Provide moving-aggregate support for a bunch of numerical aggregates.

First installment of the promised moving-aggregate support in built-in
aggregates: count(), sum(), avg(), stddev() and variance() for
assorted datatypes, though not for float4/float8.

In passing, remove a 2001-vintage kluge in interval_accum(): interval
array elements have been properly aligned since around 2003, but
nobody remembered to take out this workaround.  Also, fix a thinko
in the opr_sanity tests for moving-aggregate catalog entries.

David Rowley and Florian Pflug, reviewed by Dean Rasheed

src/backend/utils/adt/int8.c

@@ -717,13 +717,58 @@ int8inc(PG_FUNCTION_ARGS)
 	}
 }
 
+Datum
+int8dec(PG_FUNCTION_ARGS)
+{
+	/*
+	 * When int8 is pass-by-reference, we provide this special case to avoid
+	 * palloc overhead for COUNT(): when called as an aggregate, we know that
+	 * the argument is modifiable local storage, so just update it in-place.
+	 * (If int8 is pass-by-value, then of course this is useless as well as
+	 * incorrect, so just ifdef it out.)
+	 */
+#ifndef USE_FLOAT8_BYVAL		/* controls int8 too */
+	if (AggCheckCallContext(fcinfo, NULL))
+	{
+		int64	   *arg = (int64 *) PG_GETARG_POINTER(0);
+		int64		result;
+
+		result = *arg - 1;
+		/* Overflow check */
+		if (result > 0 && *arg < 0)
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("bigint out of range")));
+
+		*arg = result;
+		PG_RETURN_POINTER(arg);
+	}
+	else
+#endif
+	{
+		/* Not called as an aggregate, so just do it the dumb way */
+		int64		arg = PG_GETARG_INT64(0);
+		int64		result;
+
+		result = arg - 1;
+		/* Overflow check */
+		if (result > 0 && arg < 0)
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("bigint out of range")));
+
+		PG_RETURN_INT64(result);
+	}
+}
+
+
 /*
- * These functions are exactly like int8inc but are used for aggregates that
- * count only non-null values.	Since the functions are declared strict,
- * the null checks happen before we ever get here, and all we need do is
- * increment the state value.  We could actually make these pg_proc entries
- * point right at int8inc, but then the opr_sanity regression test would
- * complain about mismatched entries for a built-in function.
+ * These functions are exactly like int8inc/int8dec but are used for
+ * aggregates that count only non-null values.	Since the functions are
+ * declared strict, the null checks happen before we ever get here, and all we
+ * need do is increment the state value.  We could actually make these pg_proc
+ * entries point right at int8inc/int8dec, but then the opr_sanity regression
+ * test would complain about mismatched entries for a built-in function.
  */
 
 Datum
@@ -738,6 +783,12 @@ int8inc_float8_float8(PG_FUNCTION_ARGS)
 	return int8inc(fcinfo);
 }
 
+Datum
+int8dec_any(PG_FUNCTION_ARGS)
+{
+	return int8dec(fcinfo);
+}
+
 
 Datum
 int8larger(PG_FUNCTION_ARGS)

src/backend/utils/adt/timestamp.c

@@ -3229,7 +3229,6 @@ interval_mi(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DATETIME_VALUE_OUT_OF_RANGE),
 				 errmsg("interval out of range")));
 
-
 	PG_RETURN_INTERVAL_P(result);
 }
 
@@ -3376,12 +3375,18 @@ interval_div(PG_FUNCTION_ARGS)
 }
 
 /*
- * interval_accum and interval_avg implement the AVG(interval) aggregate.
+ * interval_accum, interval_accum_inv, and interval_avg implement the
+ * AVG(interval) aggregate.
  *
  * The transition datatype for this aggregate is a 2-element array of
  * intervals, where the first is the running sum and the second contains
  * the number of values so far in its 'time' field.  This is a bit ugly
  * but it beats inventing a specialized datatype for the purpose.
+ *
+ * NOTE: The inverse transition function cannot guarantee exact results
+ * when using float8 timestamps.  However, int8 timestamps are now the
+ * norm, and the probable range of values is not so wide that disastrous
+ * cancellation is likely even with float8, so we'll ignore the risk.
  */
 
 Datum
@@ -3402,17 +3407,8 @@ interval_accum(PG_FUNCTION_ARGS)
 	if (ndatums != 2)
 		elog(ERROR, "expected 2-element interval array");
 
