | 1.05× | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 169.08 µs | 1.55× | 1.49× | 1.04× | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 53.12 µs | 2.43× | 2.08× | **1.17×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 489.57 µs | 2.41× | 2.36× | 1.02× | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 1.062 ms | 3.07× | 3.07× | 1.00× | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 403.64 µs | 6.61× | 6.42× | 1.03× | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.534 ms | 2.93× | 2.94× | 1.00× | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 424.44 µs | 1.44× | 1.38× | 1.04× | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 117.36 µs | 2.51× | 2.17× | **1.16×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 1.067 ms | 2.58× | 2.55× | 1.01× | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 2.657 ms | 2.71× | 2.76× | 0.98× | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 1.607 ms | 8.20× | 8.15× | 1.01× | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.581 ms | 2.55× | 2.50× | 1.02× | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 254.80 µs | 2.49× | 2.18× | **1.14×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 2.626 ms | 2.64× | 2.60× | 1.01× | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 3.375 ms | 7.40× | 7.44× | 0.99× | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 8.114 ms | 3.17× | 3.15× | 1.00× | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 6.157 ms | 2.24× | 2.27× | 0.99× | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 586.05 µs | 2.65× | 2.40× | **1.10×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 4.160 ms | 2.48× | 2.44× | 1.02× | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 5.640 ms | 2.83× | 2.78× | 1.02× | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.306 ms | 2.72× | 2.54× | **1.07×** | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 8.392 ms | 2.78× | 2.72× | 1.02× | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 13.757 ms | 1.30× | 1.30× | 1.00× | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.320 ms | 2.43× | 2.15× | **1.13×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 13.828 ms | 6.24× | 6.26× | 1.00× | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 42.786 ms | 6.79× | 6.89× | 0.99× | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 4.526 ms | 2.73× | 2.66× | 1.02× | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 3.130 ms | 2.05× | 1.88× | **1.10×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 29.298 ms | 6.64× | 6.46× | 1.03× | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 22.337 ms | 2.68× | 2.58× | 1.04× | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 65.313 ms | 2.38× | 2.07× | **1.15×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 43.495 ms | 6.62× | 6.40× | 1.03× | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 22.578 ms | 6.03× | 5.93× | 1.02× | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 6.998 ms | 1.99× | 1.85× | **1.08×** | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 65.114 ms | 3.02× | 2.72× | **1.11×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 155.425 ms | 1.84× | 1.70× | **1.08×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 208.109 ms | 2.31× | 2.34× | 0.99× | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 25.155 ms | 2.94× | 2.79× | **1.05×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 51.696 ms | 6.10× | 5.95× | 1.03× | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 16.245 ms | 2.12× | 2.07× | 1.02× | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 132.951 ms | 2.90× | 2.78× | 1.04× | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 116.199 ms | 6.28× | 6.22× | 1.01× | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 201.371 ms | 2.70× | 2.74× | 0.99× | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 380.086 ms | 1.50× | 1.51× | 0.99× | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 100.474 ms | 6.20× | 5.93× | 1.05× | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 43.558 ms | 2.77× | 2.66× | 1.04× | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 271.175 ms | 3.39× | 3.24× | 1.04× | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 87.074 ms | 1.79× | 1.69× | **1.06×** | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 53 ns | 2.17× | 2.20× | 0.99× | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 49 ns | 3.79× | 2.26× | **1.68×** | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 150 ns | 6.78× | 5.45× | **1.24×** | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 69 ns | 3.30× | 2.16× | **1.53×** | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 192 ns | 1.40× | 1.41× | 1.00× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 341 ns | 1.65× | 1.66× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 437 ns | 5.67× | 5.81× | 0.98× | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 884 ns | 3.05× | 3.05× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 889 ns | 2.75× | 2.75× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 119 ns | 1.86× | 1.34× | **1.39×** | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.96 µs | 4.55× | 4.55× | 1.00× | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.96 µs | 3.83× | 3.83× | 1.00× | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.99 µs | 3.54× | 3.57× | 0.99× | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 405 ns | 2.83× | 2.42× | **1.17×** | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 912 ns | 5.75× | 5.33× | **1.08×** | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 2.00 µs | 1.93× | 1.91× | 1.01× | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 238 ns | 1.87× | 1.43× | **1.30×** | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 4.39 µs | 3.16× | 3.17× | 1.00× | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 4.38 µs | 3.01× | 3.01× | 1.00× | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.39 µs | 2.59× | 2.59× | 1.00× | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.44 µs | 1.64× | 1.64× | 1.00× | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 1.12 µs | 4.11× | 3.75× | **1.10×** | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.58 µs | 5.09× | 4.74× | **1.07×** | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 516 ns | 1.95× | 1.58× | **1.23×** | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.69 µs | 1.88× | 1.80× | 1.04× | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.86 µs | 3.05× | 3.06× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 10.10 µs | 1.77× | 1.77× | 1.00× | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.13 µs | 1.95× | 1.63× | **1.20×** | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 15.30 µs | 1.85× | 1.82× | 1.01× | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 5.02 µs | 3.74× | 3.58× | 1.05× | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 11.32 µs | 2.18× | 2.11× | 1.03× | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 7.55 µs | 3.90× | 3.71× | 1.05× | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.52 µs | 2.00× | 1.73× | **1.16×** | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 48.44 µs | 2.18× | 2.17× | 1.00× | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 16.72 µs | 2.09× | 2.05× | 1.02× | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 9.41 µs | 3.44× | 3.27× | **1.05×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 19.56 µs | 4.55× | 4.36× | 1.04× | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 5.59 µs | 2.02× | 1.79× | **1.13×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 15.98 µs | 3.57× | 3.39× | **1.05×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 108.84 µs | 1.95× | 1.94× | 1.00× | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 42.00 µs | 1.94× | 1.89× | 1.03× | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 52.12 µs | 0.96× | 0.94× | 1.03× | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 12.32 µs | 2.07× | 1.84× | **1.12×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 21.60 µs | 2.39× | 2.21× | **1.08×** | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 168.72 µs | 2.30× | 2.29× | 1.00× | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 240.20 µs | 1.53× | 1.53× | 1.00× | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 124.20 µs | 1.12× | 1.09× | 1.02× | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 27.12 µs | 2.07× | 1.87× | **1.11×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 93.92 µs | 3.35× | 3.23× | 1.04× | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 182.00 µs | 1.09× | 1.06× | 1.03× | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 60.00 µs | 1.69× | 1.53× | **1.10×** | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 565.57 µs | 2.13× | 2.19× | 0.97× | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.370 ms | 3.64× | 3.76× | 0.97× | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 312.88 µs | 4.31× | 4.19× | 1.03× | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.721 ms | 3.14× | 3.13× | 1.00× | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 465.85 µs | 1.04× | 1.01× | 1.03× | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 129.48 µs | 1.64× | 1.49× | **1.10×** | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.233 ms | 2.36× | 2.35× | 1.00× | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 3.312 ms | 2.92× | 2.92× | 1.00× | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 1.380 ms | 6.90× | 6.87× | 1.00× | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.891 ms | 2.24× | 2.38× | **0.94×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 307.92 µs | 1.65× | 1.57× | 1.05× | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 3.337 ms | 2.23× | 2.24× | 0.99× | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 3.136 ms | 6.45× | 6.50× | 0.99× | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 10.249 ms | 3.62× | 3.67× | 0.99× | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 7.011 ms | 2.46× | 2.41× | 1.02× | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 728.93 µs | 1.66× | 1.56× | **1.07×** | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 5.640 ms | 2.25× | 2.57× | **0.88×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 7.116 ms | 2.32× | 2.35× | 0.99× | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.547 ms | 1.74× | 1.67× | 1.04× | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 10.519 ms | 2.26× | 2.28× | 0.99× | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 15.766 ms | 1.40× | 1.39× | 1.01× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.688 ms | 1.57× | 1.48× | **1.06×** | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 16.085 ms | 4.50× | 4.58× | 0.98× | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 49.014 ms | 6.41× | 6.46× | 0.99× | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.879 ms | 2.14× | 2.10× | 1.02× | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.596 ms | 1.49× | 1.38× | **1.08×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 34.042 ms | 4.81× | 4.86× | 0.99× | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 28.629 ms | 2.27× | 2.24× | 1.02× | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 89.692 ms | 2.48× | 2.49× | 1.00× | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 50.443 ms | 4.80× | 4.80× | 1.00× | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 19.799 ms | 3.59× | 3.38× | **1.06×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 9.565 ms | 1.62× | 1.66× | 0.97× | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 91.096 ms | 2.50× | 2.62× | 0.96× | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 189.069 ms | 1.70× | 1.71× | 1.00× | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 278.676 ms | 2.82× | 2.82× | 1.00× | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 27.980 ms | 2.55× | 2.37× | **1.08×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 48.450 ms | 2.33× | 2.27× | 1.03× | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 22.495 ms | 1.68× | 1.67× | 1.01× | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 180.955 ms | 2.89× | 2.59× | **1.12×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 134.852 ms | 4.52× | 4.46× | 1.01× | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 276.310 ms | 2.45× | 2.57× | 0.95× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 400.435 ms | 1.21× | 1.21× | 1.00× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 93.102 ms | 2.53× | 2.42× | 1.05× | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 49.978 ms | 0.91× | 0.90× | 1.01× | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 264.449 ms | 2.45× | 2.34× | 1.05× | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 99.170 ms | 0.85× | 0.84× | 1.01× | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | — | 4.83× | — | — | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | — | 4.36× | — | — | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | — | 4.01× | — | — | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | — | 3.95× | — | — | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | — | 4.14× | — | — | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | — | 1.54× | — | — | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | — | 1.27× | — | — | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | — | 1.35× | — | — | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | — | 1.19× | — | — | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | — | 4.15× | — | — | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | — | 3.08× | — | — | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | — | 2.76× | — | — | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | — | 2.58× | — | — | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | — | 2.53× | — | — | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | — | 2.27× | — | — | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | — | 1.04× | — | — | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | — | 1.03× | — | — | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | — | 1.29× | — | — | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | — | 1.23× | — | — | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | — | 2.97× | — | — | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | — | 3.13× | — | — | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | — | 1.23× | — | — | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | — | 1.11× | — | — | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 671 ns | 6.92× | 5.43× | **1.27×** | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 1.96 µs | 5.38× | 4.48× | **1.20×** | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 6.87 µs | 3.92× | 3.35× | **1.17×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 27.68 µs | 3.26× | 2.81× | **1.16×** | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 122.96 µs | 3.02× | 2.63× | **1.15×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 551.49 µs | 1.80× | 1.58× | **1.14×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.539 ms | 1.96× | 1.76× | **1.11×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 11.705 ms | 2.10× | 1.95× | **1.08×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 60.006 ms | 1.79× | 1.73× | 1.04× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 671 ns | 7.84× | 5.73× | **1.37×** | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 1.91 µs | 5.03× | 3.89× | **1.29×** | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 7.01 µs | 3.51× | 2.92× | **1.20×** | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 29.24 µs | 2.85× | 2.49× | **1.15×** | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 132.00 µs | 2.53× | 2.27× | **1.12×** | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.616 ms | 1.73× | 1.73× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 3.505 ms | 2.13× | 2.17× | 0.98× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 1.993 ms | 1.06× | 1.03× | 1.03× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 601.41 µs | 1.61× | 1.47× | **1.09×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 2.820 ms | 1.58× | 1.47× | **1.07×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 10.699 ms | 3.08× | 3.40× | **0.91×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 45.080 ms | 3.21× | 3.45× | **0.93×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 13.280 ms | 1.54× | 1.52× | 1.02× | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 66.411 ms | 1.22× | 1.22× | 1.00× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | — | 6.09× | — | — | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | — | 4.81× | — | — | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | — | 4.14× | — | — | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | — | 3.84× | — | — | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | — | 3.44× | — | — | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | — | 4.99× | — | — | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | — | 3.33× | — | — | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | — | 2.63× | — | — | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | — | 2.63× | — | — | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | — | 2.03× | — | — | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 7.65 µs | 7.70× | 6.44× | **1.20×** | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 45.80 µs | 5.58× | 4.96× | **1.12×** | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 330.92 µs | 4.04× | 3.64× | **1.11×** | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 2.873 ms | 3.27× | 3.01× | **1.08×** | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 26.833 ms | 3.08× | 2.86× | **1.07×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 7.75 µs | 8.09× | 6.47× | **1.25×** | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 44.40 µs | 4.70× | 3.90× | **1.20×** | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 344.72 µs | 3.33× | 2.95× | **1.13×** | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.307 ms | 2.59× | 2.44× | **1.06×** | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 33.318 ms | 2.18× | 2.25× | 0.97× | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | — | 3.61× | — | — | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | — | 2.37× | — | — | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | — | 2.62× | — | — | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | — | 2.56× | — | — | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | — | 2.09× | — | — | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | — | 2.01× | — | — | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | — | 2.31× | — | — | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | — | 1.48× | — | — | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | — | 1.60× | — | — | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | — | 1.71× | — | — | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | — | 1.39× | — | — | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | — | 1.29× | — | — | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 15.00 µs | 2.85× | 2.27× | **1.26×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 67.08 µs | 2.08× | 1.64× | **1.26×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 327.00 µs | 2.77× | 2.27× | **1.22×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.601 ms | 2.73× | 2.32× | **1.18×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 7.955 ms | 2.38× | 2.14× | **1.12×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 38.662 ms | 2.28× | 2.03× | **1.12×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 15.58 µs | 2.98× | 2.33× | **1.28×** | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.007 ms | 1.86× | 1.61× | **1.16×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 73.84 µs | 1.96× | 1.66× | **1.18×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.353 ms | 1.85× | 1.73× | **1.07×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 364.76 µs | 1.94× | 1.71× | **1.14×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 7.621 ms | 1.89× | 1.80× | **1.05×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.770 ms | 1.90× | 1.70× | **1.12×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 9.089 ms | 1.60× | 1.48× | **1.08×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 46.990 ms | 1.35× | 1.24× | **1.09×** | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | — | 4.43× | — | — | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | — | 1.92× | — | — | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | — | 1.97× | — | — | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | — | 1.26× | — | — | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | — | 1.38× | — | — | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | — | 1.19× | — | — | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | — | 2.63× | — | — | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | — | 1.53× | — | — | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | — | 1.35× | — | — | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | — | 1.27× | — | — | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | — | 1.30× | — | — | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | — | 1.10× | — | — | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 17.30 µs | 3.36× | 2.62× | **1.28×** | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 89.60 µs | 1.88× | 1.55× | **1.21×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 468.17 µs | 1.88× | 1.62× | **1.16×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.563 ms | 1.60× | 1.44× | **1.12×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 13.039 ms | 1.22× | 1.12× | **1.09×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 68.256 ms | 1.04× | 1.00× | 1.05× | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 18.94 µs | 3.55× | 2.86× | **1.24×** | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 108.64 µs | 1.71× | 1.52× | **1.13×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 523.05 µs | 1.67× | 1.50× | **1.11×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 3.046 ms | 1.20× | 1.12× | **1.07×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 15.511 ms | 1.11× | 1.10× | 1.01× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 88.471 ms | 0.80× | 0.79× | 1.01× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `rpost`/`fftw` | `rpost` vs `int` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | — | — | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | — | — | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | — | — | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | — | — | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | — | — | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | — | — | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | — | — | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | — | — | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | — | — | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | — | — | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | — | — | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | — | — | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | — | — | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | — | — | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | — | — | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | — | — | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 2.61× (1.58–5.43) | **1.14×** (1.04–1.27) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 3.98× (2.86–6.44) | **1.12×** (1.07–1.20) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 2.71× (1.30–6.89) | **1.02×** (0.99–1.11) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 2.10× (1.64–2.32) | **1.19×** (1.12–1.26) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.48× (1.00–2.62) | **1.15×** (1.05–1.28) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 1.98× (1.15–2.66) | **1.20×** (1.02–1.57) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 2.16× (1.30–4.21) | **1.01×** (0.98–1.15) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 4.42× (1.81–8.15) | **1.06×** (0.99–1.19) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.21× (1.03–5.73) | **1.08×** (0.91–1.37) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.33× (2.25–6.47) | **1.12×** (0.97–1.25) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 2.39× (0.94–6.46) | **1.00×** (0.88–1.12) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.67× (1.24–2.33) | **1.13×** (1.05–1.28) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.36× (0.79–2.86) | **1.09×** (1.01–1.24) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.55× (0.84–2.26) | **1.15×** (0.97–1.68) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 2.29× (1.21–4.55) | **1.00×** (0.97–1.02) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 3.43× (1.67–6.87) | 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"shape": "batched_dim2", + "size": [ + 64, + 65536 + ], + "sum_im": 258630.07144466156, + "sum_re": 36466.32996170409 + }, + { + "T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.03866236, + "key": "rfft Float32 65536×64 dims=1", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369855.03, + "nthreads": 1, + "plan_min": 0.000340484, + "shape": "batched_dim1", + "size": [ + 65536, + 64 + ], + "sum_im": -665970.6, + "sum_re": 12625.125 + }, + { + "T": "Float32", + "api": "mul!", + "class": "nd", + "dims": 2, + "exec_alloc": 0, + "exec_min": 0.068255937, + "key": "rfft Float32 64×65536 dims=2", + "kind": "rfft", + "measure": false, + "n": 65536, + "norm": 369916.9, + "nthreads": 1, + "plan_min": 0.000339444, + "shape": "batched_dim2", + "size": [ + 64, + 65536 + ], + "sum_im": 439989.88, + "sum_re": -183525.22 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.005007457, + "key": "rfft Float64 256×4096 dims=1", + "kind": "rfft", + "measure": false, + "n": 256, + "norm": 11640.925722730333, + "nthreads": 1, + "plan_min": 2.8800000000000004e-6, + "shape": "batched_dim1", + "size": [ + 256, + 4096 + ], + "sum_im": 4845.767554722022, + "sum_re": 347.84713669905705 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.006353432, + "key": "rfft Float64 1024×1024 dims=1", + "kind": "rfft", + "measure": false, + "n": 1024, + "norm": 23213.33582858409, + "nthreads": 1, + "plan_min": 7.9e-6, + "shape": "batched_dim1", + "size": [ + 1024, + 1024 + ], + "sum_im": -4329.462276790569, + "sum_re": -8799.055444945068 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.007620687, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113902927, + "nthreads": 1, + "plan_min": 2.788e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255871, + "sum_re": -2384.3887021656883 + } + ] +} \ No newline at end of file From 868693621cf989146626ce07d0a3332701a8bc1a Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 13:33:58 +0000 Subject: [PATCH 14/21] benchmark: compare3 results for the lockstep SIMD codelets (aarch64, 1 thread) --- .../aarch64/simd-codelets/COMPARE3.md | 580 + .../compare3/aarch64/simd-codelets/sc_t1.json | 10975 ++++++++++++++++ 2 files changed, 11555 insertions(+) create mode 100644 benchmark/compare3/aarch64/simd-codelets/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/simd-codelets/sc_t1.json diff --git a/benchmark/compare3/aarch64/simd-codelets/COMPARE3.md b/benchmark/compare3/aarch64/simd-codelets/COMPARE3.md new file mode 100644 index 0000000..c01cf92 --- /dev/null +++ b/benchmark/compare3/aarch64/simd-codelets/COMPARE3.md @@ -0,0 +1,580 @@ +# FFT implementations side by side + +Rendered 2026-08-30T13:33:16.862 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `int` | FFTA.jl 0.3.1 @ 901692b — `FFTA.jl` | +| `large` | FFTA.jl 0.3.1 @ 605c9c3 — `FFTA-large` | +| `sc` | FFTA.jl 0.3.1 @ 0d4f433 — `FFTA-sc` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs large` is the speedup over the `large` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `int` | `large` | `sc` | `int`/`fftw` | `large`/`fftw` | `sc`/`fftw` | `int` vs `large` | `sc` vs `large` | +|:--|--:|--:|--:|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 120 ns | 118 ns | 120 ns | 3.19× | 3.15× | 3.20× | 0.99× | 0.98× | +| fft Float32 8 dims=1 | 37 ns | 24 ns | 26 ns | 26 ns | 0.65× | 0.70× | 0.70× | **1.07×** | 0.99× | +| fft Float32 12 dims=1 | 43 ns | 153 ns | 157 ns | 157 ns | 3.52× | 3.61× | 3.61× | 1.03× | 1.00× | +| fft Float32 16 dims=1 | 55 ns | 54 ns | 54 ns | 54 ns | 0.97× | 0.97× | 0.98× | 1.00× | 0.99× | +| fft Float32 17 dims=1 | 136 ns | 805 ns | 807 ns | 809 ns | 5.92× | 5.94× | 5.95× | 1.00× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.50 µs | 1.51 µs | 1.51 µs | 6.55× | 6.57× | 6.58× | 1.00× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 667 ns | 667 ns | 667 ns | 5.29× | 5.29× | 5.29× | 1.00× | 1.00× | +| fft Float32 29 dims=1 | 342 ns | 814 ns | 816 ns | 814 ns | 2.38× | 2.38× | 2.38× | 1.00× | 1.00× | +| fft Float32 31 dims=1 | 387 ns | 820 ns | 818 ns | 819 ns | 2.12× | 2.11× | 2.12× | 1.00× | 1.00× | +| fft Float32 32 dims=1 | 105 ns | 132 ns | 134 ns | 135 ns | 1.26× | 1.28× | 1.29× | 1.02× | 0.99× | +| fft Float32 37 dims=1 | 836 ns | 1.81 µs | 1.48 µs | 1.05 µs | 2.16× | 1.77× | 1.25× | **0.82×** | **1.41×** | +| fft Float32 41 dims=1 | 817 ns | 1.81 µs | 1.50 µs | 1.06 µs | 2.22× | 1.83× | 1.30× | **0.82×** | **1.41×** | +| fft Float32 43 dims=1 | 699 ns | 1.82 µs | 1.50 µs | 1.06 µs | 2.60× | 2.14× | 1.52× | **0.82×** | **1.41×** | +| fft Float32 54 dims=1 | 325 ns | 910 ns | 962 ns | 964 ns | 2.80× | 2.96× | 2.97× | **1.06×** | 1.00× | +| fft Float32 60 dims=1 | 217 ns | 1.52 µs | 1.56 µs | 1.55 µs | 7.03× | 7.20× | 7.14× | 1.02× | 1.01× | +| fft Float32 61 dims=1 | 1.19 µs | 1.87 µs | 1.55 µs | 1.11 µs | 1.57× | 1.30× | 0.93× | **0.83×** | **1.40×** | +| fft Float32 64 dims=1 | 194 ns | 328 ns | 327 ns | 326 ns | 1.69× | 1.68× | 1.68× | 1.00× | 1.00× | +| fft Float32 71 dims=1 | 2.40 µs | 4.09 µs | 3.45 µs | 2.37 µs | 1.70× | 1.44× | 0.99× | **0.84×** | **1.46×** | +| fft Float32 73 dims=1 | 1.34 µs | 4.11 µs | 3.47 µs | 2.37 µs | 3.06× | 2.58× | 1.77× | **0.84×** | **1.46×** | +| fft Float32 79 dims=1 | 1.76 µs | 4.13 µs | 3.47 µs | 2.39 µs | 2.34× | 1.97× | 1.35× | **0.84×** | **1.46×** | +| fft Float32 101 dims=1 | 1.94 µs | 4.18 µs | 3.53 µs | 2.45 µs | 2.16× | 1.83× | 1.27× | **0.84×** | **1.44×** | +| fft Float32 112 dims=1 | 360 ns | 2.51 µs | 2.53 µs | 2.52 µs | 6.97× | 7.03× | 6.99× | 1.01× | 1.01× | +| fft Float32 120 dims=1 | 392 ns | 2.94 µs | 3.01 µs | 2.96 µs | 7.50× | 7.67× | 7.54× | 1.02× | 1.02× | +| fft Float32 128 dims=1 | 390 ns | 790 ns | 625 ns | 408 ns | 2.03× | 1.60× | 1.05× | **0.79×** | **1.53×** | +| fft Float32 202 dims=1 | 4.13 µs | 9.57 µs | 8.44 µs | 6.29 µs | 2.32× | 2.04× | 1.52× | **0.88×** | **1.34×** | +| fft Float32 243 dims=1 | 1.90 µs | 3.83 µs | 3.83 µs | 3.84 µs | 2.02× | 2.02× | 2.02× | 1.00× | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 9.57 µs | 7.01 µs | 5.25 µs | 1.60× | 1.17× | 0.88× | **0.73×** | **1.34×** | +| fft Float32 256 dims=1 | 807 ns | 1.83 µs | 1.51 µs | 962 ns | 2.27× | 1.87× | 1.19× | **0.82×** | **1.57×** | +| fft Float32 303 dims=1 | 6.36 µs | 14.40 µs | 12.54 µs | 9.24 µs | 2.26× | 1.97× | 1.45× | **0.87×** | **1.36×** | +| fft Float32 360 dims=1 | 2.37 µs | 9.40 µs | 9.45 µs | 9.40 µs | 3.96× | 3.98× | 3.96× | 1.01× | 1.01× | +| fft Float32 404 dims=1 | 8.45 µs | 18.48 µs | 16.08 µs | 11.76 µs | 2.19× | 1.90× | 1.39× | **0.87×** | **1.37×** | +| fft Float32 504 dims=1 | 2.69 µs | 15.58 µs | 15.72 µs | 15.72 µs | 5.80× | 5.85× | 5.85× | 1.01× | 1.00× | +| fft Float32 512 dims=1 | 1.69 µs | 4.22 µs | 2.93 µs | 2.04 µs | 2.50× | 1.74× | 1.21× | **0.70×** | **1.44×** | +| fft Float32 593 dims=1 | 15.24 µs | 45.76 µs | 30.44 µs | 23.36 µs | 3.00× | 2.00× | 1.53× | **0.67×** | **1.30×** | +| fft Float32 606 dims=1 | 12.82 µs | 32.40 µs | 29.12 µs | 22.60 µs | 2.53× | 2.27× | 1.76× | **0.90×** | **1.29×** | +| fft Float32 720 dims=1 | 5.25 µs | 18.74 µs | 18.82 µs | 18.80 µs | 3.57× | 3.58× | 3.58× | 1.00× | 1.00× | +| fft Float32 1000 dims=1 | 6.69 µs | 43.56 µs | 43.20 µs | 43.44 µs | 6.51× | 6.45× | 6.49× | 0.99× | 0.99× | +| fft Float32 1024 dims=1 | 3.64 µs | 9.44 µs | 6.91 µs | 4.69 µs | 2.59× | 1.90× | 1.29× | **0.73×** | **1.47×** | +| fft Float32 1080 dims=1 | 8.77 µs | 30.40 µs | 30.68 µs | 30.40 µs | 3.47× | 3.50× | 3.47× | 1.01× | 1.01× | +| fft Float32 1433 dims=1 | 57.64 µs | 100.76 µs | 70.16 µs | 52.60 µs | 1.75× | 1.22× | 0.91× | **0.70×** | **1.33×** | +| fft Float32 1616 dims=1 | 36.12 µs | 73.60 µs | 63.40 µs | 46.04 µs | 2.04× | 1.76× | 1.27× | **0.86×** | **1.38×** | +| fft Float32 2018 dims=1 | 73.28 µs | 106.24 µs | 77.08 µs | 62.96 µs | 1.45× | 1.05× | 0.86× | **0.73×** | **1.22×** | +| fft Float32 2048 dims=1 | 7.68 µs | 21.04 µs | 13.42 µs | 9.86 µs | 2.74× | 1.75× | 1.28× | **0.64×** | **1.36×** | +| fft Float32 2304 dims=1 | 12.42 µs | 37.04 µs | 37.16 µs | 32.32 µs | 2.98× | 2.99× | 2.60× | 1.00× | **1.15×** | +| fft Float32 3027 dims=1 | 112.08 µs | 160.12 µs | 114.04 µs | 92.96 µs | 1.43× | 1.02× | 0.83× | **0.71×** | **1.23×** | +| fft Float32 3491 dims=1 | 158.56 µs | 224.96 µs | 143.64 µs | 116.60 µs | 1.42× | 0.91× | 0.74× | **0.64×** | **1.23×** | +| fft Float32 4036 dims=1 | 149.00 µs | 206.28 µs | 146.24 µs | 117.92 µs | 1.38× | 0.98× | 0.79× | **0.71×** | **1.24×** | +| fft Float32 4096 dims=1 | 16.88 µs | 46.68 µs | 31.32 µs | 22.60 µs | 2.77× | 1.86× | 1.34× | **0.67×** | **1.39×** | +| fft Float32 4860 dims=1 | 49.84 µs | 164.92 µs | 167.20 µs | 167.52 µs | 3.31× | 3.35× | 3.36× | 1.01× | 1.00× | +| fft Float32 6054 dims=1 | 225.88 µs | 355.84 µs | 269.12 µs | 227.84 µs | 1.58× | 1.19× | 1.01× | **0.76×** | **1.18×** | +| fft Float32 8192 dims=1 | 48.72 µs | 104.04 µs | 63.60 µs | 49.88 µs | 2.14× | 1.31× | 1.02× | **0.61×** | **1.28×** | +| fft Float32 8198 dims=1 | 411.25 µs | 1.025 ms | 699.01 µs | 646.85 µs | 2.49× | 1.70× | 1.57× | **0.68×** | **1.08×** | +| fft Float32 8443 dims=1 | 413.05 µs | 1.066 ms | 657.41 µs | 545.57 µs | 2.58× | 1.59× | 1.32× | **0.62×** | **1.21×** | +| fft Float32 10290 dims=1 | 97.28 µs | 842.69 µs | 849.05 µs | 850.25 µs | 8.66× | 8.73× | 8.74× | 1.01× | 1.00× | +| fft Float32 12297 dims=1 | 624.25 µs | 1.540 ms | 1.044 ms | 849.89 µs | 2.47× | 1.67× | 1.36× | **0.68×** | **1.23×** | +| fft Float32 16144 dims=1 | 629.25 µs | 824.97 µs | 581.25 µs | 468.17 µs | 1.31× | 0.92× | 0.74× | **0.70×** | **1.24×** | +| fft Float32 16384 dims=1 | 109.16 µs | 228.16 µs | 146.72 µs | 114.56 µs | 2.09× | 1.34× | 1.05× | **0.64×** | **1.28×** | +| fft Float32 16396 dims=1 | 831.89 µs | 2.028 ms | 1.365 ms | 1.120 ms | 2.44× | 1.64× | 1.35× | **0.67×** | **1.22×** | +| fft Float32 20507 dims=1 | 1.290 ms | 2.677 ms | 1.834 ms | 1.316 ms | 2.08× | 1.42× | 1.02× | **0.68×** | **1.39×** | +| fft Float32 21875 dims=1 | 264.12 µs | 1.885 ms | 1.886 ms | 1.893 ms | 7.14× | 7.14× | 7.17× | 1.00× | 1.00× | +| fft Float32 24594 dims=1 | 1.260 ms | 3.246 ms | 2.281 ms | 1.892 ms | 2.58× | 1.81× | 1.50× | **0.70×** | **1.21×** | +| fft Float32 32768 dims=1 | 278.20 µs | 513.45 µs | 292.96 µs | 242.72 µs | 1.85× | 1.05× | 0.87× | **0.57×** | **1.21×** | +| fft Float32 32822 dims=1 | 2.015 ms | 5.448 ms | 3.884 ms | 2.857 ms | 2.70× | 1.93× | 1.42× | **0.71×** | **1.36×** | +| fft Float32 46305 dims=1 | 560.49 µs | 3.942 ms | 3.988 ms | 4.007 ms | 7.03× | 7.11× | 7.15× | 1.01× | 1.00× | +| fft Float32 49233 dims=1 | 3.073 ms | 8.161 ms | 5.872 ms | 4.280 ms | 2.66× | 1.91× | 1.39× | **0.72×** | **1.37×** | +| fft Float32 49757 dims=1 | 2.680 ms | 6.136 ms | 4.063 ms | 3.260 ms | 2.29× | 1.52× | 1.22× | **0.66×** | **1.25×** | +| fft Float32 65536 dims=1 | 563.53 µs | 1.239 ms | 838.09 µs | 557.61 µs | 2.20× | 1.49× | 0.99× | **0.68×** | **1.50×** | +| fft Float32 65584 dims=1 | 3.557 ms | 8.304 ms | 5.644 ms | 4.838 ms | 2.33× | 1.59× | 1.36× | **0.68×** | **1.17×** | +| fft Float32 65644 dims=1 | 4.107 ms | 10.813 ms | 7.601 ms | 5.587 ms | 2.63× | 1.85× | 1.36× | **0.70×** | **1.36×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.676 ms | 2.612 ms | 2.367 ms | 2.38× | 2.32× | 2.10× | 0.98× | **1.10×** | +| fft Float32 98466 dims=1 | 6.367 ms | 17.251 ms | 12.305 ms | 9.471 ms | 2.71× | 1.93× | 1.49× | **0.71×** | **1.30×** | +| fft Float32 120779 dims=1 | 9.432 ms | 13.839 ms | 6.872 ms | 5.770 ms | 1.47× | 0.73× | 0.61× | **0.50×** | **1.19×** | +| fft Float32 131072 dims=1 | 1.322 ms | 2.828 ms | 1.867 ms | 1.362 ms | 2.14× | 1.41× | 1.03× | **0.66×** | **1.37×** | +| fft Float32 131074 dims=1 | 4.394 ms | 28.158 ms | 14.580 ms | 12.322 ms | 6.41× | 3.32× | 2.80× | **0.52×** | **1.18×** | +| fft Float32 196611 dims=1 | 6.678 ms | 42.398 ms | 21.757 ms | 18.517 ms | 6.35× | 3.26× | 2.77× | **0.51×** | **1.17×** | +| fft Float32 207360 dims=1 | 3.276 ms | 9.246 ms | 9.168 ms | 9.036 ms | 2.82× | 2.80× | 2.76× | 0.99× | 1.01× | +| fft Float32 262144 dims=1 | 3.482 ms | 6.358 ms | 2.995 ms | 2.419 ms | 1.83× | 0.86× | 0.69× | **0.47×** | **1.24×** | +| fft Float32 262148 dims=1 | 8.965 ms | 58.332 ms | 28.633 ms | 24.217 ms | 6.51× | 3.19× | 2.70× | **0.49×** | **1.18×** | +| fft Float32 262576 dims=1 | 18.216 ms | 46.404 ms | 30.738 ms | 22.815 ms | 2.55× | 1.69× | 1.25× | **0.66×** | **1.35×** | +| fft Float32 293201 dims=1 | 30.534 ms | 69.516 ms | 31.362 ms | 27.277 ms | 2.28× | 1.03× | 0.89× | **0.45×** | **1.15×** | +| fft Float32 393222 dims=1 | 13.552 ms | 90.905 ms | 47.219 ms | 39.893 ms | 6.71× | 3.48× | 2.94× | **0.52×** | **1.18×** | +| fft Float32 441000 dims=1 | 6.625 ms | 44.051 ms | 43.330 ms | 43.448 ms | 6.65× | 6.54× | 6.56× | 0.98× | 1.00× | +| fft Float32 524288 dims=1 | 11.364 ms | 12.639 ms | 6.105 ms | 5.109 ms | 1.11× | 0.54× | 0.45× | **0.48×** | **1.19×** | +| fft Float32 524294 dims=1 | 47.952 ms | 138.558 ms | 66.269 ms | 59.750 ms | 2.89× | 1.38× | 1.25× | **0.48×** | **1.11×** | +| fft Float32 711749 dims=1 | 76.629 ms | 166.553 ms | 66.578 ms | 64.097 ms | 2.17× | 0.87× | 0.84× | **0.40×** | 1.04× | +| fft Float32 786441 dims=1 | 72.471 ms | 197.644 ms | 99.818 ms | 89.962 ms | 2.73× | 1.38× | 1.24× | **0.51×** | **1.11×** | +| fft Float32 933120 dims=1 | 18.504 ms | 50.926 ms | 53.268 ms | 48.866 ms | 2.75× | 2.88× | 2.64× | 1.05× | **1.09×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 104.327 ms | 103.887 ms | 103.534 ms | 4.27× | 4.25× | 4.24× | 1.00× | 1.00× | +| fft Float32 1048576 dims=1 | 24.149 ms | 40.752 ms | 14.397 ms | 11.400 ms | 1.69× | 0.60× | 0.47× | **0.35×** | **1.26×** | +| fft Float32 1048588 dims=1 | 97.647 ms | 265.431 ms | 134.785 ms | 119.480 ms | 2.72× | 1.38× | 1.22× | **0.51×** | **1.13×** | +| fft Float32 1048592 dims=1 | 37.789 ms | 233.614 ms | 122.301 ms | 104.286 ms | 6.18× | 3.24× | 2.76× | **0.52×** | **1.17×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 404.776 ms | 212.281 ms | 195.572 ms | 2.69× | 1.41× | 1.30× | **0.52×** | **1.09×** | +| fft Float32 1727797 dims=1 | 174.941 ms | 381.490 ms | 146.465 ms | 137.569 ms | 2.18× | 0.84× | 0.79× | **0.38×** | **1.06×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 203.408 ms | 200.447 ms | 201.446 ms | 5.03× | 4.95× | 4.98× | 0.99× | 1.00× | +| fft Float32 2097152 dims=1 | 78.580 ms | 82.298 ms | 31.041 ms | 27.107 ms | 1.05× | 0.40× | 0.34× | **0.38×** | **1.15×** | +| fft Float32 4167450 dims=1 | 126.844 ms | 582.126 ms | 581.606 ms | 583.157 ms | 4.59× | 4.59× | 4.60× | 1.00× | 1.00× | +| fft Float32 4194304 dims=1 | 164.711 ms | 184.687 ms | 67.705 ms | 61.384 ms | 1.12× | 0.41× | 0.37× | **0.37×** | **1.10×** | +| fft Float64 7 dims=1 | 26 ns | 82 ns | 83 ns | 83 ns | 3.19× | 3.21× | 3.22× | 1.01× | 1.00× | +| fft Float64 8 dims=1 | 25 ns | 24 ns | 26 ns | 26 ns | 0.96× | 1.06× | 1.06× | **1.10×** | 1.00× | +| fft Float64 12 dims=1 | 33 ns | 154 ns | 162 ns | 163 ns | 4.63× | 4.88× | 4.89× | **1.05×** | 1.00× | +| fft Float64 16 dims=1 | 41 ns | 54 ns | 56 ns | 56 ns | 1.33× | 1.36× | 1.38× | 1.02× | 0.99× | +| fft Float64 17 dims=1 | 136 ns | 488 ns | 489 ns | 490 ns | 3.59× | 3.60× | 3.61× | 1.00× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 899 ns | 901 ns | 901 ns | 3.91× | 3.92× | 3.92× | 1.00× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 514 ns | 518 ns | 516 ns | 3.71× | 3.74× | 3.72× | 1.01× | 1.00× | +| fft Float64 29 dims=1 | 343 ns | 884 ns | 890 ns | 890 ns | 2.57× | 2.59× | 2.59× | 1.01× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 888 ns | 896 ns | 894 ns | 2.31× | 2.33× | 2.32× | 1.01× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 137 ns | 139 ns | 140 ns | 1.72× | 1.75× | 1.76× | 1.01× | 0.99× | +| fft Float64 37 dims=1 | 771 ns | 1.96 µs | 1.76 µs | 1.50 µs | 2.54× | 2.29× | 1.95× | **0.90×** | **1.17×** | +| fft Float64 41 dims=1 | 910 ns | 1.96 µs | 1.77 µs | 1.51 µs | 2.16× | 1.95× | 1.66× | **0.90×** | **1.17×** | +| fft Float64 43 dims=1 | 699 ns | 1.97 µs | 1.77 µs | 1.51 µs | 2.81× | 2.54× | 2.17× | **0.90×** | **1.17×** | +| fft Float64 54 dims=1 | 274 ns | 922 ns | 979 ns | 987 ns | 3.37× | 3.58× | 3.61× | **1.06×** | 0.99× | +| fft Float64 60 dims=1 | 311 ns | 1.37 µs | 1.40 µs | 1.40 µs | 4.40× | 4.49× | 4.49× | 1.02× | 1.00× | +| fft Float64 61 dims=1 | 1.39 µs | 2.02 µs | 1.84 µs | 1.56 µs | 1.46× | 1.33× | 1.13× | **0.91×** | **1.18×** | +| fft Float64 64 dims=1 | 310 ns | 338 ns | 339 ns | 340 ns | 1.09× | 1.09× | 1.10× | 1.00× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 4.39 µs | 4.01 µs | 3.49 µs | 1.44× | 1.31× | 1.14× | **0.91×** | **1.15×** | +| fft Float64 73 dims=1 | 1.74 µs | 4.39 µs | 4.02 µs | 3.49 µs | 2.52× | 2.31× | 2.00× | **0.91×** | **1.15×** | +| fft Float64 79 dims=1 | 2.50 µs | 4.42 µs | 4.03 µs | 3.50 µs | 1.77× | 1.62× | 1.40× | **0.91×** | **1.15×** | +| fft Float64 101 dims=1 | 2.37 µs | 4.46 µs | 4.09 µs | 3.55 µs | 1.88× | 1.73× | 1.50× | **0.92×** | **1.15×** | +| fft Float64 112 dims=1 | 591 ns | 1.90 µs | 1.91 µs | 1.93 µs | 3.21× | 3.24× | 3.27× | 1.01× | 0.99× | +| fft Float64 120 dims=1 | 634 ns | 2.60 µs | 2.68 µs | 2.67 µs | 4.11× | 4.23× | 4.20× | 1.03× | 1.01× | +| fft Float64 128 dims=1 | 647 ns | 803 ns | 707 ns | 579 ns | 1.24× | 1.09× | 0.89× | **0.88×** | **1.22×** | +| fft Float64 202 dims=1 | 4.97 µs | 10.18 µs | 9.68 µs | 8.69 µs | 2.05× | 1.95× | 1.75× | 0.95× | **1.11×** | +| fft Float64 243 dims=1 | 1.94 µs | 3.84 µs | 3.85 µs | 3.87 µs | 1.98× | 1.98× | 1.99× | 1.00× | 0.99× | +| fft Float64 251 dims=1 | 6.73 µs | 10.12 µs | 8.56 µs | 7.52 µs | 1.50× | 1.27× | 1.12× | **0.85×** | **1.14×** | +| fft Float64 256 dims=1 | 1.32 µs | 1.86 µs | 1.67 µs | 1.41 µs | 1.41× | 1.27× | 1.07× | **0.90×** | **1.19×** | +| fft Float64 303 dims=1 | 7.79 µs | 15.52 µs | 14.30 µs | 12.74 µs | 1.99× | 1.84× | 1.64× | **0.92×** | **1.12×** | +| fft Float64 360 dims=1 | 2.83 µs | 8.45 µs | 8.63 µs | 8.55 µs | 2.98× | 3.04× | 3.02× | 1.02× | 1.01× | +| fft Float64 404 dims=1 | 10.46 µs | 19.92 µs | 18.54 µs | 16.48 µs | 1.90× | 1.77× | 1.58× | **0.93×** | **1.12×** | +| fft Float64 504 dims=1 | 4.30 µs | 12.92 µs | 13.28 µs | 13.30 µs | 3.01× | 3.09× | 3.10× | 1.03× | 1.00× | +| fft Float64 512 dims=1 | 2.83 µs | 4.25 µs | 3.48 µs | 2.95 µs | 1.50× | 1.23× | 1.04× | **0.82×** | **1.18×** | +| fft Float64 593 dims=1 | 27.48 µs | 48.80 µs | 39.24 µs | 34.80 µs | 1.78× | 1.43× | 1.27× | **0.80×** | **1.13×** | +| fft Float64 606 dims=1 | 15.84 µs | 34.72 µs | 33.40 µs | 29.96 µs | 2.19× | 2.11× | 1.89× | 0.96× | **1.11×** | +| fft Float64 720 dims=1 | 5.64 µs | 17.02 µs | 17.44 µs | 17.18 µs | 3.02× | 3.09× | 3.05× | 1.02× | 1.02× | +| fft Float64 1000 dims=1 | 10.26 µs | 35.12 µs | 36.44 µs | 35.92 µs | 3.42× | 3.55× | 3.50× | 1.04× | 1.01× | +| fft Float64 1024 dims=1 | 6.30 µs | 9.55 µs | 8.01 µs | 6.96 µs | 1.52× | 1.27× | 1.10× | **0.84×** | **1.15×** | +| fft Float64 1080 dims=1 | 9.27 µs | 27.52 µs | 27.92 µs | 28.08 µs | 2.97× | 3.01× | 3.03× | 1.01× | 0.99× | +| fft Float64 1433 dims=1 | 77.40 µs | 109.44 µs | 90.12 µs | 81.08 µs | 1.41× | 