nanmedian might be slower than a naive implementation

[Firionus]

We were discussing some NaN-issues in Firionus/FastRunningMedian.jl#21 and @berjine noticed that nanmedian seems slower than a quick workaround implementation of mine.

script.jl:

using BenchmarkTools, NaNStatistics, Statistics

x = rand(10^6)
for i in eachindex(x)
    if rand() > .99
        x[i] = NaN
    end     
end

println("NaN: $(count(x->x===NaN, x)) of $(length(x))")

function median_ignorenan(x)
    mask = @. !isnan(x)
    masked = @view x[mask]
    masked |> isempty && return NaN
    median(masked)
end

println("\nNaNStatiscs nanmedian:")
display(@benchmark(nanmedian($x)))

println("\nnaive median_ignorenan:")
display(@benchmark(median_ignorenan($x)))

julia> include("script.jl")
NaN: 10079 of 1000000

NaNStatiscs nanmedian:
BenchmarkTools.Trial: 389 samples with 1 evaluation.
 Range (min … max):  11.439 ms … 20.864 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     12.408 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   12.856 ms ±  1.038 ms  ┊ GC (mean ± σ):  1.11% ± 2.53%

              ▂██▅▁                                            
  ▂▂▁▃▄▃▄▅▅▇▇██████▄▃▂▃▃▁▁▁▃▃▃▃▂▁▃▄▆▄▄▃▂▃▃▃▃▃▃▃▃▃▃▃▂▄▂▃▂▂▄▄▃▃ ▃
  11.4 ms         Histogram: frequency by time        15.3 ms <

 Memory estimate: 7.63 MiB, allocs estimate: 2.

naive median_ignorenan:
BenchmarkTools.Trial: 618 samples with 1 evaluation.
 Range (min … max):  7.630 ms …  11.889 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     7.725 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   7.799 ms ± 351.422 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

    ▆█▄                                                        
  ▅█████▅▆▄▃▃▄▃▃▃▃▃▂▃▂▃▁▂▂▂▁▂▂▂▁▂▁▁▁▁▁▁▁▁▁▁▁▁▁▂▁▁▁▁▁▁▂▁▁▁▁▁▁▂ ▃
  7.63 ms         Histogram: frequency by time        8.98 ms <

 Memory estimate: 22.78 MiB, allocs estimate: 10.

julia> versioninfo()
Julia Version 1.9.1
Commit 147bdf428cd (2023-06-07 08:27 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Core(TM) i7-10510U CPU @ 1.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, skylake)
  Threads: 1 on 8 virtual cores
Environment:
  JULIA_IMAGE_THREADS = 1

(nanmedian_bench) pkg> status
Status `~/Documents/temp/nanmedian_bench/Project.toml`
  [6e4b80f9] BenchmarkTools v1.3.2
  [b946abbf] NaNStatistics v0.6.30

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I'm not familiar enough with this library to comment whether this is expected or not. Just wanted to give you a heads up 😊

[brenhinkeller]

Base's sort has gotten really fast lately, so it may be worth reworking this to use that instead of rolling our own here..

[brenhinkeller]

c66fc41 mostly fixes this by switching to Base's partialsort! for large arrays (>20k elements) -- our quickselect! is faster for small arrays but for larger arrays it starts to lag significantly. Base median seems to still edge out for very large arrays but the difference is smaller now at least.

julia> println("\nNaNStatiscs nanmedian:")

NaNStatiscs nanmedian:

julia> display(@benchmark(nanmedian($x)))

BenchmarkTools.Trial: 720 samples with 1 evaluation.
 Range (min … max):  6.135 ms …  10.565 ms  ┊ GC (min … max): 0.00% … 32.23%
 Time  (median):     6.662 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   6.941 ms ± 633.197 μs  ┊ GC (mean ± σ):  6.44% ±  7.42%

     ▃▇█▅▄▁▁
  ▂▃▇███████▇▄▃▅▃▃▃▃▄▄▅▇▇▇▇█▇▅▆▄▅▄▃▄▁▄▃▃▃▁▂▂▂▃▁▂▂▂▂▂▁▁▂▂▂▁▂▁▂ ▄
  6.14 ms         Histogram: frequency by time        9.06 ms <

 Memory estimate: 18.96 MiB, allocs estimate: 6.

julia> println("\nnaive median_ignorenan:")

naive median_ignorenan:

julia> display(@benchmark(median_ignorenan($x)))
BenchmarkTools.Trial: 754 samples with 1 evaluation.
 Range (min … max):  5.478 ms …   9.034 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     5.722 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   5.771 ms ± 240.265 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     ▂█▆▂▇▂▂▅▄▂▁▁▅▂▁▁ ▁  ▂     ▁
  ▄▆████████████████████▇████▄██▅▆█▆█▄▄▄▆▄▄▄▃▃▄▃▄▃▃▂▄▁▁▃▂▂▂▃▃ ▅
  5.48 ms         Histogram: frequency by time        6.36 ms <

 Memory estimate: 22.78 MiB, allocs estimate: 10.

[brenhinkeller]

and for smaller arrays we're still looking good I think

julia> display(@benchmark(nanmedian($x)))

BenchmarkTools.Trial: 10000 samples with 9 evaluations.
 Range (min … max):  2.208 μs … 333.519 μs  ┊ GC (min … max):  0.00% … 98.69%
 Time  (median):     2.644 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   3.081 μs ±  10.022 μs  ┊ GC (mean ± σ):  11.62% ±  3.55%

         ▄█▇▁
  ▆▄▂▂▂▂▅████▅▆▇▇███▅▅▄▄▃▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂ ▃
  2.21 μs         Histogram: frequency by time        4.36 μs <

 Memory estimate: 7.94 KiB, allocs estimate: 1.

julia> println("\nnaive median_ignorenan:")

naive median_ignorenan:

julia> display(@benchmark(median_ignorenan($x)))
BenchmarkTools.Trial: 10000 samples with 7 evaluations.
 Range (min … max):  4.060 μs … 827.512 μs  ┊ GC (min … max):  0.00% … 98.91%
 Time  (median):     5.482 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   6.980 μs ±  21.866 μs  ┊ GC (mean ± σ):  19.70% ±  6.38%

               ▃█▅▃▁▁▂
  ▆▆▃▃▃▂▂▁▁▁▁▂▄████████▇▆▆▅▅▄▄▃▄▄▃▃▂▂▂▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▃
  4.06 μs         Histogram: frequency by time        8.65 μs <

 Memory estimate: 28.03 KiB, allocs estimate: 7.