Add bfloat support to XLA.

This is necessary in providing bfloat support in GPU backend.
RELNOTES: bfloat support is now added to XLA infra.
PiperOrigin-RevId: 175252067

19 files changed, 580 insertions, 44 deletions

diff --git a/tensorflow/compiler/tf2xla/type_util.cc b/tensorflow/compiler/tf2xla/type_util.cc
index 1efbe0ffb1..c969212a1b 100644
--- a/tensorflow/compiler/tf2xla/type_util.cc
+++ b/tensorflow/compiler/tf2xla/type_util.cc
@@ -49,6 +49,9 @@ Status DataTypeToPrimitiveType(DataType data_type, xla::PrimitiveType* type) {
     case tensorflow::DT_UINT64:
       *type = xla::U64;
       return Status::OK();
+    case tensorflow::DT_BFLOAT16:
+      *type = xla::BF16;
+      return Status::OK();
     case tensorflow::DT_HALF:
       *type = xla::F16;
       return Status::OK();
diff --git a/tensorflow/compiler/xla/BUILD b/tensorflow/compiler/xla/BUILD
index 660f419e46..f6e405744a 100644
--- a/tensorflow/compiler/xla/BUILD
+++ b/tensorflow/compiler/xla/BUILD
@@ -77,6 +77,7 @@ cc_library(
     hdrs = ["types.h"],
     visibility = [":friends"],
     deps = [
+        "//tensorflow/core:framework_lite",
         "//tensorflow/core:lib",
         "//third_party/eigen3",
     ],
diff --git a/tensorflow/compiler/xla/literal_util.cc b/tensorflow/compiler/xla/literal_util.cc
index 0cb2223ae5..93d3cd425f 100644
--- a/tensorflow/compiler/xla/literal_util.cc
+++ b/tensorflow/compiler/xla/literal_util.cc
@@ -33,6 +33,20 @@ limitations under the License.
 #include "tensorflow/core/lib/strings/stringprintf.h"
 #include "tensorflow/core/platform/logging.h"
 #include "tensorflow/core/platform/types.h"
+namespace {
+using tensorflow::int64;
+
+constexpr bool kLittleEndian = __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__;
+
+// Converts between little and big endian, assuming elements in the array are 16
+// bits long.
+void ConvertEndianShort(char* bytes, int64 size) {
+  CHECK_EQ(size / 2, 0);
+  for (int64 i = 0; i < size; i += 2) {
+    std::swap(bytes[i], bytes[i + 1]);
+  }
+}
+}  // namespace
 
 namespace xla {
 
@@ -169,6 +183,8 @@ Status Literal::Copy(const Literal& src_literal,
       return CopyRange<int64>(src_literal, src_base, dest_base, copy_size);
     case F16:
       return CopyRange<half>(src_literal, src_base, dest_base, copy_size);
+    case BF16:
+      return CopyRange<bfloat16>(src_literal, src_base, dest_base, copy_size);
     case F32:
       return CopyRange<float>(src_literal, src_base, dest_base, copy_size);
     case F64:
@@ -200,6 +216,8 @@ Status Literal::Copy(const Literal& src_literal,
       return *Literal::CreateR0<int64>(0);
     case F16:
       return *Literal::CreateR0<half>(static_cast<half>(0.0f));
+    case BF16:
+      return *Literal::CreateR0<bfloat16>(static_cast<bfloat16>(0.0f));
     case F32:
       return *Literal::CreateR0<float>(0);
     case F64:
@@ -285,6 +303,9 @@ Status Literal::Copy(const Literal& src_literal,
     case F16:
       return *Literal::CreateR0<half>(
           static_cast<half>(-std::numeric_limits<float>::infinity()));
+    case BF16:
+      return *Literal::CreateR0<bfloat16>(
+          static_cast<bfloat16>(-std::numeric_limits<float>::infinity()));
     case TUPLE:
       LOG(FATAL) << "tuple element type has no minimum value";
     case OPAQUE:
@@ -321,6 +342,9 @@ Status Literal::Copy(const Literal& src_literal,
     case F16:
       return *Literal::CreateR0<half>(
           static_cast<half>(std::numeric_limits<float>::infinity()));
+    case BF16:
+      return *Literal::CreateR0<bfloat16>(
+          static_cast<bfloat16>(std::numeric_limits<float>::infinity()));
     case TUPLE:
       LOG(FATAL) << "tuple element type has no maximum value";
     case OPAQUE:
@@ -428,6 +452,7 @@ std::unique_ptr<Literal> Literal::Transpose(
   // The shape with affine layout resulting from that operation will be
   // F32[8,11]{0,1}, since it leaves the original most minor (the 8 sized), the
   // most minor.
+  //
   // Essentially, given MinMaj(Di) the position of the Di dimension within the
   // minor to major vector, and given T(Di) the index that the original Di
   // dimension has within the transposed array, a layout is affine if
@@ -536,6 +561,9 @@ string Literal::GetAsString(
     }
     case F16:
       return tensorflow::strings::StrCat(Get<half>(multi_index));
+    case BF16:
+      return tensorflow::strings::StrCat(
+          static_cast<float>(Get<bfloat16>(multi_index)));
     default:
       return tensorflow::strings::StrCat(
           "[", PrimitiveType_Name(shape().element_type()), "]");
@@ -743,6 +771,8 @@ void* Literal::MutableInternalData() {
       return reinterpret_cast<void*>(c64s_.data());
     case F16:
       return reinterpret_cast<void*>(f16s_.data());
+    case BF16:
+      return reinterpret_cast<void*>(bf16s_.data());
     default:
       LOG(FATAL) << "primitive type not supported in literals: "
                  << PrimitiveType_Name(shape().element_type());
@@ -785,6 +815,9 @@ void Literal::Reserve(int64 num_elements) {
     case F16:
       Resize<half>(num_elements, static_cast<half>(0.0f));
       break;
+    case BF16:
+      Resize<bfloat16>(num_elements, static_cast<bfloat16>(0.0f));
+      break;
     default:
       LOG(FATAL) << "primitive type not supported in literals: "
                  << PrimitiveType_Name(shape().element_type());
@@ -824,6 +857,9 @@ tensorflow::Status Literal::ValidateLiteral() const {
     case F16:
       actual = f16s().size() / sizeof(half);
       break;
+    case BF16:
+      actual = bf16s().size();
+      break;
     default:
       return tensorflow::errors::Unimplemented(
           "unhandled element type for literal validation: " +
@@ -920,6 +956,7 @@ StatusOr<std::unique_ptr<Literal>> ConvertIfDestTypeMatches(
     CONVERT_IF_TYPES_MATCH(F16)
     CONVERT_IF_TYPES_MATCH(F32)
     CONVERT_IF_TYPES_MATCH(F64)
+    CONVERT_IF_TYPES_MATCH(BF16)
 #undef CONVERT_IF_TYPES_MATCH
     case C64:
       return ConvertToC64<primitive_src_type>(src_literal);
@@ -949,8 +986,9 @@ StatusOr<std::unique_ptr<Literal>> Literal::Convert(
     CONVERT_IF_DEST_TYPE_MATCHES(F16)
     CONVERT_IF_DEST_TYPE_MATCHES(F32)
     CONVERT_IF_DEST_TYPE_MATCHES(F64)
+    CONVERT_IF_DEST_TYPE_MATCHES(BF16)
 #undef CONVERT_IF_DEST_TYPE_MATCHES
-    // Other types are not yet supported.
+      // Other types are not yet supported.
     default:
       return InvalidArgument("Unimplemented: Convert from type %s to type %s",
                              PrimitiveType_Name(shape().element_type()).c_str(),
@@ -1019,6 +1057,8 @@ bool Literal::operator==(const Literal& other) const {
         return EqualElements<double>(*this, other, 0, &multi_index);
       case F16:
         return EqualElements<half>(*this, other, 0, &multi_index);
+      case BF16:
+        return EqualElements<bfloat16>(*this, other, 0, &multi_index);
       case C64:
         return EqualElements<complex64>(*this, other, 0, &multi_index);
       default:
@@ -1128,14 +1168,19 @@ tensorflow::gtl::MutableArraySlice<complex64> Literal::GetMutableArraySlice() {
 
