FP16 support in serialization

* Allow serialization of fp16 data
* Add package to support integrated half data-type (half_float::half), independent of native float: http://half.sourceforge.net/
* Allow passing of accumulate data-type in serialization

Signed-off-by: James Ward <james.ward@arm.com>
Change-Id: I54357f02e3776d81958228f699ea5044f2014f4b

22 files changed, 5431 insertions, 41 deletions

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ba0430d
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+__pycache__/
\ No newline at end of file
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 87e0825..e53aa3e 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -27,6 +27,8 @@ set(CMAKE_VERBOSE_MAKEFILE ON)
 option(BUILD_TESTS "Build test applications" ON)
 option(FLATBUFFERS_ROOT "Location where the flatbuffers 'include' and 'lib' folders to be found" Off)
 
+include_directories(${PROJECT_SOURCE_DIR}/third_party/half/include)
+
 include_directories(${CMAKE_CURRENT_SOURCE_DIR}/include)
 
 add_library(tosa_serialization_lib
diff --git a/README.md b/README.md
index 979b76f..9d852df 100644
--- a/README.md
+++ b/README.md
@@ -158,3 +158,10 @@ numpy file, (4) format and (5) usage.
 # License
 
 The *TOSA Serialization Library* is licensed under Apache-2.0.
+
+## Third Party Projects
+
+- The [half](https://half.sourceforge.net/) library is licensed under MIT license.
+
+Other third party projects are referenced as sub-modules and as such, are licensed under the licenses stated in their projects.
+
diff --git a/include/attribute.def b/include/attribute.def
index b40a77b..ebbf024 100644
--- a/include/attribute.def
+++ b/include/attribute.def
@@ -26,26 +26,29 @@
     ...: variadic variables for more arguments, depending on NUM_ARGS_IN_ATTRIBUTES
 */
 
-DEF_ATTRIBUTE(Pool, 5,
+DEF_ATTRIBUTE(Pool, 6,
               int32_t, V, pad,
               int32_t, V, kernel,
               int32_t, V, stride,
               int32_t, S, input_zp,
-              int32_t, S, output_zp)
+              int32_t, S, output_zp,
+              DType,   S, accum_dtype)
 
-DEF_ATTRIBUTE(Conv, 5,
+DEF_ATTRIBUTE(Conv, 6,
               int32_t, V, pad,
               int32_t, V, stride,
               int32_t, V, dilation,
               int32_t, S, input_zp,
-              int32_t, S, weight_zp)
+              int32_t, S, weight_zp,
+              DType,   S, accum_dtype)
 
-DEF_ATTRIBUTE(TransposeConv, 5,
+DEF_ATTRIBUTE(TransposeConv, 6,
               int32_t, V, out_pad,
               int32_t, V, stride,
               int32_t, V, output_shape,
               int32_t, S, input_zp,
-              int32_t, S, weight_zp)
+              int32_t, S, weight_zp,
+              DType,   S, accum_dtype)
 
 DEF_ATTRIBUTE(Pad, 3,
               int32_t, V, padding,
@@ -106,13 +109,15 @@ DEF_ATTRIBUTE(Transpose, 1,
 DEF_ATTRIBUTE(Table, 1,
               int16_t, V, table)
 
-DEF_ATTRIBUTE(MatMul, 2,
+DEF_ATTRIBUTE(MatMul, 3,
               int32_t, S, a_zp,
-              int32_t, S, b_zp)
+              int32_t, S, b_zp,
+              DType,   S, accum_dtype)
 
-DEF_ATTRIBUTE(FullyConnected, 2,
+DEF_ATTRIBUTE(FullyConnected, 3,
               int32_t, S, input_zp,
-              int32_t, S, weight_zp)
+              int32_t, S, weight_zp,
+              DType,   S, accum_dtype)
 
 DEF_ATTRIBUTE(Negate, 2,
               int32_t, S, input1_zp,
diff --git a/include/attribute.h b/include/attribute.h
index 93f7bc4..1178ee4 100644
--- a/include/attribute.h
+++ b/include/attribute.h
@@ -47,6 +47,7 @@ public:
 #define DEF_ARGS_VER0_S_float(V) DEF_ARGS_VER0_S_DEFAULT(V)
 #define DEF_ARGS_VER0_S_bool(V) DEF_ARGS_VER0_S_DEFAULT(V)
 #define DEF_ARGS_VER0_S_ResizeMode(V) DEF_ARGS_VER0_S_DEFAULT(V)
+#define DEF_ARGS_VER0_S_DType(V) DEF_ARGS_VER0_S_DEFAULT(V)
 #define DEF_ARGS_VER0_S_string(V) DEF_ARGS_VER0_S_STR(V)
 
 #define DEF_ARGS_VER0_S(T, V) DEF_ARGS_VER0_S_##T(V)
@@ -153,6 +154,7 @@ public:
 #undef DEF_ARGS_VER0_S_float
 #undef DEF_ARGS_VER0_S_bool
 #undef DEF_ARGS_VER0_S_ResizeMode
+#undef DEF_ARGS_VER0_S_DType
 #undef DEF_ARGS_VER0_S_string
 #undef DEF_ARGS_VER0_S_STR
 #undef DEF_ARGS_VER0_S_DEFAULT
diff --git a/include/numpy_utils.h b/include/numpy_utils.h
index c64bc17..6a20eb3 100644
--- a/include/numpy_utils.h
+++ b/include/numpy_utils.h
@@ -24,6 +24,8 @@
 #include <cstring>
 #include <vector>
 
+#include "half.hpp"
+
 class NumpyUtilities
 {
 public:
@@ -39,6 +41,8 @@ public:
 
     static NPError readFromNpyFile(const char* filename, const uint32_t elems, float* databuf);
 
+    static NPError readFromNpyFile(const char* filename, const uint32_t elems, half_float::half* databuf);
+
     static NPError readFromNpyFile(const char* filename, const uint32_t elems, int32_t* databuf);
 
     static NPError readFromNpyFile(const char* filename, const uint32_t elems, int64_t* databuf);
@@ -49,6 +53,9 @@ public:
 
     static NPError writeToNpyFile(const char* filename, const uint32_t elems, const bool* databuf);
 
+    static NPError
+        writeToNpyFile(const char* filename, const std::vector<int32_t>& shape, const half_float::half* databuf);
+
     static NPError writeToNpyFile(const char* filename, const std::vector<int32_t>& shape, const int32_t* databuf);
 
     static NPError writeToNpyFile(const char* filename, const uint32_t elems, const int32_t* databuf);
diff --git a/include/tosa_generated.h b/include/tosa_generated.h
index b54a324..f0d04d0 100644
--- a/include/tosa_generated.h
+++ b/include/tosa_generated.h
@@ -94,11 +94,12 @@ enum DType : uint32_t {
   DType_INT48 = 7,
   DType_FLOAT = 8,
   DType_UINT16 = 9,
+  DType_FP16 = 10,
   DType_MIN = DType_UNKNOWN,
-  DType_MAX = DType_UINT16
+  DType_MAX = DType_FP16
 };
 
-inline const DType (&EnumValuesDType())[10] {
+inline const DType (&EnumValuesDType())[11] {
   static const DType values[] = {
     DType_UNKNOWN,
     DType_BOOL,
@@ -109,13 +110,14 @@ inline const DType (&EnumValuesDType())[10] {
     DType_INT32,
     DType_INT48,
     DType_FLOAT,
-    DType_UINT16
+    DType_UINT16,
+    DType_FP16
   };
   return values;
 }
 
 inline const char * const *EnumNamesDType() {
-  static const char * const names[11] = {
+  static const char * const names[12] = {
     "UNKNOWN",
     "BOOL",
     "UINT8",
@@ -126,13 +128,14 @@ inline const char * const *EnumNamesDType() {
     "INT48",
     "FLOAT",
     "UINT16",
+    "FP16",
     nullptr
   };
   return names;
 }
 
 inline const char *EnumNameDType(DType e) {
-  if (flatbuffers::IsOutRange(e, DType_UNKNOWN, DType_UINT16)) return "";
+  if (flatbuffers::IsOutRange(e, DType_UNKNOWN, DType_FP16)) return "";
   const size_t index = static_cast<size_t>(e);
   return EnumNamesDType()[index];
 }
@@ -582,7 +585,8 @@ struct PoolAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
     VT_KERNEL = 6,
     VT_STRIDE = 8,
     VT_INPUT_ZP = 10,
-    VT_OUTPUT_ZP = 12
+    VT_OUTPUT_ZP = 12,
+    VT_ACCUM_DTYPE = 14
   };
   const flatbuffers::Vector<int32_t> *pad() const {
     return GetPointer<const flatbuffers::Vector<int32_t> *>(VT_PAD);
@@ -599,6 +603,9 @@ struct PoolAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
   int32_t output_zp() const {
     return GetField<int32_t>(VT_OUTPUT_ZP, 0);
   }
+  tosa::DType accum_dtype() const {
+    return static_cast<tosa::DType>(GetField<uint32_t>(VT_ACCUM_DTYPE, 0));
+  }
   bool Verify(flatbuffers::Verifier &verifier) const {
     return VerifyTableStart(verifier) &&
            VerifyOffset(verifier, VT_PAD) &&
@@ -609,6 +616,7 @@ struct PoolAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
            verifier.VerifyVector(stride()) &&
            VerifyField<int32_t>(verifier, VT_INPUT_ZP, 4) &&
            VerifyField<int32_t>(verifier, VT_OUTPUT_ZP, 4) &&
+           VerifyField<uint32_t>(verifier, VT_ACCUM_DTYPE, 4) &&
            verifier.EndTable();
   }
 };
@@ -632,6 +640,9 @@ struct PoolAttributeBuilder {
   void add_output_zp(int32_t output_zp) {
     fbb_.AddElement<int32_t>(PoolAttribute::VT_OUTPUT_ZP, output_zp, 0);
   }
+  void add_accum_dtype(tosa::DType accum_dtype) {
+    fbb_.AddElement<uint32_t>(PoolAttribute::VT_ACCUM_DTYPE, static_cast<uint32_t>(accum_dtype), 0);
+  }
   explicit PoolAttributeBuilder(flatbuffers::FlatBufferBuilder &_fbb)
         : fbb_(_fbb) {
     start_ = fbb_.StartTable();
@@ -649,8 +660,10 @@ inline flatbuffers::Offset<PoolAttribute> CreatePoolAttribute(
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> kernel = 0,
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> stride = 0,
     int32_t input_zp = 0,
-    int32_t output_zp = 0) {
+    int32_t output_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   PoolAttributeBuilder builder_(_fbb);
+  builder_.add_accum_dtype(accum_dtype);
   builder_.add_output_zp(output_zp);
   builder_.add_input_zp(input_zp);
   builder_.add_stride(stride);
@@ -665,7 +678,8 @@ inline flatbuffers::Offset<PoolAttribute> CreatePoolAttributeDirect(
     const std::vector<int32_t> *kernel = nullptr,
     const std::vector<int32_t> *stride = nullptr,
     int32_t input_zp = 0,
-    int32_t output_zp = 0) {
+    int32_t output_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   auto pad__ = pad ? _fbb.CreateVector<int32_t>(*pad) : 0;
   auto kernel__ = kernel ? _fbb.CreateVector<int32_t>(*kernel) : 0;
   auto stride__ = stride ? _fbb.CreateVector<int32_t>(*stride) : 0;
@@ -675,7 +689,8 @@ inline flatbuffers::Offset<PoolAttribute> CreatePoolAttributeDirect(
       kernel__,
       stride__,
       input_zp,
-      output_zp);
+      output_zp,
+      accum_dtype);
 }
 
 struct ConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
@@ -685,7 +700,8 @@ struct ConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
     VT_STRIDE = 6,
     VT_DILATION = 8,
     VT_INPUT_ZP = 10,
-    VT_WEIGHT_ZP = 12
+    VT_WEIGHT_ZP = 12,
+    VT_ACCUM_DTYPE = 14
   };
   const flatbuffers::Vector<int32_t> *pad() const {
     return GetPointer<const flatbuffers::Vector<int32_t> *>(VT_PAD);
@@ -702,6 +718,9 @@ struct ConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
   int32_t weight_zp() const {
     return GetField<int32_t>(VT_WEIGHT_ZP, 0);
   }
+  tosa::DType accum_dtype() const {
+    return static_cast<tosa::DType>(GetField<uint32_t>(VT_ACCUM_DTYPE, 0));
+  }
   bool Verify(flatbuffers::Verifier &verifier) const {
     return VerifyTableStart(verifier) &&
            VerifyOffset(verifier, VT_PAD) &&
@@ -712,6 +731,7 @@ struct ConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
            verifier.VerifyVector(dilation()) &&
            VerifyField<int32_t>(verifier, VT_INPUT_ZP, 4) &&
            VerifyField<int32_t>(verifier, VT_WEIGHT_ZP, 4) &&
+           VerifyField<uint32_t>(verifier, VT_ACCUM_DTYPE, 4) &&
            verifier.EndTable();
   }
 };
@@ -735,6 +755,9 @@ struct ConvAttributeBuilder {
   void add_weight_zp(int32_t weight_zp) {
     fbb_.AddElement<int32_t>(ConvAttribute::VT_WEIGHT_ZP, weight_zp, 0);
   }
+  void add_accum_dtype(tosa::DType accum_dtype) {
+    fbb_.AddElement<uint32_t>(ConvAttribute::VT_ACCUM_DTYPE, static_cast<uint32_t>(accum_dtype), 0);
+  }
   explicit ConvAttributeBuilder(flatbuffers::FlatBufferBuilder &_fbb)
         : fbb_(_fbb) {
     start_ = fbb_.StartTable();
@@ -752,8 +775,10 @@ inline flatbuffers::Offset<ConvAttribute> CreateConvAttribute(
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> stride = 0,
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> dilation = 0,
     int32_t input_zp = 0,
-    int32_t weight_zp = 0) {
+    int32_t weight_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   ConvAttributeBuilder builder_(_fbb);
+  builder_.add_accum_dtype(accum_dtype);
   builder_.add_weight_zp(weight_zp);
   builder_.add_input_zp(input_zp);
   builder_.add_dilation(dilation);
@@ -768,7 +793,8 @@ inline flatbuffers::Offset<ConvAttribute> CreateConvAttributeDirect(
     const std::vector<int32_t> *stride = nullptr,
     const std::vector<int32_t> *dilation = nullptr,
     int32_t input_zp = 0,
-    int32_t weight_zp = 0) {
+    int32_t weight_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   auto pad__ = pad ? _fbb.CreateVector<int32_t>(*pad) : 0;
   auto stride__ = stride ? _fbb.CreateVector<int32_t>(*stride) : 0;
   auto dilation__ = dilation ? _fbb.CreateVector<int32_t>(*dilation) : 0;
@@ -778,7 +804,8 @@ inline flatbuffers::Offset<ConvAttribute> CreateConvAttributeDirect(
       stride__,
       dilation__,
       input_zp,
-      weight_zp);
+      weight_zp,
+      accum_dtype);
 }
 
 struct TransposeConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
@@ -788,7 +815,8 @@ struct TransposeConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Tab
     VT_STRIDE = 6,
     VT_OUTPUT_SHAPE = 8,
     VT_INPUT_ZP = 10,
-    VT_WEIGHT_ZP = 12
+    VT_WEIGHT_ZP = 12,
+    VT_ACCUM_DTYPE = 14
   };
   const flatbuffers::Vector<int32_t> *out_pad() const {
     return GetPointer<const flatbuffers::Vector<int32_t> *>(VT_OUT_PAD);
@@ -805,6 +833,9 @@ struct TransposeConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Tab
   int32_t weight_zp() const {
     return GetField<int32_t>(VT_WEIGHT_ZP, 0);
   }
+  tosa::DType accum_dtype() const {
+    return static_cast<tosa::DType>(GetField<uint32_t>(VT_ACCUM_DTYPE, 0));
+  }
   bool Verify(flatbuffers::Verifier &verifier) const {
     return VerifyTableStart(verifier) &&
            VerifyOffset(verifier, VT_OUT_PAD) &&
@@ -815,6 +846,7 @@ struct TransposeConvAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Tab
            verifier.VerifyVector(output_shape()) &&
            VerifyField<int32_t>(verifier, VT_INPUT_ZP, 4) &&
            VerifyField<int32_t>(verifier, VT_WEIGHT_ZP, 4) &&
+           VerifyField<uint32_t>(verifier, VT_ACCUM_DTYPE, 4) &&
            verifier.EndTable();
   }
 };
@@ -838,6 +870,9 @@ struct TransposeConvAttributeBuilder {
   void add_weight_zp(int32_t weight_zp) {
     fbb_.AddElement<int32_t>(TransposeConvAttribute::VT_WEIGHT_ZP, weight_zp, 0);
   }
+  void add_accum_dtype(tosa::DType accum_dtype) {
+    fbb_.AddElement<uint32_t>(TransposeConvAttribute::VT_ACCUM_DTYPE, static_cast<uint32_t>(accum_dtype), 0);
+  }
   explicit TransposeConvAttributeBuilder(flatbuffers::FlatBufferBuilder &_fbb)
         : fbb_(_fbb) {
     start_ = fbb_.StartTable();
@@ -855,8 +890,10 @@ inline flatbuffers::Offset<TransposeConvAttribute> CreateTransposeConvAttribute(
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> stride = 0,
     flatbuffers::Offset<flatbuffers::Vector<int32_t>> output_shape = 0,
     int32_t input_zp = 0,
-    int32_t weight_zp = 0) {
+    int32_t weight_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   TransposeConvAttributeBuilder builder_(_fbb);
+  builder_.add_accum_dtype(accum_dtype);
   builder_.add_weight_zp(weight_zp);
   builder_.add_input_zp(input_zp);
   builder_.add_output_shape(output_shape);
@@ -871,7 +908,8 @@ inline flatbuffers::Offset<TransposeConvAttribute> CreateTransposeConvAttributeD
     const std::vector<int32_t> *stride = nullptr,
     const std::vector<int32_t> *output_shape = nullptr,
     int32_t input_zp = 0,
-    int32_t weight_zp = 0) {
+    int32_t weight_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   auto out_pad__ = out_pad ? _fbb.CreateVector<int32_t>(*out_pad) : 0;
   auto stride__ = stride ? _fbb.CreateVector<int32_t>(*stride) : 0;
   auto output_shape__ = output_shape ? _fbb.CreateVector<int32_t>(*output_shape) : 0;
@@ -881,7 +919,8 @@ inline flatbuffers::Offset<TransposeConvAttribute> CreateTransposeConvAttributeD
       stride__,
       output_shape__,
       input_zp,
-      weight_zp);
+      weight_zp,
+      accum_dtype);
 }
 
 struct PadAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
@@ -1772,7 +1811,8 @@ struct MatMulAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
   typedef MatMulAttributeBuilder Builder;
   enum FlatBuffersVTableOffset FLATBUFFERS_VTABLE_UNDERLYING_TYPE {
     VT_A_ZP = 4,
-    VT_B_ZP = 6
+    VT_B_ZP = 6,
+    VT_ACCUM_DTYPE = 8
   };
   int32_t a_zp() const {
     return GetField<int32_t>(VT_A_ZP, 0);
@@ -1780,10 +1820,14 @@ struct MatMulAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Table {
   int32_t b_zp() const {
     return GetField<int32_t>(VT_B_ZP, 0);
   }
+  tosa::DType accum_dtype() const {
+    return static_cast<tosa::DType>(GetField<uint32_t>(VT_ACCUM_DTYPE, 0));
+  }
   bool Verify(flatbuffers::Verifier &verifier) const {
     return VerifyTableStart(verifier) &&
            VerifyField<int32_t>(verifier, VT_A_ZP, 4) &&
            VerifyField<int32_t>(verifier, VT_B_ZP, 4) &&
+           VerifyField<uint32_t>(verifier, VT_ACCUM_DTYPE, 4) &&
            verifier.EndTable();
   }
 };
@@ -1798,6 +1842,9 @@ struct MatMulAttributeBuilder {
   void add_b_zp(int32_t b_zp) {
     fbb_.AddElement<int32_t>(MatMulAttribute::VT_B_ZP, b_zp, 0);
   }
+  void add_accum_dtype(tosa::DType accum_dtype) {
+    fbb_.AddElement<uint32_t>(MatMulAttribute::VT_ACCUM_DTYPE, static_cast<uint32_t>(accum_dtype), 0);
+  }
   explicit MatMulAttributeBuilder(flatbuffers::FlatBufferBuilder &_fbb)
         : fbb_(_fbb) {
     start_ = fbb_.StartTable();
@@ -1812,8 +1859,10 @@ struct MatMulAttributeBuilder {
 inline flatbuffers::Offset<MatMulAttribute> CreateMatMulAttribute(
     flatbuffers::FlatBufferBuilder &_fbb,
     int32_t a_zp = 0,
-    int32_t b_zp = 0) {
+    int32_t b_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   MatMulAttributeBuilder builder_(_fbb);
+  builder_.add_accum_dtype(accum_dtype);
   builder_.add_b_zp(b_zp);
   builder_.add_a_zp(a_zp);
   return builder_.Finish();
@@ -1823,7 +1872,8 @@ struct FullyConnectedAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Ta
   typedef FullyConnectedAttributeBuilder Builder;
   enum FlatBuffersVTableOffset FLATBUFFERS_VTABLE_UNDERLYING_TYPE {
     VT_INPUT_ZP = 4,
-    VT_WEIGHT_ZP = 6
+    VT_WEIGHT_ZP = 6,
+    VT_ACCUM_DTYPE = 8
   };
   int32_t input_zp() const {
     return GetField<int32_t>(VT_INPUT_ZP, 0);
@@ -1831,10 +1881,14 @@ struct FullyConnectedAttribute FLATBUFFERS_FINAL_CLASS : private flatbuffers::Ta
   int32_t weight_zp() const {
     return GetField<int32_t>(VT_WEIGHT_ZP, 0);
   }
+  tosa::DType accum_dtype() const {
+    return static_cast<tosa::DType>(GetField<uint32_t>(VT_ACCUM_DTYPE, 0));
+  }
   bool Verify(flatbuffers::Verifier &verifier) const {
     return VerifyTableStart(verifier) &&
            VerifyField<int32_t>(verifier, VT_INPUT_ZP, 4) &&
            VerifyField<int32_t>(verifier, VT_WEIGHT_ZP, 4) &&
+           VerifyField<uint32_t>(verifier, VT_ACCUM_DTYPE, 4) &&
            verifier.EndTable();
   }
 };
@@ -1849,6 +1903,9 @@ struct FullyConnectedAttributeBuilder {
   void add_weight_zp(int32_t weight_zp) {
     fbb_.AddElement<int32_t>(FullyConnectedAttribute::VT_WEIGHT_ZP, weight_zp, 0);
   }
+  void add_accum_dtype(tosa::DType accum_dtype) {
+    fbb_.AddElement<uint32_t>(FullyConnectedAttribute::VT_ACCUM_DTYPE, static_cast<uint32_t>(accum_dtype), 0);
+  }
   explicit FullyConnectedAttributeBuilder(flatbuffers::FlatBufferBuilder &_fbb)
         : fbb_(_fbb) {
     start_ = fbb_.StartTable();
@@ -1863,8 +1920,10 @@ struct FullyConnectedAttributeBuilder {
 inline flatbuffers::Offset<FullyConnectedAttribute> CreateFullyConnectedAttribute(
     flatbuffers::FlatBufferBuilder &_fbb,
     int32_t input_zp = 0,
-    int32_t weight_zp = 0) {
+    int32_t weight_zp = 0,
+    tosa::DType accum_dtype = tosa::DType_UNKNOWN) {
   FullyConnectedAttributeBuilder builder_(_fbb);
+  builder_.add_accum_dtype(accum_dtype);
   builder_.add_weight_zp(weight_zp);
   builder_.add_input_zp(input_zp);
   return builder_.Finish();
diff --git a/include/tosa_serialization_handler.h b/include/tosa_serialization_handler.h
index 2a992b2..462c7ef 100644
--- a/include/tosa_serialization_handler.h
+++ b/include/tosa_serialization_handler.h
@@ -294,6 +294,7 @@ public:
     tosa_err_t LoadFileSchema(const char* schema_filename);
 
     // data format conversion. little-endian.
+    static tosa_err_t ConvertF16toU8(const std::vector<float>& in, std::vector<uint8_t>& out);
     static tosa_err_t ConvertF32toU8(const std::vector<float>& in, std::vector<uint8_t>& out);
     static tosa_err_t ConvertI48toU8(const std::vector<int64_t>& in, std::vector<uint8_t>& out);
     static tosa_err_t ConvertI32toU8(const std::vector<int32_t>& in, std::vector<uint8_t>& out);
@@ -302,6 +303,7 @@ public:
     static tosa_err_t ConvertI4toU8(const std::vector<int8_t>& in, std::vector<uint8_t>& out);
     static tosa_err_t ConvertBooltoU8(const std::vector<bool>& in, std::vector<uint8_t>& out);
 
+    static tosa_err_t ConvertU8toF16(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<float>& out);
     static tosa_err_t ConvertU8toF32(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<float>& out);
     static tosa_err_t ConvertU8toI48(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<int64_t>& out);
     static tosa_err_t ConvertU8toI32(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<int32_t>& out);
diff --git a/python/serializer/tosa_serializer.py b/python/serializer/tosa_serializer.py
index acec4b7..fb89563 100644
--- a/python/serializer/tosa_serializer.py
+++ b/python/serializer/tosa_serializer.py
@@ -58,6 +58,7 @@ DTypeNames = [
     "INT48",
     "FLOAT",
     "UINT16",
+    "FP16",
 ]
 
 ByteMask = np.uint64(0xFF)
@@ -145,7 +146,15 @@ class TosaSerializerAttribute(TosaSerializerUnion):
     def __init__(self):
         super().__init__()
 
