Implement binary heap replace-top operation in a smarter way.

In external sort's merge phase, we maintain a binary heap holding the next
tuple from each input tape. On each step, the topmost tuple is returned,
and replaced with the next tuple from the same tape. We were doing the
replacement by deleting the top node in one operation, and inserting the
next tuple after that. However, you can do a "replace-top" operation more
efficiently, in one "sift-up". A deletion will always walk the heap from
top to bottom, but in a replacement, we can stop as soon as we find the
right place for the new tuple. This is particularly helpful, if the tapes
are not in completely random order, so that the next tuple from a tape is
likely to land near the top of the heap.

Peter Geoghegan, reviewed by Claudio Freire, with some editing by me.

Discussion: <CAM3SWZRhBhiknTF_=NjDSnNZ11hx=U_SEYwbc5vd=x7M4mMiCw@mail.gmail.com>

src/backend/utils/sort/tuplesort.c

@@ -69,25 +69,25 @@
  * using Algorithm D.
  *
  * When merging runs, we use a heap containing just the frontmost tuple from
- * each source run; we repeatedly output the smallest tuple and insert the
- * next tuple from its source tape (if any).  When the heap empties, the merge
- * is complete.  The basic merge algorithm thus needs very little memory ---
- * only M tuples for an M-way merge, and M is constrained to a small number.
- * However, we can still make good use of our full workMem allocation by
- * pre-reading additional tuples from each source tape.  Without prereading,
- * our access pattern to the temporary file would be very erratic; on average
- * we'd read one block from each of M source tapes during the same time that
- * we're writing M blocks to the output tape, so there is no sequentiality of
- * access at all, defeating the read-ahead methods used by most Unix kernels.
- * Worse, the output tape gets written into a very random sequence of blocks
- * of the temp file, ensuring that things will be even worse when it comes
- * time to read that tape.  A straightforward merge pass thus ends up doing a
- * lot of waiting for disk seeks.  We can improve matters by prereading from
- * each source tape sequentially, loading about workMem/M bytes from each tape
- * in turn.  Then we run the merge algorithm, writing but not reading until
- * one of the preloaded tuple series runs out.  Then we switch back to preread
- * mode, fill memory again, and repeat.  This approach helps to localize both
- * read and write accesses.
+ * each source run; we repeatedly output the smallest tuple and replace it
+ * with the next tuple from its source tape (if any).  When the heap empties,
+ * the merge is complete.  The basic merge algorithm thus needs very little
+ * memory --- only M tuples for an M-way merge, and M is constrained to a
+ * small number.  However, we can still make good use of our full workMem
+ * allocation by pre-reading additional tuples from each source tape.  Without
+ * prereading, our access pattern to the temporary file would be very erratic;
+ * on average we'd read one block from each of M source tapes during the same
+ * time that we're writing M blocks to the output tape, so there is no
+ * sequentiality of access at all, defeating the read-ahead methods used by
+ * most Unix kernels.  Worse, the output tape gets written into a very random
+ * sequence of blocks of the temp file, ensuring that things will be even
+ * worse when it comes time to read that tape.  A straightforward merge pass
+ * thus ends up doing a lot of waiting for disk seeks.  We can improve matters
+ * by prereading from each source tape sequentially, loading about workMem/M
+ * bytes from each tape in turn.  Then we run the merge algorithm, writing but
+ * not reading until one of the preloaded tuple series runs out.  Then we
+ * switch back to preread mode, fill memory again, and repeat.  This approach
+ * helps to localize both read and write accesses.
  *
  * When the caller requests random access to the sort result, we form
  * the final sorted run on a logical tape which is then "frozen", so
@@ -569,8 +569,10 @@ static void make_bounded_heap(Tuplesortstate *state);
 static void sort_bounded_heap(Tuplesortstate *state);
 static void tuplesort_sort_memtuples(Tuplesortstate *state);
 static void tuplesort_heap_insert(Tuplesortstate *state, SortTuple *tuple,
-					  int tupleindex, bool checkIndex);
-static void tuplesort_heap_siftup(Tuplesortstate *state, bool checkIndex);
+					  bool checkIndex);
+static void tuplesort_heap_replace_top(Tuplesortstate *state, SortTuple *tuple,
+						   bool checkIndex);
+static void tuplesort_heap_delete_top(Tuplesortstate *state, bool checkIndex);
 static void reversedirection(Tuplesortstate *state);
 static unsigned int getlen(Tuplesortstate *state, int tapenum, bool eofOK);
 static void markrunend(Tuplesortstate *state, int tapenum);
@@ -1617,10 +1619,10 @@ puttuple_common(Tuplesortstate *state, SortTuple *tuple)
 			}
 			else
 			{
-				/* discard top of heap, sift up, insert new tuple */
+				/* discard top of heap, replacing it with the new tuple */
 				free_sort_tuple(state, &state->memtuples[0]);
-				tuplesort_heap_siftup(state, false);
-				tuplesort_heap_insert(state, tuple, 0, false);
+				tuple->tupindex = 0;	/* not used */
+				tuplesort_heap_replace_top(state, tuple, false);
 			}
 			break;
 
