A new version of the patch is attached, which changes the following:

- Changed from using __int128_t to __int128.
- Actually compiles and runs code in configure to see that int128 works.
- No longer tests for __uint128_t.
- Updated pg_config.h.win32
- Renamed some things from int12 to int128, there are still some places with int16 which I am not sure what to do with.

A remaining issue is what estimate we should pick for the size of the aggregate state. This patch uses the size of the int128 version for the estimate, but I have no strong opinions on which we should use.

--
Andreas Karlsson

diff --git a/configure b/configure
index 8490eb7..d9b0e8f 100755
--- a/configure
+++ b/configure
@@ -13743,6 +13743,49 @@ _ACEOF
 fi
 
 
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking __int128" >&5
+$as_echo_n "checking __int128... " >&6; }
+if test "$cross_compiling" = yes; then :
+  have___int128=no
+else
+  cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+__int128 a = 200000000001;
+__int128 b = 400000000005;
+
+int does_int128_work()
+{
+  __int128 c,d;
+
+  c = a * b;
+  d = (c + b) / b;
+  if (d != a+1)
+    return 0;
+  return 1;
+}
+main() {
+  exit(! does_int128_work());
+}
+
+_ACEOF
+if ac_fn_c_try_run "$LINENO"; then :
+  have___int128=yes
+else
+  have___int128=no
+fi
+rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext \
+  conftest.$ac_objext conftest.beam conftest.$ac_ext
+fi
+
+{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $have___int128" >&5
+$as_echo "$have___int128" >&6; }
+if test x"$have___int128" = xyes ; then
+
+$as_echo "#define HAVE___INT128 1" >>confdefs.h
+
+fi
+
 # We also check for sig_atomic_t, which *should* be defined per ANSI
 # C, but is missing on some old platforms.
 ac_fn_c_check_type "$LINENO" "sig_atomic_t" "ac_cv_type_sig_atomic_t" "#include <signal.h>
diff --git a/configure.in b/configure.in
index b4bd09e..189e2f0 100644
--- a/configure.in
+++ b/configure.in
@@ -1760,6 +1760,30 @@ AC_DEFINE_UNQUOTED(MAXIMUM_ALIGNOF, $MAX_ALIGNOF, [Define as the maximum alignme
 AC_CHECK_TYPES([int8, uint8, int64, uint64], [], [],
 [#include <stdio.h>])
 
+AC_MSG_CHECKING([__int128])
+AC_TRY_RUN([
+__int128 a = 200000000001;
+__int128 b = 400000000005;
+
+int does_int128_work()
+{
+  __int128 c,d;
+
+  c = a * b;
+  d = (c + b) / b;
+  if (d != a+1)
+    return 0;
+  return 1;
+}
+main() {
+  exit(! does_int128_work());
+}
+  ], [have___int128=yes], [have___int128=no], [have___int128=no])
+AC_MSG_RESULT([$have___int128])
+if test x"$have___int128" = xyes ; then
+  AC_DEFINE(HAVE___INT128, 1, [Define to 1 if the system has the type `__int128'.])
+fi
+
 # We also check for sig_atomic_t, which *should* be defined per ANSI
 # C, but is missing on some old platforms.
 AC_CHECK_TYPES(sig_atomic_t, [], [], [#include <signal.h>])
diff --git a/src/backend/utils/adt/numeric.c b/src/backend/utils/adt/numeric.c
index a8609e8..8344343 100644
--- a/src/backend/utils/adt/numeric.c
+++ b/src/backend/utils/adt/numeric.c
@@ -402,6 +402,9 @@ static void apply_typmod(NumericVar *var, int32 typmod);
 static int32 numericvar_to_int4(NumericVar *var);
 static bool numericvar_to_int8(NumericVar *var, int64 *result);
 static void int8_to_numericvar(int64 val, NumericVar *var);
+#ifdef HAVE_INT128
+static void int16_to_numericvar(int128 val, NumericVar *var);
+#endif
 static double numeric_to_double_no_overflow(Numeric num);
 static double numericvar_to_double_no_overflow(NumericVar *var);
 
@@ -2659,6 +2662,9 @@ numeric_float4(PG_FUNCTION_ARGS)
  * Actually, it's a pointer to a NumericAggState allocated in the aggregate
  * context.  The digit buffers for the NumericVars will be there too.
  *
+ * On platforms which support 128-bit integers some aggergates instead use a
+ * 128-bit integer based transition datatype to speed up calculations.
+ *
  * ----------------------------------------------------------------------
  */
 