1.16× | 1.05× | **0.82×** | **1.11×** | +| fft Float64 1616 dims=1 | 44.28 µs | 79.76 µs | 73.96 µs | 65.68 µs | 1.80× | 1.67× | 1.48× | **0.93×** | **1.13×** | +| fft Float64 2018 dims=1 | 109.44 µs | 112.88 µs | 95.76 µs | 87.48 µs | 1.03× | 0.88× | 0.80× | **0.85×** | **1.09×** | +| fft Float64 2048 dims=1 | 13.52 µs | 21.72 µs | 16.98 µs | 14.88 µs | 1.61× | 1.26× | 1.10× | **0.78×** | **1.14×** | +| fft Float64 2304 dims=1 | 22.48 µs | 39.88 µs | 40.64 µs | 37.92 µs | 1.77× | 1.81× | 1.69× | 1.02× | **1.07×** | +| fft Float64 3027 dims=1 | 168.20 µs | 170.24 µs | 141.80 µs | 129.52 µs | 1.01× | 0.84× | 0.77× | **0.83×** | **1.09×** | +| fft Float64 3491 dims=1 | 222.48 µs | 240.96 µs | 189.28 µs | 174.00 µs | 1.08× | 0.85× | 0.78× | **0.79×** | **1.09×** | +| fft Float64 4036 dims=1 | 223.80 µs | 221.20 µs | 184.88 µs | 167.12 µs | 0.99× | 0.83× | 0.75× | **0.84×** | **1.11×** | +| fft Float64 4096 dims=1 | 29.80 µs | 49.32 µs | 39.48 µs | 34.96 µs | 1.66× | 1.32× | 1.17× | **0.80×** | **1.13×** | +| fft Float64 4860 dims=1 | 57.56 µs | 156.28 µs | 158.76 µs | 158.24 µs | 2.72× | 2.76× | 2.75× | 1.02× | 1.00× | +| fft Float64 6054 dims=1 | 340.04 µs | 380.88 µs | 334.20 µs | 306.40 µs | 1.12× | 0.98× | 0.90× | **0.88×** | **1.09×** | +| fft Float64 8192 dims=1 | 84.76 µs | 107.36 µs | 83.20 µs | 73.96 µs | 1.27× | 0.98× | 0.87× | **0.77×** | **1.12×** | +| fft Float64 8198 dims=1 | 506.65 µs | 1.145 ms | 928.41 µs | 860.93 µs | 2.26× | 1.83× | 1.70× | **0.81×** | **1.08×** | +| fft Float64 8443 dims=1 | 554.85 µs | 1.354 ms | 1.070 ms | 992.25 µs | 2.44× | 1.93× | 1.79× | **0.79×** | **1.08×** | +| fft Float64 10290 dims=1 | 149.96 µs | 662.53 µs | 679.13 µs | 678.73 µs | 4.42× | 4.53× | 4.53× | 1.03× | 1.00× | +| fft Float64 12297 dims=1 | 777.05 µs | 1.769 ms | 1.428 ms | 1.328 ms | 2.28× | 1.84× | 1.71× | **0.81×** | **1.07×** | +| fft Float64 16144 dims=1 | 922.45 µs | 899.77 µs | 743.29 µs | 675.69 µs | 0.98× | 0.81× | 0.73× | **0.83×** | **1.10×** | +| fft Float64 16384 dims=1 | 180.40 µs | 249.84 µs | 194.36 µs | 173.92 µs | 1.38× | 1.08× | 0.96× | **0.78×** | **1.12×** | +| fft Float64 16396 dims=1 | 1.036 ms | 2.281 ms | 1.941 ms | 1.722 ms | 2.20× | 1.87× | 1.66× | **0.85×** | **1.13×** | +| fft Float64 20507 dims=1 | 1.694 ms | 3.312 ms | 2.732 ms | 2.471 ms | 1.95× | 1.61× | 1.46× | **0.83×** | **1.11×** | +| fft Float64 21875 dims=1 | 384.44 µs | 1.573 ms | 1.574 ms | 1.612 ms | 4.09× | 4.09× | 4.19× | 1.00× | 0.98× | +| fft Float64 24594 dims=1 | 1.613 ms | 3.763 ms | 3.127 ms | 2.886 ms | 2.33× | 1.94× | 1.79× | **0.83×** | **1.08×** | +| fft Float64 32768 dims=1 | 444.61 µs | 605.73 µs | 465.17 µs | 403.36 µs | 1.36× | 1.05× | 0.91× | **0.77×** | **1.15×** | +| fft Float64 32822 dims=1 | 2.985 ms | 6.732 ms | 5.795 ms | 5.145 ms | 2.26× | 1.94× | 1.72× | **0.86×** | **1.13×** | +| fft Float64 46305 dims=1 | 1.031 ms | 3.311 ms | 3.327 ms | 3.435 ms | 3.21× | 3.23× | 3.33× | 1.00× | 0.97× | +| fft Float64 49233 dims=1 | 4.545 ms | 10.122 ms | 8.696 ms | 7.787 ms | 2.23× | 1.91× | 1.71× | **0.86×** | **1.12×** | +| fft Float64 49757 dims=1 | 4.565 ms | 7.187 ms | 5.775 ms | 5.144 ms | 1.57× | 1.27× | 1.13× | **0.80×** | **1.12×** | +| fft Float64 65536 dims=1 | 1.088 ms | 1.433 ms | 1.200 ms | 990.37 µs | 1.32× | 1.10× | 0.91× | **0.84×** | **1.21×** | +| fft Float64 65584 dims=1 | 4.401 ms | 9.489 ms | 7.562 ms | 6.970 ms | 2.16× | 1.72× | 1.58× | **0.80×** | **1.08×** | +| fft Float64 65644 dims=1 | 6.122 ms | 13.423 ms | 11.625 ms | 10.338 ms | 2.19× | 1.90× | 1.69× | **0.87×** | **1.12×** | +| fft Float64 98304 dims=1 | 1.926 ms | 2.854 ms | 2.887 ms | 2.794 ms | 1.48× | 1.50× | 1.45× | 1.01× | 1.03× | +| fft Float64 98466 dims=1 | 9.391 ms | 21.008 ms | 18.345 ms | 16.299 ms | 2.24× | 1.95× | 1.74× | **0.87×** | **1.13×** | +| fft Float64 120779 dims=1 | 12.568 ms | 16.292 ms | 9.881 ms | 9.256 ms | 1.30× | 0.79× | 0.74× | **0.61×** | **1.07×** | +| fft Float64 131072 dims=1 | 2.406 ms | 3.018 ms | 2.429 ms | 2.024 ms | 1.25× | 1.01× | 0.84× | **0.80×** | **1.20×** | +| fft Float64 131074 dims=1 | 6.943 ms | 32.213 ms | 20.828 ms | 19.619 ms | 4.64× | 3.00× | 2.83× | **0.65×** | **1.06×** | +| fft Float64 196611 dims=1 | 10.356 ms | 48.757 ms | 31.026 ms | 29.784 ms | 4.71× | 3.00× | 2.88× | **0.64×** | 1.04× | +| fft Float64 207360 dims=1 | 4.519 ms | 9.456 ms | 9.094 ms | 9.164 ms | 2.09× | 2.01× | 2.03× | 0.96× | 0.99× | +| fft Float64 262144 dims=1 | 5.670 ms | 6.419 ms | 4.137 ms | 3.789 ms | 1.13× | 0.73× | 0.67× | **0.64×** | **1.09×** | +| fft Float64 262148 dims=1 | 13.759 ms | 64.921 ms | 42.473 ms | 39.329 ms | 4.72× | 3.09× | 2.86× | **0.65×** | **1.08×** | +| fft Float64 262576 dims=1 | 25.621 ms | 57.019 ms | 48.003 ms | 41.008 ms | 2.23× | 1.87× | 1.60× | **0.84×** | **1.17×** | +| fft Float64 293201 dims=1 | 41.017 ms | 90.478 ms | 46.918 ms | 47.152 ms | 2.21× | 1.14× | 1.15× | **0.52×** | 1.00× | +| fft Float64 393222 dims=1 | 21.186 ms | 103.449 ms | 67.695 ms | 63.535 ms | 4.88× | 3.20× | 3.00× | **0.65×** | **1.07×** | +| fft Float64 441000 dims=1 | 10.759 ms | 42.476 ms | 44.293 ms | 38.207 ms | 3.95× | 4.12× | 3.55× | 1.04× | **1.16×** | +| fft Float64 524288 dims=1 | 16.863 ms | 17.631 ms | 9.028 ms | 8.186 ms | 1.05× | 0.54× | 0.49× | **0.51×** | **1.10×** | +| fft Float64 524294 dims=1 | 69.443 ms | 180.370 ms | 97.086 ms | 93.539 ms | 2.60× | 1.40× | 1.35× | **0.54×** | 1.04× | +| fft Float64 711749 dims=1 | 103.554 ms | 187.621 ms | 97.797 ms | 105.247 ms | 1.81× | 0.94× | 1.02× | **0.52×** | **0.93×** | +| fft Float64 786441 dims=1 | 104.363 ms | 266.104 ms | 144.177 ms | 144.753 ms | 2.55× | 1.38× | 1.39× | **0.54×** | 1.00× | +| fft Float64 933120 dims=1 | 32.838 ms | 57.812 ms | 55.192 ms | 54.957 ms | 1.76× | 1.68× | 1.67× | 0.95× | 1.00× | +| fft Float64 1000000 dims=1 | 50.425 ms | 100.410 ms | 99.366 ms | 99.919 ms | 1.99× | 1.97× | 1.98× | 0.99× | 0.99× | +| fft Float64 1048576 dims=1 | 52.671 ms | 44.533 ms | 21.139 ms | 19.707 ms | 0.85× | 0.40× | 0.37× | **0.47×** | **1.07×** | +| fft Float64 1048588 dims=1 | 141.957 ms | 370.972 ms | 194.454 ms | 189.831 ms | 2.61× | 1.37× | 1.34× | **0.52×** | 1.02× | +| fft Float64 1048592 dims=1 | 64.157 ms | 267.025 ms | 173.606 ms | 162.645 ms | 4.16× | 2.71× | 2.54× | **0.65×** | **1.07×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 548.306 ms | 316.420 ms | 307.726 ms | 2.51× | 1.45× | 1.41× | **0.58×** | 1.03× | +| fft Float64 1727797 dims=1 | 263.816 ms | 397.133 ms | 221.722 ms | 228.041 ms | 1.51× | 0.84× | 0.86× | **0.56×** | 0.97× | +| fft Float64 1975680 dims=1 | 76.790 ms | 192.282 ms | 189.719 ms | 187.649 ms | 2.50× | 2.47× | 2.44× | 0.99× | 1.01× | +| fft Float64 2097152 dims=1 | 119.760 ms | 91.048 ms | 45.008 ms | 46.262 ms | 0.76× | 0.38× | 0.39× | **0.49×** | 0.97× | +| fft Float64 4167450 dims=1 | 214.097 ms | 555.303 ms | 537.830 ms | 556.028 ms | 2.59× | 2.51× | 2.60× | 0.97× | 0.97× | +| fft Float64 4194304 dims=1 | 238.004 ms | 192.556 ms | 102.910 ms | 102.894 ms | 0.81× | 0.43× | 0.43× | **0.53×** | 1.00× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 52 ns | 51 ns | 51 ns | 2.15× | 2.13× | 2.12× | 0.99× | 1.01× | +| rfft Float32 8 dims=1 | 22 ns | 76 ns | 77 ns | 75 ns | 3.50× | 3.55× | 3.48× | 1.01× | 1.02× | +| rfft Float32 12 dims=1 | 27 ns | 178 ns | 183 ns | 186 ns | 6.56× | 6.76× | 6.88× | 1.03× | 0.98× | +| rfft Float32 16 dims=1 | 33 ns | 100 ns | 101 ns | 103 ns | 3.06× | 3.09× | 3.13× | 1.01× | 0.99× | +| rfft Float32 17 dims=1 | 134 ns | 178 ns | 178 ns | 179 ns | 1.33× | 1.33× | 1.34× | 1.00× | 0.99× | +| rfft Float32 23 dims=1 | 202 ns | 314 ns | 314 ns | 315 ns | 1.55× | 1.55× | 1.56× | 1.00× | 0.99× | +| rfft Float32 25 dims=1 | 76 ns | 501 ns | 502 ns | 500 ns | 6.56× | 6.57× | 6.54× | 1.00× | 1.00× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 810 ns | 810 ns | 2.82× | 2.81× | 2.81× | 1.00× | 1.00× | +| rfft Float32 31 dims=1 | 319 ns | 811 ns | 816 ns | 813 ns | 2.54× | 2.56× | 2.55× | 1.01× | 1.00× | +| rfft Float32 32 dims=1 | 101 ns | 159 ns | 160 ns | 161 ns | 1.56× | 1.58× | 1.59× | 1.01× | 0.99× | +| rfft Float32 37 dims=1 | 428 ns | 1.80 µs | 1.48 µs | 1.04 µs | 4.21× | 3.45× | 2.44× | **0.82×** | **1.42×** | +| rfft Float32 41 dims=1 | 508 ns | 1.81 µs | 1.49 µs | 1.05 µs | 3.57× | 2.93× | 2.06× | **0.82×** | **1.42×** | +| rfft Float32 43 dims=1 | 553 ns | 1.81 µs | 1.49 µs | 1.05 µs | 3.28× | 2.70× | 1.90× | **0.82×** | **1.42×** | +| rfft Float32 54 dims=1 | 213 ns | 461 ns | 457 ns | 461 ns | 2.16× | 2.14× | 2.16× | 0.99× | 0.99× | +| rfft Float32 60 dims=1 | 219 ns | 1.06 µs | 1.09 µs | 1.10 µs | 4.81× | 4.98× | 5.01× | 1.04× | 1.00× | +| rfft Float32 61 dims=1 | 1.04 µs | 1.85 µs | 1.53 µs | 1.08 µs | 1.79× | 1.47× | 1.04× | **0.82×** | **1.41×** | +| rfft Float32 64 dims=1 | 183 ns | 296 ns | 297 ns | 297 ns | 1.62× | 1.62× | 1.63× | 1.00× | 1.00× | +| rfft Float32 71 dims=1 | 1.37 µs | 4.06 µs | 3.43 µs | 2.33 µs | 2.95× | 2.50× | 1.69× | **0.85×** | **1.47×** | +| rfft Float32 73 dims=1 | 1.45 µs | 4.07 µs | 3.43 µs | 2.33 µs | 2.81× | 2.37× | 1.61× | **0.84×** | **1.47×** | +| rfft Float32 79 dims=1 | 1.68 µs | 4.09 µs | 3.44 µs | 2.34 µs | 2.43× | 2.04× | 1.39× | **0.84×** | **1.47×** | +| rfft Float32 101 dims=1 | 2.69 µs | 4.14 µs | 3.49 µs | 2.39 µs | 1.53× | 1.29× | 0.88× | **0.84×** | **1.46×** | +| rfft Float32 112 dims=1 | 288 ns | 1.52 µs | 1.54 µs | 1.56 µs | 5.28× | 5.34× | 5.41× | 1.01× | 0.99× | +| rfft Float32 120 dims=1 | 287 ns | 1.84 µs | 1.87 µs | 1.90 µs | 6.42× | 6.51× | 6.61× | 1.01× | 0.98× | +| rfft Float32 128 dims=1 | 265 ns | 606 ns | 609 ns | 609 ns | 2.29× | 2.30× | 2.30× | 1.01× | 1.00× | +| rfft Float32 202 dims=1 | 2.12 µs | 4.58 µs | 3.94 µs | 2.83 µs | 2.15× | 1.85× | 1.33× | **0.86×** | **1.39×** | +| rfft Float32 243 dims=1 | 1.18 µs | 3.82 µs | 3.82 µs | 3.83 µs | 3.24× | 3.24× | 3.25× | 1.00× | 1.00× | +| rfft Float32 251 dims=1 | 5.48 µs | 9.39 µs | 6.83 µs | 5.04 µs | 1.71× | 1.25× | 0.92× | **0.73×** | **1.35×** | +| rfft Float32 256 dims=1 | 636 ns | 1.30 µs | 1.15 µs | 904 ns | 2.05× | 1.81× | 1.42× | **0.88×** | **1.27×** | +| rfft Float32 303 dims=1 | 8.39 µs | 14.22 µs | 12.32 µs | 9.01 µs | 1.70× | 1.47× | 1.07× | **0.87×** | **1.37×** | +| rfft Float32 360 dims=1 | 1.31 µs | 5.65 µs | 5.77 µs | 5.79 µs | 4.30× | 4.39× | 4.40× | 1.02× | 1.00× | +| rfft Float32 404 dims=1 | 4.31 µs | 10.94 µs | 9.89 µs | 7.77 µs | 2.54× | 2.29× | 1.80× | **0.90×** | **1.27×** | +| rfft Float32 504 dims=1 | 1.53 µs | 9.19 µs | 9.29 µs | 9.36 µs | 6.00× | 6.06× | 6.11× | 1.01× | 0.99× | +| rfft Float32 512 dims=1 | 1.14 µs | 2.81 µs | 2.50 µs | 1.91 µs | 2.48× | 2.20× | 1.68× | **0.89×** | **1.31×** | +| rfft Float32 593 dims=1 | 21.96 µs | 45.40 µs | 30.20 µs | 22.96 µs | 2.07× | 1.38× | 1.05× | **0.67×** | **1.32×** | +| rfft Float32 606 dims=1 | 6.52 µs | 16.06 µs | 14.16 µs | 10.86 µs | 2.46× | 2.17× | 1.67× | **0.88×** | **1.30×** | +| rfft Float32 720 dims=1 | 2.87 µs | 10.76 µs | 10.94 µs | 10.96 µs | 3.74× | 3.81× | 3.81× | 1.02× | 1.00× | +| rfft Float32 1000 dims=1 | 3.13 µs | 24.40 µs | 24.40 µs | 24.48 µs | 7.81× | 7.81× | 7.83× | 1.00× | 1.00× | +| rfft Float32 1024 dims=1 | 2.20 µs | 6.14 µs | 4.95 µs | 3.91 µs | 2.79× | 2.25× | 1.78× | **0.81×** | **1.27×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 17.94 µs | 18.26 µs | 18.28 µs | 3.87× | 3.94× | 3.94× | 1.02× | 1.00× | +| rfft Float32 1433 dims=1 | 54.24 µs | 99.76 µs | 69.20 µs | 51.60 µs | 1.84× | 1.28× | 0.95× | **0.69×** | **1.34×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 39.84 µs | 34.92 µs | 26.40 µs | 2.27× | 1.99× | 1.51× | **0.88×** | **1.32×** | +| rfft Float32 2018 dims=1 | 37.16 µs | 50.64 µs | 35.24 µs | 28.16 µs | 1.36× | 0.95× | 0.76× | **0.70×** | **1.25×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 13.30 µs | 10.80 µs | 8.33 µs | 2.99× | 2.43× | 1.87× | **0.81×** | **1.30×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 21.52 µs | 21.60 µs | 19.50 µs | 3.15× | 3.16× | 2.85× | 1.00× | **1.11×** | +| rfft Float32 3027 dims=1 | 71.52 µs | 157.40 µs | 112.16 µs | 90.44 µs | 2.20× | 1.57× | 1.26× | **0.71×** | **1.24×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 222.76 µs | 141.48 µs | 114.52 µs | 1.49× | 0.94× | 0.76× | **0.64×** | **1.24×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 119.44 µs | 91.40 µs | 77.40 µs | 1.59× | 1.22× | 1.03× | **0.77×** | **1.18×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 28.84 µs | 21.52 µs | 17.34 µs | 3.07× | 2.29× | 1.84× | **0.75×** | **1.24×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 103.00 µs | 105.52 µs | 105.92 µs | 4.04× | 4.14× | 4.16× | 1.02× | 1.00× | +| rfft Float32 6054 dims=1 | 113.60 µs | 175.92 µs | 130.08 µs | 108.32 µs | 1.55× | 1.15× | 0.95× | **0.74×** | **1.20×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 62.00 µs | 47.12 µs | 37.32 µs | 2.43× | 1.84× | 1.46× | **0.76×** | **1.26×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 499.61 µs | 336.28 µs | 271.40 µs | 2.41× | 1.62× | 1.31× | **0.67×** | **1.24×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 1.060 ms | 645.65 µs | 553.13 µs | 3.07× | 1.87× | 1.60× | **0.61×** | **1.17×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 415.88 µs | 416.13 µs | 417.56 µs | 6.61× | 6.61× | 6.64× | 1.00× | 1.00× | +| rfft Float32 12297 dims=1 | 522.37 µs | 1.532 ms | 1.046 ms | 843.57 µs | 2.93× | 2.00× | 1.61× | **0.68×** | **1.24×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 441.89 µs | 322.84 µs | 266.60 µs | 1.44× | 1.05× | 0.87× | **0.73×** | **1.21×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 135.84 µs | 96.16 µs | 80.12 µs | 2.51× | 1.78× | 1.48× | **0.71×** | **1.20×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 1.079 ms | 760.37 µs | 630.45 µs | 2.58× | 1.82× | 1.51× | **0.70×** | **1.21×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 2.609 ms | 1.773 ms | 1.330 ms | 2.71× | 1.84× | 1.38× | **0.68×** | **1.33×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 1.615 ms | 1.613 ms | 1.608 ms | 8.20× | 8.19× | 8.16× | 1.00× | 1.00× | +| rfft Float32 24594 dims=1 | 631.01 µs | 1.610 ms | 1.122 ms | 918.57 µs | 2.55× | 1.78× | 1.46× | **0.70×** | **1.22×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 291.12 µs | 211.80 µs | 174.16 µs | 2.49× | 1.81× | 1.49× | **0.73×** | **1.22×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 2.663 ms | 1.902 ms | 1.387 ms | 2.64× | 1.88× | 1.37× | **0.71×** | **1.37×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 3.355 ms | 3.368 ms | 3.405 ms | 7.40× | 7.42× | 7.51× | 1.00× | 0.99× | +| rfft Float32 49233 dims=1 | 2.572 ms | 8.145 ms | 5.734 ms | 4.260 ms | 3.17× | 2.23× | 1.66× | **0.70×** | **1.35×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 6.098 ms | 4.048 ms | 3.244 ms | 2.24× | 1.49× | 1.19× | **0.66×** | **1.25×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 645.89 µs | 443.05 µs | 374.76 µs | 2.65× | 1.82× | 1.54× | **0.69×** | **1.18×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 4.237 ms | 2.911 ms | 2.397 ms | 2.48× | 1.70× | 1.40× | **0.69×** | **1.21×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 5.754 ms | 4.095 ms | 3.111 ms | 2.83× | 2.02× | 1.53× | **0.71×** | **1.32×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.402 ms | 1.387 ms | 1.252 ms | 2.72× | 2.70× | 2.43× | 0.99× | **1.11×** | +| rfft Float32 98466 dims=1 | 3.089 ms | 8.583 ms | 5.943 ms | 4.671 ms | 2.78× | 1.92× | 1.51× | **0.69×** | **1.27×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 13.816 ms | 6.774 ms | 5.723 ms | 1.30× | 0.64× | 0.54× | **0.49×** | **1.18×** | +| rfft Float32 131072 dims=1 | 614.25 µs | 1.492 ms | 1.102 ms | 830.89 µs | 2.43× | 1.79× | 1.35× | **0.74×** | **1.33×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 13.789 ms | 6.991 ms | 5.902 ms | 6.24× | 3.16× | 2.67× | **0.51×** | **1.18×** | +| rfft Float32 196611 dims=1 | 6.210 ms | 42.160 ms | 21.424 ms | 18.296 ms | 6.79× | 3.45× | 2.95× | **0.51×** | **1.17×** | +| rfft Float32 207360 dims=1 | 1.700 ms | 4.635 ms | 4.643 ms | 4.353 ms | 2.73× | 2.73× | 2.56× | 1.00× | **1.07×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 3.428 ms | 2.476 ms | 1.933 ms | 2.05× | 1.48× | 1.16× | **0.72×** | **1.28×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 30.091 ms | 15.511 ms | 13.227 ms | 6.64× | 3.42× | 2.92× | **0.52×** | **1.17×** | +| rfft Float32 262576 dims=1 | 8.653 ms | 23.147 ms | 15.935 ms | 11.847 ms | 2.68× | 1.84× | 1.37× | **0.69×** | **1.35×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 75.204 ms | 30.729 ms | 28.290 ms | 2.38× | 0.97× | 0.89× | **0.41×** | **1.09×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 44.980 ms | 23.064 ms | 19.539 ms | 6.62× | 3.39× | 2.87× | **0.51×** | **1.18×** | +| rfft Float32 441000 dims=1 | 3.804 ms | 22.935 ms | 22.762 ms | 22.912 ms | 6.03× | 5.98× | 6.02× | 0.99× | 0.99× | +| rfft Float32 524288 dims=1 | 3.783 ms | 7.534 ms | 4.288 ms | 3.809 ms | 1.99× | 1.13× | 1.01× | **0.57×** | **1.13×** | +| rfft Float32 524294 dims=1 | 23.932 ms | 72.213 ms | 31.973 ms | 28.615 ms | 3.02× | 1.34× | 1.20× | **0.44×** | **1.12×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 168.063 ms | 66.725 ms | 64.012 ms | 1.84× | 0.73× | 0.70× | **0.40×** | 1.04× | +| rfft Float32 786441 dims=1 | 89.117 ms | 205.696 ms | 99.016 ms | 89.604 ms | 2.31× | 1.11× | 1.01× | **0.48×** | **1.11×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 26.508 ms | 25.799 ms | 25.720 ms | 2.94× | 2.86× | 2.85× | 0.97× | 1.00× | +| rfft Float32 1000000 dims=1 | 8.693 ms | 53.061 ms | 52.316 ms | 52.769 ms | 6.10× | 6.02× | 6.07× | 0.99× | 0.99× | +| rfft Float32 1048576 dims=1 | 7.838 ms | 16.583 ms | 8.849 ms | 8.036 ms | 2.12× | 1.13× | 1.03× | **0.53×** | **1.10×** | +| rfft Float32 1048588 dims=1 | 47.864 ms | 138.800 ms | 71.242 ms | 65.118 ms | 2.90× | 1.49× | 1.36× | **0.51×** | **1.09×** | +| rfft Float32 1048592 dims=1 | 18.670 ms | 117.241 ms | 60.931 ms | 51.762 ms | 6.28× | 3.26× | 2.77× | **0.52×** | **1.18×** | +| rfft Float32 1572882 dims=1 | 73.534 ms | 198.825 ms | 104.629 ms | 94.989 ms | 2.70× | 1.42× | 1.29× | **0.53×** | **1.10×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 377.923 ms | 145.533 ms | 137.162 ms | 1.50× | 0.58× | 0.54× | **0.39×** | **1.06×** | +| rfft Float32 1975680 dims=1 | 16.948 ms | 105.066 ms | 102.246 ms | 104.306 ms | 6.20× | 6.03× | 6.15× | 0.97× | 0.98× | +| rfft Float32 2097152 dims=1 | 16.402 ms | 45.389 ms | 19.301 ms | 17.341 ms | 2.77× | 1.18× | 1.06× | **0.43×** | **1.11×** | +| rfft Float32 4167450 dims=1 | 83.641 ms | 283.209 ms | 278.293 ms | 277.032 ms | 3.39× | 3.33× | 3.31× | 0.98× | 1.00× | +| rfft Float32 4194304 dims=1 | 51.550 ms | 92.203 ms | 40.668 ms | 37.596 ms | 1.79× | 0.79× | 0.73× | **0.44×** | **1.08×** | +| rfft Float64 7 dims=1 | 24 ns | 52 ns | 53 ns | 54 ns | 2.17× | 2.20× | 2.26× | 1.01× | 0.97× | +| rfft Float64 8 dims=1 | 22 ns | 82 ns | 84 ns | 85 ns | 3.79× | 3.88× | 3.93× | 1.02× | 0.99× | +| rfft Float64 12 dims=1 | 28 ns | 187 ns | 194 ns | 200 ns | 6.78× | 7.07× | 7.28× | 1.04× | 0.97× | +| rfft Float64 16 dims=1 | 32 ns | 106 ns | 109 ns | 110 ns | 3.30× | 3.38× | 3.42× | 1.02× | 0.99× | +| rfft Float64 17 dims=1 | 137 ns | 191 ns | 192 ns | 192 ns | 1.40× | 1.41× | 1.40× | 1.00× | 1.00× | +| rfft Float64 23 dims=1 | 205 ns | 339 ns | 341 ns | 342 ns | 1.65× | 1.66× | 1.67× | 1.00× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 427 ns | 435 ns | 436 ns | 5.67× | 5.79× | 5.80× | 1.02× | 1.00× | +| rfft Float64 29 dims=1 | 290 ns | 886 ns | 889 ns | 893 ns | 3.05× | 3.07× | 3.08× | 1.00× | 1.00× | +| rfft Float64 31 dims=1 | 323 ns | 888 ns | 891 ns | 895 ns | 2.75× | 2.76× | 2.77× | 1.00× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 166 ns | 167 ns | 169 ns | 1.86× | 1.87× | 1.90× | 1.01× | 0.99× | +| rfft Float64 37 dims=1 | 431 ns | 1.96 µs | 1.76 µs | 1.50 µs | 4.55× | 4.10× | 3.48× | **0.90×** | **1.18×** | +| rfft Float64 41 dims=1 | 512 ns | 1.96 µs | 1.77 µs | 1.51 µs | 3.83× | 3.46× | 2.95× | **0.90×** | **1.17×** | +| rfft Float64 43 dims=1 | 556 ns | 1.97 µs | 1.77 µs | 1.51 µs | 3.54× | 3.19× | 2.72× | **0.90×** | **1.17×** | +| rfft Float64 54 dims=1 | 167 ns | 474 ns | 472 ns | 473 ns | 2.83× | 2.82× | 2.83× | 1.00× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 982 ns | 1.01 µs | 1.05 µs | 5.75× | 5.91× | 6.16× | 1.03× | 0.96× | +| rfft Float64 61 dims=1 | 1.04 µs | 2.01 µs | 1.82 µs | 1.55 µs | 1.93× | 1.74× | 1.48× | **0.90×** | **1.17×** | +| rfft Float64 64 dims=1 | 166 ns | 310 ns | 310 ns | 312 ns | 1.87× | 1.86× | 1.88× | 1.00× | 0.99× | +| rfft Float64 71 dims=1 | 1.39 µs | 4.38 µs | 3.99 µs | 3.47 µs | 3.16× | 2.88× | 2.51× | **0.91×** | **1.15×** | +| rfft Float64 73 dims=1 | 1.46 µs | 4.39 µs | 4.00 µs | 3.47 µs | 3.01× | 2.75× | 2.38× | **0.91×** | **1.15×** | +| rfft Float64 79 dims=1 | 1.69 µs | 4.39 µs | 4.00 µs | 3.49 µs | 2.59× | 2.36× | 2.06× | **0.91×** | **1.15×** | +| rfft Float64 101 dims=1 | 2.71 µs | 4.45 µs | 4.05 µs | 3.55 µs | 1.64× | 1.49× | 1.31× | **0.91×** | **1.14×** | +| rfft Float64 112 dims=1 | 297 ns | 1.22 µs | 1.25 µs | 1.26 µs | 4.11× | 4.22× | 4.23× | 1.02× | 1.00× | +| rfft Float64 120 dims=1 | 334 ns | 1.70 µs | 1.73 µs | 1.77 µs | 5.09× | 5.20× | 5.30× | 1.02× | 0.98× | +| rfft Float64 128 dims=1 | 327 ns | 637 ns | 637 ns | 640 ns | 1.95× | 1.95× | 1.96× | 1.00× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 4.90 µs | 4.50 µs | 3.98 µs | 1.88× | 1.73× | 1.53× | **0.92×** | **1.13×** | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 3.86 µs | 3.85 µs | 3.05× | 3.06× | 3.05× | 1.00× | 1.00× | +| rfft Float64 251 dims=1 | 5.71 µs | 10.10 µs | 8.52 µs | 7.49 µs | 1.77× | 1.49× | 1.31× | **0.84×** | **1.14×** | +| rfft Float64 256 dims=1 | 693 ns | 1.35 µs | 1.25 µs | 1.10 µs | 1.95× | 1.80× | 1.59× | **0.92×** | **1.13×** | +| rfft Float64 303 dims=1 | 8.40 µs | 15.50 µs | 14.20 µs | 12.72 µs | 1.85× | 1.69× | 1.51× | **0.92×** | **1.12×** | +| rfft Float64 360 dims=1 | 1.40 µs | 5.25 µs | 5.33 µs | 5.36 µs | 3.74× | 3.80× | 3.82× | 1.02× | 0.99× | +| rfft Float64 404 dims=1 | 5.36 µs | 11.70 µs | 11.08 µs | 10.22 µs | 2.18× | 2.07× | 1.91× | **0.95×** | **1.08×** | +| rfft Float64 504 dims=1 | 2.03 µs | 7.92 µs | 8.08 µs | 8.15 µs | 3.90× | 3.98× | 4.01× | 1.02× | 0.99× | +| rfft Float64 512 dims=1 | 1.46 µs | 2.92 µs | 2.72 µs | 2.41 µs | 2.00× | 1.86× | 1.65× | **0.93×** | **1.13×** | +| rfft Float64 593 dims=1 | 22.36 µs | 48.68 µs | 39.04 µs | 34.68 µs | 2.18× | 1.75× | 1.55× | **0.80×** | **1.13×** | +| rfft Float64 606 dims=1 | 8.15 µs | 17.06 µs | 16.02 µs | 14.50 µs | 2.09× | 1.97× | 1.78× | **0.94×** | **1.10×** | +| rfft Float64 720 dims=1 | 2.88 µs | 9.92 µs | 10.18 µs | 10.08 µs | 3.44× | 3.53× | 3.50× | 1.03× | 1.01× | +| rfft Float64 1000 dims=1 | 4.49 µs | 20.40 µs | 20.68 µs | 20.72 µs | 4.55× | 4.61× | 4.62× | 1.01× | 1.00× | +| rfft Float64 1024 dims=1 | 3.13 µs | 6.30 µs | 5.62 µs | 4.91 µs | 2.02× | 1.80× | 1.57× | **0.89×** | **1.14×** | +| rfft Float64 1080 dims=1 | 4.71 µs | 16.82 µs | 17.14 µs | 17.18 µs | 3.57× | 3.64× | 3.65× | 1.02× | 1.00× | +| rfft Float64 1433 dims=1 | 56.12 µs | 109.24 µs | 89.52 µs | 80.44 µs | 1.95× | 1.60× | 1.43× | **0.82×** | **1.11×** | +| rfft Float64 1616 dims=1 | 22.28 µs | 43.16 µs | 40.28 µs | 36.20 µs | 1.94× | 1.81× | 1.62× | **0.93×** | **1.11×** | +| rfft Float64 2018 dims=1 | 55.68 µs | 53.72 µs | 44.28 µs | 39.92 µs | 0.96× | 0.80× | 0.72× | **0.82×** | **1.11×** | +| rfft Float64 2048 dims=1 | 6.68 µs | 13.80 µs | 12.22 µs | 10.90 µs | 2.07× | 1.83× | 1.63× | **0.89×** | **1.12×** | +| rfft Float64 2304 dims=1 | 9.76 µs | 23.32 µs | 23.44 µs | 22.12 µs | 2.39× | 2.40× | 2.27× | 1.01× | **1.06×** | +| rfft Float64 3027 dims=1 | 73.56 µs | 169.48 µs | 140.56 µs | 127.84 µs | 2.30× | 1.91× | 1.74× | **0.83×** | **1.10×** | +| rfft Float64 3491 dims=1 | 156.80 µs | 240.52 µs | 187.60 µs | 172.28 µs | 1.53× | 1.20× | 1.10× | **0.78×** | **1.09×** | +| rfft Float64 4036 dims=1 | 113.44 µs | 126.84 µs | 109.08 µs | 102.72 µs | 1.12× | 0.96× | 0.91× | **0.86×** | **1.06×** | +| rfft Float64 4096 dims=1 | 14.52 µs | 30.08 µs | 25.52 µs | 22.76 µs | 2.07× | 1.76× | 1.57× | **0.85×** | **1.12×** | +| rfft Float64 4860 dims=1 | 29.04 µs | 97.36 µs | 99.24 µs | 101.36 µs | 3.35× | 3.42× | 3.49× | 1.02× | 0.98× | +| rfft Float64 6054 dims=1 | 171.84 µs | 186.92 µs | 158.32 µs | 146.36 µs | 1.09× | 0.92× | 0.85× | **0.85×** | **1.08×** | +| rfft Float64 8192 dims=1 | 39.12 µs | 66.20 µs | 56.52 µs | 50.68 µs | 1.69× | 1.44× | 1.30× | **0.85×** | **1.12×** | +| rfft Float64 8198 dims=1 | 258.64 µs | 550.57 µs | 454.45 µs | 416.73 µs | 2.13× | 1.76× | 1.61× | **0.83×** | **1.09×** | +| rfft Float64 8443 dims=1 | 364.37 µs | 1.326 ms | 1.086 ms | 985.37 µs | 3.64× | 2.98× | 2.70× | **0.82×** | **1.10×** | +| rfft Float64 10290 dims=1 | 74.76 µs | 322.36 µs | 324.32 µs | 322.36 µs | 4.31× | 4.34× | 4.31× | 1.01× | 1.01× | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.727 ms | 1.414 ms | 1.284 ms | 3.14× | 2.57× | 2.34× | **0.82×** | **1.10×** | +| rfft Float64 16144 dims=1 | 460.81 µs | 478.77 µs | 404.28 µs | 373.56 µs | 1.04× | 0.88× | 0.81× | **0.84×** | **1.08×** | +| rfft Float64 16384 dims=1 | 86.72 µs | 142.44 µs | 118.04 µs | 105.96 µs | 1.64× | 1.36× | 1.22× | **0.83×** | **1.11×** | +| rfft Float64 16396 dims=1 | 523.69 µs | 1.234 ms | 1.035 ms | 920.49 µs | 2.36× | 1.98× | 1.76× | **0.84×** | **1.12×** | +| rfft Float64 20507 dims=1 | 1.134 ms | 3.309 ms | 2.723 ms | 2.433 ms | 2.92× | 2.40× | 2.15× | **0.82×** | **1.12×** | +| rfft Float64 21875 dims=1 | 200.92 µs | 1.386 ms | 1.396 ms | 1.412 ms | 6.90× | 6.95× | 7.03× | 1.01× | 0.99× | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.783 ms | 1.477 ms | 1.400 ms | 2.24× | 1.86× | 1.76× | **0.83×** | **1.06×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 323.20 µs | 280.88 µs | 246.12 µs | 1.65× | 1.44× | 1.26× | **0.87×** | **1.14×** | +| rfft Float64 32822 dims=1 | 1.488 ms | 3.316 ms | 2.838 ms | 2.535 ms | 2.23× | 1.91× | 1.70× | **0.86×** | **1.12×** | +| rfft Float64 46305 dims=1 | 482.65 µs | 3.111 ms | 3.128 ms | 3.200 ms | 6.45× | 6.48× | 6.63× | 1.01× | 0.98× | +| rfft Float64 49233 dims=1 | 2.796 ms | 10.107 ms | 8.647 ms | 7.713 ms | 3.62× | 3.09× | 2.76× | **0.86×** | **1.12×** | +| rfft Float64 49757 dims=1 | 2.906 ms | 7.156 ms | 5.769 ms | 5.085 ms | 2.46× | 1.98× | 1.75× | **0.81×** | **1.13×** | +| rfft Float64 65536 dims=1 | 468.09 µs | 777.21 µs | 652.85 µs | 586.45 µs | 1.66× | 1.39× | 1.25× | **0.84×** | **1.11×** | +| rfft Float64 65584 dims=1 | 2.195 ms | 4.947 ms | 4.028 ms | 3.662 ms | 2.25× | 1.84× | 1.67× | **0.81×** | **1.10×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 7.010 ms | 6.065 ms | 5.506 ms | 2.32× | 2.01× | 1.82× | **0.87×** | **1.10×** | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.612 ms | 1.635 ms | 1.535 ms | 1.74× | 1.76× | 1.65× | 1.01× | **1.07×** | +| rfft Float64 98466 dims=1 | 4.623 ms | 10.431 ms | 9.032 ms | 8.107 ms | 2.26× | 1.95× | 1.75× | **0.87×** | **1.11×** | +| rfft Float64 120779 dims=1 | 11.377 ms | 15.972 ms | 9.859 ms | 9.218 ms | 1.40× | 0.87× | 0.81× | **0.62×** | **1.07×** | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.788 ms | 1.531 ms | 1.354 ms | 1.57× | 1.34× | 1.19× | **0.86×** | **1.13×** | +| rfft Float64 131074 dims=1 | 3.508 ms | 15.799 ms | 9.946 ms | 9.402 ms | 4.50× | 2.84× | 2.68× | **0.63×** | **1.06×** | +| rfft Float64 196611 dims=1 | 7.590 ms | 48.616 ms | 31.072 ms | 28.993 ms | 6.41× | 4.09× | 3.82× | **0.64×** | **1.07×** | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.971 ms | 4.928 ms | 4.968 ms | 2.14× | 2.12× | 2.14× | 0.99× | 0.99× | +| rfft Float64 262144 dims=1 | 2.607 ms | 3.886 ms | 3.241 ms | 2.949 ms | 1.49× | 1.24× | 1.13× | **0.83×** | **1.10×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 33.701 ms | 21.958 ms | 20.839 ms | 4.81× | 3.13× | 2.97× | **0.65×** | **1.05×** | +| rfft Float64 262576 dims=1 | 12.798 ms | 29.094 ms | 24.793 ms | 20.960 ms | 2.27× | 1.94× | 1.64× | **0.85×** | **1.18×** | +| rfft Float64 293201 dims=1 | 36.020 ms | 89.305 ms | 46.883 ms | 44.881 ms | 2.48× | 1.30× | 1.25× | **0.52×** | 1.04× | +| rfft Float64 393222 dims=1 | 10.518 ms | 50.481 ms | 32.988 ms | 30.177 ms | 4.80× | 3.14× | 2.87× | **0.65×** | **1.09×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 21.021 ms | 20.360 ms | 20.381 ms | 3.59× | 3.48× | 3.48× | 0.97× | 1.00× | +| rfft Float64 524288 dims=1 | 5.760 ms | 9.322 ms | 6.033 ms | 5.615 ms | 1.62× | 1.05× | 0.97× | **0.65×** | **1.07×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 87.086 ms | 46.377 ms | 47.558 ms | 2.50× | 1.33× | 1.37× | **0.53×** | 0.98× | +| rfft Float64 711749 dims=1 | 110.585 ms | 188.235 ms | 98.196 ms | 106.188 ms | 1.70× | 0.89× | 0.96× | **0.52×** | **0.92×** | +| rfft Float64 786441 dims=1 | 98.952 ms | 279.184 ms | 145.379 ms | 143.708 ms | 2.82× | 1.47× | 1.45× | **0.52×** | 1.01× | +| rfft Float64 933120 dims=1 | 11.815 ms | 30.104 ms | 27.975 ms | 27.500 ms | 2.55× | 2.37× | 2.33× | **0.93×** | 1.02× | +| rfft Float64 1000000 dims=1 | 21.371 ms | 49.824 ms | 49.028 ms | 49.910 ms | 2.33× | 2.29× | 2.34× | 0.98× | 0.98× | +| rfft Float64 1048576 dims=1 | 13.492 ms | 22.659 ms | 11.979 ms | 12.483 ms | 1.68× | 0.89× | 0.93× | **0.53×** | 0.96× | +| rfft Float64 1048588 dims=1 | 69.802 ms | 202.002 ms | 101.951 ms | 101.501 ms | 2.89× | 1.46× | 1.45× | **0.50×** | 1.00× | +| rfft Float64 1048592 dims=1 | 30.247 ms | 136.732 ms | 89.558 ms | 84.304 ms | 4.52× | 2.96× | 2.79× | **0.65×** | **1.06×** | +| rfft Float64 1572882 dims=1 | 107.501 ms | 263.714 ms | 151.590 ms | 145.810 ms | 2.45× | 1.41× | 1.36× | **0.57×** | 1.04× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 399.009 ms | 221.737 ms | 230.833 ms | 1.21× | 0.67× | 0.70× | **0.56×** | 0.96× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 97.390 ms | 94.130 ms | 95.263 ms | 2.53× | 2.44× | 2.47× | 0.97× | 0.99× | +| rfft Float64 2097152 dims=1 | 55.689 ms | 50.658 ms | 27.672 ms | 25.132 ms | 0.91× | 0.50× | 0.45× | **0.55×** | **1.10×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 276.903 ms | 269.150 ms | 271.446 ms | 2.45× | 2.39× | 2.41× | 0.97× | 0.99× | +| rfft Float64 4194304 dims=1 | 118.652 ms | 100.592 ms | 57.082 ms | 57.406 ms | 0.85× | 0.48× | 0.48× | **0.57×** | 0.99× | +| fft Float32 8×8 dims=1,2 | 144 ns | 695 ns | 752 ns | 725 ns | 4.83× | 5.22× | 5.03× | **1.08×** | 1.04× | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.49 µs | 2.50 µs | 2.54 µs | 4.36× | 4.39× | 4.46× | 1.01× | 0.98× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.72 µs | 10.78 µs | 10.84 µs | 4.01× | 4.03× | 4.05× | 1.01× | 0.99× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 48.76 µs | 48.88 µs | 49.00 µs | 3.95× | 3.96× | 3.97× | 1.00× | 1.00× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 249.20 µs | 208.96 µs | 153.64 µs | 4.14× | 3.47× | 2.55× | **0.84×** | **1.36×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 1.174 ms | 1.025 ms | 718.09 µs | 1.54× | 1.34× | 0.94× | **0.87×** | **1.43×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 7.114 ms | 6.109 ms | 4.443 ms | 1.27× | 1.09× | 0.79× | **0.86×** | **1.37×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 33.975 ms | 29.823 ms | 21.008 ms | 1.35× | 1.18× | 0.83× | **0.88×** | **1.42×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 159.402 ms | 133.918 ms | 97.635 ms | 1.19× | 1.00× | 0.73× | **0.84×** | **1.37×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 720 ns | 773 ns | 745 ns | 4.15× | 4.46× | 4.30× | **1.07×** | 1.04× | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.52 µs | 2.60 µs | 2.57 µs | 3.08× | 3.17× | 3.14× | 1.03× | 1.01× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.34 µs | 11.40 µs | 11.44 µs | 2.76× | 2.77× | 2.78× | 1.01× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 53.04 µs | 53.24 µs | 53.40 µs | 2.58× | 2.59× | 2.60× | 1.00× | 1.00× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 279.08 µs | 244.08 µs | 200.56 µs | 2.53× | 2.21× | 1.82× | **0.87×** | **1.22×** | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 4.074 ms | 3.573 ms | 3.153 ms | 2.27× | 1.99× | 1.76× | **0.88×** | **1.13×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 3.820 ms | 3.220 ms | 2.924 ms | 1.04× | 0.88× | 0.80× | **0.84×** | **1.10×** | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.978 ms | 3.354 ms | 3.062 ms | 1.03× | 0.87× | 0.79× | **0.84×** | **1.10×** | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.476 ms | 1.444 ms | 1.224 ms | 1.29× | 1.26× | 1.07× | 0.98× | **1.18×** | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 7.519 ms | 7.001 ms | 5.919 ms | 1.23× | 1.15× | 0.97× | **0.93×** | **1.18×** | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 19.637 ms | 19.915 ms | 19.907 ms | 2.97× | 3.01× | 3.01× | 1.01× | 1.00× | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 87.006 ms | 88.217 ms | 88.010 ms | 3.13× | 3.17× | 3.17× | 1.01× | 1.00× | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 37.090 ms | 37.334 ms | 30.742 ms | 1.23× | 1.24× | 1.02× | 1.01× | **1.21×** | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 181.709 ms | 165.449 ms | 137.403 ms | 1.11× | 1.01× | 0.84× | **0.91×** | **1.20×** | +| rfft Float32 8×8 dims=1,2 | 124 ns | 855 ns | 871 ns | 880 ns | 6.92× | 7.05× | 7.12× | 1.02× | 0.99× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.36 µs | 2.40 µs | 2.43 µs | 5.38× | 5.47× | 5.55× | 1.02× | 0.99× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 8.03 µs | 8.09 µs | 8.19 µs | 3.92× | 3.95× | 4.00× | 1.01× | 0.99× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 32.04 µs | 32.08 µs | 32.24 µs | 3.26× | 3.26× | 3.28× | 1.00× | 1.00× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 140.80 µs | 130.20 µs | 117.52 µs | 3.02× | 2.79× | 2.52× | **0.92×** | **1.11×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 626.61 µs | 542.21 µs | 410.41 µs | 1.80× | 1.56× | 1.18× | **0.87×** | **1.32×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 2.827 ms | 2.363 ms | 1.774 ms | 1.96× | 1.64× | 1.23× | **0.84×** | **1.33×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 12.647 ms | 10.225 ms | 7.700 ms | 2.10× | 1.70× | 1.28× | **0.81×** | **1.33×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 62.300 ms | 50.539 ms | 38.661 ms | 1.79× | 1.46× | 1.11× | **0.81×** | **1.31×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 918 ns | 944 ns | 946 ns | 7.84× | 8.06× | 8.08× | 1.03× | 1.00× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.47 µs | 2.52 µs | 2.50 µs | 5.03× | 5.15× | 5.10× | 1.02× | 1.01× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 8.43 µs | 8.55 µs | 8.53 µs | 3.51× | 3.56× | 3.56× | 1.01× | 1.00× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 33.56 µs | 33.76 µs | 33.80 µs | 2.85× | 2.87× | 2.87× | 1.01× | 1.00× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 147.56 µs | 141.16 µs | 128.60 µs | 2.53× | 2.42× | 2.21× | 0.96× | **1.10×** | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.621 ms | 2.305 ms | 2.031 ms | 1.73× | 1.52× | 1.34× | **0.88×** | **1.14×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 3.435 ms | 2.818 ms | 2.531 ms | 2.13× | 1.75× | 1.57× | **0.82×** | **1.11×** | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 2.061 ms | 1.737 ms | 1.592 ms | 1.06× | 0.90× | 0.82× | **0.84×** | **1.09×** | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 655.81 µs | 605.85 µs | 524.25 µs | 1.61× | 1.49× | 1.29× | **0.92×** | **1.16×** | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 3.023 ms | 2.759 ms | 2.313 ms | 1.58× | 1.44× | 1.21× | **0.91×** | **1.19×** | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 9.706 ms | 9.852 ms | 9.806 ms | 3.08× | 3.13× | 3.11× | 1.02× | 1.00× | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 41.844 ms | 43.475 ms | 42.636 ms | 3.21× | 3.33× | 3.27× | 1.04× | 1.02× | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 13.501 ms | 12.105 ms | 10.422 ms | 1.54× | 1.38× | 1.19× | **0.90×** | **1.16×** | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 66.415 ms | 60.038 ms | 53.110 ms | 1.22× | 1.10× | 0.98× | **0.90×** | **1.13×** | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.43 µs | 9.69 µs | 9.88 µs | 6.09× | 6.27× | 6.39× | 1.03× | 0.98× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 64.72 µs | 65.96 µs | 66.32 µs | 4.81× | 4.90× | 4.93× | 1.02× | 0.99× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 586.89 µs | 590.61 µs | 592.93 µs | 4.14× | 4.17× | 4.19× | 1.01× | 1.00× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.730 ms | 5.718 ms | 5.788 ms | 3.84× | 3.84× | 3.88× | 1.00× | 0.99× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 63.521 ms | 57.589 ms | 41.702 ms | 3.44× | 3.12× | 2.26× | **0.91×** | **1.38×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.88 µs | 10.04 µs | 4.99× | 5.19× | 5.27× | 1.04× | 0.98× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 66.48 µs | 67.64 µs | 67.80 µs | 3.33× | 3.39× | 3.40× | 1.02× | 1.00× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 635.97 µs | 637.93 µs | 641.97 µs | 2.63× | 2.64× | 2.65× | 1.00× | 0.99× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.546 ms | 6.585 ms | 6.662 ms | 2.63× | 2.65× | 2.68× | 1.01× | 0.99× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 79.089 ms | 76.217 ms | 63.311 ms | 2.03× | 1.96× | 1.63× | 0.96× | **1.20×** | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 9.15 µs | 9.65 µs | 9.56 µs | 7.70× | 8.13× | 8.05× | **1.06×** | 1.01× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 51.52 µs | 53.44 µs | 53.28 µs | 5.58× | 5.79× | 5.77× | 1.04× | 1.00× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 367.28 µs | 373.72 µs | 373.40 µs | 4.04× | 4.11× | 4.11× | 1.02× | 1.00× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 3.117 ms | 3.135 ms | 3.134 ms | 3.27× | 3.29× | 3.29× | 1.01× | 1.00× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 28.825 ms | 26.271 ms | 22.428 ms | 3.08× | 2.80× | 2.39× | **0.91×** | **1.17×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 9.68 µs | 10.00 µs | 10.06 µs | 8.09× | 8.35× | 8.40× | 1.03× | 0.99× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 53.44 µs | 54.32 µs | 54.80 µs | 4.70× | 4.77× | 4.82× | 1.02× | 0.99× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 389.12 µs | 390.81 µs | 391.16 µs | 3.33× | 3.34× | 3.34× | 1.00× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.502 ms | 3.473 ms | 3.530 ms | 2.59× | 2.56× | 2.61× | 0.99× | 0.98× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 32.189 ms | 31.401 ms | 28.640 ms | 2.18× | 2.12× | 1.94× | 0.98× | **1.10×** | +| fft Float32 64×64 dims=1 | 6.23 µs | 22.52 µs | 22.64 µs | 22.76 µs | 3.61× | 3.63× | 3.65× | 1.01× | 0.99× | +| fft Float32 256×64 dims=1 | 52.20 µs | 123.72 µs | 103.56 µs | 63.96 µs | 2.37× | 1.98× | 1.23× | **0.84×** | **1.62×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 641.05 µs | 479.57 µs | 321.92 µs | 2.62× | 1.96× | 1.32× | **0.75×** | **1.49×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 3.274 ms | 2.288 ms | 1.575 ms | 2.56× | 1.79× | 1.23× | **0.70×** | **1.45×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 16.238 ms | 11.169 ms | 8.207 ms | 2.09× | 1.44× | 1.06× | **0.69×** | **1.36×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 89.441 ms | 63.243 ms | 47.862 ms | 2.01× | 1.42× | 1.07× | **0.71×** | **1.32×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 23.80 µs | 23.92 µs | 24.00 µs | 2.31× | 2.32× | 2.33× | 1.01× | 1.00× | +| fft Float64 256×64 dims=1 | 87.04 µs | 128.96 µs | 116.64 µs | 93.88 µs | 1.48× | 1.34× | 1.08× | **0.90×** | **1.24×** | +| fft Float64 1024×64 dims=1 | 434.17 µs | 692.65 µs | 589.89 µs | 500.53 µs | 1.60× | 1.36× | 1.15× | **0.85×** | **1.18×** | +| fft Float64 4096×64 dims=1 | 2.162 ms | 3.704 ms | 3.145 ms | 2.538 ms | 1.71× | 1.45× | 1.17× | **0.85×** | **1.24×** | +| fft Float64 16384×64 dims=1 | 14.861 ms | 20.696 ms | 18.186 ms | 15.230 ms | 1.39× | 1.22× | 1.02× | **0.88×** | **1.19×** | +| fft Float64 65536×64 dims=1 | 88.463 ms | 114.295 ms | 95.441 ms | 85.547 ms | 1.29× | 1.08× | 0.97× | **0.84×** | **1.12×** | +| rfft Float32 64×64 dims=1 | 6.61 µs | 18.84 µs | 18.96 µs | 19.02 µs | 2.85× | 2.87× | 2.88× | 1.01× | 1.00× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 84.84 µs | 74.52 µs | 58.28 µs | 2.08× | 1.82× | 1.43× | **0.88×** | **1.28×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 398.04 µs | 323.64 µs | 251.92 µs | 2.77× | 2.25× | 1.75× | **0.81×** | **1.28×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 1.883 ms | 1.416 ms | 1.129 ms | 2.73× | 2.06× | 1.64× | **0.75×** | **1.25×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 8.886 ms | 6.331 ms | 5.244 ms | 2.38× | 1.70× | 1.41× | **0.71×** | **1.21×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 43.449 ms | 30.490 ms | 26.911 ms | 2.28× | 1.60× | 1.41× | **0.70×** | **1.13×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 19.88 µs | 20.00 µs | 20.04 µs | 2.98× | 2.99× | 3.00× | 1.01× | 1.00× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 5.795 ms | 5.333 ms | 4.905 ms | 1.86× | 1.71× | 1.58× | **0.92×** | **1.09×** | +| rfft Float64 256×64 dims=1 | 44.56 µs | 87.40 µs | 80.84 µs | 71.40 µs | 1.96× | 1.81× | 1.60× | **0.92×** | **1.13×** | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 6.792 ms | 6.023 ms | 5.521 ms | 1.85× | 1.64× | 1.50× | **0.89×** | **1.09×** | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 414.57 µs | 367.56 µs | 323.68 µs | 1.94× | 1.72× | 1.51× | **0.89×** | **1.14×** | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 8.002 ms | 6.786 ms | 6.211 ms | 1.89× | 1.60× | 1.46× | **0.85×** | **1.09×** | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.974 ms | 1.675 ms | 1.515 ms | 1.90× | 1.61× | 1.46× | **0.85×** | **1.11×** | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 9.841 ms | 8.351 ms | 7.766 ms | 1.60× | 1.36× | 1.26× | **0.85×** | **1.08×** | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 51.373 ms | 42.129 ms | 40.236 ms | 1.35× | 1.11× | 1.06× | **0.82×** | 1.05× | +| fft Float32 64×64 dims=2 | 6.13 µs | 27.16 µs | 27.32 µs | 27.44 µs | 4.43× | 4.46× | 4.48× | 1.01× | 1.00× | +| fft Float32 64×256 dims=2 | 79.52 µs | 152.72 µs | 152.96 µs | 123.28 µs | 1.92× | 1.92× | 1.55× | 1.00× | **1.24×** | +| fft Float32 64×1024 dims=2 | 433.65 µs | 855.77 µs | 837.25 µs | 677.01 µs | 1.97× | 1.93× | 1.56× | 0.98× | **1.24×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 5.921 ms | 5.970 ms | 4.695 ms | 1.26× | 1.27× | 1.00× | 1.01× | **1.27×** | +| fft Float32 64×16384 dims=2 | 24.311 ms | 33.530 ms | 31.999 ms | 26.281 ms | 1.38× | 1.32× | 1.08× | 0.95× | **1.22×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 204.301 ms | 211.237 ms | 165.618 ms | 1.19× | 1.23× | 0.96× | 1.03× | **1.28×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.56 µs | 29.00 µs | 28.84 µs | 2.63× | 2.67× | 2.66× | 1.02× | 1.01× | +| fft Float64 64×256 dims=2 | 108.96 µs | 166.52 µs | 165.52 µs | 139.28 µs | 1.53× | 1.52× | 1.28× | 0.99× | **1.19×** | +| fft Float64 64×1024 dims=2 | 883.53 µs | 1.189 ms | 1.230 ms | 1.033 ms | 1.35× | 1.39× | 1.17× | 1.03× | **1.19×** | +| fft Float64 64×4096 dims=2 | 5.347 ms | 6.816 ms | 7.142 ms | 6.249 ms | 1.27× | 1.34× | 1.17× | 1.05× | **1.14×** | +| fft Float64 64×16384 dims=2 | 34.143 ms | 44.409 ms | 47.666 ms | 39.601 ms | 1.30× | 1.40× | 1.16× | **1.07×** | **1.20×** | +| fft Float64 64×65536 dims=2 | 247.287 ms | 270.970 ms | 275.226 ms | 239.096 ms | 1.10× | 1.11× | 0.97× | 1.02× | **1.15×** | +| rfft Float32 64×64 dims=2 | 6.60 µs | 22.20 µs | 22.32 µs | 22.28 µs | 3.36× | 3.38× | 3.38× | 1.01× | 1.00× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 108.84 µs | 97.64 µs | 80.32 µs | 1.88× | 1.69× | 1.39× | **0.90×** | **1.22×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 