-    def PoolAttribute(self, kernel, stride, pad, input_zp, output_zp):
+    def PoolAttribute(
+        self,
+        kernel,
+        stride,
+        pad,
+        input_zp,
+        output_zp,
+        accum_dtype,
+    ):
         from tosa import PoolAttribute as a, Attribute
 
         self.utype = Attribute.Attribute().PoolAttribute
@@ -156,8 +165,9 @@ class TosaSerializerAttribute(TosaSerializerUnion):
         self.intvecs.append((a.AddStride, stride))
         self.ints.append((a.AddInputZp, input_zp))
         self.ints.append((a.AddOutputZp, output_zp))
+        self.ints.append((a.AddAccumDtype, accum_dtype))
 
-    def ConvAttribute(self, pad, stride, dilation, input_zp, weight_zp):
+    def ConvAttribute(self, pad, stride, dilation, input_zp, weight_zp, accum_dtype):
         from tosa import ConvAttribute as a, Attribute
 
         self.utype = Attribute.Attribute().ConvAttribute
@@ -168,8 +178,11 @@ class TosaSerializerAttribute(TosaSerializerUnion):
         self.intvecs.append((a.AddDilation, dilation))
         self.ints.append((a.AddInputZp, input_zp))
         self.ints.append((a.AddWeightZp, weight_zp))
+        self.ints.append((a.AddAccumDtype, accum_dtype))
 
-    def TransposeConvAttribute(self, outpad, stride, output_shape, input_zp, weight_zp):
+    def TransposeConvAttribute(
+        self, outpad, stride, output_shape, input_zp, weight_zp, accum_dtype
+    ):
         from tosa import TransposeConvAttribute as a, Attribute
 
         self.utype = Attribute.Attribute().TransposeConvAttribute
@@ -180,6 +193,7 @@ class TosaSerializerAttribute(TosaSerializerUnion):
         self.intvecs.append((a.AddOutputShape, output_shape))
         self.ints.append((a.AddInputZp, input_zp))
         self.ints.append((a.AddWeightZp, weight_zp))
+        self.ints.append((a.AddAccumDtype, accum_dtype))
 
     def PadAttribute(self, padding, pad_const_int, pad_const_fp):
         from tosa import PadAttribute as a, Attribute
@@ -316,7 +330,7 @@ class TosaSerializerAttribute(TosaSerializerUnion):
 
         self.intvecs.append((a.AddTable, table))
 
-    def MatMulAttribute(self, A_zp, B_zp):
+    def MatMulAttribute(self, A_zp, B_zp, accum_dtype):
         from tosa import MatMulAttribute as a, Attribute
 
         self.utype = Attribute.Attribute().MatMulAttribute
@@ -324,8 +338,9 @@ class TosaSerializerAttribute(TosaSerializerUnion):
 
         self.ints.append((a.AddAZp, A_zp))
         self.ints.append((a.AddBZp, B_zp))
+        self.ints.append((a.AddAccumDtype, accum_dtype))
 
-    def FullyConnectedAttribute(self, input_zp, weight_zp):
+    def FullyConnectedAttribute(self, input_zp, weight_zp, accum_dtype):
         from tosa import FullyConnectedAttribute as a, Attribute
 
         self.utype = Attribute.Attribute().FullyConnectedAttribute
@@ -333,6 +348,7 @@ class TosaSerializerAttribute(TosaSerializerUnion):
 
         self.ints.append((a.AddInputZp, input_zp))
         self.ints.append((a.AddWeightZp, weight_zp))
+        self.ints.append((a.AddAccumDtype, accum_dtype))
 
     def NegateAttribute(self, input1_zp, output_zp):
         from tosa import NegateAttribute as a, Attribute
@@ -364,6 +380,8 @@ class TosaSerializerTensor:
 
         if dtype == DType.FLOAT:
             fntype = np.float32
+        elif dtype == DType.FP16:
+            fntype = np.float16
         else:
             fntype = int
 
@@ -445,10 +463,18 @@ class TosaSerializerTensor:
                     b4 = (val_u64 >> np.uint64(32)) & ByteMask
                     b5 = (val_u64 >> np.uint64(40)) & ByteMask
                     u8_data.extend([b0, b1, b2, b3, b4, b5])
+            elif self.dtype == DType.FP16:
+                np_arr = np.array(self.data, dtype=np.float16)
+                u8_data.extend(np_arr.view(np.uint8))
             elif self.dtype == DType.FLOAT:
                 for val in self.data:
                     b = struct.pack("!f", val)
                     u8_data.extend([b[3], b[2], b[1], b[0]])
+            elif self.dtype == TosaDType.DType:
+                # Serialize DType enum data as uint8 bytes
+                for val in self.data:
+                    np_arr = np.array(self.data, dtype=np.uint32)
+                    u8_data.extend(np_arr.view(np.uint8))
             else:
                 raise Exception(
                     "unsupported data type {}".format(DTypeNames[self.dtype])
@@ -873,6 +899,7 @@ class TosaSerializer:
             )
             ConvAttribute.AddInputZp = ConvAttribute.ConvAttributeAddInputZp
             ConvAttribute.AddWeightZp = ConvAttribute.ConvAttributeAddWeightZp
+            ConvAttribute.AddAccumDtype = ConvAttribute.ConvAttributeAddAccumDtype
             ConvAttribute.End = ConvAttribute.ConvAttributeEnd
         from tosa import FullyConnectedAttribute
 
@@ -886,6 +913,9 @@ class TosaSerializer:
             FullyConnectedAttribute.AddWeightZp = (
                 FullyConnectedAttribute.FullyConnectedAttributeAddWeightZp
             )
+            FullyConnectedAttribute.AddAccumDtype = (
+                FullyConnectedAttribute.FullyConnectedAttributeAddAccumDtype
+            )
             FullyConnectedAttribute.End = (
                 FullyConnectedAttribute.FullyConnectedAttributeEnd
             )
@@ -895,6 +925,7 @@ class TosaSerializer:
             MatMulAttribute.Start = MatMulAttribute.MatMulAttributeStart
             MatMulAttribute.AddAZp = MatMulAttribute.MatMulAttributeAddAZp
             MatMulAttribute.AddBZp = MatMulAttribute.MatMulAttributeAddBZp
+            MatMulAttribute.AddAccumDtype = MatMulAttribute.MatMulAttributeAddAccumDtype
             MatMulAttribute.End = MatMulAttribute.MatMulAttributeEnd
         from tosa import PoolAttribute
 
@@ -910,6 +941,7 @@ class TosaSerializer:
             PoolAttribute.StartStrideVector = (
                 PoolAttribute.PoolAttributeStartStrideVector
             )
+            PoolAttribute.AddAccumDtype = PoolAttribute.PoolAttributeAddAccumDtype
             PoolAttribute.AddInputZp = PoolAttribute.PoolAttributeAddInputZp
             PoolAttribute.AddOutputZp = PoolAttribute.PoolAttributeAddOutputZp
             PoolAttribute.End = PoolAttribute.PoolAttributeEnd
@@ -944,6 +976,7 @@ class TosaSerializer:
             PoolAttribute.StartStrideVector = (
                 PoolAttribute.PoolAttributeStartStrideVector
             )
+            PoolAttribute.AddAccumDtype = PoolAttribute.PoolAttributeAddAccumDtype
             PoolAttribute.AddInputZp = PoolAttribute.PoolAttributeAddInputZp
             PoolAttribute.AddOutputZp = PoolAttribute.PoolAttributeAddOutputZp
             PoolAttribute.End = PoolAttribute.PoolAttributeEnd
@@ -1123,6 +1156,9 @@ class TosaSerializer:
             TransposeConvAttribute.AddWeightZp = (
                 TransposeConvAttribute.TransposeConvAttributeAddWeightZp
             )
+            TransposeConvAttribute.AddAccumDtype = (
+                TransposeConvAttribute.TransposeConvAttributeAddAccumDtype
+            )
             TransposeConvAttribute.End = (
                 TransposeConvAttribute.TransposeConvAttributeEnd
             )
diff --git a/python/tosa/ConvAttribute.py b/python/tosa/ConvAttribute.py
index fb22c7a..c06e8c7 100644
--- a/python/tosa/ConvAttribute.py
+++ b/python/tosa/ConvAttribute.py
@@ -123,7 +123,14 @@ class ConvAttribute(object):
             return self._tab.Get(flatbuffers.number_types.Int32Flags, o + self._tab.Pos)
         return 0
 
-def ConvAttributeStart(builder): builder.StartObject(5)
+    # ConvAttribute
+    def AccumDtype(self):
+        o = flatbuffers.number_types.UOffsetTFlags.py_type(self._tab.Offset(14))
+        if o != 0:
+            return self._tab.Get(flatbuffers.number_types.Uint32Flags, o + self._tab.Pos)
+        return 0
+
+def ConvAttributeStart(builder): builder.StartObject(6)
 def Start(builder):
     return ConvAttributeStart(builder)
 def ConvAttributeAddPad(builder, pad): builder.PrependUOffsetTRelativeSlot(0, flatbuffers.number_types.UOffsetTFlags.py_type(pad), 0)
@@ -150,6 +157,9 @@ def AddInputZp(builder, inputZp):
 def ConvAttributeAddWeightZp(builder, weightZp): builder.PrependInt32Slot(4, weightZp, 0)
 def AddWeightZp(builder, weightZp):
     return ConvAttributeAddWeightZp(builder, weightZp)
+def ConvAttributeAddAccumDtype(builder, accumDtype): builder.PrependUint32Slot(5, accumDtype, 0)
+def AddAccumDtype(builder, accumDtype):
+    return ConvAttributeAddAccumDtype(builder, accumDtype)
 def ConvAttributeEnd(builder): return builder.EndObject()
 def End(builder):
     return ConvAttributeEnd(builder)
\ No newline at end of file
diff --git a/python/tosa/DType.py b/python/tosa/DType.py
index e6b41ed..27d28c4 100644
--- a/python/tosa/DType.py
+++ b/python/tosa/DType.py
@@ -13,3 +13,4 @@ class DType(object):
     INT48 = 7
     FLOAT = 8
     UINT16 = 9
+    FP16 = 10
diff --git a/python/tosa/FullyConnectedAttribute.py b/python/tosa/FullyConnectedAttribute.py
index 892b0da..546ec60 100644
--- a/python/tosa/FullyConnectedAttribute.py
+++ b/python/tosa/FullyConnectedAttribute.py
@@ -42,7 +42,14 @@ class FullyConnectedAttribute(object):
             return self._tab.Get(flatbuffers.number_types.Int32Flags, o + self._tab.Pos)
         return 0
 
-def FullyConnectedAttributeStart(builder): builder.StartObject(2)
+    # FullyConnectedAttribute
+    def AccumDtype(self):
+        o = flatbuffers.number_types.UOffsetTFlags.py_type(self._tab.Offset(8))
+        if o != 0:
+            return self._tab.Get(flatbuffers.number_types.Uint32Flags, o + self._tab.Pos)
+        return 0
+
+def FullyConnectedAttributeStart(builder): builder.StartObject(3)
 def Start(builder):
     return FullyConnectedAttributeStart(builder)
 def FullyConnectedAttributeAddInputZp(builder, inputZp): builder.PrependInt32Slot(0, inputZp, 0)
@@ -51,6 +58,9 @@ def AddInputZp(builder, inputZp):
 def FullyConnectedAttributeAddWeightZp(builder, weightZp): builder.PrependInt32Slot(1, weightZp, 0)
 def AddWeightZp(builder, weightZp):
     return FullyConnectedAttributeAddWeightZp(builder, weightZp)
+def FullyConnectedAttributeAddAccumDtype(builder, accumDtype): builder.PrependUint32Slot(2, accumDtype, 0)
+def AddAccumDtype(builder, accumDtype):
+    return FullyConnectedAttributeAddAccumDtype(builder, accumDtype)
 def FullyConnectedAttributeEnd(builder): return builder.EndObject()
 def End(builder):
     return FullyConnectedAttributeEnd(builder)
\ No newline at end of file
diff --git a/python/tosa/MatMulAttribute.py b/python/tosa/MatMulAttribute.py
index b42ebfa..af6ba0b 100644
--- a/python/tosa/MatMulAttribute.py
+++ b/python/tosa/MatMulAttribute.py
@@ -42,7 +42,14 @@ class MatMulAttribute(object):
             return self._tab.Get(flatbuffers.number_types.Int32Flags, o + self._tab.Pos)
         return 0
 
-def MatMulAttributeStart(builder): builder.StartObject(2)
+    # MatMulAttribute
+    def AccumDtype(self):
+        o = flatbuffers.number_types.UOffsetTFlags.py_type(self._tab.Offset(8))
+        if o != 0:
+            return self._tab.Get(flatbuffers.number_types.Uint32Flags, o + self._tab.Pos)
+        return 0
+
+def MatMulAttributeStart(builder): builder.StartObject(3)
 def Start(builder):
     return MatMulAttributeStart(builder)
 def MatMulAttributeAddAZp(builder, aZp): builder.PrependInt32Slot(0, aZp, 0)
@@ -51,6 +58,9 @@ def AddAZp(builder, aZp):
 def MatMulAttributeAddBZp(builder, bZp): builder.PrependInt32Slot(1, bZp, 0)
 def AddBZp(builder, bZp):
     return MatMulAttributeAddBZp(builder, bZp)
+def MatMulAttributeAddAccumDtype(builder, accumDtype): builder.PrependUint32Slot(2, accumDtype, 0)
+def AddAccumDtype(builder, accumDtype):
+    return MatMulAttributeAddAccumDtype(builder, accumDtype)
 def MatMulAttributeEnd(builder): return builder.EndObject()
 def End(builder):
     return MatMulAttributeEnd(builder)
\ No newline at end of file
diff --git a/python/tosa/PoolAttribute.py b/python/tosa/PoolAttribute.py
index 8256a6d..4307114 100644
--- a/python/tosa/PoolAttribute.py
+++ b/python/tosa/PoolAttribute.py
@@ -123,7 +123,14 @@ class PoolAttribute(object):
             return self._tab.Get(flatbuffers.number_types.Int32Flags, o + self._tab.Pos)
         return 0
 
-def PoolAttributeStart(builder): builder.StartObject(5)
+    # PoolAttribute
+    def AccumDtype(self):
+        o = flatbuffers.number_types.UOffsetTFlags.py_type(self._tab.Offset(14))
+        if o != 0:
+            return self._tab.Get(flatbuffers.number_types.Uint32Flags, o + self._tab.Pos)
+        return 0
+
+def PoolAttributeStart(builder): builder.StartObject(6)
 def Start(builder):
     return PoolAttributeStart(builder)
 def PoolAttributeAddPad(builder, pad): builder.PrependUOffsetTRelativeSlot(0, flatbuffers.number_types.UOffsetTFlags.py_type(pad), 0)
@@ -150,6 +157,9 @@ def AddInputZp(builder, inputZp):
 def PoolAttributeAddOutputZp(builder, outputZp): builder.PrependInt32Slot(4, outputZp, 0)
 def AddOutputZp(builder, outputZp):
     return PoolAttributeAddOutputZp(builder, outputZp)
+def PoolAttributeAddAccumDtype(builder, accumDtype): builder.PrependUint32Slot(5, accumDtype, 0)
+def AddAccumDtype(builder, accumDtype):
+    return PoolAttributeAddAccumDtype(builder, accumDtype)
 def PoolAttributeEnd(builder): return builder.EndObject()
 def End(builder):
     return PoolAttributeEnd(builder)
\ No newline at end of file
diff --git a/python/tosa/TransposeConvAttribute.py b/python/tosa/TransposeConvAttribute.py
index a2824e2..1a6bbde 100644
--- a/python/tosa/TransposeConvAttribute.py
+++ b/python/tosa/TransposeConvAttribute.py
@@ -123,7 +123,14 @@ class TransposeConvAttribute(object):
             return self._tab.Get(flatbuffers.number_types.Int32Flags, o + self._tab.Pos)
         return 0
 
-def TransposeConvAttributeStart(builder): builder.StartObject(5)
+    # TransposeConvAttribute
+    def AccumDtype(self):
+        o = flatbuffers.number_types.UOffsetTFlags.py_type(self._tab.Offset(14))
+        if o != 0:
+            return self._tab.Get(flatbuffers.number_types.Uint32Flags, o + self._tab.Pos)
+        return 0
+
+def TransposeConvAttributeStart(builder): builder.StartObject(6)
 def Start(builder):
     return TransposeConvAttributeStart(builder)
 def TransposeConvAttributeAddOutPad(builder, outPad): builder.PrependUOffsetTRelativeSlot(0, flatbuffers.number_types.UOffsetTFlags.py_type(outPad), 0)
@@ -150,6 +157,9 @@ def AddInputZp(builder, inputZp):
 def TransposeConvAttributeAddWeightZp(builder, weightZp): builder.PrependInt32Slot(4, weightZp, 0)
 def AddWeightZp(builder, weightZp):
     return TransposeConvAttributeAddWeightZp(builder, weightZp)
+def TransposeConvAttributeAddAccumDtype(builder, accumDtype): builder.PrependUint32Slot(5, accumDtype, 0)
+def AddAccumDtype(builder, accumDtype):
+    return TransposeConvAttributeAddAccumDtype(builder, accumDtype)
 def TransposeConvAttributeEnd(builder): return builder.EndObject()
 def End(builder):
     return TransposeConvAttributeEnd(builder)
\ No newline at end of file
diff --git a/schema/tosa.fbs b/schema/tosa.fbs
index d6d0f22..b3ab991 100644
--- a/schema/tosa.fbs
+++ b/schema/tosa.fbs
@@ -31,6 +31,7 @@ enum DType:uint32 {
   INT48,
   FLOAT,
   UINT16,
+  FP16,
 }
 
 enum ResizeMode:uint32 {
@@ -168,6 +169,7 @@ table PoolAttribute {
   stride: [int32];
   input_zp: int32;
   output_zp: int32;
+  accum_dtype: DType;
 }
 
 table ConvAttribute {
@@ -176,6 +178,7 @@ table ConvAttribute {
   dilation: [int32];
   input_zp: int32;
   weight_zp: int32;
+  accum_dtype: DType;
 }
 
 table TransposeConvAttribute {
@@ -184,6 +187,7 @@ table TransposeConvAttribute {
   output_shape: [int32];
   input_zp: int32;
   weight_zp: int32;
+  accum_dtype: DType;
 }
 
 table PadAttribute {
@@ -262,11 +266,13 @@ table TableAttribute {
 table MatMulAttribute {
   a_zp: int32;
   b_zp: int32;
+  accum_dtype: DType;
 }
 
 table FullyConnectedAttribute {
   input_zp: int32;
   weight_zp: int32;
+  accum_dtype: DType;
 }
 
 table NegateAttribute {
diff --git a/src/numpy_utils.cpp b/src/numpy_utils.cpp
index 80c680f..c770d45 100644
--- a/src/numpy_utils.cpp
+++ b/src/numpy_utils.cpp
@@ -14,6 +14,7 @@
 //    limitations under the License.
 
 #include "numpy_utils.h"
+#include "half.hpp"
 
 // Magic NUMPY header
 static const char NUMPY_HEADER_STR[] = "\x93NUMPY\x1\x0\x76\x0{";
@@ -45,6 +46,13 @@ NumpyUtilities::NPError NumpyUtilities::readFromNpyFile(const char* filename, co
     return readFromNpyFileCommon(filename, dtype_str, sizeof(float), elems, databuf, false);
 }
 
+NumpyUtilities::NPError
+    NumpyUtilities::readFromNpyFile(const char* filename, const uint32_t elems, half_float::half* databuf)
+{
+    const char dtype_str[] = "'<f2'";
+    return readFromNpyFileCommon(filename, dtype_str, sizeof(half_float::half), elems, databuf, false);
+}
+
 NumpyUtilities::NPError NumpyUtilities::readFromNpyFileCommon(const char* filename,
                                                               const char* dtype_str,
                                                               const size_t elementsize,
@@ -307,6 +315,14 @@ NumpyUtilities::NPError
     return writeToNpyFileCommon(filename, dtype_str, sizeof(float), shape, databuf, false);
 }
 
+NumpyUtilities::NPError NumpyUtilities::writeToNpyFile(const char* filename,
+                                                       const std::vector<int32_t>& shape,
+                                                       const half_float::half* databuf)
+{
+    const char dtype_str[] = "'<f2'";
+    return writeToNpyFileCommon(filename, dtype_str, sizeof(half_float::half), shape, databuf, false);
+}
+
 NumpyUtilities::NPError NumpyUtilities::writeToNpyFileCommon(const char* filename,
                                                              const char* dtype_str,
                                                              const size_t elementsize,
diff --git a/src/tosa_serialization_handler.cpp b/src/tosa_serialization_handler.cpp
index 3a0ce43..170b313 100644
--- a/src/tosa_serialization_handler.cpp
+++ b/src/tosa_serialization_handler.cpp
@@ -14,6 +14,7 @@
 //    limitations under the License.
 
 #include "tosa_serialization_handler.h"
+#include "half.hpp"
 
 #include <iostream>
 using namespace tosa;
@@ -652,6 +653,7 @@ tosa_err_t TosaSerializationHandler::Serialize()
 #define DEF_ARGS_S_float(NAME, V) DEF_ARGS_S_DEFAULT(NAME, V)
 #define DEF_ARGS_S_bool(NAME, V) DEF_ARGS_S_DEFAULT(NAME, V)
 #define DEF_ARGS_S_ResizeMode(NAME, V) DEF_ARGS_S_DEFAULT(NAME, V)
+#define DEF_ARGS_S_DType(NAME, V) DEF_ARGS_S_DEFAULT(NAME, V)
 #define DEF_ARGS_S_string(NAME, V) DEF_ARGS_S_STR(NAME, V)
 
 #define DEF_ARGS_S(NAME, T, V) DEF_ARGS_S_##T(NAME, V)
@@ -692,6 +694,7 @@ tosa_err_t TosaSerializationHandler::Serialize()
 #undef DEF_ARGS_S_float
 #undef DEF_ARGS_S_bool
 #undef DEF_ARGS_S_ResizeMode
+#undef DEF_ARGS_S_DType
 #undef DEF_ARGS_S_string
 #undef DEF_ARGS_S_STR
 #undef DEF_ARGS_S_DEFAULT
@@ -746,6 +749,21 @@ void zero_pad(std::vector<uint8_t>& buf)
     }
 }
 
+tosa_err_t TosaSerializationHandler::ConvertF16toU8(const std::vector<float>& in, std::vector<uint8_t>& out)
+{
+    // Note: Converts fp32->fp16 before converting to uint8_t
+    out.clear();
+    for (auto val : in)
+    {
+        half_float::half val_f16 = half_float::half_cast<half_float::half, float>(val);
+        uint16_t* val_u16        = reinterpret_cast<uint16_t*>(&val_f16);
+        out.push_back(*val_u16 & 0xFF);
+        out.push_back((*val_u16 >> 8) & 0xFF);
+    }
+    zero_pad(out);
+    return TOSA_OK;
+}
+
 tosa_err_t TosaSerializationHandler::ConvertF32toU8(const std::vector<float>& in, std::vector<uint8_t>& out)
 {
     out.clear();
@@ -862,6 +880,32 @@ tosa_err_t TosaSerializationHandler::ConvertBooltoU8(const std::vector<bool>& in
 }
 
 tosa_err_t
+    TosaSerializationHandler::ConvertU8toF16(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<float>& out)
+{
+    // Note: fp16 values returned in fp32 type
+    out.clear();
+    if (in.size() < out_size * sizeof(int16_t))
+    {
+        printf("TosaSerializationHandler::ConvertU8toF16(): uint8 buffer size %ld must >= target size %ld\n", in.size(),
+               out_size * sizeof(int16_t));
+        return TOSA_USER_ERROR;
+    }
+
+    for (uint32_t i = 0; i < out_size; i++)
+    {
+        uint16_t f16_byte0 = in[i * sizeof(int16_t)];
+        uint16_t f16_byte1 = in[i * sizeof(int16_t) + 1];
+        uint16_t val_u16   = f16_byte0 + (f16_byte1 << 8);
+
+        // Reinterpret u16 byte as fp16 then convert to fp32
+        half_float::half val_f16 = *(half_float::half*)&val_u16;
+        float val_fp32           = half_float::half_cast<float, half_float::half>(val_f16);
+        out.push_back(val_fp32);
+    }
+    return TOSA_OK;
+}
+
+tosa_err_t
     TosaSerializationHandler::ConvertU8toF32(const std::vector<uint8_t>& in, uint32_t out_size, std::vector<float>& out)
 {
     out.clear();
diff --git a/third_party/half/ChangeLog.txt b/third_party/half/ChangeLog.txt
new file mode 100644
index 0000000..37f3dbf
--- /dev/null
+++ b/third_party/half/ChangeLog.txt
@@ -0,0 +1,213 @@
+Release Notes											{#changelog}

+=============

+

+2.2.0 release (2021-06-12):

+---------------------------

+

+- Added `rsqrt` function for inverse square root.

+- Improved performance of `pow` function.

+- Fixed bug that forgot to include `<immintrin.h>` for F16C intrinsics.

+

+

+2.1.0 release (2019-08-05):

+---------------------------

+

+- Added detection of IEEE floating-point exceptions to operators and functions.

+- Added configuration options for automatic exception handling.

+- Added functions for explicitly managing floating-point exception flags.

+- Improved accuracy of `pow` and `atan2` functions.

+

+

+2.0.0 release (2019-07-23):

+---------------------------

+

+- Made internal implementation independent from built-in floating point 

+  facilities for increased reliability and IEEE-conformance.

+- Changed default rounding mode to rounding to nearest.

+- Always round ties to even when rounding to nearest.

+- Extended `constexpr` support to comparison and classification functions.

+- Added support for F16C compiler intrinsics for conversions.