@@ -1665,7 +1667,8 @@ puttuple_common(Tuplesortstate *state, SortTuple *tuple)
 				 * initial COMPARETUP() call is required for the tuple, to
 				 * determine that the tuple does not belong in RUN_FIRST).
 				 */
-				tuplesort_heap_insert(state, tuple, state->currentRun, true);
+				tuple->tupindex = state->currentRun;
+				tuplesort_heap_insert(state, tuple, true);
 			}
 			else
 			{
@@ -1987,7 +1990,6 @@ tuplesort_gettuple_common(Tuplesortstate *state, bool forward,
 				 * more generally.
 				 */
 				*stup = state->memtuples[0];
-				tuplesort_heap_siftup(state, false);
 				if ((tupIndex = state->mergenext[srcTape]) == 0)
 				{
 					/*
@@ -2008,18 +2010,25 @@ tuplesort_gettuple_common(Tuplesortstate *state, bool forward,
 					 */
 					if ((tupIndex = state->mergenext[srcTape]) == 0)
 					{
+						/* Remove the top node from the heap */
+						tuplesort_heap_delete_top(state, false);
 						/* Free tape's buffer, avoiding dangling pointer */
 						if (state->batchUsed)
 							mergebatchfreetape(state, srcTape, stup, should_free);
 						return true;
 					}
 				}
-				/* pull next preread tuple from list, insert in heap */
+
+				/*
+				 * pull next preread tuple from list, and replace the returned
+				 * tuple at top of the heap with it.
+				 */
 				newtup = &state->memtuples[tupIndex];
 				state->mergenext[srcTape] = newtup->tupindex;
 				if (state->mergenext[srcTape] == 0)
 					state->mergelast[srcTape] = 0;
-				tuplesort_heap_insert(state, newtup, srcTape, false);
+				newtup->tupindex = srcTape;
+				tuplesort_heap_replace_top(state, newtup, false);
 				/* put the now-unused memtuples entry on the freelist */
 				newtup->tupindex = state->mergefreelist;
 				state->mergefreelist = tupIndex;
@@ -2394,7 +2403,8 @@ inittapes(Tuplesortstate *state)
 			/* Must copy source tuple to avoid possible overwrite */
 			SortTuple	stup = state->memtuples[j];
 