-	/*
-	 * XXX memcpy, instead of just extracting a pointer, to work around buggy
-	 * array code: it won't ensure proper alignment of Interval objects on
-	 * machines where double requires 8-byte alignment. That should be fixed,
-	 * but in the meantime...
-	 *
-	 * Note: must use DatumGetPointer here, not DatumGetIntervalP, else some
-	 * compilers optimize into double-aligned load/store anyway.
-	 */
-	memcpy((void *) &sumX, DatumGetPointer(transdatums[0]), sizeof(Interval));
-	memcpy((void *) &N, DatumGetPointer(transdatums[1]), sizeof(Interval));
+	sumX = *(DatumGetIntervalP(transdatums[0]));
+	N = *(DatumGetIntervalP(transdatums[1]));
 
 	newsum = DatumGetIntervalP(DirectFunctionCall2(interval_pl,
 												   IntervalPGetDatum(&sumX),
@@ -3428,6 +3424,41 @@ interval_accum(PG_FUNCTION_ARGS)
 	PG_RETURN_ARRAYTYPE_P(result);
 }
 
+Datum
+interval_accum_inv(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	Interval   *newval = PG_GETARG_INTERVAL_P(1);
+	Datum	   *transdatums;
+	int			ndatums;
+	Interval	sumX,
+				N;
+	Interval   *newsum;
+	ArrayType  *result;
+
+	deconstruct_array(transarray,
+					  INTERVALOID, sizeof(Interval), false, 'd',
+					  &transdatums, NULL, &ndatums);
+	if (ndatums != 2)
+		elog(ERROR, "expected 2-element interval array");
+
+	sumX = *(DatumGetIntervalP(transdatums[0]));
+	N = *(DatumGetIntervalP(transdatums[1]));
+
+	newsum = DatumGetIntervalP(DirectFunctionCall2(interval_mi,
+												   IntervalPGetDatum(&sumX),
+												 IntervalPGetDatum(newval)));
+	N.time -= 1;
+
+	transdatums[0] = IntervalPGetDatum(newsum);
+	transdatums[1] = IntervalPGetDatum(&N);
+
+	result = construct_array(transdatums, 2,
+							 INTERVALOID, sizeof(Interval), false, 'd');
+
+	PG_RETURN_ARRAYTYPE_P(result);
+}
+
 Datum
 interval_avg(PG_FUNCTION_ARGS)
 {
@@ -3443,17 +3474,8 @@ interval_avg(PG_FUNCTION_ARGS)
 	if (ndatums != 2)
 		elog(ERROR, "expected 2-element interval array");
 
-	/*
-	 * XXX memcpy, instead of just extracting a pointer, to work around buggy
-	 * array code: it won't ensure proper alignment of Interval objects on
-	 * machines where double requires 8-byte alignment. That should be fixed,
-	 * but in the meantime...
-	 *
-	 * Note: must use DatumGetPointer here, not DatumGetIntervalP, else some
-	 * compilers optimize into double-aligned load/store anyway.
-	 */
-	memcpy((void *) &sumX, DatumGetPointer(transdatums[0]), sizeof(Interval));
-	memcpy((void *) &N, DatumGetPointer(transdatums[1]), sizeof(Interval));
+	sumX = *(DatumGetIntervalP(transdatums[0]));
+	N = *(DatumGetIntervalP(transdatums[1]));
 
 	/* SQL defines AVG of no values to be NULL */
 	if (N.time == 0)
@@ -3461,7 +3483,7 @@ interval_avg(PG_FUNCTION_ARGS)
 
 	return DirectFunctionCall2(interval_div,
 							   IntervalPGetDatum(&sumX),
-							   Float8GetDatum(N.time));
+							   Float8GetDatum((double) N.time));
 }
 
 

src/include/catalog/catversion.h

@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201404121
+#define CATALOG_VERSION_NO	201404122
 
 #endif

src/include/catalog/pg_proc.h

@@ -1311,8 +1311,12 @@ DESCR("truncate interval to specified units");
 
