diff --git a/gcc/config/aarch64/aarch64-modes.def b/gcc/config/aarch64/aarch64-modes.def
index 1eeb8d88452..0b36da942b4 100644
--- a/gcc/config/aarch64/aarch64-modes.def
+++ b/gcc/config/aarch64/aarch64-modes.def
@@ -69,10 +69,10 @@ VECTOR_MODES (FLOAT, 16);     /*            V4SF V2DF.  */
 VECTOR_MODE (FLOAT, DF, 1);   /*                 V1DF.  */
 VECTOR_MODE (FLOAT, HF, 2);   /*                 V2HF.  */
 
-/* Bfloat16 modes.  */
-FLOAT_MODE (BF, 2, 0);
+/* Bfloat16 modes. Using 1 as the ORDER argument ensures that this is
+   placed after normal floating point modes in the GET_MODES_WIDER chain.  */
+FLOAT_MODE_UNRANKED (BF, 2, 0, 1);
 ADJUST_FLOAT_FORMAT (BF, &arm_bfloat_half_format);
-
 VECTOR_MODE (FLOAT, BF, 4);   /*		 V4BF.  */
 VECTOR_MODE (FLOAT, BF, 8);   /*		 V8BF.  */
 
diff --git a/gcc/config/arm/arm-modes.def b/gcc/config/arm/arm-modes.def
index ea92ef35723..86551be8e3b 100644
--- a/gcc/config/arm/arm-modes.def
+++ b/gcc/config/arm/arm-modes.def
@@ -78,7 +78,9 @@ VECTOR_MODES (FLOAT, 8);      /*            V4HF V2SF */
 VECTOR_MODES (FLOAT, 16);     /*       V8HF V4SF V2DF */
 VECTOR_MODE (FLOAT, HF, 2);   /*                 V2HF */
 
-FLOAT_MODE (BF, 2, 0);
+/* Bfloat16 modes. Using 1 as the ORDER argument ensures that this is
+   placed after normal floating point modes in the GET_MODES_WIDER chain.  */
+FLOAT_MODE_UNRANKED (BF, 2, 0, 1);
 ADJUST_FLOAT_FORMAT (BF, &arm_bfloat_half_format);
 VECTOR_MODE (FLOAT, BF, 4);   /*		 V4BF.  */
 VECTOR_MODE (FLOAT, BF, 8);   /*		 V8BF.  */
diff --git a/gcc/genmodes.c b/gcc/genmodes.c
index bd78310ea24..c4e3dd1150d 100644
--- a/gcc/genmodes.c
+++ b/gcc/genmodes.c
@@ -617,20 +617,23 @@ make_fixed_point_mode (enum mode_class cl,
   m->fbit = fbit;
 }
 
-#define FLOAT_MODE(N, Y, F)             FRACTIONAL_FLOAT_MODE (N, -1U, Y, F)
-#define FRACTIONAL_FLOAT_MODE(N, B, Y, F) \
-  make_float_mode (#N, B, Y, #F, __FILE__, __LINE__)
+#define FLOAT_MODE_UNRANKED(N, Y, F, ORDER)   \
+       FRACTIONAL_FLOAT_MODE (N, -1U, Y, F, ORDER)
+#define FLOAT_MODE(N, Y, F)             FRACTIONAL_FLOAT_MODE (N, -1U, Y, F, 0)
+#define FRACTIONAL_FLOAT_MODE(N, B, Y, F, ORDER) \
+  make_float_mode (#N, B, Y, #F, ORDER, __FILE__, __LINE__)
 
 static void
 make_float_mode (const char *name,
 		 unsigned int precision, unsigned int bytesize,
-		 const char *format,
+		 const char *format, unsigned int order,
 		 const char *file, unsigned int line)
 {
   struct mode_data *m = new_mode (MODE_FLOAT, name, file, line);
   m->bytesize = bytesize;
   m->precision = precision;
   m->format = format;
+  m->order = order;
 }
 
 #define DECIMAL_FLOAT_MODE(N, Y, F)	\