Consider secondary factors during nbtree splits.

Teach nbtree to give some consideration to how "distinguishing"
candidate leaf page split points are.  This should not noticeably affect
the balance of free space within each half of the split, while still
making suffix truncation truncate away significantly more attributes on
average.

The logic for choosing a leaf split point now uses a fallback mode in
the case where the page is full of duplicates and it isn't possible to
find even a minimally distinguishing split point.  When the page is full
of duplicates, the split should pack the left half very tightly, while
leaving the right half mostly empty.  Our assumption is that logical
duplicates will almost always be inserted in ascending heap TID order
with v4 indexes.  This strategy leaves most of the free space on the
half of the split that will likely be where future logical duplicates of
the same value need to be placed.

The number of cycles added is not very noticeable.  This is important
because deciding on a split point takes place while at least one
exclusive buffer lock is held.  We avoid using authoritative insertion
scankey comparisons to save cycles, unlike suffix truncation proper.  We
use a faster binary comparison instead.

Note that even pg_upgrade'd v3 indexes make use of these optimizations.
Benchmarking has shown that even v3 indexes benefit, despite the fact
that suffix truncation will only truncate non-key attributes in INCLUDE
indexes.  Grouping relatively similar tuples together is beneficial in
and of itself, since it reduces the number of leaf pages that must be
accessed by subsequent index scans.

Author: Peter Geoghegan
Reviewed-By: Heikki Linnakangas
Discussion: https://postgr.es/m/CAH2-WzmmoLNQOj9mAD78iQHfWLJDszHEDrAzGTUMG3mVh5xWPw@mail.gmail.com

Author: petergeoghegan

src/backend/access/nbtree/Makefile

@@ -13,6 +13,6 @@ top_builddir = ../../../..
 include $(top_builddir)/src/Makefile.global
 
 OBJS = nbtcompare.o nbtinsert.o nbtpage.o nbtree.o nbtsearch.o \
-       nbtutils.o nbtsort.o nbtvalidate.o nbtxlog.o
+       nbtsplitloc.o nbtutils.o nbtsort.o nbtvalidate.o nbtxlog.o
 
 include $(top_srcdir)/src/backend/common.mk

src/backend/access/nbtree/README

@@ -143,9 +143,9 @@ Lehman and Yao assume fixed-size keys, but we must deal with
 variable-size keys.  Therefore there is not a fixed maximum number of
 keys per page; we just stuff in as many as will fit.  When we split a
 page, we try to equalize the number of bytes, not items, assigned to
-each of the resulting pages.  Note we must include the incoming item in
-this calculation, otherwise it is possible to find that the incoming
-item doesn't fit on the split page where it needs to go!
+pages (though suffix truncation is also considered).  Note we must include
+the incoming item in this calculation, otherwise it is possible to find
+that the incoming item doesn't fit on the split page where it needs to go!
 
 The Deletion Algorithm
 ----------------------
@@ -649,6 +649,47 @@ variable-length types, such as text.  An opclass support function could
 manufacture the shortest possible key value that still correctly separates
 each half of a leaf page split.
 
+There is sophisticated criteria for choosing a leaf page split point.  The
+general idea is to make suffix truncation effective without unduly
+influencing the balance of space for each half of the page split.  The
+choice of leaf split point can be thought of as a choice among points
+*between* items on the page to be split, at least if you pretend that the
+incoming tuple was placed on the page already (you have to pretend because
+there won't actually be enough space for it on the page).  Choosing the
+split point between two index tuples where the first non-equal attribute
+appears as early as possible results in truncating away as many suffix
+attributes as possible.  Evenly balancing space among each half of the
+split is usually the first concern, but even small adjustments in the
+precise split point can allow truncation to be far more effective.
+
+Suffix truncation is primarily valuable because it makes pivot tuples
+smaller, which delays splits of internal pages, but that isn't the only
+reason why it's effective.  Even truncation that doesn't make pivot tuples
+smaller due to alignment still prevents pivot tuples from being more
+restrictive than truly necessary in how they describe which values belong
+on which pages.
+
+While it's not possible to correctly perform suffix truncation during
+internal page splits, it's still useful to be discriminating when splitting
+an internal page.  The split point that implies a downlink be inserted in
+the parent that's the smallest one available within an acceptable range of
+the fillfactor-wise optimal split point is chosen.  This idea also comes
+from the Prefix B-Tree paper.  This process has much in common with what
+happens at the leaf level to make suffix truncation effective.  The overall
+effect is that suffix truncation tends to produce smaller, more
+discriminating pivot tuples, especially early in the lifetime of the index,
+while biasing internal page splits makes the earlier, smaller pivot tuples
+end up in the root page, delaying root page splits.
+
+Logical duplicates are given special consideration.  The logic for
+selecting a split point goes to great lengths to avoid having duplicates
+span more than one page, and almost always manages to pick a split point
+between two user-key-distinct tuples, accepting a completely lopsided split
+if it must.  When a page that's already full of duplicates must be split,
+the fallback strategy assumes that duplicates are mostly inserted in
+ascending heap TID order.  The page is split in a way that leaves the left
+half of the page mostly full, and the right half of the page mostly empty.
+
 Notes About Data Representation
 -------------------------------
 