+- Enabled C++11 feature detection for Intel compilers.

+

+

+1.12.0 release (2017-03-06):

+----------------------------

+

+- Changed behaviour of `half_cast` to perform conversions to/from `double` 

+  and `long double` directly according to specified rounding mode, without an 

+  intermediate `float` conversion.

+- Added `noexcept` specifiers to constructors.

+- Fixed minor portability problem with `logb` and `ilogb`.

+- Tested for *VC++ 2015*.

+

+

+1.11.0 release (2013-11-16):

+----------------------------

+

+- Made tie-breaking behaviour in round to nearest configurable by 

+  `HALF_ROUND_TIES_TO_EVEN` macro.

+- Completed support for all C++11 mathematical functions even if single-

+  precision versions from `<cmath>` are unsupported.

+- Fixed inability to disable support for C++11 mathematical functions on 

+  *VC++ 2013*.

+

+

+1.10.0 release (2013-11-09):

+----------------------------

+

+- Made default rounding mode configurable by `HALF_ROUND_STYLE` macro.

+- Added support for non-IEEE single-precision implementations.

+- Added `HALF_ENABLE_CPP11_TYPE_TRAITS` preprocessor flag for checking 

+  support for C++11 type traits and TMP features.

+- Restricted `half_cast` to support built-in arithmetic types only.

+- Changed behaviour of `half_cast` to respect rounding mode when casting 

+  to/from integer types.

+

+

+1.9.2 release (2013-11-01):

+---------------------------

+

+- Tested for *gcc 4.8*.

+- Tested and fixed for *VC++ 2013*.

+- Removed unnecessary warnings in *MSVC*.

+

+

+1.9.1 release (2013-08-08):

+---------------------------

+

+- Fixed problems with older gcc and MSVC versions.

+- Small fix to non-C++11 implementations of `remainder` and `remquo`.

+

+

+1.9.0 release (2013-08-07):

+---------------------------

+

+- Changed behaviour of `nearbyint`, `rint`, `lrint` and `llrint` to use 

+  rounding mode of half-precision implementation (which is 

+  truncating/indeterminate) instead of single-precision rounding mode.

+- Added support for more C++11 mathematical functions even if single-

+  precision versions from `<cmath>` are unsupported, in particular 

+  `remainder`, `remquo` and `cbrt`.

+- Minor implementation changes.

+

+

+1.8.1 release (2013-01-22):

+---------------------------

+

+- Fixed bug resulting in multiple definitions of the `nanh` function due to 

+  a missing `inline` specification.

+

+

+1.8.0 release (2013-01-19):

+---------------------------

+

+- Added support for more C++11 mathematical functions even if single-

+  precision versions from `<cmath>` are unsupported, in particular 

+  exponential and logarithm functions, hyperbolic area functions and the 

+  hypotenuse function.

+- Made `fma` function use default implementation if single-precision version

+  from `<cmath>` is not faster and thus `FP_FAST_FMAH` to be defined always.

+- Fixed overload resolution issues when invoking certain mathematical 

+  functions by unqualified calls.

+

+

+1.7.0 release (2012-10-26):

+---------------------------

+

+- Added support for C++11 `noexcept` specifiers.

+- Changed C++11 `long long` to be supported on *VC++ 2003* and up.

+

+

+1.6.1 release (2012-09-13):

+---------------------------

+

+- Made `fma` and `fdim` functions available even if corresponding 

+  single-precision functions are not.

+

+

+1.6.0 release (2012-09-12):

+---------------------------

+

+- Added `HALF_ENABLE_CPP11_LONG_LONG` to control support for `long long` 

+  integers and corresponding mathematical functions.

+- Fixed C++98 compatibility on non-VC compilers.

+

+

+1.5.1 release (2012-08-17):

+---------------------------

+

+- Recorrected `std::numeric_limits::round_style` to always return 

+  `std::round_indeterminate`, due to overflow-handling deviating from 

+  correct round-toward-zero behaviour.

+

+

+1.5.0 release (2012-08-16):

+---------------------------

+

+- Added `half_cast` for explicitly casting between half and any type 

+  convertible to/from `float` and allowing the explicit specification of 

+  the rounding mode to use.

+

+

+1.4.0 release (2012-08-12):

+---------------------------

+

+- Added support for C++11 generalized constant expressions (`constexpr`).

+

+

+1.3.1 release (2012-08-11):

+---------------------------

+

+- Fixed requirement for `std::signbit` and `std::isnan` (even if C++11 

+  `<cmath>` functions disabled) on non-VC compilers.

+

+

+1.3.0 release (2012-08-10):

+---------------------------

+

+- Made requirement for `<cstdint>` and `static_assert` optional and thus 

+  made the library C++98-compatible.

+- Made support for C++11 features user-overridable through explicit 

+  definition of corresponding preprocessor symbols to either 0 or 1.

+- Renamed `HALF_ENABLE_HASH` to `HALF_ENABLE_CPP11_HASH` in correspondence 

+  with other C++11 preprocessor symbols.

+

+

+1.2.0 release (2012-08-07):

+---------------------------

+

+- Added proper preprocessor definitions for `HUGE_VALH` and `FP_FAST_FMAH` 

+  in correspondence with their single-precision counterparts from `<cmath>`.

+- Fixed internal preprocessor macros to be properly undefined after use.

+

+

+1.1.2 release (2012-08-07):

+---------------------------

+

+- Revised `std::numeric_limits::round_style` to return 

+  `std::round_toward_zero` if the `float` version also does and 

+  `std::round_indeterminate` otherwise.

+- Fixed `std::numeric_limits::round_error` to reflect worst-case round 

+  toward zero behaviour.

+

+

+1.1.1 release (2012-08-06):

+---------------------------

+

+- Fixed `std::numeric_limits::min` to return smallest positive normal 

+  number, instead of subnormal number.

+- Fixed `std::numeric_limits::round_style` to return 

+  `std::round_indeterminate` due to mixture of separately rounded 

+  single-precision arithmetics with truncating single-to-half conversions.

+

+

+1.1.0 release (2012-08-06):

+---------------------------

+

+- Added half-precision literals.

+

+

+1.0.0 release (2012-08-05):

+---------------------------

+

+- First release.

diff --git a/third_party/half/LICENSE.txt b/third_party/half/LICENSE.txt
new file mode 100644
index 0000000..45f55db
--- /dev/null
+++ b/third_party/half/LICENSE.txt
@@ -0,0 +1,21 @@
+The MIT License

+

+Copyright (c) 2012-2021 Christian Rau

+

+Permission is hereby granted, free of charge, to any person obtaining a copy

+of this software and associated documentation files (the "Software"), to deal

+in the Software without restriction, including without limitation the rights

+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

+copies of the Software, and to permit persons to whom the Software is

+furnished to do so, subject to the following conditions:

+

+The above copyright notice and this permission notice shall be included in

+all copies or substantial portions of the Software.

+

+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN

+THE SOFTWARE.

diff --git a/third_party/half/README.txt b/third_party/half/README.txt
new file mode 100644
index 0000000..3dd0d1c
--- /dev/null
+++ b/third_party/half/README.txt
@@ -0,0 +1,317 @@
+HALF-PRECISION FLOATING-POINT LIBRARY (Version 2.2.0)

+-----------------------------------------------------

+

+This is a C++ header-only library to provide an IEEE 754 conformant 16-bit 

+half-precision floating-point type along with corresponding arithmetic 

+operators, type conversions and common mathematical functions. It aims for both 

+efficiency and ease of use, trying to accurately mimic the behaviour of the 

+built-in floating-point types at the best performance possible.

+

+

+INSTALLATION AND REQUIREMENTS

+-----------------------------

+

+Conveniently, the library consists of just a single header file containing all 

+the functionality, which can be directly included by your projects, without the 

+neccessity to build anything or link to anything.

+

+Whereas this library is fully C++98-compatible, it can profit from certain 

+C++11 features. Support for those features is checked automatically at compile 

+(or rather preprocessing) time, but can be explicitly enabled or disabled by 

+predefining the corresponding preprocessor symbols to either 1 or 0 yourself 

+before including half.hpp. This is useful when the automatic detection fails 

+(for more exotic implementations) or when a feature should be explicitly 

+disabled:

+

+  - 'long long' integer type for mathematical functions returning 'long long' 

+    results (enabled for VC++ 2003 and icc 11.1 and newer, gcc and clang, 

+    overridable with 'HALF_ENABLE_CPP11_LONG_LONG').

+

+  - Static assertions for extended compile-time checks (enabled for VC++ 2010, 

+    gcc 4.3, clang 2.9, icc 11.1 and newer, overridable with 

+    'HALF_ENABLE_CPP11_STATIC_ASSERT').

+

+  - Generalized constant expressions (enabled for VC++ 2015, gcc 4.6, clang 3.1, 

+    icc 14.0 and newer, overridable with 'HALF_ENABLE_CPP11_CONSTEXPR').

+

+  - noexcept exception specifications (enabled for VC++ 2015, gcc 4.6, 

+    clang 3.0, icc 14.0 and newer, overridable with 'HALF_ENABLE_CPP11_NOEXCEPT').

+

+  - User-defined literals for half-precision literals to work (enabled for 

+    VC++ 2015, gcc 4.7, clang 3.1, icc 15.0 and newer, overridable with 

+    'HALF_ENABLE_CPP11_USER_LITERALS').

+

+  - Thread-local storage for per-thread floating-point exception flags (enabled 

+    for VC++ 2015, gcc 4.8, clang 3.3, icc 15.0 and newer, overridable with 

+    'HALF_ENABLE_CPP11_THREAD_LOCAL').

+

+  - Type traits and template meta-programming features from <type_traits> 

+    (enabled for VC++ 2010, libstdc++ 4.3, libc++ and newer, overridable with 

+    'HALF_ENABLE_CPP11_TYPE_TRAITS').

+

+  - Special integer types from <cstdint> (enabled for VC++ 2010, libstdc++ 4.3, 

+    libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CSTDINT').

+

+  - Certain C++11 single-precision mathematical functions from <cmath> for 

+    floating-point classification during conversions from higher precision types 

+    (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with 

+    'HALF_ENABLE_CPP11_CMATH').

+

+  - Floating-point environment control from <cfenv> for possible exception 

+    propagation to the built-in floating-point platform (enabled for VC++ 2013, 

+    libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CFENV').

+

+  - Hash functor 'std::hash' from <functional> (enabled for VC++ 2010, 

+    libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_HASH').

+

+The library has been tested successfully with Visual C++ 2005-2015, gcc 4-8 

+and clang 3-8 on 32- and 64-bit x86 systems. Please contact me if you have any 

+problems, suggestions or even just success testing it on other platforms.

+

+

+DOCUMENTATION

+-------------

+

+What follows are some general words about the usage of the library and its 

+implementation. For a complete documentation of its interface consult the 

+corresponding website http://half.sourceforge.net. You may also generate the 

+complete developer documentation from the library's only include file's doxygen 

+comments, but this is more relevant to developers rather than mere users.

+

+BASIC USAGE

+

+To make use of the library just include its only header file half.hpp, which 

+defines all half-precision functionality inside the 'half_float' namespace. The 

+actual 16-bit half-precision data type is represented by the 'half' type, which 

+uses the standard IEEE representation with 1 sign bit, 5 exponent bits and 11 

+mantissa bits (including the hidden bit) and supports all types of special 

+values, like subnormal values, infinity and NaNs. This type behaves like the 

+built-in floating-point types as much as possible, supporting the usual 

+arithmetic, comparison and streaming operators, which makes its use pretty 

+straight-forward:

+

+    using half_float::half;

+    half a(3.4), b(5);

+    half c = a * b;

+    c += 3;

+    if(c > a)

+        std::cout << c << std::endl;

+

+Additionally the 'half_float' namespace also defines half-precision versions 

+for all mathematical functions of the C++ standard library, which can be used 

+directly through ADL:

+

+    half a(-3.14159);

+    half s = sin(abs(a));

+    long l = lround(s);

+

+You may also specify explicit half-precision literals, since the library 

+provides a user-defined literal inside the 'half_float::literal' namespace, 

+which you just need to import (assuming support for C++11 user-defined literals):

+

+    using namespace half_float::literal;

+    half x = 1.0_h;

+

+Furthermore the library provides proper specializations for 

+'std::numeric_limits', defining various implementation properties, and 

+'std::hash' for hashing half-precision numbers (assuming support for C++11 

+'std::hash'). Similar to the corresponding preprocessor symbols from <cmath> 

+the library also defines the 'HUGE_VALH' constant and maybe the 'FP_FAST_FMAH' 

+symbol.

+

+CONVERSIONS AND ROUNDING

+

+The half is explicitly constructible/convertible from a single-precision float 

+argument. Thus it is also explicitly constructible/convertible from any type 

+implicitly convertible to float, but constructing it from types like double or 

+int will involve the usual warnings arising when implicitly converting those to 

+float because of the lost precision. On the one hand those warnings are 

+intentional, because converting those types to half neccessarily also reduces 

+precision. But on the other hand they are raised for explicit conversions from 

+those types, when the user knows what he is doing. So if those warnings keep 

+bugging you, then you won't get around first explicitly converting to float 

+before converting to half, or use the 'half_cast' described below. In addition 

+you can also directly assign float values to halfs.

+

+In contrast to the float-to-half conversion, which reduces precision, the 

+conversion from half to float (and thus to any other type implicitly 

+convertible from float) is implicit, because all values represetable with 

+half-precision are also representable with single-precision. This way the 

+half-to-float conversion behaves similar to the builtin float-to-double 

+conversion and all arithmetic expressions involving both half-precision and 

+single-precision arguments will be of single-precision type. This way you can 

+also directly use the mathematical functions of the C++ standard library, 

+though in this case you will invoke the single-precision versions which will 

+also return single-precision values, which is (even if maybe performing the 

+exact same computation, see below) not as conceptually clean when working in a 

+half-precision environment.

+

+The default rounding mode for conversions between half and more precise types 

+as well as for rounding results of arithmetic operations and mathematical 

+functions rounds to the nearest representable value. But by predefining the 

+'HALF_ROUND_STYLE' preprocessor symbol this default can be overridden with one 

+of the other standard rounding modes using their respective constants or the 

+equivalent values of 'std::float_round_style' (it can even be synchronized with 

+the built-in single-precision implementation by defining it to 

+'std::numeric_limits<float>::round_style'):

+

+  - 'std::round_indeterminate' (-1) for the fastest rounding.

+

+  - 'std::round_toward_zero' (0) for rounding toward zero.

+

+  - 'std::round_to_nearest' (1) for rounding to the nearest value (default).

+

+  - 'std::round_toward_infinity' (2) for rounding toward positive infinity.

+

+  - 'std::round_toward_neg_infinity' (3) for rounding toward negative infinity.

+

+In addition to changing the overall default rounding mode one can also use the 

+'half_cast'. This converts between half and any built-in arithmetic type using 

+a configurable rounding mode (or the default rounding mode if none is 

+specified). In addition to a configurable rounding mode, 'half_cast' has 

+another big difference to a mere 'static_cast': Any conversions are performed 

+directly using the given rounding mode, without any intermediate conversion 

+to/from 'float'. This is especially relevant for conversions to integer types, 

+which don't necessarily truncate anymore. But also for conversions from 

+'double' or 'long double' this may produce more precise results than a 

+pre-conversion to 'float' using the single-precision implementation's current 

+rounding mode would.

+

+    half a = half_cast<half>(4.2);

+    half b = half_cast<half,std::numeric_limits<float>::round_style>(4.2f);

+    assert( half_cast<int, std::round_to_nearest>( 0.7_h )     == 1 );

+    assert( half_cast<half,std::round_toward_zero>( 4097 )     == 4096.0_h );

+    assert( half_cast<half,std::round_toward_infinity>( 4097 ) == 4100.0_h );

+    assert( half_cast<half,std::round_toward_infinity>( std::numeric_limits<double>::min() ) > 0.0_h );

+

+ACCURACY AND PERFORMANCE

+

+From version 2.0 onward the library is implemented without employing the 

+underlying floating-point implementation of the system (except for conversions, 

+of course), providing an entirely self-contained half-precision implementation 

+with results independent from the system's existing single- or double-precision 

+implementation and its rounding behaviour.

+

+As to accuracy, many of the operators and functions provided by this library 

+are exact to rounding for all rounding modes, i.e. the error to the exact 

+result is at most 0.5 ULP (unit in the last place) for rounding to nearest and 

+less than 1 ULP for all other rounding modes. This holds for all the operations 

+required by the IEEE 754 standard and many more. Specifically the following 

+functions might exhibit a deviation from the correctly rounded exact result by 

+1 ULP for a select few input values: 'expm1', 'log1p', 'pow', 'atan2', 'erf', 

+'erfc', 'lgamma', 'tgamma' (for more details see the documentation of the 

+individual functions). All other functions and operators are always exact to 

+rounding or independent of the rounding mode altogether.

+

+The increased IEEE-conformance and cleanliness of this implementation comes 

+with a certain performance cost compared to doing computations and mathematical 

+functions in hardware-accelerated single-precision. On average and depending on 

+the platform, the arithemtic operators are about 75% as fast and the 

+mathematical functions about 33-50% as fast as performing the corresponding 

+operations in single-precision and converting between the inputs and outputs. 

+However, directly computing with half-precision values is a rather rare 

+use-case and usually using actual 'float' values for all computations and 

+temproraries and using 'half's only for storage is the recommended way. But 

+nevertheless the goal of this library was to provide a complete and 

+conceptually clean IEEE-confromant half-precision implementation and in the few 

+cases when you do need to compute directly in half-precision you do so for a 

+reason and want accurate results.

+

+If necessary, this internal implementation can be overridden by predefining the 

+'HALF_ARITHMETIC_TYPE' preprocessor symbol to one of the built-in 

+floating-point types ('float', 'double' or 'long double'), which will cause the 

+library to use this type for computing arithmetic operations and mathematical 

+functions (if available). However, due to using the platform's floating-point 

+implementation (and its rounding behaviour) internally, this might cause 

+results to deviate from the specified half-precision rounding mode. It will of 

+course also inhibit the automatic exception detection described below.

+

+The conversion operations between half-precision and single-precision types can 

+also make use of the F16C extension for x86 processors by using the 

+corresponding compiler intrinsics from <immintrin.h>. Support for this is 

+checked at compile-time by looking for the '__F16C__' macro which at least gcc 

+and clang define based on the target platform. It can also be enabled manually 

+by predefining the 'HALF_ENABLE_F16C_INTRINSICS' preprocessor symbol to 1, or 0 

+for explicitly disabling it. However, this will directly use the corresponding 

+intrinsics for conversion without checking if they are available at runtime 

+(possibly crashing if they are not), so make sure they are supported on the 

+target platform before enabling this.

+

+EXCEPTION HANDLING

+

+The half-precision implementation supports all 5 required floating-point 

+exceptions from the IEEE standard to indicate erroneous inputs or inexact 

+results during operations. These are represented by exception flags which 

+actually use the same values as the corresponding 'FE_...' flags defined in 

+C++11's <cfenv> header if supported, specifically:

+

+  - 'FE_INVALID' for invalid inputs to an operation.

+  - 'FE_DIVBYZERO' for finite inputs producing infinite results.

+  - 'FE_OVERFLOW' if a result is too large to represent finitely.

+  - 'FE_UNDERFLOW' for a subnormal or zero result after rounding.

+  - 'FE_INEXACT' if a result needed rounding to be representable.

+  - 'FE_ALL_EXCEPT' as a convenient OR of all possible exception flags.

+

+The internal exception flag state will start with all flags cleared and is 

+maintained per thread if C++11 thread-local storage is supported, otherwise it 

+will be maintained globally and will theoretically NOT be thread-safe (while 

+practically being as thread-safe as a simple integer variable can be). These 

+flags can be managed explicitly using the library's error handling functions, 

+which again try to mimic the built-in functions for handling floating-point 

+exceptions from <cfenv>. You can clear them with 'feclearexcept' (which is the 

+only way a flag can be cleared), test them with 'fetestexcept', explicitly 

+raise errors with 'feraiseexcept' and save and restore their state using 

+'fegetexceptflag' and 'fesetexceptflag'. You can also throw corresponding C++ 

+exceptions based on the current flag state using 'fethrowexcept'.

+

+However, any automatic exception detection and handling during half-precision 

+operations and functions is DISABLED by default, since it comes with a minor 

+performance overhead due to runtime checks, and reacting to IEEE floating-point 

+exceptions is rarely ever needed in application code. But the library fully 

+supports IEEE-conformant detection of floating-point exceptions and various 

+ways for handling them, which can be enabled by pre-defining the corresponding 

+preprocessor symbols to 1. They can be enabled individually or all at once and 

+they will be processed in the order they are listed here:

+

+  - 'HALF_ERRHANDLING_FLAGS' sets the internal exception flags described above 

+    whenever the corresponding exception occurs.

+  - 'HALF_ERRHANDLING_ERRNO' sets the value of 'errno' from <cerrno> similar to 

+    the behaviour of the built-in floating-point types when 'MATH_ERRNO' is used.

+  - 'HALF_ERRHANDLING_FENV' will propagate exceptions to the built-in 

+    floating-point implementation using 'std::feraiseexcept' if support for 

+    C++11 floating-point control is enabled. However, this does not synchronize 

+    exceptions: neither will clearing  propagate nor will it work in reverse.

+  - 'HALF_ERRHANDLING_THROW_...' can be defined to a string literal which will 

+    be used as description message for a C++ exception that is thrown whenever 

+    a 'FE_...' exception occurs, similar to the behaviour of 'fethrowexcept'.

+

+If any of the above error handling is activated, non-quiet operations on 

+half-precision values will also raise a 'FE_INVALID' exception whenever 

+they encounter a signaling NaN value, in addition to transforming the value 

+into a quiet NaN. If error handling is disabled, signaling NaNs will be 

+treated like quiet NaNs (while still getting explicitly quieted if propagated 

+to the result). There can also be additional treatment of overflow and 

+underflow errors after they have been processed as above, which is ENABLED by 

+default (but of course only takes effect if any other exception handling is 

+activated) unless overridden by pre-defining the corresponding preprocessor 

+symbol to 0:

+

+  - 'HALF_ERRHANDLING_OVERFLOW_TO_INEXACT' will cause overflow errors to also 

+    raise a 'FE_INEXACT' exception.

+  - 'HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT' will cause underflow errors to also 

+    raise a 'FE_INEXACT' exception. This will also slightly change the 

+    behaviour of the underflow exception, which will ONLY be raised if the 

+    result is actually inexact due to underflow. If this is disabled, underflow 

+    exceptions will be raised for ANY (possibly exact) subnormal result.

+

+

+CREDITS AND CONTACT

+-------------------

+

+This library is developed by CHRISTIAN RAU and released under the MIT License 

+(see LICENSE.txt). If you have any questions or problems with it, feel free to 

+contact me at rauy@users.sourceforge.net.

+

+Additional credit goes to JEROEN VAN DER ZIJP for his paper on "Fast Half Float 

+Conversions", whose algorithms have been used in the library for converting 

+between half-precision and single-precision values.

diff --git a/third_party/half/include/half.hpp b/third_party/half/include/half.hpp
new file mode 100644
index 0000000..f4d8614
--- /dev/null
+++ b/third_party/half/include/half.hpp
@@ -0,0 +1,4601 @@
+// half - IEEE 754-based half-precision floating-point library.

+//

+// Copyright (c) 2012-2021 Christian Rau <rauy@users.sourceforge.net>

+//

+// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation 

+// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, 

+// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the 

+// Software is furnished to do so, subject to the following conditions:

+//

+// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

+//

+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE 

+// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR 

+// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

+// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

+

+// Version 2.2.0

+

+/// \file

+/// Main header file for half-precision functionality.

