# Proposal: a new implementation for Data.List.sort and Data.List.sortBy, which has better performance characteristics and is more laziness-friendly.

Siddhanathan Shanmugam siddhanathan+eml at gmail.com
Sun Mar 26 15:40:52 UTC 2017

```Thank you! This identifies a space leak in base which went unnoticed for 7
years.

Your implementation can be improved further. Instead of splitting into
pairs, you could instead split into lists of sorted sublists by replacing
the pairs function with the following

pair = foldr f []
where
f x [] = [[x]]
f x (y:ys)
| x `cmp` head y == LT = (x:y):ys
| otherwise            = [x]:y:ys

This should give you the same performance improvements for sorting random
lists, but better performance while sorting ascending lists.

The version in base takes it one step further by using a DList to handle
the descending case efficiently as well, except there's a space leak right
now because of which it is slower.

On Sun, Mar 26, 2017 at 7:21 AM, Gregory Popovitch <greg7mdp at gmail.com>
wrote:

>
> Motivation:
> ----------
>
> Data.List.sort is a very important functionality in Haskell. I believe that
> the proposed implementation is:
>
> - significantly faster than the current implementation on unsorted lists,
> typically 14% to 27% faster
> - more laziness-friendly, i.e.:
>     take 3 \$ sort l
>   will require significantly less comparisons than the current
> implementation
>
> Proposed Implementation
> -----------------------
>
> sort :: (Ord a) => [a] -> [a]
> sort =  sortBy compare
>
> sortBy cmp [] = []
> sortBy cmp xs = head \$ until (null.tail) reduce (pair xs)
>   where
>     pair (x:y:t) | x `cmp` y == GT  = [y, x] : pair t
>                  | otherwise        = [x, y] : pair t
>     pair [x] = [[x]]
>     pair []  = []
>
>     reduce (v:w:x:y:t) = merge v' x' : reduce t
>                          where v' = merge v w
>                                x' = merge x y
>
>     reduce (x:y:t) = merge x y : reduce t
>     reduce xs      = xs
>
>     merge xs []           = xs
>     merge []  ys          = ys
>     merge xs@(x:xs') ys@(y:ys')
>          | x `cmp` y == GT  = y : merge xs  ys'
>          | otherwise        = x : merge xs' ys
>
>
> Effect and Interactions
> -----------------------
>
> I have a stack project with a criterion test for this new implementation,
> available at https://github.com/greg7mdp/ghc-sort.
> I ran the tests on an Ubuntu 14.0.2 VM and GHC 8.0.2, and had the following
> results:
>
> - sorting of random lists of integers is 27% faster
> - sorting of random lists of strings is 14% faster
> - sorting of already sorted lists is significantly slower, but still much
> faster than sorting random lists
> - proposed version is more laziness friendly. For example this version of
> sortBy requires 11 comparisons to find
>   the smallest element of a 15 element list, while the default
> Data.List.sortBy requires 15 comparisons.
>   (see
> https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs)
>
>
> Test results
> ------------
>
> Criterion output (descending/ascending results are for already sorted
> lists).
> I barely understand what Criterion does, and I am puzzled with the various
> "T" output - maybe there is a bug in my bench code:
>
> vagrant at vagrant-ubuntu-trusty-64:/vagrant\$ stack exec ghc-sort
> benchmarking ascending ints/ghc
> TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTtime                 160.6 ms
>  (153.4
> ms .. 167.8 ms)
>                      0.997 R²   (0.986 R² .. 1.000 R²)
> mean                 161.7 ms   (158.3 ms .. 165.9 ms)
> std dev              5.210 ms   (3.193 ms .. 7.006 ms)
> variance introduced by outliers: 12% (moderately inflated)
>
> benchmarking ascending ints/greg
> TTTTTTTTTTTTTTTTtime                 473.8 ms   (398.6 ms .. 554.9 ms)
>                      0.996 R²   (0.987 R² .. 1.000 R²)
> mean                 466.2 ms   (449.0 ms .. 475.0 ms)
> std dev              14.94 ms   (0.0 s .. 15.29 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
> benchmarking descending ints/ghc
> TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTtime                 165.1 ms
>  (148.2
> ms .. 178.2 ms)
>                      0.991 R²   (0.957 R² .. 1.000 R²)
> mean                 158.7 ms   (154.0 ms .. 164.3 ms)
> std dev              7.075 ms   (4.152 ms .. 9.903 ms)
> variance introduced by outliers: 12% (moderately inflated)
>
> benchmarking descending ints/greg
> TTTTTTTTTTTTTTTTtime                 471.7 ms   (419.8 ms .. 508.3 ms)
>                      0.999 R²   (0.995 R² .. 1.000 R²)
> mean                 476.0 ms   (467.5 ms .. 480.0 ms)
> std dev              7.447 ms   (67.99 as .. 7.865 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
> benchmarking random ints/ghc
> TTTTTTTTTTTTTTTTtime                 2.852 s    (2.564 s .. 3.019 s)
>                      0.999 R²   (0.997 R² .. 1.000 R²)
> mean                 2.812 s    (2.785 s .. 2.838 s)
> std dev              44.06 ms   (543.9 as .. 44.97 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
> benchmarking random ints/greg
> TTTTTTTTTTTTTTTTtime                 2.032 s    (1.993 s .. 2.076 s)
>                      1.000 R²   (1.000 R² .. 1.000 R²)
> mean                 2.028 s    (2.019 s .. 2.033 s)
> std dev              7.832 ms   (0.0 s .. 8.178 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
> benchmarking shakespeare/ghc
> TTTTTTTTTTTTTTTTtime                 6.504 s    (6.391 s .. 6.694 s)
>                      1.000 R²   (1.000 R² .. 1.000 R²)
> mean                 6.499 s    (6.468 s .. 6.518 s)
> std dev              28.85 ms   (0.0 s .. 32.62 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
> benchmarking shakespeare/greg
> TTTTTTTTTTTTTTTTtime                 5.560 s    (5.307 s .. 5.763 s)
>                      1.000 R²   (0.999 R² .. 1.000 R²)
> mean                 5.582 s    (5.537 s .. 5.607 s)
> std dev              39.30 ms   (0.0 s .. 43.49 ms)
> variance introduced by outliers: 19% (moderately inflated)
>
>
> Costs and Drawbacks
> -------------------
>
> The only cost I see is the reduced performance when sorting already sorted
> lists. However, since this remains quite efficient, indeed over 4 times
> faster than sorting unsorted lists, I think it is an acceptable tradeoff.
>
> Final note
> ----------
>
> My Haskell is very rusty. I worked on this a couple years ago when I was
> learning Haskell, and meant to propose it to the Haskell community, but
> never got to it at the time.
>
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