542.45 µs | 460.77 µs | 393.40 µs | 1.88× | 1.59× | 1.36× | **0.85×** | **1.17×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 2.858 ms | 2.444 ms | 2.085 ms | 1.60× | 1.37× | 1.17× | **0.86×** | **1.17×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 14.192 ms | 11.673 ms | 10.536 ms | 1.22× | 1.00× | 0.90× | **0.82×** | **1.11×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 71.405 ms | 57.642 ms | 56.336 ms | 1.04× | 0.84× | 0.82× | **0.81×** | 1.02× | +| rfft Float64 64×64 dims=2 | 6.61 µs | 23.48 µs | 23.56 µs | 23.80 µs | 3.55× | 3.56× | 3.60× | 1.00× | 0.99× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 122.84 µs | 115.84 µs | 107.12 µs | 1.71× | 1.62× | 1.50× | **0.94×** | **1.08×** | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 579.85 µs | 530.09 µs | 484.33 µs | 1.67× | 1.52× | 1.39× | **0.91×** | **1.09×** | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 3.269 ms | 2.956 ms | 2.806 ms | 1.20× | 1.09× | 1.03× | **0.90×** | **1.05×** | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 15.739 ms | 13.532 ms | 12.624 ms | 1.11× | 0.96× | 0.89× | **0.86×** | **1.07×** | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 89.091 ms | 79.682 ms | 76.462 ms | 0.80× | 0.71× | 0.68× | **0.89×** | 1.04× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `int`/`fftw` | `large`/`fftw` | `sc`/`fftw` | `int` vs `large` | `sc` vs `large` | +|:--|--:|--:|--:|--:|--:| +| ComplexF32 fft 2d | 2.53× (1.19–4.83) | 2.35× (1.00–5.22) | 1.95× (0.73–5.03) | **0.93×** (0.84–1.08) | **1.20×** (0.98–1.43) | +| ComplexF32 fft 3d | 4.38× (3.44–6.09) | 4.34× (3.12–6.27) | 4.10× (2.26–6.39) | **0.99×** (0.91–1.03) | **1.06×** (0.98–1.38) | +| ComplexF32 fft awkward | 2.68× (1.31–6.71) | 1.77× (0.92–3.48) | 1.44× (0.74–2.94) | **0.66×** (0.48–0.90) | **1.23×** (1.08–1.38) | +| ComplexF32 fft batched_dim1 | 2.50× (2.01–3.61) | 1.93× (1.42–3.63) | 1.42× (1.06–3.65) | **0.77×** (0.69–1.01) | **1.36×** (0.99–1.62) | +| ComplexF32 fft batched_dim2 | 1.81× (1.19–4.43) | 1.80× (1.23–4.46) | 1.50× (0.96–4.48) | **1.00×** (0.95–1.03) | **1.20×** (1.00–1.28) | +| ComplexF32 fft pow2 | 1.71× (0.65–2.77) | 1.11× (0.40–1.90) | 0.89× (0.34–1.68) | **0.65×** (0.35–1.07) | **1.25×** (0.99–1.57) | +| ComplexF32 fft prime | 2.34× (1.42–6.55) | 1.70× (0.73–6.57) | 1.38× (0.61–6.58) | **0.73×** (0.38–1.00) | **1.23×** (0.98–1.46) | +| ComplexF32 fft smooth | 4.45× (2.02–8.66) | 4.49× (2.02–8.73) | 4.42× (2.02–8.74) | **1.01×** (0.98–1.06) | **1.02×** (0.99–1.15) | +| ComplexF64 fft 2d | 1.95× (1.03–4.15) | 1.86× (0.87–4.46) | 1.70× (0.79–4.30) | **0.95×** (0.84–1.07) | **1.09×** (1.00–1.22) | +| ComplexF64 fft 3d | 2.98× (2.03–4.99) | 2.99× (1.96–5.19) | 2.91× (1.63–5.27) | **1.01×** (0.96–1.04) | **1.03×** (0.98–1.20) | +| ComplexF64 fft awkward | 2.21× (0.98–4.88) | 1.71× (0.81–3.20) | 1.57× (0.73–3.00) | **0.77×** (0.52–0.96) | **1.09×** (1.00–1.17) | +| ComplexF64 fft batched_dim1 | 1.60× (1.29–2.31) | 1.42× (1.08–2.32) | 1.22× (0.97–2.33) | **0.89×** (0.84–1.01) | **1.16×** (1.00–1.24) | +| ComplexF64 fft batched_dim2 | 1.46× (1.10–2.63) | 1.51× (1.11–2.67) | 1.32× (0.97–2.66) | **1.03×** (0.99–1.07) | **1.14×** (1.01–1.20) | +| ComplexF64 fft pow2 | 1.23× (0.76–1.72) | 0.94× (0.38–1.75) | 0.86× (0.37–1.76) | **0.77×** (0.47–1.10) | **1.10×** (0.97–1.22) | +| ComplexF64 fft prime | 2.00× (1.08–3.91) | 1.65× (0.79–3.92) | 1.53× (0.74–3.92) | **0.83×** (0.52–1.01) | **1.08×** (0.93–1.18) | +| ComplexF64 fft smooth | 2.92× (1.48–4.63) | 2.95× (1.50–4.88) | 2.93× (1.45–4.89) | **1.01×** (0.95–1.06) | **1.01×** (0.97–1.16) | +| Float32 rfft 2d | 2.99× (1.79–6.92) | 2.74× (1.46–7.05) | 2.40× (1.11–7.12) | **0.92×** (0.81–1.02) | **1.14×** (0.99–1.33) | +| Float32 rfft 3d | 4.45× (3.08–7.70) | 4.47× (2.80–8.13) | 4.32× (2.39–8.05) | **1.00×** (0.91–1.06) | **1.04×** (1.00–1.17) | +| Float32 rfft awkward | 2.77× (1.36–6.79) | 1.83× (0.95–3.45) | 1.49× (0.76–2.95) | **0.66×** (0.44–0.90) | **1.23×** (1.09–1.39) | +| Float32 rfft batched_dim1 | 2.50× (2.08–2.85) | 2.01× (1.60–2.87) | 1.69× (1.41–2.88) | **0.80×** (0.70–1.01) | **1.19×** (1.00–1.28) | +| Float32 rfft batched_dim2 | 1.70× (1.04–3.36) | 1.48× (0.84–3.38) | 1.33× (0.82–3.38) | **0.87×** (0.81–1.01) | **1.11×** (1.00–1.22) | +| Float32 rfft pow2 | 2.38× (1.56–3.50) | 1.79× (0.79–3.55) | 1.54× (0.73–3.48) | **0.75×** (0.43–1.01) | **1.16×** (0.99–1.33) | +| Float32 rfft prime | 2.18× (1.30–4.21) | 1.58× (0.58–3.45) | 1.28× (0.54–2.81) | **0.72×** (0.39–1.01) | **1.23×** (0.99–1.47) | +| Float32 rfft smooth | 4.68× (2.16–8.20) | 4.70× (2.14–8.19) | 4.67× (2.16–8.16) | **1.00×** (0.97–1.04) | **1.01×** (0.98–1.11) | +| Float64 rfft 2d | 2.38× (1.06–7.84) | 2.25× (0.90–8.06) | 2.09× (0.82–8.08) | **0.94×** (0.82–1.04) | **1.08×** (1.00–1.19) | +| Float64 rfft 3d | 3.72× (2.18–8.09) | 3.73× (2.12–8.35) | 3.69× (1.94–8.40) | **1.00×** (0.98–1.03) | **1.01×** (0.98–1.10) | +| Float64 rfft awkward | 2.39× (0.96–6.41) | 1.84× (0.80–4.09) | 1.70× (0.72–3.82) | **0.77×** (0.50–0.95) | **1.08×** (0.98–1.18) | +| Float64 rfft batched_dim1 | 1.89× (1.35–2.98) | 1.67× (1.11–2.99) | 1.54× (1.06–3.00) | **0.89×** (0.82–1.01) | **1.08×** (1.00–1.14) | +| Float64 rfft batched_dim2 | 1.49× (0.80–3.55) | 1.37× (0.71–3.56) | 1.29× (0.68–3.60) | **0.92×** (0.86–1.00) | **1.05×** (0.99–1.09) | +| Float64 rfft pow2 | 1.78× (0.85–3.79) | 1.48× (0.48–3.88) | 1.38× (0.45–3.93) | **0.83×** (0.53–1.02) | **1.07×** (0.96–1.14) | +| Float64 rfft prime | 2.29× (1.21–4.55) | 1.89× (0.67–4.10) | 1.75× (0.70–3.48) | **0.83×** (0.52–1.01) | **1.08×** (0.92–1.18) | +| Float64 rfft smooth | 3.61× (1.74–6.90) | 3.63× (1.76–7.07) | 3.64× (1.65–7.28) | **1.00×** (0.93–1.04) | **1.00×** (0.96–1.07) | +| **all** | 2.45× (0.65–8.66) | 2.03× (0.38–8.73) | 1.82× (0.34–8.74) | **0.83×** (0.35–1.10), 505 cases, 311 slower by >5% | **1.12×** (0.92–1.62), 505 cases, 2 slower by >5% | 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+ "exec_alloc": 0, + "exec_min": 0.0062113920000000005, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.40113902924, + "nthreads": 1, + "plan_min": 9.84e-6, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255893, + "sum_re": -2384.3887021656265 + } + ] +} \ No newline at end of file From bd1686aadd86555e2a9155d80a8ec98cf3d487f9 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 13:44:37 +0000 Subject: [PATCH 15/21] compare3: record the case selection of a column and let --skip-existing reuse only columns that cover the current run --- benchmark/compare3.jl | 32 ++++++++++++++++++++++++++++---- benchmark/compare3_worker.jl | 5 ++++- 2 files changed, 32 insertions(+), 5 deletions(-) diff --git a/benchmark/compare3.jl b/benchmark/compare3.jl index 9582351..934fbc5 100644 --- a/benchmark/compare3.jl +++ b/benchmark/compare3.jl @@ -29,7 +29,8 @@ run is therefore Environments are created under `envs/NAME/` (git-ignored) and re-used; delete one to rebuild it. `--skip-existing` keeps a column whose complete JSON file -is already in `--out` (e.g. to add one column to a finished run). Per-run JSON files land in `--out` (default +is already in `--out` and whose recorded case selection covers the current +one (e.g. to add one column to a finished run); otherwise it is re-measured. Per-run JSON files land in `--out` (default `compare3_results/`) as `NAME_tN.json`; `--render-only` re-renders the table from them without benchmarking. =# @@ -89,11 +90,34 @@ function ensure_env(impl) return dir end +# Does the case selection recorded in a results file cover the current one? +# (files without a recorded scope — older runs — are accepted with a warning) +function scope_covers(meta) + haskey(meta, "scope") || (@warn "results file has no recorded scope; assuming it covers this run"; return true) + sc = meta["scope"] + cur_only = split(getopt("--only", "1d,nd,batched,threads"), ",") + cur_kinds = split(getopt("--kinds", "fft,rfft"), ",") + cur_classes = split(getopt("--classes", "pow2,smooth,prime,awkward"), ",") + cur_maxlog2 = parse(Int, getopt("--maxlog2", QUICK ? "14" : "22")) + cur_sizes = let v = getopt("--sizes", ""); isempty(v) ? Int[] : parse.(Int, split(v, ",")) end + ok = all(o -> o in sc["only"] || (o == "threads"), cur_only) && # (the threads section is empty at 1 thread) + all(k -> k in sc["kinds"], cur_kinds) && + (!("1d" in cur_only) || all(c -> c in sc["classes"], cur_classes)) && + sc["maxlog2"] >= cur_maxlog2 && + (isempty(sc["sizes"]) || (!isempty(cur_sizes) && all(n -> n in sc["sizes"], cur_sizes))) + return ok +end + function run_worker(impl, nthreads) out = joinpath(OUTDIR, "$(impl.name)_t$(nthreads).json") - if "--skip-existing" in ARGS && isfile(out) && get(JSON.parsefile(out), "complete", false) - @info "keeping existing results" impl.name nthreads out - return out + if "--skip-existing" in ARGS && isfile(out) + d = JSON.parsefile(out) + if get(d, "complete", false) && scope_covers(d["meta"]) + @info "keeping existing results" impl.name nthreads out + return out + else + @warn "existing results do not cover this run (incomplete or narrower scope); re-measuring" impl.name nthreads out + end end dir = ensure_env(impl) kind = impl.spec == "fftw" ? "fftw" : "ffta" diff --git a/benchmark/compare3_worker.jl b/benchmark/compare3_worker.jl index 14c76cc..97fd054 100644 --- a/benchmark/compare3_worker.jl +++ b/benchmark/compare3_worker.jl @@ -81,7 +81,10 @@ end const RESULTS = Dict{String,Any}[] const META = Dict("impl" => IMPL, "version" => VERSION_STR, "julia" => string(VERSION), "threads" => NTHREADS, "arch" => String(Sys.ARCH), "cpu" => Sys.CPU_NAME, - "date" => string(now(UTC)), "seconds" => SECONDS) + "date" => string(now(UTC)), "seconds" => SECONDS, + # the case selection this column covers (checked by `--skip-existing`) + "scope" => Dict("only" => ONLY, "kinds" => String.(collect(KINDS)), "classes" => CLASSES, + "maxlog2" => MAXLOG2, "sizes" => SIZES, "measure" => MEASURE)) function flush_results(complete) open(OUTFILE, "w") do io JSON.print(io, Dict("meta" => META, "complete" => complete, "results" => RESULTS), 1) From b45c3cdfa92a978c2ad1b6b84395b889d9af78b5 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 14:08:34 +0000 Subject: [PATCH 16/21] benchmark: DSP.jl workloads at 1/4/16 threads and the 4/16-thread MEASURE sweeps on integration/experiments --- .../compare3/aarch64/final/DSP_WORKLOADS.md | 89 ++++++++++++++----- .../compare3/aarch64/final/MEASURE_t16.md | 42 ++++----- .../compare3/aarch64/final/MEASURE_t4.md | 23 +++++ 3 files changed, 113 insertions(+), 41 deletions(-) create mode 100644 benchmark/compare3/aarch64/final/MEASURE_t4.md diff --git a/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md index a2ab3d6..d7d86f0 100644 --- a/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md +++ b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md @@ -1,24 +1,73 @@ -# DSP.jl workloads, FFTW vs FFTA integration/experiments (aarch64, 1 thread, DSP.jl ffta-eval branch) +# DSP.jl workloads, FFTW vs FFTA integration/experiments @ 57ce6e3 (aarch64; DSP.jl ffta-eval branch; FFTW with set_num_threads(nthreads), FFTA plans default num_threads) +## 1 thread(s) ``` == FFTW -welch_pgram(x,1024,512) n=2^18 1.981 ms -periodogram(x) n=2^16 0.826 ms -conv(a,b) 2^16*2^12 3.507 ms -conv(512x512, 16x16) 5.062 ms -conv(64^3, 8^3) 10.857 ms -fftfilt(b257, x) n=2^18 2.589 ms -stft(x,512,256) n=2^17 1.052 ms -mt_pgram(x) n=2^14 40.45 ms -hilbert(x) n=2^17 3.735 ms -== FFTA integration/experiments -welch_pgram(x,1024,512) n=2^18 2.516 ms -periodogram(x) n=2^16 1.449 ms -conv(a,b) 2^16*2^12 4.014 ms -conv(512x512, 16x16) 7.774 ms -conv(64^3, 8^3) 26.035 ms -fftfilt(b257, x) n=2^18 3.251 ms -stft(x,512,256) n=2^17 1.343 ms -mt_pgram(x) n=2^14 40.652 ms -hilbert(x) n=2^17 6.112 ms +welch_pgram(x,1024,512) n=2^18 1.968 ms +periodogram(x) n=2^16 0.835 ms +conv(a,b) 2^16*2^12 3.555 ms +conv(512x512, 16x16) 4.359 ms +conv(64^3, 8^3) 11.402 ms +fftfilt(b257, x) n=2^18 2.575 ms +stft(x,512,256) n=2^17 1.055 ms +mt_pgram(x) n=2^14 40.408 ms +hilbert(x) n=2^17 3.728 ms +== FFTA +welch_pgram(x,1024,512) n=2^18 2.527 ms +periodogram(x) n=2^16 1.169 ms +conv(a,b) 2^16*2^12 3.953 ms +conv(512x512, 16x16) 7.852 ms +conv(64^3, 8^3) 26.442 ms +fftfilt(b257, x) n=2^18 3.262 ms +stft(x,512,256) n=2^17 1.352 ms +mt_pgram(x) n=2^14 40.492 ms +hilbert(x) n=2^17 6.18 ms +``` + +## 4 thread(s) +``` +== FFTW +welch_pgram(x,1024,512) n=2^18 1.985 ms +periodogram(x) n=2^16 0.719 ms +conv(a,b) 2^16*2^12 3.368 ms +conv(512x512, 16x16) 5.327 ms +conv(64^3, 8^3) 12.782 ms +fftfilt(b257, x) n=2^18 9.091 ms +stft(x,512,256) n=2^17 1.016 ms +mt_pgram(x) n=2^14 41.122 ms +hilbert(x) n=2^17 2.765 ms +== FFTA +welch_pgram(x,1024,512) n=2^18 2.566 ms +periodogram(x) n=2^16 1.186 ms +conv(a,b) 2^16*2^12 4.168 ms +conv(512x512, 16x16) 7.69 ms +conv(64^3, 8^3) 25.326 ms +fftfilt(b257, x) n=2^18 3.328 ms +stft(x,512,256) n=2^17 1.374 ms +mt_pgram(x) n=2^14 40.563 ms +hilbert(x) n=2^17 7.82 ms +``` + +## 16 thread(s) +``` +== FFTW +welch_pgram(x,1024,512) n=2^18 1.983 ms +periodogram(x) n=2^16 0.67 ms +conv(a,b) 2^16*2^12 2.702 ms +conv(512x512, 16x16) 5.975 ms +conv(64^3, 8^3) 12.651 ms +fftfilt(b257, x) n=2^18 5.924 ms +stft(x,512,256) n=2^17 1.071 ms +mt_pgram(x) n=2^14 41.038 ms +hilbert(x) n=2^17 2.375 ms +== FFTA +welch_pgram(x,1024,512) n=2^18 2.59 ms +periodogram(x) n=2^16 1.582 ms +conv(a,b) 2^16*2^12 6.308 ms +conv(512x512, 16x16) 7.986 ms +conv(64^3, 8^3) 25.79 ms +fftfilt(b257, x) n=2^18 3.331 ms +stft(x,512,256) n=2^17 1.388 ms +mt_pgram(x) n=2^14 40.738 ms +hilbert(x) n=2^17 9.474 ms ``` diff --git a/benchmark/compare3/aarch64/final/MEASURE_t16.md b/benchmark/compare3/aarch64/final/MEASURE_t16.md index 23574c0..5e3dbb3 100644 --- a/benchmark/compare3/aarch64/final/MEASURE_t16.md +++ b/benchmark/compare3/aarch64/final/MEASURE_t16.md @@ -1,23 +1,23 @@ | case (16 threads) | FFTW ESTIMATE | FFTW MEASURE | FFTA (all) | FFTA / MEASURE | |:--|--:|--:|--:|--:| -| fft ComplexF64 1024 dims=1 | 29.20 µs | 23.32 µs | **6.95 µs** | 0.30× | -| fft ComplexF64 65536 dims=1 | 135.20 µs | 106.80 µs | **1.089 ms** | 10.19× | -| fft ComplexF64 1048576 dims=1 | 3.265 ms | 1.889 ms | **19.815 ms** | 10.49× | -| fft ComplexF32 65536 dims=1 | 77.32 µs | 85.48 µs | **583.45 µs** | 6.83× | -| fft ComplexF32 1048576 dims=1 | 1.911 ms | 1.406 ms | **11.219 ms** | 7.98× | -| fft ComplexF64 1000 dims=1 | 42.68 µs | 33.68 µs | **14.70 µs** | 0.44× | -| fft ComplexF64 1000000 dims=1 | 3.043 ms | 2.593 ms | **48.243 ms** | 18.60× | -| fft ComplexF64 65537 dims=1 | 1.540 ms | 1.611 ms | **9.102 ms** | 5.65× | -| fft ComplexF64 12297 dims=1 | 261.72 µs | 213.96 µs | **1.321 ms** | 6.17× | -| rfft Float64 4096 dims=1 | 14.52 µs | 32.08 µs | **19.80 µs** | 0.62× | -| rfft Float64 65536 dims=1 | 336.80 µs | 165.88 µs | **513.89 µs** | 3.10× | -| rfft Float64 1048576 dims=1 | 5.139 ms | 2.427 ms | **11.567 ms** | 4.77× | -| rfft Float32 65536 dims=1 | 235.88 µs | 215.84 µs | **302.52 µs** | 1.40× | -| fft ComplexF64 256×256 dims=(1, 2) | 3.116 ms | 88.28 µs | **158.72 µs** | 1.80× | -| fft ComplexF64 1024×1024 dims=(1, 2) | 2.309 ms | 1.638 ms | **3.317 ms** | 2.02× | -| rfft Float64 1024×1024 dims=(1, 2) | 2.649 ms | 715.05 µs | **771.21 µs** | 1.08× | -| fft ComplexF64 64×64×64 dims=(1, 2, 3) | 252.68 µs | 252.72 µs | **813.57 µs** | 3.22× | -| fft ComplexF64 4096×64 dims=1 | 196.28 µs | 185.60 µs | **149.20 µs** | 0.80× | -| rfft Float64 4096×64 dims=1 | 99.96 µs | 105.48 µs | **81.80 µs** | 0.78× | -| fft ComplexF64 64×4096 dims=2 | 413.01 µs | 410.72 µs | **483.93 µs** | 1.18× | -| rfft Float64 1024×1024 dims=1 | 274.04 µs | 318.36 µs | **278.72 µs** | 0.88× | +| fft ComplexF64 1024 dims=1 | 30.32 µs | 28.76 µs | **6.97 µs** | 0.24× | +| fft ComplexF64 65536 dims=1 | 142.60 µs | 116.60 µs | **1.047 ms** | 8.98× | +| fft ComplexF64 1048576 dims=1 | 3.033 ms | 1.785 ms | **1.841 ms** | 1.03× | +| fft ComplexF32 65536 dims=1 | 83.40 µs | 86.84 µs | **639.85 µs** | 7.37× | +| fft ComplexF32 1048576 dims=1 | 2.171 ms | 1.259 ms | **1.125 ms** | 0.89× | +| fft ComplexF64 1000 dims=1 | 44.20 µs | 33.64 µs | **14.78 µs** | 0.44× | +| fft ComplexF64 1000000 dims=1 | 2.925 ms | 2.485 ms | **47.496 ms** | 19.12× | +| fft ComplexF64 65537 dims=1 | 1.532 ms | 1.506 ms | **9.104 ms** | 6.05× | +| fft ComplexF64 12297 dims=1 | 263.92 µs | 215.40 µs | **1.330 ms** | 6.18× | +| rfft Float64 4096 dims=1 | 14.54 µs | 31.44 µs | **19.82 µs** | 0.63× | +| rfft Float64 65536 dims=1 | 345.92 µs | 173.56 µs | **526.37 µs** | 3.03× | +| rfft Float64 1048576 dims=1 | 5.328 ms | 2.707 ms | **3.539 ms** | 1.31× | +| rfft Float32 65536 dims=1 | 218.16 µs | 186.32 µs | **299.56 µs** | 1.61× | +| fft ComplexF64 256×256 dims=(1, 2) | 2.916 ms | 90.56 µs | **156.36 µs** | 1.73× | +| fft ComplexF64 1024×1024 dims=(1, 2) | 2.282 ms | 1.650 ms | **3.375 ms** | 2.05× | +| rfft Float64 1024×1024 dims=(1, 2) | 2.615 ms | 719.41 µs | **779.89 µs** | 1.08× | +| fft ComplexF64 64×64×64 dims=(1, 2, 3) | 260.52 µs | 263.40 µs | **797.97 µs** | 3.03× | +| fft ComplexF64 4096×64 dims=1 | 204.12 µs | 191.20 µs | **150.68 µs** | 0.79× | +| rfft Float64 4096×64 dims=1 | 102.76 µs | 102.56 µs | **81.44 µs** | 0.79× | +| fft ComplexF64 64×4096 dims=2 | 411.53 µs | 407.77 µs | **489.01 µs** | 1.20× | +| rfft Float64 1024×1024 dims=1 | 294.48 µs | 290.36 µs | **288.96 µs** | 1.00× | diff --git a/benchmark/compare3/aarch64/final/MEASURE_t4.md b/benchmark/compare3/aarch64/final/MEASURE_t4.md new file mode 100644 index 0000000..fd206d9 --- /dev/null +++ b/benchmark/compare3/aarch64/final/MEASURE_t4.md @@ -0,0 +1,23 @@ +| case (4 threads) | FFTW ESTIMATE | FFTW MEASURE | FFTA (all) | FFTA / MEASURE | +|:--|--:|--:|--:|--:| +| fft ComplexF64 1024 dims=1 | 14.08 µs | 13.32 µs | **6.97 µs** | 0.52× | +| fft ComplexF64 65536 dims=1 | 354.16 µs | 303.96 µs | **1.062 ms** | 3.49× | +| fft ComplexF64 1048576 dims=1 | 11.399 ms | 5.510 ms | **5.451 ms** | 0.99× | +| fft ComplexF32 65536 dims=1 | 199.88 µs | 176.24 µs | **587.77 µs** | 3.33× | +| fft ComplexF32 1048576 dims=1 | 6.585 ms | 3.827 ms | **3.194 ms** | 0.83× | +| fft ComplexF64 1000 dims=1 | 14.60 µs | 14.60 µs | **14.78 µs** | 1.01× | +| fft ComplexF64 1000000 dims=1 | 10.061 ms | 7.473 ms | **49.644 ms** | 6.64× | +| fft ComplexF64 65537 dims=1 | 2.198 ms | 2.136 ms | **9.101 ms** | 4.26× | +| fft ComplexF64 12297 dims=1 | 368.04 µs | 312.64 µs | **1.345 ms** | 4.30× | +| rfft Float64 4096 dims=1 | 24.16 µs | 24.44 µs | **19.80 µs** | 0.81× | +| rfft Float64 65536 dims=1 | 388.80 µs | 283.72 µs | **537.93 µs** | 1.90× | +| rfft Float64 1048576 dims=1 | 6.353 ms | 4.746 ms | **5.368 ms** | 1.13× | +| rfft Float32 65536 dims=1 | 264.80 µs | 238.20 µs | **302.80 µs** | 1.27× | +| fft ComplexF64 256×256 dims=(1, 2) | 382.41 µs | 255.56 µs | **430.97 µs** | 1.69× | +| fft ComplexF64 1024×1024 dims=(1, 2) | 8.207 ms | 4.699 ms | **8.877 ms** | 1.89× | +| rfft Float64 1024×1024 dims=(1, 2) | 2.389 ms | 2.247 ms | **2.609 ms** | 1.16× | +| fft ComplexF64 64×64×64 dims=(1, 2, 3) | 773.81 µs | 775.33 µs | **2.214 ms** | 2.86× | +| fft ComplexF64 4096×64 dims=1 | 577.65 µs | 546.13 µs | **642.61 µs** | 1.18× | +| rfft Float64 4096×64 dims=1 | 281.96 µs | 282.84 µs | **330.48 µs** | 1.17× | +| fft ComplexF64 64×4096 dims=2 | 1.462 ms | 1.431 ms | **1.704 ms** | 1.19× | +| rfft Float64 1024×1024 dims=1 | 968.41 µs | 974.57 µs | **1.167 ms** | 1.20× | From d66f1f39fdca2c5f46622b055c3f8ac931b7d9ed Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 14:27:01 +0000 Subject: [PATCH 17/21] benchmark: DSP.jl workloads at 1/4/16 threads with lazily created workers --- .../compare3/aarch64/final/DSP_WORKLOADS.md | 56 +++++++++---------- 1 file changed, 28 insertions(+), 28 deletions(-) diff --git a/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md index d7d86f0..6ed38af 100644 --- a/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md +++ b/benchmark/compare3/aarch64/final/DSP_WORKLOADS.md @@ -1,4 +1,4 @@ -# DSP.jl workloads, FFTW vs FFTA integration/experiments @ 57ce6e3 (aarch64; DSP.jl ffta-eval branch; FFTW with set_num_threads(nthreads), FFTA plans default num_threads) +# DSP.jl workloads, FFTW vs FFTA (integration/experiments + lazy workers), aarch64; DSP.jl ffta-eval branch; FFTW with set_num_threads(nthreads), FFTA plans default num_threads ## 1 thread(s) ``` @@ -13,15 +13,15 @@ stft(x,512,256) n=2^17 1.055 ms mt_pgram(x) n=2^14 40.408 ms hilbert(x) n=2^17 3.728 ms == FFTA -welch_pgram(x,1024,512) n=2^18 2.527 ms -periodogram(x) n=2^16 1.169 ms -conv(a,b) 2^16*2^12 3.953 ms -conv(512x512, 16x16) 7.852 ms -conv(64^3, 8^3) 26.442 ms -fftfilt(b257, x) n=2^18 3.262 ms -stft(x,512,256) n=2^17 1.352 ms -mt_pgram(x) n=2^14 40.492 ms -hilbert(x) n=2^17 6.18 ms +welch_pgram(x,1024,512) n=2^18 2.536 ms +periodogram(x) n=2^16 1.5 ms +conv(a,b) 2^16*2^12 4.178 ms +conv(512x512, 16x16) 7.894 ms +conv(64^3, 8^3) 26.733 ms +fftfilt(b257, x) n=2^18 3.277 ms +stft(x,512,256) n=2^17 1.365 ms +mt_pgram(x) n=2^14 40.533 ms +hilbert(x) n=2^17 6.031 ms ``` ## 4 thread(s) @@ -37,15 +37,15 @@ stft(x,512,256) n=2^17 1.016 ms mt_pgram(x) n=2^14 41.122 ms hilbert(x) n=2^17 2.765 ms == FFTA -welch_pgram(x,1024,512) n=2^18 2.566 ms -periodogram(x) n=2^16 1.186 ms -conv(a,b) 2^16*2^12 4.168 ms -conv(512x512, 16x16) 7.69 ms -conv(64^3, 8^3) 25.326 ms -fftfilt(b257, x) n=2^18 3.328 ms -stft(x,512,256) n=2^17 1.374 ms -mt_pgram(x) n=2^14 40.563 ms -hilbert(x) n=2^17 7.82 ms +welch_pgram(x,1024,512) n=2^18 2.535 ms +periodogram(x) n=2^16 1.127 ms +conv(a,b) 2^16*2^12 4.09 ms +conv(512x512, 16x16) 7.913 ms +conv(64^3, 8^3) 25.68 ms +fftfilt(b257, x) n=2^18 3.299 ms +stft(x,512,256) n=2^17 1.326 ms +mt_pgram(x) n=2^14 40.486 ms +hilbert(x) n=2^17 5.973 ms ``` ## 16 thread(s) @@ -61,13 +61,13 @@ stft(x,512,256) n=2^17 1.071 ms mt_pgram(x) n=2^14 41.038 ms hilbert(x) n=2^17 2.375 ms == FFTA -welch_pgram(x,1024,512) n=2^18 2.59 ms -periodogram(x) n=2^16 1.582 ms -conv(a,b) 2^16*2^12 6.308 ms -conv(512x512, 16x16) 7.986 ms -conv(64^3, 8^3) 25.79 ms -fftfilt(b257, x) n=2^18 3.331 ms -stft(x,512,256) n=2^17 1.388 ms -mt_pgram(x) n=2^14 40.738 ms -hilbert(x) n=2^17 9.474 ms +welch_pgram(x,1024,512) n=2^18 2.538 ms +periodogram(x) n=2^16 1.046 ms +conv(a,b) 2^16*2^12 4.142 ms +conv(512x512, 16x16) 7.831 ms +conv(64^3, 8^3) 25.714 ms +fftfilt(b257, x) n=2^18 3.263 ms +stft(x,512,256) n=2^17 1.357 ms +mt_pgram(x) n=2^14 40.548 ms +hilbert(x) n=2^17 6.102 ms ``` From 324da83584199aae5c9f1f0f1b6bcc57a3ef46e5 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 20:24:17 +0000 Subject: [PATCH 18/21] benchmark: compare3 results for the Stockham engine (aarch64, 1 thread) --- .../compare3/aarch64/stockham/COMPARE3.md | 579 + .../compare3/aarch64/stockham/sh_t1.json | 10995 ++++++++++++++++ 2 files changed, 11574 insertions(+) create mode 100644 benchmark/compare3/aarch64/stockham/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/stockham/sh_t1.json diff --git a/benchmark/compare3/aarch64/stockham/COMPARE3.md b/benchmark/compare3/aarch64/stockham/COMPARE3.md new file mode 100644 index 0000000..f726799 --- /dev/null +++ b/benchmark/compare3/aarch64/stockham/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T20:21:52.605 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `main` | FFTA.jl 0.3.1 @ 4943d2a — `FFTA-main` | +| `sh` | FFTA.jl 0.3.1 @ 6b69e9c — `FFTA-sh` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs main` is the speedup over the `main` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `main` | `sh` | `main`/`fftw` | `sh`/`fftw` | `sh` vs `main` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 35 ns | 37 ns | 0.93× | 0.98× | 0.95× | +| fft Float32 8 dims=1 | 37 ns | 38 ns | 38 ns | 1.02× | 1.03× | 0.98× | +| fft Float32 12 dims=1 | 43 ns | 172 ns | 179 ns | 3.98× | 4.13× | 0.96× | +| fft Float32 16 dims=1 | 55 ns | 67 ns | 68 ns | 1.22× | 1.23× | 0.99× | +| fft Float32 17 dims=1 | 136 ns | 819 ns | 817 ns | 6.02× | 6.01× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.52 µs | 1.52 µs | 6.60× | 6.61× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 170 ns | 174 ns | 1.35× | 1.38× | 0.98× | +| fft Float32 29 dims=1 | 342 ns | 823 ns | 650 ns | 2.40× | 1.90× | **1.27×** | +| fft Float32 31 dims=1 | 387 ns | 831 ns | 656 ns | 2.15× | 1.69× | **1.27×** | +| fft Float32 32 dims=1 | 105 ns | 149 ns | 115 ns | 1.43× | 1.10× | **1.30×** | +| fft Float32 37 dims=1 | 836 ns | 1.07 µs | 1.06 µs | 1.28× | 1.26× | 1.01× | +| fft Float32 41 dims=1 | 817 ns | 1.08 µs | 1.06 µs | 1.32× | 1.30× | 1.01× | +| fft Float32 43 dims=1 | 699 ns | 1.08 µs | 1.08 µs | 1.55× | 1.55× | 1.00× | +| fft Float32 54 dims=1 | 325 ns | 994 ns | 397 ns | 3.06× | 1.22× | **2.50×** | +| fft Float32 60 dims=1 | 217 ns | 1.12 µs | 433 ns | 5.17× | 2.00× | **2.59×** | +| fft Float32 61 dims=1 | 1.19 µs | 1.13 µs | 1.12 µs | 0.95× | 0.94× | 1.01× | +| fft Float32 64 dims=1 | 194 ns | 341 ns | 249 ns | 1.75× | 1.28× | **1.37×** | +| fft Float32 71 dims=1 | 2.40 µs | 2.38 µs | 2.42 µs | 0.99× | 1.01× | 0.98× | +| fft Float32 73 dims=1 | 1.34 µs | 2.39 µs | 2.45 µs | 1.78× | 1.82× | 0.98× | +| fft Float32 79 dims=1 | 1.76 µs | 2.40 µs | 2.49 µs | 1.36× | 1.41× | 0.96× | +| fft Float32 101 dims=1 | 1.94 µs | 2.46 µs | 2.52 µs | 1.27× | 1.30× | 0.97× | +| fft Float32 112 dims=1 | 360 ns | 1.02 µs | 480 ns | 2.84× | 1.33× | **2.13×** | +| fft Float32 120 dims=1 | 392 ns | 2.08 µs | 765 ns | 5.31× | 1.95× | **2.72×** | +| fft Float32 128 dims=1 | 390 ns | 421 ns | 417 ns | 1.08× | 1.07× | 1.01× | +| fft Float32 202 dims=1 | 4.13 µs | 6.41 µs | 6.56 µs | 1.55× | 1.59× | 0.98× | +| fft Float32 243 dims=1 | 1.90 µs | 3.84 µs | 1.87 µs | 2.02× | 0.99× | **2.05×** | +| fft Float32 251 dims=1 | 5.99 µs | 5.29 µs | 4.86 µs | 0.88× | 0.81× | **1.09×** | +| fft Float32 256 dims=1 | 807 ns | 978 ns | 985 ns | 1.21× | 1.22× | 0.99× | +| fft Float32 303 dims=1 | 6.36 µs | 9.36 µs | 9.69 µs | 1.47× | 1.52× | 0.97× | +| fft Float32 360 dims=1 | 2.37 µs | 6.64 µs | 2.38 µs | 2.80× | 1.00× | **2.79×** | +| fft Float32 404 dims=1 | 8.45 µs | 11.88 µs | 12.18 µs | 1.41× | 1.44× | 0.98× | +| fft Float32 504 dims=1 | 2.69 µs | 8.89 µs | 3.50 µs | 3.31× | 1.30× | **2.54×** | +| fft Float32 512 dims=1 | 1.69 µs | 2.08 µs | 1.88 µs | 1.23× | 1.12× | **1.10×** | +| fft Float32 593 dims=1 | 15.24 µs | 23.56 µs | 21.12 µs | 1.55× | 1.39× | **1.12×** | +| fft Float32 606 dims=1 | 12.82 µs | 23.12 µs | 24.32 µs | 1.80× | 1.90× | 0.95× | +| fft Float32 720 dims=1 | 5.25 µs | 13.26 µs | 3.49 µs | 2.53× | 0.66× | **3.80×** | +| fft Float32 1000 dims=1 | 6.69 µs | 13.92 µs | 7.16 µs | 2.08× | 1.07× | **1.94×** | +| fft Float32 1024 dims=1 | 3.64 µs | 4.72 µs | 4.38 µs | 1.30× | 1.20× | **1.08×** | +| fft Float32 1080 dims=1 | 8.77 µs | 22.04 µs | 7.97 µs | 2.51× | 0.91× | **2.76×** | +| fft Float32 1433 dims=1 | 57.64 µs | 52.76 µs | 48.84 µs | 0.92× | 0.85× | **1.08×** | +| fft Float32 1616 dims=1 | 36.12 µs | 46.20 µs | 47.52 µs | 1.28× | 1.32× | 0.97× | +| fft Float32 2018 dims=1 | 73.28 µs | 64.20 µs | 60.40 µs | 0.88× | 0.82× | **1.06×** | +| fft Float32 2048 dims=1 | 7.68 µs | 9.98 µs | 8.68 µs | 1.30× | 1.13× | **1.15×** | +| fft Float32 2304 dims=1 | 12.42 µs | 32.80 µs | 12.26 µs | 2.64× | 0.99× | **2.68×** | +| fft Float32 3027 dims=1 | 112.08 µs | 94.60 µs | 88.24 µs | 0.84× | 0.79× | **1.07×** | +| fft Float32 3491 dims=1 | 158.56 µs | 117.68 µs | 101.36 µs | 0.74× | 0.64× | **1.16×** | +| fft Float32 4036 dims=1 | 149.00 µs | 120.08 µs | 110.92 µs | 0.81× | 0.74× | **1.08×** | +| fft Float32 4096 dims=1 | 16.88 µs | 22.76 µs | 20.52 µs | 1.35× | 1.22× | **1.11×** | +| fft Float32 4860 dims=1 | 49.84 µs | 130.20 µs | 45.04 µs | 2.61× | 0.90× | **2.89×** | +| fft Float32 6054 dims=1 | 225.88 µs | 233.32 µs | 221.40 µs | 1.03× | 0.98× | **1.05×** | +| fft Float32 8192 dims=1 | 48.72 µs | 50.40 µs | 41.96 µs | 1.03× | 0.86× | **1.20×** | +| fft Float32 8198 dims=1 | 411.25 µs | 577.29 µs | 511.53 µs | 1.40× | 1.24× | **1.13×** | +| fft Float32 8443 dims=1 | 413.05 µs | 551.49 µs | 506.93 µs | 1.34× | 1.23× | **1.09×** | +| fft Float32 10290 dims=1 | 97.28 µs | 321.36 µs | 103.44 µs | 3.30× | 1.06× | **3.11×** | +| fft Float32 12297 dims=1 | 624.25 µs | 865.85 µs | 756.05 µs | 1.39× | 1.21× | **1.15×** | +| fft Float32 16144 dims=1 | 629.25 µs | 472.61 µs | 433.69 µs | 0.75× | 0.69× | **1.09×** | +| fft Float32 16384 dims=1 | 109.16 µs | 115.04 µs | 94.32 µs | 1.05× | 0.86× | **1.22×** | +| fft Float32 16396 dims=1 | 831.89 µs | 1.125 ms | 984.09 µs | 1.35× | 1.18× | **1.14×** | +| fft Float32 20507 dims=1 | 1.290 ms | 1.319 ms | 1.128 ms | 1.02× | 0.87× | **1.17×** | +| fft Float32 21875 dims=1 | 264.12 µs | 599.13 µs | 218.52 µs | 2.27× | 0.83× | **2.74×** | +| fft Float32 24594 dims=1 | 1.260 ms | 1.919 ms | 1.715 ms | 1.52× | 1.36× | **1.12×** | +| fft Float32 32768 dims=1 | 278.20 µs | 247.76 µs | 212.04 µs | 0.89× | 0.76× | **1.17×** | +| fft Float32 32822 dims=1 | 2.015 ms | 2.837 ms | 2.510 ms | 1.41× | 1.25× | **1.13×** | +| fft Float32 46305 dims=1 | 560.49 µs | 1.556 ms | 511.25 µs | 2.78× | 0.91× | **3.04×** | +| fft Float32 49233 dims=1 | 3.073 ms | 4.245 ms | 3.644 ms | 1.38× | 1.19× | **1.17×** | +| fft Float32 49757 dims=1 | 2.680 ms | 3.163 ms | 2.472 ms | 1.18× | 0.92× | **1.28×** | +| fft Float32 65536 dims=1 | 563.53 µs | 562.65 µs | 454.09 µs | 1.00× | 0.81× | **1.24×** | +| fft Float32 65584 dims=1 | 3.557 ms | 4.610 ms | 4.007 ms | 1.30× | 1.13× | **1.15×** | +| fft Float32 65644 dims=1 | 4.107 ms | 5.608 ms | 4.665 ms | 1.37× | 1.14× | **1.20×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.359 ms | 797.25 µs | 2.10× | 0.71× | **2.96×** | +| fft Float32 98466 dims=1 | 6.367 ms | 9.314 ms | 8.022 ms | 1.46× | 1.26× | **1.16×** | +| fft Float32 120779 dims=1 | 9.432 ms | 5.703 ms | 5.772 ms | 0.60× | 0.61× | 0.99× | +| fft Float32 131072 dims=1 | 1.322 ms | 1.380 ms | 1.077 ms | 1.04× | 0.81× | **1.28×** | +| fft Float32 131074 dims=1 | 4.394 ms | 12.398 ms | 12.413 ms | 2.82× | 2.82× | 1.00× | +| fft Float32 196611 dims=1 | 6.678 ms | 18.292 ms | 18.602 ms | 2.74× | 2.79× | 0.98× | +| fft Float32 207360 dims=1 | 3.276 ms | 7.254 ms | 1.792 ms | 2.21× | 0.55× | **4.05×** | +| fft Float32 262144 dims=1 | 3.482 ms | 2.427 ms | 2.419 ms | 0.70× | 0.69× | 1.00× | +| fft Float32 262148 dims=1 | 8.965 ms | 23.956 ms | 24.373 ms | 2.67× | 2.72× | 0.98× | +| fft Float32 262576 dims=1 | 18.216 ms | 23.390 ms | 19.612 ms | 1.28× | 1.08× | **1.19×** | +| fft Float32 293201 dims=1 | 30.534 ms | 27.365 ms | 28.555 ms | 0.90× | 0.94× | 0.96× | +| fft Float32 393222 dims=1 | 13.552 ms | 40.297 ms | 42.341 ms | 2.97× | 3.12× | 0.95× | +| fft Float32 441000 dims=1 | 6.625 ms | 16.339 ms | 5.461 ms | 2.47× | 0.82× | **2.99×** | +| fft Float32 524288 dims=1 | 11.364 ms | 5.136 ms | 5.113 ms | 0.45× | 0.45× | 1.00× | +| fft Float32 524294 dims=1 | 47.952 ms | 57.984 ms | 60.781 ms | 1.21× | 1.27× | 0.95× | +| fft Float32 711749 dims=1 | 76.629 ms | 62.593 ms | 62.586 ms | 0.82× | 0.82× | 1.00× | +| fft Float32 786441 dims=1 | 72.471 ms | 89.077 ms | 91.236 ms | 1.23× | 1.26× | 0.98× | +| fft Float32 933120 dims=1 | 18.504 ms | 39.524 ms | 9.842 ms | 2.14× | 0.53× | **4.02×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 38.874 ms | 9.778 ms | 1.59× | 0.40× | **3.98×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 11.421 ms | 11.671 ms | 0.47× | 0.48× | 0.98× | +| fft Float32 1048588 dims=1 | 97.647 ms | 120.572 ms | 117.748 ms | 1.23× | 1.21× | 1.02× | +| fft Float32 1048592 dims=1 | 37.789 ms | 113.880 ms | 103.371 ms | 3.01× | 2.74× | **1.10×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 191.628 ms | 200.478 ms | 1.28× | 1.33× | 0.96× | +| fft Float32 1727797 dims=1 | 174.941 ms | 130.654 ms | 137.742 ms | 0.75× | 0.79× | **0.95×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 99.731 ms | 22.831 ms | 2.46× | 0.56× | **4.37×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 28.171 ms | 27.399 ms | 0.36× | 0.35× | 1.03× | +| fft Float32 4167450 dims=1 | 126.844 ms | 313.853 ms | 93.408 ms | 2.47× | 0.74× | **3.36×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 60.006 ms | 63.487 ms | 0.36× | 0.39× | **0.95×** | +| fft Float64 7 dims=1 | 26 ns | 39 ns | 40 ns | 1.52× | 1.55× | 0.98× | +| fft Float64 8 dims=1 | 25 ns | 39 ns | 39 ns | 1.56× | 1.57× | 0.99× | +| fft Float64 12 dims=1 | 33 ns | 179 ns | 181 ns | 5.37× | 5.45× | 0.99× | +| fft Float64 16 dims=1 | 41 ns | 69 ns | 69 ns | 1.68× | 1.68× | 1.00× | +| fft Float64 17 dims=1 | 136 ns | 502 ns | 502 ns | 3.70× | 3.70× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 914 ns | 914 ns | 3.98× | 3.98× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 174 ns | 173 ns | 1.26× | 1.25× | 1.01× | +| fft Float64 29 dims=1 | 343 ns | 899 ns | 909 ns | 2.62× | 2.65× | 0.99× | +| fft Float64 31 dims=1 | 385 ns | 903 ns | 907 ns | 2.35× | 2.36× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 152 ns | 152 ns | 1.91× | 1.91× | 1.00× | +| fft Float64 37 dims=1 | 771 ns | 1.52 µs | 1.53 µs | 1.97× | 1.98× | 1.00× | +| fft Float64 41 dims=1 | 910 ns | 1.54 µs | 1.54 µs | 1.69× | 1.69× | 1.00× | +| fft Float64 43 dims=1 | 699 ns | 1.54 µs | 1.54 µs | 2.20× | 2.20× | 1.00× | +| fft Float64 54 dims=1 | 274 ns | 1.03 µs | 504 ns | 3.76× | 1.84× | **2.04×** | +| fft Float64 60 dims=1 | 311 ns | 1.19 µs | 502 ns | 3.82× | 1.61× | **2.37×** | +| fft Float64 61 dims=1 | 1.39 µs | 1.58 µs | 1.58 µs | 1.14× | 1.14× | 1.00× | +| fft Float64 64 dims=1 | 310 ns | 350 ns | 351 ns | 1.13× | 1.13× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 3.51 µs | 3.50 µs | 1.15× | 1.14× | 1.00× | +| fft Float64 73 dims=1 | 1.74 µs | 3.50 µs | 3.51 µs | 2.01× | 2.01× | 1.00× | +| fft Float64 79 dims=1 | 2.50 µs | 3.52 µs | 3.53 µs | 1.41× | 1.41× | 1.00× | +| fft Float64 101 dims=1 | 2.37 µs | 3.57 µs | 3.59 µs | 1.51× | 1.51× | 0.99× | +| fft Float64 112 dims=1 | 591 ns | 1.10 µs | 797 ns | 1.86× | 1.35× | **1.38×** | +| fft Float64 120 dims=1 | 634 ns | 2.18 µs | 920 ns | 3.44× | 1.45× | **2.37×** | +| fft Float64 128 dims=1 | 647 ns | 589 ns | 590 ns | 0.91× | 0.91× | 1.00× | +| fft Float64 202 dims=1 | 4.97 µs | 8.79 µs | 8.89 µs | 1.77× | 1.79× | 0.99× | +| fft Float64 243 dims=1 | 1.94 µs | 3.85 µs | 2.58 µs | 1.98× | 1.33× | **1.49×** | +| fft Float64 251 dims=1 | 6.73 µs | 7.55 µs | 7.53 µs | 1.12× | 1.12× | 1.00× | +| fft Float64 256 dims=1 | 1.32 µs | 1.42 µs | 1.42 µs | 1.08× | 1.08× | 1.00× | +| fft Float64 303 dims=1 | 7.79 µs | 12.86 µs | 12.92 µs | 1.65× | 1.66× | 1.00× | +| fft Float64 360 dims=1 | 2.83 µs | 6.97 µs | 3.21 µs | 2.46× | 1.13× | **2.17×** | +| fft Float64 404 dims=1 | 10.46 µs | 16.62 µs | 16.66 µs | 1.59× | 1.59× | 1.00× | +| fft Float64 504 dims=1 | 4.30 µs | 9.51 µs | 4.90 µs | 2.21× | 1.14× | **1.94×** | +| fft Float64 512 dims=1 | 2.83 µs | 2.99 µs | 2.99 µs | 1.06× | 1.06× | 1.00× | +| fft Float64 593 dims=1 | 27.48 µs | 35.00 µs | 35.00 µs | 1.27× | 1.27× | 1.00× | +| fft Float64 606 dims=1 | 15.84 µs | 30.84 µs | 31.04 µs | 1.95× | 1.96× | 0.99× | +| fft Float64 720 dims=1 | 5.64 µs | 14.02 µs | 6.44 µs | 2.49× | 1.14× | **2.18×** | +| fft Float64 1000 dims=1 | 10.26 µs | 14.80 µs | 9.68 µs | 1.44× | 0.94× | **1.53×** | +| fft Float64 1024 dims=1 | 6.30 µs | 6.97 µs | 6.97 µs | 1.11× | 1.11× | 1.00× | +| fft Float64 1080 dims=1 | 9.27 µs | 23.32 µs | 11.32 µs | 2.52× | 1.22× | **2.06×** | +| fft Float64 1433 dims=1 | 77.40 µs | 81.12 µs | 81.00 µs | 1.05× | 1.05× | 1.00× | +| fft Float64 1616 dims=1 | 44.28 µs | 65.68 µs | 65.72 µs | 1.48× | 1.48× | 1.00× | +| fft Float64 2018 dims=1 | 109.44 µs | 88.40 µs | 88.72 µs | 0.81× | 0.81× | 1.00× | +| fft Float64 2048 dims=1 | 13.52 µs | 14.98 µs | 15.00 µs | 1.11× | 1.11× | 1.00× | +| fft Float64 2304 dims=1 | 22.48 µs | 38.44 µs | 23.52 µs | 1.71× | 1.05× | **1.63×** | +| fft Float64 3027 dims=1 | 168.20 µs | 130.08 µs | 131.00 µs | 0.77× | 0.78× | 0.99× | +| fft Float64 3491 dims=1 | 222.48 µs | 175.60 µs | 173.44 µs | 0.79× | 0.78× | 1.01× | +| fft Float64 4036 dims=1 | 223.80 µs | 168.80 µs | 169.32 µs | 0.75× | 0.76× | 1.00× | +| fft Float64 4096 dims=1 | 29.80 µs | 35.12 µs | 35.00 µs | 1.18× | 1.17× | 1.00× | +| fft Float64 4860 dims=1 | 57.56 µs | 138.32 µs | 68.20 µs | 2.40× | 1.18× | **2.03×** | +| fft Float64 6054 dims=1 | 340.04 µs | 312.24 µs | 314.92 µs | 0.92× | 0.93× | 0.99× | +| fft Float64 8192 dims=1 | 84.76 µs | 74.16 µs | 74.20 µs | 0.87× | 0.88× | 1.00× | +| fft Float64 8198 dims=1 | 506.65 µs | 875.33 µs | 876.13 µs | 1.73× | 1.73× | 1.00× | +| fft Float64 8443 dims=1 | 554.85 µs | 965.53 µs | 954.69 µs | 1.74× | 1.72× | 1.01× | +| fft Float64 10290 dims=1 | 149.96 µs | 366.04 µs | 156.16 µs | 2.44× | 1.04× | **2.34×** | +| fft Float64 12297 dims=1 | 777.05 µs | 1.290 ms | 1.371 ms | 1.66× | 1.76× | **0.94×** | +| fft Float64 16144 dims=1 | 922.45 µs | 678.69 µs | 680.49 µs | 0.74× | 0.74× | 1.00× | +| fft Float64 16384 dims=1 | 180.40 µs | 170.96 µs | 169.16 µs | 0.95× | 0.94× | 1.01× | +| fft Float64 16396 dims=1 | 1.036 ms | 1.701 ms | 1.853 ms | 1.64× | 1.79× | **0.92×** | +| fft Float64 20507 dims=1 | 1.694 ms | 2.363 ms | 2.322 ms | 1.39× | 1.37× | 1.02× | +| fft Float64 21875 dims=1 | 384.44 µs | 744.49 µs | 330.40 µs | 1.94× | 0.86× | **2.25×** | +| fft Float64 24594 dims=1 | 1.613 ms | 2.827 ms | 2.979 ms | 1.75× | 1.85× | **0.95×** | +| fft Float64 32768 dims=1 | 444.61 µs | 413.69 µs | 398.01 µs | 0.93× | 0.90× | 1.04× | +| fft Float64 32822 dims=1 | 2.985 ms | 4.980 ms | 5.057 ms | 1.67× | 1.69× | 0.98× | +| fft Float64 46305 dims=1 | 1.031 ms | 1.944 ms | 822.77 µs | 1.89× | 0.80× | **2.36×** | +| fft Float64 49233 dims=1 | 4.545 ms | 7.499 ms | 7.604 ms | 1.65× | 1.67× | 0.99× | +| fft Float64 49757 dims=1 | 4.565 ms | 4.976 ms | 4.914 ms | 1.09× | 1.08× | 1.01× | +| fft Float64 65536 dims=1 | 1.088 ms | 985.05 µs | 981.41 µs | 0.91× | 0.90× | 1.00× | +| fft Float64 65584 dims=1 | 4.401 ms | 7.025 ms | 6.894 ms | 1.60× | 1.57× | 1.02× | +| fft Float64 65644 dims=1 | 6.122 ms | 9.948 ms | 10.190 ms | 1.63× | 1.66× | 0.98× | +| fft Float64 98304 dims=1 | 1.926 ms | 2.688 ms | 1.730 ms | 1.40× | 0.90× | **1.55×** | +| fft Float64 98466 dims=1 | 9.391 ms | 16.584 ms | 15.970 ms | 1.77× | 1.70× | 1.04× | +| fft Float64 120779 dims=1 | 12.568 ms | 9.236 ms | 9.154 ms | 0.73× | 0.73× | 1.01× | +| fft Float64 131072 dims=1 | 2.406 ms | 2.028 ms | 2.003 ms | 0.84× | 0.83× | 1.01× | +| fft Float64 131074 dims=1 | 6.943 ms | 19.592 ms | 20.020 ms | 2.82× | 2.88× | 0.98× | +| fft Float64 196611 dims=1 | 10.356 ms | 29.392 ms | 29.710 ms | 2.84× | 2.87× | 0.99× | +| fft Float64 207360 dims=1 | 4.519 ms | 7.941 ms | 3.614 ms | 1.76× | 0.80× | **2.20×** | +| fft Float64 262144 dims=1 | 5.670 ms | 3.874 ms | 3.744 ms | 0.68× | 0.66× | 1.03× | +| fft Float64 262148 dims=1 | 13.759 ms | 39.175 ms | 39.153 ms | 2.85× | 2.85× | 1.00× | +| fft Float64 262576 dims=1 | 25.621 ms | 41.144 ms | 41.189 ms | 1.61× | 1.61× | 1.00× | +| fft Float64 293201 dims=1 | 41.017 ms | 46.542 ms | 47.817 ms | 1.13× | 1.17× | 0.97× | +| fft Float64 393222 dims=1 | 21.186 ms | 63.518 ms | 62.966 ms | 3.00× | 2.97× | 1.01× | +| fft Float64 441000 dims=1 | 10.759 ms | 21.823 ms | 8.974 ms | 2.03× | 0.83× | **2.43×** | +| fft Float64 524288 dims=1 | 16.863 ms | 8.403 ms | 8.283 ms | 0.50× | 0.49× | 1.01× | +| fft Float64 524294 dims=1 | 69.443 ms | 94.747 ms | 96.602 ms | 1.36× | 1.39× | 0.98× | +| fft Float64 711749 dims=1 | 103.554 ms | 105.033 ms | 101.381 ms | 1.01× | 0.98× | 1.04× | +| fft Float64 786441 dims=1 | 104.363 ms | 143.033 ms | 152.299 ms | 1.37× | 1.46× | **0.94×** | +| fft Float64 933120 dims=1 | 32.838 ms | 49.930 ms | 21.880 ms | 1.52× | 0.67× | **2.28×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 50.503 ms | 21.452 ms | 1.00× | 0.43× | **2.35×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 20.136 ms | 19.390 ms | 0.38× | 0.37× | 1.04× | +| fft Float64 1048588 dims=1 | 141.957 ms | 189.545 ms | 195.045 ms | 1.34× | 1.37× | 0.97× | +| fft Float64 1048592 dims=1 | 64.157 ms | 173.430 ms | 164.078 ms | 2.70× | 2.56× | **1.06×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 326.178 ms | 308.402 ms | 1.50× | 1.41× | **1.06×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 225.374 ms | 225.101 ms | 0.85× | 0.85× | 1.00× | +| fft Float64 1975680 dims=1 | 76.790 ms | 136.089 ms | 54.738 ms | 1.77× | 0.71× | **2.49×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 47.647 ms | 46.021 ms | 0.40× | 0.38× | 1.04× | +| fft Float64 4167450 dims=1 | 214.097 ms | 408.351 ms | 168.650 ms | 1.91× | 0.79× | **2.42×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 104.408 ms | 102.422 ms | 0.44× | 0.43× | 1.02× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 38 ns | 39 ns | 1.59× | 1.62× | 0.98× | +| rfft Float32 8 dims=1 | 22 ns | 54 ns | 54 ns | 2.47× | 2.51× | 0.99× | +| rfft Float32 12 dims=1 | 27 ns | 150 ns | 155 ns | 5.53× | 5.73× | 0.96× | +| rfft Float32 16 dims=1 | 33 ns | 75 ns | 75 ns | 2.29× | 2.28× | 1.01× | +| rfft Float32 17 dims=1 | 134 ns | 183 ns | 183 ns | 1.36× | 1.37× | 1.00× | +| rfft Float32 23 dims=1 | 202 ns | 317 ns | 319 ns | 1.57× | 1.58× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 162 ns | 164 ns | 2.13× | 2.14× | 0.99× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 639 ns | 2.82× | 2.22× | **1.27×** | +| rfft Float32 31 dims=1 | 319 ns | 814 ns | 644 ns | 2.55× | 2.02× | **1.26×** | +| rfft Float32 32 dims=1 | 101 ns | 118 ns | 120 ns | 1.16× | 1.18× | 0.98× | +| rfft Float32 37 dims=1 | 428 ns | 1.05 µs | 1.04 µs | 2.46× | 2.44× | 1.01× | +| rfft Float32 41 dims=1 | 508 ns | 1.06 µs | 1.05 µs | 2.09× | 2.06× | 1.02× | +| rfft Float32 43 dims=1 | 553 ns | 1.06 µs | 1.05 µs | 1.93× | 1.90× | 1.01× | +| rfft Float32 54 dims=1 | 213 ns | 346 ns | 345 ns | 1.62× | 1.62× | 1.00× | +| rfft Float32 60 dims=1 | 219 ns | 718 ns | 749 ns | 3.27× | 3.41× | 0.96× | +| rfft Float32 61 dims=1 | 1.04 µs | 1.10 µs | 1.08 µs | 1.06× | 1.05× | 1.01× | +| rfft Float32 64 dims=1 | 183 ns | 222 ns | 193 ns | 1.21× | 1.06× | **1.15×** | +| rfft Float32 71 dims=1 | 1.37 µs | 2.35 µs | 2.39 µs | 1.71× | 1.74× | 0.99× | +| rfft Float32 73 dims=1 | 1.45 µs | 2.35 µs | 2.37 µs | 1.62× | 1.64× | 0.99× | +| rfft Float32 79 dims=1 | 1.68 µs | 2.36 µs | 2.37 µs | 1.40× | 1.41× | 1.00× | +| rfft Float32 101 dims=1 | 2.69 µs | 2.41 µs | 2.42 µs | 0.89× | 0.90× | 1.00× | +| rfft Float32 112 dims=1 | 288 ns | 627 ns | 452 ns | 2.18× | 1.57× | **1.39×** | +| rfft Float32 120 dims=1 | 287 ns | 1.24 µs | 545 ns | 4.32× | 1.90× | **2.27×** | +| rfft Float32 128 dims=1 | 265 ns | 462 ns | 376 ns | 1.74× | 1.42× | **1.23×** | +| rfft Float32 202 dims=1 | 2.12 µs | 2.63 µs | 2.66 µs | 1.24× | 1.25× | 0.99× | +| rfft Float32 243 dims=1 | 1.18 µs | 3.83 µs | 1.83 µs | 3.25× | 1.55× | **2.10×** | +| rfft Float32 251 dims=1 | 5.48 µs | 5.12 µs | 4.86 µs | 0.93× | 0.89× | **1.05×** | +| rfft Float32 256 dims=1 | 636 ns | 638 ns | 633 ns | 1.00× | 1.00× | 1.01× | +| rfft Float32 303 dims=1 | 8.39 µs | 9.19 µs | 9.29 µs | 1.10× | 1.11× | 0.99× | +| rfft Float32 360 dims=1 | 1.31 µs | 3.81 µs | 1.55 µs | 2.90× | 1.18× | **2.46×** | +| rfft Float32 404 dims=1 | 4.31 µs | 6.72 µs | 6.87 µs | 1.56× | 1.59× | 0.98× | +| rfft Float32 504 dims=1 | 1.53 µs | 5.09 µs | 2.26 µs | 3.32× | 1.47× | **2.25×** | +| rfft Float32 512 dims=1 | 1.14 µs | 1.39 µs | 1.39 µs | 1.22× | 1.23× | 0.99× | +| rfft Float32 593 dims=1 | 21.96 µs | 23.16 µs | 20.56 µs | 1.05× | 0.94× | **1.13×** | +| rfft Float32 606 dims=1 | 6.52 µs | 9.83 µs | 10.00 µs | 1.51× | 1.53× | 0.98× | +| rfft Float32 720 dims=1 | 2.87 µs | 7.27 µs | 2.94 µs | 2.53× | 1.02× | **2.47×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 8.33 µs | 4.41 µs | 2.67× | 1.41× | **1.89×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 2.85 µs | 2.68 µs | 1.30× | 1.22× | **1.06×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 12.42 µs | 4.90 µs | 2.68× | 1.06× | **2.54×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 51.68 µs | 47.88 µs | 0.95× | 