+

+#ifndef HALF_HALF_HPP

+#define HALF_HALF_HPP

+

+#define HALF_GCC_VERSION (__GNUC__*100+__GNUC_MINOR__)

+

+#if defined(__INTEL_COMPILER)

+	#define HALF_ICC_VERSION __INTEL_COMPILER

+#elif defined(__ICC)

+	#define HALF_ICC_VERSION __ICC

+#elif defined(__ICL)

+	#define HALF_ICC_VERSION __ICL

+#else

+	#define HALF_ICC_VERSION 0

+#endif

+

+// check C++11 language features

+#if defined(__clang__)										// clang

+	#if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)

+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1

+	#endif

+	#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)

+		#define HALF_ENABLE_CPP11_CONSTEXPR 1

+	#endif

+	#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)

+		#define HALF_ENABLE_CPP11_NOEXCEPT 1

+	#endif

+	#if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)

+		#define HALF_ENABLE_CPP11_USER_LITERALS 1

+	#endif

+	#if __has_feature(cxx_thread_local) && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)

+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1

+	#endif

+	#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)

+		#define HALF_ENABLE_CPP11_LONG_LONG 1

+	#endif

+#elif HALF_ICC_VERSION && defined(__INTEL_CXX11_MODE__)		// Intel C++

+	#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)

+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1

+	#endif

+	#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)

+		#define HALF_ENABLE_CPP11_USER_LITERALS 1

+	#endif

+	#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)

+		#define HALF_ENABLE_CPP11_CONSTEXPR 1

+	#endif

+	#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)

+		#define HALF_ENABLE_CPP11_NOEXCEPT 1

+	#endif

+	#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)

+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1

+	#endif

+	#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_LONG_LONG)

+		#define HALF_ENABLE_CPP11_LONG_LONG 1

+	#endif

+#elif defined(__GNUC__)										// gcc

+	#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L

+		#if HALF_GCC_VERSION >= 408 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)

+			#define HALF_ENABLE_CPP11_THREAD_LOCAL 1

+		#endif

+		#if HALF_GCC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)

+			#define HALF_ENABLE_CPP11_USER_LITERALS 1

+		#endif

+		#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)

+			#define HALF_ENABLE_CPP11_CONSTEXPR 1

+		#endif

+		#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)

+			#define HALF_ENABLE_CPP11_NOEXCEPT 1

+		#endif

+		#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)

+			#define HALF_ENABLE_CPP11_STATIC_ASSERT 1

+		#endif

+		#if !defined(HALF_ENABLE_CPP11_LONG_LONG)

+			#define HALF_ENABLE_CPP11_LONG_LONG 1

+		#endif

+	#endif

+	#define HALF_TWOS_COMPLEMENT_INT 1

+#elif defined(_MSC_VER)										// Visual C++

+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)

+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1

+	#endif

+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)

+		#define HALF_ENABLE_CPP11_USER_LITERALS 1

+	#endif

+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)

+		#define HALF_ENABLE_CPP11_CONSTEXPR 1

+	#endif

+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)

+		#define HALF_ENABLE_CPP11_NOEXCEPT 1

+	#endif

+	#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)

+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1

+	#endif

+	#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)

+		#define HALF_ENABLE_CPP11_LONG_LONG 1

+	#endif

+	#define HALF_TWOS_COMPLEMENT_INT 1

+	#define HALF_POP_WARNINGS 1

+	#pragma warning(push)

+	#pragma warning(disable : 4099 4127 4146)	//struct vs class, constant in if, negative unsigned

+#endif

+

+// check C++11 library features

+#include <utility>

+#if defined(_LIBCPP_VERSION)								// libc++

+	#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103

+		#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS

+			#define HALF_ENABLE_CPP11_TYPE_TRAITS 1

+		#endif

+		#ifndef HALF_ENABLE_CPP11_CSTDINT

+			#define HALF_ENABLE_CPP11_CSTDINT 1

+		#endif

+		#ifndef HALF_ENABLE_CPP11_CMATH

+			#define HALF_ENABLE_CPP11_CMATH 1

+		#endif

+		#ifndef HALF_ENABLE_CPP11_HASH

+			#define HALF_ENABLE_CPP11_HASH 1

+		#endif

+		#ifndef HALF_ENABLE_CPP11_CFENV

+			#define HALF_ENABLE_CPP11_CFENV 1

+		#endif

+	#endif

+#elif defined(__GLIBCXX__)									// libstdc++

+	#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103

+		#ifdef __clang__

+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)

+				#define HALF_ENABLE_CPP11_TYPE_TRAITS 1

+			#endif

+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)

+				#define HALF_ENABLE_CPP11_CSTDINT 1

+			#endif

+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)

+				#define HALF_ENABLE_CPP11_CMATH 1

+			#endif

+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)

+				#define HALF_ENABLE_CPP11_HASH 1

+			#endif

+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CFENV)

+				#define HALF_ENABLE_CPP11_CFENV 1

+			#endif

+		#else

+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)

+				#define HALF_ENABLE_CPP11_TYPE_TRAITS 1

+			#endif

+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)

+				#define HALF_ENABLE_CPP11_CSTDINT 1

+			#endif

+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)

+				#define HALF_ENABLE_CPP11_CMATH 1

+			#endif

+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)

+				#define HALF_ENABLE_CPP11_HASH 1

+			#endif

+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CFENV)

+				#define HALF_ENABLE_CPP11_CFENV 1

+			#endif

+		#endif

+	#endif

+#elif defined(_CPPLIB_VER)									// Dinkumware/Visual C++

+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)

+		#define HALF_ENABLE_CPP11_TYPE_TRAITS 1

+	#endif

+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_CSTDINT)

+			#define HALF_ENABLE_CPP11_CSTDINT 1

+	#endif

+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_HASH)

+		#define HALF_ENABLE_CPP11_HASH 1

+	#endif

+	#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CMATH)

+		#define HALF_ENABLE_CPP11_CMATH 1

+	#endif

+	#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CFENV)

+		#define HALF_ENABLE_CPP11_CFENV 1

+	#endif

+#endif

+#undef HALF_GCC_VERSION

+#undef HALF_ICC_VERSION

+

+// any error throwing C++ exceptions?

+#if defined(HALF_ERRHANDLING_THROW_INVALID) || defined(HALF_ERRHANDLING_THROW_DIVBYZERO) || defined(HALF_ERRHANDLING_THROW_OVERFLOW) || defined(HALF_ERRHANDLING_THROW_UNDERFLOW) || defined(HALF_ERRHANDLING_THROW_INEXACT)

+#define HALF_ERRHANDLING_THROWS 1

+#endif

+

+// any error handling enabled?

+#define HALF_ERRHANDLING	(HALF_ERRHANDLING_FLAGS||HALF_ERRHANDLING_ERRNO||HALF_ERRHANDLING_FENV||HALF_ERRHANDLING_THROWS)

+

+#if HALF_ERRHANDLING

+	#define HALF_UNUSED_NOERR(name) name

+#else

+	#define HALF_UNUSED_NOERR(name)

+#endif

+

+// support constexpr

+#if HALF_ENABLE_CPP11_CONSTEXPR

+	#define HALF_CONSTEXPR				constexpr

+	#define HALF_CONSTEXPR_CONST		constexpr

+	#if HALF_ERRHANDLING

+		#define HALF_CONSTEXPR_NOERR

+	#else

+		#define HALF_CONSTEXPR_NOERR	constexpr

+	#endif

+#else

+	#define HALF_CONSTEXPR

+	#define HALF_CONSTEXPR_CONST		const

+	#define HALF_CONSTEXPR_NOERR

+#endif

+

+// support noexcept

+#if HALF_ENABLE_CPP11_NOEXCEPT

+	#define HALF_NOEXCEPT	noexcept

+	#define HALF_NOTHROW	noexcept

+#else

+	#define HALF_NOEXCEPT

+	#define HALF_NOTHROW	throw()

+#endif

+

+// support thread storage

+#if HALF_ENABLE_CPP11_THREAD_LOCAL

+	#define HALF_THREAD_LOCAL	thread_local

+#else

+	#define HALF_THREAD_LOCAL	static

+#endif

+

+#include <utility>

+#include <algorithm>

+#include <istream>

+#include <ostream>

+#include <limits>

+#include <stdexcept>

+#include <climits>

+#include <cmath>

+#include <cstring>

+#include <cstdlib>

+#if HALF_ENABLE_CPP11_TYPE_TRAITS

+	#include <type_traits>

+#endif

+#if HALF_ENABLE_CPP11_CSTDINT

+	#include <cstdint>

+#endif

+#if HALF_ERRHANDLING_ERRNO

+	#include <cerrno>

+#endif

+#if HALF_ENABLE_CPP11_CFENV

+	#include <cfenv>

+#endif

+#if HALF_ENABLE_CPP11_HASH

+	#include <functional>

+#endif

+

+

+#ifndef HALF_ENABLE_F16C_INTRINSICS

+	/// Enable F16C intruction set intrinsics.

+	/// Defining this to 1 enables the use of [F16C compiler intrinsics](https://en.wikipedia.org/wiki/F16C) for converting between 

+	/// half-precision and single-precision values which may result in improved performance. This will not perform additional checks 

+	/// for support of the F16C instruction set, so an appropriate target platform is required when enabling this feature.

+	///

+	/// Unless predefined it will be enabled automatically when the `__F16C__` symbol is defined, which some compilers do on supporting platforms.

+	#define HALF_ENABLE_F16C_INTRINSICS __F16C__

+#endif

+#if HALF_ENABLE_F16C_INTRINSICS

+	#include <immintrin.h>

+#endif

+

+#ifdef HALF_DOXYGEN_ONLY

+/// Type for internal floating-point computations.

+/// This can be predefined to a built-in floating-point type (`float`, `double` or `long double`) to override the internal 

+/// half-precision implementation to use this type for computing arithmetic operations and mathematical function (if available). 

+/// This can result in improved performance for arithmetic operators and mathematical functions but might cause results to 

+/// deviate from the specified half-precision rounding mode and inhibits proper detection of half-precision exceptions.

+#define HALF_ARITHMETIC_TYPE (undefined)

+

+/// Enable internal exception flags.

+/// Defining this to 1 causes operations on half-precision values to raise internal floating-point exception flags according to 

+/// the IEEE 754 standard. These can then be cleared and checked with clearexcept(), testexcept().

+#define HALF_ERRHANDLING_FLAGS	0

+

+/// Enable exception propagation to `errno`.

+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to 

+/// [errno](https://en.cppreference.com/w/cpp/error/errno) from `<cerrno>`. Specifically this will propagate domain errors as 

+/// [EDOM](https://en.cppreference.com/w/cpp/error/errno_macros) and pole, overflow and underflow errors as 

+/// [ERANGE](https://en.cppreference.com/w/cpp/error/errno_macros). Inexact errors won't be propagated.

+#define HALF_ERRHANDLING_ERRNO	0

+

+/// Enable exception propagation to built-in floating-point platform.

+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to the built-in 

+/// single- and double-precision implementation's exception flags using the 

+/// [C++11 floating-point environment control](https://en.cppreference.com/w/cpp/numeric/fenv) from `<cfenv>`. However, this 

+/// does not work in reverse and single- or double-precision exceptions will not raise the corresponding half-precision 

+/// exception flags, nor will explicitly clearing flags clear the corresponding built-in flags.

+#define HALF_ERRHANDLING_FENV	0

+

+/// Throw C++ exception on domain errors.

+/// Defining this to a string literal causes operations on half-precision values to throw a 

+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on domain errors.

+#define HALF_ERRHANDLING_THROW_INVALID		(undefined)

+

+/// Throw C++ exception on pole errors.

+/// Defining this to a string literal causes operations on half-precision values to throw a 

+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on pole errors.

+#define HALF_ERRHANDLING_THROW_DIVBYZERO	(undefined)

+

+/// Throw C++ exception on overflow errors.

+/// Defining this to a string literal causes operations on half-precision values to throw a 

+/// [std::overflow_error](https://en.cppreference.com/w/cpp/error/overflow_error) with the specified message on overflows.

+#define HALF_ERRHANDLING_THROW_OVERFLOW		(undefined)

+

+/// Throw C++ exception on underflow errors.

+/// Defining this to a string literal causes operations on half-precision values to throw a 

+/// [std::underflow_error](https://en.cppreference.com/w/cpp/error/underflow_error) with the specified message on underflows.

+#define HALF_ERRHANDLING_THROW_UNDERFLOW	(undefined)

+

+/// Throw C++ exception on rounding errors.

+/// Defining this to 1 causes operations on half-precision values to throw a 

+/// [std::range_error](https://en.cppreference.com/w/cpp/error/range_error) with the specified message on general rounding errors.

+#define HALF_ERRHANDLING_THROW_INEXACT		(undefined)

+#endif

+

+#ifndef HALF_ERRHANDLING_OVERFLOW_TO_INEXACT

+/// Raise INEXACT exception on overflow.

+/// Defining this to 1 (default) causes overflow errors to automatically raise inexact exceptions in addition.

+/// These will be raised after any possible handling of the underflow exception.

+#define HALF_ERRHANDLING_OVERFLOW_TO_INEXACT	1

+#endif

+

+#ifndef HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT

+/// Raise INEXACT exception on underflow.

+/// Defining this to 1 (default) causes underflow errors to automatically raise inexact exceptions in addition.

+/// These will be raised after any possible handling of the underflow exception.

+///

+/// **Note:** This will actually cause underflow (and the accompanying inexact) exceptions to be raised *only* when the result 

+/// is inexact, while if disabled bare underflow errors will be raised for *any* (possibly exact) subnormal result.

+#define HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT	1

+#endif

+

+/// Default rounding mode.

+/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and more precise types 

+/// (unless using half_cast() and specifying the rounding mode directly) as well as in arithmetic operations and mathematical 

+/// functions. It can be redefined (before including half.hpp) to one of the standard rounding modes using their respective 

+/// constants or the equivalent values of 

+/// [std::float_round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/float_round_style):

+///

+/// `std::float_round_style`         | value | rounding

+/// ---------------------------------|-------|-------------------------

+/// `std::round_indeterminate`       | -1    | fastest

+/// `std::round_toward_zero`         | 0     | toward zero

+/// `std::round_to_nearest`          | 1     | to nearest (default)

+/// `std::round_toward_infinity`     | 2     | toward positive infinity

+/// `std::round_toward_neg_infinity` | 3     | toward negative infinity

+///

+/// By default this is set to `1` (`std::round_to_nearest`), which rounds results to the nearest representable value. It can even 

+/// be set to [std::numeric_limits<float>::round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/round_style) to synchronize 

+/// the rounding mode with that of the built-in single-precision implementation (which is likely `std::round_to_nearest`, though).

+#ifndef HALF_ROUND_STYLE

+	#define HALF_ROUND_STYLE	1		// = std::round_to_nearest

+#endif

+

+/// Value signaling overflow.

+/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to a positive value signaling the overflow of an 

+/// operation, in particular it just evaluates to positive infinity.

+///

+/// **See also:** Documentation for [HUGE_VAL](https://en.cppreference.com/w/cpp/numeric/math/HUGE_VAL)

+#define HUGE_VALH	std::numeric_limits<half_float::half>::infinity()

+

+/// Fast half-precision fma function.

+/// This symbol is defined if the fma() function generally executes as fast as, or faster than, a separate 

+/// half-precision multiplication followed by an addition, which is always the case.

+///

+/// **See also:** Documentation for [FP_FAST_FMA](https://en.cppreference.com/w/cpp/numeric/math/fma)

+#define FP_FAST_FMAH	1

+

+///	Half rounding mode.

+/// In correspondence with `FLT_ROUNDS` from `<cfloat>` this symbol expands to the rounding mode used for 

+/// half-precision operations. It is an alias for [HALF_ROUND_STYLE](\ref HALF_ROUND_STYLE).

+///

+/// **See also:** Documentation for [FLT_ROUNDS](https://en.cppreference.com/w/cpp/types/climits/FLT_ROUNDS)

+#define HLF_ROUNDS	HALF_ROUND_STYLE

+

+#ifndef FP_ILOGB0

+	#define FP_ILOGB0		INT_MIN

+#endif

+#ifndef FP_ILOGBNAN

+	#define FP_ILOGBNAN		INT_MAX

+#endif

+#ifndef FP_SUBNORMAL

+	#define FP_SUBNORMAL	0

+#endif

+#ifndef FP_ZERO

+	#define FP_ZERO			1

+#endif

+#ifndef FP_NAN

+	#define FP_NAN			2

+#endif

+#ifndef FP_INFINITE

+	#define FP_INFINITE		3

+#endif

+#ifndef FP_NORMAL

+	#define FP_NORMAL		4

+#endif

+

+#if !HALF_ENABLE_CPP11_CFENV && !defined(FE_ALL_EXCEPT)

+	#define FE_INVALID		0x10

+	#define FE_DIVBYZERO	0x08

+	#define FE_OVERFLOW		0x04

+	#define FE_UNDERFLOW	0x02

+	#define FE_INEXACT		0x01

+	#define FE_ALL_EXCEPT	(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT)

+#endif

+

+

+/// Main namespace for half-precision functionality.

+/// This namespace contains all the functionality provided by the library.

+namespace half_float

+{

+	class half;

+

+#if HALF_ENABLE_CPP11_USER_LITERALS

+	/// Library-defined half-precision literals.

+	/// Import this namespace to enable half-precision floating-point literals:

+	/// ~~~~{.cpp}

+	/// using namespace half_float::literal;

+	/// half_float::half = 4.2_h;

+	/// ~~~~

+	namespace literal

+	{

+		half operator "" _h(long double);

+	}

+#endif

+

+	/// \internal

+	/// \brief Implementation details.

+	namespace detail

+	{

+	#if HALF_ENABLE_CPP11_TYPE_TRAITS

+		/// Conditional type.

+		template<bool B,typename T,typename F> struct conditional : std::conditional<B,T,F> {};

+

+		/// Helper for tag dispatching.

+		template<bool B> struct bool_type : std::integral_constant<bool,B> {};

+		using std::true_type;

+		using std::false_type;

+

+		/// Type traits for floating-point types.

+		template<typename T> struct is_float : std::is_floating_point<T> {};

+	#else

+		/// Conditional type.

+		template<bool,typename T,typename> struct conditional { typedef T type; };

+		template<typename T,typename F> struct conditional<false,T,F> { typedef F type; };

+

+		/// Helper for tag dispatching.

+		template<bool> struct bool_type {};

+		typedef bool_type<true> true_type;

+		typedef bool_type<false> false_type;

+

+		/// Type traits for floating-point types.

+		template<typename> struct is_float : false_type {};

+		template<typename T> struct is_float<const T> : is_float<T> {};

+		template<typename T> struct is_float<volatile T> : is_float<T> {};

+		template<typename T> struct is_float<const volatile T> : is_float<T> {};

+		template<> struct is_float<float> : true_type {};

+		template<> struct is_float<double> : true_type {};

+		template<> struct is_float<long double> : true_type {};

+	#endif

+

+		/// Type traits for floating-point bits.

+		template<typename T> struct bits { typedef unsigned char type; };

+		template<typename T> struct bits<const T> : bits<T> {};

+		template<typename T> struct bits<volatile T> : bits<T> {};

+		template<typename T> struct bits<const volatile T> : bits<T> {};

+

+	#if HALF_ENABLE_CPP11_CSTDINT

+		/// Unsigned integer of (at least) 16 bits width.

+		typedef std::uint_least16_t uint16;

+

+		/// Fastest unsigned integer of (at least) 32 bits width.

+		typedef std::uint_fast32_t uint32;

+

+		/// Fastest signed integer of (at least) 32 bits width.

+		typedef std::int_fast32_t int32;

+

+		/// Unsigned integer of (at least) 32 bits width.

+		template<> struct bits<float> { typedef std::uint_least32_t type; };

+

+		/// Unsigned integer of (at least) 64 bits width.

+		template<> struct bits<double> { typedef std::uint_least64_t type; };

+	#else

+		/// Unsigned integer of (at least) 16 bits width.

+		typedef unsigned short uint16;

+

+		/// Fastest unsigned integer of (at least) 32 bits width.

+		typedef unsigned long uint32;

+

+		/// Fastest unsigned integer of (at least) 32 bits width.

+		typedef long int32;

+

+		/// Unsigned integer of (at least) 32 bits width.

+		template<> struct bits<float> : conditional<std::numeric_limits<unsigned int>::digits>=32,unsigned int,unsigned long> {};

+

+		#if HALF_ENABLE_CPP11_LONG_LONG

+			/// Unsigned integer of (at least) 64 bits width.

+			template<> struct bits<double> : conditional<std::numeric_limits<unsigned long>::digits>=64,unsigned long,unsigned long long> {};

+		#else

+			/// Unsigned integer of (at least) 64 bits width.

+			template<> struct bits<double> { typedef unsigned long type; };

+		#endif

+	#endif

+

+	#ifdef HALF_ARITHMETIC_TYPE

+		/// Type to use for arithmetic computations and mathematic functions internally.

+		typedef HALF_ARITHMETIC_TYPE internal_t;

+	#endif

+

+		/// Tag type for binary construction.

+		struct binary_t {};

+

+		/// Tag for binary construction.

+		HALF_CONSTEXPR_CONST binary_t binary = binary_t();

+

+		/// \name Implementation defined classification and arithmetic

+		/// \{

+

+		/// Check for infinity.

+		/// \tparam T argument type (builtin floating-point type)

+		/// \param arg value to query

+		/// \retval true if infinity

+		/// \retval false else

+		template<typename T> bool builtin_isinf(T arg)

+		{

+		#if HALF_ENABLE_CPP11_CMATH

+			return std::isinf(arg);

+		#elif defined(_MSC_VER)

+			return !::_finite(static_cast<double>(arg)) && !::_isnan(static_cast<double>(arg));

+		#else

+			return arg == std::numeric_limits<T>::infinity() || arg == -std::numeric_limits<T>::infinity();

+		#endif

+		}

+

+		/// Check for NaN.

+		/// \tparam T argument type (builtin floating-point type)

+		/// \param arg value to query

+		/// \retval true if not a number

+		/// \retval false else

+		template<typename T> bool builtin_isnan(T arg)

+		{

+		#if HALF_ENABLE_CPP11_CMATH

+			return std::isnan(arg);

+		#elif defined(_MSC_VER)

+			return ::_isnan(static_cast<double>(arg)) != 0;

+		#else

+			return arg != arg;

+		#endif

+		}

+

+		/// Check sign.

+		/// \tparam T argument type (builtin floating-point type)

+		/// \param arg value to query

+		/// \retval true if signbit set

+		/// \retval false else

+		template<typename T> bool builtin_signbit(T arg)

+		{

+		#if HALF_ENABLE_CPP11_CMATH

+			return std::signbit(arg);

+		#else

+			return arg < T() || (arg == T() && T(1)/arg < T());

+		#endif

+		}

+

+		/// Platform-independent sign mask.

+		/// \param arg integer value in two's complement

+		/// \retval -1 if \a arg negative

+		/// \retval 0 if \a arg positive

+		inline uint32 sign_mask(uint32 arg)

+		{

+			static const int N = std::numeric_limits<uint32>::digits - 1;

+		#if HALF_TWOS_COMPLEMENT_INT

+			return static_cast<int32>(arg) >> N;

+		#else

+			return -((arg>>N)&1);

+		#endif

+		}

+

+		/// Platform-independent arithmetic right shift.

+		/// \param arg integer value in two's complement

+		/// \param i shift amount (at most 31)

+		/// \return \a arg right shifted for \a i bits with possible sign extension

+		inline uint32 arithmetic_shift(uint32 arg, int i)

+		{

+		#if HALF_TWOS_COMPLEMENT_INT

+			return static_cast<int32>(arg) >> i;

+		#else

+			return static_cast<int32>(arg)/(static_cast<int32>(1)<<i) - ((arg>>(std::numeric_limits<uint32>::digits-1))&1);

+		#endif

+		}

+

+		/// \}

+		/// \name Error handling

+		/// \{

+

+		/// Internal exception flags.

+		/// \return reference to global exception flags

+		inline int& errflags() { HALF_THREAD_LOCAL int flags = 0; return flags; }

+

+		/// Raise floating-point exception.

+		/// \param flags exceptions to raise

+		/// \param cond condition to raise exceptions for

+		inline void raise(int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond) = true)

+		{

+		#if HALF_ERRHANDLING

+			if(!cond)

+				return;

+		#if HALF_ERRHANDLING_FLAGS

+			errflags() |= flags;

+		#endif

+		#if HALF_ERRHANDLING_ERRNO

+			if(flags & FE_INVALID)

+				errno = EDOM;

+			else if(flags & (FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW))

+				errno = ERANGE;

+		#endif

+		#if HALF_ERRHANDLING_FENV && HALF_ENABLE_CPP11_CFENV

+			std::feraiseexcept(flags);

+		#endif

+		#ifdef HALF_ERRHANDLING_THROW_INVALID

+			if(flags & FE_INVALID)

+				throw std::domain_error(HALF_ERRHANDLING_THROW_INVALID);

+		#endif

+		#ifdef HALF_ERRHANDLING_THROW_DIVBYZERO

+			if(flags & FE_DIVBYZERO)

+				throw std::domain_error(HALF_ERRHANDLING_THROW_DIVBYZERO);

+		#endif

+		#ifdef HALF_ERRHANDLING_THROW_OVERFLOW

+			if(flags & FE_OVERFLOW)

+				throw std::overflow_error(HALF_ERRHANDLING_THROW_OVERFLOW);

+		#endif

+		#ifdef HALF_ERRHANDLING_THROW_UNDERFLOW

+			if(flags & FE_UNDERFLOW)

+				throw std::underflow_error(HALF_ERRHANDLING_THROW_UNDERFLOW);

+		#endif

+		#ifdef HALF_ERRHANDLING_THROW_INEXACT

+			if(flags & FE_INEXACT)

+				throw std::range_error(HALF_ERRHANDLING_THROW_INEXACT);

+		#endif

+		#if HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT

+			if((flags & FE_UNDERFLOW) && !(flags & FE_INEXACT))

+				raise(FE_INEXACT);

+		#endif

+		#if HALF_ERRHANDLING_OVERFLOW_TO_INEXACT

+			if((flags & FE_OVERFLOW) && !(flags & FE_INEXACT))

+				raise(FE_INEXACT);

+		#endif

+		#endif

+		}

+

+		/// Check and signal for any NaN.

+		/// \param x first half-precision value to check

+		/// \param y second half-precision value to check

+		/// \retval true if either \a x or \a y is NaN

+		/// \retval false else

+		/// \exception FE_INVALID if \a x or \a y is NaN

+		inline HALF_CONSTEXPR_NOERR bool compsignal(unsigned int x, unsigned int y)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_INVALID, (x&0x7FFF)>0x7C00 || (y&0x7FFF)>0x7C00);

+		#endif

+			return (x&0x7FFF) > 0x7C00 || (y&0x7FFF) > 0x7C00;

+		}

+

+		/// Signal and silence signaling NaN.

+		/// \param nan half-precision NaN value

+		/// \return quiet NaN

+		/// \exception FE_INVALID if \a nan is signaling NaN

+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int nan)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_INVALID, !(nan&0x200));

+		#endif

+			return nan | 0x200;

+		}

+

+		/// Signal and silence signaling NaNs.

+		/// \param x first half-precision value to check

+		/// \param y second half-precision value to check

+		/// \return quiet NaN

+		/// \exception FE_INVALID if \a x or \a y is signaling NaN

+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)));

+		#endif

+			return ((x&0x7FFF)>0x7C00) ? (x|0x200) : (y|0x200);

+		}

+

+		/// Signal and silence signaling NaNs.

