Use exact multinomial for bulk rand

[Tortar]

still wip, but it improves benchmarks locally, we need some tests in CI for this too

[github-actions]

Benchmark Results

	ca5d92d	58844fb	ca5d92d / 58844fb
TTFX excluding time to load	8.6 ± 0 ms	8.79 ± 0 ms	1.08,0.958,0.979
code size in bytes	1.33e+04 ± 0 h	1.56e+04 ± 0 h	0.851,0.851,0.849
code size in lines	459 ± 0 h	565 ± 0 h	0.817,0.817,0.812
code size in syntax nodes	3.44e+03 ± 0 h	4.18e+03 ± 0 h	0.823,0.823,0.822
constructor n=100 σ=0.1	6.15 ± 2.6 μs	9.06 ± 1.1 μs	0.665,0.95,0.679
constructor n=100 σ=1.0	6.88 ± 2.8 μs	7.03 ± 2.5 μs	1.07,1.01,0.979
constructor n=100 σ=10.0	6.72 ± 0.28 μs	7.01 ± 0.43 μs	1.08,1.01,0.958
constructor n=100 σ=100.0	7.07 ± 3.1 μs	6.84 ± 2.1 μs	1.25,0.976,1.03
constructor n=1000 σ=0.1	0.0433 ± 0.0017 ms	0.0454 ± 0.0052 ms	1.04,0.977,0.954
constructor n=1000 σ=1.0	0.0453 ± 0.0015 ms	0.045 ± 0.0014 ms	1.04,0.979,1.01
constructor n=1000 σ=10.0	0.0585 ± 0.0038 ms	0.0574 ± 0.0032 ms	1.04,0.985,1.02
constructor n=1000 σ=100.0	0.0595 ± 0.0015 ms	0.0591 ± 0.0012 ms	1.04,0.991,1.01
constructor n=10000 σ=0.1	0.432 ± 0.032 ms	0.428 ± 0.024 ms	1.09,0.984,1.01
constructor n=10000 σ=1.0	0.435 ± 0.019 ms	0.438 ± 0.022 ms	1.04,0.971,0.994
constructor n=10000 σ=10.0	0.463 ± 0.023 ms	0.461 ± 0.02 ms	1.03,0.971,1
constructor n=10000 σ=100.0	0.579 ± 0.02 ms	0.576 ± 0.023 ms	1.01,0.994,1
delete ∘ rand n=100 σ=0.1	4.71 ± 0.19 μs	4.68 ± 0.2 μs	1,0.996,1.01
delete ∘ rand n=100 σ=1.0	5 ± 0.2 μs	4.96 ± 0.19 μs	1,0.998,1.01
delete ∘ rand n=100 σ=10.0	5.18 ± 0.19 μs	5.16 ± 0.19 μs	0.998,0.996,1
delete ∘ rand n=100 σ=100.0	9.31 ± 0.77 μs	9.23 ± 0.74 μs	1.01,0.998,1.01
delete ∘ rand n=1000 σ=0.1	0.0467 ± 0.00088 ms	0.0463 ± 0.00079 ms	1.01,0.997,1.01
delete ∘ rand n=1000 σ=1.0	0.051 ± 0.0016 ms	0.0506 ± 0.0016 ms	1.01,0.999,1.01
delete ∘ rand n=1000 σ=10.0	0.052 ± 0.00091 ms	0.0516 ± 0.00086 ms	1,0.999,1.01
delete ∘ rand n=1000 σ=100.0	0.0612 ± 0.0014 ms	0.0608 ± 0.0012 ms	1,1,1.01
delete ∘ rand n=10000 σ=0.1	0.503 ± 0.011 ms	0.5 ± 0.012 ms	1.01,0.982,1.01
delete ∘ rand n=10000 σ=1.0	0.545 ± 0.0088 ms	0.542 ± 0.011 ms	1,0.996,1.01