0.88× | **1.08×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 24.28 µs | 24.52 µs | 1.38× | 1.40× | 0.99× | +| rfft Float32 2018 dims=1 | 37.16 µs | 26.40 µs | 24.08 µs | 0.71× | 0.65× | **1.10×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 6.29 µs | 6.08 µs | 1.41× | 1.37× | 1.03× | +| rfft Float32 2304 dims=1 | 6.84 µs | 17.48 µs | 7.09 µs | 2.56× | 1.04× | **2.46×** | +| rfft Float32 3027 dims=1 | 71.52 µs | 92.16 µs | 86.28 µs | 1.29× | 1.21× | **1.07×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 115.24 µs | 100.32 µs | 0.77× | 0.67× | **1.15×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 67.36 µs | 63.08 µs | 0.90× | 0.84× | **1.07×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 13.40 µs | 12.08 µs | 1.43× | 1.29× | **1.11×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 74.08 µs | 25.40 µs | 2.91× | 1.00× | **2.92×** | +| rfft Float32 6054 dims=1 | 113.60 µs | 99.04 µs | 92.16 µs | 0.87× | 0.81× | **1.07×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 29.08 µs | 26.84 µs | 1.14× | 1.05× | **1.08×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 264.16 µs | 239.00 µs | 1.28× | 1.15× | **1.11×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 555.41 µs | 503.65 µs | 1.61× | 1.46× | **1.10×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 129.64 µs | 56.88 µs | 2.06× | 0.90× | **2.28×** | +| rfft Float32 12297 dims=1 | 522.37 µs | 850.93 µs | 789.61 µs | 1.63× | 1.51× | **1.08×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 245.68 µs | 226.28 µs | 0.80× | 0.74× | **1.09×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 63.08 µs | 55.24 µs | 1.17× | 1.02× | **1.14×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 591.05 µs | 551.81 µs | 1.41× | 1.32× | **1.07×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 1.313 ms | 1.120 ms | 1.36× | 1.16× | **1.17×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 581.93 µs | 214.12 µs | 2.95× | 1.09× | **2.72×** | +| rfft Float32 24594 dims=1 | 631.01 µs | 880.81 µs | 819.29 µs | 1.40× | 1.30× | **1.08×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 143.12 µs | 123.12 µs | 1.22× | 1.05× | **1.16×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 1.328 ms | 1.142 ms | 1.32× | 1.13× | **1.16×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 1.459 ms | 503.25 µs | 3.22× | 1.11× | **2.90×** | +| rfft Float32 49233 dims=1 | 2.572 ms | 4.216 ms | 3.582 ms | 1.64× | 1.39× | **1.18×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 3.156 ms | 2.488 ms | 1.16× | 0.92× | **1.27×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 310.92 µs | 276.04 µs | 1.27× | 1.13× | **1.13×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 2.306 ms | 2.016 ms | 1.35× | 1.18× | **1.14×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 2.935 ms | 2.480 ms | 1.44× | 1.22× | **1.18×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.161 ms | 427.49 µs | 2.26× | 0.83× | **2.72×** | +| rfft Float32 98466 dims=1 | 3.089 ms | 4.357 ms | 3.835 ms | 1.41× | 1.24× | **1.14×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 5.675 ms | 5.713 ms | 0.54× | 0.54× | 0.99× | +| rfft Float32 131072 dims=1 | 614.25 µs | 756.21 µs | 605.33 µs | 1.23× | 0.99× | **1.25×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 5.770 ms | 5.763 ms | 2.61× | 2.61× | 1.00× | +| rfft Float32 196611 dims=1 | 6.210 ms | 18.153 ms | 18.518 ms | 2.92× | 2.98× | 0.98× | +| rfft Float32 207360 dims=1 | 1.700 ms | 3.435 ms | 1.078 ms | 2.02× | 0.63× | **3.19×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 1.772 ms | 1.314 ms | 1.06× | 0.79× | **1.35×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 12.612 ms | 12.609 ms | 2.78× | 2.78× | 1.00× | +| rfft Float32 262576 dims=1 | 8.653 ms | 11.556 ms | 9.981 ms | 1.34× | 1.15× | **1.16×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 26.776 ms | 28.215 ms | 0.85× | 0.89× | **0.95×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 18.628 ms | 18.921 ms | 2.74× | 2.78× | 0.98× | +| rfft Float32 441000 dims=1 | 3.804 ms | 8.824 ms | 3.174 ms | 2.32× | 0.83× | **2.78×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 3.387 ms | 3.384 ms | 0.90× | 0.89× | 1.00× | +| rfft Float32 524294 dims=1 | 23.932 ms | 27.188 ms | 28.945 ms | 1.14× | 1.21× | **0.94×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 60.672 ms | 63.276 ms | 0.67× | 0.69× | 0.96× | +| rfft Float32 786441 dims=1 | 89.117 ms | 86.255 ms | 91.260 ms | 0.97× | 1.02× | **0.95×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 19.031 ms | 5.622 ms | 2.11× | 0.62× | **3.39×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 20.303 ms | 5.615 ms | 2.34× | 0.65× | **3.62×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 7.115 ms | 7.083 ms | 0.91× | 0.90× | 1.00× | +| rfft Float32 1048588 dims=1 | 47.864 ms | 61.881 ms | 60.765 ms | 1.29× | 1.27× | 1.02× | +| rfft Float32 1048592 dims=1 | 18.670 ms | 50.826 ms | 50.797 ms | 2.72× | 2.72× | 1.00× | +| rfft Float32 1572882 dims=1 | 73.534 ms | 91.523 ms | 94.073 ms | 1.24× | 1.28× | 0.97× | +| rfft Float32 1727797 dims=1 | 251.742 ms | 134.464 ms | 135.904 ms | 0.53× | 0.54× | 0.99× | +| rfft Float32 1975680 dims=1 | 16.948 ms | 48.341 ms | 12.588 ms | 2.85× | 0.74× | **3.84×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 15.573 ms | 15.701 ms | 0.95× | 0.96× | 0.99× | +| rfft Float32 4167450 dims=1 | 83.641 ms | 136.156 ms | 43.439 ms | 1.63× | 0.52× | **3.13×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 34.034 ms | 34.176 ms | 0.66× | 0.66× | 1.00× | +| rfft Float64 7 dims=1 | 24 ns | 39 ns | 39 ns | 1.63× | 1.64× | 0.99× | +| rfft Float64 8 dims=1 | 22 ns | 54 ns | 56 ns | 2.51× | 2.56× | 0.98× | +| rfft Float64 12 dims=1 | 28 ns | 151 ns | 154 ns | 5.48× | 5.60× | 0.98× | +| rfft Float64 16 dims=1 | 32 ns | 75 ns | 76 ns | 2.33× | 2.37× | 0.98× | +| rfft Float64 17 dims=1 | 137 ns | 196 ns | 197 ns | 1.43× | 1.44× | 0.99× | +| rfft Float64 23 dims=1 | 205 ns | 342 ns | 342 ns | 1.67× | 1.67× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 163 ns | 165 ns | 2.17× | 2.20× | 0.99× | +| rfft Float64 29 dims=1 | 290 ns | 889 ns | 894 ns | 3.07× | 3.08× | 0.99× | +| rfft Float64 31 dims=1 | 323 ns | 897 ns | 899 ns | 2.78× | 2.78× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 126 ns | 126 ns | 1.42× | 1.42× | 1.00× | +| rfft Float64 37 dims=1 | 431 ns | 1.51 µs | 1.52 µs | 3.51× | 3.52× | 1.00× | +| rfft Float64 41 dims=1 | 512 ns | 1.52 µs | 1.56 µs | 2.96× | 3.04× | 0.97× | +| rfft Float64 43 dims=1 | 556 ns | 1.53 µs | 1.53 µs | 2.74× | 2.75× | 1.00× | +| rfft Float64 54 dims=1 | 167 ns | 370 ns | 370 ns | 2.22× | 2.22× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 765 ns | 780 ns | 4.47× | 4.56× | 0.98× | +| rfft Float64 61 dims=1 | 1.04 µs | 1.57 µs | 1.56 µs | 1.50× | 1.50× | 1.00× | +| rfft Float64 64 dims=1 | 166 ns | 251 ns | 251 ns | 1.51× | 1.51× | 1.00× | +| rfft Float64 71 dims=1 | 1.39 µs | 3.47 µs | 3.53 µs | 2.51× | 2.55× | 0.98× | +| rfft Float64 73 dims=1 | 1.46 µs | 3.48 µs | 3.48 µs | 2.39× | 2.39× | 1.00× | +| rfft Float64 79 dims=1 | 1.69 µs | 3.51 µs | 3.50 µs | 2.07× | 2.07× | 1.00× | +| rfft Float64 101 dims=1 | 2.71 µs | 3.55 µs | 3.58 µs | 1.31× | 1.32× | 0.99× | +| rfft Float64 112 dims=1 | 297 ns | 708 ns | 539 ns | 2.38× | 1.81× | **1.31×** | +| rfft Float64 120 dims=1 | 334 ns | 1.35 µs | 679 ns | 4.05× | 2.03× | **1.99×** | +| rfft Float64 128 dims=1 | 327 ns | 528 ns | 527 ns | 1.61× | 1.61× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 3.84 µs | 3.83 µs | 1.48× | 1.47× | 1.00× | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 2.54 µs | 3.05× | 2.01× | **1.51×** | +| rfft Float64 251 dims=1 | 5.71 µs | 7.53 µs | 7.49 µs | 1.32× | 1.31× | 1.01× | +| rfft Float64 256 dims=1 | 693 ns | 926 ns | 930 ns | 1.34× | 1.34× | 1.00× | +| rfft Float64 303 dims=1 | 8.40 µs | 12.74 µs | 12.84 µs | 1.52× | 1.53× | 0.99× | +| rfft Float64 360 dims=1 | 1.40 µs | 4.10 µs | 2.16 µs | 2.93× | 1.54× | **1.90×** | +| rfft Float64 404 dims=1 | 5.36 µs | 9.29 µs | 9.33 µs | 1.73× | 1.74× | 1.00× | +| rfft Float64 504 dims=1 | 2.03 µs | 5.63 µs | 3.10 µs | 2.77× | 1.52× | **1.82×** | +| rfft Float64 512 dims=1 | 1.46 µs | 2.08 µs | 2.08 µs | 1.42× | 1.42× | 1.00× | +| rfft Float64 593 dims=1 | 22.36 µs | 34.88 µs | 34.88 µs | 1.56× | 1.56× | 1.00× | +| rfft Float64 606 dims=1 | 8.15 µs | 13.78 µs | 13.84 µs | 1.69× | 1.70× | 1.00× | +| rfft Float64 720 dims=1 | 2.88 µs | 7.95 µs | 4.24 µs | 2.76× | 1.47× | **1.87×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 9.25 µs | 6.36 µs | 2.06× | 1.42× | **1.45×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 4.34 µs | 4.31 µs | 1.39× | 1.38× | 1.01× | +| rfft Float64 1080 dims=1 | 4.71 µs | 13.52 µs | 7.23 µs | 2.87× | 1.53× | **1.87×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 80.60 µs | 80.84 µs | 1.44× | 1.44× | 1.00× | +| rfft Float64 1616 dims=1 | 22.28 µs | 34.84 µs | 34.88 µs | 1.56× | 1.57× | 1.00× | +| rfft Float64 2018 dims=1 | 55.68 µs | 38.88 µs | 38.96 µs | 0.70× | 0.70× | 1.00× | +| rfft Float64 2048 dims=1 | 6.68 µs | 9.88 µs | 9.85 µs | 1.48× | 1.48× | 1.00× | +| rfft Float64 2304 dims=1 | 9.76 µs | 20.92 µs | 13.24 µs | 2.14× | 1.36× | **1.58×** | +| rfft Float64 3027 dims=1 | 73.56 µs | 129.08 µs | 129.16 µs | 1.75× | 1.76× | 1.00× | +| rfft Float64 3491 dims=1 | 156.80 µs | 173.96 µs | 172.28 µs | 1.11× | 1.10× | 1.01× | +| rfft Float64 4036 dims=1 | 113.44 µs | 93.76 µs | 94.36 µs | 0.83× | 0.83× | 0.99× | +| rfft Float64 4096 dims=1 | 14.52 µs | 20.32 µs | 20.36 µs | 1.40× | 1.40× | 1.00× | +| rfft Float64 4860 dims=1 | 29.04 µs | 80.16 µs | 39.04 µs | 2.76× | 1.34× | **2.05×** | +| rfft Float64 6054 dims=1 | 171.84 µs | 138.84 µs | 139.44 µs | 0.81× | 0.81× | 1.00× | +| rfft Float64 8192 dims=1 | 39.12 µs | 45.76 µs | 45.68 µs | 1.17× | 1.17× | 1.00× | +| rfft Float64 8198 dims=1 | 258.64 µs | 418.08 µs | 427.32 µs | 1.62× | 1.65× | 0.98× | +| rfft Float64 8443 dims=1 | 364.37 µs | 956.37 µs | 951.01 µs | 2.62× | 2.61× | 1.01× | +| rfft Float64 10290 dims=1 | 74.76 µs | 153.64 µs | 85.96 µs | 2.06× | 1.15× | **1.79×** | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.287 ms | 1.297 ms | 2.34× | 2.36× | 0.99× | +| rfft Float64 16144 dims=1 | 460.81 µs | 360.04 µs | 359.88 µs | 0.78× | 0.78× | 1.00× | +| rfft Float64 16384 dims=1 | 86.72 µs | 99.32 µs | 96.36 µs | 1.15× | 1.11× | 1.03× | +| rfft Float64 16396 dims=1 | 523.69 µs | 905.21 µs | 879.93 µs | 1.73× | 1.68× | 1.03× | +| rfft Float64 20507 dims=1 | 1.134 ms | 2.375 ms | 2.322 ms | 2.09× | 2.05× | 1.02× | +| rfft Float64 21875 dims=1 | 200.92 µs | 673.13 µs | 326.12 µs | 3.35× | 1.62× | **2.06×** | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.346 ms | 1.377 ms | 1.69× | 1.73× | 0.98× | +| rfft Float64 32768 dims=1 | 195.60 µs | 229.48 µs | 227.60 µs | 1.17× | 1.16× | 1.01× | +| rfft Float64 32822 dims=1 | 1.488 ms | 2.401 ms | 2.404 ms | 1.61× | 1.62× | 1.00× | +| rfft Float64 46305 dims=1 | 482.65 µs | 1.914 ms | 813.33 µs | 3.97× | 1.69× | **2.35×** | +| rfft Float64 49233 dims=1 | 2.796 ms | 7.411 ms | 7.427 ms | 2.65× | 2.66× | 1.00× | +| rfft Float64 49757 dims=1 | 2.906 ms | 4.927 ms | 4.891 ms | 1.70× | 1.68× | 1.01× | +| rfft Float64 65536 dims=1 | 468.09 µs | 557.89 µs | 536.57 µs | 1.19× | 1.15× | 1.04× | +| rfft Float64 65584 dims=1 | 2.195 ms | 3.655 ms | 3.745 ms | 1.67× | 1.71× | 0.98× | +| rfft Float64 65644 dims=1 | 3.025 ms | 5.108 ms | 5.185 ms | 1.69× | 1.71× | 0.99× | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.456 ms | 932.33 µs | 1.57× | 1.00× | **1.56×** | +| rfft Float64 98466 dims=1 | 4.623 ms | 7.682 ms | 7.808 ms | 1.66× | 1.69× | 0.98× | +| rfft Float64 120779 dims=1 | 11.377 ms | 9.169 ms | 9.160 ms | 0.81× | 0.81× | 1.00× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.314 ms | 1.376 ms | 1.15× | 1.21× | 0.95× | +| rfft Float64 131074 dims=1 | 3.508 ms | 9.450 ms | 9.287 ms | 2.69× | 2.65× | 1.02× | +| rfft Float64 196611 dims=1 | 7.590 ms | 30.091 ms | 29.890 ms | 3.96× | 3.94× | 1.01× | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.373 ms | 2.124 ms | 1.89× | 0.92× | **2.06×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 2.849 ms | 2.740 ms | 1.09× | 1.05× | 1.04× | +| rfft Float64 262148 dims=1 | 7.006 ms | 20.387 ms | 20.191 ms | 2.91× | 2.88× | 1.01× | +| rfft Float64 262576 dims=1 | 12.798 ms | 21.037 ms | 21.109 ms | 1.64× | 1.65× | 1.00× | +| rfft Float64 293201 dims=1 | 36.020 ms | 45.820 ms | 49.903 ms | 1.27× | 1.39× | **0.92×** | +| rfft Float64 393222 dims=1 | 10.518 ms | 30.106 ms | 29.875 ms | 2.86× | 2.84× | 1.01× | +| rfft Float64 441000 dims=1 | 5.855 ms | 11.875 ms | 5.264 ms | 2.03× | 0.90× | **2.26×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 5.210 ms | 5.434 ms | 0.90× | 0.94× | 0.96× | +| rfft Float64 524294 dims=1 | 34.813 ms | 45.048 ms | 49.034 ms | 1.29× | 1.41× | **0.92×** | +| rfft Float64 711749 dims=1 | 110.585 ms | 104.395 ms | 104.492 ms | 0.94× | 0.94× | 1.00× | +| rfft Float64 786441 dims=1 | 98.952 ms | 150.138 ms | 148.047 ms | 1.52× | 1.50× | 1.01× | +| rfft Float64 933120 dims=1 | 11.815 ms | 25.521 ms | 11.128 ms | 2.16× | 0.94× | **2.29×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 25.173 ms | 10.952 ms | 1.18× | 0.51× | **2.30×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 11.793 ms | 11.902 ms | 0.87× | 0.88× | 0.99× | +| rfft Float64 1048588 dims=1 | 69.802 ms | 104.165 ms | 99.670 ms | 1.49× | 1.43× | 1.05× | +| rfft Float64 1048592 dims=1 | 30.247 ms | 86.491 ms | 82.722 ms | 2.86× | 2.73× | 1.05× | +| rfft Float64 1572882 dims=1 | 107.501 ms | 148.590 ms | 143.851 ms | 1.38× | 1.34× | 1.03× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 225.924 ms | 224.608 ms | 0.68× | 0.68× | 1.01× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 70.680 ms | 27.853 ms | 1.83× | 0.72× | **2.54×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 24.891 ms | 26.210 ms | 0.45× | 0.47× | **0.95×** | +| rfft Float64 4167450 dims=1 | 112.796 ms | 177.205 ms | 87.182 ms | 1.57× | 0.77× | **2.03×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 58.959 ms | 58.048 ms | 0.50× | 0.49× | 1.02× | +| fft Float32 8×8 dims=1,2 | 144 ns | 747 ns | 754 ns | 5.19× | 5.23× | 0.99× | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.54 µs | 2.56 µs | 4.46× | 4.50× | 0.99× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.88 µs | 8.97 µs | 4.07× | 3.35× | **1.21×** | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 49.88 µs | 38.52 µs | 4.04× | 3.12× | **1.29×** | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 164.24 µs | 163.08 µs | 2.73× | 2.71× | 1.01× | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 757.81 µs | 767.45 µs | 0.99× | 1.00× | 0.99× | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 4.557 ms | 4.292 ms | 0.81× | 0.76× | **1.06×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 20.619 ms | 19.992 ms | 0.82× | 0.79× | 1.03× | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 91.747 ms | 89.862 ms | 0.69× | 0.67× | 1.02× | +| fft Float64 8×8 dims=1,2 | 173 ns | 809 ns | 807 ns | 4.67× | 4.66× | 1.00× | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.75 µs | 2.75 µs | 3.35× | 3.35× | 1.00× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.80 µs | 11.76 µs | 2.87× | 2.86× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 55.24 µs | 55.28 µs | 2.69× | 2.69× | 1.00× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 219.24 µs | 219.16 µs | 1.99× | 1.99× | 1.00× | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 3.203 ms | 3.213 ms | 1.78× | 1.79× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 2.987 ms | 2.992 ms | 0.81× | 0.81× | 1.00× | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.161 ms | 3.177 ms | 0.82× | 0.82× | 1.00× | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.204 ms | 1.186 ms | 1.06× | 1.04× | 1.02× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 5.963 ms | 5.953 ms | 0.98× | 0.97× | 1.00× | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 15.984 ms | 8.108 ms | 2.42× | 1.23× | **1.97×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 37.549 ms | 27.941 ms | 1.35× | 1.00× | **1.34×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 27.231 ms | 27.800 ms | 0.91× | 0.92× | 0.98× | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 120.075 ms | 119.851 ms | 0.73× | 0.73× | 1.00× | +| rfft Float32 8×8 dims=1,2 | 124 ns | 787 ns | 793 ns | 6.37× | 6.42× | 0.99× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.16 µs | 2.17 µs | 4.92× | 4.95× | 0.99× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 7.15 µs | 6.64 µs | 3.49× | 3.24× | **1.08×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 28.08 µs | 23.24 µs | 2.85× | 2.36× | **1.21×** | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 96.96 µs | 85.80 µs | 2.08× | 1.84× | **1.13×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 332.48 µs | 332.24 µs | 0.95× | 0.95× | 1.00× | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 1.534 ms | 1.503 ms | 1.06× | 1.04× | 1.02× | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 6.917 ms | 6.886 ms | 1.15× | 1.15× | 1.00× | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 37.261 ms | 36.975 ms | 1.07× | 1.06× | 1.01× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 788 ns | 795 ns | 6.73× | 6.78× | 0.99× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.15 µs | 2.20 µs | 4.38× | 4.49× | 0.98× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 7.44 µs | 7.45 µs | 3.10× | 3.11× | 1.00× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 30.40 µs | 30.44 µs | 2.59× | 2.59× | 1.00× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 116.32 µs | 117.20 µs | 2.00× | 2.01× | 0.99× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.053 ms | 2.050 ms | 1.36× | 1.35× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 2.544 ms | 2.544 ms | 1.58× | 1.58× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 1.554 ms | 1.557 ms | 0.80× | 0.80× | 1.00× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 492.13 µs | 487.29 µs | 1.21× | 1.19× | 1.01× | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 2.235 ms | 2.222 ms | 1.17× | 1.16× | 1.01× | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 7.845 ms | 3.913 ms | 2.49× | 1.24× | **2.00×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 18.757 ms | 13.331 ms | 1.44× | 1.02× | **1.41×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 9.943 ms | 10.010 ms | 1.14× | 1.15× | 0.99× | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 52.776 ms | 52.947 ms | 0.97× | 0.97× | 1.00× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.07 µs | 9.09 µs | 5.86× | 5.88× | 1.00× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 62.76 µs | 62.92 µs | 4.66× | 4.67× | 1.00× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 600.53 µs | 505.20 µs | 4.24× | 3.57× | **1.19×** | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.768 ms | 4.733 ms | 3.87× | 3.17× | **1.22×** | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 42.537 ms | 43.144 ms | 2.31× | 2.34× | 0.99× | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.49 µs | 4.99× | 4.99× | 1.00× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 68.04 µs | 68.40 µs | 3.41× | 3.43× | 0.99× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 678.49 µs | 678.33 µs | 2.81× | 2.80× | 1.00× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.550 ms | 6.575 ms | 2.63× | 2.64× | 1.00× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 59.699 ms | 59.141 ms | 1.53× | 1.52× | 1.01× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 8.24 µs | 8.41 µs | 6.94× | 7.08× | 0.98× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 47.12 µs | 47.52 µs | 5.11× | 5.15× | 0.99× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 334.28 µs | 301.36 µs | 3.68× | 3.31× | **1.11×** | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 2.821 ms | 2.298 ms | 2.96× | 2.41× | **1.23×** | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 20.396 ms | 19.073 ms | 2.18× | 2.04× | **1.07×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 8.41 µs | 8.47 µs | 7.03× | 7.07× | 0.99× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 47.92 µs | 47.64 µs | 4.21× | 4.19× | 1.01× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 356.92 µs | 355.32 µs | 3.05× | 3.04× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.185 ms | 3.157 ms | 2.35× | 2.33× | 1.01× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 26.926 ms | 26.227 ms | 1.82× | 1.77× | 1.03× | +| fft Float32 64×64 dims=1 | 6.23 µs | 23.60 µs | 18.08 µs | 3.79× | 2.90× | **1.31×** | +| fft Float32 256×64 dims=1 | 52.20 µs | 69.60 µs | 71.24 µs | 1.33× | 1.36× | 0.98× | +| fft Float32 1024×64 dims=1 | 244.64 µs | 333.80 µs | 312.68 µs | 1.36× | 1.28× | **1.07×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 1.590 ms | 1.431 ms | 1.25× | 1.12× | **1.11×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 8.176 ms | 7.230 ms | 1.05× | 0.93× | **1.13×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 45.175 ms | 34.527 ms | 1.01× | 0.77× | **1.31×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 26.00 µs | 26.12 µs | 2.52× | 2.53× | 1.00× | +| fft Float64 256×64 dims=1 | 87.04 µs | 104.84 µs | 106.04 µs | 1.20× | 1.22× | 0.99× | +| fft Float64 1024×64 dims=1 | 434.17 µs | 513.81 µs | 512.81 µs | 1.18× | 1.18× | 1.00× | +| fft Float64 4096×64 dims=1 | 2.162 ms | 2.521 ms | 2.511 ms | 1.17× | 1.16× | 1.00× | +| fft Float64 16384×64 dims=1 | 14.861 ms | 13.788 ms | 13.137 ms | 0.93× | 0.88× | 1.05× | +| fft Float64 65536×64 dims=1 | 88.463 ms | 76.362 ms | 74.814 ms | 0.86× | 0.85× | 1.02× | +| rfft Float32 64×64 dims=1 | 6.61 µs | 14.94 µs | 13.10 µs | 2.26× | 1.98× | **1.14×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 42.44 µs | 42.48 µs | 1.04× | 1.04× | 1.00× | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 187.00 µs | 177.16 µs | 1.30× | 1.23× | **1.06×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 875.53 µs | 800.53 µs | 1.27× | 1.16× | **1.09×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 4.134 ms | 3.604 ms | 1.11× | 0.97× | **1.15×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 21.259 ms | 17.912 ms | 1.12× | 0.94× | **1.19×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 16.82 µs | 17.00 µs | 2.52× | 2.54× | 0.99× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 4.180 ms | 4.233 ms | 1.34× | 1.36× | 0.99× | +| rfft Float64 256×64 dims=1 | 44.56 µs | 61.44 µs | 62.00 µs | 1.38× | 1.39× | 0.99× | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 4.793 ms | 4.790 ms | 1.31× | 1.30× | 1.00× | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 288.68 µs | 286.88 µs | 1.35× | 1.34× | 1.01× | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 5.417 ms | 5.412 ms | 1.28× | 1.28× | 1.00× | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.342 ms | 1.340 ms | 1.29× | 1.29× | 1.00× | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 6.650 ms | 6.647 ms | 1.08× | 1.08× | 1.00× | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 37.309 ms | 38.266 ms | 0.98× | 1.01× | 0.97× | +| fft Float32 64×64 dims=2 | 6.13 µs | 25.64 µs | 20.00 µs | 4.18× | 3.26× | **1.28×** | +| fft Float32 64×256 dims=2 | 79.52 µs | 109.44 µs | 111.20 µs | 1.38× | 1.40× | 0.98× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 618.69 µs | 583.81 µs | 1.43× | 1.35× | **1.06×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 3.319 ms | 3.094 ms | 0.71× | 0.66× | **1.07×** | +| fft Float32 64×16384 dims=2 | 24.311 ms | 15.082 ms | 14.162 ms | 0.62× | 0.58× | **1.06×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 86.316 ms | 82.697 ms | 0.50× | 0.48× | 1.04× | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.96 µs | 29.24 µs | 2.67× | 2.69× | 0.99× | +| fft Float64 64×256 dims=2 | 108.96 µs | 138.96 µs | 138.56 µs | 1.28× | 1.27× | 1.00× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 807.21 µs | 790.09 µs | 0.91× | 0.89× | 1.02× | +| fft Float64 64×4096 dims=2 | 5.347 ms | 4.310 ms | 4.278 ms | 0.81× | 0.80× | 1.01× | +| fft Float64 64×16384 dims=2 | 34.143 ms | 22.229 ms | 21.681 ms | 0.65× | 0.64× | 1.03× | +| fft Float64 64×65536 dims=2 | 247.287 ms | 133.456 ms | 129.002 ms | 0.54× | 0.52× | 1.03× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 17.62 µs | 15.80 µs | 2.67× | 2.39× | **1.12×** | +| rfft Float32 64×256 dims=2 | 57.92 µs | 66.68 µs | 68.80 µs | 1.15× | 1.19× | 0.97× | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 327.28 µs | 316.60 µs | 1.13× | 1.09× | 1.03× | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 1.862 ms | 1.812 ms | 1.05× | 1.02× | 1.03× | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 9.498 ms | 8.947 ms | 0.81× | 0.77× | **1.06×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 49.952 ms | 47.178 ms | 0.73× | 0.69× | **1.06×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 19.96 µs | 20.12 µs | 3.02× | 3.04× | 0.99× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 95.76 µs | 95.72 µs | 1.34× | 1.34× | 1.00× | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 449.37 µs | 450.73 µs | 1.29× | 1.30× | 1.00× | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 2.623 ms | 2.599 ms | 0.96× | 0.95× | 1.01× | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 12.216 ms | 12.023 ms | 0.86× | 0.85× | 1.02× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 77.872 ms | 77.386 ms | 0.70× | 0.69× | 1.01× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `main`/`fftw` | `sh`/`fftw` | `sh` vs `main` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 1.98× (0.69–5.19) | 1.87× (0.67–5.23) | **1.06×** (0.99–1.29) | +| ComplexF32 fft 3d | 4.01× (2.31–5.86) | 3.74× (2.34–5.88) | **1.07×** (0.99–1.22) | +| ComplexF32 fft awkward | 1.44× (0.75–3.01) | 1.36× (0.69–3.12) | **1.05×** (0.95–1.20) | +| ComplexF32 fft batched_dim1 | 1.45× (1.01–3.79) | 1.26× (0.77–2.90) | **1.14×** (0.98–1.31) | +| ComplexF32 fft batched_dim2 | 1.10× (0.50–4.18) | 1.02× (0.48–3.26) | **1.08×** (0.98–1.28) | +| ComplexF32 fft pow2 | 0.93× (0.36–1.75) | 0.84× (0.35–1.28) | **1.10×** (0.95–1.37) | +| ComplexF32 fft prime | 1.31× (0.60–6.60) | 1.25× (0.61–6.61) | **1.05×** (0.95–1.28) | +| ComplexF32 fft smooth | 2.62× (1.35–5.31) | 0.98× (0.40–4.13) | **2.67×** (0.96–4.37) | +| ComplexF64 fft 2d | 1.59× (0.73–4.67) | 1.48× (0.73–4.66) | **1.07×** (0.98–1.97) | +| ComplexF64 fft 3d | 2.86× (1.53–4.99) | 2.86× (1.52–4.99) | **1.00×** (0.99–1.01) | +| ComplexF64 fft awkward | 1.57× (0.74–3.00) | 1.59× (0.74–2.97) | **0.99×** (0.92–1.06) | +| ComplexF64 fft batched_dim1 | 1.22× (0.86–2.52) | 1.21× (0.85–2.53) | **1.01×** (0.99–1.05) | +| ComplexF64 fft batched_dim2 | 0.98× (0.54–2.67) | 0.97× (0.52–2.69) | **1.01×** (0.99–1.03) | +| ComplexF64 fft pow2 | 0.90× (0.38–1.91) | 0.89× (0.37–1.91) | **1.01×** (0.99–1.04) | +| ComplexF64 fft prime | 1.48× (0.73–3.98) | 1.48× (0.73–3.98) | **1.00×** (0.97–1.04) | +| ComplexF64 fft smooth | 2.10× (1.00–5.37) | 1.09× (0.43–5.45) | **1.93×** (0.99–2.49) | +| Float32 rfft 2d | 2.11× (0.95–6.37) | 2.01× (0.95–6.42) | **1.05×** (0.99–1.21) | +| Float32 rfft 3d | 3.84× (2.18–6.94) | 3.59× (2.04–7.08) | **1.07×** (0.98–1.23) | +| Float32 rfft awkward | 1.41× (0.71–2.92) | 1.35× (0.65–2.98) | **1.05×** (0.94–1.18) | +| Float32 rfft batched_dim1 | 1.30× (1.04–2.26) | 1.18× (0.94–1.98) | **1.10×** (1.00–1.19) | +| Float32 rfft batched_dim2 | 1.14× (0.73–2.67) | 1.09× (0.69–2.39) | **1.04×** (0.97–1.12) | +| Float32 rfft pow2 | 1.23× (0.66–2.47) | 1.14× (0.66–2.51) | **1.08×** (0.98–1.35) | +| Float32 rfft prime | 1.26× (0.53–2.82) | 1.20× (0.54–2.44) | **1.05×** (0.95–1.27) | +| Float32 rfft smooth | 2.63× (1.62–5.53) | 1.19× (0.52–5.73) | **2.21×** (0.96–3.84) | +| Float64 rfft 2d | 1.82× (0.80–6.73) | 1.70× (0.80–6.78) | **1.07×** (0.98–2.00) | +| Float64 rfft 3d | 3.29× (1.82–7.03) | 3.27× (1.77–7.07) | **1.01×** (0.99–1.03) | +| Float64 rfft awkward | 1.66× (0.70–3.96) | 1.66× (0.70–3.94) | **1.00×** (0.92–1.05) | +| Float64 rfft batched_dim1 | 1.34× (0.98–2.52) | 1.35× (1.01–2.54) | **0.99×** (0.97–1.01) | +| Float64 rfft batched_dim2 | 1.20× (0.70–3.02) | 1.20× (0.69–3.04) | **1.00×** (0.99–1.02) | +| Float64 rfft pow2 | 1.21× (0.45–2.51) | 1.21× (0.47–2.56) | **1.00×** (0.95–1.04) | +| Float64 rfft prime | 1.72× (0.68–3.51) | 1.73× (0.68–3.52) | **1.00×** (0.92–1.02) | +| Float64 rfft smooth | 2.49× (1.18–5.48) | 1.46× (0.51–5.60) | **1.71×** (0.98–2.54) | +| **all** | 1.60× (0.36–7.03) | 1.35× (0.35–7.08) | **1.18×** (0.92–4.37), 505 cases, 12 slower by >5% | diff --git a/benchmark/compare3/aarch64/stockham/sh_t1.json b/benchmark/compare3/aarch64/stockham/sh_t1.json new file mode 100644 index 0000000..18c5c17 --- /dev/null +++ b/benchmark/compare3/aarch64/stockham/sh_t1.json @@ -0,0 +1,10995 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + 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-8799.055444945056 + }, + { + "T": "Float64", + "api": "mul!", + "class": "nd", + "dims": 1, + "exec_alloc": 0, + "exec_min": 0.0054124590000000005, + "key": "rfft Float64 4096×256 dims=1", + "kind": "rfft", + "measure": false, + "n": 4096, + "norm": 46391.401139029265, + "nthreads": 1, + "plan_min": 2.7600000000000003e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255871, + "sum_re": -2384.3887021657065 + } + ] +} \ No newline at end of file From 7b128be4dce477689237e97cfe81f7d65e074cd4 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 21:08:01 +0000 Subject: [PATCH 19/21] benchmark: compare3 results for the full Stockham stack (aarch64, 1 thread) --- .../aarch64/stockham-stack/COMPARE3.md | 579 + .../aarch64/stockham-stack/ffta_t1.json | 10995 ++++++++++++++++ 2 files changed, 11574 insertions(+) create mode 100644 benchmark/compare3/aarch64/stockham-stack/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/stockham-stack/ffta_t1.json diff --git a/benchmark/compare3/aarch64/stockham-stack/COMPARE3.md b/benchmark/compare3/aarch64/stockham-stack/COMPARE3.md new file mode 100644 index 0000000..9d4a721 --- /dev/null +++ b/benchmark/compare3/aarch64/stockham-stack/COMPARE3.md @@ -0,0 +1,579 @@ +# FFT implementations side by side + +Rendered 2026-08-30T21:07:30.355 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `main` | FFTA.jl 0.3.1 @ 4943d2a — `FFTA-main` | +| `ffta` | FFTA.jl 0.3.1 @ a2fd368 — `FFTA-adj` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs main` is the speedup over the `main` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `main` | `ffta` | `main`/`fftw` | `ffta`/`fftw` | `ffta` vs `main` | +|:--|--:|--:|--:|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 35 ns | 37 ns | 0.93× | 0.98× | 0.95× | +| fft Float32 8 dims=1 | 37 ns | 38 ns | 39 ns | 1.02× | 1.04× | 0.98× | +| fft Float32 12 dims=1 | 43 ns | 172 ns | 180 ns | 3.98× | 4.16× | 0.96× | +| fft Float32 16 dims=1 | 55 ns | 67 ns | 68 ns | 1.22× | 1.23× | 0.99× | +| fft Float32 17 dims=1 | 136 ns | 819 ns | 818 ns | 6.02× | 6.02× | 1.00× | +| fft Float32 23 dims=1 | 230 ns | 1.52 µs | 1.52 µs | 6.60× | 6.61× | 1.00× | +| fft Float32 25 dims=1 | 126 ns | 170 ns | 171 ns | 1.35× | 1.35× | 1.00× | +| fft Float32 29 dims=1 | 342 ns | 823 ns | 502 ns | 2.40× | 1.47× | **1.64×** | +| fft Float32 31 dims=1 | 387 ns | 831 ns | 508 ns | 2.15× | 1.31× | **1.64×** | +| fft Float32 32 dims=1 | 105 ns | 149 ns | 85 ns | 1.43× | 0.81× | **1.76×** | +| fft Float32 37 dims=1 | 836 ns | 1.07 µs | 723 ns | 1.28× | 0.86× | **1.48×** | +| fft Float32 41 dims=1 | 817 ns | 1.08 µs | 734 ns | 1.32× | 0.90× | **1.47×** | +| fft Float32 43 dims=1 | 699 ns | 1.08 µs | 738 ns | 1.55× | 1.06× | **1.47×** | +| fft Float32 54 dims=1 | 325 ns | 994 ns | 374 ns | 3.06× | 1.15× | **2.66×** | +| fft Float32 60 dims=1 | 217 ns | 1.12 µs | 383 ns | 5.17× | 1.77× | **2.93×** | +| fft Float32 61 dims=1 | 1.19 µs | 1.13 µs | 920 ns | 0.95× | 0.77× | **1.23×** | +| fft Float32 64 dims=1 | 194 ns | 341 ns | 178 ns | 1.75× | 0.92× | **1.91×** | +| fft Float32 71 dims=1 | 2.40 µs | 2.38 µs | 1.22 µs | 0.99× | 0.51× | **1.95×** | +| fft Float32 73 dims=1 | 1.34 µs | 2.39 µs | 1.23 µs | 1.78× | 0.92× | **1.94×** | +| fft Float32 79 dims=1 | 1.76 µs | 2.40 µs | 1.24 µs | 1.36× | 0.70× | **1.93×** | +| fft Float32 101 dims=1 | 1.94 µs | 2.46 µs | 1.84 µs | 1.27× | 0.95× | **1.33×** | +| fft Float32 112 dims=1 | 360 ns | 1.02 µs | 369 ns | 2.84× | 1.02× | **2.77×** | +| fft Float32 120 dims=1 | 392 ns | 2.08 µs | 723 ns | 5.31× | 1.84× | **2.88×** | +| fft Float32 128 dims=1 | 390 ns | 421 ns | 316 ns | 1.08× | 0.81× | **1.33×** | +| fft Float32 202 dims=1 | 4.13 µs | 6.41 µs | 5.26 µs | 1.55× | 1.27× | **1.22×** | +| fft Float32 243 dims=1 | 1.90 µs | 3.84 µs | 1.89 µs | 2.02× | 0.99× | **2.03×** | +| fft Float32 251 dims=1 | 5.99 µs | 5.29 µs | 4.05 µs | 0.88× | 0.68× | **1.31×** | +| fft Float32 256 dims=1 | 807 ns | 978 ns | 737 ns | 1.21× | 0.91× | **1.33×** | +| fft Float32 303 dims=1 | 6.36 µs | 9.36 µs | 7.59 µs | 1.47× | 1.19× | **1.23×** | +| fft Float32 360 dims=1 | 2.37 µs | 6.64 µs | 2.27 µs | 2.80× | 0.96× | **2.93×** | +| fft Float32 404 dims=1 | 8.45 µs | 11.88 µs | 9.55 µs | 1.41× | 1.13× | **1.24×** | +| fft Float32 504 dims=1 | 2.69 µs | 8.89 µs | 3.34 µs | 3.31× | 1.24× | **2.66×** | +| fft Float32 512 dims=1 | 1.69 µs | 2.08 µs | 1.48 µs | 1.23× | 0.88× | **1.40×** | +| fft Float32 593 dims=1 | 15.24 µs | 23.56 µs | 12.32 µs | 1.55× | 0.81× | **1.91×** | +| fft Float32 606 dims=1 | 12.82 µs | 23.12 µs | 19.92 µs | 1.80× | 1.55× | **1.16×** | +| fft Float32 720 dims=1 | 5.25 µs | 13.26 µs | 2.85 µs | 2.53× | 0.54× | **4.65×** | +| fft Float32 1000 dims=1 | 6.69 µs | 13.92 µs | 6.76 µs | 2.08× | 1.01× | **2.06×** | +| fft Float32 1024 dims=1 | 3.64 µs | 4.72 µs | 3.47 µs | 1.30× | 0.95× | **1.36×** | +| fft Float32 1080 dims=1 | 8.77 µs | 22.04 µs | 7.57 µs | 2.51× | 0.86× | **2.91×** | +| fft Float32 1433 dims=1 | 57.64 µs | 52.76 µs | 32.52 µs | 0.92× | 0.56× | **1.62×** | +| fft Float32 1616 dims=1 | 36.12 µs | 46.20 µs | 36.56 µs | 1.28× | 1.01× | **1.26×** | +| fft Float32 2018 dims=1 | 73.28 µs | 64.20 µs | 53.64 µs | 0.88× | 0.73× | **1.20×** | +| fft Float32 2048 dims=1 | 7.68 µs | 9.98 µs | 7.23 µs | 1.30× | 0.94× | **1.38×** | +| fft Float32 2304 dims=1 | 12.42 µs | 32.80 µs | 10.10 µs | 2.64× | 0.81× | **3.25×** | +| fft Float32 3027 dims=1 | 112.08 µs | 94.60 µs | 77.84 µs | 0.84× | 0.69× | **1.22×** | +| fft Float32 3491 dims=1 | 158.56 µs | 117.68 µs | 84.20 µs | 0.74× | 0.53× | **1.40×** | +| fft Float32 4036 dims=1 | 149.00 µs | 120.08 µs | 97.68 µs | 0.81× | 0.66× | **1.23×** | +| fft Float32 4096 dims=1 | 16.88 µs | 22.76 µs | 16.64 µs | 1.35× | 0.99× | **1.37×** | +| fft Float32 4860 dims=1 | 49.84 µs | 130.20 µs | 42.64 µs | 2.61× | 0.86× | **3.05×** | +| fft Float32 6054 dims=1 | 225.88 µs | 233.32 µs | 203.08 µs | 1.03× | 0.90× | **1.15×** | +| fft Float32 8192 dims=1 | 48.72 µs | 50.40 µs | 35.20 µs | 1.03× | 0.72× | **1.43×** | +| fft Float32 8198 dims=1 | 411.25 µs | 577.29 µs | 292.96 µs | 1.40× | 0.71× | **1.97×** | +| fft Float32 8443 dims=1 | 413.05 µs | 551.49 µs | 242.48 µs | 1.34× | 0.59× | **2.27×** | +| fft Float32 10290 dims=1 | 97.28 µs | 321.36 µs | 99.28 µs | 3.30× | 1.02× | **3.24×** | +| fft Float32 12297 dims=1 | 624.25 µs | 865.85 µs | 428.16 µs | 1.39× | 0.69× | **2.02×** | +| fft Float32 16144 dims=1 | 629.25 µs | 472.61 µs | 380.76 µs | 0.75× | 0.61× | **1.24×** | +| fft Float32 16384 dims=1 | 109.16 µs | 115.04 µs | 79.72 µs | 1.05× | 0.73× | **1.44×** | +| fft Float32 16396 dims=1 | 831.89 µs | 1.125 ms | 550.09 µs | 1.35× | 0.66× | **2.04×** | +| fft Float32 20507 dims=1 | 1.290 ms | 1.319 ms | 673.65 µs | 1.02× | 0.52× | **1.96×** | +| fft Float32 21875 dims=1 | 264.12 µs | 599.13 µs | 219.00 µs | 2.27× | 0.83× | **2.74×** | +| fft Float32 24594 dims=1 | 1.260 ms | 1.919 ms | 1.059 ms | 1.52× | 0.84× | **1.81×** | +| fft Float32 32768 dims=1 | 278.20 µs | 247.76 µs | 180.72 µs | 0.89× | 0.65× | **1.37×** | +| fft Float32 32822 dims=1 | 2.015 ms | 2.837 ms | 1.320 ms | 1.41× | 0.65× | **2.15×** | +| fft Float32 46305 dims=1 | 560.49 µs | 1.556 ms | 521.37 µs | 2.78× | 0.93× | **2.98×** | +| fft Float32 49233 dims=1 | 3.073 ms | 4.245 ms | 1.944 ms | 1.38× | 0.63× | **2.18×** | +| fft Float32 49757 dims=1 | 2.680 ms | 3.163 ms | 1.667 ms | 1.18× | 0.62× | **1.90×** | +| fft Float32 65536 dims=1 | 563.53 µs | 562.65 µs | 367.40 µs | 1.00× | 0.65× | **1.53×** | +| fft Float32 65584 dims=1 | 3.557 ms | 4.610 ms | 2.256 ms | 1.30× | 0.63× | **2.04×** | +| fft Float32 65644 dims=1 | 4.107 ms | 5.608 ms | 2.508 ms | 1.37× | 0.61× | **2.24×** | +| fft Float32 98304 dims=1 | 1.126 ms | 2.359 ms | 668.89 µs | 2.10× | 0.59× | **3.53×** | +| fft Float32 98466 dims=1 | 6.367 ms | 9.314 ms | 4.763 ms | 1.46× | 0.75× | **1.96×** | +| fft Float32 120779 dims=1 | 9.432 ms | 5.703 ms | 5.713 ms | 0.60× | 0.61× | 1.00× | +| fft Float32 131072 dims=1 | 1.322 ms | 1.380 ms | 881.69 µs | 1.04× | 0.67× | **1.57×** | +| fft Float32 131074 dims=1 | 4.394 ms | 12.398 ms | 6.335 ms | 2.82× | 1.44× | **1.96×** | +| fft Float32 196611 dims=1 | 6.678 ms | 18.292 ms | 8.765 ms | 2.74× | 1.31× | **2.09×** | +| fft Float32 207360 dims=1 | 3.276 ms | 7.254 ms | 1.556 ms | 2.21× | 0.48× | **4.66×** | +| fft Float32 262144 dims=1 | 3.482 ms | 2.427 ms | 2.417 ms | 0.70× | 0.69× | 1.00× | +| fft Float32 262148 dims=1 | 8.965 ms | 23.956 ms | 11.464 ms | 2.67× | 1.28× | **2.09×** | +| fft Float32 262576 dims=1 | 18.216 ms | 23.390 ms | 10.713 ms | 1.28× | 0.59× | **2.18×** | +| fft Float32 293201 dims=1 | 30.534 ms | 27.365 ms | 11.897 ms | 0.90× | 0.39× | **2.30×** | +| fft Float32 393222 dims=1 | 13.552 ms | 40.297 ms | 21.315 ms | 2.97× | 1.57× | **1.89×** | +| fft Float32 441000 dims=1 | 6.625 ms | 16.339 ms | 5.275 ms | 2.47× | 0.80× | **3.10×** | +| fft Float32 524288 dims=1 | 11.364 ms | 5.136 ms | 5.105 ms | 0.45× | 0.45× | 1.01× | +| fft Float32 524294 dims=1 | 47.952 ms | 57.984 ms | 27.432 ms | 1.21× | 0.57× | **2.11×** | +| fft Float32 711749 dims=1 | 76.629 ms | 62.593 ms | 34.406 ms | 0.82× | 0.45× | **1.82×** | +| fft Float32 786441 dims=1 | 72.471 ms | 89.077 ms | 39.721 ms | 1.23× | 0.55× | **2.24×** | +| fft Float32 933120 dims=1 | 18.504 ms | 39.524 ms | 8.483 ms | 2.14× | 0.46× | **4.66×** | +| fft Float32 1000000 dims=1 | 24.431 ms | 38.874 ms | 8.257 ms | 1.59× | 0.34× | **4.71×** | +| fft Float32 1048576 dims=1 | 24.149 ms | 11.421 ms | 11.223 ms | 0.47× | 0.46× | 1.02× | +| fft Float32 1048588 dims=1 | 97.647 ms | 120.572 ms | 50.983 ms | 1.23× | 0.52× | **2.36×** | +| fft Float32 1048592 dims=1 | 37.789 ms | 113.880 ms | 51.572 ms | 3.01× | 1.36× | **2.21×** | +| fft Float32 1572882 dims=1 | 150.252 ms | 191.628 ms | 95.989 ms | 1.28× | 0.64× | **2.00×** | +| fft Float32 1727797 dims=1 | 174.941 ms | 130.654 ms | 116.577 ms | 0.75× | 0.67× | **1.12×** | +| fft Float32 1975680 dims=1 | 40.474 ms | 99.731 ms | 21.381 ms | 2.46× | 0.53× | **4.66×** | +| fft Float32 2097152 dims=1 | 78.580 ms | 28.171 ms | 27.386 ms | 0.36× | 0.35× | 1.03× | +| fft Float32 4167450 dims=1 | 126.844 ms | 313.853 ms | 88.457 ms | 2.47× | 0.70× | **3.55×** | +| fft Float32 4194304 dims=1 | 164.711 ms | 60.006 ms | 61.919 ms | 0.36× | 0.38× | 0.97× | +| fft Float64 7 dims=1 | 26 ns | 39 ns | 41 ns | 1.52× | 1.58× | 0.96× | +| fft Float64 8 dims=1 | 25 ns | 39 ns | 39 ns | 1.56× | 1.55× | 1.01× | +| fft Float64 12 dims=1 | 33 ns | 179 ns | 181 ns | 5.37× | 5.45× | 0.99× | +| fft Float64 16 dims=1 | 41 ns | 69 ns | 69 ns | 1.68× | 1.70× | 0.99× | +| fft Float64 17 dims=1 | 136 ns | 502 ns | 502 ns | 3.70× | 3.70× | 1.00× | +| fft Float64 23 dims=1 | 230 ns | 914 ns | 910 ns | 3.98× | 3.96× | 1.00× | +| fft Float64 25 dims=1 | 139 ns | 174 ns | 173 ns | 1.26× | 1.25× | 1.01× | +| fft Float64 29 dims=1 | 343 ns | 899 ns | 900 ns | 2.62× | 2.62× | 1.00× | +| fft Float64 31 dims=1 | 385 ns | 903 ns | 905 ns | 2.35× | 2.35× | 1.00× | +| fft Float64 32 dims=1 | 80 ns | 152 ns | 154 ns | 1.91× | 1.93× | 0.99× | +| fft Float64 37 dims=1 | 771 ns | 1.52 µs | 1.13 µs | 1.97× | 1.47× | **1.34×** | +| fft Float64 41 dims=1 | 910 ns | 1.54 µs | 1.15 µs | 1.69× | 1.26× | **1.34×** | +| fft Float64 43 dims=1 | 699 ns | 1.54 µs | 1.15 µs | 2.20× | 1.64× | **1.34×** | +| fft Float64 54 dims=1 | 274 ns | 1.03 µs | 459 ns | 3.76× | 1.68× | **2.24×** | +| fft Float64 60 dims=1 | 311 ns | 1.19 µs | 439 ns | 3.82× | 1.41× | **2.71×** | +| fft Float64 61 dims=1 | 1.39 µs | 1.58 µs | 1.58 µs | 1.14× | 1.14× | 1.00× | +| fft Float64 64 dims=1 | 310 ns | 350 ns | 351 ns | 1.13× | 1.13× | 1.00× | +| fft Float64 71 dims=1 | 3.06 µs | 3.51 µs | 1.97 µs | 1.15× | 0.64× | **1.78×** | +| fft Float64 73 dims=1 | 1.74 µs | 3.50 µs | 1.97 µs | 2.01× | 1.13× | **1.78×** | +| fft Float64 79 dims=1 | 2.50 µs | 3.52 µs | 1.98 µs | 1.41× | 0.79× | **1.78×** | +| fft Float64 101 dims=1 | 2.37 µs | 3.57 µs | 3.02 µs | 1.51× | 1.28× | **1.18×** | +| fft Float64 112 dims=1 | 591 ns | 1.10 µs | 591 ns | 1.86× | 1.00× | **1.86×** | +| fft Float64 120 dims=1 | 634 ns | 2.18 µs | 844 ns | 3.44× | 1.33× | **2.59×** | +| fft Float64 128 dims=1 | 647 ns | 589 ns | 593 ns | 0.91× | 0.92× | 0.99× | +| fft Float64 202 dims=1 | 4.97 µs | 8.79 µs | 7.73 µs | 1.77× | 1.56× | **1.14×** | +| fft Float64 243 dims=1 | 1.94 µs | 3.85 µs | 2.59 µs | 1.98× | 1.33× | **1.49×** | +| fft Float64 251 dims=1 | 6.73 µs | 7.55 µs | 7.56 µs | 1.12× | 1.12× | 1.00× | +| fft Float64 256 dims=1 | 1.32 µs | 1.42 µs | 1.42 µs | 1.08× | 1.08× | 1.00× | +| fft Float64 303 dims=1 | 7.79 µs | 12.86 µs | 11.28 µs | 1.65× | 1.45× | **1.14×** | +| fft Float64 360 dims=1 | 2.83 µs | 6.97 µs | 3.00 µs | 2.46× | 1.06× | **2.32×** | +| fft Float64 404 dims=1 | 10.46 µs | 16.62 µs | 14.42 µs | 1.59× | 1.38× | **1.15×** | +| fft Float64 504 dims=1 | 4.30 µs | 9.51 µs | 4.50 µs | 2.21× | 1.05× | **2.11×** | +| fft Float64 512 dims=1 | 2.83 µs | 2.99 µs | 2.98 µs | 1.06× | 1.05× | 1.00× | +| fft Float64 593 dims=1 | 27.48 µs | 35.00 µs | 21.56 µs | 1.27× | 0.78× | **1.62×** | +| fft Float64 606 dims=1 | 15.84 µs | 30.84 µs | 27.52 µs | 1.95× | 1.74× | **1.12×** | +| fft Float64 720 dims=1 | 5.64 µs | 14.02 µs | 5.24 µs | 2.49× | 0.93× | **2.68×** | +| fft Float64 1000 dims=1 | 10.26 µs | 14.80 µs | 9.17 µs | 1.44× | 0.89× | **1.61×** | +| fft Float64 1024 dims=1 | 6.30 µs | 6.97 µs | 6.96 µs | 1.11× | 1.10× | 1.00× | +| fft Float64 1080 dims=1 | 9.27 µs | 23.32 µs | 10.74 µs | 2.52× | 1.16× | **2.17×** | +| fft Float64 1433 dims=1 | 77.40 µs | 81.12 µs | 59.00 µs | 1.05× | 0.76× | **1.37×** | +| fft Float64 1616 dims=1 | 44.28 µs | 65.68 µs | 57.16 µs | 1.48× | 1.29× | **1.15×** | +| fft Float64 2018 dims=1 | 109.44 µs | 88.40 µs | 88.56 µs | 0.81× | 0.81× | 1.00× | +| fft Float64 2048 dims=1 | 13.52 µs | 14.98 µs | 14.98 µs | 1.11× | 1.11× | 1.00× | +| fft Float64 2304 dims=1 | 22.48 µs | 38.44 µs | 18.84 µs | 1.71× | 0.84× | **2.04×** | +| fft Float64 3027 dims=1 | 168.20 µs | 130.08 µs | 130.88 µs | 0.77× | 0.78× | 0.99× | +| fft Float64 3491 dims=1 | 222.48 µs | 175.60 µs | 153.08 µs | 0.79× | 0.69× | **1.15×** | +| fft Float64 4036 dims=1 | 223.80 µs | 168.80 µs | 169.36 µs | 0.75× | 0.76× | 1.00× | +| fft Float64 4096 dims=1 | 29.80 µs | 35.12 µs | 34.92 µs | 1.18× | 1.17× | 1.01× | +| fft Float64 4860 dims=1 | 57.56 µs | 138.32 µs | 63.60 µs | 2.40× | 1.10× | **2.17×** | +| fft Float64 6054 dims=1 | 340.04 µs | 312.24 µs | 312.72 µs | 0.92× | 0.92× | 1.00× | +| fft Float64 8192 dims=1 | 84.76 µs | 74.16 µs | 75.00 µs | 0.87× | 0.88× | 0.99× | +| fft Float64 8198 dims=1 | 506.65 µs | 875.33 µs | 485.49 µs | 1.73× | 0.96× | **1.80×** | +| fft Float64 8443 dims=1 | 554.85 µs | 965.53 µs | 490.93 µs | 1.74× | 0.88× | **1.97×** | +| fft Float64 10290 dims=1 | 149.96 µs | 366.04 µs | 146.16 µs | 2.44× | 0.97× | **2.50×** | +| fft Float64 12297 dims=1 | 777.05 µs | 1.290 ms | 721.21 µs | 1.66× | 0.93× | **1.79×** | +| fft Float64 16144 dims=1 | 922.45 µs | 678.69 µs | 679.25 µs | 0.74× | 0.74× | 1.00× | +| fft Float64 16384 dims=1 | 180.40 µs | 170.96 