Avoid scanning nulls at the beginning of a btree index scan.

If we have an inequality key that constrains the other end of the index,
it doesn't directly help us in doing the initial positioning ... but it
does imply a NOT NULL constraint on the index column.  If the index stores
nulls at this end, we can use the implied NOT NULL condition for initial
positioning, just as if it had been stated explicitly.  This avoids wasting
time when there are a lot of nulls in the column.  This is the reverse of
the examples given in bugs #6278 and #6283, which were about failing to
stop early when we encounter nulls at the end of the indexscan.

src/backend/access/nbtree/nbtsearch.c

@@ -456,6 +456,7 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 	bool		goback;
 	ScanKey		startKeys[INDEX_MAX_KEYS];
 	ScanKeyData scankeys[INDEX_MAX_KEYS];
+	ScanKeyData notnullkeys[INDEX_MAX_KEYS];
 	int			keysCount = 0;
 	int			i;
 	StrategyNumber strat_total;
@@ -506,6 +507,14 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 	 * one we use --- by definition, they are either redundant or
 	 * contradictory.
 	 *
+	 * Any regular (not SK_SEARCHNULL) key implies a NOT NULL qualifier.
+	 * If the index stores nulls at the end of the index we'll be starting
+	 * from, and we have no boundary key for the column (which means the key
+	 * we deduced NOT NULL from is an inequality key that constrains the other
+	 * end of the index), then we cons up an explicit SK_SEARCHNOTNULL key to
+	 * use as a boundary key.  If we didn't do this, we might find ourselves
+	 * traversing a lot of null entries at the start of the scan.
+	 *
 	 * In this loop, row-comparison keys are treated the same as keys on their
 	 * first (leftmost) columns.  We'll add on lower-order columns of the row
 	 * comparison below, if possible.
@@ -519,6 +528,7 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 	{
 		AttrNumber	curattr;
 		ScanKey		chosen;
+		ScanKey		impliesNN;
 		ScanKey		cur;
 
 		/*
@@ -528,6 +538,8 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 		 */
 		curattr = 1;
 		chosen = NULL;
+		/* Also remember any scankey that implies a NOT NULL constraint */
+		impliesNN = NULL;
 
 		/*
 		 * Loop iterates from 0 to numberOfKeys inclusive; we use the last
@@ -540,8 +552,32 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 			{
 				/*
 				 * Done looking at keys for curattr.  If we didn't find a
-				 * usable boundary key, quit; else save the boundary key
-				 * pointer in startKeys.
+				 * usable boundary key, see if we can deduce a NOT NULL key.
+				 */
+				if (chosen == NULL && impliesNN != NULL &&
+					((impliesNN->sk_flags & SK_BT_NULLS_FIRST) ?
+					 ScanDirectionIsForward(dir) :
+					 ScanDirectionIsBackward(dir)))
+				{
+					/* Yes, so build the key in notnullkeys[keysCount] */
+					chosen = &notnullkeys[keysCount];
+					ScanKeyEntryInitialize(chosen,
+										   (SK_SEARCHNOTNULL | SK_ISNULL |
+											(impliesNN->sk_flags &
+											 (SK_BT_DESC | SK_BT_NULLS_FIRST))),
+										   curattr,
+										   ((impliesNN->sk_flags & SK_BT_NULLS_FIRST) ?
+											BTGreaterStrategyNumber :
+											BTLessStrategyNumber),
+										   InvalidOid,
+										   InvalidOid,
+										   InvalidOid,
+										   (Datum) 0);
+				}
+
+				/*
+				 * If we still didn't find a usable boundary key, quit; else
+				 * save the boundary key pointer in startKeys.
 				 */
 				if (chosen == NULL)
 					break;
@@ -574,15 +610,27 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 				 */
 				curattr = cur->sk_attno;
 				chosen = NULL;
+				impliesNN = NULL;
 			}
 
-			/* Can we use this key as a starting boundary for this attr? */
+			/*
+			 * Can we use this key as a starting boundary for this attr?
+			 *
+			 * If not, does it imply a NOT NULL constraint?  (Because
+			 * SK_SEARCHNULL keys are always assigned BTEqualStrategyNumber,
+			 * *any* inequality key works for that; we need not test.)
+			 */
 			switch (cur->sk_strategy)
 			{
 				case BTLessStrategyNumber:
 				case BTLessEqualStrategyNumber:
-					if (chosen == NULL && ScanDirectionIsBackward(dir))
+					if (chosen == NULL)
+					{
+						if (ScanDirectionIsBackward(dir))
 							chosen = cur;
+						else
+							impliesNN = cur;
+					}
 					break;
 				case BTEqualStrategyNumber:
 					/* override any non-equality choice */
@@ -590,8 +638,13 @@ _bt_first(IndexScanDesc scan, ScanDirection dir)
 					break;
 				case BTGreaterEqualStrategyNumber:
 				case BTGreaterStrategyNumber:
-					if (chosen == NULL && ScanDirectionIsForward(dir))
+					if (chosen == NULL)
+					{
+						if (ScanDirectionIsForward(dir))
 							chosen = cur;
+						else
+							impliesNN = cur;
+					}
 					break;
 			}
 		}