 template <>
 tensorflow::gtl::MutableArraySlice<half> Literal::GetMutableArraySlice<half>() {
-  // TODO - there is an endianess problem here. fix it, or wait for uint16
-  //        support in protobuf
   auto values = mutable_f16s();
   return tensorflow::gtl::MutableArraySlice<half>(values->data(),
                                                   values->size());
 }
 
 template <>
+tensorflow::gtl::MutableArraySlice<bfloat16>
+Literal::GetMutableArraySlice<bfloat16>() {
+  auto values = mutable_bf16s();
+  return {values->data(), values->size()};
+}
+
+template <>
 tensorflow::gtl::ArraySlice<bool> Literal::GetArraySlice<bool>() const {
   CHECK_EQ(shape().element_type(), PRED);
   return tensorflow::gtl::ArraySlice<bool>(
@@ -1206,6 +1251,12 @@ tensorflow::gtl::ArraySlice<half> Literal::GetArraySlice<half>() const {
 }
 
 template <>
+tensorflow::gtl::ArraySlice<bfloat16> Literal::GetArraySlice<bfloat16>() const {
+  CHECK_EQ(shape().element_type(), BF16);
+  return {bf16s().data(), bf16s().size()};
+}
+
+template <>
 tensorflow::gtl::ArraySlice<complex64> Literal::GetArraySlice<complex64>()
     const {
   CHECK_EQ(shape().element_type(), C64);
@@ -1253,6 +1304,9 @@ bool Literal::IsAll(int8 value) const {
       return AllElementsEqualValue<double>(*this, value);
     case F16:
       return AllElementsEqualValue<half>(*this, static_cast<half>(value));
+    case BF16:
+      return AllElementsEqualValue<bfloat16>(*this,
+                                             static_cast<bfloat16>(value));
     case PRED:
       if (value == 0) {
         return AllElementsEqualValue<bool>(*this, false);
@@ -1274,6 +1328,9 @@ bool Literal::IsAllFloat(float value) const {
       return AllElementsEqualValue<double>(*this, value);
     case F16:
       return AllElementsEqualValue<half>(*this, static_cast<half>(value));
+    case BF16:
+      return AllElementsEqualValue<bfloat16>(*this,
+                                             static_cast<bfloat16>(value));
     default:
       return false;
   }
@@ -1310,6 +1367,8 @@ bool Literal::IsZero(tensorflow::gtl::ArraySlice<int64> indices) const {
       return Get<complex64>(indices) == complex64(0.0f, 0.0f);
     case F16:
       return Get<half>(indices) == static_cast<half>(0.0f);
+    case BF16:
+      return Get<bfloat16>(indices) == static_cast<bfloat16>(0.0f);
     case PRED:
       return Get<bool>(indices) == false;
     default:
@@ -1378,6 +1437,12 @@ void Literal::Resize<half>(int64 num_elements, half value) {
 }
 