µs | 168.88 µs | 0.95× | 0.94× | 1.01× | +| fft Float64 16396 dims=1 | 1.036 ms | 1.701 ms | 946.33 µs | 1.64× | 0.91× | **1.80×** | +| fft Float64 20507 dims=1 | 1.694 ms | 2.363 ms | 1.344 ms | 1.39× | 0.79× | **1.76×** | +| fft Float64 21875 dims=1 | 384.44 µs | 744.49 µs | 330.60 µs | 1.94× | 0.86× | **2.25×** | +| fft Float64 24594 dims=1 | 1.613 ms | 2.827 ms | 1.725 ms | 1.75× | 1.07× | **1.64×** | +| fft Float64 32768 dims=1 | 444.61 µs | 413.69 µs | 390.76 µs | 0.93× | 0.88× | **1.06×** | +| fft Float64 32822 dims=1 | 2.985 ms | 4.980 ms | 2.323 ms | 1.67× | 0.78× | **2.14×** | +| fft Float64 46305 dims=1 | 1.031 ms | 1.944 ms | 818.33 µs | 1.89× | 0.79× | **2.38×** | +| fft Float64 49233 dims=1 | 4.545 ms | 7.499 ms | 3.547 ms | 1.65× | 0.78× | **2.11×** | +| fft Float64 49757 dims=1 | 4.565 ms | 4.976 ms | 3.269 ms | 1.09× | 0.72× | **1.52×** | +| fft Float64 65536 dims=1 | 1.088 ms | 985.05 µs | 992.29 µs | 0.91× | 0.91× | 0.99× | +| fft Float64 65584 dims=1 | 4.401 ms | 7.025 ms | 3.973 ms | 1.60× | 0.90× | **1.77×** | +| fft Float64 65644 dims=1 | 6.122 ms | 9.948 ms | 4.535 ms | 1.63× | 0.74× | **2.19×** | +| fft Float64 98304 dims=1 | 1.926 ms | 2.688 ms | 1.336 ms | 1.40× | 0.69× | **2.01×** | +| fft Float64 98466 dims=1 | 9.391 ms | 16.584 ms | 7.842 ms | 1.77× | 0.84× | **2.11×** | +| fft Float64 120779 dims=1 | 12.568 ms | 9.236 ms | 9.196 ms | 0.73× | 0.73× | 1.00× | +| fft Float64 131072 dims=1 | 2.406 ms | 2.028 ms | 2.021 ms | 0.84× | 0.84× | 1.00× | +| fft Float64 131074 dims=1 | 6.943 ms | 19.592 ms | 11.025 ms | 2.82× | 1.59× | **1.78×** | +| fft Float64 196611 dims=1 | 10.356 ms | 29.392 ms | 16.455 ms | 2.84× | 1.59× | **1.79×** | +| fft Float64 207360 dims=1 | 4.519 ms | 7.941 ms | 3.043 ms | 1.76× | 0.67× | **2.61×** | +| fft Float64 262144 dims=1 | 5.670 ms | 3.874 ms | 3.766 ms | 0.68× | 0.66× | 1.03× | +| fft Float64 262148 dims=1 | 13.759 ms | 39.175 ms | 21.969 ms | 2.85× | 1.60× | **1.78×** | +| fft Float64 262576 dims=1 | 25.621 ms | 41.144 ms | 18.653 ms | 1.61× | 0.73× | **2.21×** | +| fft Float64 293201 dims=1 | 41.017 ms | 46.542 ms | 22.972 ms | 1.13× | 0.56× | **2.03×** | +| fft Float64 393222 dims=1 | 21.186 ms | 63.518 ms | 36.883 ms | 3.00× | 1.74× | **1.72×** | +| fft Float64 441000 dims=1 | 10.759 ms | 21.823 ms | 8.643 ms | 2.03× | 0.80× | **2.52×** | +| fft Float64 524288 dims=1 | 16.863 ms | 8.403 ms | 8.038 ms | 0.50× | 0.48× | 1.05× | +| fft Float64 524294 dims=1 | 69.443 ms | 94.747 ms | 50.527 ms | 1.36× | 0.73× | **1.88×** | +| fft Float64 711749 dims=1 | 103.554 ms | 105.033 ms | 85.972 ms | 1.01× | 0.83× | **1.22×** | +| fft Float64 786441 dims=1 | 104.363 ms | 143.033 ms | 74.241 ms | 1.37× | 0.71× | **1.93×** | +| fft Float64 933120 dims=1 | 32.838 ms | 49.930 ms | 18.693 ms | 1.52× | 0.57× | **2.67×** | +| fft Float64 1000000 dims=1 | 50.425 ms | 50.503 ms | 17.764 ms | 1.00× | 0.35× | **2.84×** | +| fft Float64 1048576 dims=1 | 52.671 ms | 20.136 ms | 19.401 ms | 0.38× | 0.37× | 1.04× | +| fft Float64 1048588 dims=1 | 141.957 ms | 189.545 ms | 104.784 ms | 1.34× | 0.74× | **1.81×** | +| fft Float64 1048592 dims=1 | 64.157 ms | 173.430 ms | 93.798 ms | 2.70× | 1.46× | **1.85×** | +| fft Float64 1572882 dims=1 | 218.031 ms | 326.178 ms | 179.676 ms | 1.50× | 0.82× | **1.82×** | +| fft Float64 1727797 dims=1 | 263.816 ms | 225.374 ms | 259.341 ms | 0.85× | 0.98× | **0.87×** | +| fft Float64 1975680 dims=1 | 76.790 ms | 136.089 ms | 50.430 ms | 1.77× | 0.66× | **2.70×** | +| fft Float64 2097152 dims=1 | 119.760 ms | 47.647 ms | 45.411 ms | 0.40× | 0.38× | 1.05× | +| fft Float64 4167450 dims=1 | 214.097 ms | 408.351 ms | 159.645 ms | 1.91× | 0.75× | **2.56×** | +| fft Float64 4194304 dims=1 | 238.004 ms | 104.408 ms | 103.128 ms | 0.44× | 0.43× | 1.01× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | — | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | — | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | — | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | — | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | — | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | — | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | — | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | — | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | — | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | — | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | — | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | — | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | — | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | — | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | — | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | — | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | — | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | — | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | — | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | — | — | — | +| rfft Float32 7 dims=1 | 24 ns | 38 ns | 38 ns | 1.59× | 1.60× | 1.00× | +| rfft Float32 8 dims=1 | 22 ns | 54 ns | 54 ns | 2.47× | 2.51× | 0.99× | +| rfft Float32 12 dims=1 | 27 ns | 150 ns | 154 ns | 5.53× | 5.70× | 0.97× | +| rfft Float32 16 dims=1 | 33 ns | 75 ns | 75 ns | 2.29× | 2.30× | 1.00× | +| rfft Float32 17 dims=1 | 134 ns | 183 ns | 183 ns | 1.36× | 1.37× | 1.00× | +| rfft Float32 23 dims=1 | 202 ns | 317 ns | 318 ns | 1.57× | 1.57× | 1.00× | +| rfft Float32 25 dims=1 | 76 ns | 162 ns | 163 ns | 2.13× | 2.14× | 0.99× | +| rfft Float32 29 dims=1 | 288 ns | 812 ns | 494 ns | 2.82× | 1.72× | **1.64×** | +| rfft Float32 31 dims=1 | 319 ns | 814 ns | 492 ns | 2.55× | 1.54× | **1.65×** | +| rfft Float32 32 dims=1 | 101 ns | 118 ns | 120 ns | 1.16× | 1.18× | 0.98× | +| rfft Float32 37 dims=1 | 428 ns | 1.05 µs | 708 ns | 2.46× | 1.66× | **1.49×** | +| rfft Float32 41 dims=1 | 508 ns | 1.06 µs | 717 ns | 2.09× | 1.41× | **1.48×** | +| rfft Float32 43 dims=1 | 553 ns | 1.06 µs | 722 ns | 1.93× | 1.31× | **1.48×** | +| rfft Float32 54 dims=1 | 213 ns | 346 ns | 349 ns | 1.62× | 1.63× | 0.99× | +| rfft Float32 60 dims=1 | 219 ns | 718 ns | 745 ns | 3.27× | 3.39× | 0.96× | +| rfft Float32 61 dims=1 | 1.04 µs | 1.10 µs | 882 ns | 1.06× | 0.85× | **1.24×** | +| rfft Float32 64 dims=1 | 183 ns | 222 ns | 163 ns | 1.21× | 0.89× | **1.36×** | +| rfft Float32 71 dims=1 | 1.37 µs | 2.35 µs | 1.19 µs | 1.71× | 0.86× | **1.98×** | +| rfft Float32 73 dims=1 | 1.45 µs | 2.35 µs | 1.19 µs | 1.62× | 0.82× | **1.97×** | +| rfft Float32 79 dims=1 | 1.68 µs | 2.36 µs | 1.20 µs | 1.40× | 0.71× | **1.97×** | +| rfft Float32 101 dims=1 | 2.69 µs | 2.41 µs | 1.80 µs | 0.89× | 0.67× | **1.34×** | +| rfft Float32 112 dims=1 | 288 ns | 627 ns | 434 ns | 2.18× | 1.51× | **1.44×** | +| rfft Float32 120 dims=1 | 287 ns | 1.24 µs | 496 ns | 4.32× | 1.73× | **2.50×** | +| rfft Float32 128 dims=1 | 265 ns | 462 ns | 301 ns | 1.74× | 1.14× | **1.53×** | +| rfft Float32 202 dims=1 | 2.12 µs | 2.63 µs | 2.02 µs | 1.24× | 0.95× | **1.30×** | +| rfft Float32 243 dims=1 | 1.18 µs | 3.83 µs | 1.83 µs | 3.25× | 1.55× | **2.10×** | +| rfft Float32 251 dims=1 | 5.48 µs | 5.12 µs | 3.92 µs | 0.93× | 0.72× | **1.31×** | +| rfft Float32 256 dims=1 | 636 ns | 638 ns | 531 ns | 1.00× | 0.84× | **1.20×** | +| rfft Float32 303 dims=1 | 8.39 µs | 9.19 µs | 7.43 µs | 1.10× | 0.89× | **1.24×** | +| rfft Float32 360 dims=1 | 1.31 µs | 3.81 µs | 1.44 µs | 2.90× | 1.10× | **2.64×** | +| rfft Float32 404 dims=1 | 4.31 µs | 6.72 µs | 5.60 µs | 1.56× | 1.30× | **1.20×** | +| rfft Float32 504 dims=1 | 1.53 µs | 5.09 µs | 2.09 µs | 3.32× | 1.36× | **2.44×** | +| rfft Float32 512 dims=1 | 1.14 µs | 1.39 µs | 1.14 µs | 1.22× | 1.01× | **1.21×** | +| rfft Float32 593 dims=1 | 21.96 µs | 23.16 µs | 11.80 µs | 1.05× | 0.54× | **1.96×** | +| rfft Float32 606 dims=1 | 6.52 µs | 9.83 µs | 8.11 µs | 1.51× | 1.24× | **1.21×** | +| rfft Float32 720 dims=1 | 2.87 µs | 7.27 µs | 2.82 µs | 2.53× | 0.98× | **2.57×** | +| rfft Float32 1000 dims=1 | 3.13 µs | 8.33 µs | 4.20 µs | 2.67× | 1.34× | **1.98×** | +| rfft Float32 1024 dims=1 | 2.20 µs | 2.85 µs | 2.25 µs | 1.30× | 1.02× | **1.27×** | +| rfft Float32 1080 dims=1 | 4.64 µs | 12.42 µs | 4.54 µs | 2.68× | 0.98× | **2.73×** | +| rfft Float32 1433 dims=1 | 54.24 µs | 51.68 µs | 31.60 µs | 0.95× | 0.58× | **1.64×** | +| rfft Float32 1616 dims=1 | 17.54 µs | 24.28 µs | 19.38 µs | 1.38× | 1.10× | **1.25×** | +| rfft Float32 2018 dims=1 | 37.16 µs | 26.40 µs | 20.72 µs | 0.71× | 0.56× | **1.27×** | +| rfft Float32 2048 dims=1 | 4.45 µs | 6.29 µs | 5.16 µs | 1.41× | 1.16× | **1.22×** | +| rfft Float32 2304 dims=1 | 6.84 µs | 17.48 µs | 6.28 µs | 2.56× | 0.92× | **2.78×** | +| rfft Float32 3027 dims=1 | 71.52 µs | 92.16 µs | 75.60 µs | 1.29× | 1.06× | **1.22×** | +| rfft Float32 3491 dims=1 | 149.84 µs | 115.24 µs | 81.48 µs | 0.77× | 0.54× | **1.41×** | +| rfft Float32 4036 dims=1 | 75.00 µs | 67.36 µs | 56.76 µs | 0.90× | 0.76× | **1.19×** | +| rfft Float32 4096 dims=1 | 9.40 µs | 13.40 µs | 10.52 µs | 1.43× | 1.12× | **1.27×** | +| rfft Float32 4860 dims=1 | 25.48 µs | 74.08 µs | 24.68 µs | 2.91× | 0.97× | **3.00×** | +| rfft Float32 6054 dims=1 | 113.60 µs | 99.04 µs | 82.56 µs | 0.87× | 0.73× | **1.20×** | +| rfft Float32 8192 dims=1 | 25.56 µs | 29.08 µs | 22.92 µs | 1.14× | 0.90× | **1.27×** | +| rfft Float32 8198 dims=1 | 207.04 µs | 264.16 µs | 121.32 µs | 1.28× | 0.59× | **2.18×** | +| rfft Float32 8443 dims=1 | 345.44 µs | 555.41 µs | 234.44 µs | 1.61× | 0.68× | **2.37×** | +| rfft Float32 10290 dims=1 | 62.92 µs | 129.64 µs | 56.76 µs | 2.06× | 0.90× | **2.28×** | +| rfft Float32 12297 dims=1 | 522.37 µs | 850.93 µs | 419.81 µs | 1.63× | 0.80× | **2.03×** | +| rfft Float32 16144 dims=1 | 307.68 µs | 245.68 µs | 200.96 µs | 0.80× | 0.65× | **1.22×** | +| rfft Float32 16384 dims=1 | 54.04 µs | 63.08 µs | 48.00 µs | 1.17× | 0.89× | **1.31×** | +| rfft Float32 16396 dims=1 | 418.08 µs | 591.05 µs | 306.88 µs | 1.41× | 0.73× | **1.93×** | +| rfft Float32 20507 dims=1 | 962.05 µs | 1.313 ms | 659.73 µs | 1.36× | 0.69× | **1.99×** | +| rfft Float32 21875 dims=1 | 197.00 µs | 581.93 µs | 214.52 µs | 2.95× | 1.09× | **2.71×** | +| rfft Float32 24594 dims=1 | 631.01 µs | 880.81 µs | 450.00 µs | 1.40× | 0.71× | **1.96×** | +| rfft Float32 32768 dims=1 | 117.04 µs | 143.12 µs | 106.08 µs | 1.22× | 0.91× | **1.35×** | +| rfft Float32 32822 dims=1 | 1.010 ms | 1.328 ms | 557.21 µs | 1.32× | 0.55× | **2.38×** | +| rfft Float32 46305 dims=1 | 453.65 µs | 1.459 ms | 509.09 µs | 3.22× | 1.12× | **2.87×** | +| rfft Float32 49233 dims=1 | 2.572 ms | 4.216 ms | 1.919 ms | 1.64× | 0.75× | **2.20×** | +| rfft Float32 49757 dims=1 | 2.717 ms | 3.156 ms | 1.601 ms | 1.16× | 0.59× | **1.97×** | +| rfft Float32 65536 dims=1 | 244.00 µs | 310.92 µs | 242.28 µs | 1.27× | 0.99× | **1.28×** | +| rfft Float32 65584 dims=1 | 1.708 ms | 2.306 ms | 1.145 ms | 1.35× | 0.67× | **2.01×** | +| rfft Float32 65644 dims=1 | 2.032 ms | 2.935 ms | 1.387 ms | 1.44× | 0.68× | **2.12×** | +| rfft Float32 98304 dims=1 | 514.45 µs | 1.161 ms | 383.56 µs | 2.26× | 0.75× | **3.03×** | +| rfft Float32 98466 dims=1 | 3.089 ms | 4.357 ms | 2.053 ms | 1.41× | 0.66× | **2.12×** | +| rfft Float32 120779 dims=1 | 10.598 ms | 5.675 ms | 5.664 ms | 0.54× | 0.53× | 1.00× | +| rfft Float32 131072 dims=1 | 614.25 µs | 756.21 µs | 504.37 µs | 1.23× | 0.82× | **1.50×** | +| rfft Float32 131074 dims=1 | 2.210 ms | 5.770 ms | 2.679 ms | 2.61× | 1.21× | **2.15×** | +| rfft Float32 196611 dims=1 | 6.210 ms | 18.153 ms | 8.614 ms | 2.92× | 1.39× | **2.11×** | +| rfft Float32 207360 dims=1 | 1.700 ms | 3.435 ms | 968.53 µs | 2.02× | 0.57× | **3.55×** | +| rfft Float32 262144 dims=1 | 1.669 ms | 1.772 ms | 1.266 ms | 1.06× | 0.76× | **1.40×** | +| rfft Float32 262148 dims=1 | 4.534 ms | 12.612 ms | 6.409 ms | 2.78× | 1.41× | **1.97×** | +| rfft Float32 262576 dims=1 | 8.653 ms | 11.556 ms | 5.375 ms | 1.34× | 0.62× | **2.15×** | +| rfft Float32 293201 dims=1 | 31.617 ms | 26.776 ms | 11.578 ms | 0.85× | 0.37× | **2.31×** | +| rfft Float32 393222 dims=1 | 6.798 ms | 18.628 ms | 9.274 ms | 2.74× | 1.36× | **2.01×** | +| rfft Float32 441000 dims=1 | 3.804 ms | 8.824 ms | 3.073 ms | 2.32× | 0.81× | **2.87×** | +| rfft Float32 524288 dims=1 | 3.783 ms | 3.387 ms | 3.377 ms | 0.90× | 0.89× | 1.00× | +| rfft Float32 524294 dims=1 | 23.932 ms | 27.188 ms | 11.595 ms | 1.14× | 0.48× | **2.34×** | +| rfft Float32 711749 dims=1 | 91.203 ms | 60.672 ms | 32.891 ms | 0.67× | 0.36× | **1.84×** | +| rfft Float32 786441 dims=1 | 89.117 ms | 86.255 ms | 40.781 ms | 0.97× | 0.46× | **2.12×** | +| rfft Float32 933120 dims=1 | 9.020 ms | 19.031 ms | 5.444 ms | 2.11× | 0.60× | **3.50×** | +| rfft Float32 1000000 dims=1 | 8.693 ms | 20.303 ms | 5.484 ms | 2.34× | 0.63× | **3.70×** | +| rfft Float32 1048576 dims=1 | 7.838 ms | 7.115 ms | 7.182 ms | 0.91× | 0.92× | 0.99× | +| rfft Float32 1048588 dims=1 | 47.864 ms | 61.881 ms | 29.229 ms | 1.29× | 0.61× | **2.12×** | +| rfft Float32 1048592 dims=1 | 18.670 ms | 50.826 ms | 25.063 ms | 2.72× | 1.34× | **2.03×** | +| rfft Float32 1572882 dims=1 | 73.534 ms | 91.523 ms | 42.256 ms | 1.24× | 0.57× | **2.17×** | +| rfft Float32 1727797 dims=1 | 251.742 ms | 134.464 ms | 115.869 ms | 0.53× | 0.46× | **1.16×** | +| rfft Float32 1975680 dims=1 | 16.948 ms | 48.341 ms | 11.234 ms | 2.85× | 0.66× | **4.30×** | +| rfft Float32 2097152 dims=1 | 16.402 ms | 15.573 ms | 15.536 ms | 0.95× | 0.95× | 1.00× | +| rfft Float32 4167450 dims=1 | 83.641 ms | 136.156 ms | 41.395 ms | 1.63× | 0.49× | **3.29×** | +| rfft Float32 4194304 dims=1 | 51.550 ms | 34.034 ms | 34.315 ms | 0.66× | 0.67× | 0.99× | +| rfft Float64 7 dims=1 | 24 ns | 39 ns | 39 ns | 1.63× | 1.63× | 1.00× | +| rfft Float64 8 dims=1 | 22 ns | 54 ns | 55 ns | 2.51× | 2.55× | 0.98× | +| rfft Float64 12 dims=1 | 28 ns | 151 ns | 152 ns | 5.48× | 5.52× | 0.99× | +| rfft Float64 16 dims=1 | 32 ns | 75 ns | 76 ns | 2.33× | 2.38× | 0.98× | +| rfft Float64 17 dims=1 | 137 ns | 196 ns | 196 ns | 1.43× | 1.43× | 1.00× | +| rfft Float64 23 dims=1 | 205 ns | 342 ns | 342 ns | 1.67× | 1.67× | 1.00× | +| rfft Float64 25 dims=1 | 75 ns | 163 ns | 163 ns | 2.17× | 2.17× | 1.00× | +| rfft Float64 29 dims=1 | 290 ns | 889 ns | 897 ns | 3.07× | 3.09× | 0.99× | +| rfft Float64 31 dims=1 | 323 ns | 897 ns | 899 ns | 2.78× | 2.78× | 1.00× | +| rfft Float64 32 dims=1 | 89 ns | 126 ns | 125 ns | 1.42× | 1.41× | 1.01× | +| rfft Float64 37 dims=1 | 431 ns | 1.51 µs | 1.12 µs | 3.51× | 2.60× | **1.35×** | +| rfft Float64 41 dims=1 | 512 ns | 1.52 µs | 1.13 µs | 2.96× | 2.20× | **1.35×** | +| rfft Float64 43 dims=1 | 556 ns | 1.53 µs | 1.13 µs | 2.74× | 2.03× | **1.35×** | +| rfft Float64 54 dims=1 | 167 ns | 370 ns | 371 ns | 2.22× | 2.22× | 1.00× | +| rfft Float64 60 dims=1 | 171 ns | 765 ns | 782 ns | 4.47× | 4.57× | 0.98× | +| rfft Float64 61 dims=1 | 1.04 µs | 1.57 µs | 1.55 µs | 1.50× | 1.49× | 1.01× | +| rfft Float64 64 dims=1 | 166 ns | 251 ns | 250 ns | 1.51× | 1.51× | 1.01× | +| rfft Float64 71 dims=1 | 1.39 µs | 3.47 µs | 1.99 µs | 2.51× | 1.43× | **1.75×** | +| rfft Float64 73 dims=1 | 1.46 µs | 3.48 µs | 1.95 µs | 2.39× | 1.34× | **1.78×** | +| rfft Float64 79 dims=1 | 1.69 µs | 3.51 µs | 1.95 µs | 2.07× | 1.15× | **1.80×** | +| rfft Float64 101 dims=1 | 2.71 µs | 3.55 µs | 2.99 µs | 1.31× | 1.10× | **1.19×** | +| rfft Float64 112 dims=1 | 297 ns | 708 ns | 506 ns | 2.38× | 1.70× | **1.40×** | +| rfft Float64 120 dims=1 | 334 ns | 1.35 µs | 604 ns | 4.05× | 1.81× | **2.24×** | +| rfft Float64 128 dims=1 | 327 ns | 528 ns | 530 ns | 1.61× | 1.62× | 1.00× | +| rfft Float64 202 dims=1 | 2.60 µs | 3.84 µs | 3.29 µs | 1.48× | 1.27× | **1.17×** | +| rfft Float64 243 dims=1 | 1.26 µs | 3.85 µs | 2.56 µs | 3.05× | 2.02× | **1.51×** | +| rfft Float64 251 dims=1 | 5.71 µs | 7.53 µs | 7.43 µs | 1.32× | 1.30× | 1.01× | +| rfft Float64 256 dims=1 | 693 ns | 926 ns | 941 ns | 1.34× | 1.36× | 0.98× | +| rfft Float64 303 dims=1 | 8.40 µs | 12.74 µs | 11.06 µs | 1.52× | 1.32× | **1.15×** | +| rfft Float64 360 dims=1 | 1.40 µs | 4.10 µs | 1.93 µs | 2.93× | 1.38× | **2.12×** | +| rfft Float64 404 dims=1 | 5.36 µs | 9.29 µs | 8.32 µs | 1.73× | 1.55× | **1.12×** | +| rfft Float64 504 dims=1 | 2.03 µs | 5.63 µs | 2.97 µs | 2.77× | 1.46× | **1.90×** | +| rfft Float64 512 dims=1 | 1.46 µs | 2.08 µs | 2.08 µs | 1.42× | 1.42× | 1.00× | +| rfft Float64 593 dims=1 | 22.36 µs | 34.88 µs | 21.32 µs | 1.56× | 0.95× | **1.64×** | +| rfft Float64 606 dims=1 | 8.15 µs | 13.78 µs | 12.08 µs | 1.69× | 1.48× | **1.14×** | +| rfft Float64 720 dims=1 | 2.88 µs | 7.95 µs | 3.98 µs | 2.76× | 1.38× | **1.99×** | +| rfft Float64 1000 dims=1 | 4.49 µs | 9.25 µs | 5.78 µs | 2.06× | 1.29× | **1.60×** | +| rfft Float64 1024 dims=1 | 3.13 µs | 4.34 µs | 4.31 µs | 1.39× | 1.38× | 1.01× | +| rfft Float64 1080 dims=1 | 4.71 µs | 13.52 µs | 6.73 µs | 2.87× | 1.43× | **2.01×** | +| rfft Float64 1433 dims=1 | 56.12 µs | 80.60 µs | 58.32 µs | 1.44× | 1.04× | **1.38×** | +| rfft Float64 1616 dims=1 | 22.28 µs | 34.84 µs | 30.52 µs | 1.56× | 1.37× | **1.14×** | +| rfft Float64 2018 dims=1 | 55.68 µs | 38.88 µs | 38.92 µs | 0.70× | 0.70× | 1.00× | +| rfft Float64 2048 dims=1 | 6.68 µs | 9.88 µs | 9.84 µs | 1.48× | 1.47× | 1.00× | +| rfft Float64 2304 dims=1 | 9.76 µs | 20.92 µs | 11.38 µs | 2.14× | 1.17× | **1.84×** | +| rfft Float64 3027 dims=1 | 73.56 µs | 129.08 µs | 128.84 µs | 1.75× | 1.75× | 1.00× | +| rfft Float64 3491 dims=1 | 156.80 µs | 173.96 µs | 151.96 µs | 1.11× | 0.97× | **1.14×** | +| rfft Float64 4036 dims=1 | 113.44 µs | 93.76 µs | 94.12 µs | 0.83× | 0.83× | 1.00× | +| rfft Float64 4096 dims=1 | 14.52 µs | 20.32 µs | 20.32 µs | 1.40× | 1.40× | 1.00× | +| rfft Float64 4860 dims=1 | 29.04 µs | 80.16 µs | 37.32 µs | 2.76× | 1.29× | **2.15×** | +| rfft Float64 6054 dims=1 | 171.84 µs | 138.84 µs | 138.76 µs | 0.81× | 0.81× | 1.00× | +| rfft Float64 8192 dims=1 | 39.12 µs | 45.76 µs | 45.96 µs | 1.17× | 1.17× | 1.00× | +| rfft Float64 8198 dims=1 | 258.64 µs | 418.08 µs | 223.44 µs | 1.62× | 0.86× | **1.87×** | +| rfft Float64 8443 dims=1 | 364.37 µs | 956.37 µs | 488.69 µs | 2.62× | 1.34× | **1.96×** | +| rfft Float64 10290 dims=1 | 74.76 µs | 153.64 µs | 86.72 µs | 2.06× | 1.16× | **1.77×** | +| rfft Float64 12297 dims=1 | 549.53 µs | 1.287 ms | 716.57 µs | 2.34× | 1.30× | **1.80×** | +| rfft Float64 16144 dims=1 | 460.81 µs | 360.04 µs | 359.84 µs | 0.78× | 0.78× | 1.00× | +| rfft Float64 16384 dims=1 | 86.72 µs | 99.32 µs | 99.52 µs | 1.15× | 1.15× | 1.00× | +| rfft Float64 16396 dims=1 | 523.69 µs | 905.21 µs | 519.93 µs | 1.73× | 0.99× | **1.74×** | +| rfft Float64 20507 dims=1 | 1.134 ms | 2.375 ms | 1.351 ms | 2.09× | 1.19× | **1.76×** | +| rfft Float64 21875 dims=1 | 200.92 µs | 673.13 µs | 325.80 µs | 3.35× | 1.62× | **2.07×** | +| rfft Float64 24594 dims=1 | 794.97 µs | 1.346 ms | 779.89 µs | 1.69× | 0.98× | **1.73×** | +| rfft Float64 32768 dims=1 | 195.60 µs | 229.48 µs | 238.96 µs | 1.17× | 1.22× | 0.96× | +| rfft Float64 32822 dims=1 | 1.488 ms | 2.401 ms | 1.047 ms | 1.61× | 0.70× | **2.29×** | +| rfft Float64 46305 dims=1 | 482.65 µs | 1.914 ms | 806.53 µs | 3.97× | 1.67× | **2.37×** | +| rfft Float64 49233 dims=1 | 2.796 ms | 7.411 ms | 3.416 ms | 2.65× | 1.22× | **2.17×** | +| rfft Float64 49757 dims=1 | 2.906 ms | 4.927 ms | 3.275 ms | 1.70× | 1.13× | **1.50×** | +| rfft Float64 65536 dims=1 | 468.09 µs | 557.89 µs | 548.17 µs | 1.19× | 1.17× | 1.02× | +| rfft Float64 65584 dims=1 | 2.195 ms | 3.655 ms | 2.133 ms | 1.67× | 0.97× | **1.71×** | +| rfft Float64 65644 dims=1 | 3.025 ms | 5.108 ms | 2.465 ms | 1.69× | 0.81× | **2.07×** | +| rfft Float64 98304 dims=1 | 928.13 µs | 1.456 ms | 814.01 µs | 1.57× | 0.88× | **1.79×** | +| rfft Float64 98466 dims=1 | 4.623 ms | 7.682 ms | 3.651 ms | 1.66× | 0.79× | **2.10×** | +| rfft Float64 120779 dims=1 | 11.377 ms | 9.169 ms | 9.180 ms | 0.81× | 0.81× | 1.00× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.314 ms | 1.299 ms | 1.15× | 1.14× | 1.01× | +| rfft Float64 131074 dims=1 | 3.508 ms | 9.450 ms | 5.365 ms | 2.69× | 1.53× | **1.76×** | +| rfft Float64 196611 dims=1 | 7.590 ms | 30.091 ms | 16.933 ms | 3.96× | 2.23× | **1.78×** | +| rfft Float64 207360 dims=1 | 2.319 ms | 4.373 ms | 1.849 ms | 1.89× | 0.80× | **2.36×** | +| rfft Float64 262144 dims=1 | 2.607 ms | 2.849 ms | 2.692 ms | 1.09× | 1.03× | **1.06×** | +| rfft Float64 262148 dims=1 | 7.006 ms | 20.387 ms | 11.305 ms | 2.91× | 1.61× | **1.80×** | +| rfft Float64 262576 dims=1 | 12.798 ms | 21.037 ms | 10.264 ms | 1.64× | 0.80× | **2.05×** | +| rfft Float64 293201 dims=1 | 36.020 ms | 45.820 ms | 23.039 ms | 1.27× | 0.64× | **1.99×** | +| rfft Float64 393222 dims=1 | 10.518 ms | 30.106 ms | 16.774 ms | 2.86× | 1.59× | **1.79×** | +| rfft Float64 441000 dims=1 | 5.855 ms | 11.875 ms | 4.915 ms | 2.03× | 0.84× | **2.42×** | +| rfft Float64 524288 dims=1 | 5.760 ms | 5.210 ms | 5.730 ms | 0.90× | 0.99× | **0.91×** | +| rfft Float64 524294 dims=1 | 34.813 ms | 45.048 ms | 23.570 ms | 1.29× | 0.68× | **1.91×** | +| rfft Float64 711749 dims=1 | 110.585 ms | 104.395 ms | 85.730 ms | 0.94× | 0.78× | **1.22×** | +| rfft Float64 786441 dims=1 | 98.952 ms | 150.138 ms | 79.290 ms | 1.52× | 0.80× | **1.89×** | +| rfft Float64 933120 dims=1 | 11.815 ms | 25.521 ms | 10.631 ms | 2.16× | 0.90× | **2.40×** | +| rfft Float64 1000000 dims=1 | 21.371 ms | 25.173 ms | 10.807 ms | 1.18× | 0.51× | **2.33×** | +| rfft Float64 1048576 dims=1 | 13.492 ms | 11.793 ms | 12.217 ms | 0.87× | 0.91× | 0.97× | +| rfft Float64 1048588 dims=1 | 69.802 ms | 104.165 ms | 51.585 ms | 1.49× | 0.74× | **2.02×** | +| rfft Float64 1048592 dims=1 | 30.247 ms | 86.491 ms | 48.388 ms | 2.86× | 1.60× | **1.79×** | +| rfft Float64 1572882 dims=1 | 107.501 ms | 148.590 ms | 76.639 ms | 1.38× | 0.71× | **1.94×** | +| rfft Float64 1727797 dims=1 | 329.992 ms | 225.924 ms | 270.180 ms | 0.68× | 0.82× | **0.84×** | +| rfft Float64 1975680 dims=1 | 38.541 ms | 70.680 ms | 23.570 ms | 1.83× | 0.61× | **3.00×** | +| rfft Float64 2097152 dims=1 | 55.689 ms | 24.891 ms | 25.884 ms | 0.45× | 0.46× | 0.96× | +| rfft Float64 4167450 dims=1 | 112.796 ms | 177.205 ms | 86.539 ms | 1.57× | 0.77× | **2.05×** | +| rfft Float64 4194304 dims=1 | 118.652 ms | 58.959 ms | 57.457 ms | 0.50× | 0.48× | 1.03× | +| fft Float32 8×8 dims=1,2 | 144 ns | 747 ns | 757 ns | 5.19× | 5.26× | 0.99× | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.54 µs | 2.57 µs | 4.46× | 4.51× | 0.99× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 10.88 µs | 6.97 µs | 4.07× | 2.61× | **1.56×** | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 49.88 µs | 28.88 µs | 4.04× | 2.34× | **1.73×** | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 164.24 µs | 136.64 µs | 2.73× | 2.27× | **1.20×** | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 757.81 µs | 619.69 µs | 0.99× | 0.81× | **1.22×** | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 4.557 ms | 3.844 ms | 0.81× | 0.68× | **1.19×** | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 20.619 ms | 17.629 ms | 0.82× | 0.70× | **1.17×** | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 91.747 ms | 78.568 ms | 0.69× | 0.59× | **1.17×** | +| fft Float64 8×8 dims=1,2 | 173 ns | 809 ns | 798 ns | 4.67× | 4.61× | 1.01× | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.75 µs | 2.75 µs | 3.35× | 3.35× | 1.00× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 11.80 µs | 11.76 µs | 2.87× | 2.86× | 1.00× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 55.24 µs | 55.04 µs | 2.69× | 2.68× | 1.00× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 219.24 µs | 219.16 µs | 1.99× | 1.99× | 1.00× | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 3.203 ms | 2.297 ms | 1.78× | 1.28× | **1.39×** | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 2.987 ms | 2.972 ms | 0.81× | 0.81× | 1.00× | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.161 ms | 3.159 ms | 0.82× | 0.82× | 1.00× | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.204 ms | 1.203 ms | 1.06× | 1.05× | 1.00× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 5.963 ms | 5.862 ms | 0.98× | 0.96× | 1.02× | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 15.984 ms | 6.904 ms | 2.42× | 1.04× | **2.32×** | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 37.549 ms | 25.826 ms | 1.35× | 0.93× | **1.45×** | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 27.231 ms | 26.869 ms | 0.91× | 0.89× | 1.01× | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 120.075 ms | 118.900 ms | 0.73× | 0.73× | 1.01× | +| rfft Float32 8×8 dims=1,2 | 124 ns | 787 ns | 797 ns | 6.37× | 6.45× | 0.99× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.16 µs | 2.17 µs | 4.92× | 4.95× | 0.99× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 7.15 µs | 6.09 µs | 3.49× | 2.97× | **1.17×** | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 28.08 µs | 18.66 µs | 2.85× | 1.90× | **1.50×** | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 96.96 µs | 69.52 µs | 2.08× | 1.49× | **1.39×** | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 332.48 µs | 276.16 µs | 0.95× | 0.79× | **1.20×** | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 1.534 ms | 1.246 ms | 1.06× | 0.86× | **1.23×** | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 6.917 ms | 5.729 ms | 1.15× | 0.95× | **1.21×** | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 37.261 ms | 31.270 ms | 1.07× | 0.90× | **1.19×** | +| rfft Float64 8×8 dims=1,2 | 117 ns | 788 ns | 800 ns | 6.73× | 6.83× | 0.98× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.15 µs | 2.15 µs | 4.38× | 4.39× | 1.00× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 7.44 µs | 7.47 µs | 3.10× | 3.11× | 1.00× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 30.40 µs | 30.36 µs | 2.59× | 2.58× | 1.00× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 116.32 µs | 116.84 µs | 2.00× | 2.01× | 1.00× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 2.053 ms | 1.600 ms | 1.36× | 1.06× | **1.28×** | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 2.544 ms | 2.538 ms | 1.58× | 1.57× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 1.554 ms | 1.545 ms | 0.80× | 0.80× | 1.01× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 492.13 µs | 487.85 µs | 1.21× | 1.20× | 1.01× | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 2.235 ms | 2.188 ms | 1.17× | 1.14× | 1.02× | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 7.845 ms | 3.483 ms | 2.49× | 1.11× | **2.25×** | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 18.757 ms | 12.127 ms | 1.44× | 0.93× | **1.55×** | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 9.943 ms | 9.832 ms | 1.14× | 1.12× | 1.01× | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 52.776 ms | 52.791 ms | 0.97× | 0.97× | 1.00× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 9.07 µs | 9.29 µs | 5.86× | 6.01× | 0.98× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 62.76 µs | 63.36 µs | 4.66× | 4.71× | 0.99× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 600.53 µs | 413.53 µs | 4.24× | 2.92× | **1.45×** | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 5.768 ms | 3.807 ms | 3.87× | 2.55× | **1.52×** | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 42.537 ms | 37.300 ms | 2.31× | 2.02× | **1.14×** | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 9.51 µs | 9.53 µs | 4.99× | 5.01× | 1.00× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 68.04 µs | 68.68 µs | 3.41× | 3.44× | 0.99× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 678.49 µs | 674.09 µs | 2.81× | 2.79× | 1.01× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 6.550 ms | 6.568 ms | 2.63× | 2.64× | 1.00× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 59.699 ms | 60.360 ms | 1.53× | 1.55× | 0.99× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 8.24 µs | 8.39 µs | 6.94× | 7.06× | 0.98× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 47.12 µs | 47.76 µs | 5.11× | 5.18× | 0.99× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 334.28 µs | 268.36 µs | 3.68× | 2.95× | **1.25×** | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 2.821 ms | 1.881 ms | 2.96× | 1.97× | **1.50×** | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 20.396 ms | 15.965 ms | 2.18× | 1.70× | **1.28×** | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 8.41 µs | 8.44 µs | 7.03× | 7.05× | 1.00× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 47.92 µs | 48.12 µs | 4.21× | 4.23× | 1.00× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 356.92 µs | 358.68 µs | 3.05× | 3.07× | 1.00× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.185 ms | 3.241 ms | 2.35× | 2.39× | 0.98× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 26.926 ms | 26.611 ms | 1.82× | 1.80× | 1.01× | +| fft Float32 64×64 dims=1 | 6.23 µs | 23.60 µs | 13.12 µs | 3.79× | 2.11× | **1.80×** | +| fft Float32 256×64 dims=1 | 52.20 µs | 69.60 µs | 54.44 µs | 1.33× | 1.04× | **1.28×** | +| fft Float32 1024×64 dims=1 | 244.64 µs | 333.80 µs | 255.12 µs | 1.36× | 1.04× | **1.31×** | +| fft Float32 4096×64 dims=1 | 1.277 ms | 1.590 ms | 1.194 ms | 1.25× | 0.94× | **1.33×** | +| fft Float32 16384×64 dims=1 | 7.758 ms | 8.176 ms | 5.883 ms | 1.05× | 0.76× | **1.39×** | +| fft Float32 65536×64 dims=1 | 44.555 ms | 45.175 ms | 28.369 ms | 1.01× | 0.64× | **1.59×** | +| fft Float64 64×64 dims=1 | 10.32 µs | 26.00 µs | 26.00 µs | 2.52× | 2.52× | 1.00× | +| fft Float64 256×64 dims=1 | 87.04 µs | 104.84 µs | 104.56 µs | 1.20× | 1.20× | 1.00× | +| fft Float64 1024×64 dims=1 | 434.17 µs | 513.81 µs | 513.65 µs | 1.18× | 1.18× | 1.00× | +| fft Float64 4096×64 dims=1 | 2.162 ms | 2.521 ms | 2.527 ms | 1.17× | 1.17× | 1.00× | +| fft Float64 16384×64 dims=1 | 14.861 ms | 13.788 ms | 13.305 ms | 0.93× | 0.90× | 1.04× | +| fft Float64 65536×64 dims=1 | 88.463 ms | 76.362 ms | 76.238 ms | 0.86× | 0.86× | 1.00× | +| rfft Float32 64×64 dims=1 | 6.61 µs | 14.94 µs | 11.02 µs | 2.26× | 1.67× | **1.36×** | +| rfft Float32 256×64 dims=1 | 40.84 µs | 42.44 µs | 35.60 µs | 1.04× | 0.87× | **1.19×** | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 187.00 µs | 148.32 µs | 1.30× | 1.03× | **1.26×** | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 875.53 µs | 695.41 µs | 1.27× | 1.01× | **1.26×** | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 4.134 ms | 3.153 ms | 1.11× | 0.85× | **1.31×** | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 21.259 ms | 15.836 ms | 1.12× | 0.83× | **1.34×** | +| rfft Float64 64×64 dims=1 | 6.68 µs | 16.82 µs | 17.02 µs | 2.52× | 2.55× | 0.99× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 4.180 ms | 4.173 ms | 1.34× | 1.34× | 1.00× | +| rfft Float64 256×64 dims=1 | 44.56 µs | 61.44 µs | 61.68 µs | 1.38× | 1.38× | 1.00× | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 4.793 ms | 4.777 ms | 1.31× | 1.30× | 1.00× | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 288.68 µs | 291.20 µs | 1.35× | 1.36× | 0.99× | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 5.417 ms | 5.399 ms | 1.28× | 1.27× | 1.00× | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.342 ms | 1.343 ms | 1.29× | 1.29× | 1.00× | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 6.650 ms | 6.663 ms | 1.08× | 1.09× | 1.00× | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 37.309 ms | 36.092 ms | 0.98× | 0.95× | 1.03× | +| fft Float32 64×64 dims=2 | 6.13 µs | 25.64 µs | 15.42 µs | 4.18× | 2.52× | **1.66×** | +| fft Float32 64×256 dims=2 | 79.52 µs | 109.44 µs | 95.76 µs | 1.38× | 1.20× | **1.14×** | +| fft Float32 64×1024 dims=2 | 433.65 µs | 618.69 µs | 447.28 µs | 1.43× | 1.03× | **1.38×** | +| fft Float32 64×4096 dims=2 | 4.699 ms | 3.319 ms | 2.824 ms | 0.71× | 0.60× | **1.18×** | +| fft Float32 64×16384 dims=2 | 24.311 ms | 15.082 ms | 13.011 ms | 0.62× | 0.54× | **1.16×** | +| fft Float32 64×65536 dims=2 | 172.367 ms | 86.316 ms | 73.301 ms | 0.50× | 0.43× | **1.18×** | +| fft Float64 64×64 dims=2 | 10.86 µs | 28.96 µs | 29.32 µs | 2.67× | 2.70× | 0.99× | +| fft Float64 64×256 dims=2 | 108.96 µs | 138.96 µs | 140.12 µs | 1.28× | 1.29× | 0.99× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 807.21 µs | 799.57 µs | 0.91× | 0.90× | 1.01× | +| fft Float64 64×4096 dims=2 | 5.347 ms | 4.310 ms | 4.297 ms | 0.81× | 0.80× | 1.00× | +| fft Float64 64×16384 dims=2 | 34.143 ms | 22.229 ms | 21.453 ms | 0.65× | 0.63× | 1.04× | +| fft Float64 64×65536 dims=2 | 247.287 ms | 133.456 ms | 128.797 ms | 0.54× | 0.52× | 1.04× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 17.62 µs | 13.72 µs | 2.67× | 2.08× | **1.28×** | +| rfft Float32 64×256 dims=2 | 57.92 µs | 66.68 µs | 60.16 µs | 1.15× | 1.04× | **1.11×** | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 327.28 µs | 293.92 µs | 1.13× | 1.02× | **1.11×** | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 1.862 ms | 1.696 ms | 1.05× | 0.95× | **1.10×** | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 9.498 ms | 8.464 ms | 0.81× | 0.73× | **1.12×** | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 49.952 ms | 46.357 ms | 0.73× | 0.68× | **1.08×** | +| rfft Float64 64×64 dims=2 | 6.61 µs | 19.96 µs | 19.82 µs | 3.02× | 3.00× | 1.01× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 95.76 µs | 95.60 µs | 1.34× | 1.33× | 1.00× | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 449.37 µs | 445.09 µs | 1.29× | 1.28× | 1.01× | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 2.623 ms | 2.595 ms | 0.96× | 0.95× | 1.01× | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 12.216 ms | 11.997 ms | 0.86× | 0.85× | 1.02× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 77.872 ms | 76.784 ms | 0.70× | 0.69× | 1.01× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `main`/`fftw` | `ffta`/`fftw` | `ffta` vs `main` | +|:--|--:|--:|--:| +| ComplexF32 fft 2d | 1.98× (0.69–5.19) | 1.62× (0.59–5.26) | **1.23×** (0.99–1.73) | +| ComplexF32 fft 3d | 4.01× (2.31–5.86) | 3.36× (2.02–6.01) | **1.19×** (0.98–1.52) | +| ComplexF32 fft awkward | 1.44× (0.75–3.01) | 0.83× (0.52–1.57) | **1.73×** (1.15–2.36) | +| ComplexF32 fft batched_dim1 | 1.45× (1.01–3.79) | 1.01× (0.64–2.11) | **1.44×** (1.28–1.80) | +| ComplexF32 fft batched_dim2 | 1.10× (0.50–4.18) | 0.87× (0.43–2.52) | **1.27×** (1.14–1.66) | +| ComplexF32 fft pow2 | 0.93× (0.36–1.75) | 0.72× (0.35–1.23) | **1.28×** (0.97–1.91) | +| ComplexF32 fft prime | 1.31× (0.60–6.60) | 0.87× (0.39–6.61) | **1.52×** (0.95–2.30) | +| ComplexF32 fft smooth | 2.62× (1.35–5.31) | 0.90× (0.34–4.16) | **2.90×** (0.96–4.71) | +| ComplexF64 fft 2d | 1.59× (0.73–4.67) | 1.41× (0.73–4.61) | **1.12×** (1.00–2.32) | +| ComplexF64 fft 3d | 2.86× (1.53–4.99) | 2.88× (1.55–5.01) | **1.00×** (0.99–1.01) | +| ComplexF64 fft awkward | 1.57× (0.74–3.00) | 1.02× (0.71–1.74) | **1.55×** (0.99–2.21) | +| ComplexF64 fft batched_dim1 | 1.22× (0.86–2.52) | 1.22× (0.86–2.52) | **1.01×** (1.00–1.04) | +| ComplexF64 fft batched_dim2 | 0.98× (0.54–2.67) | 0.97× (0.52–2.70) | **1.01×** (0.99–1.04) | +| ComplexF64 fft pow2 | 0.90× (0.38–1.91) | 0.89× (0.37–1.93) | **1.01×** (0.99–1.06) | +| ComplexF64 fft prime | 1.48× (0.73–3.98) | 1.15× (0.56–3.96) | **1.29×** (0.87–2.03) | +| ComplexF64 fft smooth | 2.10× (1.00–5.37) | 0.98× (0.35–5.45) | **2.14×** (0.99–2.84) | +| Float32 rfft 2d | 2.11× (0.95–6.37) | 1.75× (0.79–6.45) | **1.20×** (0.99–1.50) | +| Float32 rfft 3d | 3.84× (2.18–6.94) | 3.25× (1.70–7.06) | **1.18×** (0.98–1.50) | +| Float32 rfft awkward | 1.41× (0.71–2.92) | 0.81× (0.46–1.41) | **1.75×** (1.19–2.38) | +| Float32 rfft batched_dim1 | 1.30× (1.04–2.26) | 1.01× (0.83–1.67) | **1.29×** (1.19–1.36) | +| Float32 rfft batched_dim2 | 1.14× (0.73–2.67) | 1.00× (0.68–2.08) | **1.13×** (1.08–1.28) | +| Float32 rfft pow2 | 1.23× (0.66–2.47) | 1.03× (0.67–2.51) | **1.19×** (0.98–1.53) | +| Float32 rfft prime | 1.26× (0.53–2.82) | 0.82× (0.36–1.72) | **1.54×** (1.00–2.37) | +| Float32 rfft smooth | 2.63× (1.62–5.53) | 1.14× (0.49–5.70) | **2.31×** (0.96–4.30) | +| Float64 rfft 2d | 1.82× (0.80–6.73) | 1.64× (0.80–6.83) | **1.11×** (0.98–2.25) | +| Float64 rfft 3d | 3.29× (1.82–7.03) | 3.30× (1.80–7.05) | **1.00×** (0.98–1.01) | +| Float64 rfft awkward | 1.66× (0.70–3.96) | 1.07× (0.68–2.23) | **1.56×** (1.00–2.29) | +| Float64 rfft batched_dim1 | 1.34× (0.98–2.52) | 1.34× (0.95–2.55) | **1.00×** (0.99–1.03) | +| Float64 rfft batched_dim2 | 1.20× (0.70–3.02) | 1.19× (0.69–3.00) | **1.01×** (1.00–1.02) | +| Float64 rfft pow2 | 1.21× (0.45–2.51) | 1.22× (0.46–2.55) | **0.99×** (0.91–1.06) | +| Float64 rfft prime | 1.72× (0.68–3.51) | 1.34× (0.64–3.09) | **1.29×** (0.84–1.99) | +| Float64 rfft smooth | 2.49× (1.18–5.48) | 1.38× (0.51–5.52) | **1.80×** (0.98–3.00) | +| **all** | 1.60× (0.36–7.03) | 1.09× (0.34–7.06) | **1.46×** (0.84–4.71), 505 cases, 3 slower by >5% | diff --git a/benchmark/compare3/aarch64/stockham-stack/ffta_t1.json b/benchmark/compare3/aarch64/stockham-stack/ffta_t1.json new file mode 100644 index 0000000..6f50a4a --- /dev/null +++ b/benchmark/compare3/aarch64/stockham-stack/ffta_t1.json @@ -0,0 +1,10995 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T20:57:56.076", + "impl": "ffta", + "julia": "1.12.6", + "scope": { + "classes": [ + "pow2", + "smooth", + "prime", + "awkward" + ], + "kinds": [ + "fft", + "rfft" + ], + "maxlog2": 22, + "measure": true, + "only": [ + "1d", + "nd", + "batched" + ], + "sizes": [] + }, + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ a2fd368" + }, + "results": [ + { + "T": "Float64", 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2.7760000000000002e-5, + "shape": "batched_dim1", + "size": [ + 4096, + 256 + ], + "sum_im": 7792.696853255871, + "sum_re": -2384.3887021657065 + } + ] +} \ No newline at end of file From e6d63a4d965f505af9dd818464bb972cc2d02561 Mon Sep 17 00:00:00 2001 From: Panagiotis Georgakopoulos Date: Sun, 30 Aug 2026 21:30:32 +0000 Subject: [PATCH 20/21] benchmark: 16-thread compare3 for the Stockham stack --- .../stockham-stack/COMPARE3_16threads.md | 578 + .../aarch64/stockham-stack/ffta_t16.json | 10995 ++++++++++++++++ 2 files changed, 11573 insertions(+) create mode 100644 benchmark/compare3/aarch64/stockham-stack/COMPARE3_16threads.md create mode 100644 benchmark/compare3/aarch64/stockham-stack/ffta_t16.json diff --git a/benchmark/compare3/aarch64/stockham-stack/COMPARE3_16threads.md b/benchmark/compare3/aarch64/stockham-stack/COMPARE3_16threads.md new file mode 100644 index 0000000..346bfc7 --- /dev/null +++ b/benchmark/compare3/aarch64/stockham-stack/COMPARE3_16threads.md @@ -0,0 +1,578 @@ +# FFT implementations side by side + +Rendered 2026-08-30T21:26:36.644 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `ffta` | FFTA.jl 0.3.1 @ a2fd368 — `FFTA-adj` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs ffta` is the speedup over the `ffta` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + +| case | `fftw` | `ffta` | `ffta`/`fftw` | | +|:--|--:|--:|--:| +| fft Float32 7 dims=1 (16 thr) | 39 ns | 36 ns | 0.93× | +| fft Float32 8 dims=1 (16 thr) | 39 ns | 38 ns | 0.99× | +| fft Float32 12 dims=1 (16 thr) | 47 ns | 181 ns | 3.86× | +| fft Float32 16 dims=1 (16 thr) | 55 ns | 68 ns | 1.24× | +| fft Float32 17 dims=1 (16 thr) | 138 ns | 814 ns | 5.90× | +| fft Float32 23 dims=1 (16 thr) | 231 ns | 1.52 µs | 6.58× | +| fft Float32 25 dims=1 (16 thr) | 121 ns | 173 ns | 1.43× | +| fft Float32 29 dims=1 (16 thr) | 345 ns | 508 ns | 1.47× | +| fft Float32 31 dims=1 (16 thr) | 572 ns | 509 ns | 0.89× | +| fft Float32 32 dims=1 (16 thr) | 106 ns | 86 ns | 0.81× | +| fft Float32 37 dims=1 (16 thr) | 68.84 µs | 725 ns | 0.01× | +| fft Float32 41 dims=1 (16 thr) | 32.20 µs | 738 ns | 0.02× | +| fft Float32 43 dims=1 (16 thr) | 128.00 µs | 742 ns | 0.01× | +| fft Float32 54 dims=1 (16 thr) | 28.96 µs | 373 ns | 0.01× | +| fft Float32 60 dims=1 (16 thr) | 13.08 µs | 386 ns | 0.03× | +| fft Float32 61 dims=1 (16 thr) | 33.20 µs | 918 ns | 0.03× | +| fft Float32 64 dims=1 (16 thr) | 213 ns | 178 ns | 0.83× | +| fft Float32 71 dims=1 (16 thr) | 146.48 µs | 1.22 µs | 0.01× | +| fft Float32 73 dims=1 (16 thr) | 74.80 µs | 1.23 µs | 0.02× | +| fft Float32 79 dims=1 (16 thr) | 90.56 µs | 1.24 µs | 0.01× | +| fft Float32 101 dims=1 (16 thr) | 34.04 µs | 1.85 µs | 0.05× | +| fft Float32 112 dims=1 (16 thr) | 33.76 µs | 367 ns | 0.01× | +| fft Float32 120 dims=1 (16 thr) | 34.68 µs | 720 ns | 0.02× | +| fft Float32 128 dims=1 (16 thr) | 443 ns | 314 ns | 0.71× | +| fft Float32 202 dims=1 (16 thr) | 84.16 µs | 5.29 µs | 0.06× | +| fft Float32 243 dims=1 (16 thr) | 37.92 µs | 1.89 µs | 0.05× | +| fft Float32 251 dims=1 (16 thr) | 100.60 µs | 4.05 µs | 0.04× | +| fft Float32 256 dims=1 (16 thr) | 22.00 µs | 737 ns | 0.03× | +| fft Float32 303 dims=1 (16 thr) | 81.08 µs | 7.59 µs | 0.09× | +| fft Float32 360 dims=1 (16 thr) | 47.00 µs | 2.26 µs | 0.05× | +| fft Float32 404 dims=1 (16 thr) | 63.28 µs | 9.49 µs | 0.15× | +| fft Float32 504 dims=1 (16 thr) | 45.28 µs | 3.31 µs | 0.07× | +| fft Float32 512 dims=1 (16 thr) | 27.56 µs | 1.46 µs | 0.05× | +| fft Float32 593 dims=1 (16 thr) | 146.64 µs | 12.22 µs | 0.08× | +| fft Float32 606 dims=1 (16 thr) | 56.00 µs | 19.96 µs | 0.36× | +| fft Float32 720 dims=1 (16 thr) | 37.48 µs | 2.89 µs | 0.08× | +| fft Float32 1000 dims=1 (16 thr) | 32.16 µs | 6.85 µs | 0.21× | +| fft Float32 1024 dims=1 (16 thr) | 28.52 µs | 3.51 µs | 0.12× | +| fft Float32 1080 dims=1 (16 thr) | 34.04 µs | 7.48 µs | 0.22× | +| fft Float32 1433 dims=1 (16 thr) | 166.00 µs | 32.56 µs | 0.20× | +| fft Float32 1616 dims=1 (16 thr) | 41.60 µs | 36.52 µs | 0.88× | +| fft Float32 2018 dims=1 (16 thr) | 179.92 µs | 53.80 µs | 0.30× | +| fft Float32 2048 dims=1 (16 thr) | 28.80 µs | 7.23 µs | 0.25× | +| fft Float32 2304 dims=1 (16 thr) | 40.80 µs | 10.04 µs | 0.25× | +| fft Float32 3027 dims=1 (16 thr) | 145.12 µs | 77.76 µs | 0.54× | +| fft Float32 3491 dims=1 (16 thr) | 195.88 µs | 84.32 µs | 0.43× | +| fft Float32 4036 dims=1 (16 thr) | 105.12 µs | 97.72 µs | 0.93× | +| fft Float32 4096 dims=1 (16 thr) | 30.32 µs | 16.60 µs | 0.55× | +| fft Float32 4860 dims=1 (16 thr) | 45.88 µs | 42.56 µs | 0.93× | +| fft Float32 6054 dims=1 (16 thr) | 108.32 µs | 202.52 µs | 1.87× | +| fft Float32 8192 dims=1 (16 thr) | 35.76 µs | 35.32 µs | 0.99× | +| fft Float32 8198 dims=1 (16 thr) | 226.72 µs | 293.28 µs | 1.29× | +| fft Float32 8443 dims=1 (16 thr) | 245.64 µs | 240.92 µs | 0.98× | +| fft Float32 10290 dims=1 (16 thr) | 49.48 µs | 98.52 µs | 1.99× | +| fft Float32 12297 dims=1 (16 thr) | 223.80 µs | 429.33 µs | 1.92× | +| fft Float32 16144 dims=1 (16 thr) | 76.04 µs | 381.24 µs | 5.01× | +| fft Float32 16384 dims=1 (16 thr) | 39.08 µs | 83.96 µs | 2.15× | +| fft Float32 16396 dims=1 (16 thr) | 194.04 µs | 548.81 µs | 2.83× | +| fft Float32 20507 dims=1 (16 thr) | 348.28 µs | 669.17 µs | 1.92× | +| fft Float32 21875 dims=1 (16 thr) | 69.36 µs | 217.84 µs | 3.14× | +| fft Float32 24594 dims=1 (16 thr) | 242.08 µs | 1.063 ms | 4.39× | +| fft Float32 32768 dims=1 (16 thr) | 49.76 µs | 182.40 µs | 3.67× | +| fft Float32 32822 dims=1 (16 thr) | 505.97 µs | 1.333 ms | 2.63× | +| fft Float32 46305 dims=1 (16 thr) | 139.20 µs | 511.97 µs | 3.68× | +| fft Float32 49233 dims=1 (16 thr) | 579.33 µs | 1.945 ms | 3.36× | +| fft Float32 49757 dims=1 (16 thr) | 991.93 µs | 1.665 ms | 1.68× | +| fft Float32 65536 dims=1 (16 thr) | 78.80 µs | 403.29 µs | 5.12× | +| fft Float32 65584 dims=1 (16 thr) | 337.00 µs | 2.264 ms | 6.72× | +| fft Float32 65644 dims=1 (16 thr) | 639.65 µs | 2.501 ms | 3.91× | +| fft Float32 98304 dims=1 (16 thr) | 131.64 µs | 650.25 µs | 4.94× | +| fft Float32 98466 dims=1 (16 thr) | 843.01 µs | 4.771 ms | 5.66× | +| fft Float32 120779 dims=1 (16 thr) | 2.499 ms | 5.774 ms | 2.31× | +| fft Float32 131072 dims=1 (16 thr) | 151.72 µs | 851.93 µs | 5.62× | +| fft Float32 131074 dims=1 (16 thr) | 1.900 ms | 6.319 ms | 3.33× | +| fft Float32 196611 dims=1 (16 thr) | 2.014 ms | 8.859 ms | 4.40× | +| fft Float32 207360 dims=1 (16 thr) | 470.29 µs | 1.551 ms | 3.30× | +| fft Float32 262144 dims=1 (16 thr) | 