delete ∘ rand n=10000 σ=10.0	0.556 ± 0.019 ms	0.546 ± 0.011 ms	1,0.994,1.02
delete ∘ rand n=10000 σ=100.0	0.546 ± 0.011 ms	0.542 ± 0.01 ms	1.01,1,1.01
empty constructor	1.92 ± 0.29 μs	2.02 ± 0.53 μs	1.18,1.01,0.948
intermixed_h n=100 σ=0.1	14.9 ± 1.7 μs	15 ± 1.9 μs	1.02,1.02,0.994
intermixed_h n=100 σ=1.0	12.1 ± 1.1 μs	12.1 ± 1.3 μs	1.07,0.978,1
intermixed_h n=100 σ=10.0	11.7 ± 1.2 μs	11.8 ± 1.4 μs	1.03,0.966,0.998
intermixed_h n=100 σ=100.0	13.2 ± 1.6 μs	13.2 ± 1.6 μs	1.06,0.986,1
intermixed_h n=1000 σ=0.1	0.113 ± 0.01 ms	0.11 ± 0.0097 ms	1.01,0.986,1.03
intermixed_h n=1000 σ=1.0	0.114 ± 0.0084 ms	0.114 ± 0.0095 ms	1.02,0.997,1
intermixed_h n=1000 σ=10.0	0.109 ± 0.0088 ms	0.108 ± 0.0087 ms	1.01,0.988,1.01
intermixed_h n=1000 σ=100.0	0.121 ± 0.014 ms	0.122 ± 0.014 ms	1.01,0.984,0.992
intermixed_h n=10000 σ=0.1	1.18 ± 0.21 ms	1.22 ± 0.16 ms	0.976,0.977,0.969
intermixed_h n=10000 σ=1.0	1.21 ± 0.15 ms	1.21 ± 0.17 ms	0.995,0.976,1
intermixed_h n=10000 σ=10.0	1.14 ± 0.2 ms	1.09 ± 0.16 ms	0.991,0.982,1.04
intermixed_h n=10000 σ=100.0	1.2 ± 0.24 ms	1.19 ± 0.17 ms	1.01,0.972,1.01
pathological 1	0.0456 ± 0.0002 μs	0.0457 ± 0.00022 μs	0.999,0.993,0.999
pathological 1′	0.212 ± 0.0017 μs	0.2 ± 0.0018 μs	1.04,1.04,1.06
pathological 2	0.0629 ± 0.0003 μs	0.063 ± 0.00026 μs	1,0.999,0.998
pathological 2′	0.182 ± 0.0016 μs	0.177 ± 0.0033 μs	1,1.04,1.03
pathological 3	19.5 ± 0.36 ns	18.6 ± 0.24 ns	1,1.01,1.05
pathological 4	0.0623 ± 0.0003 μs	0.0624 ± 0.00028 μs	0.999,1,0.999
pathological 4′	0.241 ± 0.0016 μs	0.219 ± 0.0029 μs	1.07,1.08,1.1
pathological 5a	0.0558 ± 0.00011 μs	0.0448 ± 0.0002 μs	1,0.995,1.25
pathological 5b	0.045 ± 0.00023 μs	0.0451 ± 0.00023 μs	1,1,0.998
pathological 5b′	0.474 ± 0.0069 μs	0.451 ± 0.0084 μs	1.08,1.06,1.05
sample (bulk) n=1000 k=10000 σ=0.1	0.239 ± 0.049 ms	0.152 ± 0.043 ms	1.54,1.38,1.57
sample (bulk) n=1000 k=10000 σ=1.0	0.332 ± 0.023 ms	0.204 ± 0.02 ms	1.68,1.61,1.63
sample (bulk) n=1000 k=10000 σ=10.0	0.202 ± 0.06 ms	0.152 ± 0.029 ms	1.26,1.31,1.33
sample (bulk) n=1000 k=10000 σ=100.0	0.166 ± 0.042 ms	0.168 ± 0.045 ms	0.994,1.02,0.986