src/backend/access/nbtree/nbtinsert.c

@@ -28,26 +28,6 @@
 /* Minimum tree height for application of fastpath optimization */
 #define BTREE_FASTPATH_MIN_LEVEL	2
 
-typedef struct
-{
-	/* context data for _bt_checksplitloc */
-	Size		newitemsz;		/* size of new item to be inserted */
-	int			fillfactor;		/* needed when splitting rightmost page */
-	bool		is_leaf;		/* T if splitting a leaf page */
-	bool		is_rightmost;	/* T if splitting a rightmost page */
-	OffsetNumber newitemoff;	/* where the new item is to be inserted */
-	int			leftspace;		/* space available for items on left page */
-	int			rightspace;		/* space available for items on right page */
-	int			olddataitemstotal;	/* space taken by old items */
-
-	bool		have_split;		/* found a valid split? */
-
-	/* these fields valid only if have_split is true */
-	bool		newitemonleft;	/* new item on left or right of best split */
-	OffsetNumber firstright;	/* best split point */
-	int			best_delta;		/* best size delta so far */
-} FindSplitData;
-
 
 static Buffer _bt_newroot(Relation rel, Buffer lbuf, Buffer rbuf);
 
@@ -73,13 +53,6 @@ static Buffer _bt_split(Relation rel, BTScanInsert itup_key, Buffer buf,
 		  Size newitemsz, IndexTuple newitem, bool newitemonleft);
 static void _bt_insert_parent(Relation rel, Buffer buf, Buffer rbuf,
 				  BTStack stack, bool is_root, bool is_only);
-static OffsetNumber _bt_findsplitloc(Relation rel, Page page,
-				 OffsetNumber newitemoff,
-				 Size newitemsz,
-				 bool *newitemonleft);
-static void _bt_checksplitloc(FindSplitData *state,
-				  OffsetNumber firstoldonright, bool newitemonleft,
-				  int dataitemstoleft, Size firstoldonrightsz);
 static bool _bt_pgaddtup(Page page, Size itemsize, IndexTuple itup,
 			 OffsetNumber itup_off);
 static bool _bt_isequal(TupleDesc itupdesc, BTScanInsert itup_key,
@@ -1003,7 +976,7 @@ _bt_insertonpg(Relation rel,
 
 		/* Choose the split point */
 		firstright = _bt_findsplitloc(rel, page,
-									  newitemoff, itemsz,
+									  newitemoff, itemsz, itup,
 									  &newitemonleft);
 
 		/* split the buffer into left and right halves */
@@ -1687,264 +1660,6 @@ _bt_split(Relation rel, BTScanInsert itup_key, Buffer buf, Buffer cbuf,
 	return rbuf;
 }
 
