Add some randomness to the choice of which GiST page to insert to.

When descending the tree for an insert, and there are multiple equally good
pages we could insert to, make the choice in random. Previously, we would
always choose the tuple with lowest offset number. That meant that when two
non-leaf pages overlap - in the extreme case they might have exactly the same
key - all but the first such page went unused. That wasn't optimal for space
usage; if you deleted some tuples from the non-first pages, the space would
never be reused.

With this patch, the other pages are sometimes chosen too, although there's
still a heavy bias towards low-offset tuples, so that we don't lose cache
locality when doing a lot of inserts with similar keys.

Original idea by Alexander Korotkov, although this patch version was written
by me and copy-edited by Tom Lane.

src/backend/access/gist/gistutil.c

@@ -379,6 +379,7 @@ gistchoose(Relation r, Page p, IndexTuple it,	/* it has compressed entry */
 	GISTENTRY	entry,
 				identry[INDEX_MAX_KEYS];
 	bool		isnull[INDEX_MAX_KEYS];
+	int			keep_current_best;
 
 	Assert(!GistPageIsLeaf(p));
 
@@ -401,6 +402,31 @@ gistchoose(Relation r, Page p, IndexTuple it,	/* it has compressed entry */
 	 */
 	best_penalty[0] = -1;
 
+	/*
+	 * If we find a tuple that's exactly as good as the currently best one, we
+	 * could use either one.  When inserting a lot of tuples with the same or
+	 * similar keys, it's preferable to descend down the same path when
+	 * possible, as that's more cache-friendly.  On the other hand, if all
+	 * inserts land on the same leaf page after a split, we're never going to
+	 * insert anything to the other half of the split, and will end up using
+	 * only 50% of the available space.  Distributing the inserts evenly would
+	 * lead to better space usage, but that hurts cache-locality during
+	 * insertion.  To get the best of both worlds, when we find a tuple that's
+	 * exactly as good as the previous best, choose randomly whether to stick
+	 * to the old best, or use the new one.  Once we decide to stick to the
+	 * old best, we keep sticking to it for any subsequent equally good tuples
+	 * we might find.  This favors tuples with low offsets, but still allows
+	 * some inserts to go to other equally-good subtrees.
+	 *
+	 * keep_current_best is -1 if we haven't yet had to make a random choice
+	 * whether to keep the current best tuple.  If we have done so, and
+	 * decided to keep it, keep_current_best is 1; if we've decided to
+	 * replace, keep_current_best is 0.  (This state will be reset to -1 as
+	 * soon as we've made the replacement, but sometimes we make the choice in
+	 * advance of actually finding a replacement best tuple.)
+	 */
+	keep_current_best = -1;
+
 	/*
 	 * Loop over tuples on page.
 	 */
@@ -446,6 +472,9 @@ gistchoose(Relation r, Page p, IndexTuple it,	/* it has compressed entry */
 
 				if (j < r->rd_att->natts - 1)
 					best_penalty[j + 1] = -1;
+
+				/* we have new best, so reset keep-it decision */
+				keep_current_best = -1;
 			}
 			else if (best_penalty[j] == usize)
 			{
@@ -468,12 +497,41 @@ gistchoose(Relation r, Page p, IndexTuple it,	/* it has compressed entry */
 		}
 
 		/*
-		 * If we find a tuple with zero penalty for all columns, there's no
-		 * need to examine remaining tuples; just break out of the loop and
-		 * return it.
+		 * If we looped past the last column, and did not update "result",
+		 * then this tuple is exactly as good as the prior best tuple.
+		 */
+		if (j == r->rd_att->natts && result != i)
+		{
+			if (keep_current_best == -1)
+			{
+				/* we didn't make the random choice yet for this old best */
+				keep_current_best = (random() <= (MAX_RANDOM_VALUE / 2)) ? 1 : 0;
+			}
+			if (keep_current_best == 0)
+			{
+				/* we choose to use the new tuple */
+				result = i;
+				/* choose again if there are even more exactly-as-good ones */
+				keep_current_best = -1;
+			}
+		}
+
+		/*
+		 * If we find a tuple with zero penalty for all columns, and we've
+		 * decided we don't want to search for another tuple with equal
+		 * penalty, there's no need to examine remaining tuples; just break
+		 * out of the loop and return it.
 		 */
 		if (zero_penalty)
-			break;
+		{
+			if (keep_current_best == -1)
+			{
+				/* we didn't make the random choice yet for this old best */
+				keep_current_best = (random() <= (MAX_RANDOM_VALUE / 2)) ? 1 : 0;
+			}
+			if (keep_current_best == 1)
+				break;
+		}
 	}
 
 	return result;