 template <>
+void Literal::Resize<bfloat16>(int64 num_elements, bfloat16 value) {
+  CHECK_EQ(ShapeUtil::ElementsIn(shape()), num_elements);
+  mutable_bf16s()->resize(num_elements, value);
+}
+
+template <>
 void Literal::Resize<complex64>(int64 num_elements, complex64 value) {
   CHECK_EQ(ShapeUtil::ElementsIn(shape()), num_elements);
   mutable_c64s()->resize(num_elements, value);
@@ -1425,6 +1490,19 @@ LiteralProto Literal::ToProto() const {
       *proto.mutable_f16s() =
           string(reinterpret_cast<const char*>(f16s_.data()),
                  f16s_.size() * sizeof(half));
+      if (!kLittleEndian) {
+        ConvertEndianShort(const_cast<char*>(proto.mutable_f16s()->data()),
+                           proto.f16s().size());
+      }
+      break;
+    case BF16:
+      *proto.mutable_bf16s() =
+          string(reinterpret_cast<const char*>(bf16s_.data()),
+                 bf16s_.size() * sizeof(bfloat16));
+      if (!kLittleEndian) {
+        ConvertEndianShort(const_cast<char*>(proto.mutable_bf16s()->data()),
+                           proto.bf16s().size());
+      }
       break;
     case F32:
       CopyToRepeatedField(proto.mutable_f32s(), f32s());
@@ -1493,6 +1571,21 @@ void Literal::CopyFromProto(const LiteralProto& literal_proto) {
       CHECK_EQ(0, s.size() % sizeof(half));
       f16s_ = std::vector<half>(s.size() / sizeof(half));
       memcpy(f16s_.data(), s.data(), s.size());
+
+      if (!kLittleEndian) {
+        ConvertEndianShort(reinterpret_cast<char*>(f16s_.data()), s.size());
+      }
+      break;
+    }
+    case BF16: {
+      const string& s(literal_proto.bf16s());
+      CHECK_EQ(0, s.size() % sizeof(bfloat16));
+      bf16s_ = std::vector<bfloat16>(s.size() / sizeof(bfloat16));
+      memcpy(bf16s_.data(), s.data(), s.size());
+
+      if (!kLittleEndian) {
+        ConvertEndianShort(reinterpret_cast<char*>(bf16s_.data()), s.size());
+      }
       break;
     }
     case F32:
diff --git a/tensorflow/compiler/xla/literal_util.h b/tensorflow/compiler/xla/literal_util.h
index 667f926c46..f37e529caf 100644
--- a/tensorflow/compiler/xla/literal_util.h
+++ b/tensorflow/compiler/xla/literal_util.h
@@ -163,6 +163,11 @@ class Literal {
   const std::vector<complex64>& c64s() const { return c64s_; }
   std::vector<complex64>* mutable_c64s() { return &c64s_; }
 
+  int bf16s_size() const { return bf16s().size(); }
+  bfloat16 bf16s(int i) const { return bf16s_[i]; }
+  const std::vector<bfloat16>& bf16s() const { return bf16s_; }
+  std::vector<bfloat16>* mutable_bf16s() { return &bf16s_; }
+
   int tuple_literals_size() const { return tuple_literals().size(); }
   const Literal& tuple_literals(int i) const { return tuple_literals_[i]; }
   Literal* add_tuple_literals() {
@@ -622,6 +627,7 @@ class Literal {
   std::vector<uint16> u16s_;
   std::vector<uint32> u32s_;
   std::vector<uint64> u64s_;
+  std::vector<bfloat16> bf16s_;
   std::vector<half> f16s_;
   std::vector<float> f32s_;
   std::vector<double> f64s_;
@@ -675,6 +681,9 @@ template <>
 tensorflow::gtl::ArraySlice<half> Literal::GetArraySlice<half>() const;
 
 template <>
+tensorflow::gtl::ArraySlice<bfloat16> Literal::GetArraySlice<bfloat16>() const;
+
+template <>
 tensorflow::gtl::ArraySlice<complex64> Literal::GetArraySlice<complex64>()
     const;
 
@@ -715,6 +724,9 @@ template <>
 tensorflow::gtl::MutableArraySlice<half> Literal::GetMutableArraySlice();
 
 template <>
+tensorflow::gtl::MutableArraySlice<bfloat16> Literal::GetMutableArraySlice();
+
+template <>
 tensorflow::gtl::MutableArraySlice<complex64> Literal::GetMutableArraySlice();
 
 template <>
@@ -748,6 +760,9 @@ template <>
 void Literal::Resize<half>(int64 num_elements, half value);
 
 template <>
+void Literal::Resize<bfloat16>(int64 num_elements, bfloat16 value);
+
+template <>
 void Literal::Resize<complex64>(int64 num_elements, complex64 value);
 
 template <typename NativeT>
@@ -990,6 +1005,14 @@ inline half Literal::Get<half>(
   return GetArraySlice<half>()[linear_index];
 }
 
+template <>
+inline bfloat16 Literal::Get<bfloat16>(
+    tensorflow::gtl::ArraySlice<int64> multi_index) const {
+  CHECK(shape().element_type() == BF16);
+  int64 linear_index = LinearIndex(multi_index);
+  return GetArraySlice<bfloat16>()[linear_index];
+}
+
 template <typename NativeT>
 void Literal::Set(tensorflow::gtl::ArraySlice<int64> multi_index,
                   NativeT value) {
diff --git a/tensorflow/compiler/xla/literal_util_test.cc b/tensorflow/compiler/xla/literal_util_test.cc
index 6d596da4ad..1e08101759 100644
--- a/tensorflow/compiler/xla/literal_util_test.cc
+++ b/tensorflow/compiler/xla/literal_util_test.cc
@@ -110,6 +110,18 @@ TEST_F(LiteralUtilTest, LiteralScalarToString) {
 
   auto c64_lit = Literal::CreateR0<complex64>({3.14f, 2.78f});
   ASSERT_EQ("(3.14, 2.78)", c64_lit->ToString());
+
+  auto bf16_lit = Literal::CreateR0<bfloat16>(static_cast<bfloat16>(0.5f));
+  ASSERT_EQ("0.5", bf16_lit->ToString());
+
+  // 3.14 will be rounded to 3.125 in bfloat16 format (Round to nearest even).
+  auto bf16_lit_truncated =
+      Literal::CreateR0<bfloat16>(static_cast<bfloat16>(3.14f));
+  ASSERT_EQ("3.140625", bf16_lit_truncated->ToString());
+
+  auto bf16_lit_truncated2 =
+      Literal::CreateR0<bfloat16>(static_cast<bfloat16>(9.001f));
+  ASSERT_EQ("9", bf16_lit_truncated2->ToString());
 }
 
 TEST_F(LiteralUtilTest, LiteralVectorToString) {
@@ -397,6 +409,18 @@ TEST_F(LiteralUtilTest, IsAll) {
   EXPECT_FALSE(Literal::CreateR2<half>({{h8}, {h9}})->IsAll(8));
   EXPECT_FALSE(Literal::CreateR2<half>({{h9}, {h8}})->IsAll(8));
 
