diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index 08434dc7ee..245030f531 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -217,6 +217,8 @@ float4in(PG_FUNCTION_ARGS)
 	/* did we not see anything that looks like a double? */
 	if (endptr == num || errno != 0)
 	{
+		int		save_errno = errno;
+
 		/*
 		 * C99 requires that strtod() accept NaN and [-]Infinity, but not all
 		 * platforms support that yet (and some accept them but set ERANGE
@@ -237,11 +239,21 @@ float4in(PG_FUNCTION_ARGS)
 			val = -get_float4_infinity();
 			endptr = num + 9;
 		}
-		else if (errno == ERANGE)
-			ereport(ERROR,
-					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("\"%s\" is out of range for type real",
-							orig_num)));
+		else if (save_errno == ERANGE)
+		{
+			/*
+			 * Some platforms return ERANGE for denormalized numbers (those
+			 * that are not zero, but are too close to zero to have full
+			 * precision).  We'd prefer not to throw error for that, so try
+			 * to detect whether it's a "real" out-of-range condition by
+			 * checking to see if the result is zero or huge.
+			 */
+			if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("\"%s\" is out of range for type real",
+								orig_num)));
+		}
 		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
@@ -410,6 +422,8 @@ float8in(PG_FUNCTION_ARGS)
 	/* did we not see anything that looks like a double? */
 	if (endptr == num || errno != 0)
 	{
+		int		save_errno = errno;
+
 		/*
 		 * C99 requires that strtod() accept NaN and [-]Infinity, but not all
 		 * platforms support that yet (and some accept them but set ERANGE
@@ -430,11 +444,21 @@ float8in(PG_FUNCTION_ARGS)
 			val = -get_float8_infinity();
 			endptr = num + 9;
 		}
-		else if (errno == ERANGE)
-			ereport(ERROR,
-					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-				   errmsg("\"%s\" is out of range for type double precision",
-						  orig_num)));
+		else if (save_errno == ERANGE)
+		{
+			/*
+			 * Some platforms return ERANGE for denormalized numbers (those
+			 * that are not zero, but are too close to zero to have full
+			 * precision).  We'd prefer not to throw error for that, so try
+			 * to detect whether it's a "real" out-of-range condition by
+			 * checking to see if the result is zero or huge.
+			 */
+			if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("\"%s\" is out of range for type double precision",
+								orig_num)));
+		}
 		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),