-			tuplesort_heap_insert(state, &stup, 0, false);
+			stup.tupindex = RUN_FIRST;
+			tuplesort_heap_insert(state, &stup, false);
 		}
 		Assert(state->memtupcount == ntuples);
 	}
@@ -2642,22 +2652,29 @@ mergeonerun(Tuplesortstate *state)
 		/* writetup adjusted total free space, now fix per-tape space */
 		spaceFreed = state->availMem - priorAvail;
 		state->mergeavailmem[srcTape] += spaceFreed;
-		/* compact the heap */
-		tuplesort_heap_siftup(state, false);
 		if ((tupIndex = state->mergenext[srcTape]) == 0)
 		{
 			/* out of preloaded data on this tape, try to read more */
 			mergepreread(state);
 			/* if still no data, we've reached end of run on this tape */
 			if ((tupIndex = state->mergenext[srcTape]) == 0)
+			{
+				/* remove the written-out tuple from the heap */
+				tuplesort_heap_delete_top(state, false);
 				continue;
 			}
-		/* pull next preread tuple from list, insert in heap */
+		}
+
+		/*
+		 * pull next preread tuple from list, and replace the written-out
+		 * tuple in the heap with it.
+		 */
 		tup = &state->memtuples[tupIndex];
 		state->mergenext[srcTape] = tup->tupindex;
 		if (state->mergenext[srcTape] == 0)
 			state->mergelast[srcTape] = 0;
-		tuplesort_heap_insert(state, tup, srcTape, false);
+		tup->tupindex = srcTape;
+		tuplesort_heap_replace_top(state, tup, false);
 		/* put the now-unused memtuples entry on the freelist */
 		tup->tupindex = state->mergefreelist;
 		state->mergefreelist = tupIndex;
@@ -2793,7 +2810,8 @@ beginmerge(Tuplesortstate *state, bool finalMergeBatch)
 			state->mergenext[srcTape] = tup->tupindex;
 			if (state->mergenext[srcTape] == 0)
 				state->mergelast[srcTape] = 0;
-			tuplesort_heap_insert(state, tup, srcTape, false);
+			tup->tupindex = srcTape;
+			tuplesort_heap_insert(state, tup, false);
 			/* put the now-unused memtuples entry on the freelist */
 			tup->tupindex = state->mergefreelist;
 			state->mergefreelist = tupIndex;
@@ -3275,13 +3293,12 @@ dumptuples(Tuplesortstate *state, bool alltuples)
 			 * Still holding out for a case favorable to replacement
 			 * selection. Still incrementally spilling using heap.
 			 *
-			 * Dump the heap's frontmost entry, and sift up to remove it from
-			 * the heap.
+			 * Dump the heap's frontmost entry, and remove it from the heap.
 			 */
 			Assert(state->memtupcount > 0);
 			WRITETUP(state, state->tp_tapenum[state->destTape],
 					 &state->memtuples[0]);
-			tuplesort_heap_siftup(state, true);
+			tuplesort_heap_delete_top(state, true);
 		}
 		else
 		{
@@ -3644,27 +3661,29 @@ make_bounded_heap(Tuplesortstate *state)
 	state->memtupcount = 0;		/* make the heap empty */
 	for (i = 0; i < tupcount; i++)
 	{
-		if (state->memtupcount >= state->bound &&
-		  COMPARETUP(state, &state->memtuples[i], &state->memtuples[0]) <= 0)
-		{
-			/* New tuple would just get thrown out, so skip it */
-			free_sort_tuple(state, &state->memtuples[i]);
-			CHECK_FOR_INTERRUPTS();
-		}
-		else
+		if (state->memtupcount < state->bound)
 		{
 			/* Insert next tuple into heap */
 			/* Must copy source tuple to avoid possible overwrite */
 			SortTuple	stup = state->memtuples[i];
 
-			tuplesort_heap_insert(state, &stup, 0, false);
-
-			/* If heap too full, discard largest entry */
-			if (state->memtupcount > state->bound)
+			stup.tupindex = 0;	/* not used */
+			tuplesort_heap_insert(state, &stup, false);
+		}
+		else
 		{
-				free_sort_tuple(state, &state->memtuples[0]);
-				tuplesort_heap_siftup(state, false);
+			/*
+			 * The heap is full.  Replace the largest entry with the new
+			 * tuple, or just discard it, if it's larger than anything already
+			 * in the heap.
+			 */
+			if (COMPARETUP(state, &state->memtuples[i], &state->memtuples[0]) <= 0)
+			{
+				free_sort_tuple(state, &state->memtuples[i]);
+				CHECK_FOR_INTERRUPTS();
 			}
+			else
+				tuplesort_heap_replace_top(state, &state->memtuples[i], false);
 		}
 	}
 
@@ -3685,16 +3704,16 @@ sort_bounded_heap(Tuplesortstate *state)
 	Assert(tupcount == state->bound);
 
 	/*
-	 * We can unheapify in place because each sift-up will remove the largest
-	 * entry, which we can promptly store in the newly freed slot at the end.
-	 * Once we're down to a single-entry heap, we're done.
+	 * We can unheapify in place because each delete-top call will remove the
+	 * largest entry, which we can promptly store in the newly freed slot at
+	 * the end.  Once we're down to a single-entry heap, we're done.
 	 */
 	while (state->memtupcount > 1)
 	{
 		SortTuple	stup = state->memtuples[0];
 