+  bfloat16 b8(8.0f);
+  bfloat16 b9(9.0f);
+
+  EXPECT_TRUE(Literal::CreateR2<bfloat16>({{b8}, {b8}})->IsAll(8));
+  EXPECT_FALSE(Literal::CreateR2<bfloat16>({{b8}, {b9}})->IsAll(8));
+  EXPECT_FALSE(Literal::CreateR2<bfloat16>({{b9}, {b8}})->IsAll(8));
+
+  // 9.001 will be truncated to 9.0
+  bfloat16 b91(9.001f);
+  bfloat16 b90(9.00f);
+  EXPECT_TRUE(Literal::CreateR2<bfloat16>({{b91}, {b90}})->IsAll(9.0));
+
   complex64 c8_9 = {8, 9};
   EXPECT_FALSE(Literal::CreateR2<complex64>({{c8_9}, {c8_9}})->IsAll(8));
 
@@ -691,6 +715,30 @@ TEST_F(LiteralUtilTest, PopulateR2C64) {
   EXPECT_EQ(output, *expected);
 }
 
+TEST_F(LiteralUtilTest, PopulateWithValueR0BF16) {
+  Literal output;
+  bfloat16 h(0.25f);
+  output.PopulateWithValue<bfloat16>(h, {});
+  auto expected = Literal::CreateR0<bfloat16>(h);
+  EXPECT_EQ(output, *expected);
+}
+
+TEST_F(LiteralUtilTest, PopulateWithValueR1BF16) {
+  Literal output;
+  bfloat16 h(0.5f);
+  output.PopulateWithValue<bfloat16>(h, {3});
+  auto expected = Literal::CreateR1<bfloat16>({h, h, h});
+  EXPECT_EQ(output, *expected);
+}
+
+TEST_F(LiteralUtilTest, PopulateWithValueR2BF16) {
+  Literal output;
+  bfloat16 h(2.0f);
+  output.PopulateWithValue<bfloat16>(h, {2, 2});
+  auto expected = Literal::CreateR2<bfloat16>({{h, h}, {h, h}});
+  EXPECT_EQ(output, *expected);
+}
+
 TEST_F(LiteralUtilTest, PopulateWithValueR0F32) {
   Literal output;
   output.PopulateWithValue<float>(2.5f, {});
@@ -975,6 +1023,14 @@ TEST_F(LiteralUtilTest, ConvertIfTypesMatch) {
     {{half(26.0), half(0.0), half(28.0), half(0.0)},
      {half(0.0), half(31.0), half(0.0), half(33.0)}},
   }}, layout_r4_dim0major_);
+  auto bf16 = Literal::CreateR4WithLayout<bfloat16>({{
+    {{bfloat16(10.0), bfloat16(0.0), bfloat16(12.0), bfloat16(0.0)},
+     {bfloat16(0.0), bfloat16(15.0), bfloat16(0.0), bfloat16(17.0)}},
+    {{bfloat16(0.0), bfloat16(19.0), bfloat16(0.0), bfloat16(21.0)},
+     {bfloat16(22.0), bfloat16(0.0), bfloat16(24.0), bfloat16(0.0)}},
+    {{bfloat16(26.0), bfloat16(0.0), bfloat16(28.0), bfloat16(0.0)},
+     {bfloat16(0.0), bfloat16(31.0), bfloat16(0.0), bfloat16(33.0)}},
+  }}, layout_r4_dim0major_);
   auto f32 = Literal::CreateR4WithLayout<float>({{
     {{10.0f, 0.0f, 12.0f, 0.0f}, {0.0f, 15.0f, 0.0f, 17.0f}},
     {{0.0f, 19.0f, 0.0f, 21.0f}, {22.0f, 0.0f, 24.0f, 0.0f}},
@@ -1008,6 +1064,12 @@ TEST_F(LiteralUtilTest, ConvertIfTypesMatch) {
   conv = s8->Convert(PRED).ConsumeValueOrDie();
   EXPECT_EQ(*conv, *pred);
 
+  conv = bf16->Convert(S32).ConsumeValueOrDie();
+  EXPECT_EQ(*conv, *s32);
+
+  conv = bf16->Convert(F32).ConsumeValueOrDie();
+  EXPECT_EQ(*conv, *f32);
+
   conv = pred->Convert(S32).ConsumeValueOrDie();
   EXPECT_EQ(*conv, *int32_pred);
 
diff --git a/tensorflow/compiler/xla/primitive_util.cc b/tensorflow/compiler/xla/primitive_util.cc
index 2113b5e06f..2bce56b7bd 100644
--- a/tensorflow/compiler/xla/primitive_util.cc
+++ b/tensorflow/compiler/xla/primitive_util.cc
@@ -79,6 +79,11 @@ PrimitiveType NativeToPrimitiveType<double>() {
 }
 
 template <>
+PrimitiveType NativeToPrimitiveType<bfloat16>() {
+  return BF16;
+}
+
+template <>
 PrimitiveType NativeToPrimitiveType<half>() {
   return F16;
 }
@@ -89,7 +94,7 @@ PrimitiveType NativeToPrimitiveType<complex64>() {
 }
 
 bool IsFloatingPointType(PrimitiveType type) {
-  return type == F16 || type == F32 || type == F64;
+  return type == F16 || type == F32 || type == F64 || type == BF16;
 }
 
 bool IsComplexType(PrimitiveType type) { return type == C64; }
@@ -118,6 +123,7 @@ int BitWidth(PrimitiveType type) {
     case S16:
     case U16:
     case F16:
+    case BF16:
       return 16;
 
     case U32:
diff --git a/tensorflow/compiler/xla/primitive_util.h b/tensorflow/compiler/xla/primitive_util.h
index a49c8b86fc..19c6a13888 100644
--- a/tensorflow/compiler/xla/primitive_util.h
+++ b/tensorflow/compiler/xla/primitive_util.h
@@ -77,6 +77,8 @@ template <>
 PrimitiveType NativeToPrimitiveType<double>();
 template <>
 PrimitiveType NativeToPrimitiveType<half>();
+template <>
+PrimitiveType NativeToPrimitiveType<bfloat16>();
 
 // Complex
 template <>
@@ -167,6 +169,11 @@ struct PrimitiveTypeToNative<F16> {
   using type = half;
 };
 
+template <>
+struct PrimitiveTypeToNative<BF16> {
+  using type = bfloat16;
+};
+
 // Complex
 template <>
 struct PrimitiveTypeToNative<C64> {
diff --git a/tensorflow/compiler/xla/service/backend.cc b/tensorflow/compiler/xla/service/backend.cc
index 9abe30e3f3..05f2d06278 100644
--- a/tensorflow/compiler/xla/service/backend.cc
+++ b/tensorflow/compiler/xla/service/backend.cc
@@ -13,14 +13,14 @@ See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
 