335.56 µs | 521.17 µs | 1.55× | +| fft Float32 262148 dims=1 (16 thr) | 2.046 ms | 11.766 ms | 5.75× | +| fft Float32 262576 dims=1 (16 thr) | 1.306 ms | 10.774 ms | 8.25× | +| fft Float32 293201 dims=1 (16 thr) | 9.679 ms | 12.048 ms | 1.24× | +| fft Float32 393222 dims=1 (16 thr) | 2.309 ms | 21.424 ms | 9.28× | +| fft Float32 441000 dims=1 (16 thr) | 687.41 µs | 5.253 ms | 7.64× | +| fft Float32 524288 dims=1 (16 thr) | 1.027 ms | 574.77 µs | 0.56× | +| fft Float32 524294 dims=1 (16 thr) | 7.465 ms | 26.755 ms | 3.58× | +| fft Float32 711749 dims=1 (16 thr) | 14.723 ms | 36.183 ms | 2.46× | +| fft Float32 786441 dims=1 (16 thr) | 8.949 ms | 39.941 ms | 4.46× | +| fft Float32 933120 dims=1 (16 thr) | 2.122 ms | 8.496 ms | 4.00× | +| fft Float32 1000000 dims=1 (16 thr) | 2.078 ms | 8.392 ms | 4.04× | +| fft Float32 1048576 dims=1 (16 thr) | 1.852 ms | 1.125 ms | 0.61× | +| fft Float32 1048588 dims=1 (16 thr) | 9.354 ms | 54.011 ms | 5.77× | +| fft Float32 1048592 dims=1 (16 thr) | 3.759 ms | 51.328 ms | 13.65× | +| fft Float32 1572882 dims=1 (16 thr) | 14.408 ms | 94.390 ms | 6.55× | +| fft Float32 1727797 dims=1 (16 thr) | 35.191 ms | 119.850 ms | 3.41× | +| fft Float32 1975680 dims=1 (16 thr) | 4.527 ms | 21.227 ms | 4.69× | +| fft Float32 2097152 dims=1 (16 thr) | 4.818 ms | 2.543 ms | 0.53× | +| fft Float32 4167450 dims=1 (16 thr) | 10.806 ms | 88.042 ms | 8.15× | +| fft Float32 4194304 dims=1 (16 thr) | 13.475 ms | 6.383 ms | 0.47× | +| fft Float64 7 dims=1 (16 thr) | 28 ns | 41 ns | 1.44× | +| fft Float64 8 dims=1 (16 thr) | 26 ns | 39 ns | 1.49× | +| fft Float64 12 dims=1 (16 thr) | 34 ns | 183 ns | 5.39× | +| fft Float64 16 dims=1 (16 thr) | 42 ns | 69 ns | 1.66× | +| fft Float64 17 dims=1 (16 thr) | 139 ns | 501 ns | 3.61× | +| fft Float64 23 dims=1 (16 thr) | 231 ns | 914 ns | 3.96× | +| fft Float64 25 dims=1 (16 thr) | 10.28 µs | 172 ns | 0.02× | +| fft Float64 29 dims=1 (16 thr) | 345 ns | 903 ns | 2.62× | +| fft Float64 31 dims=1 (16 thr) | 388 ns | 903 ns | 2.33× | +| fft Float64 32 dims=1 (16 thr) | 81 ns | 153 ns | 1.89× | +| fft Float64 37 dims=1 (16 thr) | 25.20 µs | 1.13 µs | 0.04× | +| fft Float64 41 dims=1 (16 thr) | 29.48 µs | 1.15 µs | 0.04× | +| fft Float64 43 dims=1 (16 thr) | 702 ns | 1.15 µs | 1.64× | +| fft Float64 54 dims=1 (16 thr) | 15.64 µs | 461 ns | 0.03× | +| fft Float64 60 dims=1 (16 thr) | 16.96 µs | 439 ns | 0.03× | +| fft Float64 61 dims=1 (16 thr) | 37.20 µs | 1.58 µs | 0.04× | +| fft Float64 64 dims=1 (16 thr) | 15.68 µs | 351 ns | 0.02× | +| fft Float64 71 dims=1 (16 thr) | 133.64 µs | 1.96 µs | 0.01× | +| fft Float64 73 dims=1 (16 thr) | 35.72 µs | 2.01 µs | 0.06× | +| fft Float64 79 dims=1 (16 thr) | 143.40 µs | 1.98 µs | 0.01× | +| fft Float64 101 dims=1 (16 thr) | 41.04 µs | 3.03 µs | 0.07× | +| fft Float64 112 dims=1 (16 thr) | 20.88 µs | 596 ns | 0.03× | +| fft Float64 120 dims=1 (16 thr) | 20.84 µs | 844 ns | 0.04× | +| fft Float64 128 dims=1 (16 thr) | 22.48 µs | 592 ns | 0.03× | +| fft Float64 202 dims=1 (16 thr) | 83.28 µs | 7.68 µs | 0.09× | +| fft Float64 243 dims=1 (16 thr) | 36.92 µs | 2.59 µs | 0.07× | +| fft Float64 251 dims=1 (16 thr) | 92.56 µs | 7.59 µs | 0.08× | +| fft Float64 256 dims=1 (16 thr) | 28.72 µs | 1.42 µs | 0.05× | +| fft Float64 303 dims=1 (16 thr) | 84.48 µs | 11.28 µs | 0.13× | +| fft Float64 360 dims=1 (16 thr) | 37.80 µs | 2.98 µs | 0.08× | +| fft Float64 404 dims=1 (16 thr) | 67.80 µs | 14.44 µs | 0.21× | +| fft Float64 504 dims=1 (16 thr) | 39.48 µs | 4.59 µs | 0.12× | +| fft Float64 512 dims=1 (16 thr) | 28.56 µs | 2.98 µs | 0.10× | +| fft Float64 593 dims=1 (16 thr) | 185.28 µs | 21.52 µs | 0.12× | +| fft Float64 606 dims=1 (16 thr) | 58.80 µs | 27.52 µs | 0.47× | +| fft Float64 720 dims=1 (16 thr) | 32.36 µs | 5.22 µs | 0.16× | +| fft Float64 1000 dims=1 (16 thr) | 40.20 µs | 9.12 µs | 0.23× | +| fft Float64 1024 dims=1 (16 thr) | 29.08 µs | 6.97 µs | 0.24× | +| fft Float64 1080 dims=1 (16 thr) | 32.64 µs | 10.70 µs | 0.33× | +| fft Float64 1433 dims=1 (16 thr) | 173.68 µs | 58.72 µs | 0.34× | +| fft Float64 1616 dims=1 (16 thr) | 31.00 µs | 56.76 µs | 1.83× | +| fft Float64 2018 dims=1 (16 thr) | 167.20 µs | 88.60 µs | 0.53× | +| fft Float64 2048 dims=1 (16 thr) | 29.76 µs | 14.94 µs | 0.50× | +| fft Float64 2304 dims=1 (16 thr) | 33.68 µs | 18.88 µs | 0.56× | +| fft Float64 3027 dims=1 (16 thr) | 152.16 µs | 131.04 µs | 0.86× | +| fft Float64 3491 dims=1 (16 thr) | 220.04 µs | 153.36 µs | 0.70× | +| fft Float64 4036 dims=1 (16 thr) | 114.04 µs | 169.28 µs | 1.48× | +| fft Float64 4096 dims=1 (16 thr) | 34.04 µs | 35.00 µs | 1.03× | +| fft Float64 4860 dims=1 (16 thr) | 39.76 µs | 62.92 µs | 1.58× | +| fft Float64 6054 dims=1 (16 thr) | 123.12 µs | 312.48 µs | 2.54× | +| fft Float64 8192 dims=1 (16 thr) | 37.96 µs | 74.16 µs | 1.95× | +| fft Float64 8198 dims=1 (16 thr) | 249.20 µs | 494.73 µs | 1.99× | +| fft Float64 8443 dims=1 (16 thr) | 296.48 µs | 490.37 µs | 1.65× | +| fft Float64 10290 dims=1 (16 thr) | 59.44 µs | 146.08 µs | 2.46× | +| fft Float64 12297 dims=1 (16 thr) | 269.40 µs | 730.57 µs | 2.71× | +| fft Float64 16144 dims=1 (16 thr) | 98.76 µs | 682.33 µs | 6.91× | +| fft Float64 16384 dims=1 (16 thr) | 47.52 µs | 170.56 µs | 3.59× | +| fft Float64 16396 dims=1 (16 thr) | 236.72 µs | 951.65 µs | 4.02× | +| fft Float64 20507 dims=1 (16 thr) | 614.81 µs | 1.321 ms | 2.15× | +| fft Float64 21875 dims=1 (16 thr) | 74.56 µs | 327.28 µs | 4.39× | +| fft Float64 24594 dims=1 (16 thr) | 299.28 µs | 1.710 ms | 5.71× | +| fft Float64 32768 dims=1 (16 thr) | 68.04 µs | 417.88 µs | 6.14× | +| fft Float64 32822 dims=1 (16 thr) | 650.53 µs | 2.276 ms | 3.50× | +| fft Float64 46305 dims=1 (16 thr) | 165.20 µs | 820.41 µs | 4.97× | +| fft Float64 49233 dims=1 (16 thr) | 821.77 µs | 3.553 ms | 4.32× | +| fft Float64 49757 dims=1 (16 thr) | 1.525 ms | 3.214 ms | 2.11× | +| fft Float64 65536 dims=1 (16 thr) | 141.92 µs | 1.026 ms | 7.23× | +| fft Float64 65584 dims=1 (16 thr) | 352.76 µs | 3.925 ms | 11.13× | +| fft Float64 65644 dims=1 (16 thr) | 906.93 µs | 4.630 ms | 5.11× | +| fft Float64 98304 dims=1 (16 thr) | 220.80 µs | 1.323 ms | 5.99× | +| fft Float64 98466 dims=1 (16 thr) | 1.182 ms | 7.822 ms | 6.62× | +| fft Float64 120779 dims=1 (16 thr) | 3.331 ms | 9.355 ms | 2.81× | +| fft Float64 131072 dims=1 (16 thr) | 267.08 µs | 1.998 ms | 7.48× | +| fft Float64 131074 dims=1 (16 thr) | 2.202 ms | 11.364 ms | 5.16× | +| fft Float64 196611 dims=1 (16 thr) | 2.454 ms | 16.912 ms | 6.89× | +| fft Float64 207360 dims=1 (16 thr) | 673.37 µs | 3.021 ms | 4.49× | +| fft Float64 262144 dims=1 (16 thr) | 477.41 µs | 458.56 µs | 0.96× | +| fft Float64 262148 dims=1 (16 thr) | 2.658 ms | 22.207 ms | 8.36× | +| fft Float64 262576 dims=1 (16 thr) | 1.976 ms | 18.987 ms | 9.61× | +| fft Float64 293201 dims=1 (16 thr) | 13.075 ms | 23.868 ms | 1.83× | +| fft Float64 393222 dims=1 (16 thr) | 3.018 ms | 36.969 ms | 12.25× | +| fft Float64 441000 dims=1 (16 thr) | 1.119 ms | 8.646 ms | 7.73× | +| fft Float64 524288 dims=1 (16 thr) | 1.292 ms | 907.93 µs | 0.70× | +| fft Float64 524294 dims=1 (16 thr) | 9.388 ms | 49.128 ms | 5.23× | +| fft Float64 711749 dims=1 (16 thr) | 21.364 ms | 85.541 ms | 4.00× | +| fft Float64 786441 dims=1 (16 thr) | 13.710 ms | 79.059 ms | 5.77× | +| fft Float64 933120 dims=1 (16 thr) | 3.641 ms | 18.249 ms | 5.01× | +| fft Float64 1000000 dims=1 (16 thr) | 2.683 ms | 17.876 ms | 6.66× | +| fft Float64 1048576 dims=1 (16 thr) | 3.035 ms | 1.824 ms | 0.60× | +| fft Float64 1048588 dims=1 (16 thr) | 15.898 ms | 97.450 ms | 6.13× | +| fft Float64 1048592 dims=1 (16 thr) | 5.266 ms | 89.876 ms | 17.07× | +| fft Float64 1572882 dims=1 (16 thr) | 25.599 ms | 173.206 ms | 6.77× | +| fft Float64 1727797 dims=1 (16 thr) | 74.126 ms | 271.807 ms | 3.67× | +| fft Float64 1975680 dims=1 (16 thr) | 9.586 ms | 50.377 ms | 5.26× | +| fft Float64 2097152 dims=1 (16 thr) | 7.987 ms | 4.178 ms | 0.52× | +| fft Float64 4167450 dims=1 (16 thr) | 19.462 ms | 159.475 ms | 8.19× | +| fft Float64 4194304 dims=1 (16 thr) | 18.247 ms | 10.167 ms | 0.56× | +| fft Float64 8 dims=1 (16 thr) MEASURE | 26 ns | — | — | +| fft Float64 16 dims=1 (16 thr) MEASURE | 41 ns | — | — | +| fft Float64 32 dims=1 (16 thr) MEASURE | 82 ns | — | — | +| fft Float64 64 dims=1 (16 thr) MEASURE | 169 ns | — | — | +| fft Float64 128 dims=1 (16 thr) MEASURE | 375 ns | — | — | +| fft Float64 256 dims=1 (16 thr) MEASURE | 19.68 µs | — | — | +| fft Float64 512 dims=1 (16 thr) MEASURE | 20.72 µs | — | — | +| fft Float64 1024 dims=1 (16 thr) MEASURE | 23.84 µs | — | — | +| fft Float64 2048 dims=1 (16 thr) MEASURE | 29.96 µs | — | — | +| fft Float64 4096 dims=1 (16 thr) MEASURE | 33.72 µs | — | — | +| fft Float64 8192 dims=1 (16 thr) MEASURE | 36.68 µs | — | — | +| fft Float64 16384 dims=1 (16 thr) MEASURE | 46.96 µs | — | — | +| fft Float64 32768 dims=1 (16 thr) MEASURE | 65.48 µs | — | — | +| fft Float64 65536 dims=1 (16 thr) MEASURE | 113.16 µs | — | — | +| fft Float64 131072 dims=1 (16 thr) MEASURE | 198.32 µs | — | — | +| fft Float64 262144 dims=1 (16 thr) MEASURE | 392.00 µs | — | — | +| fft Float64 524288 dims=1 (16 thr) MEASURE | 912.53 µs | — | — | +| fft Float64 1048576 dims=1 (16 thr) MEASURE | 1.822 ms | — | — | +| fft Float64 2097152 dims=1 (16 thr) MEASURE | 4.515 ms | — | — | +| fft Float64 4194304 dims=1 (16 thr) MEASURE | 8.503 ms | — | — | +| rfft Float32 7 dims=1 (16 thr) | 25 ns | 40 ns | 1.61× | +| rfft Float32 8 dims=1 (16 thr) | 23 ns | 55 ns | 2.35× | +| rfft Float32 12 dims=1 (16 thr) | 28 ns | 154 ns | 5.59× | +| rfft Float32 16 dims=1 (16 thr) | 33 ns | 76 ns | 2.29× | +| rfft Float32 17 dims=1 (16 thr) | 135 ns | 183 ns | 1.35× | +| rfft Float32 23 dims=1 (16 thr) | 205 ns | 319 ns | 1.56× | +| rfft Float32 25 dims=1 (16 thr) | 78 ns | 164 ns | 2.11× | +| rfft Float32 29 dims=1 (16 thr) | 291 ns | 493 ns | 1.70× | +| rfft Float32 31 dims=1 (16 thr) | 322 ns | 497 ns | 1.54× | +| rfft Float32 32 dims=1 (16 thr) | 104 ns | 121 ns | 1.16× | +| rfft Float32 37 dims=1 (16 thr) | 430 ns | 716 ns | 1.67× | +| rfft Float32 41 dims=1 (16 thr) | 513 ns | 720 ns | 1.40× | +| rfft Float32 43 dims=1 (16 thr) | 555 ns | 722 ns | 1.30× | +| rfft Float32 54 dims=1 (16 thr) | 3.68 µs | 349 ns | 0.09× | +| rfft Float32 60 dims=1 (16 thr) | 9.36 µs | 745 ns | 0.08× | +| rfft Float32 61 dims=1 (16 thr) | 1.04 µs | 895 ns | 0.86× | +| rfft Float32 64 dims=1 (16 thr) | 183 ns | 161 ns | 0.88× | +| rfft Float32 71 dims=1 (16 thr) | 1.38 µs | 1.19 µs | 0.86× | +| rfft Float32 73 dims=1 (16 thr) | 1.45 µs | 1.20 µs | 0.83× | +| rfft Float32 79 dims=1 (16 thr) | 1.68 µs | 1.21 µs | 0.72× | +| rfft Float32 101 dims=1 (16 thr) | 2.69 µs | 1.79 µs | 0.66× | +| rfft Float32 112 dims=1 (16 thr) | 7.80 µs | 435 ns | 0.06× | +| rfft Float32 120 dims=1 (16 thr) | 5.12 µs | 496 ns | 0.10× | +| rfft Float32 128 dims=1 (16 thr) | 349 ns | 301 ns | 0.86× | +| rfft Float32 202 dims=1 (16 thr) | 33.48 µs | 2.01 µs | 0.06× | +| rfft Float32 243 dims=1 (16 thr) | 39.04 µs | 1.84 µs | 0.05× | +| rfft Float32 251 dims=1 (16 thr) | 157.00 µs | 3.99 µs | 0.03× | +| rfft Float32 256 dims=1 (16 thr) | 693 ns | 531 ns | 0.77× | +| rfft Float32 303 dims=1 (16 thr) | 22.20 µs | 7.43 µs | 0.33× | +| rfft Float32 360 dims=1 (16 thr) | 33.32 µs | 1.44 µs | 0.04× | +| rfft Float32 404 dims=1 (16 thr) | 70.44 µs | 5.57 µs | 0.08× | +| rfft Float32 504 dims=1 (16 thr) | 31.80 µs | 2.08 µs | 0.07× | +| rfft Float32 512 dims=1 (16 thr) | 8.88 µs | 1.14 µs | 0.13× | +| rfft Float32 593 dims=1 (16 thr) | 91.84 µs | 11.82 µs | 0.13× | +| rfft Float32 606 dims=1 (16 thr) | 67.96 µs | 8.09 µs | 0.12× | +| rfft Float32 720 dims=1 (16 thr) | 48.00 µs | 2.82 µs | 0.06× | +| rfft Float32 1000 dims=1 (16 thr) | 35.40 µs | 4.17 µs | 0.12× | +| rfft Float32 1024 dims=1 (16 thr) | 16.16 µs | 2.25 µs | 0.14× | +| rfft Float32 1080 dims=1 (16 thr) | 46.28 µs | 4.62 µs | 0.10× | +| rfft Float32 1433 dims=1 (16 thr) | 181.20 µs | 31.52 µs | 0.17× | +| rfft Float32 1616 dims=1 (16 thr) | 43.60 µs | 19.46 µs | 0.45× | +| rfft Float32 2018 dims=1 (16 thr) | 180.68 µs | 20.76 µs | 0.11× | +| rfft Float32 2048 dims=1 (16 thr) | 4.46 µs | 5.13 µs | 1.15× | +| rfft Float32 2304 dims=1 (16 thr) | 29.80 µs | 6.25 µs | 0.21× | +| rfft Float32 3027 dims=1 (16 thr) | 116.32 µs | 75.64 µs | 0.65× | +| rfft Float32 3491 dims=1 (16 thr) | 244.20 µs | 81.72 µs | 0.33× | +| rfft Float32 4036 dims=1 (16 thr) | 170.36 µs | 56.76 µs | 0.33× | +| rfft Float32 4096 dims=1 (16 thr) | 9.43 µs | 10.52 µs | 1.12× | +| rfft Float32 4860 dims=1 (16 thr) | 51.08 µs | 24.52 µs | 0.48× | +| rfft Float32 6054 dims=1 (16 thr) | 142.60 µs | 82.52 µs | 0.58× | +| rfft Float32 8192 dims=1 (16 thr) | 41.24 µs | 22.92 µs | 0.56× | +| rfft Float32 8198 dims=1 (16 thr) | 229.48 µs | 121.48 µs | 0.53× | +| rfft Float32 8443 dims=1 (16 thr) | 318.96 µs | 238.28 µs | 0.75× | +| rfft Float32 10290 dims=1 (16 thr) | 54.56 µs | 56.80 µs | 1.04× | +| rfft Float32 12297 dims=1 (16 thr) | 243.92 µs | 421.05 µs | 1.73× | +| rfft Float32 16144 dims=1 (16 thr) | 137.60 µs | 201.04 µs | 1.46× | +| rfft Float32 16384 dims=1 (16 thr) | 64.12 µs | 47.92 µs | 0.75× | +| rfft Float32 16396 dims=1 (16 thr) | 224.60 µs | 307.40 µs | 1.37× | +| rfft Float32 20507 dims=1 (16 thr) | 525.97 µs | 656.25 µs | 1.25× | +| rfft Float32 21875 dims=1 (16 thr) | 72.68 µs | 214.76 µs | 2.95× | +| rfft Float32 24594 dims=1 (16 thr) | 249.96 µs | 451.09 µs | 1.80× | +| rfft Float32 32768 dims=1 (16 thr) | 105.36 µs | 106.64 µs | 1.01× | +| rfft Float32 32822 dims=1 (16 thr) | 410.44 µs | 559.45 µs | 1.36× | +| rfft Float32 46305 dims=1 (16 thr) | 127.44 µs | 503.33 µs | 3.95× | +| rfft Float32 49233 dims=1 (16 thr) | 658.81 µs | 1.913 ms | 2.90× | +| rfft Float32 49757 dims=1 (16 thr) | 1.215 ms | 1.614 ms | 1.33× | +| rfft Float32 65536 dims=1 (16 thr) | 227.44 µs | 238.56 µs | 1.05× | +| rfft Float32 65584 dims=1 (16 thr) | 429.85 µs | 1.144 ms | 2.66× | +| rfft Float32 65644 dims=1 (16 thr) | 667.05 µs | 1.401 ms | 2.10× | +| rfft Float32 98304 dims=1 (16 thr) | 398.04 µs | 387.96 µs | 0.97× | +| rfft Float32 98466 dims=1 (16 thr) | 741.13 µs | 2.067 ms | 2.79× | +| rfft Float32 120779 dims=1 (16 thr) | 6.107 ms | 5.732 ms | 0.94× | +| rfft Float32 131072 dims=1 (16 thr) | 535.29 µs | 521.81 µs | 0.97× | +| rfft Float32 131074 dims=1 (16 thr) | 1.454 ms | 2.627 ms | 1.81× | +| rfft Float32 196611 dims=1 (16 thr) | 1.935 ms | 9.277 ms | 4.79× | +| rfft Float32 207360 dims=1 (16 thr) | 690.81 µs | 963.53 µs | 1.39× | +| rfft Float32 262144 dims=1 (16 thr) | 912.61 µs | 1.283 ms | 1.41× | +| rfft Float32 262148 dims=1 (16 thr) | 2.519 ms | 6.728 ms | 2.67× | +| rfft Float32 262576 dims=1 (16 thr) | 1.716 ms | 5.385 ms | 3.14× | +| rfft Float32 293201 dims=1 (16 thr) | 19.338 ms | 12.032 ms | 0.62× | +| rfft Float32 393222 dims=1 (16 thr) | 2.937 ms | 9.606 ms | 3.27× | +| rfft Float32 441000 dims=1 (16 thr) | 1.594 ms | 3.045 ms | 1.91× | +| rfft Float32 524288 dims=1 (16 thr) | 2.109 ms | 1.297 ms | 0.61× | +| rfft Float32 524294 dims=1 (16 thr) | 5.824 ms | 11.960 ms | 2.05× | +| rfft Float32 711749 dims=1 (16 thr) | 51.434 ms | 35.068 ms | 0.68× | +| rfft Float32 786441 dims=1 (16 thr) | 54.431 ms | 40.240 ms | 0.74× | +| rfft Float32 933120 dims=1 (16 thr) | 2.969 ms | 5.486 ms | 1.85× | +| rfft Float32 1000000 dims=1 (16 thr) | 3.723 ms | 5.416 ms | 1.45× | +| rfft Float32 1048576 dims=1 (16 thr) | 3.541 ms | 2.007 ms | 0.57× | +| rfft Float32 1048588 dims=1 (16 thr) | 9.372 ms | 29.906 ms | 3.19× | +| rfft Float32 1048592 dims=1 (16 thr) | 5.149 ms | 24.945 ms | 4.84× | +| rfft Float32 1572882 dims=1 (16 thr) | 11.866 ms | 41.466 ms | 3.49× | +| rfft Float32 1727797 dims=1 (16 thr) | 130.512 ms | 122.806 ms | 0.94× | +| rfft Float32 1975680 dims=1 (16 thr) | 5.803 ms | 11.134 ms | 1.92× | +| rfft Float32 2097152 dims=1 (16 thr) | 6.686 ms | 3.883 ms | 0.58× | +| rfft Float32 4167450 dims=1 (16 thr) | 20.383 ms | 41.024 ms | 2.01× | +| rfft Float32 4194304 dims=1 (16 thr) | 16.569 ms | 9.563 ms | 0.58× | +| rfft Float64 7 dims=1 (16 thr) | 25 ns | 40 ns | 1.59× | +| rfft Float64 8 dims=1 (16 thr) | 23 ns | 57 ns | 2.44× | +| rfft Float64 12 dims=1 (16 thr) | 28 ns | 152 ns | 5.46× | +| rfft Float64 16 dims=1 (16 thr) | 33 ns | 76 ns | 2.34× | +| rfft Float64 17 dims=1 (16 thr) | 139 ns | 198 ns | 1.42× | +| rfft Float64 23 dims=1 (16 thr) | 210 ns | 345 ns | 1.64× | +| rfft Float64 25 dims=1 (16 thr) | 77 ns | 165 ns | 2.14× | +| rfft Float64 29 dims=1 (16 thr) | 294 ns | 896 ns | 3.05× | +| rfft Float64 31 dims=1 (16 thr) | 328 ns | 897 ns | 2.74× | +| rfft Float64 32 dims=1 (16 thr) | 3.20 µs | 128 ns | 0.04× | +| rfft Float64 37 dims=1 (16 thr) | 434 ns | 1.12 µs | 2.59× | +| rfft Float64 41 dims=1 (16 thr) | 515 ns | 1.13 µs | 2.19× | +| rfft Float64 43 dims=1 (16 thr) | 560 ns | 1.13 µs | 2.02× | +| rfft Float64 54 dims=1 (16 thr) | 3.88 µs | 374 ns | 0.10× | +| rfft Float64 60 dims=1 (16 thr) | 5.86 µs | 777 ns | 0.13× | +| rfft Float64 61 dims=1 (16 thr) | 1.05 µs | 1.56 µs | 1.49× | +| rfft Float64 64 dims=1 (16 thr) | 5.22 µs | 252 ns | 0.05× | +| rfft Float64 71 dims=1 (16 thr) | 1.39 µs | 1.94 µs | 1.39× | +| rfft Float64 73 dims=1 (16 thr) | 1.46 µs | 1.97 µs | 1.35× | +| rfft Float64 79 dims=1 (16 thr) | 1.70 µs | 1.95 µs | 1.15× | +| rfft Float64 101 dims=1 (16 thr) | 2.72 µs | 2.97 µs | 1.09× | +| rfft Float64 112 dims=1 (16 thr) | 4.88 µs | 506 ns | 0.10× | +| rfft Float64 120 dims=1 (16 thr) | 3.80 µs | 607 ns | 0.16× | +| rfft Float64 128 dims=1 (16 thr) | 5.00 µs | 530 ns | 0.11× | +| rfft Float64 202 dims=1 (16 thr) | 41.40 µs | 3.30 µs | 0.08× | +| rfft Float64 243 dims=1 (16 thr) | 36.64 µs | 2.55 µs | 0.07× | +| rfft Float64 251 dims=1 (16 thr) | 155.64 µs | 7.47 µs | 0.05× | +| rfft Float64 256 dims=1 (16 thr) | 5.56 µs | 931 ns | 0.17× | +| rfft Float64 303 dims=1 (16 thr) | 23.72 µs | 10.98 µs | 0.46× | +| rfft Float64 360 dims=1 (16 thr) | 26.52 µs | 1.95 µs | 0.07× | +| rfft Float64 404 dims=1 (16 thr) | 71.16 µs | 8.35 µs | 0.12× | +| rfft Float64 504 dims=1 (16 thr) | 30.60 µs | 2.86 µs | 0.09× | +| rfft Float64 512 dims=1 (16 thr) | 1.47 µs | 2.08 µs | 1.42× | +| rfft Float64 593 dims=1 (16 thr) | 87.48 µs | 21.24 µs | 0.24× | +| rfft Float64 606 dims=1 (16 thr) | 70.80 µs | 12.04 µs | 0.17× | +| rfft Float64 720 dims=1 (16 thr) | 29.52 µs | 3.97 µs | 0.13× | +| rfft Float64 1000 dims=1 (16 thr) | 28.00 µs | 5.74 µs | 0.20× | +| rfft Float64 1024 dims=1 (16 thr) | 3.13 µs | 4.36 µs | 1.39× | +| rfft Float64 1080 dims=1 (16 thr) | 31.96 µs | 6.68 µs | 0.21× | +| rfft Float64 1433 dims=1 (16 thr) | 177.96 µs | 58.16 µs | 0.33× | +| rfft Float64 1616 dims=1 (16 thr) | 47.92 µs | 30.44 µs | 0.64× | +| rfft Float64 2018 dims=1 (16 thr) | 199.36 µs | 38.76 µs | 0.19× | +| rfft Float64 2048 dims=1 (16 thr) | 6.69 µs | 9.85 µs | 1.47× | +| rfft Float64 2304 dims=1 (16 thr) | 31.72 µs | 11.42 µs | 0.36× | +| rfft Float64 3027 dims=1 (16 thr) | 121.64 µs | 129.12 µs | 1.06× | +| rfft Float64 3491 dims=1 (16 thr) | 241.68 µs | 152.40 µs | 0.63× | +| rfft Float64 4036 dims=1 (16 thr) | 184.48 µs | 94.08 µs | 0.51× | +| rfft Float64 4096 dims=1 (16 thr) | 14.52 µs | 20.32 µs | 1.40× | +| rfft Float64 4860 dims=1 (16 thr) | 45.72 µs | 37.20 µs | 0.81× | +| rfft Float64 6054 dims=1 (16 thr) | 159.84 µs | 138.64 µs | 0.87× | +| rfft Float64 8192 dims=1 (16 thr) | 53.16 µs | 45.68 µs | 0.86× | +| rfft Float64 8198 dims=1 (16 thr) | 213.32 µs | 222.44 µs | 1.04× | +| rfft Float64 8443 dims=1 (16 thr) | 346.68 µs | 488.77 µs | 1.41× | +| rfft Float64 10290 dims=1 (16 thr) | 62.32 µs | 85.96 µs | 1.38× | +| rfft Float64 12297 dims=1 (16 thr) | 259.40 µs | 720.93 µs | 2.78× | +| rfft Float64 16144 dims=1 (16 thr) | 174.56 µs | 359.20 µs | 2.06× | +| rfft Float64 16384 dims=1 (16 thr) | 92.16 µs | 99.24 µs | 1.08× | +| rfft Float64 16396 dims=1 (16 thr) | 280.84 µs | 520.73 µs | 1.85× | +| rfft Float64 20507 dims=1 (16 thr) | 584.29 µs | 1.311 ms | 2.24× | +| rfft Float64 21875 dims=1 (16 thr) | 70.68 µs | 324.00 µs | 4.58× | +| rfft Float64 24594 dims=1 (16 thr) | 307.24 µs | 770.05 µs | 2.51× | +| rfft Float64 32768 dims=1 (16 thr) | 174.36 µs | 233.32 µs | 1.34× | +| rfft Float64 32822 dims=1 (16 thr) | 723.17 µs | 1.065 ms | 1.47× | +| rfft Float64 46305 dims=1 (16 thr) | 133.36 µs | 807.53 µs | 6.06× | +| rfft Float64 49233 dims=1 (16 thr) | 1.810 ms | 3.414 ms | 1.89× | +| rfft Float64 49757 dims=1 (16 thr) | 1.390 ms | 3.298 ms | 2.37× | +| rfft Float64 65536 dims=1 (16 thr) | 338.12 µs | 591.93 µs | 1.75× | +| rfft Float64 65584 dims=1 (16 thr) | 571.45 µs | 2.121 ms | 3.71× | +| rfft Float64 65644 dims=1 (16 thr) | 869.25 µs | 2.487 ms | 2.86× | +| rfft Float64 98304 dims=1 (16 thr) | 616.21 µs | 756.65 µs | 1.23× | +| rfft Float64 98466 dims=1 (16 thr) | 1.106 ms | 3.647 ms | 3.30× | +| rfft Float64 120779 dims=1 (16 thr) | 6.417 ms | 9.408 ms | 1.47× | +| rfft Float64 131072 dims=1 (16 thr) | 828.85 µs | 1.252 ms | 1.51× | +| rfft Float64 131074 dims=1 (16 thr) | 1.730 ms | 5.382 ms | 3.11× | +| rfft Float64 196611 dims=1 (16 thr) | 2.391 ms | 15.917 ms | 6.66× | +| rfft Float64 207360 dims=1 (16 thr) | 1.295 ms | 1.967 ms | 1.52× | +| rfft Float64 262144 dims=1 (16 thr) | 1.300 ms | 2.880 ms | 2.22× | +| rfft Float64 262148 dims=1 (16 thr) | 3.397 ms | 11.362 ms | 3.35× | +| rfft Float64 262576 dims=1 (16 thr) | 2.406 ms | 10.285 ms | 4.27× | +| rfft Float64 293201 dims=1 (16 thr) | 20.044 ms | 24.353 ms | 1.21× | +| rfft Float64 393222 dims=1 (16 thr) | 4.047 ms | 18.150 ms | 4.48× | +| rfft Float64 441000 dims=1 (16 thr) | 2.164 ms | 4.957 ms | 2.29× | +| rfft Float64 524288 dims=1 (16 thr) | 3.322 ms | 1.780 ms | 0.54× | +| rfft Float64 524294 dims=1 (16 thr) | 8.073 ms | 24.744 ms | 3.07× | +| rfft Float64 711749 dims=1 (16 thr) | 56.179 ms | 84.307 ms | 1.50× | +| rfft Float64 786441 dims=1 (16 thr) | 59.865 ms | 74.297 ms | 1.24× | +| rfft Float64 933120 dims=1 (16 thr) | 4.502 ms | 10.668 ms | 2.37× | +| rfft Float64 1000000 dims=1 (16 thr) | 5.087 ms | 10.646 ms | 2.09× | +| rfft Float64 1048576 dims=1 (16 thr) | 5.382 ms | 3.678 ms | 0.68× | +| rfft Float64 1048588 dims=1 (16 thr) | 12.307 ms | 51.936 ms | 4.22× | +| rfft Float64 1048592 dims=1 (16 thr) | 7.365 ms | 49.137 ms | 6.67× | +| rfft Float64 1572882 dims=1 (16 thr) | 18.314 ms | 77.658 ms | 4.24× | +| rfft Float64 1727797 dims=1 (16 thr) | 144.678 ms | 270.877 ms | 1.87× | +| rfft Float64 1975680 dims=1 (16 thr) | 8.742 ms | 23.209 ms | 2.65× | +| rfft Float64 2097152 dims=1 (16 thr) | 7.822 ms | 6.925 ms | 0.89× | +| rfft Float64 4167450 dims=1 (16 thr) | 23.643 ms | 85.604 ms | 3.62× | +| rfft Float64 4194304 dims=1 (16 thr) | 22.592 ms | 17.874 ms | 0.79× | +| fft Float32 8×8 dims=1,2 (16 thr) | 15.60 µs | 754 ns | 0.05× | +| fft Float32 16×16 dims=1,2 (16 thr) | 28.40 µs | 2.58 µs | 0.09× | +| fft Float32 32×32 dims=1,2 (16 thr) | 29.28 µs | 6.97 µs | 0.24× | +| fft Float32 64×64 dims=1,2 (16 thr) | 32.88 µs | 28.80 µs | 0.88× | +| fft Float32 128×128 dims=1,2 (16 thr) | 36.96 µs | 137.32 µs | 3.72× | +| fft Float32 256×256 dims=1,2 (16 thr) | 99.44 µs | 73.92 µs | 0.74× | +| fft Float32 512×512 dims=1,2 (16 thr) | 469.33 µs | 436.88 µs | 0.93× | +| fft Float32 1024×1024 dims=1,2 (16 thr) | 1.918 ms | 1.899 ms | 0.99× | +| fft Float32 2048×2048 dims=1,2 (16 thr) | 9.854 ms | 8.065 ms | 0.82× | +| fft Float64 8×8 dims=1,2 (16 thr) | 15.76 µs | 793 ns | 0.05× | +| fft Float64 16×16 dims=1,2 (16 thr) | 28.16 µs | 2.75 µs | 0.10× | +| fft Float64 32×32 dims=1,2 (16 thr) | 28.92 µs | 11.76 µs | 0.41× | +| fft Float64 64×64 dims=1,2 (16 thr) | 32.96 µs | 55.24 µs | 1.68× | +| fft Float64 128×128 dims=1,2 (16 thr) | 41.80 µs | 217.76 µs | 5.21× | +| fft Float64 127×257 dims=1,2 (16 thr) | 160.96 µs | 2.298 ms | 14.27× | +| fft Float64 1009×64 dims=1,2 (16 thr) | 294.96 µs | 268.96 µs | 0.91× | +| fft Float64 64×1009 dims=1,2 (16 thr) | 298.04 µs | 297.56 µs | 1.00× | +| fft Float64 256×256 dims=1,2 (16 thr) | 2.987 ms | 158.48 µs | 0.05× | +| fft Float64 512×512 dims=1,2 (16 thr) | 506.37 µs | 762.17 µs | 1.51× | +| fft Float64 720×480 dims=1,2 (16 thr) | 567.45 µs | 978.89 µs | 1.73× | +| fft Float64 1000×1000 dims=1,2 (16 thr) | 6.752 ms | 3.107 ms | 0.46× | +| fft Float64 1024×1024 dims=1,2 (16 thr) | 2.458 ms | 3.215 ms | 1.31× | +| fft Float64 2048×2048 dims=1,2 (16 thr) | 14.192 ms | 14.715 ms | 1.04× | +| rfft Float32 8×8 dims=1,2 (16 thr) | 13.32 µs | 798 ns | 0.06× | +| rfft Float32 16×16 dims=1,2 (16 thr) | 23.44 µs | 2.16 µs | 0.09× | +| rfft Float32 32×32 dims=1,2 (16 thr) | 33.32 µs | 6.10 µs | 0.18× | +| rfft Float32 64×64 dims=1,2 (16 thr) | 28.80 µs | 18.80 µs | 0.65× | +| rfft Float32 128×128 dims=1,2 (16 thr) | 44.56 µs | 69.44 µs | 1.56× | +| rfft Float32 256×256 dims=1,2 (16 thr) | 101.72 µs | 38.64 µs | 0.38× | +| rfft Float32 512×512 dims=1,2 (16 thr) | 170.44 µs | 139.00 µs | 0.82× | +| rfft Float32 1024×1024 dims=1,2 (16 thr) | 509.13 µs | 472.97 µs | 0.93× | +| rfft Float32 2048×2048 dims=1,2 (16 thr) | 2.814 ms | 1.938 ms | 0.69× | +| rfft Float64 8×8 dims=1,2 (16 thr) | 12.92 µs | 800 ns | 0.06× | +| rfft Float64 16×16 dims=1,2 (16 thr) | 22.52 µs | 2.16 µs | 0.10× | +| rfft Float64 32×32 dims=1,2 (16 thr) | 33.00 µs | 7.44 µs | 0.23× | +| rfft Float64 64×64 dims=1,2 (16 thr) | 29.04 µs | 30.44 µs | 1.05× | +| rfft Float64 128×128 dims=1,2 (16 thr) | 46.00 µs | 117.00 µs | 2.54× | +| rfft Float64 127×257 dims=1,2 (16 thr) | 1.282 ms | 1.594 ms | 1.24× | +| rfft Float64 1009×64 dims=1,2 (16 thr) | 7.528 ms | 470.25 µs | 0.06× | +| rfft Float64 64×1009 dims=1,2 (16 thr) | 259.56 µs | 172.36 µs | 0.66× | +| rfft Float64 256×256 dims=1,2 (16 thr) | 4.152 ms | 50.88 µs | 0.01× | +| rfft Float64 512×512 dims=1,2 (16 thr) | 2.877 ms | 204.16 µs | 0.07× | +| rfft Float64 720×480 dims=1,2 (16 thr) | 299.36 µs | 278.72 µs | 0.93× | +| rfft Float64 1000×1000 dims=1,2 (16 thr) | 1.243 ms | 883.41 µs | 0.71× | +| rfft Float64 1024×1024 dims=1,2 (16 thr) | 2.654 ms | 757.41 µs | 0.29× | +| rfft Float64 2048×2048 dims=1,2 (16 thr) | 4.152 ms | 3.398 ms | 0.82× | +| fft Float32 8×8×8 dims=1,2,3 (16 thr) | 39.72 µs | 9.25 µs | 0.23× | +| fft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.28 µs | 63.20 µs | 2.16× | +| fft Float32 32×32×32 dims=1,2,3 (16 thr) | 44.72 µs | 45.48 µs | 1.02× | +| fft Float32 64×64×64 dims=1,2,3 (16 thr) | 164.64 µs | 427.01 µs | 2.59× | +| fft Float32 128×128×128 dims=1,2,3 (16 thr) | 1.501 ms | 3.943 ms | 2.63× | +| fft Float64 8×8×8 dims=1,2,3 (16 thr) | 38.76 µs | 9.59 µs | 0.25× | +| fft Float64 16×16×16 dims=1,2,3 (16 thr) | 31.56 µs | 68.36 µs | 2.17× | +| fft Float64 32×32×32 dims=1,2,3 (16 thr) | 52.88 µs | 73.88 µs | 1.40× | +| fft Float64 64×64×64 dims=1,2,3 (16 thr) | 259.56 µs | 823.97 µs | 3.17× | +| fft Float64 128×128×128 dims=1,2,3 (16 thr) | 2.719 ms | 6.577 ms | 2.42× | +| rfft Float32 8×8×8 dims=1,2,3 (16 thr) | 57.20 µs | 8.43 µs | 0.15× | +| rfft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.40 µs | 47.60 µs | 1.62× | +| rfft Float32 32×32×32 dims=1,2,3 (16 thr) | 37.56 µs | 174.52 µs | 4.65× | +| rfft Float32 64×64×64 dims=1,2,3 (16 thr) | 115.28 µs | 148.16 µs | 1.29× | +| rfft Float32 128×128×128 dims=1,2,3 (16 thr) | 739.45 µs | 1.192 ms | 1.61× | +| rfft Float64 8×8×8 dims=1,2,3 (16 thr) | 51.48 µs | 8.45 µs | 0.16× | +| rfft Float64 16×16×16 dims=1,2,3 (16 thr) | 29.84 µs | 48.12 µs | 1.61× | +| rfft Float64 32×32×32 dims=1,2,3 (16 thr) | 42.44 µs | 271.32 µs | 6.39× | +| rfft Float64 64×64×64 dims=1,2,3 (16 thr) | 150.04 µs | 260.20 µs | 1.73× | +| rfft Float64 128×128×128 dims=1,2,3 (16 thr) | 1.107 ms | 1.864 ms | 1.68× | +| fft Float32 64×64 dims=1 (16 thr) | 14.40 µs | 13.28 µs | 0.92× | +| fft Float32 256×64 dims=1 (16 thr) | 20.44 µs | 54.40 µs | 2.66× | +| fft Float32 1024×64 dims=1 (16 thr) | 34.76 µs | 17.20 µs | 0.49× | +| fft Float32 4096×64 dims=1 (16 thr) | 116.96 µs | 75.28 µs | 0.64× | +| fft Float32 16384×64 dims=1 (16 thr) | 620.21 µs | 389.76 µs | 0.63× | +| fft Float32 65536×64 dims=1 (16 thr) | 3.277 ms | 2.253 ms | 0.69× | +| fft Float64 64×64 dims=1 (16 thr) | 14.64 µs | 26.00 µs | 1.78× | +| fft Float64 256×64 dims=1 (16 thr) | 21.76 µs | 106.32 µs | 4.89× | +| fft Float64 1024×64 dims=1 (16 thr) | 47.32 µs | 33.12 µs | 0.70× | +| fft Float64 4096×64 dims=1 (16 thr) | 190.80 µs | 157.16 µs | 0.82× | +| fft Float64 16384×64 dims=1 (16 thr) | 1.133 ms | 886.33 µs | 0.78× | +| fft Float64 65536×64 dims=1 (16 thr) | 6.859 ms | 5.854 ms | 0.85× | +| rfft Float32 64×64 dims=1 (16 thr) | 14.28 µs | 10.96 µs | 0.77× | +| rfft Float32 256×64 dims=1 (16 thr) | 16.96 µs | 35.56 µs | 2.10× | +| rfft Float32 1024×64 dims=1 (16 thr) | 26.16 µs | 10.96 µs | 0.42× | +| rfft Float32 4096×64 dims=1 (16 thr) | 64.80 µs | 44.12 µs | 0.68× | +| rfft Float32 16384×64 dims=1 (16 thr) | 290.84 µs | 198.40 µs | 0.68× | +| rfft Float32 65536×64 dims=1 (16 thr) | 1.552 ms | 1.089 ms | 0.70× | +| rfft Float64 64×64 dims=1 (16 thr) | 14.32 µs | 17.14 µs | 1.20× | +| rfft Float64 256×4096 dims=1 (16 thr) | 288.96 µs | 255.08 µs | 0.88× | +| rfft Float64 256×64 dims=1 (16 thr) | 17.44 µs | 61.68 µs | 3.54× | +| rfft Float64 1024×1024 dims=1 (16 thr) | 302.40 µs | 291.20 µs | 0.96× | +| rfft Float64 1024×64 dims=1 (16 thr) | 30.40 µs | 19.32 µs | 0.64× | +| rfft Float64 4096×256 dims=1 (16 thr) | 377.84 µs | 335.44 µs | 0.89× | +| rfft Float64 4096×64 dims=1 (16 thr) | 101.80 µs | 83.24 µs | 0.82× | +| rfft Float64 16384×64 dims=1 (16 thr) | 557.33 µs | 426.37 µs | 0.77× | +| rfft Float64 65536×64 dims=1 (16 thr) | 2.895 ms | 2.579 ms | 0.89× | +| fft Float32 64×64 dims=2 (16 thr) | 14.68 µs | 15.28 µs | 1.04× | +| fft Float32 64×256 dims=2 (16 thr) | 36.92 µs | 95.12 µs | 2.58× | +| fft Float32 64×1024 dims=2 (16 thr) | 115.16 µs | 64.04 µs | 0.56× | +| fft Float32 64×4096 dims=2 (16 thr) | 607.17 µs | 276.76 µs | 0.46× | +| fft Float32 64×16384 dims=2 (16 thr) | 2.301 ms | 1.074 ms | 0.47× | +| fft Float32 64×65536 dims=2 (16 thr) | 14.567 ms | 6.966 ms | 0.48× | +| fft Float64 64×64 dims=2 (16 thr) | 14.64 µs | 29.16 µs | 1.99× | +| fft Float64 64×256 dims=2 (16 thr) | 23.04 µs | 139.08 µs | 6.04× | +| fft Float64 64×1024 dims=2 (16 thr) | 78.08 µs | 50.48 µs | 0.65× | +| fft Float64 64×4096 dims=2 (16 thr) | 445.32 µs | 281.92 µs | 0.63× | +| fft Float64 64×16384 dims=2 (16 thr) | 2.219 ms | 1.467 ms | 0.66× | +| fft Float64 64×65536 dims=2 (16 thr) | 20.453 ms | 11.660 ms | 0.57× | +| rfft Float32 64×64 dims=2 (16 thr) | 14.08 µs | 13.80 µs | 0.98× | +| rfft Float32 64×256 dims=2 (16 thr) | 27.56 µs | 59.64 µs | 2.16× | +| rfft Float32 64×1024 dims=2 (16 thr) | 71.96 µs | 38.28 µs | 0.53× | +| rfft Float32 64×4096 dims=2 (16 thr) | 284.92 µs | 173.40 µs | 0.61× | +| rfft Float32 64×16384 dims=2 (16 thr) | 1.344 ms | 689.21 µs | 0.51× | +| rfft Float32 64×65536 dims=2 (16 thr) | 6.026 ms | 4.123 ms | 0.68× | +| rfft Float64 64×64 dims=2 (16 thr) | 14.24 µs | 19.68 µs | 1.38× | +| rfft Float64 64×256 dims=2 (16 thr) | 19.64 µs | 95.56 µs | 4.87× | +| rfft Float64 64×1024 dims=2 (16 thr) | 42.84 µs | 31.88 µs | 0.74× | +| rfft Float64 64×4096 dims=2 (16 thr) | 258.56 µs | 174.00 µs | 0.67× | +| rfft Float64 64×16384 dims=2 (16 thr) | 1.100 ms | 794.45 µs | 0.72× | +| rfft Float64 64×65536 dims=2 (16 thr) | 9.087 ms | 6.631 ms | 0.73× | + +### Summary (16 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `ffta`/`fftw` | | +|:--|--:| +| ComplexF32 fft 2d | 0.50× (0.05–3.72) | +| ComplexF32 fft 3d | 1.28× (0.23–2.63) | +| ComplexF32 fft awkward | 2.03× (0.06–13.65) | +| ComplexF32 fft batched_dim1 | 0.83× (0.49–2.66) | +| ComplexF32 fft batched_dim2 | 0.73× (0.46–2.58) | +| ComplexF32 fft pow2 | 0.68× (0.03–5.62) | +| ComplexF32 fft prime | 0.25× (0.01–6.58) | +| ComplexF32 fft smooth | 0.51× (0.01–8.15) | +| ComplexF64 fft 2d | 0.75× (0.05–14.27) | +| ComplexF64 fft 3d | 1.42× (0.25–3.17) | +| ComplexF64 fft awkward | 2.84× (0.09–17.07) | +| ComplexF64 fft batched_dim1 | 1.22× (0.70–4.89) | +| ComplexF64 fft batched_dim2 | 1.11× (0.57–6.04) | +| ComplexF64 fft pow2 | 0.68× (0.02–7.48) | +| ComplexF64 fft prime | 0.47× (0.01–4.00) | +| ComplexF64 fft smooth | 0.62× (0.02–8.19) | +| Float32 rfft 2d | 0.39× (0.06–1.56) | +| Float32 rfft 3d | 1.18× (0.15–4.65) | +| Float32 rfft awkward | 1.06× (0.06–4.84) | +| Float32 rfft batched_dim1 | 0.78× (0.42–2.10) | +| Float32 rfft batched_dim2 | 0.79× (0.51–2.16) | +| Float32 rfft pow2 | 0.77× (0.13–2.35) | +| Float32 rfft prime | 0.74× (0.03–1.70) | +| Float32 rfft smooth | 0.43× (0.04–5.59) | +| Float64 rfft 2d | 0.29× (0.01–2.54) | +| Float64 rfft 3d | 1.38× (0.16–6.39) | +| Float64 rfft awkward | 1.47× (0.08–6.67) | +| Float64 rfft batched_dim1 | 1.01× (0.64–3.54) | +| Float64 rfft batched_dim2 | 1.10× (0.67–4.87) | +| Float64 rfft pow2 | 0.72× (0.04–2.44) | +| Float64 rfft prime | 1.22× (0.05–3.05) | +| Float64 rfft smooth | 0.63× (0.07–6.06) | +| **all** | 0.80× (0.01–17.07) | diff --git a/benchmark/compare3/aarch64/stockham-stack/ffta_t16.json b/benchmark/compare3/aarch64/stockham-stack/ffta_t16.json new file mode 100644 index 0000000..5bf68ba --- /dev/null +++ b/benchmark/compare3/aarch64/stockham-stack/ffta_t16.json @@ -0,0 +1,10995 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T21:17:20.048", + "impl": "ffta", + "julia": "1.12.6", + "scope": { + "classes": [ + "pow2", + "smooth", + "prime", + "awkward" + ], + "kinds": [ + "fft", + "rfft" + ], + "maxlog2": 22, + "measure": true, + "only": [ + "1d", + "nd", + "batched" + ], + "sizes": [] + }, + "seconds": 0.5, + "threads": 16, + "version": "FFTA.jl 0.3.1 @ a2fd368" + }, + "results": [ + { 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threading and batched N-d pencils (aarch64, 1+16 threads) --- .../aarch64/stack-threads-nd/COMPARE3.md | 1661 +++ .../aarch64/stack-threads-nd/ffta_t1.json | 10996 +++++++++++++++ .../aarch64/stack-threads-nd/ffta_t16.json | 10996 +++++++++++++++ .../aarch64/stack-threads-nd/fftw_t1.json | 11375 +++++++++++++++ .../aarch64/stack-threads-nd/fftw_t16.json | 11395 ++++++++++++++++ 5 files changed, 46423 insertions(+) create mode 100644 benchmark/compare3/aarch64/stack-threads-nd/COMPARE3.md create mode 100644 benchmark/compare3/aarch64/stack-threads-nd/ffta_t1.json create mode 100644 benchmark/compare3/aarch64/stack-threads-nd/ffta_t16.json create mode 100644 benchmark/compare3/aarch64/stack-threads-nd/fftw_t1.json create mode 100644 benchmark/compare3/aarch64/stack-threads-nd/fftw_t16.json diff --git a/benchmark/compare3/aarch64/stack-threads-nd/COMPARE3.md b/benchmark/compare3/aarch64/stack-threads-nd/COMPARE3.md new file mode 100644 index 0000000..5fdfbdf --- /dev/null +++ b/benchmark/compare3/aarch64/stack-threads-nd/COMPARE3.md @@ -0,0 +1,1661 @@ +# FFT implementations side by side + +Rendered 2026-08-30T23:44:34.519 UTC on neoverse-n1 (aarch64), Julia 1.12.6. + +| column | implementation | +|:--|:--| +| `fftw` | FFTW.jl 1.10.0 / FFTW 3.3.11 (fftw) — `fftw` | +| `ffta` | FFTA.jl 0.3.1 @ 4f9ff88 — `/home/pgeorgakopoulos/ai-requests/issue-7/FFTA-nd2` | + +Times are minimum planned-execution times (`mul!`, or `*` where a plan has no `mul!`). `/fftw` is the time divided by the `fftw` time (lower is better); `vs ffta` is the speedup over the `ffta` column (higher is better). ✗ = threw. A checksum mismatch against `fftw` is flagged with ⚠. + + +## 1 thread + +| case | `fftw` | `ffta` | `ffta`/`fftw` | | +|:--|--:|--:|--:| +| fft Float32 7 dims=1 | 38 ns | 35 ns | 0.94× | +| fft Float32 8 dims=1 | 37 ns | 39 ns | 1.04× | +| fft Float32 12 dims=1 | 43 ns | 181 ns | 4.16× | +| fft Float32 16 dims=1 | 55 ns | 67 ns | 1.21× | +| fft Float32 17 dims=1 | 136 ns | 817 ns | 6.01× | +| fft Float32 23 dims=1 | 230 ns | 1.52 µs | 6.63× | +| fft Float32 25 dims=1 | 126 ns | 171 ns | 1.36× | +| fft Float32 29 dims=1 | 342 ns | 552 ns | 1.61× | +| fft Float32 31 dims=1 | 387 ns | 556 ns | 1.44× | +| fft Float32 32 dims=1 | 105 ns | 104 ns | 0.99× | +| fft Float32 37 dims=1 | 836 ns | 777 ns | 0.93× | +| fft Float32 41 dims=1 | 817 ns | 789 ns | 0.97× | +| fft Float32 43 dims=1 | 699 ns | 791 ns | 1.13× | +| fft Float32 54 dims=1 | 325 ns | 422 ns | 1.30× | +| fft Float32 60 dims=1 | 217 ns | 430 ns | 1.98× | +| fft Float32 61 dims=1 | 1.19 µs | 962 ns | 0.81× | +| fft Float32 64 dims=1 | 194 ns | 204 ns | 1.05× | +| fft Float32 71 dims=1 | 2.40 µs | 1.28 µs | 0.53× | +| fft Float32 73 dims=1 | 1.34 µs | 1.29 µs | 0.96× | +| fft Float32 79 dims=1 | 1.76 µs | 1.30 µs | 0.74× | +| fft Float32 101 dims=1 | 1.94 µs | 1.91 µs | 0.99× | +| fft Float32 112 dims=1 | 360 ns | 395 ns | 1.10× | +| fft Float32 120 dims=1 | 392 ns | 763 ns | 1.95× | +| fft Float32 128 dims=1 | 390 ns | 340 ns | 0.87× | +| fft Float32 202 dims=1 | 4.13 µs | 5.39 µs | 1.31× | +| fft Float32 243 dims=1 | 1.90 µs | 1.90 µs | 1.00× | +| fft Float32 251 dims=1 | 5.99 µs | 4.10 µs | 0.68× | +| fft Float32 256 dims=1 | 807 ns | 760 ns | 0.94× | +| fft Float32 303 dims=1 | 6.36 µs | 7.75 µs | 1.22× | +| fft Float32 360 dims=1 | 2.37 µs | 2.30 µs | 0.97× | +| fft Float32 404 dims=1 | 8.45 µs | 9.71 µs | 1.15× | +| fft Float32 504 dims=1 | 2.69 µs | 3.39 µs | 1.26× | +| fft Float32 512 dims=1 | 1.69 µs | 1.48 µs | 0.88× | +| fft Float32 593 dims=1 | 15.24 µs | 12.38 µs | 0.81× | +| fft Float32 606 dims=1 | 12.82 µs | 20.40 µs | 1.59× | +| fft Float32 720 dims=1 | 5.25 µs | 2.93 µs | 0.56× | +| fft Float32 1000 dims=1 | 6.69 µs | 6.87 µs | 1.03× | +| fft Float32 1024 dims=1 | 3.64 µs | 3.47 µs | 0.95× | +| fft Float32 1080 dims=1 | 8.77 µs | 7.71 µs | 0.88× | +| fft Float32 1433 dims=1 | 57.64 µs | 32.60 µs | 0.57× | +| fft Float32 1616 dims=1 | 36.12 µs | 37.36 µs | 1.03× | +| fft Float32 2018 dims=1 | 73.28 µs | 53.52 µs | 0.73× | +| fft Float32 2048 dims=1 | 7.68 µs | 7.17 µs | 0.93× | +| fft Float32 2304 dims=1 | 12.42 µs | 10.06 µs | 0.81× | +| fft Float32 3027 dims=1 | 112.08 µs | 78.04 µs | 0.70× | +| fft Float32 3491 dims=1 | 158.56 µs | 84.36 µs | 0.53× | +| fft Float32 4036 dims=1 | 149.00 µs | 97.48 µs | 0.65× | +| fft Float32 4096 dims=1 | 16.88 µs | 16.70 µs | 0.99× | +| fft Float32 4860 dims=1 | 49.84 µs | 42.72 µs | 0.86× | +| fft Float32 6054 dims=1 | 225.88 µs | 202.76 µs | 0.90× | +| fft Float32 8192 dims=1 | 48.72 µs | 35.08 µs | 0.72× | +| fft Float32 8198 dims=1 | 411.25 µs | 293.72 µs | 0.71× | +| fft Float32 8443 dims=1 | 413.05 µs | 241.28 µs | 0.58× | +| fft Float32 10290 dims=1 | 97.28 µs | 98.28 µs | 1.01× | +| fft Float32 12297 dims=1 | 624.25 µs | 429.01 µs | 0.69× | +| fft Float32 16144 dims=1 | 629.25 µs | 381.12 µs | 0.61× | +| fft Float32 16384 dims=1 | 109.16 µs | 79.28 µs | 0.73× | +| fft Float32 16396 dims=1 | 831.89 µs | 549.37 µs | 0.66× | +| fft Float32 20507 dims=1 | 1.290 ms | 667.05 µs | 0.52× | +| fft Float32 21875 dims=1 | 264.12 µs | 217.28 µs | 0.82× | +| fft Float32 24594 dims=1 | 1.260 ms | 1.059 ms | 0.84× | +| fft Float32 32768 dims=1 | 278.20 µs | 180.48 µs | 0.65× | +| fft Float32 32822 dims=1 | 2.015 ms | 1.347 ms | 0.67× | +| fft Float32 46305 dims=1 | 560.49 µs | 510.61 µs | 0.91× | +| fft Float32 49233 dims=1 | 3.073 ms | 1.930 ms | 0.63× | +| fft Float32 49757 dims=1 | 2.680 ms | 1.648 ms | 0.61× | +| fft Float32 65536 dims=1 | 563.53 µs | 387.52 µs | 0.69× | +| fft Float32 65584 dims=1 | 3.557 ms | 2.265 ms | 0.64× | +| fft Float32 65644 dims=1 | 4.107 ms | 2.503 ms | 0.61× | +| fft Float32 98304 dims=1 | 1.126 ms | 652.77 µs | 0.58× | +| fft Float32 98466 dims=1 | 6.367 ms | 4.751 ms | 0.75× | +| fft Float32 120779 dims=1 | 9.432 ms | 5.735 ms | 0.61× | +| fft Float32 131072 dims=1 | 1.322 ms | 871.21 µs | 0.66× | +| fft Float32 131074 dims=1 | 4.394 ms | 6.299 ms | 1.43× | +| fft Float32 196611 dims=1 | 6.678 ms | 8.834 ms | 1.32× | +| fft Float32 207360 dims=1 | 3.276 ms | 1.543 ms | 0.47× | +| fft Float32 262144 dims=1 | 3.482 ms | 2.407 ms | 0.69× | +| fft Float32 262148 dims=1 | 8.965 ms | 11.625 ms | 1.30× | +| fft Float32 262576 dims=1 | 18.216 ms | 10.710 ms | 0.59× | +| fft Float32 293201 dims=1 | 30.534 ms | 12.151 ms | 0.40× | +| fft Float32 393222 dims=1 | 13.552 ms | 21.466 ms | 1.58× | +| fft Float32 441000 dims=1 | 6.625 ms | 5.226 ms | 0.79× | +| fft Float32 524288 dims=1 | 11.364 ms | 5.105 ms | 0.45× | +| fft Float32 524294 dims=1 | 47.952 ms | 27.221 ms | 0.57× | +| fft Float32 711749 dims=1 | 76.629 ms | 34.609 ms | 0.45× | +| fft Float32 786441 dims=1 | 72.471 ms | 39.761 ms | 0.55× | +| fft Float32 933120 dims=1 | 18.504 ms | 8.452 ms | 0.46× | +| fft Float32 1000000 dims=1 | 24.431 ms | 8.466 ms | 0.35× | +| fft Float32 1048576 dims=1 | 24.149 ms | 11.169 ms | 0.46× | +| fft Float32 1048588 dims=1 | 97.647 ms | 51.300 ms | 0.53× | +| fft Float32 1048592 dims=1 | 37.789 ms | 52.110 ms | 1.38× | +| fft Float32 1572882 dims=1 | 150.252 ms | 95.213 ms | 0.63× | +| fft Float32 1727797 dims=1 | 174.941 ms | 120.163 ms | 0.69× | +| fft Float32 1975680 dims=1 | 40.474 ms | 21.387 ms | 0.53× | +| fft Float32 2097152 dims=1 | 78.580 ms | 27.025 ms | 0.34× | +| fft Float32 4167450 dims=1 | 126.844 ms | 89.844 ms | 0.71× | +| fft Float32 4194304 dims=1 | 164.711 ms | 60.253 ms | 0.37× | +| fft Float64 7 dims=1 | 26 ns | 40 ns | 1.55× | +| fft Float64 8 dims=1 | 25 ns | 38 ns | 1.54× | +| fft Float64 12 dims=1 | 33 ns | 180 ns | 5.39× | +| fft Float64 16 dims=1 | 41 ns | 69 ns | 1.69× | +| fft Float64 17 dims=1 | 136 ns | 500 ns | 3.68× | +| fft Float64 23 dims=1 | 230 ns | 910 ns | 3.96× | +| fft Float64 25 dims=1 | 139 ns | 172 ns | 1.24× | +| fft Float64 29 dims=1 | 343 ns | 899 ns | 2.62× | +| fft Float64 31 dims=1 | 385 ns | 908 ns | 2.36× | +| fft Float64 32 dims=1 | 80 ns | 153 ns | 1.92× | +| fft Float64 37 dims=1 | 771 ns | 1.20 µs | 1.55× | +| fft Float64 41 dims=1 | 910 ns | 1.20 µs | 1.32× | +| fft Float64 43 dims=1 | 699 ns | 1.21 µs | 1.73× | +| fft Float64 54 dims=1 | 274 ns | 505 ns | 1.85× | +| fft Float64 60 dims=1 | 311 ns | 480 ns | 1.54× | +| fft Float64 61 dims=1 | 1.39 µs | 1.58 µs | 1.14× | +| fft Float64 64 dims=1 | 310 ns | 351 ns | 1.13× | +| fft Float64 71 dims=1 | 3.06 µs | 2.05 µs | 0.67× | +| fft Float64 73 dims=1 | 1.74 µs | 2.08 µs | 1.19× | +| fft Float64 79 dims=1 | 2.50 µs | 2.04 µs | 0.82× | +| fft Float64 101 dims=1 | 2.37 µs | 3.03 µs | 1.28× | +| fft Float64 112 dims=1 | 591 ns | 621 ns | 1.05× | +| fft Float64 120 dims=1 | 634 ns | 888 ns | 1.40× | +| fft Float64 128 dims=1 | 647 ns | 591 ns | 0.91× | +| fft Float64 202 dims=1 | 4.97 µs | 7.77 µs | 1.56× | +| fft Float64 243 dims=1 | 1.94 µs | 2.68 µs | 1.38× | +| fft Float64 251 dims=1 | 6.73 µs | 7.57 µs | 1.12× | +| fft Float64 256 dims=1 | 1.32 µs | 1.42 µs | 1.08× | +| fft Float64 303 dims=1 | 7.79 µs | 11.46 µs | 1.47× | +| fft Float64 360 dims=1 | 2.83 µs | 3.15 µs | 1.11× | +| fft Float64 404 dims=1 | 10.46 µs | 14.70 µs | 1.41× | +| fft Float64 504 dims=1 | 4.30 µs | 4.61 µs | 1.07× | +| fft Float64 512 dims=1 | 2.83 µs | 2.99 µs | 1.06× | +| fft Float64 593 dims=1 | 27.48 µs | 21.76 µs | 0.79× | +| fft Float64 606 dims=1 | 15.84 µs | 27.84 µs | 1.76× | +| fft Float64 720 dims=1 | 5.64 µs | 5.31 µs | 0.94× | +| fft Float64 1000 dims=1 | 10.26 µs | 9.39 µs | 0.91× | +| fft Float64 1024 dims=1 | 6.30 µs | 6.97 µs | 1.11× | +| fft Float64 1080 dims=1 | 9.27 µs | 11.02 µs | 1.19× | +| fft Float64 1433 dims=1 | 77.40 µs | 59.28 µs | 0.77× | +| fft Float64 1616 dims=1 | 44.28 µs | 57.72 µs | 1.30× | +| fft Float64 2018 dims=1 | 109.44 µs | 89.12 µs | 0.81× | +| fft Float64 2048 dims=1 | 13.52 µs | 15.02 µs | 1.11× | +| fft Float64 2304 dims=1 | 22.48 µs | 19.30 µs | 0.86× | +| fft Float64 3027 dims=1 | 168.20 µs | 130.52 µs | 0.78× | +| fft Float64 3491 dims=1 | 222.48 µs | 153.28 µs | 0.69× | +| fft Float64 4036 dims=1 | 223.80 µs | 169.20 µs | 0.76× | +| fft Float64 4096 dims=1 | 29.80 µs | 35.04 µs | 1.18× | +| fft Float64 4860 dims=1 | 57.56 µs | 64.52 µs | 1.12× | +| fft Float64 6054 dims=1 | 340.04 µs | 313.72 µs | 0.92× | +| fft Float64 8192 dims=1 | 84.76 µs | 74.20 µs | 0.88× | +| fft Float64 8198 dims=1 | 506.65 µs | 491.89 µs | 0.97× | +| fft Float64 8443 dims=1 | 554.85 