 		/* this sifts-up the next-largest entry and decreases memtupcount */
-		tuplesort_heap_siftup(state, false);
+		tuplesort_heap_delete_top(state, false);
 		state->memtuples[state->memtupcount] = stup;
 	}
 	state->memtupcount = tupcount;
@@ -3738,30 +3757,21 @@ tuplesort_sort_memtuples(Tuplesortstate *state)
  * Insert a new tuple into an empty or existing heap, maintaining the
  * heap invariant.  Caller is responsible for ensuring there's room.
  *
- * Note: we assume *tuple is a temporary variable that can be scribbled on.
- * For some callers, tuple actually points to a memtuples[] entry above the
+ * Note: For some callers, tuple points to a memtuples[] entry above the
  * end of the heap.  This is safe as long as it's not immediately adjacent
  * to the end of the heap (ie, in the [memtupcount] array entry) --- if it
  * is, it might get overwritten before being moved into the heap!
  */
 static void
 tuplesort_heap_insert(Tuplesortstate *state, SortTuple *tuple,
-					  int tupleindex, bool checkIndex)
+					  bool checkIndex)
 {
 	SortTuple  *memtuples;
 	int			j;
 
-	/*
-	 * Save the tupleindex --- see notes above about writing on *tuple. It's a
-	 * historical artifact that tupleindex is passed as a separate argument
-	 * and not in *tuple, but it's notationally convenient so let's leave it
-	 * that way.
-	 */
-	tuple->tupindex = tupleindex;
-
 	memtuples = state->memtuples;
 	Assert(state->memtupcount < state->memtupsize);
-	Assert(!checkIndex || tupleindex == RUN_FIRST);
+	Assert(!checkIndex || tuple->tupindex == RUN_FIRST);
 
 	CHECK_FOR_INTERRUPTS();
 
@@ -3783,25 +3793,51 @@ tuplesort_heap_insert(Tuplesortstate *state, SortTuple *tuple,
 }
 
 /*
- * The tuple at state->memtuples[0] has been removed from the heap.
- * Decrement memtupcount, and sift up to maintain the heap invariant.
+ * Remove the tuple at state->memtuples[0] from the heap.  Decrement
+ * memtupcount, and sift up to maintain the heap invariant.
+ *
+ * The caller has already free'd the tuple the top node points to,
+ * if necessary.
  */
 static void
-tuplesort_heap_siftup(Tuplesortstate *state, bool checkIndex)
+tuplesort_heap_delete_top(Tuplesortstate *state, bool checkIndex)
 {
 	SortTuple  *memtuples = state->memtuples;
 	SortTuple  *tuple;
-	int			i,
-				n;
 
 	Assert(!checkIndex || state->currentRun == RUN_FIRST);
 	if (--state->memtupcount <= 0)
 		return;
 
+	/*
+	 * Remove the last tuple in the heap, and re-insert it, by replacing the
+	 * current top node with it.
+	 */
+	tuple = &memtuples[state->memtupcount];
+	tuplesort_heap_replace_top(state, tuple, checkIndex);
+}
+
+/*
+ * Replace the tuple at state->memtuples[0] with a new tuple.  Sift up to
+ * maintain the heap invariant.
+ *
+ * This corresponds to Knuth's "sift-up" algorithm (Algorithm 5.2.3H,
+ * Heapsort, steps H3-H8).
+ */
+static void
+tuplesort_heap_replace_top(Tuplesortstate *state, SortTuple *tuple,
+						   bool checkIndex)
+{
+	SortTuple  *memtuples = state->memtuples;
+	int			i,
+				n;
+
+	Assert(!checkIndex || state->currentRun == RUN_FIRST);
+	Assert(state->memtupcount >= 1);
+
 	CHECK_FOR_INTERRUPTS();
 
 	n = state->memtupcount;
-	tuple = &memtuples[n];		/* tuple that must be reinserted */
 	i = 0;						/* i is where the "hole" is */
 	for (;;)
 	{