diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 7b97d2be6ca..5d8954a34d0 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -3319,9 +3319,15 @@ float8_stddev_samp(PG_FUNCTION_ARGS)
  * As with the preceding aggregates, we use the Youngs-Cramer algorithm to
  * reduce rounding errors in the aggregate final functions.
  *
- * The transition datatype for all these aggregates is a 6-element array of
+ * The transition datatype for all these aggregates is a 9-element array of
  * float8, holding the values N, Sx=sum(X), Sxx=sum((X-Sx/N)^2), Sy=sum(Y),
- * Syy=sum((Y-Sy/N)^2), Sxy=sum((X-Sx/N)*(Y-Sy/N)) in that order.
+ * Syy=sum((Y-Sy/N)^2), Sxy=sum((X-Sx/N)*(Y-Sy/N)), firstX, firstY, DIFF,
+ * in that order.
+ *
+ * DIFF, like N, is treated as an integer.  Bit 0 is set if we saw distinct
+ * X inputs, and bit 1 is set if we saw distinct Y inputs.  This allows us
+ * to detect constant inputs exactly, which is important for deciding whether
+ * some outputs should be NULL.
  *
  * Note that Y is the first argument to all these aggregates!
  *
@@ -3345,17 +3351,23 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 				Sy,
 				Syy,
 				Sxy,
+				firstX,
+				firstY,
 				tmpX,
 				tmpY,
 				scale;
+	int			diff;
 
-	transvalues = check_float8_array(transarray, "float8_regr_accum", 6);
+	transvalues = check_float8_array(transarray, "float8_regr_accum", 9);
 	N = transvalues[0];
 	Sx = transvalues[1];
 	Sxx = transvalues[2];
 	Sy = transvalues[3];
 	Syy = transvalues[4];
 	Sxy = transvalues[5];
+	firstX = transvalues[6];
+	firstY = transvalues[7];
+	diff = transvalues[8];
 
 	/*
 	 * Use the Youngs-Cramer algorithm to incorporate the new values into the
@@ -3373,6 +3385,19 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 		Syy += tmpY * tmpY * scale;
 		Sxy += tmpX * tmpY * scale;
 
+		/*
+		 * Check to see if we have seen distinct inputs.  In normal use, diff
+		 * will reach 3 very soon and then we can stop checking.
+		 */
+		if (diff != 3)
+		{
+			/* Need SQL-style comparison of NaNs here */
+			if (float8_ne(newvalX, firstX))
+				diff |= 1;
+			if (float8_ne(newvalY, firstY))
+				diff |= 2;
+		}
+
 		/*
 		 * Overflow check.  We only report an overflow error when finite
 		 * inputs lead to infinite results.  Note also that Sxx, Syy and Sxy
@@ -3410,6 +3435,8 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 			Sxx = Sxy = get_float8_nan();
 		if (isnan(newvalY) || isinf(newvalY))
 			Syy = Sxy = get_float8_nan();
+		firstX = newvalX;
+		firstY = newvalY;
 	}
 
 	/*
@@ -3425,12 +3452,15 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 		transvalues[3] = Sy;
 		transvalues[4] = Syy;
 		transvalues[5] = Sxy;
+		transvalues[6] = firstX;
+		transvalues[7] = firstY;
+		transvalues[8] = diff;
 
 		PG_RETURN_ARRAYTYPE_P(transarray);
 	}
 	else
 	{
-		Datum		transdatums[6];
+		Datum		transdatums[9];
 		ArrayType  *result;
 
 		transdatums[0] = Float8GetDatumFast(N);
@@ -3439,8 +3469,11 @@ float8_regr_accum(PG_FUNCTION_ARGS)
 		transdatums[3] = Float8GetDatumFast(Sy);
 		transdatums[4] = Float8GetDatumFast(Syy);
 		transdatums[5] = Float8GetDatumFast(Sxy);
+		transdatums[6] = Float8GetDatumFast(firstX);
+		transdatums[7] = Float8GetDatumFast(firstY);
+		transdatums[8] = Float8GetDatum(diff);
 
-		result = construct_array_builtin(transdatums, 6, FLOAT8OID);
+		result = construct_array_builtin(transdatums, 9, FLOAT8OID);
 
 		PG_RETURN_ARRAYTYPE_P(result);
 	}
@@ -3730,27 +3763,25 @@ float8_corr(PG_FUNCTION_ARGS)
 {
 	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
 	float8	   *transvalues;
-	float8		N,
-				Sxx,
+	float8		Sxx,
 				Syy,
 				Sxy;
+	int			diff;
 
-	transvalues = check_float8_array(transarray, "float8_corr", 6);
-	N = transvalues[0];
+	transvalues = check_float8_array(transarray, "float8_corr", 9);
 	Sxx = transvalues[2];
 	Syy = transvalues[4];
 	Sxy = transvalues[5];
+	diff = transvalues[8];
 
-	/* if N is 0 we should return NULL */
-	if (N < 1.0)
+	/*
+	 * Per spec, we must return NULL if N is zero, all X inputs are equal, or
+	 * all Y inputs are equal.  Checking the diff mask covers all three cases.
+	 */
+	if (diff != 3)
 		PG_RETURN_NULL();
 
 	/* Note that Sxx and Syy are guaranteed to be non-negative */
-
-	/* per spec, return NULL for horizontal and vertical lines */
-	if (Sxx == 0 || Syy == 0)
-		PG_RETURN_NULL();
-
 	PG_RETURN_FLOAT8(Sxy / sqrt(Sxx * Syy));
 }
 
diff --git a/src/include/catalog/pg_aggregate.dat b/src/include/catalog/pg_aggregate.dat
index 870769e8f14..68dc1329ea0 100644
--- a/src/include/catalog/pg_aggregate.dat
+++ b/src/include/catalog/pg_aggregate.dat
@@ -505,7 +505,7 @@
   aggtranstype => '_float8', agginitval => '{0,0,0,0,0,0}' },
 { aggfnoid => 'corr', aggtransfn => 'float8_regr_accum',
   aggfinalfn => 'float8_corr', aggcombinefn => 'float8_regr_combine',
-  aggtranstype => '_float8', agginitval => '{0,0,0,0,0,0}' },
+  aggtranstype => '_float8', agginitval => '{0,0,0,0,0,0,0,0,0}' },
 
 # boolean-and and boolean-or
 { aggfnoid => 'bool_and', aggtransfn => 'booland_statefunc',