+		/// \param x first half-precision value to check

+		/// \param y second half-precision value to check

+		/// \param z third half-precision value to check

+		/// \return quiet NaN

+		/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN

+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y, unsigned int z)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)) || ((z&0x7FFF)>0x7C00 && !(z&0x200)));

+		#endif

+			return ((x&0x7FFF)>0x7C00) ? (x|0x200) : ((y&0x7FFF)>0x7C00) ? (y|0x200) : (z|0x200);

+		}

+

+		/// Select value or signaling NaN.

+		/// \param x preferred half-precision value

+		/// \param y ignored half-precision value except for signaling NaN

+		/// \return \a y if signaling NaN, \a x otherwise

+		/// \exception FE_INVALID if \a y is signaling NaN

+		inline HALF_CONSTEXPR_NOERR unsigned int select(unsigned int x, unsigned int HALF_UNUSED_NOERR(y))

+		{

+		#if HALF_ERRHANDLING

+			return (((y&0x7FFF)>0x7C00) && !(y&0x200)) ? signal(y) : x;

+		#else

+			return x;

+		#endif

+		}

+

+		/// Raise domain error and return NaN.

+		/// return quiet NaN

+		/// \exception FE_INVALID

+		inline HALF_CONSTEXPR_NOERR unsigned int invalid()

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_INVALID);

+		#endif

+			return 0x7FFF;

+		}

+

+		/// Raise pole error and return infinity.

+		/// \param sign half-precision value with sign bit only

+		/// \return half-precision infinity with sign of \a sign

+		/// \exception FE_DIVBYZERO

+		inline HALF_CONSTEXPR_NOERR unsigned int pole(unsigned int sign = 0)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_DIVBYZERO);

+		#endif

+			return sign | 0x7C00;

+		}

+

+		/// Check value for underflow.

+		/// \param arg non-zero half-precision value to check

+		/// \return \a arg

+		/// \exception FE_UNDERFLOW if arg is subnormal

+		inline HALF_CONSTEXPR_NOERR unsigned int check_underflow(unsigned int arg)

+		{

+		#if HALF_ERRHANDLING && !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT

+			raise(FE_UNDERFLOW, !(arg&0x7C00));

+		#endif

+			return arg;

+		}

+

+		/// \}

+		/// \name Conversion and rounding

+		/// \{

+

+		/// Half-precision overflow.

+		/// \tparam R rounding mode to use

+		/// \param sign half-precision value with sign bit only

+		/// \return rounded overflowing half-precision value

+		/// \exception FE_OVERFLOW

+		template<std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int overflow(unsigned int sign = 0)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_OVERFLOW);

+		#endif

+			return	(R==std::round_toward_infinity) ? (sign+0x7C00-(sign>>15)) :

+					(R==std::round_toward_neg_infinity) ? (sign+0x7BFF+(sign>>15)) :

+					(R==std::round_toward_zero) ? (sign|0x7BFF) :

+					(sign|0x7C00);

+		}

+

+		/// Half-precision underflow.

+		/// \tparam R rounding mode to use

+		/// \param sign half-precision value with sign bit only

+		/// \return rounded underflowing half-precision value

+		/// \exception FE_UNDERFLOW

+		template<std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int underflow(unsigned int sign = 0)

+		{

+		#if HALF_ERRHANDLING

+			raise(FE_UNDERFLOW);

+		#endif

+			return	(R==std::round_toward_infinity) ? (sign+1-(sign>>15)) :

+					(R==std::round_toward_neg_infinity) ? (sign+(sign>>15)) :

+					sign;

+		}

+

+		/// Round half-precision number.

+		/// \tparam R rounding mode to use

+		/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results

+		/// \param value finite half-precision number to round

+		/// \param g guard bit (most significant discarded bit)

+		/// \param s sticky bit (or of all but the most significant discarded bits)

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`

+		template<std::float_round_style R,bool I> HALF_CONSTEXPR_NOERR unsigned int rounded(unsigned int value, int g, int s)

+		{

+		#if HALF_ERRHANDLING

+			value +=	(R==std::round_to_nearest) ? (g&(s|value)) :

+						(R==std::round_toward_infinity) ? (~(value>>15)&(g|s)) :

+						(R==std::round_toward_neg_infinity) ? ((value>>15)&(g|s)) : 0;

+			if((value&0x7C00) == 0x7C00)

+				raise(FE_OVERFLOW);

+			else if(value & 0x7C00)

+				raise(FE_INEXACT, I || (g|s)!=0);

+			else

+				raise(FE_UNDERFLOW, !(HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT) || I || (g|s)!=0);

+			return value;

+		#else

+			return	(R==std::round_to_nearest) ? (value+(g&(s|value))) :

+					(R==std::round_toward_infinity) ? (value+(~(value>>15)&(g|s))) :

+					(R==std::round_toward_neg_infinity) ? (value+((value>>15)&(g|s))) :

+					value;

+		#endif

+		}

+

+		/// Round half-precision number to nearest integer value.

+		/// \tparam R rounding mode to use

+		/// \tparam E `true` for round to even, `false` for round away from zero

+		/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it

+		/// \param value half-precision value to round

+		/// \return half-precision bits for nearest integral value

+		/// \exception FE_INVALID for signaling NaN

+		/// \exception FE_INEXACT if value had to be rounded and \a I is `true`

+		template<std::float_round_style R,bool E,bool I> unsigned int integral(unsigned int value)

+		{

+			unsigned int abs = value & 0x7FFF;

+			if(abs < 0x3C00)

+			{

+				raise(FE_INEXACT, I);

+				return ((R==std::round_to_nearest) ? (0x3C00&-static_cast<unsigned>(abs>=(0x3800+E))) :

+						(R==std::round_toward_infinity) ? (0x3C00&-(~(value>>15)&(abs!=0))) :

+						(R==std::round_toward_neg_infinity) ? (0x3C00&-static_cast<unsigned>(value>0x8000)) :

+						0) | (value&0x8000);

+			}

+			if(abs >= 0x6400)

+				return (abs>0x7C00) ? signal(value) : value;

+			unsigned int exp = 25 - (abs>>10), mask = (1<<exp) - 1;

+			raise(FE_INEXACT, I && (value&mask));

+			return ((	(R==std::round_to_nearest) ? ((1<<(exp-1))-(~(value>>exp)&E)) :

+						(R==std::round_toward_infinity) ? (mask&((value>>15)-1)) :

+						(R==std::round_toward_neg_infinity) ? (mask&-(value>>15)) :

+						0) + value) & ~mask;

+		}

+

+		/// Convert fixed point to half-precision floating-point.

+		/// \tparam R rounding mode to use

+		/// \tparam F number of fractional bits in [11,31]

+		/// \tparam S `true` for signed, `false` for unsigned

+		/// \tparam N `true` for additional normalization step, `false` if already normalized to 1.F

+		/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results

+		/// \param m mantissa in Q1.F fixed point format

+		/// \param exp biased exponent - 1

+		/// \param sign half-precision value with sign bit only

+		/// \param s sticky bit (or of all but the most significant already discarded bits)

+		/// \return value converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`

+		template<std::float_round_style R,unsigned int F,bool S,bool N,bool I> unsigned int fixed2half(uint32 m, int exp = 14, unsigned int sign = 0, int s = 0)

+		{

+			if(S)

+			{

+				uint32 msign = sign_mask(m);

+				m = (m^msign) - msign;

+				sign = msign & 0x8000;

+			}

+			if(N)

+				for(; m<(static_cast<uint32>(1)<<F) && exp; m<<=1,--exp) ;

+			else if(exp < 0)

+				return rounded<R,I>(sign+(m>>(F-10-exp)), (m>>(F-11-exp))&1, s|((m&((static_cast<uint32>(1)<<(F-11-exp))-1))!=0));

+			return rounded<R,I>(sign+(exp<<10)+(m>>(F-10)), (m>>(F-11))&1, s|((m&((static_cast<uint32>(1)<<(F-11))-1))!=0));

+		}

+

+		/// Convert IEEE single-precision to half-precision.

+		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).

+		/// \tparam R rounding mode to use

+		/// \param value single-precision value to convert

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R> unsigned int float2half_impl(float value, true_type)

+		{

+		#if HALF_ENABLE_F16C_INTRINSICS

+			return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_set_ss(value),

+				(R==std::round_to_nearest) ? _MM_FROUND_TO_NEAREST_INT :

+				(R==std::round_toward_zero) ? _MM_FROUND_TO_ZERO :

+				(R==std::round_toward_infinity) ? _MM_FROUND_TO_POS_INF :

+				(R==std::round_toward_neg_infinity) ? _MM_FROUND_TO_NEG_INF :

+				_MM_FROUND_CUR_DIRECTION));

+		#else

+			bits<float>::type fbits;

+			std::memcpy(&fbits, &value, sizeof(float));

+		#if 1

+			unsigned int sign = (fbits>>16) & 0x8000;

+			fbits &= 0x7FFFFFFF;

+			if(fbits >= 0x7F800000)

+				return sign | 0x7C00 | ((fbits>0x7F800000) ? (0x200|((fbits>>13)&0x3FF)) : 0);

+			if(fbits >= 0x47800000)

+				return overflow<R>(sign);

+			if(fbits >= 0x38800000)

+				return rounded<R,false>(sign|(((fbits>>23)-112)<<10)|((fbits>>13)&0x3FF), (fbits>>12)&1, (fbits&0xFFF)!=0);

+			if(fbits >= 0x33000000)

+			{

+				int i = 125 - (fbits>>23);

+				fbits = (fbits&0x7FFFFF) | 0x800000;

+				return rounded<R,false>(sign|(fbits>>(i+1)), (fbits>>i)&1, (fbits&((static_cast<uint32>(1)<<i)-1))!=0);

+			}

+			if(fbits != 0)

+				return underflow<R>(sign);

+			return sign;

+		#else

+			static const uint16 base_table[512] = {

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 

+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, 

+				0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, 

+				0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 

+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7C00, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 

+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 

+				0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 

+				0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 

+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFC00 };

+			static const unsigned char shift_table[256] = {

+				24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 

+				25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 

+				25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 

+				25, 25, 25, 25, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 

+				13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 

+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 

+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 

+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };

+			int sexp = fbits >> 23, exp = sexp & 0xFF, i = shift_table[exp];

+			fbits &= 0x7FFFFF;

+			uint32 m = (fbits|((exp!=0)<<23)) & -static_cast<uint32>(exp!=0xFF);

+			return rounded<R,false>(base_table[sexp]+(fbits>>i), (m>>(i-1))&1, (((static_cast<uint32>(1)<<(i-1))-1)&m)!=0);

+		#endif

+		#endif

+		}

+

+		/// Convert IEEE double-precision to half-precision.

+		/// \tparam R rounding mode to use

+		/// \param value double-precision value to convert

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R> unsigned int float2half_impl(double value, true_type)

+		{

+		#if HALF_ENABLE_F16C_INTRINSICS

+			if(R == std::round_indeterminate)

+				return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_cvtpd_ps(_mm_set_sd(value)), _MM_FROUND_CUR_DIRECTION));

+		#endif

+			bits<double>::type dbits;

+			std::memcpy(&dbits, &value, sizeof(double));

+			uint32 hi = dbits >> 32, lo = dbits & 0xFFFFFFFF;

+			unsigned int sign = (hi>>16) & 0x8000;

+			hi &= 0x7FFFFFFF;

+			if(hi >= 0x7FF00000)

+				return sign | 0x7C00 | ((dbits&0xFFFFFFFFFFFFF) ? (0x200|((hi>>10)&0x3FF)) : 0);

+			if(hi >= 0x40F00000)

+				return overflow<R>(sign);

+			if(hi >= 0x3F100000)

+				return rounded<R,false>(sign|(((hi>>20)-1008)<<10)|((hi>>10)&0x3FF), (hi>>9)&1, ((hi&0x1FF)|lo)!=0);

+			if(hi >= 0x3E600000)

+			{

+				int i = 1018 - (hi>>20);

+				hi = (hi&0xFFFFF) | 0x100000;

+				return rounded<R,false>(sign|(hi>>(i+1)), (hi>>i)&1, ((hi&((static_cast<uint32>(1)<<i)-1))|lo)!=0);

+			}

+			if((hi|lo) != 0)

+				return underflow<R>(sign);

+			return sign;

+		}

+

+		/// Convert non-IEEE floating-point to half-precision.

+		/// \tparam R rounding mode to use

+		/// \tparam T source type (builtin floating-point type)

+		/// \param value floating-point value to convert

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R,typename T> unsigned int float2half_impl(T value, ...)

+		{

+			unsigned int hbits = static_cast<unsigned>(builtin_signbit(value)) << 15;

+			if(value == T())

+				return hbits;

+			if(builtin_isnan(value))

+				return hbits | 0x7FFF;

+			if(builtin_isinf(value))

+				return hbits | 0x7C00;

+			int exp;

+			std::frexp(value, &exp);

+			if(exp > 16)

+				return overflow<R>(hbits);

+			if(exp < -13)

+				value = std::ldexp(value, 25);

+			else

+			{

+				value = std::ldexp(value, 12-exp);

+				hbits |= ((exp+13)<<10);

+			}

+			T ival, frac = std::modf(value, &ival);

+			int m = std::abs(static_cast<int>(ival));

+			return rounded<R,false>(hbits+(m>>1), m&1, frac!=T());

+		}

+

+		/// Convert floating-point to half-precision.

+		/// \tparam R rounding mode to use

+		/// \tparam T source type (builtin floating-point type)

+		/// \param value floating-point value to convert

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R,typename T> unsigned int float2half(T value)

+		{

+			return float2half_impl<R>(value, bool_type<std::numeric_limits<T>::is_iec559&&sizeof(typename bits<T>::type)==sizeof(T)>());

+		}

+

+		/// Convert integer to half-precision floating-point.

+		/// \tparam R rounding mode to use

+		/// \tparam T type to convert (builtin integer type)

+		/// \param value integral value to convert

+		/// \return rounded half-precision value

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R,typename T> unsigned int int2half(T value)

+		{

+			unsigned int bits = static_cast<unsigned>(value<0) << 15;

+			if(!value)

+				return bits;

+			if(bits)

+				value = -value;

+			if(value > 0xFFFF)

+				return overflow<R>(bits);

+			unsigned int m = static_cast<unsigned int>(value), exp = 24;

+			for(; m<0x400; m<<=1,--exp) ;

+			for(; m>0x7FF; m>>=1,++exp) ;

+			bits |= (exp<<10) + m;

+			return (exp>24) ? rounded<R,false>(bits, (value>>(exp-25))&1, (((1<<(exp-25))-1)&value)!=0) : bits;

+		}

+

+		/// Convert half-precision to IEEE single-precision.

+		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).

+		/// \param value half-precision value to convert

+		/// \return single-precision value

+		inline float half2float_impl(unsigned int value, float, true_type)

+		{

+		#if HALF_ENABLE_F16C_INTRINSICS

+			return _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(value)));

+		#else

+		#if 0

+			bits<float>::type fbits = static_cast<bits<float>::type>(value&0x8000) << 16;

+			int abs = value & 0x7FFF;

+			if(abs)

+			{

+				fbits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);

+				for(; abs<0x400; abs<<=1,fbits-=0x800000) ;

+				fbits += static_cast<bits<float>::type>(abs) << 13;

+			}

+		#else

+			static const bits<float>::type mantissa_table[2048] = {

+				0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000, 

+				0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, 

+				0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 

+				0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 

+				0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, 

+				0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, 

+				0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, 

+				0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, 

+				0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 

+				0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, 

+				0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, 

+				0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, 

+				0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 

+				0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, 

+				0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000, 

+				0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 

+				0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 

+				0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, 

+				0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, 

+				0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, 

+				0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, 

+				0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 

+				0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, 

+				0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, 

+				0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, 

+				0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, 

+				0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, 

+				0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, 

+				0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, 

+				0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, 

+				0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 

+				0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, 

+				0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, 

+				0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 

+				0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, 

+				0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, 

+				0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, 

+				0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, 

+				0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, 

+				0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, 

+				0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, 

+				0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, 

+				0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, 

+				0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 

+				0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, 

+				0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000, 

+				0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000, 

+				0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, 

+				0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 

+				0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, 

+				0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, 

+				0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, 

+				0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, 

+				0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, 

+				0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, 

+				0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, 

+				0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, 

+				0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 

+				0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 

+				0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, 

+				0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000, 

+				0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, 

+				0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, 

+				0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, 

+				0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, 

+				0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, 

+				0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, 

+				0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, 

+				0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, 

+				0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, 

+				0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, 

+				0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, 

+				0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, 

+				0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, 

+				0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, 

+				0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 

+				0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, 

+				0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000, 

+				0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, 

+				0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, 

+				0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, 

+				0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000, 

+				0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, 

+				0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 

+				0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, 

+				0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 

+				0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, 

+				0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, 

+				0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 

+				0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 

+				0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, 

+				0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, 

+				0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 

+				0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 

+				0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, 

+				0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, 

+				0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, 

+				0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, 

+				0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 

+				0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, 

+				0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, 

+				0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, 

+				0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, 

+				0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 

+				0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, 

+				0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, 

+				0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 

+				0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 

+				0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, 

+				0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, 

+				0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 

+				0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, 

+				0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, 

+				0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 

+				0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, 

+				0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, 

+				0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, 

+				0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, 

+				0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, 

+				0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, 

+				0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 

+				0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 

+				0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, 

+				0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, 

+				0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 

+				0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, 

+				0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, 

+				0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };

+			static const bits<float>::type exponent_table[64] = {

+				0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000, 

+				0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000, 

+				0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, 

+				0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };

+			static const unsigned short offset_table[64] = {

+				0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 

+				0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };

+			bits<float>::type fbits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];

+		#endif

+			float out;

+			std::memcpy(&out, &fbits, sizeof(float));

+			return out;

+		#endif

+		}

+

+		/// Convert half-precision to IEEE double-precision.

+		/// \param value half-precision value to convert

+		/// \return double-precision value

+		inline double half2float_impl(unsigned int value, double, true_type)

+		{

+		#if HALF_ENABLE_F16C_INTRINSICS

+			return _mm_cvtsd_f64(_mm_cvtps_pd(_mm_cvtph_ps(_mm_cvtsi32_si128(value))));

+		#else

+			uint32 hi = static_cast<uint32>(value&0x8000) << 16;

+			unsigned int abs = value & 0x7FFF;

+			if(abs)

+			{

+				hi |= 0x3F000000 << static_cast<unsigned>(abs>=0x7C00);

+				for(; abs<0x400; abs<<=1,hi-=0x100000) ;

+				hi += static_cast<uint32>(abs) << 10;

+			}

+			bits<double>::type dbits = static_cast<bits<double>::type>(hi) << 32;

+			double out;

+			std::memcpy(&out, &dbits, sizeof(double));

+			return out;

+		#endif

+		}

+

+		/// Convert half-precision to non-IEEE floating-point.

+		/// \tparam T type to convert to (builtin integer type)

+		/// \param value half-precision value to convert

+		/// \return floating-point value

+		template<typename T> T half2float_impl(unsigned int value, T, ...)

+		{

+			T out;

+			unsigned int abs = value & 0x7FFF;

+			if(abs > 0x7C00)

+				out = (std::numeric_limits<T>::has_signaling_NaN && !(abs&0x200)) ? std::numeric_limits<T>::signaling_NaN() :

+					std::numeric_limits<T>::has_quiet_NaN ? std::numeric_limits<T>::quiet_NaN() : T();

+			else if(abs == 0x7C00)

+				out = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : std::numeric_limits<T>::max();

+			else if(abs > 0x3FF)

+				out = std::ldexp(static_cast<T>((abs&0x3FF)|0x400), (abs>>10)-25);

+			else

+				out = std::ldexp(static_cast<T>(abs), -24);

+			return (value&0x8000) ? -out : out;

+		}

+

+		/// Convert half-precision to floating-point.

+		/// \tparam T type to convert to (builtin integer type)

+		/// \param value half-precision value to convert

+		/// \return floating-point value

+		template<typename T> T half2float(unsigned int value)

+		{

+			return half2float_impl(value, T(), bool_type<std::numeric_limits<T>::is_iec559&&sizeof(typename bits<T>::type)==sizeof(T)>());

+		}

+

+		/// Convert half-precision floating-point to integer.

+		/// \tparam R rounding mode to use

+		/// \tparam E `true` for round to even, `false` for round away from zero

+		/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it

+		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)

+		/// \param value half-precision value to convert

+		/// \return rounded integer value

+		/// \exception FE_INVALID if value is not representable in type \a T

+		/// \exception FE_INEXACT if value had to be rounded and \a I is `true`

+		template<std::float_round_style R,bool E,bool I,typename T> T half2int(unsigned int value)

+		{

+			unsigned int abs = value & 0x7FFF;

+			if(abs >= 0x7C00)

+			{

+				raise(FE_INVALID);

+				return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();

+			}

+			if(abs < 0x3800)

+			{

+				raise(FE_INEXACT, I);

+				return	(R==std::round_toward_infinity) ? T(~(value>>15)&(abs!=0)) :

+						(R==std::round_toward_neg_infinity) ? -T(value>0x8000) :

+						T();

+			}

+			int exp = 25 - (abs>>10);

+			unsigned int m = (value&0x3FF) | 0x400;

+			int32 i = static_cast<int32>((exp<=0) ? (m<<-exp) : ((m+(

+				(R==std::round_to_nearest) ? ((1<<(exp-1))-(~(m>>exp)&E)) :

+				(R==std::round_toward_infinity) ? (((1<<exp)-1)&((value>>15)-1)) :

+				(R==std::round_toward_neg_infinity) ? (((1<<exp)-1)&-(value>>15)) : 0))>>exp));

+			if((!std::numeric_limits<T>::is_signed && (value&0x8000)) || (std::numeric_limits<T>::digits<16 &&

+				((value&0x8000) ? (-i<std::numeric_limits<T>::min()) : (i>std::numeric_limits<T>::max()))))

+				raise(FE_INVALID);

+			else if(I && exp > 0 && (m&((1<<exp)-1)))

+				raise(FE_INEXACT);

+			return static_cast<T>((value&0x8000) ? -i : i);

+		}

+

+		/// \}

+		/// \name Mathematics

+		/// \{

+

+		/// upper part of 64-bit multiplication.

+		/// \tparam R rounding mode to use

+		/// \param x first factor

+		/// \param y second factor

+		/// \return upper 32 bit of \a x * \a y

+		template<std::float_round_style R> uint32 mulhi(uint32 x, uint32 y)

+		{

+			uint32 xy = (x>>16) * (y&0xFFFF), yx = (x&0xFFFF) * (y>>16), c = (xy&0xFFFF) + (yx&0xFFFF) + (((x&0xFFFF)*(y&0xFFFF))>>16);

+			return (x>>16)*(y>>16) + (xy>>16) + (yx>>16) + (c>>16) +

+				((R==std::round_to_nearest) ? ((c>>15)&1) : (R==std::round_toward_infinity) ? ((c&0xFFFF)!=0) : 0);

+		}

+

+		/// 64-bit multiplication.

+		/// \param x first factor

+		/// \param y second factor

+		/// \return upper 32 bit of \a x * \a y rounded to nearest

+		inline uint32 multiply64(uint32 x, uint32 y)

+		{

+		#if HALF_ENABLE_CPP11_LONG_LONG

+			return static_cast<uint32>((static_cast<unsigned long long>(x)*static_cast<unsigned long long>(y)+0x80000000)>>32);

+		#else

+			return mulhi<std::round_to_nearest>(x, y);

+		#endif

+		}

+

+		/// 64-bit division.

+		/// \param x upper 32 bit of dividend

+		/// \param y divisor

+		/// \param s variable to store sticky bit for rounding

+		/// \return (\a x << 32) / \a y

+		inline uint32 divide64(uint32 x, uint32 y, int &s)

+		{

+		#if HALF_ENABLE_CPP11_LONG_LONG

+			unsigned long long xx = static_cast<unsigned long long>(x) << 32;

+			return s = (xx%y!=0), static_cast<uint32>(xx/y);

+		#else

+			y >>= 1;

+			uint32 rem = x, div = 0;

+			for(unsigned int i=0; i<32; ++i)

+			{

+				div <<= 1;

+				if(rem >= y)

+				{

+					rem -= y;

+					div |= 1;

+				}

+				rem <<= 1;

+			}

+			return s = rem > 1, div;

+		#endif

+		}

+

+		/// Half precision positive modulus.

+		/// \tparam Q `true` to compute full quotient, `false` else

+		/// \tparam R `true` to compute signed remainder, `false` for positive remainder

+		/// \param x first operand as positive finite half-precision value

+		/// \param y second operand as positive finite half-precision value

+		/// \param quo adress to store quotient at, `nullptr` if \a Q `false`

+		/// \return modulus of \a x / \a y

+		template<bool Q,bool R> unsigned int mod(unsigned int x, unsigned int y, int *quo = NULL)

+		{

+			unsigned int q = 0;

+			if(x > y)

+			{

+				int absx = x, absy = y, expx = 0, expy = 0;

+				for(; absx<0x400; absx<<=1,--expx) ;

+				for(; absy<0x400; absy<<=1,--expy) ;

+				expx += absx >> 10;

+				expy += absy >> 10;

+				int mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;

+				for(int d=expx-expy; d; --d)

+				{

+					if(!Q && mx == my)

+						return 0;

+					if(mx >= my)

+					{

+						mx -= my;

+						q += Q;

+					}

+					mx <<= 1;

+					q <<= static_cast<int>(Q);

+				}

+				if(!Q && mx == my)

+					return 0;

+				if(mx >= my)

+				{

+					mx -= my;

+					++q;

+				}

+				if(Q)

+				{

+					q &= (1<<(std::numeric_limits<int>::digits-1)) - 1;

+					if(!mx)

+						return *quo = q, 0;

+				}

+				for(; mx<0x400; mx<<=1,--expy) ;

+				x = (expy>0) ? ((expy<<10)|(mx&0x3FF)) : (mx>>(1-expy));

+			}

+			if(R)

+			{

+				unsigned int a, b;

+				if(y < 0x800)

+				{

+					a = (x<0x400) ? (x<<1) : (x+0x400);

+					b = y;

+				}

+				else

+				{

+					a = x;

+					b = y - 0x400;

+				}

+				if(a > b || (a == b && (q&1)))

+				{

+					int exp = (y>>10) + (y<=0x3FF), d = exp - (x>>10) - (x<=0x3FF);

+					int m = (((y&0x3FF)|((y>0x3FF)<<10))<<1) - (((x&0x3FF)|((x>0x3FF)<<10))<<(1-d));

+					for(; m<0x800 && exp>1; m<<=1,--exp) ;

+					x = 0x8000 + ((exp-1)<<10) + (m>>1);

+					q += Q;

+				}

+			}

+			if(Q)

+				*quo = q;

+			return x;

+		}

+

+		/// Fixed point square root.