sample (bulk) n=1000 k=100000 σ=0.1	2.46 ± 0.41 ms	1.44 ± 0.66 ms	1.32,1.62,1.7
sample (bulk) n=1000 k=100000 σ=1.0	3.31 ± 0.25 ms	1.95 ± 0.17 ms	1.76,1.76,1.7
sample (bulk) n=1000 k=100000 σ=10.0	1.95 ± 0.42 ms	1.4 ± 0.26 ms	1.48,1.46,1.39
sample (bulk) n=1000 k=100000 σ=100.0	1.59 ± 0.39 ms	1.51 ± 0.34 ms	1,1.08,1.05
sample (bulk) n=1000 k=1000000 σ=0.1	23.4 ± 0.13 ms	19.2 ± 3.4 ms	1.46,1.62,1.22
sample (bulk) n=1000 k=1000000 σ=1.0	0.0392 ± 0.0015 s	19.4 ± 1 ms	1.66,1.63,2.02
sample (bulk) n=1000 k=1000000 σ=10.0	20.4 ± 2.8 ms	14 ± 2.1 ms	1.45,1.49,1.46
sample (bulk) n=1000 k=1000000 σ=100.0	15.9 ± 3.4 ms	17.8 ± 2.1 ms	1.04,1.13,0.892
sample (bulk) n=1000000 k=10000 σ=0.1	0.628 ms	0.255 ms	2.91,2.27,2.47
sample (bulk) n=1000000 k=10000 σ=1.0	1.04 ms	0.372 ms	3.58,2.25,2.79
sample (bulk) n=1000000 k=10000 σ=10.0	0.179 ms	0.209 ms	1.04,1.18,0.857
sample (bulk) n=1000000 k=10000 σ=100.0	0.238 ms	0.19 ms	1.14,0.318,1.25
sample (bulk) n=1000000 k=100000 σ=0.1	5.77 ± 0.3 ms	3.1 ± 0.31 ms	2.58,1.95,1.86
sample (bulk) n=1000000 k=100000 σ=1.0	7.39 ± 0.25 ms	3.12 ± 0.031 ms	3.35,2.45,2.37
sample (bulk) n=1000000 k=100000 σ=10.0	2.8 ± 0.15 ms	1.41 ± 0.1 ms	1.89,1.86,1.98
sample (bulk) n=1000000 k=100000 σ=100.0	1.91 ± 0.054 ms	2 ± 0.01 ms	0.933,0.848,0.953
sample (bulk) n=1000000 k=1000000 σ=0.1	0.0399 ± 0.0013 s	20.8 ± 0.21 ms	3.57,1.83,1.92
sample (bulk) n=1000000 k=1000000 σ=1.0	0.0604 s	23.1 ms	3.07,2.39,2.61
sample (bulk) n=1000000 k=1000000 σ=10.0	21.2 ± 5.1 ms	14.9 ± 0.26 ms	1.94,2.91,1.43
sample (bulk) n=1000000 k=1000000 σ=100.0	14.4 ms	13.3 ms	0.716,1.36,1.08
sample (single) n=100 σ=0.1	28 ± 0.64 ns	27.5 ± 0.61 ns	1.02,1.03,1.02
sample (single) n=100 σ=1.0	0.0325 ± 0.0024 μs	0.0321 ± 0.0023 μs	0.998,1.02,1.01
sample (single) n=100 σ=10.0	21.4 ± 5.3 ns	21.4 ± 5.1 ns	0.998,1.01,1
sample (single) n=100 σ=100.0	18.5 ± 4.2 ns	18.5 ± 3.8 ns	1,0.978,1
sample (single) n=1000 σ=0.1	25.9 ± 4.5 ns	25.5 ± 4.5 ns	1.01,1.02,1.02
sample (single) n=1000 σ=1.0	0.0354 ± 0.0023 μs	0.0347 ± 0.0022 μs	1.02,1.03,1.02
sample (single) n=1000 σ=10.0	22.4 ± 6.3 ns	22.5 ± 5.6 ns	1.01,1.01,0.993