@@ -2917,6 +2923,65 @@ numeric_accum_inv(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(state);
 }
 
+#ifdef HAVE_INT128
+typedef struct Int128AggState
+{
+	bool	calcSumX2;	/* if true, calculate sumX2 */
+	int64	N;			/* count of processed numbers */
+	int128	sumX;		/* sum of processed numbers */
+	int128	sumX2;		/* sum of squares of processed numbers */
+} Int128AggState;
+
+/*
+ * Prepare state data for a 128-bit aggregate function that needs to compute
+ * sum, count and optionally sum of squares of the input.
+ */
+static Int128AggState *
+makeInt128AggState(FunctionCallInfo fcinfo, bool calcSumX2)
+{
+	Int128AggState *state;
+	MemoryContext agg_context;
+	MemoryContext old_context;
+
+	if (!AggCheckCallContext(fcinfo, &agg_context))
+		elog(ERROR, "aggregate function called in non-aggregate context");
+
+	old_context = MemoryContextSwitchTo(agg_context);
+
+	state = (Int128AggState *) palloc0(sizeof(Int128AggState));
+	state->calcSumX2 = calcSumX2;
+
+	MemoryContextSwitchTo(old_context);
+
+	return state;
+}
+
+/*
+ * Accumulate a new input value for 128-bit aggregate functions.
+ */
+static void
+do_int128_accum(Int128AggState *state, int128 newval)
+{
+	if (state->calcSumX2)
+		state->sumX2 += newval * newval;
+
+	state->sumX += newval;
+	state->N++;
+}
+
+/*
+ * Remove an input value from the aggregated state.
+ */
+static void
+do_int128_discard(Int128AggState *state, int128 newval)
+{
+	if (state->calcSumX2)
+		state->sumX2 -= newval * newval;
+
+	state->sumX -= newval;
+	state->N--;
+}
+#endif
 
 /*
  * Integer data types all use Numeric accumulators to share code and
@@ -2925,11 +2990,27 @@ numeric_accum_inv(PG_FUNCTION_ARGS)
  * for the sum(X*X) value.  Hence, we use int2_accum and int4_accum only
  * for stddev/variance --- there are faster special-purpose accumulator
  * routines for SUM and AVG of these datatypes.
+ *
+ * Similarily we can, where available, use 128-bit integer accumulators
+ * for sum(X) for int8 and sum(X*X) for int2 and int4, but not sum(X*X)
+ * for int8.
  */
 
 Datum
 int2_accum(PG_FUNCTION_ARGS)
 {
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Create the state data on the first call */
+	if (state == NULL)
+		state = makeInt128AggState(fcinfo, true);
+
+	if (!PG_ARGISNULL(1))
+		do_int128_accum(state, (int128) PG_GETARG_INT16(1));
+#else
 	NumericAggState *state;
 
 	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
@@ -2946,6 +3027,7 @@ int2_accum(PG_FUNCTION_ARGS)
 													 PG_GETARG_DATUM(1)));
 		do_numeric_accum(state, newval);
 	}
+#endif
 
 	PG_RETURN_POINTER(state);
 }
@@ -2953,6 +3035,18 @@ int2_accum(PG_FUNCTION_ARGS)
 Datum
 int4_accum(PG_FUNCTION_ARGS)
 {
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Create the state data on the first call */
+	if (state == NULL)
+		state = makeInt128AggState(fcinfo, true);
+
+	if (!PG_ARGISNULL(1))
+		do_int128_accum(state, (int128) PG_GETARG_INT32(1));
+#else
 	NumericAggState *state;
 
 	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
@@ -2969,6 +3063,7 @@ int4_accum(PG_FUNCTION_ARGS)
 													 PG_GETARG_DATUM(1)));
 		do_numeric_accum(state, newval);
 	}
+#endif
 
 	PG_RETURN_POINTER(state);
 }
@@ -3002,6 +3097,19 @@ int8_accum(PG_FUNCTION_ARGS)
 Datum
 int8_avg_accum(PG_FUNCTION_ARGS)
 {
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Create the state data on the first call */
+	if (state == NULL)
+		state = makeInt128AggState(fcinfo, false);
+
+	if (!PG_ARGISNULL(1))
+		do_int128_accum(state, (int128) PG_GETARG_INT64(1));
+
+#else
 	NumericAggState *state;
 
 	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
@@ -3018,6 +3126,7 @@ int8_avg_accum(PG_FUNCTION_ARGS)
 													 PG_GETARG_DATUM(1)));
 		do_numeric_accum(state, newval);
 	}
+#endif
 
