Add type_convert implementations for bf16

include/ck/utility/data_type.hpp

 // SPDX-License-Identifier: MIT
-// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
 
 #pragma once
 
@@ -1010,6 +1010,60 @@ inline __host__ __device__ constexpr bhalf_t type_convert<bhalf_t, float>(float
     return uint16_t(u.int32 >> 16);
 }
 
+// convert bfp16 to fp16 via fp32
+template <>
+inline __host__ __device__ constexpr half_t type_convert<half_t, bhalf_t>(bhalf_t x)
+{
+    float x_fp32 = type_convert<float>(x);
+
+    return static_cast<half_t>(x_fp32);
+}
+
+// convert fp16 to bfp16 via fp32
+template <>
+inline __host__ __device__ constexpr bhalf_t type_convert<bhalf_t, half_t>(half_t x)
+{
+    float x_fp32 = static_cast<float>(x);
+
+    return type_convert<bhalf_t>(x_fp32);
+}
+
+// convert bfp16 to int32 via fp32
+template <>
+inline __host__ __device__ constexpr int32_t type_convert<int32_t, bhalf_t>(bhalf_t x)
+{
+    float x_fp32 = type_convert<float>(x);
+
+    return static_cast<int32_t>(x_fp32);
+}
+
+// convert int32 to bfp16 via fp32
+template <>
+inline __host__ __device__ constexpr bhalf_t type_convert<bhalf_t, int32_t>(int32_t x)
+{
+    float x_fp32 = static_cast<float>(x);
+
+    return type_convert<bhalf_t>(x_fp32);
+}
+
+// convert bfp16 to int8 via fp32
+template <>
+inline __host__ __device__ constexpr int8_t type_convert<int8_t, bhalf_t>(bhalf_t x)
+{
+    float x_fp32 = type_convert<float>(x);
+
+    return static_cast<int8_t>(x_fp32);
+}
+
+// convert int8 to bfp16 via fp32
+template <>
+inline __host__ __device__ constexpr bhalf_t type_convert<bhalf_t, int8_t>(int8_t x)
+{
+    float x_fp32 = static_cast<float>(x);
+
+    return type_convert<bhalf_t>(x_fp32);
+}
+
 template <typename T>
 struct NumericLimits
 {