-/*
- *	_bt_findsplitloc() -- find an appropriate place to split a page.
- *
- * The idea here is to equalize the free space that will be on each split
- * page, *after accounting for the inserted tuple*.  (If we fail to account
- * for it, we might find ourselves with too little room on the page that
- * it needs to go into!)
- *
- * If the page is the rightmost page on its level, we instead try to arrange
- * to leave the left split page fillfactor% full.  In this way, when we are
- * inserting successively increasing keys (consider sequences, timestamps,
- * etc) we will end up with a tree whose pages are about fillfactor% full,
- * instead of the 50% full result that we'd get without this special case.
- * This is the same as nbtsort.c produces for a newly-created tree.  Note
- * that leaf and nonleaf pages use different fillfactors.
- *
- * We are passed the intended insert position of the new tuple, expressed as
- * the offsetnumber of the tuple it must go in front of.  (This could be
- * maxoff+1 if the tuple is to go at the end.)
- *
- * We return the index of the first existing tuple that should go on the
- * righthand page, plus a boolean indicating whether the new tuple goes on
- * the left or right page.  The bool is necessary to disambiguate the case
- * where firstright == newitemoff.
- */
-static OffsetNumber
-_bt_findsplitloc(Relation rel,
-				 Page page,
-				 OffsetNumber newitemoff,
-				 Size newitemsz,
-				 bool *newitemonleft)
-{
-	BTPageOpaque opaque;
-	OffsetNumber offnum;
-	OffsetNumber maxoff;
-	ItemId		itemid;
-	FindSplitData state;
-	int			leftspace,
-				rightspace,
-				goodenough,
-				olddataitemstotal,
-				olddataitemstoleft;
-	bool		goodenoughfound;
-
-	opaque = (BTPageOpaque) PageGetSpecialPointer(page);
-
-	/* Passed-in newitemsz is MAXALIGNED but does not include line pointer */
-	newitemsz += sizeof(ItemIdData);
-
-	/* Total free space available on a btree page, after fixed overhead */
-	leftspace = rightspace =
-		PageGetPageSize(page) - SizeOfPageHeaderData -
-		MAXALIGN(sizeof(BTPageOpaqueData));
-
-	/* The right page will have the same high key as the old page */
-	if (!P_RIGHTMOST(opaque))
-	{
-		itemid = PageGetItemId(page, P_HIKEY);
-		rightspace -= (int) (MAXALIGN(ItemIdGetLength(itemid)) +
-							 sizeof(ItemIdData));
-	}
-
-	/* Count up total space in data items without actually scanning 'em */
-	olddataitemstotal = rightspace - (int) PageGetExactFreeSpace(page);
-
-	state.newitemsz = newitemsz;
-	state.is_leaf = P_ISLEAF(opaque);
-	state.is_rightmost = P_RIGHTMOST(opaque);
-	state.have_split = false;
-	if (state.is_leaf)
-		state.fillfactor = RelationGetFillFactor(rel,
-												 BTREE_DEFAULT_FILLFACTOR);
-	else
-		state.fillfactor = BTREE_NONLEAF_FILLFACTOR;
-	state.newitemonleft = false;	/* these just to keep compiler quiet */
-	state.firstright = 0;
-	state.best_delta = 0;
-	state.leftspace = leftspace;
-	state.rightspace = rightspace;
-	state.olddataitemstotal = olddataitemstotal;
-	state.newitemoff = newitemoff;
-
-	/*
-	 * Finding the best possible split would require checking all the possible
-	 * split points, because of the high-key and left-key special cases.
-	 * That's probably more work than it's worth; instead, stop as soon as we
-	 * find a "good-enough" split, where good-enough is defined as an
-	 * imbalance in free space of no more than pagesize/16 (arbitrary...) This
-	 * should let us stop near the middle on most pages, instead of plowing to
-	 * the end.
-	 */
-	goodenough = leftspace / 16;
-
-	/*
-	 * Scan through the data items and calculate space usage for a split at
-	 * each possible position.
-	 */
-	olddataitemstoleft = 0;
-	goodenoughfound = false;
-	maxoff = PageGetMaxOffsetNumber(page);
-
-	for (offnum = P_FIRSTDATAKEY(opaque);
-		 offnum <= maxoff;
-		 offnum = OffsetNumberNext(offnum))
-	{
-		Size		itemsz;
-
-		itemid = PageGetItemId(page, offnum);
-		itemsz = MAXALIGN(ItemIdGetLength(itemid)) + sizeof(ItemIdData);
-
-		/*
-		 * Will the new item go to left or right of split?
-		 */
-		if (offnum > newitemoff)
-			_bt_checksplitloc(&state, offnum, true,
-							  olddataitemstoleft, itemsz);
-
-		else if (offnum < newitemoff)
-			_bt_checksplitloc(&state, offnum, false,