 DATA(insert OID = 1219 (  int8inc		   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 20 "20" _null_ _null_ _null_ _null_ int8inc _null_ _null_ _null_ ));
 DESCR("increment");
+DATA(insert OID = 3546 (  int8dec		   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 20 "20" _null_ _null_ _null_ _null_ int8dec _null_ _null_ _null_ ));
+DESCR("decrement");
 DATA(insert OID = 2804 (  int8inc_any	   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 20 "20 2276" _null_ _null_ _null_ _null_ int8inc_any _null_ _null_ _null_ ));
 DESCR("increment, ignores second argument");
+DATA(insert OID = 3547 (  int8dec_any	   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 20 "20 2276" _null_ _null_ _null_ _null_ int8dec_any _null_ _null_ _null_ ));
+DESCR("decrement, ignores second argument");
 DATA(insert OID = 1230 (  int8abs		   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 20 "20" _null_ _null_ _null_ _null_ int8abs _null_ _null_ _null_ ));
 
 DATA(insert OID = 1236 (  int8larger	   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 20 "20 20" _null_ _null_ _null_ _null_ int8larger _null_ _null_ _null_ ));
@@ -2423,6 +2427,8 @@ DATA(insert OID = 1833 (  numeric_accum    PGNSP PGUID 12 1 0 0 0 f f f f f f i
 DESCR("aggregate transition function");
 DATA(insert OID = 2858 (  numeric_avg_accum    PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 1700" _null_ _null_ _null_ _null_ numeric_avg_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3548 (  numeric_accum_inv    PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 1700" _null_ _null_ _null_ _null_ numeric_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 1834 (  int2_accum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 21" _null_ _null_ _null_ _null_ int2_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
 DATA(insert OID = 1835 (  int4_accum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 23" _null_ _null_ _null_ _null_ int4_accum _null_ _null_ _null_ ));
@@ -2431,6 +2437,12 @@ DATA(insert OID = 1836 (  int8_accum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0
 DESCR("aggregate transition function");
 DATA(insert OID = 2746 (  int8_avg_accum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 20" _null_ _null_ _null_ _null_ int8_avg_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3567 (  int2_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 21" _null_ _null_ _null_ _null_ int2_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
+DATA(insert OID = 3568 (  int4_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 23" _null_ _null_ _null_ _null_ int4_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
+DATA(insert OID = 3569 (  int8_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 2281 "2281 20" _null_ _null_ _null_ _null_ int8_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 3178 (  numeric_sum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_sum _null_ _null_ _null_ ));
 DESCR("aggregate final function");
 DATA(insert OID = 1837 (  numeric_avg	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_avg _null_ _null_ _null_ ));
@@ -2451,14 +2463,22 @@ DATA(insert OID = 1842 (  int8_sum		   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0
 DESCR("aggregate transition function");
 DATA(insert OID = 1843 (  interval_accum   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1187 "1187 1186" _null_ _null_ _null_ _null_ interval_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3549 (  interval_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1187 "1187 1186" _null_ _null_ _null_ _null_ interval_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 1844 (  interval_avg	   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 1186 "1187" _null_ _null_ _null_ _null_ interval_avg _null_ _null_ _null_ ));
 DESCR("aggregate final function");
 DATA(insert OID = 1962 (  int2_avg_accum   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1016 "1016 21" _null_ _null_ _null_ _null_ int2_avg_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
 DATA(insert OID = 1963 (  int4_avg_accum   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1016 "1016 23" _null_ _null_ _null_ _null_ int4_avg_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3570 (  int2_avg_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1016 "1016 21" _null_ _null_ _null_ _null_ int2_avg_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
+DATA(insert OID = 3571 (  int4_avg_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f t f i 2 0 1016 "1016 23" _null_ _null_ _null_ _null_ int4_avg_accum_inv _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 1964 (  int8_avg		   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 1700 "1016" _null_ _null_ _null_ _null_ int8_avg _null_ _null_ _null_ ));
 DESCR("aggregate final function");
+DATA(insert OID = 3572 (  int2int4_sum	   PGNSP PGUID 12 1 0 0 0 f f f f t f i 1 0 20 "1016" _null_ _null_ _null_ _null_ int2int4_sum _null_ _null_ _null_ ));
+DESCR("aggregate final function");
 DATA(insert OID = 2805 (  int8inc_float8_float8		PGNSP PGUID 12 1 0 0 0 f f f f t f i 3 0 20 "20 701 701" _null_ _null_ _null_ _null_ int8inc_float8_float8 _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
 DATA(insert OID = 2806 (  float8_regr_accum			PGNSP PGUID 12 1 0 0 0 f f f f t f i 3 0 1022 "1022 701 701" _null_ _null_ _null_ _null_ float8_regr_accum _null_ _null_ _null_ ));

