GiST penalty functions [PoC]

Hi, hackers!

Some time ago I put a patch to commitfest that optimizes slightly GiST
inserts and updates. It's effect in general is quite modest (15% perf
improved), but for sorted data inserts are 3 times quicker. This
effect I attribute to mitigation of deficiencies of old split
algorithm.
Alexander Korotkov advised me to lookup some features of the RR*-tree.

The RR*-tree differs from combination of Gist + cube extension in two
algorithms:
1. Algorithm to choose subtree for insertion
2. Split algorithm

This is the message regarding implementation of first one in GiST. I
think that both of this algorithms will improve querying performance.

Long story short, there are two problems in choose subtree algorithm.
1. GiST chooses subtree via penalty calculation for each entry,
while RR*-tree employs complicated conditional logic: when there are
MBBs (Minimum Bounding Box) which do not require extensions, smallest
of them is chosen; in some cases, entries are chosen not by volume,
but by theirs margin.
2. RR*-tree algorithm jumps through entry comparation non-linearly,
I think this means that GiST penalty computation function will have to
access other entries on a page.

In this message I address only first problem. I want to construct a
penalty function that will choose:
1. Entry with a zero volume and smallest margin, that can
accommodate insertion tuple without extension, if one exists;
2. Entry with smallest volume, that can accommodate insertion tuple
without extension, if one exists;
3. Entry with zero volume increase after insert and smallest margin
increase, if one exists;
4. Entry with minimal volume increase after insert.

Current cube behavior inspects only 4th option by returning as a
penalty (float) MBB’s volume increase. To implement all 4 options, I
use a hack: order of positive floats corresponds exactly to order of
integers with same binary representation (I’m not sure this stands for
every single supported platform). So I use two bits of float as if it
were integer, and all others are used as shifted bits of corresponding
float: option 4 – volume increase, 3 - margin increase, 2 – MBB
volume, 1 – MBB margin. You can check the reinterpretation cast
function pack_float() in the patch.

I’ve tested patch performance with attached test. On my machine patch
slows index construction time from 60 to 76 seconds, reduces size of
the index from 85Mb to 82Mb, reduces time of aggregates computation
from 36 seconds to 29 seconds.

I do not know: should I continue this work in cube, or it’d be better
to fork cube?
Maybe anyone have tried already RR*-tree implementation? Science
papers show very good search performance increase.

Please let me know if you have any ideas, information or interest in this topic.

Best regards, Andrey Borodin, Octonica & Ural Federal University.