 	PG_RETURN_POINTER(state);
 }
@@ -3030,6 +3139,18 @@ int8_avg_accum(PG_FUNCTION_ARGS)
 Datum
 int2_accum_inv(PG_FUNCTION_ARGS)
 {
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Should not get here with no state */
+	if (state == NULL)
+		elog(ERROR, "int2_accum_inv called with NULL state");
+
+	if (!PG_ARGISNULL(1))
+		do_int128_discard(state, (int128) PG_GETARG_INT16(1));
+#else
 	NumericAggState *state;
 
 	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
@@ -3049,6 +3170,7 @@ int2_accum_inv(PG_FUNCTION_ARGS)
 		if (!do_numeric_discard(state, newval))
 			elog(ERROR, "do_numeric_discard failed unexpectedly");
 	}
+#endif
 
 	PG_RETURN_POINTER(state);
 }
@@ -3056,6 +3178,18 @@ int2_accum_inv(PG_FUNCTION_ARGS)
 Datum
 int4_accum_inv(PG_FUNCTION_ARGS)
 {
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Should not get here with no state */
+	if (state == NULL)
+		elog(ERROR, "int4_accum_inv called with NULL state");
+
+	if (!PG_ARGISNULL(1))
+		do_int128_discard(state, (int128) PG_GETARG_INT32(1));
+#else
 	NumericAggState *state;
 
 	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
@@ -3075,6 +3209,7 @@ int4_accum_inv(PG_FUNCTION_ARGS)
 		if (!do_numeric_discard(state, newval))
 			elog(ERROR, "do_numeric_discard failed unexpectedly");
 	}
+#endif
 
 	PG_RETURN_POINTER(state);
 }
@@ -3106,6 +3241,103 @@ int8_accum_inv(PG_FUNCTION_ARGS)
 }
 
 Datum
+int8_avg_accum_inv(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* Should not get here with no state */
+	if (state == NULL)
+		elog(ERROR, "int8_avg_accum_inv called with NULL state");
+
+	if (!PG_ARGISNULL(1))
+		do_int128_discard(state, (int128) PG_GETARG_INT64(1));
+#else
+	NumericAggState *state;
+
+	state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
+
+	/* Should not get here with no state */
+	if (state == NULL)
+		elog(ERROR, "int8_avg_accum_inv called with NULL state");
+
+	if (!PG_ARGISNULL(1))
+	{
+		Numeric		newval;
+
+		newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric,
+													 PG_GETARG_DATUM(1)));
+
+		/* Should never fail, all inputs have dscale 0 */
+		if (!do_numeric_discard(state, newval))
+			elog(ERROR, "do_numeric_discard failed unexpectedly");
+	}
+#endif
+
+	PG_RETURN_POINTER(state);
+}
+
+Datum
+numeric_int16_sum(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState	*state;
+	Numeric			res;
+	NumericVar		result;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* If there were no non-null inputs, return NULL */
+	if (state == NULL || state->N == 0)
+		PG_RETURN_NULL();
+
+	init_var(&result);
+
+	int16_to_numericvar(state->sumX, &result);
+
+	res = make_result(&result);
+
+	free_var(&result);
+
+	PG_RETURN_NUMERIC(res);
+#else
+	return numeric_sum(fcinfo);
+#endif
+}
+
+Datum
+numeric_int16_avg(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState	*state;
+	NumericVar		result;
+	Datum			countd, sumd;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	/* If there were no non-null inputs, return NULL */
+	if (state == NULL || state->N == 0)
+		PG_RETURN_NULL();
+
+	init_var(&result);
+
+	int16_to_numericvar(state->sumX, &result);
+
+	countd = DirectFunctionCall1(int8_numeric,
+								 Int64GetDatumFast(state->N));
+	sumd = NumericGetDatum(make_result(&result));
+
+	free_var(&result);
+
+	PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumd, countd));
+#else
+	return numeric_avg(fcinfo);
+#endif
+}
+
+Datum
 numeric_avg(PG_FUNCTION_ARGS)
 {
 	NumericAggState *state;
@@ -3307,6 +3539,124 @@ numeric_stddev_pop(PG_FUNCTION_ARGS)
 		PG_RETURN_NUMERIC(res);
 }
 