+#define EIGEN_USE_THREADS
+
 #include "tensorflow/compiler/xla/service/backend.h"
 
 #include <algorithm>
 #include <string>
 #include <utility>
 
-#define EIGEN_USE_THREADS
-
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/compiler/xla/service/compiler.h"
 #include "tensorflow/compiler/xla/service/platform_util.h"
diff --git a/tensorflow/compiler/xla/service/cpu/cpu_runtime_test.cc b/tensorflow/compiler/xla/service/cpu/cpu_runtime_test.cc
index f8e260dd90..f385829cdf 100644
--- a/tensorflow/compiler/xla/service/cpu/cpu_runtime_test.cc
+++ b/tensorflow/compiler/xla/service/cpu/cpu_runtime_test.cc
@@ -12,15 +12,13 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
-
+#define EIGEN_USE_THREADS
 #include "tensorflow/compiler/xla/service/cpu/cpu_runtime.h"
 
 #include <memory>
 #include <string>
 #include <tuple>
 
-#define EIGEN_USE_THREADS
-
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/compiler/xla/array2d.h"
 #include "tensorflow/compiler/xla/client/local_client.h"
diff --git a/tensorflow/compiler/xla/service/hlo_evaluator.cc b/tensorflow/compiler/xla/service/hlo_evaluator.cc
index 88b77ccdd0..a722d1b3d9 100644
--- a/tensorflow/compiler/xla/service/hlo_evaluator.cc
+++ b/tensorflow/compiler/xla/service/hlo_evaluator.cc
@@ -1450,6 +1450,10 @@ HloEvaluator::HloEvaluator() {
   typed_visitors_[F32] = MakeUnique<TypedVisitor<float>>(this);
   typed_visitors_[F64] = MakeUnique<TypedVisitor<double>>(this);
   typed_visitors_[C64] = MakeUnique<TypedVisitor<complex64>>(this);
+
+  typed_visitors_[BF16] = MakeUnique<FunctionVisitor>([](HloInstruction*) {
+    return Unimplemented("HloEvaluator: unhandled primitive type: BF16.");
+  });
   typed_visitors_[TUPLE] = MakeUnique<FunctionVisitor>([](HloInstruction*) {
     return Unimplemented("HloEvaluator: unhandled primitive type: TUPLE.");
   });
diff --git a/tensorflow/compiler/xla/service/hlo_runner.cc b/tensorflow/compiler/xla/service/hlo_runner.cc
index f463e57d99..158fb9a546 100644
--- a/tensorflow/compiler/xla/service/hlo_runner.cc
+++ b/tensorflow/compiler/xla/service/hlo_runner.cc
@@ -12,6 +12,7 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
+#define EIGEN_USE_THREADS
 
 #include "tensorflow/compiler/xla/service/hlo_runner.h"
 
@@ -19,8 +20,6 @@ limitations under the License.
 #include <string>
 #include <utility>
 
-#define EIGEN_USE_THREADS
-
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/compiler/xla/layout_util.h"
 #include "tensorflow/compiler/xla/ptr_util.h"
diff --git a/tensorflow/compiler/xla/shape_util.cc b/tensorflow/compiler/xla/shape_util.cc
index b5eb81dfc6..4d0bafa908 100644
--- a/tensorflow/compiler/xla/shape_util.cc
+++ b/tensorflow/compiler/xla/shape_util.cc
@@ -263,6 +263,7 @@ StatusOr<Shape> MakeShapeWithLayoutInternal(
     case S32:
     case S64:
     case F16:
+    case BF16:
     case F32:
     case F64:
       return true;
diff --git a/tensorflow/compiler/xla/tests/literal_test_util.cc b/tensorflow/compiler/xla/tests/literal_test_util.cc
index 95a52ecd2f..75c9a0d3fb 100644
--- a/tensorflow/compiler/xla/tests/literal_test_util.cc
+++ b/tensorflow/compiler/xla/tests/literal_test_util.cc
@@ -116,16 +116,18 @@ template <typename FloatT, typename UnsignedT>
 ::testing::AssertionResult CompareFloatsBitwiseEqual(FloatT lhs, FloatT rhs) {
   auto ulhs = tensorflow::bit_cast<UnsignedT>(lhs);
   auto urhs = tensorflow::bit_cast<UnsignedT>(rhs);
+  auto lhs_double = static_cast<double>(lhs);
+  auto rhs_double = static_cast<double>(rhs);
   if (ulhs != urhs) {
     return ::testing::AssertionFailure() << tensorflow::strings::Printf(
                "floating values are not bitwise-equal; and equality testing "
                "was requested: %s=%g=%a vs %s=%g=%a",
                tensorflow::strings::StrCat(tensorflow::strings::Hex(ulhs))
                    .c_str(),
-               lhs, lhs,
+               lhs_double, lhs_double,
                tensorflow::strings::StrCat(tensorflow::strings::Hex(urhs))
                    .c_str(),
-               rhs, rhs);
+               rhs_double, rhs_double);
   }
   return ::testing::AssertionSuccess();
 }
@@ -149,6 +151,10 @@ template <typename NativeT>
 // Specializations for floating types that do bitwise comparisons when equality
 // comparison is requested.
 template <>
+::testing::AssertionResult CompareEqual<bfloat16>(bfloat16 lhs, bfloat16 rhs) {
+  return CompareFloatsBitwiseEqual<bfloat16, uint16>(lhs, rhs);
+}
+template <>
 ::testing::AssertionResult CompareEqual<float>(float lhs, float rhs) {
   return CompareFloatsBitwiseEqual<float, uint32>(lhs, rhs);
 }
@@ -238,6 +244,9 @@ bool ExpectLiteralsEqual(const Literal& expected, const Literal& actual,
     case U64:
       match = ExpectLiteralsEqual<uint64>(expected, actual, &multi_index, 0);
       break;
+    case BF16:
+      match = ExpectLiteralsEqual<bfloat16>(expected, actual, &multi_index, 0);
+      break;
     case F32:
       match = ExpectLiteralsEqual<float>(expected, actual, &multi_index, 0);
       break;
diff --git a/tensorflow/compiler/xla/tests/local_client_test_base.cc b/tensorflow/compiler/xla/tests/local_client_test_base.cc
index c11e1df0a7..d98875dbc2 100644
--- a/tensorflow/compiler/xla/tests/local_client_test_base.cc
+++ b/tensorflow/compiler/xla/tests/local_client_test_base.cc
@@ -12,13 +12,12 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
+#define EIGEN_USE_THREADS
 