+		/// \tparam F number of fractional bits

+		/// \param r radicand in Q1.F fixed point format

+		/// \param exp exponent

+		/// \return square root as Q1.F/2

+		template<unsigned int F> uint32 sqrt(uint32 &r, int &exp)

+		{

+			int i = exp & 1;

+			r <<= i;

+			exp = (exp-i) / 2;

+			uint32 m = 0;

+			for(uint32 bit=static_cast<uint32>(1)<<F; bit; bit>>=2)

+			{

+				if(r < m+bit)

+					m >>= 1;

+				else

+				{

+					r -= m + bit;

+					m = (m>>1) + bit;

+				}

+			}

+			return m;

+		}

+

+		/// Fixed point binary exponential.

+		/// This uses the BKM algorithm in E-mode.

+		/// \param m exponent in [0,1) as Q0.31

+		/// \param n number of iterations (at most 32)

+		/// \return 2 ^ \a m as Q1.31

+		inline uint32 exp2(uint32 m, unsigned int n = 32)

+		{

+			static const uint32 logs[] = {

+				0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,

+				0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,

+				0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,

+				0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };

+			if(!m)

+				return 0x80000000;

+			uint32 mx = 0x80000000, my = 0;

+			for(unsigned int i=1; i<n; ++i)

+			{

+				uint32 mz = my + logs[i];

+				if(mz <= m)

+				{

+					my = mz;

+					mx += mx >> i;

+				}

+			}

+			return mx;

+		}

+

+		/// Fixed point binary logarithm.

+		/// This uses the BKM algorithm in L-mode.

+		/// \param m mantissa in [1,2) as Q1.30

+		/// \param n number of iterations (at most 32)

+		/// \return log2(\a m) as Q0.31

+		inline uint32 log2(uint32 m, unsigned int n = 32)

+		{

+			static const uint32 logs[] = {

+				0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,

+				0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,

+				0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,

+				0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };

+			if(m == 0x40000000)

+				return 0;

+			uint32 mx = 0x40000000, my = 0;

+			for(unsigned int i=1; i<n; ++i)

+			{

+				uint32 mz = mx + (mx>>i);

+				if(mz <= m)

+				{

+					mx = mz;

+					my += logs[i];

+				}

+			}

+			return my;

+		}

+

+		/// Fixed point sine and cosine.

+		/// This uses the CORDIC algorithm in rotation mode.

+		/// \param mz angle in [-pi/2,pi/2] as Q1.30

+		/// \param n number of iterations (at most 31)

+		/// \return sine and cosine of \a mz as Q1.30

+		inline std::pair<uint32,uint32> sincos(uint32 mz, unsigned int n = 31)

+		{

+			static const uint32 angles[] = {

+				0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, 0x007FFF55,

+				0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000, 0x00008000,

+				0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,

+				0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };

+			uint32 mx = 0x26DD3B6A, my = 0;

+			for(unsigned int i=0; i<n; ++i)

+			{

+				uint32 sign = sign_mask(mz);

+				uint32 tx = mx - (arithmetic_shift(my, i)^sign) + sign;

+				uint32 ty = my + (arithmetic_shift(mx, i)^sign) - sign;

+				mx = tx; my = ty; mz -= (angles[i]^sign) - sign;

+			}

+			return std::make_pair(my, mx);

+		}

+

+		/// Fixed point arc tangent.

+		/// This uses the CORDIC algorithm in vectoring mode.

+		/// \param my y coordinate as Q0.30

+		/// \param mx x coordinate as Q0.30

+		/// \param n number of iterations (at most 31)

+		/// \return arc tangent of \a my / \a mx as Q1.30

+		inline uint32 atan2(uint32 my, uint32 mx, unsigned int n = 31)

+		{

+			static const uint32 angles[] = {

+				0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, 0x007FFF55,

+				0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000, 0x00008000,

+				0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,

+				0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };

+			uint32 mz = 0;

+			for(unsigned int i=0; i<n; ++i)

+			{

+				uint32 sign = sign_mask(my);

+				uint32 tx = mx + (arithmetic_shift(my, i)^sign) - sign;

+				uint32 ty = my - (arithmetic_shift(mx, i)^sign) + sign;

+				mx = tx; my = ty; mz += (angles[i]^sign) - sign;

+			}

+			return mz;

+		}

+

+		/// Reduce argument for trigonometric functions.

+		/// \param abs half-precision floating-point value

+		/// \param k value to take quarter period

+		/// \return \a abs reduced to [-pi/4,pi/4] as Q0.30

+		inline uint32 angle_arg(unsigned int abs, int &k)

+		{

+			uint32 m = (abs&0x3FF) | ((abs>0x3FF)<<10);

+			int exp = (abs>>10) + (abs<=0x3FF) - 15;

+			if(abs < 0x3A48)

+				return k = 0, m << (exp+20);

+		#if HALF_ENABLE_CPP11_LONG_LONG

+			unsigned long long y = m * 0xA2F9836E4E442, mask = (1ULL<<(62-exp)) - 1, yi = (y+(mask>>1)) & ~mask, f = y - yi;

+			uint32 sign = -static_cast<uint32>(f>>63);

+			k = static_cast<int>(yi>>(62-exp));

+			return (multiply64(static_cast<uint32>((sign ? -f : f)>>(31-exp)), 0xC90FDAA2)^sign) - sign;

+		#else

+			uint32 yh = m*0xA2F98 + mulhi<std::round_toward_zero>(m, 0x36E4E442), yl = (m*0x36E4E442) & 0xFFFFFFFF;

+			uint32 mask = (static_cast<uint32>(1)<<(30-exp)) - 1, yi = (yh+(mask>>1)) & ~mask, sign = -static_cast<uint32>(yi>yh);

+			k = static_cast<int>(yi>>(30-exp));

+			uint32 fh = (yh^sign) + (yi^~sign) - ~sign, fl = (yl^sign) - sign;

+			return (multiply64((exp>-1) ? (((fh<<(1+exp))&0xFFFFFFFF)|((fl&0xFFFFFFFF)>>(31-exp))) : fh, 0xC90FDAA2)^sign) - sign;

+		#endif

+		}

+

+		/// Get arguments for atan2 function.

+		/// \param abs half-precision floating-point value

+		/// \return \a abs and sqrt(1 - \a abs^2) as Q0.30

+		inline std::pair<uint32,uint32> atan2_args(unsigned int abs)

+		{

+			int exp = -15;

+			for(; abs<0x400; abs<<=1,--exp) ;

+			exp += abs >> 10;

+			uint32 my = ((abs&0x3FF)|0x400) << 5, r = my * my;

+			int rexp = 2 * exp;

+			r = 0x40000000 - ((rexp>-31) ? ((r>>-rexp)|((r&((static_cast<uint32>(1)<<-rexp)-1))!=0)) : 1);

+			for(rexp=0; r<0x40000000; r<<=1,--rexp) ;

+			uint32 mx = sqrt<30>(r, rexp);

+			int d = exp - rexp;

+			if(d < 0)

+				return std::make_pair((d<-14) ? ((my>>(-d-14))+((my>>(-d-15))&1)) : (my<<(14+d)), (mx<<14)+(r<<13)/mx);

+			if(d > 0)

+				return std::make_pair(my<<14, (d>14) ? ((mx>>(d-14))+((mx>>(d-15))&1)) : ((d==14) ? mx : ((mx<<(14-d))+(r<<(13-d))/mx)));

+			return std::make_pair(my<<13, (mx<<13)+(r<<12)/mx);

+		}

+

+		/// Get exponentials for hyperbolic computation

+		/// \param abs half-precision floating-point value

+		/// \param exp variable to take unbiased exponent of larger result

+		/// \param n number of BKM iterations (at most 32)

+		/// \return exp(abs) and exp(-\a abs) as Q1.31 with same exponent

+		inline std::pair<uint32,uint32> hyperbolic_args(unsigned int abs, int &exp, unsigned int n = 32)

+		{

+			uint32 mx = detail::multiply64(static_cast<uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29), my;

+			int e = (abs>>10) + (abs<=0x3FF);

+			if(e < 14)

+			{

+				exp = 0;

+				mx >>= 14 - e;

+			}

+			else

+			{

+				exp = mx >> (45-e);

+				mx = (mx<<(e-14)) & 0x7FFFFFFF;

+			}

+			mx = exp2(mx, n);

+			int d = exp << 1, s;

+			if(mx > 0x80000000)

+			{

+				my = divide64(0x80000000, mx, s);

+				my |= s;

+				++d;

+			}

+			else

+				my = mx;

+			return std::make_pair(mx, (d<31) ? ((my>>d)|((my&((static_cast<uint32>(1)<<d)-1))!=0)) : 1);

+		}

+

+		/// Postprocessing for binary exponential.

+		/// \tparam R rounding mode to use

+		/// \param m fractional part of as Q0.31

+		/// \param exp absolute value of unbiased exponent

+		/// \param esign sign of actual exponent

+		/// \param sign sign bit of result

+		/// \param n number of BKM iterations (at most 32)

+		/// \return value converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`

+		template<std::float_round_style R> unsigned int exp2_post(uint32 m, int exp, bool esign, unsigned int sign = 0, unsigned int n = 32)

+		{

+			if(esign)

+			{

+				exp = -exp - (m!=0);

+				if(exp < -25)

+					return underflow<R>(sign);

+				else if(exp == -25)

+					return rounded<R,false>(sign, 1, m!=0);

+			}

+			else if(exp > 15)

+				return overflow<R>(sign);

+			if(!m)

+				return sign | (((exp+=15)>0) ? (exp<<10) : check_underflow(0x200>>-exp));

+			m = exp2(m, n);

+			int s = 0;

+			if(esign)

+				m = divide64(0x80000000, m, s);

+			return fixed2half<R,31,false,false,true>(m, exp+14, sign, s);

+		}

+

+		/// Postprocessing for binary logarithm.

+		/// \tparam R rounding mode to use

+		/// \tparam L logarithm for base transformation as Q1.31

+		/// \param m fractional part of logarithm as Q0.31

+		/// \param ilog signed integer part of logarithm

+		/// \param exp biased exponent of result

+		/// \param sign sign bit of result

+		/// \return value base-transformed and converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if no other exception occurred

+		template<std::float_round_style R,uint32 L> unsigned int log2_post(uint32 m, int ilog, int exp, unsigned int sign = 0)

+		{

+			uint32 msign = sign_mask(ilog);

+			m = (((static_cast<uint32>(ilog)<<27)+(m>>4))^msign) - msign;

+			if(!m)

+				return 0;

+			for(; m<0x80000000; m<<=1,--exp) ;

+			int i = m >= L, s;

+			exp += i;

+			m >>= 1 + i;

+			sign ^= msign & 0x8000;

+			if(exp < -11)

+				return underflow<R>(sign);

+			m = divide64(m, L, s);

+			return fixed2half<R,30,false,false,true>(m, exp, sign, 1);

+		}

+

+		/// Hypotenuse square root and postprocessing.

+		/// \tparam R rounding mode to use

+		/// \param r mantissa as Q2.30

+		/// \param exp biased exponent

+		/// \return square root converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if value had to be rounded

+		template<std::float_round_style R> unsigned int hypot_post(uint32 r, int exp)

+		{

+			int i = r >> 31;

+			if((exp+=i) > 46)

+				return overflow<R>();

+			if(exp < -34)

+				return underflow<R>();

+			r = (r>>i) | (r&i);

+			uint32 m = sqrt<30>(r, exp+=15);

+			return fixed2half<R,15,false,false,false>(m, exp-1, 0, r!=0);

+		}

+

+		/// Division and postprocessing for tangents.

+		/// \tparam R rounding mode to use

+		/// \param my dividend as Q1.31

+		/// \param mx divisor as Q1.31

+		/// \param exp biased exponent of result

+		/// \param sign sign bit of result

+		/// \return quotient converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if no other exception occurred

+		template<std::float_round_style R> unsigned int tangent_post(uint32 my, uint32 mx, int exp, unsigned int sign = 0)

+		{

+			int i = my >= mx, s;

+			exp += i;

+			if(exp > 29)

+				return overflow<R>(sign);

+			if(exp < -11)

+				return underflow<R>(sign);

+			uint32 m = divide64(my>>(i+1), mx, s);

+			return fixed2half<R,30,false,false,true>(m, exp, sign, s);

+		}

+

+		/// Area function and postprocessing.

+		/// This computes the value directly in Q2.30 using the representation `asinh|acosh(x) = log(x+sqrt(x^2+|-1))`.

+		/// \tparam R rounding mode to use

+		/// \tparam S `true` for asinh, `false` for acosh

+		/// \param arg half-precision argument

+		/// \return asinh|acosh(\a arg) converted to half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if no other exception occurred

+		template<std::float_round_style R,bool S> unsigned int area(unsigned int arg)

+		{

+			int abs = arg & 0x7FFF, expx = (abs>>10) + (abs<=0x3FF) - 15, expy = -15, ilog, i;

+			uint32 mx = static_cast<uint32>((abs&0x3FF)|((abs>0x3FF)<<10)) << 20, my, r;

+			for(; abs<0x400; abs<<=1,--expy) ;

+			expy += abs >> 10;

+			r = ((abs&0x3FF)|0x400) << 5;

+			r *= r;

+			i = r >> 31;

+			expy = 2*expy + i;

+			r >>= i;

+			if(S)

+			{

+				if(expy < 0)

+				{

+					r = 0x40000000 + ((expy>-30) ? ((r>>-expy)|((r&((static_cast<uint32>(1)<<-expy)-1))!=0)) : 1);

+					expy = 0;

+				}

+				else

+				{

+					r += 0x40000000 >> expy;

+					i = r >> 31;

+					r = (r>>i) | (r&i);

+					expy += i;

+				}

+			}

+			else

+			{

+				r -= 0x40000000 >> expy;

+				for(; r<0x40000000; r<<=1,--expy) ;

+			}

+			my = sqrt<30>(r, expy);

+			my = (my<<15) + (r<<14)/my;

+			if(S)

+			{

+				mx >>= expy - expx;

+				ilog = expy;

+			}

+			else

+			{

+				my >>= expx - expy;

+				ilog = expx;

+			}

+			my += mx;

+			i = my >> 31;

+			static const int G = S && (R==std::round_to_nearest);

+			return log2_post<R,0xB8AA3B2A>(log2(my>>i, 26+S+G)+(G<<3), ilog+i, 17, arg&(static_cast<unsigned>(S)<<15));

+		}

+

+		/// Class for 1.31 unsigned floating-point computation

+		struct f31

+		{

+			/// Constructor.

+			/// \param mant mantissa as 1.31

+			/// \param e exponent

+			HALF_CONSTEXPR f31(uint32 mant, int e) : m(mant), exp(e) {}

+

+			/// Constructor.

+			/// \param abs unsigned half-precision value

+			f31(unsigned int abs) : exp(-15)

+			{

+				for(; abs<0x400; abs<<=1,--exp) ;

+				m = static_cast<uint32>((abs&0x3FF)|0x400) << 21;

+				exp += (abs>>10);

+			}

+

+			/// Addition operator.

+			/// \param a first operand

+			/// \param b second operand

+			/// \return \a a + \a b

+			friend f31 operator+(f31 a, f31 b)

+			{

+				if(b.exp > a.exp)

+					std::swap(a, b);

+				int d = a.exp - b.exp;

+				uint32 m = a.m + ((d<32) ? (b.m>>d) : 0);

+				int i = (m&0xFFFFFFFF) < a.m;

+				return f31(((m+i)>>i)|0x80000000, a.exp+i);

+			}

+

+			/// Subtraction operator.

+			/// \param a first operand

+			/// \param b second operand

+			/// \return \a a - \a b

+			friend f31 operator-(f31 a, f31 b)

+			{

+				int d = a.exp - b.exp, exp = a.exp;

+				uint32 m = a.m - ((d<32) ? (b.m>>d) : 0);

+				if(!m)

+					return f31(0, -32);

+				for(; m<0x80000000; m<<=1,--exp) ;

+				return f31(m, exp);

+			}

+

+			/// Multiplication operator.

+			/// \param a first operand

+			/// \param b second operand

+			/// \return \a a * \a b

+			friend f31 operator*(f31 a, f31 b)

+			{

+				uint32 m = multiply64(a.m, b.m);

+				int i = m >> 31;

+				return f31(m<<(1-i), a.exp + b.exp + i);

+			}

+

+			/// Division operator.

+			/// \param a first operand

+			/// \param b second operand

+			/// \return \a a / \a b

+			friend f31 operator/(f31 a, f31 b)

+			{

+				int i = a.m >= b.m, s;

+				uint32 m = divide64((a.m+i)>>i, b.m, s);

+				return f31(m, a.exp - b.exp + i - 1);

+			}

+

+			uint32 m;			///< mantissa as 1.31.

+			int exp;			///< exponent.

+		};

+

+		/// Error function and postprocessing.

+		/// This computes the value directly in Q1.31 using the approximations given 

+		/// [here](https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions).

+		/// \tparam R rounding mode to use

+		/// \tparam C `true` for comlementary error function, `false` else

+		/// \param arg half-precision function argument

+		/// \return approximated value of error function in half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if no other exception occurred

+		template<std::float_round_style R,bool C> unsigned int erf(unsigned int arg)

+		{

+			unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;

+			f31 x(abs), x2 = x * x * f31(0xB8AA3B29, 0), t = f31(0x80000000, 0) / (f31(0x80000000, 0)+f31(0xA7BA054A, -2)*x), t2 = t * t;

+			f31 e = ((f31(0x87DC2213, 0)*t2+f31(0xB5F0E2AE, 0))*t2+f31(0x82790637, -2)-(f31(0xBA00E2B8, 0)*t2+f31(0x91A98E62, -2))*t) * t /

+					((x2.exp<0) ? f31(exp2((x2.exp>-32) ? (x2.m>>-x2.exp) : 0, 30), 0) : f31(exp2((x2.m<<x2.exp)&0x7FFFFFFF, 22), x2.m>>(31-x2.exp)));

+			return (!C || sign) ? fixed2half<R,31,false,true,true>(0x80000000-(e.m>>(C-e.exp)), 14+C, sign&(C-1U)) :

+					(e.exp<-25) ? underflow<R>() : fixed2half<R,30,false,false,true>(e.m>>1, e.exp+14, 0, e.m&1);

+		}

+

+		/// Gamma function and postprocessing.

+		/// This approximates the value of either the gamma function or its logarithm directly in Q1.31.

+		/// \tparam R rounding mode to use

+		/// \tparam L `true` for lograithm of gamma function, `false` for gamma function

+		/// \param arg half-precision floating-point value

+		/// \return lgamma/tgamma(\a arg) in half-precision

+		/// \exception FE_OVERFLOW on overflows

+		/// \exception FE_UNDERFLOW on underflows

+		/// \exception FE_INEXACT if \a arg is not a positive integer

+		template<std::float_round_style R,bool L> unsigned int gamma(unsigned int arg)

+		{

+/*			static const double p[] ={ 2.50662827563479526904, 225.525584619175212544, -268.295973841304927459, 80.9030806934622512966, -5.00757863970517583837, 0.0114684895434781459556 };

+			double t = arg + 4.65, s = p[0];

+			for(unsigned int i=0; i<5; ++i)

+				s += p[i+1] / (arg+i);

+			return std::log(s) + (arg-0.5)*std::log(t) - t;

+*/			static const f31 pi(0xC90FDAA2, 1), lbe(0xB8AA3B29, 0);

+			unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;

+			bool bsign = sign != 0;

+			f31 z(abs), x = sign ? (z+f31(0x80000000, 0)) : z, t = x + f31(0x94CCCCCD, 2), s =

+				f31(0xA06C9901, 1) + f31(0xBBE654E2, -7)/(x+f31(0x80000000, 2)) + f31(0xA1CE6098, 6)/(x+f31(0x80000000, 1))

+				+ f31(0xE1868CB7, 7)/x - f31(0x8625E279, 8)/(x+f31(0x80000000, 0)) - f31(0xA03E158F, 2)/(x+f31(0xC0000000, 1));

+			int i = (s.exp>=2) + (s.exp>=4) + (s.exp>=8) + (s.exp>=16);

+			s = f31((static_cast<uint32>(s.exp)<<(31-i))+(log2(s.m>>1, 28)>>i), i) / lbe;

+			if(x.exp != -1 || x.m != 0x80000000)

+			{

+				i = (t.exp>=2) + (t.exp>=4) + (t.exp>=8);

+				f31 l = f31((static_cast<uint32>(t.exp)<<(31-i))+(log2(t.m>>1, 30)>>i), i) / lbe;

+				s = (x.exp<-1) ? (s-(f31(0x80000000, -1)-x)*l) : (s+(x-f31(0x80000000, -1))*l);

+			}

+			s = x.exp ? (s-t) : (t-s);

+			if(bsign)

+			{

+				if(z.exp >= 0)

+				{

+					sign &= (L|((z.m>>(31-z.exp))&1)) - 1;

+					for(z=f31((z.m<<(1+z.exp))&0xFFFFFFFF, -1); z.m<0x80000000; z.m<<=1,--z.exp) ;

+				}

+				if(z.exp == -1)

+					z = f31(0x80000000, 0) - z;

+				if(z.exp < -1)

+				{

+					z = z * pi;

+					z.m = sincos(z.m>>(1-z.exp), 30).first;

+					for(z.exp=1; z.m<0x80000000; z.m<<=1,--z.exp) ;

+				}

+				else

+					z = f31(0x80000000, 0);

+			}

+			if(L)

+			{

+				if(bsign)

+				{

+					f31 l(0x92868247, 0);

+					if(z.exp < 0)

+					{

+						uint32 m = log2((z.m+1)>>1, 27);

+						z = f31(-((static_cast<uint32>(z.exp)<<26)+(m>>5)), 5);

+						for(; z.m<0x80000000; z.m<<=1,--z.exp) ;

+						l = l + z / lbe;

+					}

+					sign = static_cast<unsigned>(x.exp&&(l.exp<s.exp||(l.exp==s.exp&&l.m<s.m))) << 15;

+					s = sign ? (s-l) : x.exp ? (l-s) : (l+s);

+				}

+				else

+				{

+					sign = static_cast<unsigned>(x.exp==0) << 15;

+					if(s.exp < -24)

+						return underflow<R>(sign);

+					if(s.exp > 15)

+						return overflow<R>(sign);

+				}

+			}

+			else

+			{

+				s = s * lbe;

+				uint32 m;

+				if(s.exp < 0)

+				{

+					m = s.m >> -s.exp;

+					s.exp = 0;

+				}

+				else

+				{

+					m = (s.m<<s.exp) & 0x7FFFFFFF;

+					s.exp = (s.m>>(31-s.exp));

+				}

+				s.m = exp2(m, 27);

+				if(!x.exp)

+					s = f31(0x80000000, 0) / s;

+				if(bsign)

+				{

+					if(z.exp < 0)

+						s = s * z;

+					s = pi / s;

+					if(s.exp < -24)

+						return underflow<R>(sign);

+				}

+				else if(z.exp > 0 && !(z.m&((1<<(31-z.exp))-1)))

+					return ((s.exp+14)<<10) + (s.m>>21);

+				if(s.exp > 15)

+					return overflow<R>(sign);

+			}

+			return fixed2half<R,31,false,false,true>(s.m, s.exp+14, sign);

+		}

+		/// \}

+

+		template<typename,typename,std::float_round_style> struct half_caster;

+	}

+

+	/// Half-precision floating-point type.

+	/// This class implements an IEEE-conformant half-precision floating-point type with the usual arithmetic 

+	/// operators and conversions. It is implicitly convertible to single-precision floating-point, which makes artihmetic 

+	/// expressions and functions with mixed-type operands to be of the most precise operand type.

+	///

+	/// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and 

+	/// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which 

+	/// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the 

+	/// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of 

+	/// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most 

+	/// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit 

+	/// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if 

+	/// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on 

+	/// nearly any reasonable platform.

+	///

+	/// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable 

+	/// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.

+	class half

+	{

+	public:

+		/// \name Construction and assignment

+		/// \{

+

+		/// Default constructor.

+		/// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics 

+		/// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.

+		HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}

+

+		/// Conversion constructor.

+		/// \param rhs float to convert

+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+		explicit half(float rhs) : data_(static_cast<detail::uint16>(detail::float2half<round_style>(rhs))) {}

+	

+		/// Conversion to single-precision.

+		/// \return single precision value representing expression value

+		operator float() const { return detail::half2float<float>(data_); }

+

+		/// Assignment operator.

+		/// \param rhs single-precision value to copy from

+		/// \return reference to this half

+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+		half& operator=(float rhs) { data_ = static_cast<detail::uint16>(detail::float2half<round_style>(rhs)); return *this; }

+

+		/// \}

+		/// \name Arithmetic updates

+		/// \{

+

+		/// Arithmetic assignment.

+		/// \tparam T type of concrete half expression

+		/// \param rhs half expression to add

+		/// \return reference to this half

+		/// \exception FE_... according to operator+(half,half)

+		half& operator+=(half rhs) { return *this = *this + rhs; }

+

+		/// Arithmetic assignment.