src/include/utils/builtins.h

@@ -1005,9 +1005,13 @@ extern Datum float4_numeric(PG_FUNCTION_ARGS);
 extern Datum numeric_float4(PG_FUNCTION_ARGS);
 extern Datum numeric_accum(PG_FUNCTION_ARGS);
 extern Datum numeric_avg_accum(PG_FUNCTION_ARGS);
+extern Datum numeric_accum_inv(PG_FUNCTION_ARGS);
 extern Datum int2_accum(PG_FUNCTION_ARGS);
 extern Datum int4_accum(PG_FUNCTION_ARGS);
 extern Datum int8_accum(PG_FUNCTION_ARGS);
+extern Datum int2_accum_inv(PG_FUNCTION_ARGS);
+extern Datum int4_accum_inv(PG_FUNCTION_ARGS);
+extern Datum int8_accum_inv(PG_FUNCTION_ARGS);
 extern Datum int8_avg_accum(PG_FUNCTION_ARGS);
 extern Datum numeric_avg(PG_FUNCTION_ARGS);
 extern Datum numeric_sum(PG_FUNCTION_ARGS);
@@ -1020,7 +1024,10 @@ extern Datum int4_sum(PG_FUNCTION_ARGS);
 extern Datum int8_sum(PG_FUNCTION_ARGS);
 extern Datum int2_avg_accum(PG_FUNCTION_ARGS);
 extern Datum int4_avg_accum(PG_FUNCTION_ARGS);
+extern Datum int2_avg_accum_inv(PG_FUNCTION_ARGS);
+extern Datum int4_avg_accum_inv(PG_FUNCTION_ARGS);
 extern Datum int8_avg(PG_FUNCTION_ARGS);
+extern Datum int2int4_sum(PG_FUNCTION_ARGS);
 extern Datum width_bucket_numeric(PG_FUNCTION_ARGS);
 extern Datum hash_numeric(PG_FUNCTION_ARGS);
 

src/include/utils/int8.h

@@ -74,8 +74,10 @@ extern Datum int8div(PG_FUNCTION_ARGS);
 extern Datum int8abs(PG_FUNCTION_ARGS);
 extern Datum int8mod(PG_FUNCTION_ARGS);
 extern Datum int8inc(PG_FUNCTION_ARGS);
+extern Datum int8dec(PG_FUNCTION_ARGS);
 extern Datum int8inc_any(PG_FUNCTION_ARGS);
 extern Datum int8inc_float8_float8(PG_FUNCTION_ARGS);
+extern Datum int8dec_any(PG_FUNCTION_ARGS);
 extern Datum int8larger(PG_FUNCTION_ARGS);
 extern Datum int8smaller(PG_FUNCTION_ARGS);
 

src/include/utils/timestamp.h

@@ -184,6 +184,7 @@ extern Datum interval_mul(PG_FUNCTION_ARGS);
 extern Datum mul_d_interval(PG_FUNCTION_ARGS);
 extern Datum interval_div(PG_FUNCTION_ARGS);
 extern Datum interval_accum(PG_FUNCTION_ARGS);
+extern Datum interval_accum_inv(PG_FUNCTION_ARGS);
 extern Datum interval_avg(PG_FUNCTION_ARGS);
 
 extern Datum timestamp_mi(PG_FUNCTION_ARGS);

src/test/regress/expected/opr_sanity.out

@@ -936,13 +936,13 @@ WHERE a.aggfnoid = p.oid AND
 ----------+---------+-----+---------
 (0 rows)
 
--- transfn and mtransfn should have same strictness setting.
-SELECT a.aggfnoid::oid, p.proname, ptr.oid, ptr.proname, mptr.oid, mptr.proname
-FROM pg_aggregate AS a, pg_proc AS p, pg_proc AS ptr, pg_proc AS mptr
+-- mtransfn and minvtransfn should have same strictness setting.
+SELECT a.aggfnoid::oid, p.proname, ptr.oid, ptr.proname, iptr.oid, iptr.proname
+FROM pg_aggregate AS a, pg_proc AS p, pg_proc AS ptr, pg_proc AS iptr
 WHERE a.aggfnoid = p.oid AND
-    a.aggtransfn = ptr.oid AND
-    a.aggmtransfn = mptr.oid AND
-    ptr.proisstrict != mptr.proisstrict;
+    a.aggmtransfn = ptr.oid AND
+    a.aggminvtransfn = iptr.oid AND
+    ptr.proisstrict != iptr.proisstrict;
  aggfnoid | proname | oid | proname | oid | proname 
 ----------+---------+-----+---------+-----+---------
 (0 rows)

src/test/regress/sql/opr_sanity.sql

@@ -760,14 +760,14 @@ WHERE a.aggfnoid = p.oid AND
     a.aggminitval IS NULL AND
     NOT binary_coercible(p.proargtypes[0], a.aggmtranstype);
 
--- transfn and mtransfn should have same strictness setting.
+-- mtransfn and minvtransfn should have same strictness setting.
 