+#ifdef HAVE_INT128
+static Numeric
+numeric_int16_stddev_internal(Int128AggState *state,
+						bool variance, bool sample,
+						bool *is_null)
+{
+	NumericAggState numstate;
+	Numeric		res;
+
+	init_var(&numstate.sumX);
+	init_var(&numstate.sumX2);
+	numstate.NaNcount = 0;
+	numstate.agg_context = NULL;
+
+	if (state)
+	{
+		numstate.N = state->N;
+		int16_to_numericvar(state->sumX, &numstate.sumX);
+		int16_to_numericvar(state->sumX2, &numstate.sumX2);
+	}
+	else
+	{
+		numstate.N = 0;
+	}
+
+	res = numeric_stddev_internal(&numstate, variance, sample, is_null);
+
+	free_var(&numstate.sumX);
+	free_var(&numstate.sumX2);
+
+	return res;
+}
+#endif
+
+Datum
+numeric_int16_var_samp(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState *state;
+	Numeric		res;
+	bool		is_null;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	res = numeric_int16_stddev_internal(state, true, true, &is_null);
+
+	if (is_null)
+		PG_RETURN_NULL();
+	else
+		PG_RETURN_NUMERIC(res);
+#else
+	return numeric_var_samp(fcinfo);
+#endif
+}
+
+Datum
+numeric_int16_stddev_samp(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState *state;
+	Numeric		res;
+	bool		is_null;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	res = numeric_int16_stddev_internal(state, false, true, &is_null);
+
+	if (is_null)
+		PG_RETURN_NULL();
+	else
+		PG_RETURN_NUMERIC(res);
+#else
+	return numeric_stddev_samp(fcinfo);
+#endif
+}
+
+Datum
+numeric_int16_var_pop(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState *state;
+	Numeric		res;
+	bool		is_null;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	res = numeric_int16_stddev_internal(state, true, false, &is_null);
+
+	if (is_null)
+		PG_RETURN_NULL();
+	else
+		PG_RETURN_NUMERIC(res);
+#else
+	return numeric_var_pop(fcinfo);
+#endif
+}
+
+Datum
+numeric_int16_stddev_pop(PG_FUNCTION_ARGS)
+{
+#ifdef HAVE_INT128
+	Int128AggState *state;
+	Numeric		res;
+	bool		is_null;
+
+	state = PG_ARGISNULL(0) ? NULL : (Int128AggState *) PG_GETARG_POINTER(0);
+
+	res = numeric_int16_stddev_internal(state, false, false, &is_null);
+
+	if (is_null)
+		PG_RETURN_NULL();
+	else
+		PG_RETURN_NUMERIC(res);
+#else
+	return numeric_stddev_pop(fcinfo);
+#endif
+}
+
 /*
  * SUM transition functions for integer datatypes.
  *
@@ -4529,6 +4879,53 @@ int8_to_numericvar(int64 val, NumericVar *var)
 	var->weight = ndigits - 1;
 }
 
+#ifdef HAVE_INT128
+/*
+ * Convert 128 bit integer to numeric.
+ */
+static void
+int16_to_numericvar(int128 val, NumericVar *var)
+{
+	uint128		uval,
+				newuval;
+	NumericDigit *ptr;
+	int			ndigits;
+
+	/* int16 can require at most 39 decimal digits; add one for safety */
+	alloc_var(var, 40 / DEC_DIGITS);
+	if (val < 0)
+	{
+		var->sign = NUMERIC_NEG;
+		uval = -val;
+	}
+	else
+	{
+		var->sign = NUMERIC_POS;
+		uval = val;
+	}
+	var->dscale = 0;
+	if (val == 0)
+	{
+		var->ndigits = 0;
+		var->weight = 0;
+		return;
+	}
+	ptr = var->digits + var->ndigits;
+	ndigits = 0;
+	do
+	{
+		ptr--;
+		ndigits++;
+		newuval = uval / NBASE;
+		*ptr = uval - newuval * NBASE;
+		uval = newuval;
+	} while (uval);
+	var->digits = ptr;
+	var->ndigits = ndigits;
+	var->weight = ndigits - 1;
+}
+#endif
+
 /*
  * Convert numeric to float8; if out of range, return +/- HUGE_VAL
  */
diff --git a/src/include/c.h b/src/include/c.h
index c929d3d..b119ea3 100644
--- a/src/include/c.h
+++ b/src/include/c.h
@@ -297,6 +297,16 @@ typedef unsigned long long int uint64;
 #define HAVE_INT64_TIMESTAMP
 #endif
 