+		/// \tparam T type of concrete half expression

+		/// \param rhs half expression to subtract

+		/// \return reference to this half

+		/// \exception FE_... according to operator-(half,half)

+		half& operator-=(half rhs) { return *this = *this - rhs; }

+

+		/// Arithmetic assignment.

+		/// \tparam T type of concrete half expression

+		/// \param rhs half expression to multiply with

+		/// \return reference to this half

+		/// \exception FE_... according to operator*(half,half)

+		half& operator*=(half rhs) { return *this = *this * rhs; }

+

+		/// Arithmetic assignment.

+		/// \tparam T type of concrete half expression

+		/// \param rhs half expression to divide by

+		/// \return reference to this half

+		/// \exception FE_... according to operator/(half,half)

+		half& operator/=(half rhs) { return *this = *this / rhs; }

+

+		/// Arithmetic assignment.

+		/// \param rhs single-precision value to add

+		/// \return reference to this half

+		/// \exception FE_... according to operator=()

+		half& operator+=(float rhs) { return *this = *this + rhs; }

+

+		/// Arithmetic assignment.

+		/// \param rhs single-precision value to subtract

+		/// \return reference to this half

+		/// \exception FE_... according to operator=()

+		half& operator-=(float rhs) { return *this = *this - rhs; }

+

+		/// Arithmetic assignment.

+		/// \param rhs single-precision value to multiply with

+		/// \return reference to this half

+		/// \exception FE_... according to operator=()

+		half& operator*=(float rhs) { return *this = *this * rhs; }

+

+		/// Arithmetic assignment.

+		/// \param rhs single-precision value to divide by

+		/// \return reference to this half

+		/// \exception FE_... according to operator=()

+		half& operator/=(float rhs) { return *this = *this / rhs; }

+

+		/// \}

+		/// \name Increment and decrement

+		/// \{

+

+		/// Prefix increment.

+		/// \return incremented half value

+		/// \exception FE_... according to operator+(half,half)

+		half& operator++() { return *this = *this + half(detail::binary, 0x3C00); }

+

+		/// Prefix decrement.

+		/// \return decremented half value

+		/// \exception FE_... according to operator-(half,half)

+		half& operator--() { return *this = *this + half(detail::binary, 0xBC00); }

+

+		/// Postfix increment.

+		/// \return non-incremented half value

+		/// \exception FE_... according to operator+(half,half)

+		half operator++(int) { half out(*this); ++*this; return out; }

+

+		/// Postfix decrement.

+		/// \return non-decremented half value

+		/// \exception FE_... according to operator-(half,half)

+		half operator--(int) { half out(*this); --*this; return out; }

+		/// \}

+	

+	private:

+		/// Rounding mode to use

+		static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);

+

+		/// Constructor.

+		/// \param bits binary representation to set half to

+		HALF_CONSTEXPR half(detail::binary_t, unsigned int bits) HALF_NOEXCEPT : data_(static_cast<detail::uint16>(bits)) {}

+

+		/// Internal binary representation

+		detail::uint16 data_;

+

+	#ifndef HALF_DOXYGEN_ONLY

+		friend HALF_CONSTEXPR_NOERR bool operator==(half, half);

+		friend HALF_CONSTEXPR_NOERR bool operator!=(half, half);

+		friend HALF_CONSTEXPR_NOERR bool operator<(half, half);

+		friend HALF_CONSTEXPR_NOERR bool operator>(half, half);

+		friend HALF_CONSTEXPR_NOERR bool operator<=(half, half);

+		friend HALF_CONSTEXPR_NOERR bool operator>=(half, half);

+		friend HALF_CONSTEXPR half operator-(half);

+		friend half operator+(half, half);

+		friend half operator-(half, half);

+		friend half operator*(half, half);

+		friend half operator/(half, half);

+		template<typename charT,typename traits> friend std::basic_ostream<charT,traits>& operator<<(std::basic_ostream<charT,traits>&, half);

+		template<typename charT,typename traits> friend std::basic_istream<charT,traits>& operator>>(std::basic_istream<charT,traits>&, half&);

+		friend HALF_CONSTEXPR half fabs(half);

+		friend half fmod(half, half);

+		friend half remainder(half, half);

+		friend half remquo(half, half, int*);

+		friend half fma(half, half, half);

+		friend HALF_CONSTEXPR_NOERR half fmax(half, half);

+		friend HALF_CONSTEXPR_NOERR half fmin(half, half);

+		friend half fdim(half, half);

+		friend half nanh(const char*);

+		friend half exp(half);

+		friend half exp2(half);

+		friend half expm1(half);

+		friend half log(half);

+		friend half log10(half);

+		friend half log2(half);

+		friend half log1p(half);

+		friend half sqrt(half);

+		friend half rsqrt(half);

+		friend half cbrt(half);

+		friend half hypot(half, half);

+		friend half hypot(half, half, half);

+		friend half pow(half, half);

+		friend void sincos(half, half*, half*);

+		friend half sin(half);

+		friend half cos(half);

+		friend half tan(half);

+		friend half asin(half);

+		friend half acos(half);

+		friend half atan(half);

+		friend half atan2(half, half);

+		friend half sinh(half);

+		friend half cosh(half);

+		friend half tanh(half);

+		friend half asinh(half);

+		friend half acosh(half);

+		friend half atanh(half);

+		friend half erf(half);

+		friend half erfc(half);

+		friend half lgamma(half);

+		friend half tgamma(half);

+		friend half ceil(half);

+		friend half floor(half);

+		friend half trunc(half);

+		friend half round(half);

+		friend long lround(half);

+		friend half rint(half);

+		friend long lrint(half);

+		friend half nearbyint(half);

+	#ifdef HALF_ENABLE_CPP11_LONG_LONG

+		friend long long llround(half);

+		friend long long llrint(half);

+	#endif

+		friend half frexp(half, int*);

+		friend half scalbln(half, long);

+		friend half modf(half, half*);

+		friend int ilogb(half);

+		friend half logb(half);

+		friend half nextafter(half, half);

+		friend half nexttoward(half, long double);

+		friend HALF_CONSTEXPR half copysign(half, half);

+		friend HALF_CONSTEXPR int fpclassify(half);

+		friend HALF_CONSTEXPR bool isfinite(half);

+		friend HALF_CONSTEXPR bool isinf(half);

+		friend HALF_CONSTEXPR bool isnan(half);

+		friend HALF_CONSTEXPR bool isnormal(half);

+		friend HALF_CONSTEXPR bool signbit(half);

+		friend HALF_CONSTEXPR bool isgreater(half, half);

+		friend HALF_CONSTEXPR bool isgreaterequal(half, half);

+		friend HALF_CONSTEXPR bool isless(half, half);

+		friend HALF_CONSTEXPR bool islessequal(half, half);

+		friend HALF_CONSTEXPR bool islessgreater(half, half);

+		template<typename,typename,std::float_round_style> friend struct detail::half_caster;

+		friend class std::numeric_limits<half>;

+	#if HALF_ENABLE_CPP11_HASH

+		friend struct std::hash<half>;

+	#endif

+	#if HALF_ENABLE_CPP11_USER_LITERALS

+		friend half literal::operator "" _h(long double);

+	#endif

+	#endif

+	};

+

+#if HALF_ENABLE_CPP11_USER_LITERALS

+	namespace literal

+	{

+		/// Half literal.

+		/// While this returns a properly rounded half-precision value, half literals can unfortunately not be constant 

+		/// expressions due to rather involved conversions. So don't expect this to be a literal literal without involving 

+		/// conversion operations at runtime. It is a convenience feature, not a performance optimization.

+		/// \param value literal value

+		/// \return half with of given value (possibly rounded)

+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+		inline half operator "" _h(long double value) { return half(detail::binary, detail::float2half<half::round_style>(value)); }

+	}

+#endif

+

+	namespace detail

+	{

+		/// Helper class for half casts.

+		/// This class template has to be specialized for all valid cast arguments to define an appropriate static 

+		/// `cast` member function and a corresponding `type` member denoting its return type.

+		/// \tparam T destination type

+		/// \tparam U source type

+		/// \tparam R rounding mode to use

+		template<typename T,typename U,std::float_round_style R=(std::float_round_style)(HALF_ROUND_STYLE)> struct half_caster {};

+		template<typename U,std::float_round_style R> struct half_caster<half,U,R>

+		{

+		#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS

+			static_assert(std::is_arithmetic<U>::value, "half_cast from non-arithmetic type unsupported");

+		#endif

+

+			static half cast(U arg) { return cast_impl(arg, is_float<U>()); };

+

+		private:

+			static half cast_impl(U arg, true_type) { return half(binary, float2half<R>(arg)); }

+			static half cast_impl(U arg, false_type) { return half(binary, int2half<R>(arg)); }

+		};

+		template<typename T,std::float_round_style R> struct half_caster<T,half,R>

+		{

+		#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS

+			static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");

+		#endif

+

+			static T cast(half arg) { return cast_impl(arg, is_float<T>()); }

+

+		private:

+			static T cast_impl(half arg, true_type) { return half2float<T>(arg.data_); }

+			static T cast_impl(half arg, false_type) { return half2int<R,true,true,T>(arg.data_); }

+		};

+		template<std::float_round_style R> struct half_caster<half,half,R>

+		{

+			static half cast(half arg) { return arg; }

+		};

+	}

+}

+

+/// Extensions to the C++ standard library.

+namespace std

+{

+	/// Numeric limits for half-precision floats.

+	/// **See also:** Documentation for [std::numeric_limits](https://en.cppreference.com/w/cpp/types/numeric_limits)

+	template<> class numeric_limits<half_float::half>

+	{

+	public:

+		/// Is template specialization.

+		static HALF_CONSTEXPR_CONST bool is_specialized = true;

+

+		/// Supports signed values.

+		static HALF_CONSTEXPR_CONST bool is_signed = true;

+

+		/// Is not an integer type.

+		static HALF_CONSTEXPR_CONST bool is_integer = false;

+

+		/// Is not exact.

+		static HALF_CONSTEXPR_CONST bool is_exact = false;

+

+		/// Doesn't provide modulo arithmetic.

+		static HALF_CONSTEXPR_CONST bool is_modulo = false;

+

+		/// Has a finite set of values.

+		static HALF_CONSTEXPR_CONST bool is_bounded = true;

+

+		/// IEEE conformant.

+		static HALF_CONSTEXPR_CONST bool is_iec559 = true;

+

+		/// Supports infinity.

+		static HALF_CONSTEXPR_CONST bool has_infinity = true;

+

+		/// Supports quiet NaNs.

+		static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;

+

+		/// Supports signaling NaNs.

+		static HALF_CONSTEXPR_CONST bool has_signaling_NaN = true;

+

+		/// Supports subnormal values.

+		static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;

+

+		/// Supports no denormalization detection.

+		static HALF_CONSTEXPR_CONST bool has_denorm_loss = false;

+

+	#if HALF_ERRHANDLING_THROWS

+		static HALF_CONSTEXPR_CONST bool traps = true;

+	#else

+		/// Traps only if [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID) is acitvated.

+		static HALF_CONSTEXPR_CONST bool traps = false;

+	#endif

+

+		/// Does not support no pre-rounding underflow detection.

+		static HALF_CONSTEXPR_CONST bool tinyness_before = false;

+

+		/// Rounding mode.

+		static HALF_CONSTEXPR_CONST float_round_style round_style = half_float::half::round_style;

+

+		/// Significant digits.

+		static HALF_CONSTEXPR_CONST int digits = 11;

+

+		/// Significant decimal digits.

+		static HALF_CONSTEXPR_CONST int digits10 = 3;

+

+		/// Required decimal digits to represent all possible values.

+		static HALF_CONSTEXPR_CONST int max_digits10 = 5;

+

+		/// Number base.

+		static HALF_CONSTEXPR_CONST int radix = 2;

+

+		/// One more than smallest exponent.

+		static HALF_CONSTEXPR_CONST int min_exponent = -13;

+

+		/// Smallest normalized representable power of 10.

+		static HALF_CONSTEXPR_CONST int min_exponent10 = -4;

+

+		/// One more than largest exponent

+		static HALF_CONSTEXPR_CONST int max_exponent = 16;

+

+		/// Largest finitely representable power of 10.

+		static HALF_CONSTEXPR_CONST int max_exponent10 = 4;

+

+		/// Smallest positive normal value.

+		static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); }

+

+		/// Smallest finite value.

+		static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); }

+

+		/// Largest finite value.

+		static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); }

+

+		/// Difference between 1 and next representable value.

+		static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); }

+

+		/// Maximum rounding error in ULP (units in the last place).

+		static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW

+			{ return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); }

+

+		/// Positive infinity.

+		static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); }

+

+		/// Quiet NaN.

+		static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); }

+

+		/// Signaling NaN.

+		static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); }

+

+		/// Smallest positive subnormal value.

+		static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); }

+	};

+

+#if HALF_ENABLE_CPP11_HASH

+	/// Hash function for half-precision floats.

+	/// This is only defined if C++11 `std::hash` is supported and enabled.

+	///

+	/// **See also:** Documentation for [std::hash](https://en.cppreference.com/w/cpp/utility/hash)

+	template<> struct hash<half_float::half>

+	{

+		/// Type of function argument.

+		typedef half_float::half argument_type;

+

+		/// Function return type.

+		typedef size_t result_type;

+

+		/// Compute hash function.

+		/// \param arg half to hash

+		/// \return hash value

+		result_type operator()(argument_type arg) const { return hash<half_float::detail::uint16>()(arg.data_&-static_cast<unsigned>(arg.data_!=0x8000)); }

+	};

+#endif

+}

+

+namespace half_float

+{

+	/// \anchor compop

+	/// \name Comparison operators

+	/// \{

+

+	/// Comparison for equality.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if operands equal

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator==(half x, half y)

+	{

+		return !detail::compsignal(x.data_, y.data_) && (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF));

+	}

+

+	/// Comparison for inequality.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if operands not equal

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator!=(half x, half y)

+	{

+		return detail::compsignal(x.data_, y.data_) || (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF));

+	}

+

+	/// Comparison for less than.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x less than \a y

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator<(half x, half y)

+	{

+		return !detail::compsignal(x.data_, y.data_) &&

+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));

+	}

+

+	/// Comparison for greater than.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x greater than \a y

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator>(half x, half y)

+	{

+		return !detail::compsignal(x.data_, y.data_) &&

+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));

+	}

+

+	/// Comparison for less equal.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x less equal \a y

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator<=(half x, half y)

+	{

+		return !detail::compsignal(x.data_, y.data_) &&

+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));

+	}

+

+	/// Comparison for greater equal.

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x greater equal \a y

+	/// \retval false else

+	/// \exception FE_INVALID if \a x or \a y is NaN

+	inline HALF_CONSTEXPR_NOERR bool operator>=(half x, half y)

+	{

+		return !detail::compsignal(x.data_, y.data_) &&

+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));

+	}

+

+	/// \}

+	/// \anchor arithmetics

+	/// \name Arithmetic operators

+	/// \{

+

+	/// Identity.

+	/// \param arg operand

+	/// \return unchanged operand

+	inline HALF_CONSTEXPR half operator+(half arg) { return arg; }

+

+	/// Negation.

+	/// \param arg operand

+	/// \return negated operand

+	inline HALF_CONSTEXPR half operator-(half arg) { return half(detail::binary, arg.data_^0x8000); }

+

+	/// Addition.

+	/// This operation is exact to rounding for all rounding modes.

+	/// \param x left operand

+	/// \param y right operand

+	/// \return sum of half expressions

+	/// \exception FE_INVALID if \a x and \a y are infinities with different signs or signaling NaNs

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half operator+(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)+detail::half2float<detail::internal_t>(y.data_)));

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF;

+		bool sub = ((x.data_^y.data_)&0x8000) != 0;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : (absy!=0x7C00) ? x.data_ :

+										(sub && absx==0x7C00) ? detail::invalid() : y.data_);

+		if(!absx)

+			return absy ? y : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (x.data_|y.data_) : (x.data_&y.data_));

+		if(!absy)

+			return x;

+		unsigned int sign = ((sub && absy>absx) ? y.data_ : x.data_) & 0x8000;

+		if(absy > absx)

+			std::swap(absx, absy);

+		int exp = (absx>>10) + (absx<=0x3FF), d = exp - (absy>>10) - (absy<=0x3FF), mx = ((absx&0x3FF)|((absx>0x3FF)<<10)) << 3, my;

+		if(d < 13)

+		{

+			my = ((absy&0x3FF)|((absy>0x3FF)<<10)) << 3;

+			my = (my>>d) | ((my&((1<<d)-1))!=0);

+		}

+		else

+			my = 1;

+		if(sub)

+		{

+			if(!(mx-=my))

+				return half(detail::binary, static_cast<unsigned>(half::round_style==std::round_toward_neg_infinity)<<15);

+			for(; mx<0x2000 && exp>1; mx<<=1,--exp) ;

+		}

+		else

+		{

+			mx += my;

+			int i = mx >> 14;

+			if((exp+=i) > 30)

+				return half(detail::binary, detail::overflow<half::round_style>(sign));

+			mx = (mx>>i) | (mx&i);

+		}

+		return half(detail::binary, detail::rounded<half::round_style,false>(sign+((exp-1)<<10)+(mx>>3), (mx>>2)&1, (mx&0x3)!=0));

+	#endif

+	}

+

+	/// Subtraction.

+	/// This operation is exact to rounding for all rounding modes.

+	/// \param x left operand

+	/// \param y right operand

+	/// \return difference of half expressions

+	/// \exception FE_INVALID if \a x and \a y are infinities with equal signs or signaling NaNs

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half operator-(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)-detail::half2float<detail::internal_t>(y.data_)));

+	#else

+		return x + -y;

+	#endif

+	}

+

+	/// Multiplication.

+	/// This operation is exact to rounding for all rounding modes.

+	/// \param x left operand

+	/// \param y right operand

+	/// \return product of half expressions

+	/// \exception FE_INVALID if multiplying 0 with infinity or if \a x or \a y is signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half operator*(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)*detail::half2float<detail::internal_t>(y.data_)));

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -16;

+		unsigned int sign = (x.data_^y.data_) & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										((absx==0x7C00 && !absy)||(absy==0x7C00 && !absx)) ? detail::invalid() : (sign|0x7C00));

+		if(!absx || !absy)

+			return half(detail::binary, sign);

+		for(; absx<0x400; absx<<=1,--exp) ;

+		for(; absy<0x400; absy<<=1,--exp) ;

+		detail::uint32 m = static_cast<detail::uint32>((absx&0x3FF)|0x400) * static_cast<detail::uint32>((absy&0x3FF)|0x400);

+		int i = m >> 21, s = m & i;

+		exp += (absx>>10) + (absy>>10) + i;

+		if(exp > 29)

+			return half(detail::binary, detail::overflow<half::round_style>(sign));

+		else if(exp < -11)

+			return half(detail::binary, detail::underflow<half::round_style>(sign));

+		return half(detail::binary, detail::fixed2half<half::round_style,20,false,false,false>(m>>i, exp, sign, s));

+	#endif

+	}

+

+	/// Division.

+	/// This operation is exact to rounding for all rounding modes.

+	/// \param x left operand

+	/// \param y right operand

+	/// \return quotient of half expressions

+	/// \exception FE_INVALID if dividing 0s or infinities with each other or if \a x or \a y is signaling NaN

+	/// \exception FE_DIVBYZERO if dividing finite value by 0

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half operator/(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)/detail::half2float<detail::internal_t>(y.data_)));

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = 14;

+		unsigned int sign = (x.data_^y.data_) & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										(absx==absy) ? detail::invalid() : (sign|((absx==0x7C00) ? 0x7C00 : 0)));

+		if(!absx)

+			return half(detail::binary, absy ? sign : detail::invalid());

+		if(!absy)

+			return half(detail::binary, detail::pole(sign));

+		for(; absx<0x400; absx<<=1,--exp) ;

+		for(; absy<0x400; absy<<=1,++exp) ;

+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;

+		int i = mx < my;

+		exp += (absx>>10) - (absy>>10) - i;

+		if(exp > 29)

+			return half(detail::binary, detail::overflow<half::round_style>(sign));

+		else if(exp < -11)

+			return half(detail::binary, detail::underflow<half::round_style>(sign));

+		mx <<= 12 + i;

+		my <<= 1;

+		return half(detail::binary, detail::fixed2half<half::round_style,11,false,false,false>(mx/my, exp, sign, mx%my!=0));

+	#endif

+	}

+

+	/// \}

+	/// \anchor streaming

+	/// \name Input and output

+	/// \{

+

+	/// Output operator.

+	///	This uses the built-in functionality for streaming out floating-point numbers.

+	/// \param out output stream to write into

+	/// \param arg half expression to write

+	/// \return reference to output stream

+	template<typename charT,typename traits> std::basic_ostream<charT,traits>& operator<<(std::basic_ostream<charT,traits> &out, half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return out << detail::half2float<detail::internal_t>(arg.data_);

+	#else

+		return out << detail::half2float<float>(arg.data_);

+	#endif

+	}

+

+	/// Input operator.

+	///	This uses the built-in functionality for streaming in floating-point numbers, specifically double precision floating 

+	/// point numbers (unless overridden with [HALF_ARITHMETIC_TYPE](\ref HALF_ARITHMETIC_TYPE)). So the input string is first 

+	/// rounded to double precision using the underlying platform's current floating-point rounding mode before being rounded 

+	/// to half-precision using the library's half-precision rounding mode.

+	/// \param in input stream to read from

+	/// \param arg half to read into

+	/// \return reference to input stream

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	template<typename charT,typename traits> std::basic_istream<charT,traits>& operator>>(std::basic_istream<charT,traits> &in, half &arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		detail::internal_t f;

+	#else

+		double f;

+	#endif

+		if(in >> f)

+			arg.data_ = detail::float2half<half::round_style>(f);

+		return in;

+	}

+

+	/// \}

+	/// \anchor basic

+	/// \name Basic mathematical operations

+	/// \{

+

+	/// Absolute value.

+	/// **See also:** Documentation for [std::fabs](https://en.cppreference.com/w/cpp/numeric/math/fabs).

+	/// \param arg operand

+	/// \return absolute value of \a arg

+	inline HALF_CONSTEXPR half fabs(half arg) { return half(detail::binary, arg.data_&0x7FFF); }

+

+	/// Absolute value.

+	/// **See also:** Documentation for [std::abs](https://en.cppreference.com/w/cpp/numeric/math/fabs).

+	/// \param arg operand

+	/// \return absolute value of \a arg

+	inline HALF_CONSTEXPR half abs(half arg) { return fabs(arg); }

+

+	/// Remainder of division.

+	/// **See also:** Documentation for [std::fmod](https://en.cppreference.com/w/cpp/numeric/math/fmod).

+	/// \param x first operand

+	/// \param y second operand

+	/// \return remainder of floating-point division.

+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN

+	inline half fmod(half x, half y)

+	{

+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										(absx==0x7C00) ? detail::invalid() : x.data_);

+		if(!absy)

+			return half(detail::binary, detail::invalid());

+		if(!absx)

+			return x;

+		if(absx == absy)

+			return half(detail::binary, sign);

+		return half(detail::binary, sign|detail::mod<false,false>(absx, absy));

+	}

+

+	/// Remainder of division.

+	/// **See also:** Documentation for [std::remainder](https://en.cppreference.com/w/cpp/numeric/math/remainder).

+	/// \param x first operand

+	/// \param y second operand

+	/// \return remainder of floating-point division.

+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN

+	inline half remainder(half x, half y)

+	{

+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										(absx==0x7C00) ? detail::invalid() : x.data_);

+		if(!absy)

+			return half(detail::binary, detail::invalid());

+		if(absx == absy)

+			return half(detail::binary, sign);

+		return half(detail::binary, sign^detail::mod<false,true>(absx, absy));

+	}

+

+	/// Remainder of division.

+	/// **See also:** Documentation for [std::remquo](https://en.cppreference.com/w/cpp/numeric/math/remquo).

+	/// \param x first operand

+	/// \param y second operand

+	/// \param quo address to store some bits of quotient at

+	/// \return remainder of floating-point division.

+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN

+	inline half remquo(half x, half y, int *quo)

+	{

+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, value = x.data_ & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										(absx==0x7C00) ? detail::invalid() : (*quo = 0, x.data_));

+		if(!absy)

+			return half(detail::binary, detail::invalid());

+		bool qsign = ((value^y.data_)&0x8000) != 0;

+		int q = 1;

+		if(absx != absy)

+			value ^= detail::mod<true, true>(absx, absy, &q);

+		return *quo = qsign ? -q : q, half(detail::binary, value);

+	}

+

+	/// Fused multiply add.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::fma](https://en.cppreference.com/w/cpp/numeric/math/fma).

+	/// \param x first operand

+	/// \param y second operand

+	/// \param z third operand

+	/// \return ( \a x * \a y ) + \a z rounded as one operation.

