New portion of improvements for Dual-Pivot Quicksort
Vladimir Iaroslavski
iaroslavski at mail.ru
Tue Jun 8 14:09:42 UTC 2010
Hello,
Good catch! I agree with k!=p condition, but have doubt about using
Float.isNaN(ak) instead of ak != ak in for loop. Float.isNaN does exactly
the same comparison and at the same time it is called for all elements
of the array.
I checked now and see that it is better to eliminate while loop,
and the best case is:
for (int k = right; k >= left; k--) {
float ak = a[k];
if (ak != ak) { // a[k] is NaN
a[k] = a[right];
a[right--] = ak;
}
}
If we have a lot of NaNs, it will be proceeded on linear time
and only small amount of elements will be sorted. If there are
no NaNs [at the end] - more probably use case - this code works
faster. I run simple test and it shows that case without while loop
is little bit faster, ~0.5%.
Please, see attached version.
Thank you,
Vladimir
Dmytro Sheyko wrote:
> Hi,
>
> Coming back to NaN processing.
> It appeared that current code unnecessarily stirs up NaNs in the end of
> array even when they are just on their places.
> So I propose to replace these code
> /*
> * Phase 1: Move NaNs to the end of the array.
> */
> for (int k = left; k <= right; k++) {
> float ak = a[k];
> if (ak != ak) { // a[k] is NaN
> a[k--] = a[right];
> a[right--] = ak;
> }
> }
> with following
> /*
> * Phase 1: Move NaNs to the end of the array.
> */
> while (left <= right && Float.isNaN(a[right])) {
> right--;
> }
> for (int k = right - 1; k >= left; k--) {
> float ak = a[k];
> if (Float.isNaN(ak)) {
> a[k] = a[right];
> a[right] = ak;
> right--;
> }
> }
>
> Also I would like to note that while we are processing negative zeros,
> condition (k != p) is unnecessary.
>
> for (int k = left + 1, p = left; k <= right; k++) {
> float ak = a[k];
> if (ak != 0.0f) {
> return;
> }
> if (Float.floatToRawIntBits(ak) < 0) { // ak is -0.0f
> if (k != p) { // !!! always true
> a[k] = +0.0f;
> a[p] = -0.0f;
> }
> p++;
> }
> }
>
> Here k is strictly greater than p initially and then grows faster than p.
>
>
> > From: iaroslavski at mail.ru
> > To: dmytro_sheyko at hotmail.com
> > CC: core-libs-dev at openjdk.java.net; iaroslavski at mail.ru
> > Subject: Re[4]: New portion of improvements for Dual-Pivot Quicksort
> > Date: Sat, 5 Jun 2010 23:40:31 +0400
> >
> > I tried with separate method sortPivotCandidates(...), no changes in
> behaviour,
> > but at the same time I don't see that the method makes sources much
> cleaner,
> > inline comments are enough. I attach the latest version of DPQ.
> >
> > Fri, 4 Jun 2010 14:21:58 +0700 письмо от Dmytro Sheyko
> <dmytro_sheyko at hotmail.com>:
> >
> > > Seems good,
> > >
> > > One note. Since we gave up to sort pivot candidates in local
> variables, maybe we can move this out to separate procedure (in order to
> make sources cleaner a bit), e.g.
> > >
> > > private static void sortPivotCandidates(double[] a, int ae1, int
> ae2, int ae3, int ae4, int ae5)
> > >
> > > Hope the compiler is able to inline it without extra cost.
> > >
> > > Thanks,
> > > Dmytro Sheyko
> > >
> > > > From: iaroslavski at mail.ru
> > > > To: dmytro_sheyko at hotmail.com
> > > > CC: core-libs-dev at openjdk.java.net; iaroslavski at mail.ru
> > > > Subject: Re[2]: New portion of improvements for Dual-Pivot Quicksort
> > > > Date: Fri, 4 Jun 2010 01:17:57 +0400
> > > >
> > > > Hello,
> > > >
> > > > I tried your case (which is selection sort) and it works as
> expected: not worse
> > > > than "network" or "bubble" sorting. But nevertheless, the best
> choice is to use
> > > > insertion sort, I wrote more elegant implementation, see:
> > > >
> > > > ///int ae1 = a[e1], ae3 = a[e3], ae5 = a[e5], ae2 = a[e2], ae4 =
> a[e4];
> > > >
> > > > // Sort these elements using insertion sort
> > > > if (a[e2] < a[e1]) { int t = a[e2]; a[e2] = a[e1]; a[e1] = t; }
> > > >
> > > > if (a[e3] < a[e2]) { int t = a[e3]; a[e3] = a[e2]; a[e2] = t;
> > > > if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
> > > > }
> > > > if (a[e4] < a[e3]) { int t = a[e4]; a[e4] = a[e3]; a[e3] = t;
> > > > if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;
> > > > if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
> > > > }
> > > > }
> > > > if (a[e5] < a[e4]) { int t = a[e5]; a[e5] = a[e4]; a[e4] = t;
> > > > if (t < a[e3]) { a[e4] = a[e3]; a[e3] = t;
> > > > if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;
> > > > if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }
> > > > }
> > > > }
> > > > }
> > > >
> > > > ///a[e1] = ae1; a[e3] = ae3; a[e5] = ae5; a[e2] = ae2; a[e4] = ae4;
> > > >
> > > > Note that this implementation doesn't use local variables ae1, ..
> , ae5
> > > > at all, and without variables it works faster. This code is not
> too long,
> > > > extra 4 lines only. And if on client VM it works as other "network"
> > > > implementations, but on server VM it wins 1.2%.
> > > >
> > > > In compare with first implementation of Dual-Pivot Quicksort, which
> > > > is used now in JDK 7, suggested version wins ~15% and 6% for client
> > > > and server modes.
> > > >
> > > > Updated version of the class I will send tomorrow.
> > > >
> > > > Dmytro,
> > > > could you please look at suggested insertion sort for 5 elements?
> > > >
> > > > Do you have any comments/improvements? One place to be improved
> > > > is last two ifs "if (a[e4] < ..." and "if (a[e5] < ..." where
> > > > element is compared with all sorted elements, whereas we can save
> > > > comparisons by binary fork. But implementation becomes too complex
> > > > and long.
> > > >
> > > > As it can be expected, the best sorting for small arrays is
> insertion,
> > > > then selection and then only bubble sort, even for 5 elements.
> > > >
> > > > Best regards,
> > > > Vladimir
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