+/*
+ * 128-bit integers
+ */
+#if defined(HAVE___INT128)
+typedef __int128 int128;
+typedef unsigned __int128 uint128;
+
+#define HAVE_INT128
+#endif
+
 /* sig_atomic_t is required by ANSI C, but may be missing on old platforms */
 #ifndef HAVE_SIG_ATOMIC_T
 typedef int sig_atomic_t;
diff --git a/src/include/catalog/pg_aggregate.h b/src/include/catalog/pg_aggregate.h
index 5e1196d..0e7bd9a 100644
--- a/src/include/catalog/pg_aggregate.h
+++ b/src/include/catalog/pg_aggregate.h
@@ -125,23 +125,23 @@ typedef FormData_pg_aggregate *Form_pg_aggregate;
  */
 
 /* avg */
-DATA(insert ( 2100	n 0 int8_avg_accum	numeric_avg		int8_avg_accum	int8_accum_inv	numeric_avg		f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2101	n 0 int4_avg_accum	int8_avg		int4_avg_accum	int4_avg_accum_inv	int8_avg	f f 0	1016	0	1016	0	"{0,0}" "{0,0}" ));
-DATA(insert ( 2102	n 0 int2_avg_accum	int8_avg		int2_avg_accum	int2_avg_accum_inv	int8_avg	f f 0	1016	0	1016	0	"{0,0}" "{0,0}" ));
-DATA(insert ( 2103	n 0 numeric_avg_accum numeric_avg	numeric_avg_accum numeric_accum_inv numeric_avg f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2104	n 0 float4_accum	float8_avg		-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2105	n 0 float8_accum	float8_avg		-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2106	n 0 interval_accum	interval_avg	interval_accum	interval_accum_inv interval_avg f f 0	1187	0	1187	0	"{0 second,0 second}" "{0 second,0 second}" ));
+DATA(insert ( 2100	n 0 int8_avg_accum	numeric_int16_avg		int8_avg_accum	int8_avg_accum_inv	numeric_int16_avg	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2101	n 0 int4_avg_accum	int8_avg		int4_avg_accum	int4_avg_accum_inv	int8_avg					f f 0	1016	0	1016	0	"{0,0}" "{0,0}" ));
+DATA(insert ( 2102	n 0 int2_avg_accum	int8_avg		int2_avg_accum	int2_avg_accum_inv	int8_avg					f f 0	1016	0	1016	0	"{0,0}" "{0,0}" ));
+DATA(insert ( 2103	n 0 numeric_avg_accum numeric_avg	numeric_avg_accum numeric_accum_inv numeric_avg 				f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2104	n 0 float4_accum	float8_avg		-				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2105	n 0 float8_accum	float8_avg		-				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2106	n 0 interval_accum	interval_avg	interval_accum	interval_accum_inv interval_avg					f f 0	1187	0	1187	0	"{0 second,0 second}" "{0 second,0 second}" ));
 
 /* sum */
-DATA(insert ( 2107	n 0 int8_avg_accum	numeric_sum		int8_avg_accum	int8_accum_inv	numeric_sum		f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2108	n 0 int4_sum		-				int4_avg_accum	int4_avg_accum_inv int2int4_sum f f 0	20		0	1016	0	_null_ "{0,0}" ));
-DATA(insert ( 2109	n 0 int2_sum		-				int2_avg_accum	int2_avg_accum_inv int2int4_sum f f 0	20		0	1016	0	_null_ "{0,0}" ));
-DATA(insert ( 2110	n 0 float4pl		-				-				-				-				f f 0	700		0	0		0	_null_ _null_ ));
-DATA(insert ( 2111	n 0 float8pl		-				-				-				-				f f 0	701		0	0		0	_null_ _null_ ));
-DATA(insert ( 2112	n 0 cash_pl			-				cash_pl			cash_mi			-				f f 0	790		0	790		0	_null_ _null_ ));
-DATA(insert ( 2113	n 0 interval_pl		-				interval_pl		interval_mi		-				f f 0	1186	0	1186	0	_null_ _null_ ));
-DATA(insert ( 2114	n 0 numeric_avg_accum	numeric_sum numeric_avg_accum numeric_accum_inv numeric_sum f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2107	n 0 int8_avg_accum	numeric_int16_sum		int8_avg_accum	int8_avg_accum_inv numeric_int16_sum	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2108	n 0 int4_sum		-				int4_avg_accum	int4_avg_accum_inv int2int4_sum 				f f 0	20		0	1016	0	_null_ "{0,0}" ));
+DATA(insert ( 2109	n 0 int2_sum		-				int2_avg_accum	int2_avg_accum_inv int2int4_sum 				f f 0	20		0	1016	0	_null_ "{0,0}" ));
+DATA(insert ( 2110	n 0 float4pl		-				-				-				-								f f 0	700		0	0		0	_null_ _null_ ));
+DATA(insert ( 2111	n 0 float8pl		-				-				-				-								f f 0	701		0	0		0	_null_ _null_ ));
+DATA(insert ( 2112	n 0 cash_pl			-				cash_pl			cash_mi			-								f f 0	790		0	790		0	_null_ _null_ ));
+DATA(insert ( 2113	n 0 interval_pl		-				interval_pl		interval_mi		-								f f 0	1186	0	1186	0	_null_ _null_ ));
+DATA(insert ( 2114	n 0 numeric_avg_accum	numeric_sum numeric_avg_accum numeric_accum_inv numeric_sum					f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* max */
 DATA(insert ( 2115	n 0 int8larger		-				-				-				-				f f 413		20		0	0		0	_null_ _null_ ));
@@ -194,52 +194,52 @@ DATA(insert ( 2147	n 0 int8inc_any		-				int8inc_any		int8dec_any		-				f f 0		2
 DATA(insert ( 2803	n 0 int8inc			-				int8inc			int8dec			-				f f 0		20		0	20		0	"0" "0" ));
 
