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Date: Thu, 9 Feb 2023 14:03:16 -0500
From: Rich Felker <dalias@...c.org>
To: Markus Wichmann <nullplan@....net>
Cc: musl@...ts.openwall.com
Subject: Re: Re:Re: qsort
On Wed, Feb 01, 2023 at 07:01:15PM +0100, Markus Wichmann wrote:
> On Mon, Jan 30, 2023 at 06:04:39PM +0800, David Wang wrote:
> > WIth glibc, average report is "qsort:3351271634 vs sort:4358412048"
> > But on alpine, it is "qsort:9585927992 vs sort:4354856330"
> >
> > On average, qsort with musl is significantly slower than c++ sort,
> > while with glibc the average performance of qsort is bettern than c++
> > sort.
> >
>
> It seems to me as though smoothsort does not optimize for the number of
> comparisons.
>
> > Is there any story about the implementation of qsort in musl? I feel
> > it focused on performance improvement for some special kind of domain,
> > but not clear what it is.
> >
>
> Smoothsort has the desirable property of being adaptive. Its runtime
> gets closer to O(n) the more sorted the input already is. glibc uses
> mergesort or quicksort (the latter as fallback) and neither of them has
> that property. Plus, mergesort requires scratch storage and has a
> significantly harder time sorting arrays with large elements, because
> you end up constantly copying stuff. glibc tries to mitigate this by
> indirectly sorting once the elements go above 32 bytes in size.
>
> Basically, glibc is optimized for the comparisons, musl more for the
> number of swaps. Although we really shouldn't loose sight of the
> compares entirely, since those are indirect function calls, and current
> processors seem to dislike those.
>
> Anyway, there is an inefficiency in musl's smoothsort implementation,
> namely in the sift() function:
>
>
> | if(cmp(ar[0], lf, arg) >= 0 && cmp(ar[0], rt, arg) >= 0) {
> | break;
> | }
> | if(cmp(lf, rt, arg) >= 0) {
> | ar[i++] = lf;
> | head = lf;
> | pshift -= 1;
> | } else {
> | ar[i++] = rt;
> | head = rt;
> | pshift -= 2;
> | }
>
> As you can see, this does two or three comparisions, but actually needs
> to do only two in any case: If we detect ar[0] >= lf && ar[0] < rt, then
> by transitivity we have also detected rt > lf, so there is no need to
> compare lf and rt directly anymore. I have not really found a good way
> to formulate code that takes advantage of that, maybe something like
> this?
>
>
> if(cmp(ar[0], lf, arg) < 0) {
> if(cmp(lf, rt, arg) >= 0) {
> ar[i++] = lf;
> head = lf;
> pshift -= 1;
> } else {
> go_right:
> ar[i++] = rt;
> head = rt;
> pshift -= 2;
> }
> } else if (cmp(ar[0], rt, arg) < 0) {
> goto go_right;
> } else {
> break;
> }
>
> Yeah, not great. But it does use only two compares ever. This ought to
> lower the number of compares in your test somewhat.
I think we should pursue this. IIRC there was another fairly
significant missed optimization in qsort discussed a while back, where
discussion dropped off because the person involved turned out to be
impossible to work with.
On the overall topic of qsort and quicksort, quicksort is just not a
viable algorithm by itself because it's O(n²) time. glibc does not use
it by itself, but uses "introsort", a fancy way to say it introspects
the quicksort (rather just counts the depth) and switches to an O(n
log n) algorithm once it's descended too many levels. Alternatively,
there are ways to pick the pivot element (quickselect) that guarantee
O(n log n) overall performance, but the pivot selection is so heavy as
to make it impractical.
It might make sense for us to adopt an approach like introsort, using
smoothsort as the fallback, especially if we could preserve the
property of being fast on mostly/entirely sorted inputs. But I'm not
sure if that's possible.
Before we consider any such change though we should probably see
profiling data to determine where the time is being spent in
smoothsort, in case it's stupid stuff that's fixable.
Rich
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