-							  olddataitemstoleft, itemsz);
-		else
-		{
-			/* need to try it both ways! */
-			_bt_checksplitloc(&state, offnum, true,
-							  olddataitemstoleft, itemsz);
-
-			_bt_checksplitloc(&state, offnum, false,
-							  olddataitemstoleft, itemsz);
-		}
-
-		/* Abort scan once we find a good-enough choice */
-		if (state.have_split && state.best_delta <= goodenough)
-		{
-			goodenoughfound = true;
-			break;
-		}
-
-		olddataitemstoleft += itemsz;
-	}
-
-	/*
-	 * If the new item goes as the last item, check for splitting so that all
-	 * the old items go to the left page and the new item goes to the right
-	 * page.
-	 */
-	if (newitemoff > maxoff && !goodenoughfound)
-		_bt_checksplitloc(&state, newitemoff, false, olddataitemstotal, 0);
-
-	/*
-	 * I believe it is not possible to fail to find a feasible split, but just
-	 * in case ...
-	 */
-	if (!state.have_split)
-		elog(ERROR, "could not find a feasible split point for index \"%s\"",
-			 RelationGetRelationName(rel));
-
-	*newitemonleft = state.newitemonleft;
-	return state.firstright;
-}
-
-/*
- * Subroutine to analyze a particular possible split choice (ie, firstright
- * and newitemonleft settings), and record the best split so far in *state.
- *
- * firstoldonright is the offset of the first item on the original page
- * that goes to the right page, and firstoldonrightsz is the size of that
- * tuple. firstoldonright can be > max offset, which means that all the old
- * items go to the left page and only the new item goes to the right page.
- * In that case, firstoldonrightsz is not used.
- *
- * olddataitemstoleft is the total size of all old items to the left of
- * firstoldonright.
- */
-static void
-_bt_checksplitloc(FindSplitData *state,
-				  OffsetNumber firstoldonright,
-				  bool newitemonleft,
-				  int olddataitemstoleft,
-				  Size firstoldonrightsz)
-{
-	int			leftfree,
-				rightfree;
-	Size		firstrightitemsz;
-	bool		newitemisfirstonright;
-
-	/* Is the new item going to be the first item on the right page? */
-	newitemisfirstonright = (firstoldonright == state->newitemoff
-							 && !newitemonleft);
-
-	if (newitemisfirstonright)
-		firstrightitemsz = state->newitemsz;
-	else
-		firstrightitemsz = firstoldonrightsz;
-
-	/* Account for all the old tuples */
-	leftfree = state->leftspace - olddataitemstoleft;
-	rightfree = state->rightspace -
-		(state->olddataitemstotal - olddataitemstoleft);
-
-	/*
-	 * The first item on the right page becomes the high key of the left page;
-	 * therefore it counts against left space as well as right space. When
-	 * index has included attributes, then those attributes of left page high
-	 * key will be truncated leaving that page with slightly more free space.
-	 * However, that shouldn't affect our ability to find valid split
-	 * location, because anyway split location should exists even without high
-	 * key truncation.
-	 */
-	leftfree -= firstrightitemsz;
-
-	/* account for the new item */
-	if (newitemonleft)
-		leftfree -= (int) state->newitemsz;
-	else
-		rightfree -= (int) state->newitemsz;
-
-	/*
-	 * If we are not on the leaf level, we will be able to discard the key
-	 * data from the first item that winds up on the right page.
-	 */
-	if (!state->is_leaf)
-		rightfree += (int) firstrightitemsz -
-			(int) (MAXALIGN(sizeof(IndexTupleData)) + sizeof(ItemIdData));
-
-	/*
-	 * If feasible split point, remember best delta.
-	 */
-	if (leftfree >= 0 && rightfree >= 0)
-	{
-		int			delta;
-
-		if (state->is_rightmost)
-		{
-			/*
-			 * If splitting a rightmost page, try to put (100-fillfactor)% of
-			 * free space on left page. See comments for _bt_findsplitloc.
-			 */
-			delta = (state->fillfactor * leftfree)
-				- ((100 - state->fillfactor) * rightfree);
-		}
-		else
-		{
-			/* Otherwise, aim for equal free space on both sides */
-			delta = leftfree - rightfree;
-		}
-
-		if (delta < 0)
-			delta = -delta;
-		if (!state->have_split || delta < state->best_delta)
-		{
-			state->have_split = true;
-			state->newitemonleft = newitemonleft;
-			state->firstright = firstoldonright;
-			state->best_delta = delta;
-		}
-	}
-}
-
 /*
  * _bt_insert_parent() -- Insert downlink into parent after a page split.
  *