 /* var_pop */
-DATA(insert ( 2718	n 0 int8_accum	numeric_var_pop		int8_accum		int8_accum_inv	numeric_var_pop f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2719	n 0 int4_accum	numeric_var_pop		int4_accum		int4_accum_inv	numeric_var_pop f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2720	n 0 int2_accum	numeric_var_pop		int2_accum		int2_accum_inv	numeric_var_pop f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2721	n 0 float4_accum	float8_var_pop	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2722	n 0 float8_accum	float8_var_pop	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2723	n 0 numeric_accum	numeric_var_pop numeric_accum numeric_accum_inv numeric_var_pop f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2718	n 0 int8_accum	numeric_var_pop		int8_accum		int8_accum_inv	numeric_var_pop 				f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2719	n 0 int4_accum	numeric_int16_var_pop		int4_accum		int4_accum_inv	numeric_int16_var_pop	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2720	n 0 int2_accum	numeric_int16_var_pop		int2_accum		int2_accum_inv	numeric_int16_var_pop	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2721	n 0 float4_accum	float8_var_pop	-				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2722	n 0 float8_accum	float8_var_pop	-				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2723	n 0 numeric_accum	numeric_var_pop numeric_accum numeric_accum_inv numeric_var_pop					f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* var_samp */
-DATA(insert ( 2641	n 0 int8_accum	numeric_var_samp	int8_accum		int8_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2642	n 0 int4_accum	numeric_var_samp	int4_accum		int4_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2643	n 0 int2_accum	numeric_var_samp	int2_accum		int2_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2644	n 0 float4_accum	float8_var_samp -				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2645	n 0 float8_accum	float8_var_samp -				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2646	n 0 numeric_accum	numeric_var_samp numeric_accum numeric_accum_inv numeric_var_samp f f 0 2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2641	n 0 int8_accum	numeric_var_samp	int8_accum		int8_accum_inv	numeric_var_samp				f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2642	n 0 int4_accum	numeric_int16_var_samp		int4_accum		int4_accum_inv	numeric_int16_var_samp	f f 0	2281	48 	2281	48	_null_ _null_ ));
+DATA(insert ( 2643	n 0 int2_accum	numeric_int16_var_samp		int2_accum		int2_accum_inv	numeric_int16_var_samp	f f 0	2281	48 	2281	48	_null_ _null_ ));
+DATA(insert ( 2644	n 0 float4_accum	float8_var_samp -				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2645	n 0 float8_accum	float8_var_samp -				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2646	n 0 numeric_accum	numeric_var_samp numeric_accum numeric_accum_inv numeric_var_samp 				f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* variance: historical Postgres syntax for var_samp */
-DATA(insert ( 2148	n 0 int8_accum	numeric_var_samp	int8_accum		int8_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2149	n 0 int4_accum	numeric_var_samp	int4_accum		int4_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2150	n 0 int2_accum	numeric_var_samp	int2_accum		int2_accum_inv	numeric_var_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2151	n 0 float4_accum	float8_var_samp -				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2152	n 0 float8_accum	float8_var_samp -				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2153	n 0 numeric_accum	numeric_var_samp numeric_accum numeric_accum_inv numeric_var_samp f f 0 2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2148	n 0 int8_accum	numeric_var_samp	int8_accum		int8_accum_inv	numeric_var_samp				f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2149	n 0 int4_accum	numeric_int16_var_samp		int4_accum		int4_accum_inv	numeric_int16_var_samp	f f 0	2281	48 	2281	48 	_null_ _null_ ));
+DATA(insert ( 2150	n 0 int2_accum	numeric_int16_var_samp		int2_accum		int2_accum_inv	numeric_int16_var_samp	f f 0	2281	48 	2281	48 	_null_ _null_ ));
+DATA(insert ( 2151	n 0 float4_accum	float8_var_samp -				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2152	n 0 float8_accum	float8_var_samp -				-				-								f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2153	n 0 numeric_accum	numeric_var_samp numeric_accum numeric_accum_inv numeric_var_samp				f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* stddev_pop */
-DATA(insert ( 2724	n 0 int8_accum	numeric_stddev_pop		int8_accum	int8_accum_inv	numeric_stddev_pop	f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2725	n 0 int4_accum	numeric_stddev_pop		int4_accum	int4_accum_inv	numeric_stddev_pop	f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2726	n 0 int2_accum	numeric_stddev_pop		int2_accum	int2_accum_inv	numeric_stddev_pop	f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2727	n 0 float4_accum	float8_stddev_pop	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2728	n 0 float8_accum	float8_stddev_pop	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2729	n 0 numeric_accum	numeric_stddev_pop numeric_accum numeric_accum_inv numeric_stddev_pop f f 0 2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2724	n 0 int8_accum	numeric_stddev_pop	int8_accum	int8_accum_inv	numeric_stddev_pop					f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2725	n 0 int4_accum	numeric_int16_stddev_pop	int4_accum	int4_accum_inv	numeric_int16_stddev_pop	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2726	n 0 int2_accum	numeric_int16_stddev_pop	int2_accum	int2_accum_inv	numeric_int16_stddev_pop	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2727	n 0 float4_accum	float8_stddev_pop	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2728	n 0 float8_accum	float8_stddev_pop	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2729	n 0 numeric_accum	numeric_stddev_pop numeric_accum numeric_accum_inv numeric_stddev_pop			f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* stddev_samp */
-DATA(insert ( 2712	n 0 int8_accum	numeric_stddev_samp		int8_accum	int8_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2713	n 0 int4_accum	numeric_stddev_samp		int4_accum	int4_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2714	n 0 int2_accum	numeric_stddev_samp		int2_accum	int2_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2715	n 0 float4_accum	float8_stddev_samp	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2716	n 0 float8_accum	float8_stddev_samp	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2717	n 0 numeric_accum	numeric_stddev_samp numeric_accum numeric_accum_inv numeric_stddev_samp f f 0 2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2712	n 0 int8_accum	numeric_stddev_samp		int8_accum	int8_accum_inv	numeric_stddev_samp				f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2713	n 0 int4_accum	numeric_int16_stddev_samp	int4_accum	int4_accum_inv	numeric_int16_stddev_samp	f f 0	2281	48 	2281	48	_null_ _null_ ));
+DATA(insert ( 2714	n 0 int2_accum	numeric_int16_stddev_samp	int2_accum	int2_accum_inv	numeric_int16_stddev_samp	f f 0	2281	48 	2281	48	_null_ _null_ ));
+DATA(insert ( 2715	n 0 float4_accum	float8_stddev_samp	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2716	n 0 float8_accum	float8_stddev_samp	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2717	n 0 numeric_accum	numeric_stddev_samp numeric_accum numeric_accum_inv numeric_stddev_samp			f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* stddev: historical Postgres syntax for stddev_samp */
-DATA(insert ( 2154	n 0 int8_accum	numeric_stddev_samp		int8_accum	int8_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2155	n 0 int4_accum	numeric_stddev_samp		int4_accum	int4_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2156	n 0 int2_accum	numeric_stddev_samp		int2_accum	int2_accum_inv	numeric_stddev_samp f f 0	2281	128 2281	128 _null_ _null_ ));
-DATA(insert ( 2157	n 0 float4_accum	float8_stddev_samp	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2158	n 0 float8_accum	float8_stddev_samp	-				-				-				f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
-DATA(insert ( 2159	n 0 numeric_accum	numeric_stddev_samp numeric_accum numeric_accum_inv numeric_stddev_samp f f 0 2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2154	n 0 int8_accum	numeric_stddev_samp		int8_accum	int8_accum_inv	numeric_stddev_samp 			f f 0	2281	128 2281	128 _null_ _null_ ));
+DATA(insert ( 2155	n 0 int4_accum	numeric_int16_stddev_samp	int4_accum	int4_accum_inv	numeric_int16_stddev_samp	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2156	n 0 int2_accum	numeric_int16_stddev_samp	int2_accum	int2_accum_inv	numeric_int16_stddev_samp	f f 0	2281	48	2281	48	_null_ _null_ ));
+DATA(insert ( 2157	n 0 float4_accum	float8_stddev_samp	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2158	n 0 float8_accum	float8_stddev_samp	-				-				-							f f 0	1022	0	0		0	"{0,0,0}" _null_ ));
+DATA(insert ( 2159	n 0 numeric_accum	numeric_stddev_samp numeric_accum numeric_accum_inv numeric_stddev_samp			f f 0	2281	128 2281	128 _null_ _null_ ));
 