µs | 499.45 µs | 0.90× | +| fft Float64 10290 dims=1 | 149.96 µs | 149.12 µs | 0.99× | +| fft Float64 12297 dims=1 | 777.05 µs | 729.05 µs | 0.94× | +| fft Float64 16144 dims=1 | 922.45 µs | 681.41 µs | 0.74× | +| fft Float64 16384 dims=1 | 180.40 µs | 172.56 µs | 0.96× | +| fft Float64 16396 dims=1 | 1.036 ms | 954.17 µs | 0.92× | +| fft Float64 20507 dims=1 | 1.694 ms | 1.337 ms | 0.79× | +| fft Float64 21875 dims=1 | 384.44 µs | 334.20 µs | 0.87× | +| fft Float64 24594 dims=1 | 1.613 ms | 1.718 ms | 1.06× | +| fft Float64 32768 dims=1 | 444.61 µs | 405.04 µs | 0.91× | +| fft Float64 32822 dims=1 | 2.985 ms | 2.366 ms | 0.79× | +| fft Float64 46305 dims=1 | 1.031 ms | 823.09 µs | 0.80× | +| fft Float64 49233 dims=1 | 4.545 ms | 3.534 ms | 0.78× | +| fft Float64 49757 dims=1 | 4.565 ms | 3.258 ms | 0.71× | +| fft Float64 65536 dims=1 | 1.088 ms | 976.89 µs | 0.90× | +| fft Float64 65584 dims=1 | 4.401 ms | 3.942 ms | 0.90× | +| fft Float64 65644 dims=1 | 6.122 ms | 4.629 ms | 0.76× | +| fft Float64 98304 dims=1 | 1.926 ms | 1.341 ms | 0.70× | +| fft Float64 98466 dims=1 | 9.391 ms | 7.871 ms | 0.84× | +| fft Float64 120779 dims=1 | 12.568 ms | 9.227 ms | 0.73× | +| fft Float64 131072 dims=1 | 2.406 ms | 1.827 ms | 0.76× | +| fft Float64 131074 dims=1 | 6.943 ms | 11.028 ms | 1.59× | +| fft Float64 196611 dims=1 | 10.356 ms | 16.880 ms | 1.63× | +| fft Float64 207360 dims=1 | 4.519 ms | 3.036 ms | 0.67× | +| fft Float64 262144 dims=1 | 5.670 ms | 3.756 ms | 0.66× | +| fft Float64 262148 dims=1 | 13.759 ms | 21.962 ms | 1.60× | +| fft Float64 262576 dims=1 | 25.621 ms | 18.893 ms | 0.74× | +| fft Float64 293201 dims=1 | 41.017 ms | 23.067 ms | 0.56× | +| fft Float64 393222 dims=1 | 21.186 ms | 36.066 ms | 1.70× | +| fft Float64 441000 dims=1 | 10.759 ms | 8.718 ms | 0.81× | +| fft Float64 524288 dims=1 | 16.863 ms | 7.957 ms | 0.47× | +| fft Float64 524294 dims=1 | 69.443 ms | 50.082 ms | 0.72× | +| fft Float64 711749 dims=1 | 103.554 ms | 86.618 ms | 0.84× | +| fft Float64 786441 dims=1 | 104.363 ms | 72.164 ms | 0.69× | +| fft Float64 933120 dims=1 | 32.838 ms | 18.723 ms | 0.57× | +| fft Float64 1000000 dims=1 | 50.425 ms | 17.901 ms | 0.36× | +| fft Float64 1048576 dims=1 | 52.671 ms | 19.287 ms | 0.37× | +| fft Float64 1048588 dims=1 | 141.957 ms | 105.530 ms | 0.74× | +| fft Float64 1048592 dims=1 | 64.157 ms | 92.436 ms | 1.44× | +| fft Float64 1572882 dims=1 | 218.031 ms | 187.086 ms | 0.86× | +| fft Float64 1727797 dims=1 | 263.816 ms | 261.774 ms | 0.99× | +| fft Float64 1975680 dims=1 | 76.790 ms | 51.302 ms | 0.67× | +| fft Float64 2097152 dims=1 | 119.760 ms | 45.030 ms | 0.38× | +| fft Float64 4167450 dims=1 | 214.097 ms | 164.241 ms | 0.77× | +| fft Float64 4194304 dims=1 | 238.004 ms | 96.527 ms | 0.41× | +| fft Float64 8 dims=1 MEASURE | 25 ns | — | — | +| fft Float64 16 dims=1 MEASURE | 41 ns | — | — | +| fft Float64 32 dims=1 MEASURE | 80 ns | — | — | +| fft Float64 64 dims=1 MEASURE | 168 ns | — | — | +| fft Float64 128 dims=1 MEASURE | 373 ns | — | — | +| fft Float64 256 dims=1 MEASURE | 1.02 µs | — | — | +| fft Float64 512 dims=1 MEASURE | 2.36 µs | — | — | +| fft Float64 1024 dims=1 MEASURE | 5.31 µs | — | — | +| fft Float64 2048 dims=1 MEASURE | 12.16 µs | — | — | +| fft Float64 4096 dims=1 MEASURE | 27.48 µs | — | — | +| fft Float64 8192 dims=1 MEASURE | 67.60 µs | — | — | +| fft Float64 16384 dims=1 MEASURE | 161.36 µs | — | — | +| fft Float64 32768 dims=1 MEASURE | 399.25 µs | — | — | +| fft Float64 65536 dims=1 MEASURE | 832.45 µs | — | — | +| fft Float64 131072 dims=1 MEASURE | 1.863 ms | — | — | +| fft Float64 262144 dims=1 MEASURE | 4.102 ms | — | — | +| fft Float64 524288 dims=1 MEASURE | 9.334 ms | — | — | +| fft Float64 1048576 dims=1 MEASURE | 20.841 ms | — | — | +| fft Float64 2097152 dims=1 MEASURE | 48.407 ms | — | — | +| fft Float64 4194304 dims=1 MEASURE | 102.209 ms | — | — | +| rfft Float32 7 dims=1 | 24 ns | 40 ns | 1.67× | +| rfft Float32 8 dims=1 | 22 ns | 55 ns | 2.54× | +| rfft Float32 12 dims=1 | 27 ns | 155 ns | 5.72× | +| rfft Float32 16 dims=1 | 33 ns | 76 ns | 2.32× | +| rfft Float32 17 dims=1 | 134 ns | 183 ns | 1.37× | +| rfft Float32 23 dims=1 | 202 ns | 320 ns | 1.58× | +| rfft Float32 25 dims=1 | 76 ns | 164 ns | 2.15× | +| rfft Float32 29 dims=1 | 288 ns | 541 ns | 1.88× | +| rfft Float32 31 dims=1 | 319 ns | 545 ns | 1.71× | +| rfft Float32 32 dims=1 | 101 ns | 120 ns | 1.18× | +| rfft Float32 37 dims=1 | 428 ns | 760 ns | 1.78× | +| rfft Float32 41 dims=1 | 508 ns | 769 ns | 1.51× | +| rfft Float32 43 dims=1 | 553 ns | 770 ns | 1.39× | +| rfft Float32 54 dims=1 | 213 ns | 349 ns | 1.63× | +| rfft Float32 60 dims=1 | 219 ns | 745 ns | 3.39× | +| rfft Float32 61 dims=1 | 1.04 µs | 928 ns | 0.90× | +| rfft Float32 64 dims=1 | 183 ns | 181 ns | 0.99× | +| rfft Float32 71 dims=1 | 1.37 µs | 1.25 µs | 0.91× | +| rfft Float32 73 dims=1 | 1.45 µs | 1.25 µs | 0.86× | +| rfft Float32 79 dims=1 | 1.68 µs | 1.26 µs | 0.75× | +| rfft Float32 101 dims=1 | 2.69 µs | 1.85 µs | 0.69× | +| rfft Float32 112 dims=1 | 288 ns | 465 ns | 1.61× | +| rfft Float32 120 dims=1 | 287 ns | 544 ns | 1.89× | +| rfft Float32 128 dims=1 | 265 ns | 328 ns | 1.24× | +| rfft Float32 202 dims=1 | 2.12 µs | 2.08 µs | 0.98× | +| rfft Float32 243 dims=1 | 1.18 µs | 1.88 µs | 1.60× | +| rfft Float32 251 dims=1 | 5.48 µs | 3.92 µs | 0.72× | +| rfft Float32 256 dims=1 | 636 ns | 558 ns | 0.88× | +| rfft Float32 303 dims=1 | 8.39 µs | 7.65 µs | 0.91× | +| rfft Float32 360 dims=1 | 1.31 µs | 1.52 µs | 1.15× | +| rfft Float32 404 dims=1 | 4.31 µs | 5.75 µs | 1.33× | +| rfft Float32 504 dims=1 | 1.53 µs | 2.14 µs | 1.40× | +| rfft Float32 512 dims=1 | 1.14 µs | 1.18 µs | 1.04× | +| rfft Float32 593 dims=1 | 21.96 µs | 11.84 µs | 0.54× | +| rfft Float32 606 dims=1 | 6.52 µs | 8.37 µs | 1.28× | +| rfft Float32 720 dims=1 | 2.87 µs | 2.87 µs | 1.00× | +| rfft Float32 1000 dims=1 | 3.13 µs | 4.21 µs | 1.35× | +| rfft Float32 1024 dims=1 | 2.20 µs | 2.29 µs | 1.04× | +| rfft Float32 1080 dims=1 | 4.64 µs | 4.64 µs | 1.00× | +| rfft Float32 1433 dims=1 | 54.24 µs | 31.48 µs | 0.58× | +| rfft Float32 1616 dims=1 | 17.54 µs | 20.00 µs | 1.14× | +| rfft Float32 2018 dims=1 | 37.16 µs | 20.68 µs | 0.56× | +| rfft Float32 2048 dims=1 | 4.45 µs | 5.13 µs | 1.15× | +| rfft Float32 2304 dims=1 | 6.84 µs | 6.23 µs | 0.91× | +| rfft Float32 3027 dims=1 | 71.52 µs | 75.44 µs | 1.05× | +| rfft Float32 3491 dims=1 | 149.84 µs | 81.88 µs | 0.55× | +| rfft Float32 4036 dims=1 | 75.00 µs | 56.84 µs | 0.76× | +| rfft Float32 4096 dims=1 | 9.40 µs | 10.54 µs | 1.12× | +| rfft Float32 4860 dims=1 | 25.48 µs | 24.64 µs | 0.97× | +| rfft Float32 6054 dims=1 | 113.60 µs | 82.24 µs | 0.72× | +| rfft Float32 8192 dims=1 | 25.56 µs | 22.84 µs | 0.89× | +| rfft Float32 8198 dims=1 | 207.04 µs | 120.88 µs | 0.58× | +| rfft Float32 8443 dims=1 | 345.44 µs | 234.00 µs | 0.68× | +| rfft Float32 10290 dims=1 | 62.92 µs | 56.72 µs | 0.90× | +| rfft Float32 12297 dims=1 | 522.37 µs | 418.77 µs | 0.80× | +| rfft Float32 16144 dims=1 | 307.68 µs | 200.20 µs | 0.65× | +| rfft Float32 16384 dims=1 | 54.04 µs | 47.88 µs | 0.89× | +| rfft Float32 16396 dims=1 | 418.08 µs | 306.96 µs | 0.73× | +| rfft Float32 20507 dims=1 | 962.05 µs | 657.21 µs | 0.68× | +| rfft Float32 21875 dims=1 | 197.00 µs | 215.32 µs | 1.09× | +| rfft Float32 24594 dims=1 | 631.01 µs | 452.61 µs | 0.72× | +| rfft Float32 32768 dims=1 | 117.04 µs | 106.84 µs | 0.91× | +| rfft Float32 32822 dims=1 | 1.010 ms | 559.53 µs | 0.55× | +| rfft Float32 46305 dims=1 | 453.65 µs | 502.72 µs | 1.11× | +| rfft Float32 49233 dims=1 | 2.572 ms | 1.896 ms | 0.74× | +| rfft Float32 49757 dims=1 | 2.717 ms | 1.621 ms | 0.60× | +| rfft Float32 65536 dims=1 | 244.00 µs | 241.28 µs | 0.99× | +| rfft Float32 65584 dims=1 | 1.708 ms | 1.155 ms | 0.68× | +| rfft Float32 65644 dims=1 | 2.032 ms | 1.411 ms | 0.69× | +| rfft Float32 98304 dims=1 | 514.45 µs | 391.08 µs | 0.76× | +| rfft Float32 98466 dims=1 | 3.089 ms | 2.031 ms | 0.66× | +| rfft Float32 120779 dims=1 | 10.598 ms | 5.672 ms | 0.54× | +| rfft Float32 131072 dims=1 | 614.25 µs | 510.05 µs | 0.83× | +| rfft Float32 131074 dims=1 | 2.210 ms | 2.761 ms | 1.25× | +| rfft Float32 196611 dims=1 | 6.210 ms | 9.177 ms | 1.48× | +| rfft Float32 207360 dims=1 | 1.700 ms | 961.33 µs | 0.57× | +| rfft Float32 262144 dims=1 | 1.669 ms | 1.232 ms | 0.74× | +| rfft Float32 262148 dims=1 | 4.534 ms | 6.742 ms | 1.49× | +| rfft Float32 262576 dims=1 | 8.653 ms | 5.348 ms | 0.62× | +| rfft Float32 293201 dims=1 | 31.617 ms | 11.145 ms | 0.35× | +| rfft Float32 393222 dims=1 | 6.798 ms | 9.558 ms | 1.41× | +| rfft Float32 441000 dims=1 | 3.804 ms | 3.028 ms | 0.80× | +| rfft Float32 524288 dims=1 | 3.783 ms | 3.320 ms | 0.88× | +| rfft Float32 524294 dims=1 | 23.932 ms | 11.923 ms | 0.50× | +| rfft Float32 711749 dims=1 | 91.203 ms | 34.424 ms | 0.38× | +| rfft Float32 786441 dims=1 | 89.117 ms | 38.910 ms | 0.44× | +| rfft Float32 933120 dims=1 | 9.020 ms | 5.574 ms | 0.62× | +| rfft Float32 1000000 dims=1 | 8.693 ms | 5.413 ms | 0.62× | +| rfft Float32 1048576 dims=1 | 7.838 ms | 7.069 ms | 0.90× | +| rfft Float32 1048588 dims=1 | 47.864 ms | 28.524 ms | 0.60× | +| rfft Float32 1048592 dims=1 | 18.670 ms | 25.747 ms | 1.38× | +| rfft Float32 1572882 dims=1 | 73.534 ms | 42.406 ms | 0.58× | +| rfft Float32 1727797 dims=1 | 251.742 ms | 118.005 ms | 0.47× | +| rfft Float32 1975680 dims=1 | 16.948 ms | 11.433 ms | 0.67× | +| rfft Float32 2097152 dims=1 | 16.402 ms | 15.549 ms | 0.95× | +| rfft Float32 4167450 dims=1 | 83.641 ms | 41.320 ms | 0.49× | +| rfft Float32 4194304 dims=1 | 51.550 ms | 33.445 ms | 0.65× | +| rfft Float64 7 dims=1 | 24 ns | 39 ns | 1.63× | +| rfft Float64 8 dims=1 | 22 ns | 56 ns | 2.56× | +| rfft Float64 12 dims=1 | 28 ns | 152 ns | 5.53× | +| rfft Float64 16 dims=1 | 32 ns | 76 ns | 2.37× | +| rfft Float64 17 dims=1 | 137 ns | 196 ns | 1.43× | +| rfft Float64 23 dims=1 | 205 ns | 342 ns | 1.67× | +| rfft Float64 25 dims=1 | 75 ns | 164 ns | 2.18× | +| rfft Float64 29 dims=1 | 290 ns | 892 ns | 3.08× | +| rfft Float64 31 dims=1 | 323 ns | 898 ns | 2.78× | +| rfft Float64 32 dims=1 | 89 ns | 127 ns | 1.43× | +| rfft Float64 37 dims=1 | 431 ns | 1.19 µs | 2.77× | +| rfft Float64 41 dims=1 | 512 ns | 1.20 µs | 2.34× | +| rfft Float64 43 dims=1 | 556 ns | 1.21 µs | 2.17× | +| rfft Float64 54 dims=1 | 167 ns | 375 ns | 2.24× | +| rfft Float64 60 dims=1 | 171 ns | 776 ns | 4.54× | +| rfft Float64 61 dims=1 | 1.04 µs | 1.56 µs | 1.50× | +| rfft Float64 64 dims=1 | 166 ns | 251 ns | 1.51× | +| rfft Float64 71 dims=1 | 1.39 µs | 2.01 µs | 1.45× | +| rfft Float64 73 dims=1 | 1.46 µs | 2.03 µs | 1.39× | +| rfft Float64 79 dims=1 | 1.69 µs | 2.05 µs | 1.21× | +| rfft Float64 101 dims=1 | 2.71 µs | 3.02 µs | 1.11× | +| rfft Float64 112 dims=1 | 297 ns | 539 ns | 1.81× | +| rfft Float64 120 dims=1 | 334 ns | 648 ns | 1.94× | +| rfft Float64 128 dims=1 | 327 ns | 529 ns | 1.62× | +| rfft Float64 202 dims=1 | 2.60 µs | 3.37 µs | 1.30× | +| rfft Float64 243 dims=1 | 1.26 µs | 2.65 µs | 2.10× | +| rfft Float64 251 dims=1 | 5.71 µs | 7.53 µs | 1.32× | +| rfft Float64 256 dims=1 | 693 ns | 930 ns | 1.34× | +| rfft Float64 303 dims=1 | 8.40 µs | 11.36 µs | 1.35× | +| rfft Float64 360 dims=1 | 1.40 µs | 2.02 µs | 1.44× | +| rfft Float64 404 dims=1 | 5.36 µs | 8.39 µs | 1.56× | +| rfft Float64 504 dims=1 | 2.03 µs | 2.94 µs | 1.45× | +| rfft Float64 512 dims=1 | 1.46 µs | 2.09 µs | 1.43× | +| rfft Float64 593 dims=1 | 22.36 µs | 21.52 µs | 0.96× | +| rfft Float64 606 dims=1 | 8.15 µs | 12.22 µs | 1.50× | +| rfft Float64 720 dims=1 | 2.88 µs | 4.03 µs | 1.40× | +| rfft Float64 1000 dims=1 | 4.49 µs | 5.88 µs | 1.31× | +| rfft Float64 1024 dims=1 | 3.13 µs | 4.36 µs | 1.39× | +| rfft Float64 1080 dims=1 | 4.71 µs | 6.88 µs | 1.46× | +| rfft Float64 1433 dims=1 | 56.12 µs | 58.84 µs | 1.05× | +| rfft Float64 1616 dims=1 | 22.28 µs | 30.76 µs | 1.38× | +| rfft Float64 2018 dims=1 | 55.68 µs | 38.92 µs | 0.70× | +| rfft Float64 2048 dims=1 | 6.68 µs | 9.85 µs | 1.48× | +| rfft Float64 2304 dims=1 | 9.76 µs | 11.54 µs | 1.18× | +| rfft Float64 3027 dims=1 | 73.56 µs | 129.12 µs | 1.76× | +| rfft Float64 3491 dims=1 | 156.80 µs | 152.24 µs | 0.97× | +| rfft Float64 4036 dims=1 | 113.44 µs | 94.56 µs | 0.83× | +| rfft Float64 4096 dims=1 | 14.52 µs | 20.32 µs | 1.40× | +| rfft Float64 4860 dims=1 | 29.04 µs | 38.08 µs | 1.31× | +| rfft Float64 6054 dims=1 | 171.84 µs | 138.84 µs | 0.81× | +| rfft Float64 8192 dims=1 | 39.12 µs | 45.96 µs | 1.17× | +| rfft Float64 8198 dims=1 | 258.64 µs | 224.20 µs | 0.87× | +| rfft Float64 8443 dims=1 | 364.37 µs | 490.96 µs | 1.35× | +| rfft Float64 10290 dims=1 | 74.76 µs | 86.72 µs | 1.16× | +| rfft Float64 12297 dims=1 | 549.53 µs | 724.45 µs | 1.32× | +| rfft Float64 16144 dims=1 | 460.81 µs | 359.84 µs | 0.78× | +| rfft Float64 16384 dims=1 | 86.72 µs | 98.32 µs | 1.13× | +| rfft Float64 16396 dims=1 | 523.69 µs | 522.97 µs | 1.00× | +| rfft Float64 20507 dims=1 | 1.134 ms | 1.335 ms | 1.18× | +| rfft Float64 21875 dims=1 | 200.92 µs | 326.80 µs | 1.63× | +| rfft Float64 24594 dims=1 | 794.97 µs | 767.29 µs | 0.97× | +| rfft Float64 32768 dims=1 | 195.60 µs | 228.04 µs | 1.17× | +| rfft Float64 32822 dims=1 | 1.488 ms | 1.053 ms | 0.71× | +| rfft Float64 46305 dims=1 | 482.65 µs | 814.61 µs | 1.69× | +| rfft Float64 49233 dims=1 | 2.796 ms | 3.498 ms | 1.25× | +| rfft Float64 49757 dims=1 | 2.906 ms | 3.315 ms | 1.14× | +| rfft Float64 65536 dims=1 | 468.09 µs | 545.21 µs | 1.16× | +| rfft Float64 65584 dims=1 | 2.195 ms | 2.130 ms | 0.97× | +| rfft Float64 65644 dims=1 | 3.025 ms | 2.477 ms | 0.82× | +| rfft Float64 98304 dims=1 | 928.13 µs | 789.37 µs | 0.85× | +| rfft Float64 98466 dims=1 | 4.623 ms | 3.735 ms | 0.81× | +| rfft Float64 120779 dims=1 | 11.377 ms | 9.263 ms | 0.81× | +| rfft Float64 131072 dims=1 | 1.139 ms | 1.261 ms | 1.11× | +| rfft Float64 131074 dims=1 | 3.508 ms | 5.327 ms | 1.52× | +| rfft Float64 196611 dims=1 | 7.590 ms | 16.856 ms | 2.22× | +| rfft Float64 207360 dims=1 | 2.319 ms | 1.854 ms | 0.80× | +| rfft Float64 262144 dims=1 | 2.607 ms | 2.518 ms | 0.97× | +| rfft Float64 262148 dims=1 | 7.006 ms | 11.497 ms | 1.64× | +| rfft Float64 262576 dims=1 | 12.798 ms | 10.317 ms | 0.81× | +| rfft Float64 293201 dims=1 | 36.020 ms | 24.163 ms | 0.67× | +| rfft Float64 393222 dims=1 | 10.518 ms | 18.027 ms | 1.71× | +| rfft Float64 441000 dims=1 | 5.855 ms | 4.985 ms | 0.85× | +| rfft Float64 524288 dims=1 | 5.760 ms | 5.343 ms | 0.93× | +| rfft Float64 524294 dims=1 | 34.813 ms | 25.039 ms | 0.72× | +| rfft Float64 711749 dims=1 | 110.585 ms | 86.895 ms | 0.79× | +| rfft Float64 786441 dims=1 | 98.952 ms | 72.237 ms | 0.73× | +| rfft Float64 933120 dims=1 | 11.815 ms | 10.653 ms | 0.90× | +| rfft Float64 1000000 dims=1 | 21.371 ms | 11.087 ms | 0.52× | +| rfft Float64 1048576 dims=1 | 13.492 ms | 11.353 ms | 0.84× | +| rfft Float64 1048588 dims=1 | 69.802 ms | 52.481 ms | 0.75× | +| rfft Float64 1048592 dims=1 | 30.247 ms | 47.329 ms | 1.56× | +| rfft Float64 1572882 dims=1 | 107.501 ms | 80.092 ms | 0.75× | +| rfft Float64 1727797 dims=1 | 329.992 ms | 265.197 ms | 0.80× | +| rfft Float64 1975680 dims=1 | 38.541 ms | 23.596 ms | 0.61× | +| rfft Float64 2097152 dims=1 | 55.689 ms | 24.469 ms | 0.44× | +| rfft Float64 4167450 dims=1 | 112.796 ms | 88.527 ms | 0.78× | +| rfft Float64 4194304 dims=1 | 118.652 ms | 57.378 ms | 0.48× | +| fft Float32 8×8 dims=1,2 | 144 ns | 650 ns | 4.52× | +| fft Float32 16×16 dims=1,2 | 570 ns | 2.25 µs | 3.95× | +| fft Float32 32×32 dims=1,2 | 2.68 µs | 6.36 µs | 2.38× | +| fft Float32 64×64 dims=1,2 | 12.34 µs | 25.16 µs | 2.04× | +| fft Float32 128×128 dims=1,2 | 60.20 µs | 88.12 µs | 1.46× | +| fft Float32 256×256 dims=1,2 | 764.93 µs | 444.88 µs | 0.58× | +| fft Float32 512×512 dims=1,2 | 5.615 ms | 2.047 ms | 0.36× | +| fft Float32 1024×1024 dims=1,2 | 25.213 ms | 9.667 ms | 0.38× | +| fft Float32 2048×2048 dims=1,2 | 133.497 ms | 51.553 ms | 0.39× | +| fft Float64 8×8 dims=1,2 | 173 ns | 656 ns | 3.78× | +| fft Float64 16×16 dims=1,2 | 819 ns | 2.29 µs | 2.79× | +| fft Float64 32×32 dims=1,2 | 4.11 µs | 10.22 µs | 2.49× | +| fft Float64 64×64 dims=1,2 | 20.56 µs | 50.52 µs | 2.46× | +| fft Float64 128×128 dims=1,2 | 110.32 µs | 198.76 µs | 1.80× | +| fft Float64 127×257 dims=1,2 | 1.795 ms | 2.264 ms | 1.26× | +| fft Float64 1009×64 dims=1,2 | 3.673 ms | 2.816 ms | 0.77× | +| fft Float64 64×1009 dims=1,2 | 3.853 ms | 3.227 ms | 0.84× | +| fft Float64 256×256 dims=1,2 | 1.141 ms | 1.083 ms | 0.95× | +| fft Float64 512×512 dims=1,2 | 6.111 ms | 5.384 ms | 0.88× | +| fft Float64 720×480 dims=1,2 | 6.618 ms | 6.063 ms | 0.92× | +| fft Float64 1000×1000 dims=1,2 | 27.802 ms | 21.480 ms | 0.77× | +| fft Float64 1024×1024 dims=1,2 | 30.068 ms | 26.236 ms | 0.87× | +| fft Float64 2048×2048 dims=1,2 | 163.978 ms | 124.619 ms | 0.76× | +| rfft Float32 8×8 dims=1,2 | 124 ns | 805 ns | 6.52× | +| rfft Float32 16×16 dims=1,2 | 438 ns | 2.21 µs | 5.06× | +| rfft Float32 32×32 dims=1,2 | 2.05 µs | 6.45 µs | 3.15× | +| rfft Float32 64×64 dims=1,2 | 9.84 µs | 20.80 µs | 2.11× | +| rfft Float32 128×128 dims=1,2 | 46.68 µs | 75.08 µs | 1.61× | +| rfft Float32 256×256 dims=1,2 | 348.32 µs | 285.84 µs | 0.82× | +| rfft Float32 512×512 dims=1,2 | 1.444 ms | 1.261 ms | 0.87× | +| rfft Float32 1024×1024 dims=1,2 | 6.011 ms | 5.673 ms | 0.94× | +| rfft Float32 2048×2048 dims=1,2 | 34.732 ms | 31.575 ms | 0.91× | +| rfft Float64 8×8 dims=1,2 | 117 ns | 812 ns | 6.93× | +| rfft Float64 16×16 dims=1,2 | 490 ns | 2.22 µs | 4.54× | +| rfft Float64 32×32 dims=1,2 | 2.40 µs | 7.55 µs | 3.14× | +| rfft Float64 64×64 dims=1,2 | 11.76 µs | 30.44 µs | 2.59× | +| rfft Float64 128×128 dims=1,2 | 58.24 µs | 117.40 µs | 2.02× | +| rfft Float64 127×257 dims=1,2 | 1.513 ms | 1.613 ms | 1.07× | +| rfft Float64 1009×64 dims=1,2 | 1.615 ms | 2.553 ms | 1.58× | +| rfft Float64 64×1009 dims=1,2 | 1.939 ms | 1.556 ms | 0.80× | +| rfft Float64 256×256 dims=1,2 | 407.93 µs | 486.05 µs | 1.19× | +| rfft Float64 512×512 dims=1,2 | 1.914 ms | 2.202 ms | 1.15× | +| rfft Float64 720×480 dims=1,2 | 3.150 ms | 3.599 ms | 1.14× | +| rfft Float64 1000×1000 dims=1,2 | 13.055 ms | 12.414 ms | 0.95× | +| rfft Float64 1024×1024 dims=1,2 | 8.741 ms | 9.990 ms | 1.14× | +| rfft Float64 2048×2048 dims=1,2 | 54.345 ms | 52.857 ms | 0.97× | +| fft Float32 8×8×8 dims=1,2,3 | 1.55 µs | 8.51 µs | 5.50× | +| fft Float32 16×16×16 dims=1,2,3 | 13.46 µs | 58.08 µs | 4.32× | +| fft Float32 32×32×32 dims=1,2,3 | 141.64 µs | 240.40 µs | 1.70× | +| fft Float32 64×64×64 dims=1,2,3 | 1.491 ms | 2.684 ms | 1.80× | +| fft Float32 128×128×128 dims=1,2,3 | 18.449 ms | 22.118 ms | 1.20× | +| fft Float64 8×8×8 dims=1,2,3 | 1.90 µs | 8.47 µs | 4.45× | +| fft Float64 16×16×16 dims=1,2,3 | 19.96 µs | 60.36 µs | 3.02× | +| fft Float64 32×32×32 dims=1,2,3 | 241.88 µs | 609.37 µs | 2.52× | +| fft Float64 64×64×64 dims=1,2,3 | 2.488 ms | 5.922 ms | 2.38× | +| fft Float64 128×128×128 dims=1,2,3 | 38.936 ms | 60.583 ms | 1.56× | +| rfft Float32 8×8×8 dims=1,2,3 | 1.19 µs | 8.41 µs | 7.08× | +| rfft Float32 16×16×16 dims=1,2,3 | 9.23 µs | 47.56 µs | 5.15× | +| rfft Float32 32×32×32 dims=1,2,3 | 90.92 µs | 250.72 µs | 2.76× | +| rfft Float32 64×64×64 dims=1,2,3 | 953.73 µs | 1.867 ms | 1.96× | +| rfft Float32 128×128×128 dims=1,2,3 | 9.369 ms | 14.146 ms | 1.51× | +| rfft Float64 8×8×8 dims=1,2,3 | 1.20 µs | 8.37 µs | 6.99× | +| rfft Float64 16×16×16 dims=1,2,3 | 11.38 µs | 48.12 µs | 4.23× | +| rfft Float64 32×32×32 dims=1,2,3 | 116.96 µs | 357.76 µs | 3.06× | +| rfft Float64 64×64×64 dims=1,2,3 | 1.354 ms | 3.185 ms | 2.35× | +| rfft Float64 128×128×128 dims=1,2,3 | 14.791 ms | 26.783 ms | 1.81× | +| fft Float32 64×64 dims=1 | 6.23 µs | 12.64 µs | 2.03× | +| fft Float32 256×64 dims=1 | 52.20 µs | 50.16 µs | 0.96× | +| fft Float32 1024×64 dims=1 | 244.64 µs | 229.48 µs | 0.94× | +| fft Float32 4096×64 dims=1 | 1.277 ms | 1.088 ms | 0.85× | +| fft Float32 16384×64 dims=1 | 7.758 ms | 5.247 ms | 0.68× | +| fft Float32 65536×64 dims=1 | 44.555 ms | 24.743 ms | 0.56× | +| fft Float64 64×64 dims=1 | 10.32 µs | 22.36 µs | 2.17× | +| fft Float64 256×64 dims=1 | 87.04 µs | 92.36 µs | 1.06× | +| fft Float64 1024×64 dims=1 | 434.17 µs | 499.45 µs | 1.15× | +| fft Float64 4096×64 dims=1 | 2.162 ms | 2.582 ms | 1.19× | +| fft Float64 16384×64 dims=1 | 14.861 ms | 14.342 ms | 0.97× | +| fft Float64 65536×64 dims=1 | 88.463 ms | 81.644 ms | 0.92× | +| rfft Float32 64×64 dims=1 | 6.61 µs | 12.22 µs | 1.85× | +| rfft Float32 256×64 dims=1 | 40.84 µs | 37.36 µs | 0.91× | +| rfft Float32 1024×64 dims=1 | 143.92 µs | 149.08 µs | 1.04× | +| rfft Float32 4096×64 dims=1 | 688.89 µs | 692.53 µs | 1.01× | +| rfft Float32 16384×64 dims=1 | 3.726 ms | 3.141 ms | 0.84× | +| rfft Float32 65536×64 dims=1 | 19.029 ms | 16.414 ms | 0.86× | +| rfft Float64 64×64 dims=1 | 6.68 µs | 16.92 µs | 2.53× | +| rfft Float64 256×4096 dims=1 | 3.113 ms | 4.192 ms | 1.35× | +| rfft Float64 256×64 dims=1 | 44.56 µs | 61.56 µs | 1.38× | +| rfft Float64 1024×1024 dims=1 | 3.671 ms | 4.833 ms | 1.32× | +| rfft Float64 1024×64 dims=1 | 213.84 µs | 289.76 µs | 1.36× | +| rfft Float64 4096×256 dims=1 | 4.244 ms | 5.415 ms | 1.28× | +| rfft Float64 4096×64 dims=1 | 1.040 ms | 1.344 ms | 1.29× | +| rfft Float64 16384×64 dims=1 | 6.139 ms | 6.667 ms | 1.09× | +| rfft Float64 65536×64 dims=1 | 37.997 ms | 37.616 ms | 0.99× | +| fft Float32 64×64 dims=2 | 6.13 µs | 12.32 µs | 2.01× | +| fft Float32 64×256 dims=2 | 79.52 µs | 55.84 µs | 0.70× | +| fft Float32 64×1024 dims=2 | 433.65 µs | 315.24 µs | 0.73× | +| fft Float32 64×4096 dims=2 | 4.699 ms | 1.479 ms | 0.31× | +| fft Float32 64×16384 dims=2 | 24.311 ms | 8.036 ms | 0.33× | +| fft Float32 64×65536 dims=2 | 172.367 ms | 42.526 ms | 0.25× | +| fft Float64 64×64 dims=2 | 10.86 µs | 29.16 µs | 2.69× | +| fft Float64 64×256 dims=2 | 108.96 µs | 138.76 µs | 1.27× | +| fft Float64 64×1024 dims=2 | 883.53 µs | 812.29 µs | 0.92× | +| fft Float64 64×4096 dims=2 | 5.347 ms | 4.328 ms | 0.81× | +| fft Float64 64×16384 dims=2 | 34.143 ms | 23.753 ms | 0.70× | +| fft Float64 64×65536 dims=2 | 247.287 ms | 134.191 ms | 0.54× | +| rfft Float32 64×64 dims=2 | 6.60 µs | 14.84 µs | 2.25× | +| rfft Float32 64×256 dims=2 | 57.92 µs | 60.72 µs | 1.05× | +| rfft Float32 64×1024 dims=2 | 289.24 µs | 290.48 µs | 1.00× | +| rfft Float32 64×4096 dims=2 | 1.781 ms | 1.720 ms | 0.97× | +| rfft Float32 64×16384 dims=2 | 11.659 ms | 8.557 ms | 0.73× | +| rfft Float32 64×65536 dims=2 | 68.581 ms | 45.141 ms | 0.66× | +| rfft Float64 64×64 dims=2 | 6.61 µs | 19.84 µs | 3.00× | +| rfft Float64 64×256 dims=2 | 71.64 µs | 95.72 µs | 1.34× | +| rfft Float64 64×1024 dims=2 | 347.88 µs | 448.05 µs | 1.29× | +| rfft Float64 64×4096 dims=2 | 2.724 ms | 2.646 ms | 0.97× | +| rfft Float64 64×16384 dims=2 | 14.144 ms | 12.813 ms | 0.91× | +| rfft Float64 64×65536 dims=2 | 111.711 ms | 79.547 ms | 0.71× | + +### Summary (1 thread) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `ffta`/`fftw` | | +|:--|--:| +| ComplexF32 fft 2d | 1.17× (0.36–4.52) | +| ComplexF32 fft 3d | 2.44× (1.20–5.50) | +| ComplexF32 fft awkward | 0.84× (0.53–1.59) | +| ComplexF32 fft batched_dim1 | 0.91× (0.56–2.03) | +| ComplexF32 fft batched_dim2 | 0.55× (0.25–2.01) | +| ComplexF32 fft pow2 | 0.74× (0.34–1.21) | +| ComplexF32 fft prime | 0.89× (0.40–6.63) | +| ComplexF32 fft smooth | 0.92× (0.35–4.16) | +| ComplexF64 fft 2d | 1.29× (0.76–3.78) | +| ComplexF64 fft 3d | 2.63× (1.56–4.45) | +| ComplexF64 fft awkward | 1.02× (0.69–1.76) | +| ComplexF64 fft batched_dim1 | 1.19× (0.92–2.17) | +| ComplexF64 fft batched_dim2 | 0.99× (0.54–2.69) | +| ComplexF64 fft pow2 | 0.88× (0.37–1.92) | +| ComplexF64 fft prime | 1.16× (0.56–3.96) | +| ComplexF64 fft smooth | 1.01× (0.36–5.39) | +| Float32 rfft 2d | 1.82× (0.82–6.52) | +| Float32 rfft 3d | 3.12× (1.51–7.08) | +| Float32 rfft awkward | 0.82× (0.44–1.49) | +| Float32 rfft batched_dim1 | 1.04× (0.84–1.85) | +| Float32 rfft batched_dim2 | 1.02× (0.66–2.25) | +| Float32 rfft pow2 | 1.04× (0.65–2.54) | +| Float32 rfft prime | 0.85× (0.35–1.88) | +| Float32 rfft smooth | 1.15× (0.49–5.72) | +| Float64 rfft 2d | 1.65× (0.80–6.93) | +| Float64 rfft 3d | 3.29× (1.81–6.99) | +| Float64 rfft awkward | 1.07× (0.70–2.22) | +| Float64 rfft batched_dim1 | 1.35× (0.99–2.53) | +| Float64 rfft batched_dim2 | 1.22× (0.71–3.00) | +| Float64 rfft pow2 | 1.20× (0.44–2.56) | +| Float64 rfft prime | 1.36× (0.67–3.08) | +| Float64 rfft smooth | 1.40× (0.52–5.53) | +| **all** | 1.08× (0.25–7.08) | + +## 16 threads + +| case | `fftw` | `ffta` | `ffta`/`fftw` | | +|:--|--:|--:|--:| +| fft Float32 7 dims=1 (16 thr) | 39 ns | 36 ns | 0.91× | +| fft Float32 8 dims=1 (16 thr) | 39 ns | 39 ns | 1.00× | +| fft Float32 12 dims=1 (16 thr) | 47 ns | 182 ns | 3.90× | +| fft Float32 16 dims=1 (16 thr) | 55 ns | 69 ns | 1.25× | +| fft Float32 17 dims=1 (16 thr) | 138 ns | 817 ns | 5.92× | +| fft Float32 23 dims=1 (16 thr) | 231 ns | 1.52 µs | 6.58× | +| fft Float32 25 dims=1 (16 thr) | 121 ns | 172 ns | 1.42× | +| fft Float32 29 dims=1 (16 thr) | 345 ns | 555 ns | 1.61× | +| fft Float32 31 dims=1 (16 thr) | 572 ns | 558 ns | 0.97× | +| fft Float32 32 dims=1 (16 thr) | 106 ns | 104 ns | 0.98× | +| fft Float32 37 dims=1 (16 thr) | 68.84 µs | 777 ns | 0.01× | +| fft Float32 41 dims=1 (16 thr) | 32.20 µs | 785 ns | 0.02× | +| fft Float32 43 dims=1 (16 thr) | 128.00 µs | 802 ns | 0.01× | +| fft Float32 54 dims=1 (16 thr) | 28.96 µs | 421 ns | 0.01× | +| fft Float32 60 dims=1 (16 thr) | 13.08 µs | 432 ns | 0.03× | +| fft Float32 61 dims=1 (16 thr) | 33.20 µs | 958 ns | 0.03× | +| fft Float32 64 dims=1 (16 thr) | 213 ns | 205 ns | 0.96× | +| fft Float32 71 dims=1 (16 thr) | 146.48 µs | 1.28 µs | 0.01× | +| fft Float32 73 dims=1 (16 thr) | 74.80 µs | 1.29 µs | 0.02× | +| fft Float32 79 dims=1 (16 thr) | 90.56 µs | 1.30 µs | 0.01× | +| fft Float32 101 dims=1 (16 thr) | 34.04 µs | 1.89 µs | 0.06× | +| fft Float32 112 dims=1 (16 thr) | 33.76 µs | 393 ns | 0.01× | +| fft Float32 120 dims=1 (16 thr) | 34.68 µs | 765 ns | 0.02× | +| fft Float32 128 dims=1 (16 thr) | 443 ns | 339 ns | 0.77× | +| fft Float32 202 dims=1 (16 thr) | 84.16 µs | 5.37 µs | 0.06× | +| fft Float32 243 dims=1 (16 thr) | 37.92 µs | 1.89 µs | 0.05× | +| fft Float32 251 dims=1 (16 thr) | 100.60 µs | 4.12 µs | 0.04× | +| fft Float32 256 dims=1 (16 thr) | 22.00 µs | 762 ns | 0.03× | +| fft Float32 303 dims=1 (16 thr) | 81.08 µs | 7.73 µs | 0.10× | +| fft Float32 360 dims=1 (16 thr) | 47.00 µs | 2.31 µs | 0.05× | +| fft Float32 404 dims=1 (16 thr) | 63.28 µs | 9.68 µs | 0.15× | +| fft Float32 504 dims=1 (16 thr) | 45.28 µs | 3.41 µs | 0.08× | +| fft Float32 512 dims=1 (16 thr) | 27.56 µs | 1.50 µs | 0.05× | +| fft Float32 593 dims=1 (16 thr) | 146.64 µs | 12.32 µs | 0.08× | +| fft Float32 606 dims=1 (16 thr) | 56.00 µs | 20.16 µs | 0.36× | +| fft Float32 720 dims=1 (16 thr) | 37.48 µs | 2.89 µs | 0.08× | +| fft Float32 1000 dims=1 (16 thr) | 32.16 µs | 6.89 µs | 0.21× | +| fft Float32 1024 dims=1 (16 thr) | 28.52 µs | 3.42 µs | 0.12× | +| fft Float32 1080 dims=1 (16 thr) | 34.04 µs | 7.72 µs | 0.23× | +| fft Float32 1433 dims=1 (16 thr) | 166.00 µs | 32.64 µs | 0.20× | +| fft Float32 1616 dims=1 (16 thr) | 41.60 µs | 37.32 µs | 0.90× | +| fft Float32 2018 dims=1 (16 thr) | 179.92 µs | 53.76 µs | 0.30× | +| fft Float32 2048 dims=1 (16 thr) | 28.80 µs | 7.28 µs | 0.25× | +| fft Float32 2304 dims=1 (16 thr) | 40.80 µs | 10.12 µs | 0.25× | +| fft Float32 3027 dims=1 (16 thr) | 145.12 µs | 78.12 µs | 0.54× | +| fft Float32 3491 dims=1 (16 thr) | 195.88 µs | 84.08 µs | 0.43× | +| fft Float32 4036 dims=1 (16 thr) | 105.12 µs | 97.72 µs | 0.93× | +| fft Float32 4096 dims=1 (16 thr) | 30.32 µs | 16.68 µs | 0.55× | +| fft Float32 4860 dims=1 (16 thr) | 45.88 µs | 42.72 µs | 0.93× | +| fft Float32 6054 dims=1 (16 thr) | 108.32 µs | 203.16 µs | 1.88× | +| fft Float32 8192 dims=1 (16 thr) | 35.76 µs | 35.12 µs | 0.98× | +| fft Float32 8198 dims=1 (16 thr) | 226.72 µs | 295.24 µs | 1.30× | +| fft Float32 8443 dims=1 (16 thr) | 245.64 µs | 242.96 µs | 0.99× | +| fft Float32 10290 dims=1 (16 thr) | 49.48 µs | 98.76 µs | 2.00× | +| fft Float32 12297 dims=1 (16 thr) | 223.80 µs | 430.69 µs | 1.92× | +| fft Float32 16144 dims=1 (16 thr) | 76.04 µs | 382.96 µs | 5.04× | +| fft Float32 16384 dims=1 (16 thr) | 39.08 µs | 83.00 µs | 2.12× | +| fft Float32 16396 dims=1 (16 thr) | 194.04 µs | 548.25 µs | 2.83× | +| fft Float32 20507 dims=1 (16 thr) | 348.28 µs | 677.61 µs | 1.95× | +| fft Float32 21875 dims=1 (16 thr) | 69.36 µs | 218.68 µs | 3.15× | +| fft Float32 24594 dims=1 (16 thr) | 242.08 µs | 1.061 ms | 4.38× | +| fft Float32 32768 dims=1 (16 thr) | 49.76 µs | 179.08 µs | 3.60× | +| fft Float32 32822 dims=1 (16 thr) | 505.97 µs | 1.324 ms | 2.62× | +| fft Float32 46305 dims=1 (16 thr) | 139.20 µs | 509.25 µs | 3.66× | +| fft Float32 49233 dims=1 (16 thr) | 579.33 µs | 1.944 ms | 3.35× | +| fft Float32 49757 dims=1 (16 thr) | 991.93 µs | 1.636 ms | 1.65× | +| fft Float32 65536 dims=1 (16 thr) | 78.80 µs | 410.96 µs | 5.22× | +| fft Float32 65584 dims=1 (16 thr) | 337.00 µs | 2.286 ms | 6.78× | +| fft Float32 65644 dims=1 (16 thr) | 639.65 µs | 2.501 ms | 3.91× | +| fft Float32 98304 dims=1 (16 thr) | 131.64 µs | 650.77 µs | 4.94× | +| fft Float32 98466 dims=1 (16 thr) | 843.01 µs | 4.787 ms | 5.68× | +| fft Float32 120779 dims=1 (16 thr) | 2.499 ms | 5.885 ms | 2.35× | +| fft Float32 131072 dims=1 (16 thr) | 151.72 µs | 154.16 µs | 1.02× | +| fft Float32 131074 dims=1 (16 thr) | 1.900 ms | 3.257 ms | 1.71× | +| fft Float32 196611 dims=1 (16 thr) | 2.014 ms | 4.917 ms | 2.44× | +| fft Float32 207360 dims=1 (16 thr) | 470.29 µs | 236.24 µs | 0.50× | +| fft Float32 262144 dims=1 (16 thr) | 335.56 µs | 521.61 µs | 1.55× | +| fft Float32 262148 dims=1 (16 thr) | 2.046 ms | 6.268 ms | 3.06× | +| fft Float32 262576 dims=1 (16 thr) | 1.306 ms | 10.846 ms | 8.30× | +| fft Float32 293201 dims=1 (16 thr) | 9.679 ms | 3.611 ms | 0.37× | +| fft Float32 393222 dims=1 (16 thr) | 2.309 ms | 14.351 ms | 6.22× | +| fft Float32 441000 dims=1 (16 thr) | 687.41 µs | 508.53 µs | 0.74× | +| fft Float32 524288 dims=1 (16 thr) | 1.027 ms | 560.61 µs | 0.55× | +| fft Float32 524294 dims=1 (16 thr) | 7.465 ms | 12.081 ms | 1.62× | +| fft Float32 711749 dims=1 (16 thr) | 14.723 ms | 9.122 ms | 0.62× | +| fft Float32 786441 dims=1 (16 thr) | 8.949 ms | 18.386 ms | 2.05× | +| fft Float32 933120 dims=1 (16 thr) | 2.122 ms | 959.97 µs | 0.45× | +| fft Float32 1000000 dims=1 (16 thr) | 2.078 ms | 806.97 µs | 0.39× | +| fft Float32 1048576 dims=1 (16 thr) | 1.852 ms | 1.242 ms | 0.67× | +| fft Float32 1048588 dims=1 (16 thr) | 9.354 ms | 23.364 ms | 2.50× | +| fft Float32 1048592 dims=1 (16 thr) | 3.759 ms | 31.228 ms | 8.31× | +| fft Float32 1572882 dims=1 (16 thr) | 14.408 ms | 53.218 ms | 3.69× | +| fft Float32 1727797 dims=1 (16 thr) | 35.191 ms | 26.245 ms | 0.75× | +| fft Float32 1975680 dims=1 (16 thr) | 4.527 ms | 1.833 ms | 0.40× | +| fft Float32 2097152 dims=1 (16 thr) | 4.818 ms | 2.366 ms | 0.49× | +| fft Float32 4167450 dims=1 (16 thr) | 10.806 ms | 8.247 ms | 0.76× | +| fft Float32 4194304 dims=1 (16 thr) | 13.475 ms | 5.071 ms | 0.38× | +| fft Float64 7 dims=1 (16 thr) | 28 ns | 40 ns | 1.43× | +| fft Float64 8 dims=1 (16 thr) | 26 ns | 39 ns | 1.50× | +| fft Float64 12 dims=1 (16 thr) | 34 ns | 182 ns | 5.35× | +| fft Float64 16 dims=1 (16 thr) | 42 ns | 69 ns | 1.66× | +| fft Float64 17 dims=1 (16 thr) | 139 ns | 501 ns | 3.61× | +| fft Float64 23 dims=1 (16 thr) | 231 ns | 912 ns | 3.95× | +| fft Float64 25 dims=1 (16 thr) | 10.28 µs | 172 ns | 0.02× | +| fft Float64 29 dims=1 (16 thr) | 345 ns | 902 ns | 2.62× | +| fft Float64 31 dims=1 (16 thr) | 388 ns | 906 ns | 2.34× | +| fft Float64 32 dims=1 (16 thr) | 81 ns | 154 ns | 1.89× | +| fft Float64 37 dims=1 (16 thr) | 25.20 µs | 1.20 µs | 0.05× | +| fft Float64 41 dims=1 (16 thr) | 29.48 µs | 1.21 µs | 0.04× | +| fft Float64 43 dims=1 (16 thr) | 702 ns | 1.21 µs | 1.72× | +| fft Float64 54 dims=1 (16 thr) | 15.64 µs | 505 ns | 0.03× | +| fft Float64 60 dims=1 (16 thr) | 16.96 µs | 479 ns | 0.03× | +| fft Float64 61 dims=1 (16 thr) | 37.20 µs | 1.58 µs | 0.04× | +| fft Float64 64 dims=1 (16 thr) | 15.68 µs | 350 ns | 0.02× | +| fft Float64 71 dims=1 (16 thr) | 133.64 µs | 2.08 µs | 0.02× | +| fft Float64 73 dims=1 (16 thr) | 35.72 µs | 2.04 µs | 0.06× | +| fft Float64 79 dims=1 (16 thr) | 143.40 µs | 2.04 µs | 0.01× | +| fft Float64 101 dims=1 (16 thr) | 41.04 µs | 3.07 µs | 0.07× | +| fft Float64 112 dims=1 (16 thr) | 20.88 µs | 623 ns | 0.03× | +| fft Float64 120 dims=1 (16 thr) | 20.84 µs | 890 ns | 0.04× | +| fft Float64 128 dims=1 (16 thr) | 22.48 µs | 592 ns | 0.03× | +| fft Float64 202 dims=1 (16 thr) | 83.28 µs | 7.84 µs | 0.09× | +| fft Float64 243 dims=1 (16 thr) | 36.92 µs | 2.68 µs | 0.07× | +| fft Float64 251 dims=1 (16 thr) | 92.56 µs | 7.56 µs | 0.08× | +| fft Float64 256 dims=1 (16 thr) | 28.72 µs | 1.42 µs | 0.05× | +| fft Float64 303 dims=1 (16 thr) | 84.48 µs | 11.44 µs | 0.14× | +| fft Float64 360 dims=1 (16 thr) | 37.80 µs | 3.08 µs | 0.08× | +| fft Float64 404 dims=1 (16 thr) | 67.80 µs | 14.70 µs | 0.22× | +| fft Float64 504 dims=1 (16 thr) | 39.48 µs | 4.62 µs | 0.12× | +| fft Float64 512 dims=1 (16 thr) | 28.56 µs | 2.98 µs | 0.10× | +| fft Float64 593 dims=1 (16 thr) | 185.28 µs | 21.68 µs | 0.12× | +| fft Float64 606 dims=1 (16 thr) | 58.80 µs | 27.72 µs | 0.47× | +| fft Float64 720 dims=1 (16 thr) | 32.36 µs | 5.33 µs | 0.16× | +| fft Float64 1000 dims=1 (16 thr) | 40.20 µs | 9.29 µs | 0.23× | +| fft Float64 1024 dims=1 (16 thr) | 29.08 µs | 6.96 µs | 0.24× | +| fft Float64 1080 dims=1 (16 thr) | 32.64 µs | 11.02 µs | 0.34× | +| fft Float64 1433 dims=1 (16 thr) | 173.68 µs | 59.36 µs | 0.34× | +| fft Float64 1616 dims=1 (16 thr) | 31.00 µs | 57.92 µs | 1.87× | +| fft Float64 2018 dims=1 (16 thr) | 167.20 µs | 88.84 µs | 0.53× | +| fft Float64 2048 dims=1 (16 thr) | 29.76 µs | 15.00 µs | 0.50× | +| fft Float64 2304 dims=1 (16 thr) | 33.68 µs | 19.18 µs | 0.57× | +| fft Float64 3027 dims=1 (16 thr) | 152.16 µs | 131.04 µs | 0.86× | +| fft Float64 3491 dims=1 (16 thr) | 220.04 µs | 153.72 µs | 0.70× | +| fft Float64 4036 dims=1 (16 thr) | 114.04 µs | 169.08 µs | 1.48× | +| fft Float64 4096 dims=1 (16 thr) | 34.04 µs | 35.12 µs | 1.03× | +| fft Float64 4860 dims=1 (16 thr) | 39.76 µs | 64.36 µs | 1.62× | +| fft Float64 6054 dims=1 (16 thr) | 123.12 µs | 312.88 µs | 2.54× | +| fft Float64 8192 dims=1 (16 thr) | 37.96 µs | 80.48 µs | 2.12× | +| fft Float64 8198 dims=1 (16 thr) | 249.20 µs | 487.69 µs | 1.96× | +| fft Float64 8443 dims=1 (16 thr) | 296.48 µs | 502.28 µs | 1.69× | +| fft Float64 10290 dims=1 (16 thr) | 59.44 µs | 147.68 µs | 2.48× | +| fft Float64 12297 dims=1 (16 thr) | 269.40 µs | 727.57 µs | 2.70× | +| fft Float64 16144 dims=1 (16 thr) | 98.76 µs | 681.25 µs | 6.90× | +| fft Float64 16384 dims=1 (16 thr) | 47.52 µs | 177.56 µs | 3.74× | +| fft Float64 16396 dims=1 (16 thr) | 236.72 µs | 959.25 µs | 4.05× | +| fft Float64 20507 dims=1 (16 thr) | 614.81 µs | 1.349 ms | 2.19× | +| fft Float64 21875 dims=1 (16 thr) | 74.56 µs | 335.52 µs | 4.50× | +| fft Float64 24594 dims=1 (16 thr) | 299.28 µs | 1.731 ms | 5.78× | +| fft Float64 32768 dims=1 (16 thr) | 68.04 µs | 407.40 µs | 5.99× | +| fft Float64 32822 dims=1 (16 thr) | 650.53 µs | 2.364 ms | 3.63× | +| fft Float64 46305 dims=1 (16 thr) | 165.20 µs | 824.85 µs | 4.99× | +| fft Float64 49233 dims=1 (16 thr) | 821.77 µs | 3.605 ms | 4.39× | +| fft Float64 49757 dims=1 (16 thr) | 1.525 ms | 3.354 ms | 2.20× | +| fft Float64 65536 dims=1 (16 thr) | 141.92 µs | 977.89 µs | 6.89× | +| fft Float64 65584 dims=1 (16 thr) | 352.76 µs | 4.016 ms | 11.38× | +| fft Float64 65644 dims=1 (16 thr) | 906.93 µs | 4.680 ms | 5.16× | +| fft Float64 98304 dims=1 (16 thr) | 220.80 µs | 1.425 ms | 6.46× | +| fft Float64 98466 dims=1 (16 thr) | 1.182 ms | 7.934 ms | 6.71× | +| fft Float64 120779 dims=1 (16 thr) | 3.331 ms | 9.543 ms | 2.86× | +| fft Float64 131072 dims=1 (16 thr) | 267.08 µs | 264.12 µs | 0.99× | +| fft Float64 131074 dims=1 (16 thr) | 2.202 ms | 4.912 ms | 2.23× | +| fft Float64 196611 dims=1 (16 thr) | 2.454 ms | 7.480 ms | 3.05× | +| fft Float64 207360 dims=1 (16 thr) | 673.37 µs | 410.81 µs | 0.61× | +| fft Float64 262144 dims=1 (16 thr) | 477.41 µs | 450.93 µs | 0.94× | +| fft Float64 262148 dims=1 (16 thr) | 2.658 ms | 9.701 ms | 3.65× | +| fft Float64 262576 dims=1 (16 thr) | 1.976 ms | 19.223 ms | 9.73× | +| fft Float64 293201 dims=1 (16 thr) | 13.075 ms | 6.195 ms | 0.47× | +| fft Float64 393222 dims=1 (16 thr) | 3.018 ms | 20.031 ms | 6.64× | +| fft Float64 441000 dims=1 (16 thr) | 1.119 ms | 792.69 µs | 0.71× | +| fft Float64 524288 dims=1 (16 thr) | 1.292 ms | 964.41 µs | 0.75× | +| fft Float64 524294 dims=1 (16 thr) | 9.388 ms | 18.454 ms | 1.97× | +| fft Float64 711749 dims=1 (16 thr) | 21.364 ms | 18.100 ms | 0.85× | +| fft Float64 786441 dims=1 (16 thr) | 13.710 ms | 27.712 ms | 2.02× | +| fft Float64 933120 dims=1 (16 thr) | 3.641 ms | 1.941 ms | 0.53× | +| fft Float64 1000000 dims=1 (16 thr) | 2.683 ms | 1.709 ms | 0.64× | +| fft Float64 1048576 dims=1 (16 thr) | 3.035 ms | 1.925 ms | 0.63× | +| fft Float64 1048588 dims=1 (16 thr) | 15.898 ms | 37.492 ms | 2.36× | +| fft Float64 1048592 dims=1 (16 thr) | 5.266 ms | 45.425 ms | 8.63× | +| fft Float64 1572882 dims=1 (16 thr) | 25.599 ms | 85.619 ms | 3.34× | +| fft Float64 1727797 dims=1 (16 thr) | 74.126 ms | 49.721 ms | 0.67× | +| fft Float64 1975680 dims=1 (16 thr) | 9.586 ms | 5.152 ms | 0.54× | +| fft Float64 2097152 dims=1 (16 thr) | 7.987 ms | 4.547 ms | 0.57× | +| fft Float64 4167450 dims=1 (16 thr) | 19.462 ms | 17.234 ms | 0.89× | +| fft Float64 4194304 dims=1 (16 thr) | 18.247 ms | 10.121 ms | 0.55× | +| fft Float64 8 dims=1 (16 thr) MEASURE | 26 ns | — | — | +| fft Float64 16 dims=1 (16 thr) MEASURE | 41 ns | — | — | +| fft Float64 32 dims=1 (16 thr) MEASURE | 82 ns | — | — | +| fft Float64 64 dims=1 (16 thr) MEASURE | 169 ns | — | — | +| fft Float64 128 dims=1 (16 thr) MEASURE | 375 ns | — | — | +| fft Float64 256 dims=1 (16 thr) MEASURE | 19.68 µs | — | — | +| fft Float64 512 dims=1 (16 thr) MEASURE | 20.72 µs | — | — | +| fft Float64 1024 dims=1 (16 thr) MEASURE | 23.84 µs | — | — | +| fft Float64 2048 dims=1 (16 thr) MEASURE | 29.96 µs | — | — | +| fft Float64 4096 dims=1 (16 thr) MEASURE | 33.72 µs | — | — | +| fft Float64 8192 dims=1 (16 thr) MEASURE | 36.68 µs | — | — | +| fft Float64 16384 dims=1 (16 thr) MEASURE | 46.96 µs | — | — | +| fft Float64 32768 dims=1 (16 thr) MEASURE | 65.48 µs | — | — | +| fft Float64 65536 dims=1 (16 thr) MEASURE | 113.16 µs | — | — | +| fft Float64 131072 dims=1 (16 thr) MEASURE | 198.32 µs | — | — | +| fft Float64 262144 dims=1 (16 thr) MEASURE | 392.00 µs | — | — | +| fft Float64 524288 dims=1 (16 thr) MEASURE | 912.53 µs | — | — | +| fft Float64 1048576 dims=1 (16 thr) MEASURE | 1.822 ms | — | — | +| fft Float64 2097152 dims=1 (16 thr) MEASURE | 4.515 ms | — | — | +| fft Float64 4194304 dims=1 (16 thr) MEASURE | 8.503 ms | — | — | +| rfft Float32 7 dims=1 (16 thr) | 25 ns | 40 ns | 1.60× | +| rfft Float32 8 dims=1 (16 thr) | 23 ns | 56 ns | 2.39× | +| rfft Float32 12 dims=1 (16 thr) | 28 ns | 157 ns | 5.69× | +| rfft Float32 16 dims=1 (16 thr) | 33 ns | 76 ns | 2.31× | +| rfft Float32 17 dims=1 (16 thr) | 135 ns | 184 ns | 1.36× | +| rfft Float32 23 dims=1 (16 thr) | 205 ns | 320 ns | 1.56× | +| rfft Float32 25 dims=1 (16 thr) | 78 ns | 164 ns | 2.11× | +| rfft Float32 29 dims=1 (16 thr) | 291 ns | 545 ns | 1.87× | +| rfft Float32 31 dims=1 (16 thr) | 322 ns | 547 ns | 1.70× | +| rfft Float32 32 dims=1 (16 thr) | 104 ns | 120 ns | 1.15× | +| rfft Float32 37 dims=1 (16 thr) | 430 ns | 762 ns | 1.77× | +| rfft Float32 41 dims=1 (16 thr) | 513 ns | 769 ns | 1.50× | +| rfft Float32 43 dims=1 (16 thr) | 555 ns | 773 ns | 1.39× | +| rfft Float32 54 dims=1 (16 thr) | 3.68 µs | 350 ns | 0.10× | +| rfft Float32 60 dims=1 (16 thr) | 9.36 µs | 748 ns | 0.08× | +| rfft Float32 61 dims=1 (16 thr) | 1.04 µs | 928 ns | 0.89× | +| rfft Float32 64 dims=1 (16 thr) | 183 ns | 181 ns | 0.99× | +| rfft Float32 71 dims=1 (16 thr) | 1.38 µs | 1.26 µs | 0.91× | +| rfft Float32 73 dims=1 (16 thr) | 1.45 µs | 1.25 µs | 0.86× | +| rfft Float32 79 dims=1 (16 thr) | 1.68 µs | 1.26 µs | 0.75× | +| rfft Float32 101 dims=1 (16 thr) | 2.69 µs | 1.86 µs | 0.69× | +| rfft Float32 112 dims=1 (16 thr) | 7.80 µs | 463 ns | 0.06× | +| rfft Float32 120 dims=1 (16 thr) | 5.12 µs | 546 ns | 0.11× | +| rfft Float32 128 dims=1 (16 thr) | 349 ns | 329 ns | 0.94× | +| rfft Float32 202 dims=1 (16 thr) | 33.48 µs | 2.08 µs | 0.06× | +| rfft Float32 243 dims=1 (16 thr) | 39.04 µs | 1.88 µs | 0.05× | +| rfft Float32 251 dims=1 (16 thr) | 157.00 µs | 3.98 µs | 0.03× | +| rfft Float32 256 dims=1 (16 thr) | 693 ns | 554 ns | 0.80× | +| rfft Float32 303 dims=1 (16 thr) | 22.20 µs | 7.60 µs | 0.34× | +| rfft Float32 360 dims=1 (16 thr) | 33.32 µs | 1.49 µs | 0.04× | +| rfft Float32 404 dims=1 (16 thr) | 70.44 µs | 5.67 µs | 0.08× | +| rfft Float32 504 dims=1 (16 thr) | 31.80 µs | 2.16 µs | 0.07× | +| rfft Float32 512 dims=1 (16 thr) | 8.88 µs | 1.16 µs | 0.13× | +| rfft Float32 593 dims=1 (16 thr) | 91.84 µs | 11.94 µs | 0.13× | +| rfft Float32 606 dims=1 (16 thr) | 67.96 µs | 8.24 µs | 0.12× | +| rfft Float32 720 dims=1 (16 thr) | 48.00 µs | 2.86 µs | 0.06× | +| rfft Float32 1000 dims=1 (16 thr) | 35.40 µs | 4.22 µs | 0.12× | +| rfft Float32 1024 dims=1 (16 thr) | 16.16 µs | 2.30 µs | 0.14× | +| rfft Float32 1080 dims=1 (16 thr) | 46.28 µs | 4.65 µs | 0.10× | +| rfft Float32 1433 dims=1 (16 thr) | 181.20 µs | 31.56 µs | 0.17× | +| rfft Float32 1616 dims=1 (16 thr) | 43.60 µs | 19.96 µs | 0.46× | +| rfft Float32 2018 dims=1 (16 thr) | 180.68 µs | 20.60 µs | 0.11× | +| rfft Float32 2048 dims=1 (16 thr) | 4.46 µs | 5.08 µs | 1.14× | +| rfft Float32 2304 dims=1 (16 thr) | 29.80 µs | 6.22 µs | 0.21× | +| rfft Float32 3027 dims=1 (16 thr) | 116.32 µs | 75.20 µs | 0.65× | +| rfft Float32 3491 dims=1 (16 thr) | 244.20 µs | 81.40 µs | 0.33× | +| rfft Float32 4036 dims=1 (16 thr) | 170.36 µs | 57.04 µs | 0.33× | +| rfft Float32 4096 dims=1 (16 thr) | 9.43 µs | 10.52 µs | 1.12× | +| rfft Float32 4860 dims=1 (16 thr) | 51.08 µs | 24.56 µs | 0.48× | +| rfft Float32 6054 dims=1 (16 thr) | 142.60 µs | 82.36 µs | 0.58× | +| rfft Float32 8192 dims=1 (16 thr) | 41.24 µs | 23.00 µs | 0.56× | +| rfft Float32 8198 dims=1 (16 thr) | 229.48 µs | 121.68 µs | 0.53× | +| rfft Float32 8443 dims=1 (16 thr) | 318.96 µs | 232.60 µs | 0.73× | +| rfft Float32 10290 dims=1 (16 thr) | 54.56 µs | 56.52 µs | 1.04× | +| rfft Float32 12297 dims=1 (16 thr) | 243.92 µs | 420.33 µs | 1.72× | +| rfft Float32 16144 dims=1 (16 thr) | 137.60 µs | 200.52 µs | 1.46× | +| rfft Float32 16384 dims=1 (16 thr) | 64.12 µs | 47.44 µs | 0.74× | +| rfft Float32 16396 dims=1 (16 thr) | 224.60 µs | 308.84 µs | 1.38× | +| rfft Float32 20507 dims=1 (16 thr) | 525.97 µs | 661.09 µs | 1.26× | +| rfft Float32 21875 dims=1 (16 thr) | 72.68 µs | 214.56 µs | 2.95× | +| rfft Float32 24594 dims=1 (16 thr) | 249.96 µs | 451.81 µs | 1.81× | +| rfft Float32 32768 dims=1 (16 thr) | 105.36 µs | 106.24 µs | 1.01× | +| rfft Float32 32822 dims=1 (16 thr) | 410.44 µs | 558.37 µs | 1.36× | +| rfft Float32 46305 dims=1 (16 thr) | 127.44 µs | 502.33 µs | 3.94× | +| rfft Float32 49233 dims=1 (16 thr) | 658.81 µs | 1.939 ms | 2.94× | +| rfft Float32 49757 dims=1 (16 thr) | 1.215 ms | 1.645 ms | 1.35× | +| rfft Float32 65536 dims=1 (16 thr) | 227.44 µs | 238.48 µs | 1.05× | +| rfft Float32 65584 dims=1 (16 thr) | 429.85 µs | 1.148 ms | 2.67× | +| rfft Float32 65644 dims=1 (16 thr) | 667.05 µs | 1.395 ms | 2.09× | +| rfft Float32 98304 dims=1 (16 thr) | 398.04 µs | 382.21 µs | 0.96× | +| rfft Float32 98466 dims=1 (16 thr) | 741.13 µs | 2.052 ms | 2.77× | +| rfft Float32 120779 dims=1 (16 thr) | 6.107 ms | 5.826 ms | 0.95× | +| rfft Float32 131072 dims=1 (16 thr) | 