Turns out we don't need seq at all. A simple refactoring of the merge function does the trick equally well.

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

mergePairs xs = xs

merge f as@(a:as') bs@(b:bs')

| a `cmp` b == GT = merge (f.(b:)) as bs'

| otherwise = merge (f.(a:)) as' bs

merge f [] bs = f bs

merge f as [] = f as

This variant is 10% faster in my tests.

On Mon, Mar 27, 2017 at 5:49 PM, Dan Burton <danburton.email@gmail.com> wrote:

Does this rely on Common Subexpression Elimination optimization in order to work? Would it work more reliably if the `seq`-ed expression were let-bound?

I don't think it relies heavily on CSE. The seq's are there to avoid a cascading series of thunk evaluations. Using let expressions doesn't seem to affect the benchmarks.

-- Dan Burton

On Mon, Mar 27, 2017 at 5:41 PM, David Feuer <david.feuer@gmail.com> wrote:

The first seq is useless: constructor application is never suspended. I haven't had a chance to look at the rest yet.

On Mar 27, 2017 7:59 PM, "Gregory Popovitch" <greg7mdp@gmail.com> wrote:

Sid,

I'd be delighted to submit the patch, as long as I have permission (which I probably don't), you feel confident about the change and maybe a couple of other people agree.

Here is the proposed change. Tests shows significant speed improvement (30%) when sorting lists of random numbers, and same efficiency for sorting already sorted lists (both ascending and descending).

Thanks,

greg

From: siddhanathan@gmail.com [mailto:siddhanathan@gmail.com] On Behalf Of Siddhanathan Shanmugam
Sent: Monday, March 27, 2017 6:53 PM
To: Gregory Popovitch
Subject: RE: Proposal: a new implementation for Data.List.sort and Data.List.sortBy, which has better performance characteristics and is more laziness-friendly.

Since I don't see any regressions, this doesn't really need CLC approval. The changes are also small enough that a Github PR may be accepted (otherwise, the change goes in via Phabricator).

Are you interested in implementing this patch? If yes, a standard Github PR should be fine. Right now gSort is a three line change I think. It will be changed in ghc/libraries/base/Data/OldList.hs on the ghc/ghc repo on Github.

I'm hoping for some more comments from other Haskellers, before pushing for this change in base. I feel like we may be missing a potential optimization that someone else might spot. So probably going to wait a few days.

On Mar 27, 2017 11:43 AM, "Gregory Popovitch" <greg7mdp@gmail.com> wrote:

Hi Sid,

Thanks, glad you looked into that. My understanding of the Haskell execution model is really poor, so I can't say one way or the other, but I felt that laziness ought to be considered as well, and I'm glad it was :-)

So in conclusion it looks like we have a winner with your latest gSortBy version. How do we get this pushed to the GHC library?

Thanks,

greg

From: siddhanathan@gmail.com [mailto:siddhanathan@gmail.com] On Behalf Of Siddhanathan Shanmugam
Sent: Monday, March 27, 2017 2:12 PM
To: Gregory Popovitch

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

Hi Greg,

On Mon, Mar 27, 2017 at 10:19 AM, Gregory Popovitch <greg7mdp@gmail.com> wrote:

Unfortunately, this optimization makes the sort less lazy, so doing something like:

take 4 $ sort l

requires more sorting of the list l with this change. I'm not sure it is a good tradeoff.

This can be verified with: https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs

I think you're running without optimizations turned on. It is lazy in my case.

Also, the difference should be negligible (if any at all). Here's an example of the list being sorted:

[11,4,6,8,2,5,1,7,9,55,11,3]

...

[[4,11],[6,8],[2,5],[1,7,9,55],[3,11],[]]

...

[[1,2,4,5,6,7,8,9,11,55],[3,11]]

* 1 3

* 2 3

* 4 3

* 4 11

[1,2,3,4]

The number of operations saved is only in the last merge. It's only lazy at this step.

So we save at most one traversal of the list, which is not too expensive since our worst case bounds is O(n log n) anyway.

This should mean that the asymptotic performance should be identical, regardless of the number of comparisons saved. Of course, you do get better constants, but I would be surprised if those constants translated to significantly better performance for a reasonable size list.

I do agree that it would be nice to have a more serious validation test suite.

Thanks,

greg

From: siddhanathan@gmail.com [mailto:siddhanathan@gmail.com] On Behalf Of Siddhanathan Shanmugam
Sent: Monday, March 27, 2017 12:53 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.

We can improve things a bit further by forcing evaluation (with seq) along the way appropriately.

gregSortBy cmp [] = []

gregSortBy 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' `seq` merge v' x' : reduce t

where v' = merge v w `seq` merge v w

x' = merge x y `seq` merge x y

reduce (x:y:t) = merge x y `seq` 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

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) `seq` (a:as) : sequences bs

ascending a as (b:bs)

| a `cmp` b /= GT = ascending b (as . (a:)) 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 `seq` 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

Before the change:

benchmarking random ints/ghc

time 3.687 s (3.541 s .. NaN s)

1.000 R² (1.000 R² .. 1.000 R²)

mean 3.691 s (3.669 s .. 3.705 s)

std dev 21.45 ms (0.0 s .. 24.76 ms)

variance introduced by outliers: 19% (moderately inflated)

benchmarking random ints/greg

time 2.648 s (2.482 s .. 2.822 s)

0.999 R² (0.998 R² .. 1.000 R²)

mean 2.704 s (2.670 s .. 2.736 s)

std dev 52.68 ms (0.0 s .. 54.49 ms)

variance introduced by outliers: 19% (moderately inflated)

benchmarking random ints/gSort

time 2.733 s (2.682 s .. 2.758 s)

1.000 R² (1.000 R² .. 1.000 R²)

mean 2.707 s (2.689 s .. 2.718 s)

std dev 16.84 ms (0.0 s .. 19.20 ms)

variance introduced by outliers: 19% (moderately inflated)

After the change:

benchmarking random ints/greg

time 2.576 s (2.548 s .. 2.628 s)

1.000 R² (1.000 R² .. 1.000 R²)

mean 2.590 s (2.578 s .. 2.599 s)

std dev 12.99 ms (0.0 s .. 14.89 ms)

variance introduced by outliers: 19% (moderately inflated)

benchmarking random ints/gSort

time 2.538 s (2.412 s .. 2.627 s)

1.000 R² (0.999 R² .. 1.000 R²)

mean 2.543 s (2.517 s .. 2.560 s)

std dev 26.16 ms (0.0 s .. 30.21 ms)

variance introduced by outliers: 19% (moderately inflated)

On Sun, Mar 26, 2017 at 1:54 PM, Siddhanathan Shanmugam <siddhanathan+eml@gmail.com> wrote:

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 <greg7mdp@gmail.com> 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

________________________________

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 <greg7mdp@gmail.com>
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

________________________________

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
<greg7mdp@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
<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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