 /* SQL2003 binary regression aggregates */
 DATA(insert ( 2818	n 0 int8inc_float8_float8	-					-				-				-				f f 0	20		0	0		0	"0" _null_ ));
diff --git a/src/include/catalog/pg_proc.h b/src/include/catalog/pg_proc.h
index 9edfdb8..d11e355 100644
--- a/src/include/catalog/pg_proc.h
+++ b/src/include/catalog/pg_proc.h
@@ -2491,6 +2491,8 @@ DATA(insert OID = 3568 (  int4_accum_inv   PGNSP PGUID 12 1 0 0 0 f f f f f f i
 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 = 3387 (  int8_avg_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_avg_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_ ));
@@ -2509,6 +2511,19 @@ DATA(insert OID = 1841 (  int4_sum		   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0
 DESCR("aggregate transition function");
 DATA(insert OID = 1842 (  int8_sum		   PGNSP PGUID 12 1 0 0 0 f f f f f f i 2 0 1700 "1700 20" _null_ _null_ _null_ _null_ int8_sum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3388 (  numeric_int16_sum	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_int16_sum _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 3389 (  numeric_int16_avg	   PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_int16_avg _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 3390 (  numeric_int16_var_pop  PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_int16_var_pop _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 3391 (  numeric_int16_var_samp PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_int16_var_samp _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 3392 (  numeric_int16_stddev_pop PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_	numeric_int16_stddev_pop _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 3393 (  numeric_int16_stddev_samp	PGNSP PGUID 12 1 0 0 0 f f f f f f i 1 0 1700 "2281" _null_ _null_ _null_ _null_ numeric_int16_stddev_samp _null_ _null_ _null_ ));
+DESCR("aggregate final 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_ ));
diff --git a/src/include/pg_config.h.in b/src/include/pg_config.h.in
index 995fb65..d8a1971 100644
--- a/src/include/pg_config.h.in
+++ b/src/include/pg_config.h.in
@@ -678,6 +678,9 @@
 /* Define to 1 if your compiler understands __VA_ARGS__ in macros. */
 #undef HAVE__VA_ARGS
 
