Support hashed aggregation with grouping sets.

This extends the Aggregate node with two new features: HashAggregate
can now run multiple hashtables concurrently, and a new strategy
MixedAggregate populates hashtables while doing sorted grouping.

The planner will now attempt to save as many sorts as possible when
planning grouping sets queries, while not exceeding work_mem for the
estimated combined sizes of all hashtables used.  No SQL-level changes
are required.  There should be no user-visible impact other than the
new EXPLAIN output and possible changes to result ordering when ORDER
BY was not used (which affected a few regression tests).  The
enable_hashagg option is respected.

Author: Andrew Gierth
Reviewers: Mark Dilger, Andres Freund
Discussion: https://postgr.es/m/87vatszyhj.fsf@news-spur.riddles.org.uk

src/backend/lib/Makefile

@@ -12,7 +12,7 @@ subdir = src/backend/lib
 top_builddir = ../../..
 include $(top_builddir)/src/Makefile.global
 
-OBJS = binaryheap.o bipartite_match.o hyperloglog.o ilist.o pairingheap.o \
-       rbtree.o stringinfo.o
+OBJS = binaryheap.o bipartite_match.o hyperloglog.o ilist.o knapsack.o \
+       pairingheap.o rbtree.o stringinfo.o
 
 include $(top_srcdir)/src/backend/common.mk

src/backend/lib/knapsack.c

@@ -0,0 +1,114 @@
+/*-------------------------------------------------------------------------
+ *
+ * knapsack.c
+ *	  Knapsack problem solver
+ *
+ * Given input vectors of integral item weights (must be >= 0) and values
+ * (double >= 0), compute the set of items which produces the greatest total
+ * value without exceeding a specified total weight; each item is included at
+ * most once (this is the 0/1 knapsack problem).  Weight 0 items will always be
+ * included.
+ *
+ * The performance of this algorithm is pseudo-polynomial, O(nW) where W is the
+ * weight limit.  To use with non-integral weights or approximate solutions,
+ * the caller should pre-scale the input weights to a suitable range.  This
+ * allows approximate solutions in polynomial time (the general case of the
+ * exact problem is NP-hard).
+ *
+ * Copyright (c) 2017, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ *	  src/backend/lib/knapsack.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include <math.h>
+#include <limits.h>
+
+#include "lib/knapsack.h"
+#include "miscadmin.h"
+#include "nodes/bitmapset.h"
+#include "utils/builtins.h"
+#include "utils/memutils.h"
+#include "utils/palloc.h"
+
+/*
+ * DiscreteKnapsack
+ *
+ * The item_values input is optional; if omitted, all the items are assumed to
+ * have value 1.
+ *
+ * Returns a Bitmapset of the 0..(n-1) indexes of the items chosen for
+ * inclusion in the solution.
+ *
+ * This uses the usual dynamic-programming algorithm, adapted to reuse the
+ * memory on each pass (by working from larger weights to smaller).  At the
+ * start of pass number i, the values[w] array contains the largest value
+ * computed with total weight <= w, using only items with indices < i; and
+ * sets[w] contains the bitmap of items actually used for that value.  (The
+ * bitmapsets are all pre-initialized with an unused high bit so that memory
+ * allocation is done only once.)
+ */
+Bitmapset *
+DiscreteKnapsack(int max_weight, int num_items,
+				 int *item_weights, double *item_values)
+{
+	MemoryContext local_ctx = AllocSetContextCreate(CurrentMemoryContext,
+													"Knapsack",
+													ALLOCSET_SMALL_MINSIZE,
+													ALLOCSET_SMALL_INITSIZE,
+													ALLOCSET_SMALL_MAXSIZE);
+	MemoryContext oldctx = MemoryContextSwitchTo(local_ctx);
+	double	   *values;
+	Bitmapset **sets;
+	Bitmapset  *result;
+	int			i,
+				j;
+
+	Assert(max_weight >= 0);
+	Assert(num_items > 0 && item_weights);
+
+	values = palloc((1 + max_weight) * sizeof(double));
+	sets = palloc((1 + max_weight) * sizeof(Bitmapset *));
+
+	for (i = 0; i <= max_weight; ++i)
+	{
+		values[i] = 0;
+		sets[i] = bms_make_singleton(num_items);
+	}
+
+	for (i = 0; i < num_items; ++i)
+	{
+		int			iw = item_weights[i];
+		double		iv = item_values ? item_values[i] : 1;
+
+		for (j = max_weight; j >= iw; --j)
+		{
+			int			ow = j - iw;
+
+			if (values[j] <= values[ow] + iv)
+			{
+				/* copy sets[ow] to sets[j] without realloc */
+				if (j != ow)
+				{
+					sets[j] = bms_del_members(sets[j], sets[j]);
+					sets[j] = bms_add_members(sets[j], sets[ow]);
+				}
+
+				sets[j] = bms_add_member(sets[j], i);
+
+				values[j] = values[ow] + iv;
+			}
+		}
+	}
+
+	MemoryContextSwitchTo(oldctx);
+
+	result = bms_del_member(bms_copy(sets[max_weight]), num_items);
+
+	MemoryContextDelete(local_ctx);
+
+	return result;
+}