 #include "tensorflow/compiler/xla/tests/local_client_test_base.h"
 
 #include <vector>
 
-#define EIGEN_USE_THREADS
-
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/compiler/xla/client/local_client.h"
 #include "tensorflow/compiler/xla/map_util.h"
diff --git a/tensorflow/compiler/xla/types.h b/tensorflow/compiler/xla/types.h
index 3b19ca321c..9fa4297523 100644
--- a/tensorflow/compiler/xla/types.h
+++ b/tensorflow/compiler/xla/types.h
@@ -19,6 +19,7 @@ limitations under the License.
 #include <complex>
 
 #include "third_party/eigen3/Eigen/Core"
+#include "tensorflow/core/framework/numeric_types.h"
 #include "tensorflow/core/platform/types.h"
 
 #include <Eigen/Core>
@@ -32,6 +33,8 @@ using ::tensorflow::int16;
 using ::tensorflow::int32;
 using ::tensorflow::int64;
 
+using ::tensorflow::bfloat16;
+
 using ::tensorflow::uint8;
 using ::tensorflow::uint16;
 using ::tensorflow::uint32;
diff --git a/tensorflow/compiler/xla/xla_data.proto b/tensorflow/compiler/xla/xla_data.proto
index 7146604708..eac8f2ff07 100644
--- a/tensorflow/compiler/xla/xla_data.proto
+++ b/tensorflow/compiler/xla/xla_data.proto
@@ -46,6 +46,12 @@ enum PrimitiveType {
   // converted to f16 from f32 at arbirary points in the computation.
   F16 = 10;
   F32 = 11;
+
+  // Truncated 16 bit floating-point format. This is similar to IEEE's 16 bit
+  // floating-point format, but uses 1 bit for the sign, 8 bits for the exponent
+  // and 7 bits for the mantissa.
+  BF16 = 16;
+
   F64 = 12;
 
   // Complex values of fixed width.
@@ -63,6 +69,8 @@ enum PrimitiveType {
   // An opaque type used for passing context specific data to a custom
   // operation.
   OPAQUE = 14;
+
+  // Next = 17
 }
 
 // Describes the value held inside padding elements.
@@ -310,7 +318,10 @@ message LiteralProto {
   repeated double f64s = 9;
   repeated float c64s = 12;  // Stored as interleaved real, imag floats.
   repeated LiteralProto tuple_literals = 10;
-  bytes f16s = 11;  // Note: the F16s are encoded in little endian byte order
+  // The F16s and BF16s are encoded in little endian byte order
+  bytes f16s = 11;
+  bytes bf16s = 13;
+  // Next = 14
 }
 
 message WindowDimension {
diff --git a/tensorflow/core/framework/bfloat16.cc b/tensorflow/core/framework/bfloat16.cc
index a5ac0e1a8d..1a6f355c77 100644
--- a/tensorflow/core/framework/bfloat16.cc
+++ b/tensorflow/core/framework/bfloat16.cc
@@ -18,32 +18,24 @@ limitations under the License.
 namespace tensorflow {
 
 void FloatToBFloat16(const float* src, bfloat16* dst, int64 size) {
-  const uint16_t* p = reinterpret_cast<const uint16_t*>(src);
-  uint16_t* q = reinterpret_cast<uint16_t*>(dst);
-#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
-    for (; size != 0; p += 2, q++, size--) {  
-      *q = p[0];  
-    }  
-#else
-    for (; size != 0; p += 2, q++, size--) {  
-     *q = p[1];  
-    }  
-#endif
+  for (int64 i = 0; i < size; ++i) {
+    dst[i] = bfloat16(src[i]);
+  }
 }
 
 void BFloat16ToFloat(const bfloat16* src, float* dst, int64 size) {
   const uint16_t* p = reinterpret_cast<const uint16_t*>(src);
   uint16_t* q = reinterpret_cast<uint16_t*>(dst);
 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
-    for (; size != 0; p++, q += 2, size--) {  
-      q[0] = *p;  
-      q[1] = 0;  
+  for (; size != 0; p++, q += 2, size--) {
+    q[0] = *p;
+    q[1] = 0;
     }
-#else  
-    for (; size != 0; p++, q += 2, size--) {  
-      q[0] = 0;  
-      q[1] = *p;  
-    } 
+#else
+  for (; size != 0; p++, q += 2, size--) {
+    q[0] = 0;
+    q[1] = *p;
+  }
 #endif
 }
 
diff --git a/tensorflow/core/framework/bfloat16_test.cc b/tensorflow/core/framework/bfloat16_test.cc
index af4e6a4411..a25b764ea2 100644
--- a/tensorflow/core/framework/bfloat16_test.cc
+++ b/tensorflow/core/framework/bfloat16_test.cc
@@ -15,6 +15,7 @@ limitations under the License.
 
 #include "tensorflow/core/framework/bfloat16.h"
 
+#include "tensorflow/core/lib/core/casts.h"
 #include "tensorflow/core/platform/test.h"
 #include "tensorflow/core/platform/test_benchmark.h"
 
@@ -27,6 +28,97 @@ TEST(Bfloat16Test, Simple) {
   EXPECT_EQ(0x4140, a.value);
 }
 