-SELECT a.aggfnoid::oid, p.proname, ptr.oid, ptr.proname, mptr.oid, mptr.proname
-FROM pg_aggregate AS a, pg_proc AS p, pg_proc AS ptr, pg_proc AS mptr
+SELECT a.aggfnoid::oid, p.proname, ptr.oid, ptr.proname, iptr.oid, iptr.proname
+FROM pg_aggregate AS a, pg_proc AS p, pg_proc AS ptr, pg_proc AS iptr
 WHERE a.aggfnoid = p.oid AND
-    a.aggtransfn = ptr.oid AND
-    a.aggmtransfn = mptr.oid AND
-    ptr.proisstrict != mptr.proisstrict;
+    a.aggmtransfn = ptr.oid AND
+    a.aggminvtransfn = iptr.oid AND
+    ptr.proisstrict != iptr.proisstrict;
 
 -- Cross-check aggsortop (if present) against pg_operator.
 -- We expect to find entries for bool_and, bool_or, every, max, and min.

src/test/regress/sql/window.sql

@@ -476,3 +476,144 @@ JOIN sum_following ON sum_following.i = vs.i
 WINDOW fwd AS (
 	ORDER BY vs.i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
 );
+
+--
+-- Test various built-in aggregates that have moving-aggregate support
+--
+
+-- test inverse transition functions handle NULLs properly
+SELECT i,AVG(v::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,AVG(v::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,AVG(v::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,AVG(v::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1.5),(2,2.5),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,AVG(v::interval) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,'1 sec'),(2,'2 sec'),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::money) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,'1.10'),(2,'2.20'),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::interval) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,'1 sec'),(2,'2 sec'),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1.1),(2,2.2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT SUM(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1.01),(2,2),(3,3)) v(i,n);
+
+SELECT i,COUNT(v) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,COUNT(*) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT VAR_POP(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_POP(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_POP(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_POP(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_SAMP(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_SAMP(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_SAMP(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VAR_SAMP(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VARIANCE(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VARIANCE(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VARIANCE(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT VARIANCE(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT STDDEV_POP(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_POP(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_POP(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_POP(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_SAMP(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_SAMP(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_SAMP(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV_SAMP(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(1,NULL),(2,600),(3,470),(4,170),(5,430),(6,300)) r(i,n);
+
+SELECT STDDEV(n::bigint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(0,NULL),(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT STDDEV(n::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(0,NULL),(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT STDDEV(n::smallint) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(0,NULL),(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+SELECT STDDEV(n::numeric) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING)
+  FROM (VALUES(0,NULL),(1,600),(2,470),(3,170),(4,430),(5,300)) r(i,n);
+
+-- test that inverse transition functions work with various frame options
+SELECT i,SUM(v::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND CURRENT ROW)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::int) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND 1 FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,NULL),(4,NULL)) t(i,v);
+
+SELECT i,SUM(v::int) OVER (ORDER BY i ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+  FROM (VALUES(1,1),(2,2),(3,3),(4,4)) t(i,v);
+
+-- ensure aggregate over numeric properly recovers from NaN values
+SELECT a, b,
+       SUM(b) OVER(ORDER BY A ROWS BETWEEN 1 PRECEDING AND CURRENT ROW)
+FROM (VALUES(1,1::numeric),(2,2),(3,'NaN'),(4,3),(5,4)) t(a,b);
+
+-- It might be tempting for someone to add an inverse trans function for
+-- float and double precision. This should not be done as it can give incorrect
+-- results. This test should fail if anyone ever does this without thinking too
+-- hard about it.
+SELECT to_char(SUM(n::float8) OVER (ORDER BY i ROWS BETWEEN CURRENT ROW AND 1 FOLLOWING),'999999999999999999999D9')
+  FROM (VALUES(1,1e20),(2,1)) n(i,n);