+/* Define to 1 if the system has the type `__int128'. */
+#undef HAVE___INT128
+
 /* Define to the appropriate snprintf length modifier for 64-bit ints. */
 #undef INT64_MODIFIER
 
diff --git a/src/include/pg_config.h.win32 b/src/include/pg_config.h.win32
index 69d0e31..26a7e80 100644
--- a/src/include/pg_config.h.win32
+++ b/src/include/pg_config.h.win32
@@ -532,6 +532,9 @@
 /* Define to 1 if your compiler understands __VA_ARGS__ in macros. */
 #define HAVE__VA_ARGS 1
 
+/* Define to 1 if the system has the type `__int128'. */
+#define HAVE___INT128 1
+
 /* Define to the appropriate snprintf length modifier for 64-bit ints. */
 #define INT64_MODIFIER "ll"
 
diff --git a/src/include/utils/builtins.h b/src/include/utils/builtins.h
index bc4517d..4e770a3 100644
--- a/src/include/utils/builtins.h
+++ b/src/include/utils/builtins.h
@@ -1027,6 +1027,12 @@ extern Datum numeric_var_pop(PG_FUNCTION_ARGS);
 extern Datum numeric_var_samp(PG_FUNCTION_ARGS);
 extern Datum numeric_stddev_pop(PG_FUNCTION_ARGS);
 extern Datum numeric_stddev_samp(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_sum(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_avg(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_var_pop(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_var_samp(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_stddev_pop(PG_FUNCTION_ARGS);
+extern Datum numeric_int16_stddev_samp(PG_FUNCTION_ARGS);
 extern Datum int2_sum(PG_FUNCTION_ARGS);
 extern Datum int4_sum(PG_FUNCTION_ARGS);
 extern Datum int8_sum(PG_FUNCTION_ARGS);
@@ -1034,6 +1040,7 @@ 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_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);
-- 
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