+float BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa,
+                    uint32_t low_mantissa) {
+  return bit_cast<float>((sign << 31) + (exponent << 23) +
+                         (high_mantissa << 16) + low_mantissa);
+}
+
+struct Bfloat16TestParam {
+  float input;
+  float expected;
+};
+
+class Bfloat16Test : public ::testing::Test,
+                     public ::testing::WithParamInterface<Bfloat16TestParam> {};
+
+TEST_P(Bfloat16Test, RoundOrTruncate) {
+  bfloat16 a(GetParam().input);
+  if (std::isnan(GetParam().input)) {
+    EXPECT_TRUE(std::isnan(float(a)));
+    return;
+  }
+  EXPECT_EQ(GetParam().expected, float(a));
+}
+
+INSTANTIATE_TEST_CASE_P(
+    Bfloat16Test_Instantiation, Bfloat16Test,
+    ::testing::Values(
+        // More than half.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b1111010111000011),
+            BinaryToFloat(0, 0b10000000, 0b1001001, 0b0000000000000000)},
+
+        Bfloat16TestParam{
+            BinaryToFloat(1, 0b10000000, 0b1001000, 0b1111010111000011),
+            BinaryToFloat(1, 0b10000000, 0b1001001, 0b0000000000000000)},
+
+        // Exact half.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b1000000000000000),
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0000000000000000)},
+
+        // NaN stays at NaN.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b11111111, 0b0000000, 0b0000000000000001),
+            BinaryToFloat(0, 0b11111111, 0b1000000, 0b0000000000000000)},
+
+        // NaN stays at NaN -- no exponents overflow.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b11111111, 0b1111111, 0b1111111111111111),
+            BinaryToFloat(0, 0b11111111, 0b1000000, 0b0000000000000000)},
+
+        // More than half, round to an odd number.
+        Bfloat16TestParam{
+            BinaryToFloat(1, 0b10000000, 0b1001000, 0b1100000000000000),
+            BinaryToFloat(1, 0b10000000, 0b1001001, 0b0000000000000000)},
+
+        // Less than half, truncate.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0000000000000000),
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0000000000000000)},
+
+        // Less than half, truncate.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0100000000000000),
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0000000000000000)},
+
+        // Exact at half, but result is already even.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b1000000000000000),
+            BinaryToFloat(0, 0b10000000, 0b1001000, 0b0000000000000000)},
+
+        // Denormal values.
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b00000000, 0b1001000, 0b1000000000000000),
+            BinaryToFloat(0, 0b00000000, 0b1001000, 0b0000000000000000)},
+        Bfloat16TestParam{
+            BinaryToFloat(0, 0b00000000, 0b1111111, 0b1100000000000000),
+            BinaryToFloat(0, 0b00000001, 0b0000000, 0b0000000000000000)}));
+TEST(Bfloat16Test, RoundWithFractionOverflow) {
+  // Still works with fraction overflow -- round to 4./
+  //
+  // Input 3.9960938:
+  // Sign |  Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit)
+  //  0     1 0 0 0 0 0 0      1 1 1 1 1 1 1     1100000000000000
+  //
+  // Should round to 4.0:
+  // Sign |  Exp (8 bit)  | Frac (first 7 bit)
+  //  0     1 0 0 0 0 0 1      0 0 0 0 0 0 0
+  bfloat16 a(3.9960938f);
+  EXPECT_EQ(4.0, float(a));
+}
+
 TEST(Bfloat16Test, Conversion) {
   float a[100];
   for (int i = 0; i < 100; ++i) {
diff --git a/tensorflow/core/framework/numeric_types.h b/tensorflow/core/framework/numeric_types.h
index a630bee38d..d005de2af1 100644
--- a/tensorflow/core/framework/numeric_types.h
+++ b/tensorflow/core/framework/numeric_types.h
@@ -44,29 +44,262 @@ typedef Eigen::QUInt16 quint16;
 // see framework/bfloat16.h for description.
 struct bfloat16 {
   EIGEN_DEVICE_FUNC bfloat16() {}
-  EIGEN_DEVICE_FUNC explicit bfloat16(const float v) {
-    const uint16_t* p = reinterpret_cast<const uint16_t*>(&v);
+
+  explicit EIGEN_DEVICE_FUNC bfloat16(float v) {
+    uint32_t input;
+    memcpy(&input, &v, sizeof(uint32_t));
+
+    if ((~input & 0x7f800000) == 0 && (input & 0x007fffff) != 0) {
+      // If the value is a NaN, squash it to a qNaN with msb of fraction set,
+      // this makes sure after truncation we don't end up with an inf.
+      //
+      // qNaN magic: All exponent bits set + most significant bit of fraction
+      // set.
+      value = 0x7fc0;
+    } else {
+      // Fast rounding algorithm that rounds a half value to nearest even. This
+      // reduces expected error when we convert a large number of floats. Here
+      // is how it works:
+      //
+      // Definitions:
+      // To convert a float 32 to bfloat16, a float 32 can be viewed as 32 bits
+      // with the following tags:
+      //
+      // Sign |  Exp (8 bits) | Frac (23 bits)
+      //  S     EEEEEEEE         FFFFFFLRTTTTTTTTTTTTTTT
+      //
+      //  S: Sign bit.
+      //  E: Exponent bits.
+      //  F: First 6 bits of fraction.
+      //  L: Least significant bit of resulting bfloat16 if we truncate away the
+      //  rest of the float32. This is also the 7th bit of fraction
+      //  R: Rounding bit, 8th bit of fraction.
+      //  T: Sticky bits, rest of fraction, 15 bits.
+      //
+      // To round half to nearest even, there are 3 cases where we want to round
+      // down (simply truncate the result of the bits away, which consists of
+      // rounding bit and sticky bits) and two cases where we want to round up
+      // (truncate then add one to the result).
+      //
+      // The fast converting algorithm simply adds lsb (L) to 0x7fff (15 bits of
+      // 1s) as the rounding bias, adds the rounding bias to the input, then
+      // truncates the last 16 bits away.
+      //
+      // To understand how it works, we can analyze this algorithm case by case:
+      //
+      // 1. L = 0, R = 0:
+      //   Expect: round down, this is less than half value.
+      //
+      //   Algorithm:
+      //   - Rounding bias: 0x7fff + 0 = 0x7fff
+      //   - Adding rounding bias to input may create any carry, depending on
+      //   whether there is any value set to 1 in T bits.
+      //   - R may be set to 1 if there is a carry.
+      //   - L remains 0.
+      //   - Note that this case also handles Inf and -Inf, where all fraction
+      //   bits, including L, R and Ts are all 0. The output remains Inf after
+      //   this algorithm.
+      //
+      // 2. L = 1, R = 0:
+      //   Expect: round down, this is less than half value.
+      //
+      //   Algorithm:
+      //   - Rounding bias: 0x7fff + 1 = 0x8000
+      //   - Adding rounding bias to input doesn't change sticky bits but
+      //   adds 1 to rounding bit.
+      //   - L remains 1.
+      //
+      // 3. L = 0, R = 1, all of T are 0:
+      //   Expect: round down, this is exactly at half, the result is already
+      //   even (L=0).
+      //
+      //   Algorithm:
+      //   - Rounding bias: 0x7fff + 0 = 0x7fff
+      //   - Adding rounding bias to input sets all sticky bits to 1, but
+      //   doesn't create a carry.
+      //   - R remains 1.
+      //   - L remains 0.
+      //
+      // 4. L = 1, R = 1:
+      //   Expect: round up, this is exactly at half, the result needs to be
+      //   round to the next even number.
+      //
+      //   Algorithm:
+      //   - Rounding bias: 0x7fff + 1 = 0x8000
+      //   - Adding rounding bias to input doesn't change sticky bits, but
+      //   creates a carry from rounding bit.
+      //   - The carry sets L to 0, creates another carry bit and propagate
+      //   forward to F bits.
+      //   - If all the F bits are 1, a carry then propagates to the exponent
+      //   bits, which then creates the minimum value with the next exponent
+      //   value. Note that we won't have the case where exponents are all 1,
+      //   since that's either a NaN (handled in the other if condition) or inf
+      //   (handled in case 1).
+      //
+      // 5. L = 0, R = 1, any of T is 1:
+      //   Expect: round up, this is greater than half.
+      //
+      //   Algorithm:
+      //   - Rounding bias: 0x7fff + 0 = 0x7fff
+      //   - Adding rounding bias to input creates a carry from sticky bits,
+      //   sets rounding bit to 0, then create another carry.
+      //   - The second carry sets L to 1.
+      //
+      // Examples:
+      //
+      //  Exact half value that is already even:
+      //    Input:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)
+      //     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT
+      //     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0     1000000000000000
+      //
+      //     This falls into case 3. We truncate the rest of 16 bits and no
+      //     carry is created into F and L:
+      //
+      //    Output:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit)
+      //     S     E E E E E E E E      F F F F F F L
+      //     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0
+      //
+      //  Exact half value, round to next even number:
+      //    Input:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)
+      //     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT
+      //     0     0 0 0 0 0 0 0 0      0 0 0 0 0 0 1     1000000000000000
+      //
+      //     This falls into case 4. We create a carry from R and T,
+      //     which then propagates into L and F:
+      //
+      //    Output:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit)
+      //     S     E E E E E E E E      F F F F F F L
+      //     0     0 0 0 0 0 0 0 0      0 0 0 0 0 1 0
+      //
+      //
+      //  Max denormal value round to min normal value:
+      //    Input:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)
+      //     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT
+      //     0     0 0 0 0 0 0 0 0      1 1 1 1 1 1 1     1111111111111111
+      //
+      //     This falls into case 4. We create a carry from R and T,
+      //     propagate into L and F, which then propagates into exponent
+      //     bits:
+      //
+      //    Output:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit)
+      //     S     E E E E E E E E      F F F F F F L
+      //     0     0 0 0 0 0 0 0 1      0 0 0 0 0 0 0
+      //
+      //  Max normal value round to Inf:
+      //    Input:
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit) | Frac (last 16 bit)
+      //     S     E E E E E E E E      F F F F F F L     RTTTTTTTTTTTTTTT
+      //     0     1 1 1 1 1 1 1 0      1 1 1 1 1 1 1     1111111111111111
+      //
+      //     This falls into case 4. We create a carry from R and T,
+      //     propagate into L and F, which then propagates into exponent
+      //     bits:
+      //
+      //    Sign |  Exp (8 bit)     | Frac (first 7 bit)
+      //     S     E E E E E E E E      F F F F F F L
+      //     0     1 1 1 1 1 1 1 1      0 0 0 0 0 0 0
+      //
+      //
+      // Least significant bit of resulting bfloat.
+      uint32_t lsb = (input >> 16) & 1;
+      uint32_t rounding_bias = 0x7fff + lsb;
+      input += rounding_bias;
+      value = static_cast<uint16_t>(input >> 16);
+    }
+  }
+
+  template <class T>
+  explicit EIGEN_DEVICE_FUNC bfloat16(const T& val)
+      : bfloat16(static_cast<float>(val)) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const {
+    float result;
+
+    uint16_t* q = reinterpret_cast<uint16_t*>(&result);
+
 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
-    value = p[0];
+    q[0] = value;
+    q[1] = 0;
 #else
-    value = p[1];
+    q[0] = 0;
+    q[1] = value;
 #endif
+    return result;
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator bool() const {
+    return static_cast<bool>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator Eigen::half() const {
+    return static_cast<Eigen::half>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator short() const {
+    return static_cast<short>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator int() const {
+    return static_cast<int>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator char() const {
+    return static_cast<char>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator signed char() const {
+    return static_cast<signed char>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator unsigned char() const {
+    return static_cast<unsigned char>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator unsigned int() const {
+    return static_cast<unsigned int>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator unsigned long() const {
+    return static_cast<unsigned long>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator unsigned long long() const {
+    return static_cast<unsigned long long>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator long long() const {
+    return static_cast<long long>(float(*this));
+  }
+
+  EIGEN_DEVICE_FUNC explicit operator double() const {
+    return static_cast<double>(float(*this));
   }
 
   uint16_t value;
 };
 
+inline bool operator==(const bfloat16 a, const bfloat16 b) {
+  return a.value == b.value;
+}
+
+inline bool operator!=(const bfloat16 a, const bfloat16 b) {
+  return a.value != b.value;
+}
+
 }  // end namespace tensorflow
 
 namespace Eigen {
 template <>
 struct NumTraits<tensorflow::bfloat16> : GenericNumTraits<uint16_t> {};
 
-EIGEN_STRONG_INLINE bool operator==(const tensorflow::bfloat16 a,
-                                    const tensorflow::bfloat16 b) {
-  return a.value == b.value;
-}
-
+using ::tensorflow::operator==;
+using ::tensorflow::operator!=;
 }  // namespace Eigen
 
 #ifdef COMPILER_MSVC