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Map.toList performance in Haskell

In the code below, I am comparing my implementation of Bucket Sort.

The function bucketsortuses the result from _bucketsort, but aligns it to a single list. To my surprise, this process ( Map.toList) takes a lot of time.

module Main where
import System.Random
import Criterion.Main
import qualified Data.List as List
import qualified Data.Map as Map
import Data.Maybe

insert :: (Ord a) => a -> [a] -> [a]
insert x [] = [x]
insert x (y:xs)
    | x <= y    = x:y:xs
    | otherwise = y : insert x xs

bucketsort :: (Integral a) => [a] -> [a]
bucketsort xs = List.concatMap (snd) . Map.toList $ _bucketsort xs Map.empty

_bucketsort :: (Integral k) => [k] -> Map.Map k [k] -> Map.Map k [k]
_bucketsort [] map = map
_bucketsort (x:xs) map =
    let bucket = x `div` 3
        bucketlist = maybeToList $ Map.lookup bucket map
        bucketInsert x [] = [x]
        bucketInsert x xs = insert x $ head xs
        ys = bucketInsert x bucketlist
        newMap = Map.insert bucket ys map
    in _bucketsort xs newMap

dataset n = List.take n $ randomRs (0, 9999) (mkStdGen 42)

main = defaultMain [ bench "bucketsort 96080" $ whnf bucketsort ((dataset 96080) :: [Int])
                   , bench "_bucketsort 96080" $ whnf _bucketsort ((dataset 96080):: [Int])]

And here is the result of a benchmark test by the criterion:

C:\>benchmark_bucketsort.exe
warming up
estimating clock resolution...
mean is 1.353299 us (640001 iterations)
found 1278266 outliers among 639999 samples (199.7%)
  638267 (99.7%) low severe
  639999 (100.0%) high severe
estimating cost of a clock call...
mean is 105.8728 ns (8 iterations)
found 14 outliers among 8 samples (175.0%)
  7 (87.5%) low severe
  7 (87.5%) high severe

benchmarking bucketsort 96080
collecting 100 samples, 1 iterations each, in estimated 24.35308 s
Warning: Couldn't open /dev/urandom
Warning: using system clock for seed instead (quality will be lower)
mean: 187.2037 ms, lb 182.7181 ms, ub 191.3842 ms, ci 0.950
std dev: 22.15054 ms, lb 19.47241 ms, ub 25.64983 ms, ci 0.950
variance introduced by outliers: 84.194%
variance is severely inflated by outliers

benchmarking _bucketsort 96080
mean: 8.823789 ns, lb 8.654692 ns, ub 9.049314 ns, ci 0.950
std dev: 952.9240 ps, lb 723.0241 ps, ub 1.154097 ns, ci 0.950
found 13 outliers among 100 samples (13.0%)
  13 (13.0%) high severe
variance introduced by outliers: 82.077%
variance is severely inflated by outliers

I would not be surprised if my function bucketsortcould be written much better and, hopefully, faster. But so far I have not figured out how.

Also, any improvements / comments in my Haskell code are more than welcome.

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1 answer

_bucketsort WHNF, .

main = defaultMain [ bench "bucketsort 96080"  $ whnf bucketsort ((dataset 96080) :: [Int])
                   , bench "_bucketsort 96080" $ whnf (flip _bucketsort Map.empty) ((dataset 96080):: [Int])]

( ):

warming up
estimating clock resolution...
mean is 2.357120 us (320001 iterations)
found 2630 outliers among 319999 samples (0.8%)
  2427 (0.8%) high severe
estimating cost of a clock call...
mean is 666.7750 ns (14 iterations)
found 1 outliers among 14 samples (7.1%)
  1 (7.1%) high severe

benchmarking bucketsort 96080
collecting 100 samples, 1 iterations each, in estimated 34.66980 s
mean: 244.3280 ms, lb 238.0601 ms, ub 250.6725 ms, ci 0.950
std dev: 32.37658 ms, lb 28.02356 ms, ub 38.10187 ms, ci 0.950
found 3 outliers among 100 samples (3.0%)
  3 (3.0%) low mild
variance introduced by outliers: 87.311%
variance is severely inflated by outliers

benchmarking _bucketsort 96080
collecting 100 samples, 1 iterations each, in estimated 24.65911 s
mean: 244.9425 ms, lb 239.1011 ms, ub 251.0300 ms, ci 0.950
std dev: 30.68877 ms, lb 26.48151 ms, ub 36.20961 ms, ci 0.950
variance introduced by outliers: 86.247%
variance is severely inflated by outliers

, , whnf . , ​​ . nf 369.3022ms 354.3513ms , bucketsort .

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