# New portion of improvements for Dual-Pivot Quicksort

Tue Jun 8 07:09:42 PDT 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%.

Thank you,

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,
>  >
>  > 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,