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

Theoretically, we could do better. We currently only exploit monotonic runs in merge sort, but we could also exploit bitonic runs: dlist as = as [] `seq` as [] sequences [] = [[]] sequences [a] = [[a]] sequences (a:xs) = bitonic a a (a:) xs bitonic min max as (b:bs) | b `cmp` max /= LT = bitonic min b (as . (b:)) bs | b `cmp` min /= GT = bitonic b max ((b:) . as) bs | otherwise = dlist as : sequences (b:bs) bitonic _ _ as [] = [dlist as] The constant factors here might be too high to notice the difference though.

However, still my version is more laziness-friendly, i.e. it requires fewer comparisons to get the N smallest elements of a list (see https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs).

I wonder if this might not be a more useful trait than being able to sort already sorted lists super fast.

This comes down to a discussion of merge sort vs natural merge sort. Data.List.sort is an implementation of a variant of merge sort called natural merge sort. The algorithm is linearithmic in the worst case, but linear in the best case (already sorted list). On Sun, Mar 26, 2017 at 10:47 AM, Gregory Popovitch wrote:

Thanks again @Siddhanathan! Looks like your gSort fixes the main issue with Data.List.sort().

I have updated the test programs in https://github.com/greg7mdp/ghc-sort to include your new version.

Here are the results (your new version looks like a definite improvement vs the current GHC one):

input GHC sort My Orig proposal gSort ------------------------------------------------------------ ---------------- --- sorted ints (ascending) 151 456 148 sorted ints (descending) 152 466 155 random ints 2732 2006 2004 random strings 6564 5549 5528

So replacing the current GHC version with gSort is a no brainer, as it is better in all regards.

However, still my version is more laziness-friendly, i.e. it requires fewer comparisons to get the N smallest elements of a list (see https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs).

I wonder if this might not be a more useful trait than being able to sort already sorted lists super fast.

Thanks,

greg

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From: siddhanathan@gmail.com [mailto:siddhanathan@gmail.com] On Behalf Of Siddhanathan Shanmugam Sent: Sunday, March 26, 2017 1:05 PM To: Gregory Popovitch Cc: Haskell Libraries Subject: Re: Proposal: a new implementation for Data.List.sort and Data.List.sortBy, which has better performance characteristics and is more laziness-friendly.

Interesting. You are right, performance for sorting random lists has priority over performance for sorting already-sorted lists.

Ignore the numbers for my previous version. Can you compare GHC's sort, your proposal, and gSort below?

gSort :: Ord a => [a] -> [a] gSort = gSortBy compare gSortBy cmp = mergeAll . sequences where sequences (a:b:xs) | a `cmp` b == GT = descending b [a] xs | otherwise = ascending b (a:) xs sequences xs = [xs]

descending a as (b:bs) | a `cmp` b == GT = descending b (a:as) bs descending a as bs = (a:as) : sequences bs

ascending a as (b:bs) | a `cmp` b /= GT = ascending b (\ys -> as (a:ys)) bs ascending a as bs = as [a] `seq` as [a] : sequences bs

mergeAll [x] = x mergeAll xs = mergeAll (mergePairs xs)

mergePairs (a:b:xs) = merge a b : mergePairs xs mergePairs xs = xs

merge as@(a:as') bs@(b:bs') | a `cmp` b == GT = b : merge as bs' | otherwise = a : merge as' bs merge [] bs = bs merge as [] = as

Thanks, Sid

On Sun, Mar 26, 2017 at 9:19 AM, Gregory Popovitch wrote:

Thank you @Siddhanathan! I welcome any improvement you may make, as I said I am very far from a Haskell expert.

I just tested your change with my test project (https://github.com/greg7mdp/ghc-sort https://github.com/greg7mdp/ghc-sort ) and here are my results (mean times in ms):

input GHC sort Orig proposal your change

------------------------------------------------------------ ---------------- --- sorted ints (ascending) 153 467 139 sorted ints (descending) 152 472 599 random ints 2824 2077 2126 random strings 6564 5613 5983

Your change is a definite improvement for sorted integers in ascending order, but is worse for other cases.

Is there a real need to optimize the sort for already sorted list? Of course it should not be a degenerate case and take longer than sorting random numbers, but this is not the case here. Sorting already sorted lists is, even with my version, over 4 times faster than sorting random lists. This sounds perfectly acceptable to me, and I feel that trying to optimize this specific case further, if it comes at the detriment of the general case, is not desirable.

Thanks,

greg

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From: siddhanathan@gmail.com [mailto:siddhanathan@gmail.com] On Behalf Of Siddhanathan Shanmugam Sent: Sunday, March 26, 2017 11:41 AM To: Gregory Popovitch Cc: Haskell Libraries Subject: Re: Proposal: a new implementation for Data.List.sort and Data.List.sortBy, which has better performance characteristics and is more laziness-friendly.

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 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 https://github.com/greg7mdp/ghc-sort

<https://github.com/greg7mdp/ghc-sort 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 https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs

<https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs 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@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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