sample (single) n=1000 σ=100.0	18.8 ± 4.2 ns	18.5 ± 4 ns	1.01
sample (single) n=10000 σ=0.1	0.0342 ± 0.0012 μs	0.0336 ± 0.0013 μs	1.02
sample (single) n=10000 σ=1.0	0.0378 ± 0.0012 μs	0.0368 ± 0.001 μs	1.03,1.01,1.03
sample (single) n=10000 σ=10.0	22.8 ± 6.8 ns	23.9 ± 6.5 ns	0.975,1.04,0.953
sample (single) n=10000 σ=100.0	18.7 ± 4.2 ns	19.3 ± 3.9 ns	0.965,0.991,0.972
summarysize n=100 σ=0.1	1.13e+05 ± 0 h	1.13e+05 ± 0 h	1
summarysize n=100 σ=1.0	1.13e+05 ± 0 h	1.13e+05 ± 0 h	1
summarysize n=100 σ=10.0	1.13e+05 ± 0 h	1.13e+05 ± 0 h	1
summarysize n=100 σ=100.0	1.13e+05 ± 0 h	1.13e+05 ± 0 h	1
summarysize n=1000 σ=0.1	1.42e+05 ± 0 h	1.42e+05 ± 0 h	1
summarysize n=1000 σ=1.0	1.42e+05 ± 0 h	1.42e+05 ± 0 h	1
summarysize n=1000 σ=10.0	1.42e+05 ± 0 h	1.42e+05 ± 0 h	1
summarysize n=1000 σ=100.0	1.42e+05 ± 0 h	1.42e+05 ± 0 h	1
summarysize n=10000 σ=0.1	1e+06 ± 0 h	1e+06 ± 0 h	1
summarysize n=10000 σ=1.0	1e+06 ± 0 h	1e+06 ± 0 h	1
summarysize n=10000 σ=10.0	1e+06 ± 0 h	1e+06 ± 0 h	1
summarysize n=10000 σ=100.0	1e+06 ± 0 h	1e+06 ± 0 h	1
update ∘ rand n=100 σ=0.1	0.0872 ± 0.0024 μs	0.0853 ± 0.0023 μs	1.03,0.935,1.02
update ∘ rand n=100 σ=1.0	0.0932 ± 0.0028 μs	0.0922 ± 0.003 μs	1.02,0.94,1.01
update ∘ rand n=100 σ=10.0	0.1 ± 0.0036 μs	0.104 ± 0.004 μs	0.999,0.971,0.959
update ∘ rand n=100 σ=100.0	0.228 ± 0.024 μs	0.231 ± 0.027 μs	1.03,0.996,0.986
update ∘ rand n=1000 σ=0.1	0.0878 ± 0.0022 μs	0.086 ± 0.0024 μs	1.02,0.938,1.02
update ∘ rand n=1000 σ=1.0	0.0941 ± 0.003 μs	0.0925 ± 0.0027 μs	1.02,0.938,1.02
update ∘ rand n=1000 σ=10.0	0.0993 ± 0.0017 μs	0.0988 ± 0.0019 μs	1.01,0.943,1
update ∘ rand n=1000 σ=100.0	0.22 ± 0.0083 μs	0.224 ± 0.0093 μs	1.02,1,0.979
update ∘ rand n=10000 σ=0.1	0.0955 ± 0.0013 μs	0.0934 ± 0.00099 μs	1.02,0.944,1.02
update ∘ rand n=10000 σ=1.0	0.0986 ± 0.0014 μs	0.0979 ± 0.0027 μs	1.04,0.938,1.01
update ∘ rand n=10000 σ=10.0	0.0986 ± 0.0015 μs	0.0967 ± 0.001 μs	1.02,0.925,1.02
update ∘ rand n=10000 σ=100.0	0.196 ± 0.0025 μs	0.196 ± 0.003 μs	1.01,0.977,0.997
time_to_load	0.0742 ± 0.00045 s	0.368 ± 0.0012 s	0.202,0.205,0.202

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).