535.29 µs | 524.85 µs | 0.98× | +| rfft Float32 131074 dims=1 (16 thr) | 1.454 ms | 2.763 ms | 1.90× | +| rfft Float32 196611 dims=1 (16 thr) | 1.935 ms | 9.009 ms | 4.66× | +| rfft Float32 207360 dims=1 (16 thr) | 690.81 µs | 963.49 µs | 1.39× | +| rfft Float32 262144 dims=1 (16 thr) | 912.61 µs | 1.236 ms | 1.35× | +| rfft Float32 262148 dims=1 (16 thr) | 2.519 ms | 6.715 ms | 2.67× | +| rfft Float32 262576 dims=1 (16 thr) | 1.716 ms | 5.317 ms | 3.10× | +| rfft Float32 293201 dims=1 (16 thr) | 19.338 ms | 12.488 ms | 0.65× | +| rfft Float32 393222 dims=1 (16 thr) | 2.937 ms | 9.224 ms | 3.14× | +| rfft Float32 441000 dims=1 (16 thr) | 1.594 ms | 3.098 ms | 1.94× | +| rfft Float32 524288 dims=1 (16 thr) | 2.109 ms | 1.276 ms | 0.61× | +| rfft Float32 524294 dims=1 (16 thr) | 5.824 ms | 11.749 ms | 2.02× | +| rfft Float32 711749 dims=1 (16 thr) | 51.434 ms | 36.880 ms | 0.72× | +| rfft Float32 786441 dims=1 (16 thr) | 54.431 ms | 42.335 ms | 0.78× | +| rfft Float32 933120 dims=1 (16 thr) | 2.969 ms | 5.475 ms | 1.84× | +| rfft Float32 1000000 dims=1 (16 thr) | 3.723 ms | 5.590 ms | 1.50× | +| rfft Float32 1048576 dims=1 (16 thr) | 3.541 ms | 2.084 ms | 0.59× | +| rfft Float32 1048588 dims=1 (16 thr) | 9.372 ms | 28.137 ms | 3.00× | +| rfft Float32 1048592 dims=1 (16 thr) | 5.149 ms | 24.945 ms | 4.84× | +| rfft Float32 1572882 dims=1 (16 thr) | 11.866 ms | 44.540 ms | 3.75× | +| rfft Float32 1727797 dims=1 (16 thr) | 130.512 ms | 122.140 ms | 0.94× | +| rfft Float32 1975680 dims=1 (16 thr) | 5.803 ms | 11.274 ms | 1.94× | +| rfft Float32 2097152 dims=1 (16 thr) | 6.686 ms | 4.102 ms | 0.61× | +| rfft Float32 4167450 dims=1 (16 thr) | 20.383 ms | 45.593 ms | 2.24× | +| rfft Float32 4194304 dims=1 (16 thr) | 16.569 ms | 9.592 ms | 0.58× | +| rfft Float64 7 dims=1 (16 thr) | 25 ns | 41 ns | 1.61× | +| rfft Float64 8 dims=1 (16 thr) | 23 ns | 56 ns | 2.40× | +| rfft Float64 12 dims=1 (16 thr) | 28 ns | 151 ns | 5.44× | +| rfft Float64 16 dims=1 (16 thr) | 33 ns | 76 ns | 2.33× | +| rfft Float64 17 dims=1 (16 thr) | 139 ns | 197 ns | 1.42× | +| rfft Float64 23 dims=1 (16 thr) | 210 ns | 343 ns | 1.63× | +| rfft Float64 25 dims=1 (16 thr) | 77 ns | 165 ns | 2.14× | +| rfft Float64 29 dims=1 (16 thr) | 294 ns | 893 ns | 3.04× | +| rfft Float64 31 dims=1 (16 thr) | 328 ns | 898 ns | 2.74× | +| rfft Float64 32 dims=1 (16 thr) | 3.20 µs | 129 ns | 0.04× | +| rfft Float64 37 dims=1 (16 thr) | 434 ns | 1.19 µs | 2.74× | +| rfft Float64 41 dims=1 (16 thr) | 515 ns | 1.20 µs | 2.32× | +| rfft Float64 43 dims=1 (16 thr) | 560 ns | 1.20 µs | 2.14× | +| rfft Float64 54 dims=1 (16 thr) | 3.88 µs | 376 ns | 0.10× | +| rfft Float64 60 dims=1 (16 thr) | 5.86 µs | 779 ns | 0.13× | +| rfft Float64 61 dims=1 (16 thr) | 1.05 µs | 1.56 µs | 1.49× | +| rfft Float64 64 dims=1 (16 thr) | 5.22 µs | 253 ns | 0.05× | +| rfft Float64 71 dims=1 (16 thr) | 1.39 µs | 2.04 µs | 1.47× | +| rfft Float64 73 dims=1 (16 thr) | 1.46 µs | 2.03 µs | 1.39× | +| rfft Float64 79 dims=1 (16 thr) | 1.70 µs | 2.03 µs | 1.20× | +| rfft Float64 101 dims=1 (16 thr) | 2.72 µs | 3.03 µs | 1.12× | +| rfft Float64 112 dims=1 (16 thr) | 4.88 µs | 538 ns | 0.11× | +| rfft Float64 120 dims=1 (16 thr) | 3.80 µs | 648 ns | 0.17× | +| rfft Float64 128 dims=1 (16 thr) | 5.00 µs | 533 ns | 0.11× | +| rfft Float64 202 dims=1 (16 thr) | 41.40 µs | 3.33 µs | 0.08× | +| rfft Float64 243 dims=1 (16 thr) | 36.64 µs | 2.63 µs | 0.07× | +| rfft Float64 251 dims=1 (16 thr) | 155.64 µs | 7.51 µs | 0.05× | +| rfft Float64 256 dims=1 (16 thr) | 5.56 µs | 928 ns | 0.17× | +| rfft Float64 303 dims=1 (16 thr) | 23.72 µs | 11.28 µs | 0.48× | +| rfft Float64 360 dims=1 (16 thr) | 26.52 µs | 2.01 µs | 0.08× | +| rfft Float64 404 dims=1 (16 thr) | 71.16 µs | 8.36 µs | 0.12× | +| rfft Float64 504 dims=1 (16 thr) | 30.60 µs | 2.91 µs | 0.10× | +| rfft Float64 512 dims=1 (16 thr) | 1.47 µs | 2.09 µs | 1.42× | +| rfft Float64 593 dims=1 (16 thr) | 87.48 µs | 21.52 µs | 0.25× | +| rfft Float64 606 dims=1 (16 thr) | 70.80 µs | 12.18 µs | 0.17× | +| rfft Float64 720 dims=1 (16 thr) | 29.52 µs | 4.10 µs | 0.14× | +| rfft Float64 1000 dims=1 (16 thr) | 28.00 µs | 5.85 µs | 0.21× | +| rfft Float64 1024 dims=1 (16 thr) | 3.13 µs | 4.42 µs | 1.41× | +| rfft Float64 1080 dims=1 (16 thr) | 31.96 µs | 6.83 µs | 0.21× | +| rfft Float64 1433 dims=1 (16 thr) | 177.96 µs | 59.00 µs | 0.33× | +| rfft Float64 1616 dims=1 (16 thr) | 47.92 µs | 30.64 µs | 0.64× | +| rfft Float64 2018 dims=1 (16 thr) | 199.36 µs | 38.88 µs | 0.20× | +| rfft Float64 2048 dims=1 (16 thr) | 6.69 µs | 9.85 µs | 1.47× | +| rfft Float64 2304 dims=1 (16 thr) | 31.72 µs | 11.52 µs | 0.36× | +| rfft Float64 3027 dims=1 (16 thr) | 121.64 µs | 129.56 µs | 1.07× | +| rfft Float64 3491 dims=1 (16 thr) | 241.68 µs | 152.84 µs | 0.63× | +| rfft Float64 4036 dims=1 (16 thr) | 184.48 µs | 94.00 µs | 0.51× | +| rfft Float64 4096 dims=1 (16 thr) | 14.52 µs | 20.32 µs | 1.40× | +| rfft Float64 4860 dims=1 (16 thr) | 45.72 µs | 38.20 µs | 0.84× | +| rfft Float64 6054 dims=1 (16 thr) | 159.84 µs | 138.68 µs | 0.87× | +| rfft Float64 8192 dims=1 (16 thr) | 53.16 µs | 46.12 µs | 0.87× | +| rfft Float64 8198 dims=1 (16 thr) | 213.32 µs | 224.36 µs | 1.05× | +| rfft Float64 8443 dims=1 (16 thr) | 346.68 µs | 490.29 µs | 1.41× | +| rfft Float64 10290 dims=1 (16 thr) | 62.32 µs | 86.76 µs | 1.39× | +| rfft Float64 12297 dims=1 (16 thr) | 259.40 µs | 724.81 µs | 2.79× | +| rfft Float64 16144 dims=1 (16 thr) | 174.56 µs | 358.64 µs | 2.05× | +| rfft Float64 16384 dims=1 (16 thr) | 92.16 µs | 100.32 µs | 1.09× | +| rfft Float64 16396 dims=1 (16 thr) | 280.84 µs | 525.88 µs | 1.87× | +| rfft Float64 20507 dims=1 (16 thr) | 584.29 µs | 1.342 ms | 2.30× | +| rfft Float64 21875 dims=1 (16 thr) | 70.68 µs | 326.96 µs | 4.63× | +| rfft Float64 24594 dims=1 (16 thr) | 307.24 µs | 779.09 µs | 2.54× | +| rfft Float64 32768 dims=1 (16 thr) | 174.36 µs | 246.36 µs | 1.41× | +| rfft Float64 32822 dims=1 (16 thr) | 723.17 µs | 1.080 ms | 1.49× | +| rfft Float64 46305 dims=1 (16 thr) | 133.36 µs | 814.13 µs | 6.10× | +| rfft Float64 49233 dims=1 (16 thr) | 1.810 ms | 3.546 ms | 1.96× | +| rfft Float64 49757 dims=1 (16 thr) | 1.390 ms | 3.197 ms | 2.30× | +| rfft Float64 65536 dims=1 (16 thr) | 338.12 µs | 557.37 µs | 1.65× | +| rfft Float64 65584 dims=1 (16 thr) | 571.45 µs | 2.160 ms | 3.78× | +| rfft Float64 65644 dims=1 (16 thr) | 869.25 µs | 2.470 ms | 2.84× | +| rfft Float64 98304 dims=1 (16 thr) | 616.21 µs | 762.13 µs | 1.24× | +| rfft Float64 98466 dims=1 (16 thr) | 1.106 ms | 3.824 ms | 3.46× | +| rfft Float64 120779 dims=1 (16 thr) | 6.417 ms | 9.775 ms | 1.52× | +| rfft Float64 131072 dims=1 (16 thr) | 828.85 µs | 1.334 ms | 1.61× | +| rfft Float64 131074 dims=1 (16 thr) | 1.730 ms | 5.545 ms | 3.21× | +| rfft Float64 196611 dims=1 (16 thr) | 2.391 ms | 17.746 ms | 7.42× | +| rfft Float64 207360 dims=1 (16 thr) | 1.295 ms | 1.865 ms | 1.44× | +| rfft Float64 262144 dims=1 (16 thr) | 1.300 ms | 2.578 ms | 1.98× | +| rfft Float64 262148 dims=1 (16 thr) | 3.397 ms | 12.041 ms | 3.54× | +| rfft Float64 262576 dims=1 (16 thr) | 2.406 ms | 10.222 ms | 4.25× | +| rfft Float64 293201 dims=1 (16 thr) | 20.044 ms | 22.248 ms | 1.11× | +| rfft Float64 393222 dims=1 (16 thr) | 4.047 ms | 16.925 ms | 4.18× | +| rfft Float64 441000 dims=1 (16 thr) | 2.164 ms | 5.001 ms | 2.31× | +| rfft Float64 524288 dims=1 (16 thr) | 3.322 ms | 1.755 ms | 0.53× | +| rfft Float64 524294 dims=1 (16 thr) | 8.073 ms | 25.301 ms | 3.13× | +| rfft Float64 711749 dims=1 (16 thr) | 56.179 ms | 94.897 ms | 1.69× | +| rfft Float64 786441 dims=1 (16 thr) | 59.865 ms | 75.503 ms | 1.26× | +| rfft Float64 933120 dims=1 (16 thr) | 4.502 ms | 10.957 ms | 2.43× | +| rfft Float64 1000000 dims=1 (16 thr) | 5.087 ms | 11.113 ms | 2.18× | +| rfft Float64 1048576 dims=1 (16 thr) | 5.382 ms | 3.845 ms | 0.71× | +| rfft Float64 1048588 dims=1 (16 thr) | 12.307 ms | 53.598 ms | 4.36× | +| rfft Float64 1048592 dims=1 (16 thr) | 7.365 ms | 47.606 ms | 6.46× | +| rfft Float64 1572882 dims=1 (16 thr) | 18.314 ms | 79.122 ms | 4.32× | +| rfft Float64 1727797 dims=1 (16 thr) | 144.678 ms | 267.454 ms | 1.85× | +| rfft Float64 1975680 dims=1 (16 thr) | 8.742 ms | 25.702 ms | 2.94× | +| rfft Float64 2097152 dims=1 (16 thr) | 7.822 ms | 6.612 ms | 0.85× | +| rfft Float64 4167450 dims=1 (16 thr) | 23.643 ms | 89.010 ms | 3.76× | +| rfft Float64 4194304 dims=1 (16 thr) | 22.592 ms | 16.759 ms | 0.74× | +| fft Float32 8×8 dims=1,2 (16 thr) | 15.60 µs | 651 ns | 0.04× | +| fft Float32 16×16 dims=1,2 (16 thr) | 28.40 µs | 2.25 µs | 0.08× | +| fft Float32 32×32 dims=1,2 (16 thr) | 29.28 µs | 6.32 µs | 0.22× | +| fft Float32 64×64 dims=1,2 (16 thr) | 32.88 µs | 25.16 µs | 0.77× | +| fft Float32 128×128 dims=1,2 (16 thr) | 36.96 µs | 88.88 µs | 2.40× | +| fft Float32 256×256 dims=1,2 (16 thr) | 99.44 µs | 85.48 µs | 0.86× | +| fft Float32 512×512 dims=1,2 (16 thr) | 469.33 µs | 225.24 µs | 0.48× | +| fft Float32 1024×1024 dims=1,2 (16 thr) | 1.918 ms | 857.53 µs | 0.45× | +| fft Float32 2048×2048 dims=1,2 (16 thr) | 9.854 ms | 4.237 ms | 0.43× | +| fft Float64 8×8 dims=1,2 (16 thr) | 15.76 µs | 655 ns | 0.04× | +| fft Float64 16×16 dims=1,2 (16 thr) | 28.16 µs | 2.29 µs | 0.08× | +| fft Float64 32×32 dims=1,2 (16 thr) | 28.92 µs | 10.26 µs | 0.35× | +| fft Float64 64×64 dims=1,2 (16 thr) | 32.96 µs | 50.48 µs | 1.53× | +| fft Float64 128×128 dims=1,2 (16 thr) | 41.80 µs | 206.44 µs | 4.94× | +| fft Float64 127×257 dims=1,2 (16 thr) | 160.96 µs | 2.264 ms | 14.07× | +| fft Float64 1009×64 dims=1,2 (16 thr) | 294.96 µs | 191.60 µs | 0.65× | +| fft Float64 64×1009 dims=1,2 (16 thr) | 298.04 µs | 223.88 µs | 0.75× | +| fft Float64 256×256 dims=1,2 (16 thr) | 2.987 ms | 88.60 µs | 0.03× | +| fft Float64 512×512 dims=1,2 (16 thr) | 506.37 µs | 398.40 µs | 0.79× | +| fft Float64 720×480 dims=1,2 (16 thr) | 567.45 µs | 561.89 µs | 0.99× | +| fft Float64 1000×1000 dims=1,2 (16 thr) | 6.752 ms | 1.471 ms | 0.22× | +| fft Float64 1024×1024 dims=1,2 (16 thr) | 2.458 ms | 1.754 ms | 0.71× | +| fft Float64 2048×2048 dims=1,2 (16 thr) | 14.192 ms | 10.253 ms | 0.72× | +| rfft Float32 8×8 dims=1,2 (16 thr) | 13.32 µs | 802 ns | 0.06× | +| rfft Float32 16×16 dims=1,2 (16 thr) | 23.44 µs | 2.18 µs | 0.09× | +| rfft Float32 32×32 dims=1,2 (16 thr) | 33.32 µs | 6.46 µs | 0.19× | +| rfft Float32 64×64 dims=1,2 (16 thr) | 28.80 µs | 20.80 µs | 0.72× | +| rfft Float32 128×128 dims=1,2 (16 thr) | 44.56 µs | 74.56 µs | 1.67× | +| rfft Float32 256×256 dims=1,2 (16 thr) | 101.72 µs | 38.84 µs | 0.38× | +| rfft Float32 512×512 dims=1,2 (16 thr) | 170.44 µs | 150.92 µs | 0.89× | +| rfft Float32 1024×1024 dims=1,2 (16 thr) | 509.13 µs | 479.45 µs | 0.94× | +| rfft Float32 2048×2048 dims=1,2 (16 thr) | 2.814 ms | 1.931 ms | 0.69× | +| rfft Float64 8×8 dims=1,2 (16 thr) | 12.92 µs | 812 ns | 0.06× | +| rfft Float64 16×16 dims=1,2 (16 thr) | 22.52 µs | 2.25 µs | 0.10× | +| rfft Float64 32×32 dims=1,2 (16 thr) | 33.00 µs | 7.52 µs | 0.23× | +| rfft Float64 64×64 dims=1,2 (16 thr) | 29.04 µs | 30.60 µs | 1.05× | +| rfft Float64 128×128 dims=1,2 (16 thr) | 46.00 µs | 117.68 µs | 2.56× | +| rfft Float64 127×257 dims=1,2 (16 thr) | 1.282 ms | 1.605 ms | 1.25× | +| rfft Float64 1009×64 dims=1,2 (16 thr) | 7.528 ms | 471.33 µs | 0.06× | +| rfft Float64 64×1009 dims=1,2 (16 thr) | 259.56 µs | 172.52 µs | 0.66× | +| rfft Float64 256×256 dims=1,2 (16 thr) | 4.152 ms | 51.36 µs | 0.01× | +| rfft Float64 512×512 dims=1,2 (16 thr) | 2.877 ms | 206.60 µs | 0.07× | +| rfft Float64 720×480 dims=1,2 (16 thr) | 299.36 µs | 281.76 µs | 0.94× | +| rfft Float64 1000×1000 dims=1,2 (16 thr) | 1.243 ms | 890.13 µs | 0.72× | +| rfft Float64 1024×1024 dims=1,2 (16 thr) | 2.654 ms | 741.85 µs | 0.28× | +| rfft Float64 2048×2048 dims=1,2 (16 thr) | 4.152 ms | 3.384 ms | 0.81× | +| fft Float32 8×8×8 dims=1,2,3 (16 thr) | 39.72 µs | 8.51 µs | 0.21× | +| fft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.28 µs | 58.16 µs | 1.99× | +| fft Float32 32×32×32 dims=1,2,3 (16 thr) | 44.72 µs | 62.72 µs | 1.40× | +| fft Float32 64×64×64 dims=1,2,3 (16 thr) | 164.64 µs | 272.96 µs | 1.66× | +| fft Float32 128×128×128 dims=1,2,3 (16 thr) | 1.501 ms | 1.850 ms | 1.23× | +| fft Float64 8×8×8 dims=1,2,3 (16 thr) | 38.76 µs | 8.49 µs | 0.22× | +| fft Float64 16×16×16 dims=1,2,3 (16 thr) | 31.56 µs | 60.28 µs | 1.91× | +| fft Float64 32×32×32 dims=1,2,3 (16 thr) | 52.88 µs | 56.48 µs | 1.07× | +| fft Float64 64×64×64 dims=1,2,3 (16 thr) | 259.56 µs | 489.25 µs | 1.88× | +| fft Float64 128×128×128 dims=1,2,3 (16 thr) | 2.719 ms | 3.754 ms | 1.38× | +| rfft Float32 8×8×8 dims=1,2,3 (16 thr) | 57.20 µs | 8.43 µs | 0.15× | +| rfft Float32 16×16×16 dims=1,2,3 (16 thr) | 29.40 µs | 47.68 µs | 1.62× | +| rfft Float32 32×32×32 dims=1,2,3 (16 thr) | 37.56 µs | 155.36 µs | 4.14× | +| rfft Float32 64×64×64 dims=1,2,3 (16 thr) | 115.28 µs | 180.04 µs | 1.56× | +| rfft Float32 128×128×128 dims=1,2,3 (16 thr) | 739.45 µs | 1.150 ms | 1.56× | +| rfft Float64 8×8×8 dims=1,2,3 (16 thr) | 51.48 µs | 8.36 µs | 0.16× | +| rfft Float64 16×16×16 dims=1,2,3 (16 thr) | 29.84 µs | 48.48 µs | 1.62× | +| rfft Float64 32×32×32 dims=1,2,3 (16 thr) | 42.44 µs | 269.92 µs | 6.36× | +| rfft Float64 64×64×64 dims=1,2,3 (16 thr) | 150.04 µs | 263.56 µs | 1.76× | +| rfft Float64 128×128×128 dims=1,2,3 (16 thr) | 1.107 ms | 1.850 ms | 1.67× | +| fft Float32 64×64 dims=1 (16 thr) | 14.40 µs | 12.58 µs | 0.87× | +| fft Float32 256×64 dims=1 (16 thr) | 20.44 µs | 50.28 µs | 2.46× | +| fft Float32 1024×64 dims=1 (16 thr) | 34.76 µs | 15.80 µs | 0.45× | +| fft Float32 4096×64 dims=1 (16 thr) | 116.96 µs | 68.80 µs | 0.59× | +| fft Float32 16384×64 dims=1 (16 thr) | 620.21 µs | 345.76 µs | 0.56× | +| fft Float32 65536×64 dims=1 (16 thr) | 3.277 ms | 1.749 ms | 0.53× | +| fft Float64 64×64 dims=1 (16 thr) | 14.64 µs | 22.40 µs | 1.53× | +| fft Float64 256×64 dims=1 (16 thr) | 21.76 µs | 92.24 µs | 4.24× | +| fft Float64 1024×64 dims=1 (16 thr) | 47.32 µs | 29.96 µs | 0.63× | +| fft Float64 4096×64 dims=1 (16 thr) | 190.80 µs | 147.20 µs | 0.77× | +| fft Float64 16384×64 dims=1 (16 thr) | 1.133 ms | 789.37 µs | 0.70× | +| fft Float64 65536×64 dims=1 (16 thr) | 6.859 ms | 6.302 ms | 0.92× | +| rfft Float32 64×64 dims=1 (16 thr) | 14.28 µs | 12.16 µs | 0.85× | +| rfft Float32 256×64 dims=1 (16 thr) | 16.96 µs | 37.20 µs | 2.19× | +| rfft Float32 1024×64 dims=1 (16 thr) | 26.16 µs | 10.88 µs | 0.42× | +| rfft Float32 4096×64 dims=1 (16 thr) | 64.80 µs | 43.96 µs | 0.68× | +| rfft Float32 16384×64 dims=1 (16 thr) | 290.84 µs | 197.04 µs | 0.68× | +| rfft Float32 65536×64 dims=1 (16 thr) | 1.552 ms | 1.093 ms | 0.70× | +| rfft Float64 64×64 dims=1 (16 thr) | 14.32 µs | 17.00 µs | 1.19× | +| rfft Float64 256×4096 dims=1 (16 thr) | 288.96 µs | 255.48 µs | 0.88× | +| rfft Float64 256×64 dims=1 (16 thr) | 17.44 µs | 61.92 µs | 3.55× | +| rfft Float64 1024×1024 dims=1 (16 thr) | 302.40 µs | 291.36 µs | 0.96× | +| rfft Float64 1024×64 dims=1 (16 thr) | 30.40 µs | 19.24 µs | 0.63× | +| rfft Float64 4096×256 dims=1 (16 thr) | 377.84 µs | 334.64 µs | 0.89× | +| rfft Float64 4096×64 dims=1 (16 thr) | 101.80 µs | 84.24 µs | 0.83× | +| rfft Float64 16384×64 dims=1 (16 thr) | 557.33 µs | 425.37 µs | 0.76× | +| rfft Float64 65536×64 dims=1 (16 thr) | 2.895 ms | 2.618 ms | 0.90× | +| fft Float32 64×64 dims=2 (16 thr) | 14.68 µs | 12.52 µs | 0.85× | +| fft Float32 64×256 dims=2 (16 thr) | 36.92 µs | 55.96 µs | 1.52× | +| fft Float32 64×1024 dims=2 (16 thr) | 115.16 µs | 197.60 µs | 1.72× | +| fft Float32 64×4096 dims=2 (16 thr) | 607.17 µs | 913.05 µs | 1.50× | +| fft Float32 64×16384 dims=2 (16 thr) | 2.301 ms | 4.942 ms | 2.15× | +| fft Float32 64×65536 dims=2 (16 thr) | 14.567 ms | 28.441 ms | 1.95× | +| fft Float64 64×64 dims=2 (16 thr) | 14.64 µs | 29.44 µs | 2.01× | +| fft Float64 64×256 dims=2 (16 thr) | 23.04 µs | 139.12 µs | 6.04× | +| fft Float64 64×1024 dims=2 (16 thr) | 78.08 µs | 52.32 µs | 0.67× | +| fft Float64 64×4096 dims=2 (16 thr) | 445.32 µs | 284.96 µs | 0.64× | +| fft Float64 64×16384 dims=2 (16 thr) | 2.219 ms | 1.447 ms | 0.65× | +| fft Float64 64×65536 dims=2 (16 thr) | 20.453 ms | 11.890 ms | 0.58× | +| rfft Float32 64×64 dims=2 (16 thr) | 14.08 µs | 14.84 µs | 1.05× | +| rfft Float32 64×256 dims=2 (16 thr) | 27.56 µs | 61.56 µs | 2.23× | +| rfft Float32 64×1024 dims=2 (16 thr) | 71.96 µs | 37.56 µs | 0.52× | +| rfft Float32 64×4096 dims=2 (16 thr) | 284.92 µs | 168.20 µs | 0.59× | +| rfft Float32 64×16384 dims=2 (16 thr) | 1.344 ms | 698.85 µs | 0.52× | +| rfft Float32 64×65536 dims=2 (16 thr) | 6.026 ms | 4.218 ms | 0.70× | +| rfft Float64 64×64 dims=2 (16 thr) | 14.24 µs | 19.78 µs | 1.39× | +| rfft Float64 64×256 dims=2 (16 thr) | 19.64 µs | 95.60 µs | 4.87× | +| rfft Float64 64×1024 dims=2 (16 thr) | 42.84 µs | 32.32 µs | 0.75× | +| rfft Float64 64×4096 dims=2 (16 thr) | 258.56 µs | 176.76 µs | 0.68× | +| rfft Float64 64×16384 dims=2 (16 thr) | 1.100 ms | 815.29 µs | 0.74× | +| rfft Float64 64×65536 dims=2 (16 thr) | 9.087 ms | 6.705 ms | 0.74× | + +### Summary (16 threads) + +Geometric means over the cases of each group; `(min–max)` in brackets. + +| group | `ffta`/`fftw` | | +|:--|--:| +| ComplexF32 fft 2d | 0.36× (0.04–2.40) | +| ComplexF32 fft 3d | 1.04× (0.21–1.99) | +| ComplexF32 fft awkward | 1.67× (0.06–8.31) | +| ComplexF32 fft batched_dim1 | 0.75× (0.45–2.46) | +| ComplexF32 fft batched_dim2 | 1.55× (0.85–2.15) | +| ComplexF32 fft pow2 | 0.64× (0.03–5.22) | +| ComplexF32 fft prime | 0.22× (0.01–6.58) | +| ComplexF32 fft smooth | 0.30× (0.01–4.94) | +| ComplexF64 fft 2d | 0.54× (0.03–14.07) | +| ComplexF64 fft 3d | 1.03× (0.22–1.91) | +| ComplexF64 fft awkward | 2.21× (0.09–11.38) | +| ComplexF64 fft batched_dim1 | 1.13× (0.63–4.24) | +| ComplexF64 fft batched_dim2 | 1.12× (0.58–6.04) | +| ComplexF64 fft pow2 | 0.62× (0.02–6.89) | +| ComplexF64 fft prime | 0.40× (0.01–3.95) | +| ComplexF64 fft smooth | 0.36× (0.02–6.46) | +| Float32 rfft 2d | 0.40× (0.06–1.67) | +| Float32 rfft 3d | 1.19× (0.15–4.14) | +| Float32 rfft awkward | 1.06× (0.06–4.84) | +| Float32 rfft batched_dim1 | 0.79× (0.42–2.19) | +| Float32 rfft batched_dim2 | 0.80× (0.52–2.23) | +| Float32 rfft pow2 | 0.79× (0.13–2.39) | +| Float32 rfft prime | 0.76× (0.03–1.87) | +| Float32 rfft smooth | 0.44× (0.04–5.69) | +| Float64 rfft 2d | 0.29× (0.01–2.56) | +| Float64 rfft 3d | 1.38× (0.16–6.36) | +| Float64 rfft awkward | 1.49× (0.08–7.42) | +| Float64 rfft batched_dim1 | 1.02× (0.63–3.55) | +| Float64 rfft batched_dim2 | 1.11× (0.68–4.87) | +| Float64 rfft pow2 | 0.72× (0.04–2.40) | +| Float64 rfft prime | 1.24× (0.05–3.04) | +| Float64 rfft smooth | 0.64× (0.07–6.10) | +| **all** | 0.72× (0.01–14.07) | + +## Thread scaling (time at 1 thread / time at N threads) + +| case | `fftw` ×16 | `ffta` ×16 | +|:--|--:|--:| +| fft Float64 41 dims=1 | 0.03× | 1.00× | +| rfft Float64 64×1024 dims=2 | 8.12× | 13.86× | +| fft Float64 17 dims=1 | 0.98× | 1.00× | +| rfft Float64 79 dims=1 | 1.00× | 1.01× | +| fft Float32 504 dims=1 | 0.06× | 0.99× | +| rfft Float32 64×64 dims=2 | 0.47× | 1.00× | +| rfft Float64 8×8×8 dims=1,2,3 | 0.02× | 1.00× | +| rfft Float64 61 dims=1 | 1.00× | 1.00× | +| rfft Float64 64×256 dims=2 | 3.65× | 1.00× | +| rfft Float32 32 dims=1 | 0.98× | 1.00× | +| fft Float32 23 dims=1 | 0.99× | 1.00× | +| fft Float32 7 dims=1 | 0.96× | 0.99× | +| fft Float64 786441 dims=1 | 7.61× | 2.60× | +| fft Float32 524294 dims=1 | 6.42× | 2.25× | +| rfft Float64 303 dims=1 | 0.35× | 1.01× | +| fft Float32 1000 dims=1 | 0.21× | 1.00× | +| fft Float32 65584 dims=1 | 10.56× | 0.99× | +| rfft Float32 49757 dims=1 | 2.24× | 0.99× | +| fft Float64 131072 dims=1 | 9.01× | 6.92× | +| fft Float64 64×1009 dims=1,2 | 12.93× | 14.42× | +| fft Float64 32 dims=1 | 0.98× | 0.99× | +| fft Float64 54 dims=1 | 0.02× | 1.00× | +| fft Float64 4194304 dims=1 | 13.04× | 9.54× | +| rfft Float64 64×16384 dims=2 | 12.86× | 15.72× | +| fft Float32 262144 dims=1 | 10.38× | 4.61× | +| fft Float32 16384 dims=1 | 2.79× | 0.96× | +| rfft Float32 37 dims=1 | 1.00× | 1.00× | +| rfft Float64 8 dims=1 | 0.92× | 0.98× | +| fft Float32 786441 dims=1 | 8.10× | 2.16× | +| rfft Float64 7 dims=1 | 0.95× | 0.96× | +| rfft Float32 1727797 dims=1 | 1.93× | 0.97× | +| rfft Float64 32768 dims=1 | 1.12× | 0.93× | +| fft Float32 1048588 dims=1 | 10.44× | 2.20× | +| fft Float64 524288 dims=1 | 13.06× | 8.25× | +| fft Float32 1572882 dims=1 | 10.43× | 1.79× | +| fft Float64 504 dims=1 | 0.11× | 1.00× | +| fft Float64 720×480 dims=1,2 | 11.66× | 10.79× | +| fft Float64 24594 dims=1 | 5.39× | 0.99× | +| fft Float64 1000×1000 dims=1,2 | 4.12× | 14.60× | +| rfft Float64 1975680 dims=1 | 4.41× | 0.92× | +| fft Float32 256 dims=1 | 0.04× | 1.00× | +| fft Float64 32768 dims=1 | 6.53× | 0.99× | +| fft Float64 79 dims=1 | 0.02× | 1.00× | +| fft Float64 64×256 dims=2 | 4.73× | 1.00× | +| fft Float64 1024×1024 dims=1,2 | 12.23× | 14.96× | +| fft Float32 41 dims=1 | 0.03× | 1.01× | +| fft Float64 8198 dims=1 | 2.03× | 1.01× | +| rfft Float32 1000 dims=1 | 0.09× | 1.00× | +| rfft Float32 1048576 dims=1 | 2.21× | 3.39× | +| rfft Float32 1000000 dims=1 | 2.33× | 0.97× | +| fft Float64 120779 dims=1 | 3.77× | 0.97× | +| rfft Float32 41 dims=1 | 0.99× | 1.00× | +| rfft Float64 131074 dims=1 | 2.03× | 0.96× | +| fft Float64 23 dims=1 | 0.99× | 1.00× | +| fft Float64 43 dims=1 | 1.00× | 1.00× | +| rfft Float64 1024×1024 dims=1,2 | 3.29× | 13.47× | +| fft Float32 1727797 dims=1 | 4.97× | 4.58× | +| rfft Float64 3027 dims=1 | 0.60× | 1.00× | +| rfft Float64 64 dims=1 | 0.03× | 0.99× | +| fft Float32 8×8 dims=1,2 | 0.01× | 1.00× | +| rfft Float64 512×512 dims=1,2 | 0.67× | 10.66× | +| rfft Float32 262148 dims=1 | 1.80× | 1.00× | +| rfft Float32 32×32 dims=1,2 | 0.06× | 1.00× | +| fft Float64 29 dims=1 | 1.00× | 1.00× | +| rfft Float32 32822 dims=1 | 2.46× | 1.00× | +| fft Float32 1433 dims=1 | 0.35× | 1.00× | +| rfft Float64 98304 dims=1 | 1.51× | 1.04× | +| rfft Float32 524294 dims=1 | 4.11× | 1.01× | +| fft Float64 8×8×8 dims=1,2,3 | 0.05× | 1.00× | +| rfft Float32 256×256 dims=1,2 | 3.42× | 7.36× | +| fft Float32 16×16 dims=1,2 | 0.02× | 1.00× | +| fft Float32 1024×64 dims=1 | 7.04× | 14.52× | +| rfft Float32 98304 dims=1 | 1.29× | 1.02× | +| rfft Float32 262576 dims=1 | 5.04× | 1.01× | +| fft Float64 16144 dims=1 | 9.34× | 1.00× | +| fft Float32 64×16384 dims=2 | 10.57× | 1.63× | +| fft Float64 1024×64 dims=1 | 9.18× | 16.67× | +| fft Float32 2048 dims=1 | 0.27× | 0.99× | +| rfft Float64 207360 dims=1 | 1.79× | 0.99× | +| fft Float32 73 dims=1 | 0.02× | 1.00× | +| fft Float64 3027 dims=1 | 1.11× | 1.00× | +| rfft Float32 393222 dims=1 | 2.31× | 1.04× | +| rfft Float64 4096×256 dims=1 | 11.23× | 16.18× | +| rfft Float64 16384 dims=1 | 0.94× | 0.98× | +| rfft Float64 1024 dims=1 | 1.00× | 0.99× | +| rfft Float32 251 dims=1 | 0.03× | 0.98× | +| fft Float32 112 dims=1 | 0.01× | 1.00× | +| fft Float64 31 dims=1 | 0.99× | 1.00× | +| rfft Float32 593 dims=1 | 0.24× | 0.99× | +| rfft Float32 441000 dims=1 | 2.39× | 0.98× | +| rfft Float64 37 dims=1 | 0.99× | 1.00× | +| rfft Float32 128×128×128 dims=1,2,3 | 12.67× | 12.30× | +| fft Float32 4167450 dims=1 | 11.74× | 10.89× | +| rfft Float32 4096×64 dims=1 | 10.63× | 15.75× | +| fft Float32 43 dims=1 | 0.01× | 0.99× | +| rfft Float64 64×64×64 dims=1,2,3 | 9.03× | 12.09× | +| rfft Float64 6054 dims=1 | 1.08× | 1.00× | +| fft Float32 1000000 dims=1 | 11.76× | 10.49× | +| fft Float64 7 dims=1 | 0.92× | 0.99× | +| fft Float32 243 dims=1 | 0.05× | 1.01× | +| fft Float32 64×64 dims=1,2 | 0.38× | 1.00× | +| fft Float64 207360 dims=1 | 6.71× | 7.39× | +| fft Float64 720 dims=1 | 0.17× | 1.00× | +| rfft Float32 256 dims=1 | 0.92× | 1.01× | +| rfft Float64 4860 dims=1 | 0.64× | 1.00× | +| fft Float64 1727797 dims=1 | 3.56× | 5.26× | +| fft Float64 1048592 dims=1 | 12.18× | 2.03× | +| fft Float64 128×128×128 dims=1,2,3 | 14.32× | 16.14× | +| fft Float64 49233 dims=1 | 5.53× | 0.98× | +| fft Float32 8443 dims=1 | 1.68× | 0.99× | +| fft Float64 524294 dims=1 | 7.40× | 2.71× | +| rfft Float32 256×64 dims=1 | 2.41× | 1.00× | +| fft Float64 16384 dims=1 | 3.80× | 0.97× | +| fft Float32 3027 dims=1 | 0.77× | 1.00× | +| rfft Float32 73 dims=1 | 1.00× | 1.00× | +| rfft Float32 4096 dims=1 | 1.00× | 1.00× | +| rfft Float32 404 dims=1 | 0.06× | 1.01× | +| rfft Float64 29 dims=1 | 0.99× | 1.00× | +| fft Float32 262576 dims=1 | 13.95× | 0.99× | +| rfft Float64 16396 dims=1 | 1.86× | 0.99× | +| fft Float64 8443 dims=1 | 1.87× | 0.99× | +| rfft Float64 17 dims=1 | 0.99× | 0.99× | +| fft Float64 46305 dims=1 | 6.24× | 1.00× | +| rfft Float64 293201 dims=1 | 1.80× | 1.09× | +| fft Float64 711749 dims=1 | 4.85× | 4.79× | +| rfft Float64 32822 dims=1 | 2.06× | 0.97× | +| rfft Float32 3491 dims=1 | 0.61× | 1.01× | +| fft Float32 65536 dims=1 | 7.15× | 0.94× | +| fft Float32 4096 dims=1 | 0.56× | 1.00× | +| rfft Float32 12297 dims=1 | 2.14× | 1.00× | +| fft Float64 60 dims=1 | 0.02× | 1.00× | +| rfft Float32 8198 dims=1 | 0.90× | 0.99× | +| rfft Float64 64×4096 dims=2 | 10.53× | 14.97× | +| rfft Float32 16384×64 dims=1 | 12.81× | 15.94× | +| rfft Float32 3027 dims=1 | 0.61× | 1.00× | +| fft Float64 4036 dims=1 | 1.96× | 1.00× | +| fft Float32 65536×64 dims=1 | 13.60× | 14.15× | +| fft Float64 64×64×64 dims=1,2,3 | 9.58× | 12.10× | +| fft Float64 32822 dims=1 | 4.59× | 1.00× | +| rfft Float32 16×16×16 dims=1,2,3 | 0.31× | 1.00× | +| rfft Float32 512×512 dims=1,2 | 8.47× | 8.36× | +| rfft Float32 98466 dims=1 | 4.17× | 0.99× | +| rfft Float64 43 dims=1 | 0.99× | 1.01× | +| fft Float64 262148 dims=1 | 5.18× | 2.26× | +| rfft Float32 1080 dims=1 | 0.10× | 1.00× | +| rfft Float64 786441 dims=1 | 1.65× | 0.96× | +| rfft Float32 32×32×32 dims=1,2,3 | 2.42× | 1.61× | +| rfft Float64 65536×64 dims=1 | 13.12× | 14.37× | +| rfft Float64 4194304 dims=1 | 5.25× | 3.42× | +| fft Float64 1024 dims=1 | 0.22× | 1.00× | +| rfft Float32 8192 dims=1 | 0.62× | 0.99× | +| fft Float32 24594 dims=1 | 5.20× | 1.00× | +| fft Float32 32822 dims=1 | 3.98× | 1.02× | +| rfft Float64 2048 dims=1 | 1.00× | 1.00× | +| fft Float32 17 dims=1 | 0.99× | 1.00× | +| fft Float32 1048576 dims=1 | 13.04× | 8.99× | +| rfft Float64 10290 dims=1 | 1.20× | 1.00× | +| rfft Float64 65536 dims=1 | 1.38× | 0.98× | +| rfft Float32 303 dims=1 | 0.38× | 1.01× | +| rfft Float32 60 dims=1 | 0.02× | 1.00× | +| rfft Float64 1048576 dims=1 | 2.51× | 2.95× | +| fft Float64 16×16 dims=1,2 | 0.03× | 1.00× | +| rfft Float64 12297 dims=1 | 2.12× | 1.00× | +| fft Float32 128 dims=1 | 0.88× | 1.00× | +| fft Float64 8×8 dims=1,2 | 0.01× | 1.00× | +| fft Float32 606 dims=1 | 0.23× | 1.01× | +| fft Float32 71 dims=1 | 0.02× | 1.00× | +| fft Float32 393222 dims=1 | 5.87× | 1.50× | +| rfft Float64 54 dims=1 | 0.04× | 1.00× | +| rfft Float64 1048592 dims=1 | 4.11× | 0.99× | +| rfft Float32 10290 dims=1 | 1.15× | 1.00× | +| rfft Float64 512 dims=1 | 1.00× | 1.00× | +| fft Float64 2048×2048 dims=1,2 | 11.55× | 12.15× | +| fft Float64 131074 dims=1 | 3.15× | 2.24× | +| fft Float32 512×512 dims=1,2 | 11.96× | 9.09× | +| rfft Float64 1000 dims=1 | 0.16× | 1.01× | +| fft Float64 16384×64 dims=1 | 13.12× | 18.17× | +| fft Float64 256×256 dims=1,2 | 0.38× | 12.23× | +| rfft Float64 933120 dims=1 | 2.62× | 0.97× | +| fft Float32 1080 dims=1 | 0.26× | 1.00× | +| fft Float32 512 dims=1 | 0.06× | 0.99× | +| rfft Float32 196611 dims=1 | 3.21× | 1.02× | +| fft Float32 10290 dims=1 | 1.97× | 1.00× | +| rfft Float32 293201 dims=1 | 1.63× | 0.89× | +| fft Float64 21875 dims=1 | 5.16× | 1.00× | +| fft Float32 202 dims=1 | 0.05× | 1.00× | +| rfft Float64 524294 dims=1 | 4.31× | 0.99× | +| fft Float64 512×512 dims=1,2 | 12.07× | 13.51× | +| rfft Float32 64×64×64 dims=1,2,3 | 8.27× | 10.37× | +| rfft Float32 16 dims=1 | 0.99× | 1.00× | +| fft Float32 128×128×128 dims=1,2,3 | 12.29× | 11.96× | +| fft Float32 720 dims=1 | 0.14× | 1.01× | +| fft Float32 64×64×64 dims=1,2,3 | 9.05× | 9.83× | +| fft Float64 1000 dims=1 | 0.26× | 1.01× | +| rfft Float64 1433 dims=1 | 0.32× | 1.00× | +| fft Float64 512 dims=1 | 0.10× | 1.00× | +| fft Float64 262144 dims=1 | 11.88× | 8.33× | +| rfft Float32 120 dims=1 | 0.06× | 1.00× | +| fft Float32 2304 dims=1 | 0.30× | 0.99× | +| fft Float64 262576 dims=1 | 12.97× | 0.98× | +| rfft Float64 20507 dims=1 | 1.94× | 0.99× | +| fft Float64 1572882 dims=1 | 8.52× | 2.19× | +| rfft Float64 1024×1024 dims=1 | 12.14× | 16.59× | +| fft Float64 404 dims=1 | 0.15× | 1.00× | +| rfft Float32 1024 dims=1 | 0.14× | 1.00× | +| rfft Float64 46305 dims=1 | 3.62× | 1.00× | +| rfft Float32 131074 dims=1 | 1.52× | 1.00× | +| fft Float32 12297 dims=1 | 2.79× | 1.00× | +| rfft Float64 8198 dims=1 | 1.21× | 1.00× | +| fft Float32 711749 dims=1 | 5.20× | 3.79× | +| rfft Float32 65584 dims=1 | 3.97× | 1.01× | +| rfft Float64 593 dims=1 | 0.26× | 1.00× | +| fft Float64 65584 dims=1 | 12.48× | 0.98× | +| fft Float32 64×256 dims=2 | 2.15× | 1.00× | +| fft Float32 4860 dims=1 | 1.09× | 1.00× | +| fft Float32 101 dims=1 | 0.06× | 1.01× | +| rfft Float64 720 dims=1 | 0.10× | 0.98× | +| rfft Float32 8×8×8 dims=1,2,3 | 0.02× | 1.00× | +| rfft Float64 504 dims=1 | 0.07× | 1.01× | +| fft Float32 16×16×16 dims=1,2,3 | 0.46× | 1.00× | +| rfft Float32 1975680 dims=1 | 2.92× | 1.01× | +| fft Float64 2048 dims=1 | 0.45× | 1.00× | +| rfft Float64 41 dims=1 | 0.99× | 1.00× | +| fft Float64 4096×64 dims=1 | 11.33× | 17.54× | +| fft Float64 127×257 dims=1,2 | 11.15× | 1.00× | +| fft Float64 10290 dims=1 | 2.52× | 1.01× | +| rfft Float32 64×4096 dims=2 | 6.25× | 10.23× | +| rfft Float64 120779 dims=1 | 1.77× | 0.95× | +| fft Float32 16144 dims=1 | 8.28× | 1.00× | +| rfft Float32 524288 dims=1 | 1.79× | 2.60× | +| fft Float32 196611 dims=1 | 3.32× | 1.80× | +| rfft Float32 8 dims=1 | 0.93× | 0.99× | +| rfft Float64 8×8 dims=1,2 | 0.01× | 1.00× | +| rfft Float32 1048588 dims=1 | 5.11× | 1.01× | +| fft Float32 120 dims=1 | 0.01× | 1.00× | +| rfft Float64 60 dims=1 | 0.03× | 1.00× | +| rfft Float64 64×1009 dims=1,2 | 7.47× | 9.02× | +| fft Float32 303 dims=1 | 0.08× | 1.00× | +| rfft Float32 1572882 dims=1 | 6.20× | 0.95× | +| fft Float32 49757 dims=1 | 2.70× | 1.01× | +| fft Float64 6054 dims=1 | 2.76× | 1.00× | +| fft Float64 16396 dims=1 | 4.38× | 0.99× | +| rfft Float64 262144 dims=1 | 2.01× | 0.98× | +| rfft Float32 65536 dims=1 | 1.07× | 1.01× | +| fft Float64 933120 dims=1 | 9.02× | 9.65× | +| rfft Float32 61 dims=1 | 1.00× | 1.00× | +| rfft Float32 29 dims=1 | 0.99× | 0.99× | +| fft Float64 3491 dims=1 | 1.01× | 1.00× | +| rfft Float32 131072 dims=1 | 1.15× | 0.97× | +| fft Float64 593 dims=1 | 0.15× | 1.00× | +| fft Float32 64×64 dims=1 | 0.43× | 1.00× | +| fft Float64 64×64 dims=1 | 0.70× | 1.00× | +| fft Float64 1009×64 dims=1,2 | 12.45× | 14.70× | +| rfft Float32 64 dims=1 | 1.00× | 1.00× | +| fft Float64 37 dims=1 | 0.03× | 1.00× | +| fft Float32 262148 dims=1 | 4.38× | 1.85× | +| fft Float64 12 dims=1 | 0.98× | 0.99× | +| fft Float64 49757 dims=1 | 2.99× | 0.97× | +| rfft Float32 2048 dims=1 | 1.00× | 1.01× | +| rfft Float64 21875 dims=1 | 2.84× | 1.00× | +| rfft Float64 127×257 dims=1,2 | 1.18× | 1.00× | +| rfft Float64 23 dims=1 | 0.98× | 1.00× | +| fft Float32 79 dims=1 | 0.02× | 1.00× | +| fft Float32 32×32×32 dims=1,2,3 | 3.17× | 3.83× | +| fft Float32 2018 dims=1 | 0.41× | 1.00× | +| fft Float32 49233 dims=1 | 5.30× | 0.99× | +| rfft Float32 6054 dims=1 | 0.80× | 1.00× | +| fft Float64 101 dims=1 | 0.06× | 0.99× | +| rfft Float64 98466 dims=1 | 4.18× | 0.98× | +| fft Float32 2097152 dims=1 | 16.31× | 11.42× | +| rfft Float32 786441 dims=1 | 1.64× | 0.92× | +| rfft Float32 79 dims=1 | 1.00× | 1.00× | +| rfft Float64 1009×64 dims=1,2 | 0.21× | 5.42× | +| fft Float64 16 dims=1 | 0.98× | 1.00× | +| fft Float64 64 dims=1 | 0.02× | 1.00× | +| fft Float64 202 dims=1 | 0.06× | 0.99× | +| rfft Float64 196611 dims=1 | 3.17× | 0.95× | +| fft Float64 2097152 dims=1 | 14.99× | 9.90× | +| fft Float32 16 dims=1 | 1.01× | 0.98× | +| fft Float32 2048×2048 dims=1,2 | 13.55× | 12.17× | +| rfft Float64 4096×64 dims=1 | 10.22× | 15.95× | +| rfft Float64 49757 dims=1 | 2.09× | 1.04× | +| rfft Float64 128 dims=1 | 0.07× | 0.99× | +| fft Float32 593 dims=1 | 0.10× | 1.00× | +| rfft Float32 17 dims=1 | 0.99× | 1.00× | +| fft Float32 29 dims=1 | 0.99× | 1.00× | +| fft Float32 65644 dims=1 | 6.42× | 1.00× | +| fft Float64 64×64 dims=2 | 0.74× | 0.99× | +| fft Float32 20507 dims=1 | 3.70× | 0.98× | +| rfft Float64 65584 dims=1 | 3.84× | 0.99× | +| rfft Float32 64×1024 dims=2 | 4.02× | 7.73× | +| fft Float64 64×4096 dims=2 | 12.01× | 15.19× | +| rfft Float32 128×128 dims=1,2 | 1.05× | 1.01× | +| rfft Float64 4167450 dims=1 | 4.77× | 0.99× | +| fft Float64 1616 dims=1 | 1.43× | 1.00× | +| fft Float32 8×8×8 dims=1,2,3 | 0.04× | 1.00× | +| rfft Float32 25 dims=1 | 0.98× | 1.00× | +| fft Float64 65644 dims=1 | 6.75× | 0.99× | +| fft Float32 207360 dims=1 | 6.97× | 6.53× | +| rfft Float32 4860 dims=1 | 0.50× | 1.00× | +| rfft Float64 16×16 dims=1,2 | 0.02× | 0.99× | +| fft Float64 16×16×16 dims=1,2,3 | 0.63× | 1.00× | +| rfft Float32 24594 dims=1 | 2.52× | 1.00× | +| rfft Float32 2018 dims=1 | 0.21× | 1.00× | +| fft Float64 73 dims=1 | 0.05× | 1.02× | +| fft Float32 256×64 dims=1 | 2.55× | 1.00× | +| rfft Float32 31 dims=1 | 0.99× | 1.00× | +| rfft Float64 3491 dims=1 | 0.65× | 1.00× | +| fft Float32 98466 dims=1 | 7.55× | 0.99× | +| rfft Float32 8443 dims=1 | 1.08× | 1.01× | +| rfft Float32 16396 dims=1 | 1.86× | 0.99× | +| rfft Float64 12 dims=1 | 0.99× | 1.01× | +| fft Float32 8 dims=1 | 0.96× | 0.99× | +| rfft Float64 4036 dims=1 | 0.61× | 1.01× | +| rfft Float32 512 dims=1 | 0.13× | 1.01× | +| rfft Float32 49233 dims=1 | 3.90× | 0.98× | +| rfft Float64 606 dims=1 | 0.12× | 1.00× | +| rfft Float64 16384×64 dims=1 | 11.02× | 15.67× | +| fft Float32 37 dims=1 | 0.01× | 1.00× | +| fft Float32 131074 dims=1 | 2.31× | 1.93× | +| fft Float64 606 dims=1 | 0.27× | 1.00× | +| fft Float32 64 dims=1 | 0.91× | 1.00× | +| fft Float64 1000000 dims=1 | 18.79× | 10.47× | +| fft Float64 393222 dims=1 | 7.02× | 1.80× | +| fft Float32 21875 dims=1 | 3.81× | 0.99× | +| rfft Float64 49233 dims=1 | 1.54× | 0.99× | +| rfft Float32 1024×1024 dims=1,2 | 11.81× | 11.83× | +| rfft Float64 1000×1000 dims=1,2 | 10.50× | 13.95× | +| fft Float32 6054 dims=1 | 2.09× | 1.00× | +| rfft Float32 112 dims=1 | 0.04× | 1.00× | +| rfft Float32 606 dims=1 | 0.10× | 1.02× | +| rfft Float32 16384 dims=1 | 0.84× | 1.01× | +| rfft Float32 46305 dims=1 | 3.56× | 1.00× | +| fft Float64 128×128 dims=1,2 | 2.64× | 0.96× | +| fft Float32 1024 dims=1 | 0.13× | 1.02× | +| fft Float32 293201 dims=1 | 3.15× | 3.36× | +| rfft Float64 262148 dims=1 | 2.06× | 0.95× | +| rfft Float64 2304 dims=1 | 0.31× | 1.00× | +| rfft Float64 71 dims=1 | 0.99× | 0.98× | +| fft Float64 293201 dims=1 | 3.14× | 3.72× | +| rfft Float32 71 dims=1 | 1.00× | 0.99× | +| rfft Float64 243 dims=1 | 0.03× | 1.01× | +| fft Float32 25 dims=1 | 1.04× | 1.00× | +| rfft Float64 2018 dims=1 | 0.28× | 1.00× | +| rfft Float64 256 dims=1 | 0.12× | 1.00× | +| rfft Float64 1048588 dims=1 | 5.67× | 0.98× | +| rfft Float64 25 dims=1 | 0.98× | 0.99× | +| rfft Float64 32 dims=1 | 0.03× | 0.99× | +| fft Float32 4194304 dims=1 | 12.22× | 11.88× | +| rfft Float32 2097152 dims=1 | 2.45× | 3.79× | +| fft Float64 1048588 dims=1 | 8.93× | 2.81× | +| fft Float32 32×32 dims=1,2 | 0.09× | 1.01× | +| rfft Float32 64×64 dims=1,2 | 0.34× | 1.00× | +| rfft Float64 441000 dims=1 | 2.71× | 1.00× | +| rfft Float32 262144 dims=1 | 1.83× | 1.00× | +| fft Float64 243 dims=1 | 0.05× | 1.00× | +| fft Float64 71 dims=1 | 0.02× | 0.98× | +| fft Float64 360 dims=1 | 0.07× | 1.02× | +| rfft Float64 1024×64 dims=1 | 7.03× | 15.06× | +| rfft Float32 7 dims=1 | 0.95× | 0.99× | +| fft Float64 2018 dims=1 | 0.65× | 1.00× | +| fft Float32 54 dims=1 | 0.01× | 1.00× | +| rfft Float32 64×65536 dims=2 | 11.38× | 10.70× | +| rfft Float64 131072 dims=1 | 1.37× | 0.95× | +| rfft Float64 393222 dims=1 | 2.60× | 1.07× | +| rfft Float32 1433 dims=1 | 0.30× | 1.00× | +| rfft Float64 202 dims=1 | 0.06× | 1.01× | +| fft Float64 1048576 dims=1 | 17.35× | 10.02× | +| fft Float64 120 dims=1 | 0.03× | 1.00× | +| rfft Float64 112 dims=1 | 0.06× | 1.00× | +| rfft Float32 2304 dims=1 | 0.23× | 1.00× | +| rfft Float64 404 dims=1 | 0.08× | 1.00× | +| rfft Float32 720 dims=1 | 0.06× | 1.00× | +| rfft Float32 4167450 dims=1 | 4.10× | 0.91× | +| fft Float32 64×4096 dims=2 | 7.74× | 1.62× | +| rfft Float32 711749 dims=1 | 1.77× | 0.93× | +| rfft Float32 243 dims=1 | 0.03× | 1.00× | +| rfft Float64 128×128 dims=1,2 | 1.27× | 1.00× | +| rfft Float64 720×480 dims=1,2 | 10.52× | 12.77× | +| rfft Float64 64×64 dims=1 | 0.47× | 1.00× | +| fft Float32 933120 dims=1 | 8.72× | 8.80× | +| rfft Float64 1616 dims=1 | 0.46× | 1.00× | +| fft Float32 4096×64 dims=1 | 10.92× | 15.82× | +| rfft Float32 128 dims=1 | 0.76× | 1.00× | +| rfft Float32 23 dims=1 | 0.99× | 1.00× | +| fft Float64 1080 dims=1 | 0.28× | 1.00× | +| rfft Float64 120 dims=1 | 0.09× | 1.00× | +| fft Float64 98466 dims=1 | 7.94× | 0.99× | +| fft Float32 64×64 dims=2 | 0.42× | 0.98× | +| fft Float32 16384×64 dims=1 | 12.51× | 15.17× | +| rfft Float64 1080 dims=1 | 0.15× | 1.01× | +| fft Float64 32×32 dims=1,2 | 0.14× | 1.00× | +| rfft Float64 128×128×128 dims=1,2,3 | 13.36× | 14.48× | +| rfft Float32 1616 dims=1 | 0.40× | 1.00× | +| rfft Float64 101 dims=1 | 1.00× | 0.99× | +| fft Float64 4167450 dims=1 | 11.00× | 9.53× | +| rfft Float64 4096 dims=1 | 1.00× | 1.00× | +| fft Float64 4860 dims=1 | 1.45× | 1.00× | +| fft Float32 131072 dims=1 | 8.71× | 5.65× | +| rfft Float32 101 dims=1 | 1.00× | 1.00× | +| rfft Float64 16144 dims=1 | 2.64× | 1.00× | +| fft Float32 1975680 dims=1 | 8.94× | 11.66× | +| rfft Float64 1572882 dims=1 | 5.87× | 1.01× | +| rfft Float32 21875 dims=1 | 2.71× | 1.00× | +| rfft Float64 1000000 dims=1 | 4.20× | 1.00× | +| rfft Float64 64×64 dims=1,2 | 0.40× | 0.99× | +| rfft Float32 20507 dims=1 | 1.83× | 0.99× | +| rfft Float32 1048592 dims=1 | 3.63× | 1.03× | +| rfft Float64 262576 dims=1 | 5.32× | 1.01× | +| fft Float64 441000 dims=1 | 9.61× | 11.00× | +| rfft Float32 504 dims=1 | 0.05× | 0.99× | +| rfft Float64 73 dims=1 | 1.00× | 1.00× | +| rfft Float64 256×4096 dims=1 | 10.77× | 16.41× | +| fft Float32 64×65536 dims=2 | 11.83× | 1.50× | +| fft Float64 25 dims=1 | 0.01× | 1.00× | +| fft Float64 12297 dims=1 | 2.88× | 1.00× | +| fft Float32 60 dims=1 | 0.02× | 1.00× | +| fft Float64 64×65536 dims=2 | 12.09× | 11.29× | +| rfft Float32 64×256 dims=2 | 2.10× | 0.99× | +| fft Float64 256 dims=1 | 0.05× | 1.00× | +| rfft Float64 31 dims=1 | 0.99× | 1.00× | +| fft Float32 3491 dims=1 | 0.81× | 1.00× | +| rfft Float32 8×8 dims=1,2 | 0.01× | 1.00× | +| fft Float64 64×64 dims=1,2 | 0.62× | 1.00× | +| fft Float64 256×64 dims=1 | 4.00× | 1.00× | +| fft Float64 4096 dims=1 | 0.88× | 1.00× | +| rfft Float64 64×64 dims=2 | 0.46× | 1.00× | +| fft Float64 32×32×32 dims=1,2,3 | 4.57× | 10.79× | +| rfft Float32 16×16 dims=1,2 | 0.02× | 1.02× | +| rfft Float64 360 dims=1 | 0.05× | 1.01× | +| fft Float32 128×128 dims=1,2 | 1.63× | 0.99× | +| rfft Float32 360 dims=1 | 0.04× | 1.02× | +| fft Float32 12 dims=1 | 0.93× | 0.99× | +| fft Float64 112 dims=1 | 0.03× | 1.00× | +| fft Float64 1975680 dims=1 | 8.01× | 9.96× | +| fft Float32 31 dims=1 | 0.68× | 1.00× | +| fft Float64 61 dims=1 | 0.04× | 1.00× | +| fft Float32 61 dims=1 | 0.04× | 1.00× | +| rfft Float32 202 dims=1 | 0.06× | 1.00× | +| fft Float64 251 dims=1 | 0.07× | 1.00× | +| fft Float32 441000 dims=1 | 9.64× | 10.28× | +| rfft Float32 43 dims=1 | 1.00× | 1.00× | +| rfft Float64 251 dims=1 | 0.04× | 1.00× | +| rfft Float32 32768 dims=1 | 1.11× | 1.01× | +| rfft Float32 64×16384 dims=2 | 8.68× | 12.24× | +| fft Float32 8192 dims=1 | 1.36× | 1.00× | +| fft Float64 64×16384 dims=2 | 15.39× | 16.41× | +| rfft Float32 54 dims=1 | 0.06× | 1.00× | +| fft Float32 1616 dims=1 | 0.87× | 1.00× | +| fft Float32 404 dims=1 | 0.13× | 1.00× | +| rfft Float32 65644 dims=1 | 3.05× | 1.01× | +| rfft Float64 2048×2048 dims=1,2 | 13.09× | 15.62× | +| fft Float64 65536×64 dims=1 | 12.90× | 12.96× | +| fft Float64 98304 dims=1 | 8.72× | 0.94× | +| rfft Float32 65536×64 dims=1 | 12.26× | 15.02× | +| fft Float32 120779 dims=1 | 3.77× | 0.97× | +| rfft Float32 1024×64 dims=1 | 5.50× | 13.70× | +| fft Float64 8192 dims=1 | 2.23× | 0.92× | +| rfft Float32 120779 dims=1 | 1.74× | 0.97× | +| rfft Float64 256×256 dims=1,2 | 0.10× | 9.46× | +| fft Float64 20507 dims=1 | 2.76× | 0.99× | +| fft Float32 1024×1024 dims=1,2 | 13.15× | 11.27× | +| rfft Float64 1727797 dims=1 | 2.28× | 0.99× | +| rfft Float64 65644 dims=1 | 3.48× | 1.00× | +| rfft Float64 524288 dims=1 | 1.73× | 3.04× | +| rfft Float32 207360 dims=1 | 2.46× | 1.00× | +| fft Float32 4036 dims=1 | 1.42× | 1.00× | +| rfft Float64 64×65536 dims=2 | 12.29× | 11.86× | +| rfft Float64 8192 dims=1 | 0.74× | 1.00× | +| rfft Float64 24594 dims=1 | 2.59× | 0.98× | +| fft Float64 196611 dims=1 | 4.22× | 2.26× | +| rfft Float64 16 dims=1 | 0.99× | 1.00× | +| fft Float32 1048592 dims=1 | 10.05× | 1.67× | +| rfft Float64 32×32×32 dims=1,2,3 | 2.76× | 1.33× | +| rfft Float64 8443 dims=1 | 1.05× | 1.00× | +| fft Float32 32 dims=1 | 0.99× | 1.00× | +| rfft Float32 12 dims=1 | 0.98× | 0.99× | +| fft Float64 65536 dims=1 | 7.67× | 1.00× | +| fft Float64 128 dims=1 | 0.03× | 1.00× | +| rfft Float64 2097152 dims=1 | 7.12× | 3.70× | +| fft Float32 32768 dims=1 | 5.59× | 1.01× | +| fft Float32 8198 dims=1 | 1.81× | 0.99× | +| rfft Float32 2048×2048 dims=1,2 | 12.34× | 16.35× | +| fft Float32 64×1024 dims=2 | 3.77× | 1.60× | +| fft Float64 1433 dims=1 | 0.45× | 1.00× | +| rfft Float32 4194304 dims=1 | 3.11× | 3.49× | +| fft Float64 64×1024 dims=2 | 11.32× | 15.53× | +| fft Float64 8 dims=1 | 0.95× | 0.98× | +| rfft Float64 711749 dims=1 | 1.97× | 0.92× | +| rfft Float32 64×64 dims=1 | 0.46× | 1.00× | +| rfft Float64 256×64 dims=1 | 2.56× | 0.99× | +| fft Float32 360 dims=1 | 0.05× | 1.00× | +| fft Float64 303 dims=1 | 0.09× | 1.00× | +| rfft Float32 933120 dims=1 | 3.04× | 1.02× | +| fft Float32 256×256 dims=1,2 | 7.69× | 5.20× | +| fft Float32 524288 dims=1 | 11.06× | 9.11× | +| rfft Float64 32×32 dims=1,2 | 0.07× | 1.00× | +| rfft Float32 4036 dims=1 | 0.44× | 1.00× | +| fft Float64 2304 dims=1 | 0.67× | 1.01× | +| fft Float32 16396 dims=1 | 4.29× | 1.00× | +| rfft Float64 16×16×16 dims=1,2,3 | 0.38× | 0.99× | +| fft Float32 251 dims=1 | 0.06× | 0.99× | +| fft Float32 98304 dims=1 | 8.55× | 1.00× | +| fft Float32 46305 dims=1 | 4.03× | 1.00× | +| rfft Float32 16144 dims=1 | 2.24× | 1.00× | diff --git a/benchmark/compare3/aarch64/stack-threads-nd/ffta_t1.json b/benchmark/compare3/aarch64/stack-threads-nd/ffta_t1.json new file mode 100644 index 0000000..b50603a --- /dev/null +++ b/benchmark/compare3/aarch64/stack-threads-nd/ffta_t1.json @@ -0,0 +1,10996 @@ +{ + "complete": true, + "meta": { + "arch": "aarch64", + "cpu": "neoverse-n1", + "date": "2026-08-30T23:25:53.988", + "impl": "ffta", + "julia": "1.12.6", + "scope": { + "classes": [ + "pow2", + "smooth", + "prime", + "awkward" + ], + "kinds": [ + "fft", + "rfft" + ], + "maxlog2": 22, + "measure": true, + "only": [ + "1d", + "nd", + "batched", + "threads" + ], + "sizes": [] + }, + "seconds": 0.5, + "threads": 1, + "version": "FFTA.jl 0.3.1 @ 4f9ff88" + }, + "results": [ + { + "T": "Float64", + "api": "mul!", + "class": "pow2", + "dims": 1, + "exec_alloc": 0, + "exec_min": 3.84e-8, + "key": "fft Float64 8 dims=1", + "kind": "fft", + "measure": false, + "n": 8, + "norm": 7.309465464900843, + "nthreads": 1, + "plan_min": 4.5411764705882356e-7, + "shape": "1d", + "size": [ + 8 + ], + "sum_im": 0.8256906191951683, + "sum_re": -5.70079646874149 + }, + { + "T": "Float64", + "api": "mul!", + "class": "pow2", + "dims": 1, + "exec_alloc": 0, + "exec_min": 5.55688622754491e-8, + "key": "rfft Float64 8 dims=1", + "kind": "rfft", + "measure": false, + "n": 8, + "norm": 6.916282852095683, + "nthreads": 1, + "plan_min": 4.177777777777778e-7, + "shape": "1d", + "size": [ + 8 + ], + "sum_im": 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