+	/// \exception FE_INVALID according to operator*() and operator+() unless any argument is a quiet NaN and no argument is a signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding the final addition

+	inline half fma(half x, half y, half z)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_), fz = detail::half2float<detail::internal_t>(z.data_);

+		#if HALF_ENABLE_CPP11_CMATH && FP_FAST_FMA

+			return half(detail::binary, detail::float2half<half::round_style>(std::fma(fx, fy, fz)));

+		#else

+			return half(detail::binary, detail::float2half<half::round_style>(fx*fy+fz));

+		#endif

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, exp = -15;

+		unsigned int sign = (x.data_^y.data_) & 0x8000;

+		bool sub = ((sign^z.data_)&0x8000) != 0;

+		if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)

+			return	(absx>0x7C00 || absy>0x7C00 || absz>0x7C00) ? half(detail::binary, detail::signal(x.data_, y.data_, z.data_)) :

+					(absx==0x7C00) ? half(detail::binary, (!absy || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) :

+					(absy==0x7C00) ? half(detail::binary, (!absx || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) : z;

+		if(!absx || !absy)

+			return absz ? z : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (z.data_|sign) : (z.data_&sign));

+		for(; absx<0x400; absx<<=1,--exp) ;

+		for(; absy<0x400; absy<<=1,--exp) ;

+		detail::uint32 m = static_cast<detail::uint32>((absx&0x3FF)|0x400) * static_cast<detail::uint32>((absy&0x3FF)|0x400);

+		int i = m >> 21;

+		exp += (absx>>10) + (absy>>10) + i;

+		m <<= 3 - i;

+		if(absz)

+		{

+			int expz = 0;

+			for(; absz<0x400; absz<<=1,--expz) ;

+			expz += absz >> 10;

+			detail::uint32 mz = static_cast<detail::uint32>((absz&0x3FF)|0x400) << 13;

+			if(expz > exp || (expz == exp && mz > m))

+			{

+				std::swap(m, mz);

+				std::swap(exp, expz);

+				if(sub)

+					sign = z.data_ & 0x8000;

+			}

+			int d = exp - expz;

+			mz = (d<23) ? ((mz>>d)|((mz&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;

+			if(sub)

+			{

+				m = m - mz;

+				if(!m)

+					return half(detail::binary, static_cast<unsigned>(half::round_style==std::round_toward_neg_infinity)<<15);

+				for(; m<0x800000; m<<=1,--exp) ;

+			}

+			else

+			{

+				m += mz;

+				i = m >> 24;

+				m = (m>>i) | (m&i);

+				exp += i;

+			}

+		}

+		if(exp > 30)

+			return half(detail::binary, detail::overflow<half::round_style>(sign));

+		else if(exp < -10)

+			return half(detail::binary, detail::underflow<half::round_style>(sign));

+		return half(detail::binary, detail::fixed2half<half::round_style,23,false,false,false>(m, exp-1, sign));

+	#endif

+	}

+

+	/// Maximum of half expressions.

+	/// **See also:** Documentation for [std::fmax](https://en.cppreference.com/w/cpp/numeric/math/fmax).

+	/// \param x first operand

+	/// \param y second operand

+	/// \return maximum of operands, ignoring quiet NaNs

+	/// \exception FE_INVALID if \a x or \a y is signaling NaN

+	inline HALF_CONSTEXPR_NOERR half fmax(half x, half y)

+	{

+		return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) < 

+			(y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_));

+	}

+

+	/// Minimum of half expressions.

+	/// **See also:** Documentation for [std::fmin](https://en.cppreference.com/w/cpp/numeric/math/fmin).

+	/// \param x first operand

+	/// \param y second operand

+	/// \return minimum of operands, ignoring quiet NaNs

+	/// \exception FE_INVALID if \a x or \a y is signaling NaN

+	inline HALF_CONSTEXPR_NOERR half fmin(half x, half y)

+	{

+		return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) >

+			(y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_));

+	}

+

+	/// Positive difference.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::fdim](https://en.cppreference.com/w/cpp/numeric/math/fdim).

+	/// \param x first operand

+	/// \param y second operand

+	/// \return \a x - \a y or 0 if difference negative

+	/// \exception FE_... according to operator-(half,half)

+	inline half fdim(half x, half y)

+	{

+		if(isnan(x) || isnan(y))

+			return half(detail::binary, detail::signal(x.data_, y.data_));

+		return (x.data_^(0x8000|(0x8000-(x.data_>>15)))) <= (y.data_^(0x8000|(0x8000-(y.data_>>15)))) ? half(detail::binary, 0) : (x-y);

+	}

+

+	/// Get NaN value.

+	/// **See also:** Documentation for [std::nan](https://en.cppreference.com/w/cpp/numeric/math/nan).

+	/// \param arg string code

+	/// \return quiet NaN

+	inline half nanh(const char *arg)

+	{

+		unsigned int value = 0x7FFF;

+		while(*arg)

+			value ^= static_cast<unsigned>(*arg++) & 0xFF;

+		return half(detail::binary, value);

+	}

+

+	/// \}

+	/// \anchor exponential

+	/// \name Exponential functions

+	/// \{

+

+	/// Exponential function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::exp](https://en.cppreference.com/w/cpp/numeric/math/exp).

+	/// \param arg function argument

+	/// \return e raised to \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half exp(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::exp(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, e = (abs>>10) + (abs<=0x3FF), exp;

+		if(!abs)

+			return half(detail::binary, 0x3C00);

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_));

+		if(abs >= 0x4C80)

+			return half(detail::binary, (arg.data_&0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());

+		detail::uint32 m = detail::multiply64(static_cast<detail::uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29);

+		if(e < 14)

+		{

+			exp = 0;

+			m >>= 14 - e;

+		}

+		else

+		{

+			exp = m >> (45-e);

+			m = (m<<(e-14)) & 0x7FFFFFFF;

+		}

+		return half(detail::binary, detail::exp2_post<half::round_style>(m, exp, (arg.data_&0x8000)!=0, 0, 26));

+	#endif

+	}

+

+	/// Binary exponential.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::exp2](https://en.cppreference.com/w/cpp/numeric/math/exp2).

+	/// \param arg function argument

+	/// \return 2 raised to \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half exp2(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::exp2(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, e = (abs>>10) + (abs<=0x3FF), exp = (abs&0x3FF) + ((abs>0x3FF)<<10);

+		if(!abs)

+			return half(detail::binary, 0x3C00);

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_));

+		if(abs >= 0x4E40)

+			return half(detail::binary, (arg.data_&0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());

+		return half(detail::binary, detail::exp2_post<half::round_style>(

+			(static_cast<detail::uint32>(exp)<<(6+e))&0x7FFFFFFF, exp>>(25-e), (arg.data_&0x8000)!=0, 0, 28));

+	#endif

+	}

+

+	/// Exponential minus one.

+	/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` 

+	/// and in <1% of inputs for any other rounding mode.

+	///

+	/// **See also:** Documentation for [std::expm1](https://en.cppreference.com/w/cpp/numeric/math/expm1).

+	/// \param arg function argument

+	/// \return e raised to \a arg and subtracted by 1

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half expm1(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::expm1(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000, e = (abs>>10) + (abs<=0x3FF), exp;

+		if(!abs)

+			return arg;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? (0x7C00+(sign>>1)) : detail::signal(arg.data_));

+		if(abs >= 0x4A00)

+			return half(detail::binary, (arg.data_&0x8000) ? detail::rounded<half::round_style,true>(0xBBFF, 1, 1) : detail::overflow<half::round_style>());

+		detail::uint32 m = detail::multiply64(static_cast<detail::uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29);

+		if(e < 14)

+		{

+			exp = 0;

+			m >>= 14 - e;

+		}

+		else

+		{

+			exp = m >> (45-e);

+			m = (m<<(e-14)) & 0x7FFFFFFF;

+		}

+		m = detail::exp2(m);

+		if(sign)

+		{

+			int s = 0;

+			if(m > 0x80000000)

+			{

+				++exp;

+				m = detail::divide64(0x80000000, m, s);

+			}

+			m = 0x80000000 - ((m>>exp)|((m&((static_cast<detail::uint32>(1)<<exp)-1))!=0)|s);

+			exp = 0;

+		}

+		else

+			m -= (exp<31) ? (0x80000000>>exp) : 1;

+		for(exp+=14; m<0x80000000 && exp; m<<=1,--exp) ;

+		if(exp > 29)

+			return half(detail::binary, detail::overflow<half::round_style>());

+		return half(detail::binary, detail::rounded<half::round_style,true>(sign+(exp<<10)+(m>>21), (m>>20)&1, (m&0xFFFFF)!=0));

+	#endif

+	}

+

+	/// Natural logarithm.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::log](https://en.cppreference.com/w/cpp/numeric/math/log).

+	/// \param arg function argument

+	/// \return logarithm of \a arg to base e

+	/// \exception FE_INVALID for signaling NaN or negative argument

+	/// \exception FE_DIVBYZERO for 0

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half log(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::log(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = -15;

+		if(!abs)

+			return half(detail::binary, detail::pole(0x8000));

+		if(arg.data_ & 0x8000)

+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs >= 0x7C00)

+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));

+		for(; abs<0x400; abs<<=1,--exp) ;

+		exp += abs >> 10;

+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(

+			detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 27)+8, exp, 17));

+	#endif

+	}

+

+	/// Common logarithm.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::log10](https://en.cppreference.com/w/cpp/numeric/math/log10).

+	/// \param arg function argument

+	/// \return logarithm of \a arg to base 10

+	/// \exception FE_INVALID for signaling NaN or negative argument

+	/// \exception FE_DIVBYZERO for 0

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half log10(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::log10(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = -15;

+		if(!abs)

+			return half(detail::binary, detail::pole(0x8000));

+		if(arg.data_ & 0x8000)

+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs >= 0x7C00)

+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));

+		switch(abs)

+		{

+			case 0x4900: return half(detail::binary, 0x3C00);

+			case 0x5640: return half(detail::binary, 0x4000);

+			case 0x63D0: return half(detail::binary, 0x4200);

+			case 0x70E2: return half(detail::binary, 0x4400);

+		}

+		for(; abs<0x400; abs<<=1,--exp) ;

+		exp += abs >> 10;

+		return half(detail::binary, detail::log2_post<half::round_style,0xD49A784C>(

+			detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 27)+8, exp, 16));

+	#endif

+	}

+

+	/// Binary logarithm.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::log2](https://en.cppreference.com/w/cpp/numeric/math/log2).

+	/// \param arg function argument

+	/// \return logarithm of \a arg to base 2

+	/// \exception FE_INVALID for signaling NaN or negative argument

+	/// \exception FE_DIVBYZERO for 0

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half log2(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::log2(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = -15, s = 0;

+		if(!abs)

+			return half(detail::binary, detail::pole(0x8000));

+		if(arg.data_ & 0x8000)

+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs >= 0x7C00)

+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));

+		if(abs == 0x3C00)

+			return half(detail::binary, 0);

+		for(; abs<0x400; abs<<=1,--exp) ;

+		exp += (abs>>10);

+		if(!(abs&0x3FF))

+		{

+			unsigned int value = static_cast<unsigned>(exp<0) << 15, m = std::abs(exp) << 6;

+			for(exp=18; m<0x400; m<<=1,--exp) ;

+			return half(detail::binary, value+(exp<<10)+m);

+		}

+		detail::uint32 ilog = exp, sign = detail::sign_mask(ilog), m = 

+			(((ilog<<27)+(detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 28)>>4))^sign) - sign;

+		if(!m)

+			return half(detail::binary, 0);

+		for(exp=14; m<0x8000000 && exp; m<<=1,--exp) ;

+		for(; m>0xFFFFFFF; m>>=1,++exp)

+			s |= m & 1;

+		return half(detail::binary, detail::fixed2half<half::round_style,27,false,false,true>(m, exp, sign&0x8000, s));

+	#endif

+	}

+

+	/// Natural logarithm plus one.

+	/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` 

+	/// and in ~1% of inputs for any other rounding mode.

+	///

+	/// **See also:** Documentation for [std::log1p](https://en.cppreference.com/w/cpp/numeric/math/log1p).

+	/// \param arg function argument

+	/// \return logarithm of \a arg plus 1 to base e

+	/// \exception FE_INVALID for signaling NaN or argument <-1

+	/// \exception FE_DIVBYZERO for -1

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half log1p(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::log1p(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		if(arg.data_ >= 0xBC00)

+			return half(detail::binary, (arg.data_==0xBC00) ? detail::pole(0x8000) : (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));

+		int abs = arg.data_ & 0x7FFF, exp = -15;

+		if(!abs || abs >= 0x7C00)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		for(; abs<0x400; abs<<=1,--exp) ;

+		exp += abs >> 10;

+		detail::uint32 m = static_cast<detail::uint32>((abs&0x3FF)|0x400) << 20;

+		if(arg.data_ & 0x8000)

+		{

+			m = 0x40000000 - (m>>-exp);

+			for(exp=0; m<0x40000000; m<<=1,--exp) ;

+		}

+		else

+		{

+			if(exp < 0)

+			{

+				m = 0x40000000 + (m>>-exp);

+				exp = 0;

+			}

+			else

+			{

+				m += 0x40000000 >> exp;

+				int i = m >> 31;

+				m >>= i;

+				exp += i;

+			}

+		}

+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(detail::log2(m), exp, 17));

+	#endif

+	}

+

+	/// \}

+	/// \anchor power

+	/// \name Power functions

+	/// \{

+

+	/// Square root.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::sqrt](https://en.cppreference.com/w/cpp/numeric/math/sqrt).

+	/// \param arg function argument

+	/// \return square root of \a arg

+	/// \exception FE_INVALID for signaling NaN and negative arguments

+	/// \exception FE_INEXACT according to rounding

+	inline half sqrt(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = 15;

+		if(!abs || arg.data_ >= 0x7C00)

+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_>0x8000) ? detail::invalid() : arg.data_);

+		for(; abs<0x400; abs<<=1,--exp) ;

+		detail::uint32 r = static_cast<detail::uint32>((abs&0x3FF)|0x400) << 10, m = detail::sqrt<20>(r, exp+=abs>>10);

+		return half(detail::binary, detail::rounded<half::round_style,false>((exp<<10)+(m&0x3FF), r>m, r!=0));

+	#endif

+	}

+

+	/// Inverse square root.

+	/// This function is exact to rounding for all rounding modes and thus generally more accurate than directly computing 

+	/// 1 / sqrt(\a arg) in half-precision, in addition to also being faster.

+	/// \param arg function argument

+	/// \return reciprocal of square root of \a arg

+	/// \exception FE_INVALID for signaling NaN and negative arguments

+	/// \exception FE_INEXACT according to rounding

+	inline half rsqrt(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(detail::internal_t(1)/std::sqrt(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, bias = 0x4000;

+		if(!abs || arg.data_ >= 0x7C00)

+			return half(detail::binary,	(abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_>0x8000) ?

+										detail::invalid() : !abs ? detail::pole(arg.data_&0x8000) : 0);

+		for(; abs<0x400; abs<<=1,bias-=0x400) ;

+		unsigned int frac = (abs+=bias) & 0x7FF;

+		if(frac == 0x400)

+			return half(detail::binary, 0x7A00-(abs>>1));

+		if((half::round_style == std::round_to_nearest && (frac == 0x3FE || frac == 0x76C)) ||

+		   (half::round_style != std::round_to_nearest && (frac == 0x15A || frac == 0x3FC || frac == 0x401 || frac == 0x402 || frac == 0x67B)))

+			return pow(arg, half(detail::binary, 0xB800));

+		detail::uint32 f = 0x17376 - abs, mx = (abs&0x3FF) | 0x400, my = ((f>>1)&0x3FF) | 0x400, mz = my * my;

+		int expy = (f>>11) - 31, expx = 32 - (abs>>10), i = mz >> 21;

+		for(mz=0x60000000-(((mz>>i)*mx)>>(expx-2*expy-i)); mz<0x40000000; mz<<=1,--expy) ;

+		i = (my*=mz>>10) >> 31;

+		expy += i;

+		my = (my>>(20+i)) + 1;

+		i = (mz=my*my) >> 21;

+		for(mz=0x60000000-(((mz>>i)*mx)>>(expx-2*expy-i)); mz<0x40000000; mz<<=1,--expy) ;

+		i = (my*=(mz>>10)+1) >> 31;

+		return half(detail::binary, detail::fixed2half<half::round_style,30,false,false,true>(my>>i, expy+i+14));

+	#endif

+	}

+

+	/// Cubic root.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::cbrt](https://en.cppreference.com/w/cpp/numeric/math/cbrt).

+	/// \param arg function argument

+	/// \return cubic root of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT according to rounding

+	inline half cbrt(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::cbrt(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = -15;

+		if(!abs || abs == 0x3C00 || abs >= 0x7C00)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		for(; abs<0x400; abs<<=1, --exp);

+		detail::uint32 ilog = exp + (abs>>10), sign = detail::sign_mask(ilog), f, m = 

+			(((ilog<<27)+(detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 24)>>4))^sign) - sign;

+		for(exp=2; m<0x80000000; m<<=1,--exp) ;

+		m = detail::multiply64(m, 0xAAAAAAAB);

+		int i = m >> 31, s;

+		exp += i;

+		m <<= 1 - i;

+		if(exp < 0)

+		{

+			f = m >> -exp;

+			exp = 0;

+		}

+		else

+		{

+			f = (m<<exp) & 0x7FFFFFFF;

+			exp = m >> (31-exp);

+		}

+		m = detail::exp2(f, (half::round_style==std::round_to_nearest) ? 29 : 26);

+		if(sign)

+		{

+			if(m > 0x80000000)

+			{

+				m = detail::divide64(0x80000000, m, s);

+				++exp;

+			}

+			exp = -exp;

+		}

+		return half(detail::binary, (half::round_style==std::round_to_nearest) ?

+			detail::fixed2half<half::round_style,31,false,false,false>(m, exp+14, arg.data_&0x8000) :

+			detail::fixed2half<half::round_style,23,false,false,false>((m+0x80)>>8, exp+14, arg.data_&0x8000));

+	#endif

+	}

+

+	/// Hypotenuse function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot).

+	/// \param x first argument

+	/// \param y second argument

+	/// \return square root of sum of squares without internal over- or underflows

+	/// \exception FE_INVALID if \a x or \a y is signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root

+	inline half hypot(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_);

+		#if HALF_ENABLE_CPP11_CMATH

+			return half(detail::binary, detail::float2half<half::round_style>(std::hypot(fx, fy)));

+		#else

+			return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx*fx+fy*fy)));

+		#endif

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx==0x7C00) ? detail::select(0x7C00, y.data_) :

+				(absy==0x7C00) ? detail::select(0x7C00, x.data_) : detail::signal(x.data_, y.data_));

+		if(!absx)

+			return half(detail::binary, absy ? detail::check_underflow(absy) : 0);

+		if(!absy)

+			return half(detail::binary, detail::check_underflow(absx));

+		if(absy > absx)

+			std::swap(absx, absy);

+		for(; absx<0x400; absx<<=1,--expx) ;

+		for(; absy<0x400; absy<<=1,--expy) ;

+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;

+		mx *= mx;

+		my *= my;

+		int ix = mx >> 21, iy = my >> 21;

+		expx = 2*(expx+(absx>>10)) - 15 + ix;

+		expy = 2*(expy+(absy>>10)) - 15 + iy;

+		mx <<= 10 - ix;

+		my <<= 10 - iy;

+		int d = expx - expy;

+		my = (d<30) ? ((my>>d)|((my&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;

+		return half(detail::binary, detail::hypot_post<half::round_style>(mx+my, expx));

+	#endif

+	}

+

+	/// Hypotenuse function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot).

+	/// \param x first argument

+	/// \param y second argument

+	/// \param z third argument

+	/// \return square root of sum of squares without internal over- or underflows

+	/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root

+	inline half hypot(half x, half y, half z)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_), fz = detail::half2float<detail::internal_t>(z.data_);

+		return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx*fx+fy*fy+fz*fz)));

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, expx = 0, expy = 0, expz = 0;

+		if(!absx)

+			return hypot(y, z);

+		if(!absy)

+			return hypot(x, z);

+		if(!absz)

+			return hypot(x, y);

+		if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)

+			return half(detail::binary,	(absx==0x7C00) ? detail::select(0x7C00, detail::select(y.data_, z.data_)) :

+										(absy==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, z.data_)) :

+										(absz==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, y.data_)) :

+										detail::signal(x.data_, y.data_, z.data_));

+		if(absz > absy)

+			std::swap(absy, absz);

+		if(absy > absx)

+			std::swap(absx, absy);

+		if(absz > absy)

+			std::swap(absy, absz);

+		for(; absx<0x400; absx<<=1,--expx) ;

+		for(; absy<0x400; absy<<=1,--expy) ;

+		for(; absz<0x400; absz<<=1,--expz) ;

+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400, mz = (absz&0x3FF) | 0x400;

+		mx *= mx;

+		my *= my;

+		mz *= mz;

+		int ix = mx >> 21, iy = my >> 21, iz = mz >> 21;

+		expx = 2*(expx+(absx>>10)) - 15 + ix;

+		expy = 2*(expy+(absy>>10)) - 15 + iy;

+		expz = 2*(expz+(absz>>10)) - 15 + iz;

+		mx <<= 10 - ix;

+		my <<= 10 - iy;

+		mz <<= 10 - iz;

+		int d = expy - expz;

+		mz = (d<30) ? ((mz>>d)|((mz&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;

+		my += mz;

+		if(my & 0x80000000)

+		{

+			my = (my>>1) | (my&1);

+			if(++expy > expx)

+			{

+				std::swap(mx, my);

+				std::swap(expx, expy);

+			}

+		}

+		d = expx - expy;

+		my = (d<30) ? ((my>>d)|((my&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;

+		return half(detail::binary, detail::hypot_post<half::round_style>(mx+my, expx));

+	#endif

+	}

+

+	/// Power function.

+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.00025% of inputs.

+	///

+	/// **See also:** Documentation for [std::pow](https://en.cppreference.com/w/cpp/numeric/math/pow).

+	/// \param x base

+	/// \param y exponent

+	/// \return \a x raised to \a y

+	/// \exception FE_INVALID if \a x or \a y is signaling NaN or if \a x is finite an negative and \a y is finite and not integral

+	/// \exception FE_DIVBYZERO if \a x is 0 and \a y is negative

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half pow(half x, half y)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::pow(detail::half2float<detail::internal_t>(x.data_), detail::half2float<detail::internal_t>(y.data_))));

+	#else

+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -15;

+		if(!absy || x.data_ == 0x3C00)

+			return half(detail::binary, detail::select(0x3C00, (x.data_==0x3C00) ? y.data_ : x.data_));

+		bool is_int = absy >= 0x6400 || (absy>=0x3C00 && !(absy&((1<<(25-(absy>>10)))-1)));

+		unsigned int sign = x.data_ & (static_cast<unsigned>((absy<0x6800)&&is_int&&((absy>>(25-(absy>>10)))&1))<<15);

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :

+										(absy==0x7C00) ? ((absx==0x3C00) ? 0x3C00 : (!absx && y.data_==0xFC00) ? detail::pole() :

+										(0x7C00&-((y.data_>>15)^(absx>0x3C00)))) : (sign|(0x7C00&((y.data_>>15)-1U))));

+		if(!absx)

+			return half(detail::binary, (y.data_&0x8000) ? detail::pole(sign) : sign);

+		if((x.data_&0x8000) && !is_int)

+			return half(detail::binary, detail::invalid());

+		if(x.data_ == 0xBC00)

+			return half(detail::binary, sign|0x3C00);

+		switch(y.data_)

+		{

+			case 0x3800: return sqrt(x);

+			case 0x3C00: return half(detail::binary, detail::check_underflow(x.data_));

+			case 0x4000: return x * x;

+			case 0xBC00: return half(detail::binary, 0x3C00) / x;

+		}

+		for(; absx<0x400; absx<<=1,--exp) ;

+		detail::uint32 ilog = exp + (absx>>10), msign = detail::sign_mask(ilog), f, m = 

+			(((ilog<<27)+((detail::log2(static_cast<detail::uint32>((absx&0x3FF)|0x400)<<20)+8)>>4))^msign) - msign;

+		for(exp=-11; m<0x80000000; m<<=1,--exp) ;

+		for(; absy<0x400; absy<<=1,--exp) ;

+		m = detail::multiply64(m, static_cast<detail::uint32>((absy&0x3FF)|0x400)<<21);

+		int i = m >> 31;

+		exp += (absy>>10) + i;

+		m <<= 1 - i;

+		if(exp < 0)

+		{

+			f = m >> -exp;

+			exp = 0;

+		}

+		else

+		{

+			f = (m<<exp) & 0x7FFFFFFF;

+			exp = m >> (31-exp);

+		}

+		return half(detail::binary, detail::exp2_post<half::round_style>(f, exp, ((msign&1)^(y.data_>>15))!=0, sign));

+	#endif

+	}

+

+	/// \}

+	/// \anchor trigonometric

+	/// \name Trigonometric functions

+	/// \{

+

+	/// Compute sine and cosine simultaneously.

+	///	This returns the same results as sin() and cos() but is faster than calling each function individually.

+	///

+	/// This function is exact to rounding for all rounding modes.

+	/// \param arg function argument

+	/// \param sin variable to take sine of \a arg

+	/// \param cos variable to take cosine of \a arg

+	/// \exception FE_INVALID for signaling NaN or infinity

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline void sincos(half arg, half *sin, half *cos)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		detail::internal_t f = detail::half2float<detail::internal_t>(arg.data_);

+		*sin = half(detail::binary, detail::float2half<half::round_style>(std::sin(f)));

+		*cos = half(detail::binary, detail::float2half<half::round_style>(std::cos(f)));

+	#else

+		int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15, k;

+		if(abs >= 0x7C00)

+			*sin = *cos = half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		else if(!abs)

+		{

+			*sin = arg;

+			*cos = half(detail::binary, 0x3C00);

+		}

+		else if(abs < 0x2500)

+		{

+			*sin = half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));

+			*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));

+		}

+		else

+		{

+			if(half::round_style != std::round_to_nearest)

+			{

+				switch(abs)

+				{

+				case 0x48B7:

+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x1D07, 1, 1));

+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0xBBFF, 1, 1));

+					return;

+				case 0x598C:

+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));

+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x80FC, 1, 1));

+					return;

+				case 0x6A64:

+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x3BFE, 1, 1));

+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x27FF, 1, 1));

+					return;

+				case 0x6D8C:

+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x0FE6, 1, 1));

+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));

+					return;

+				}

+			}

+			std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);

+			switch(k & 3)

+			{

+				case 1: sc = std::make_pair(sc.second, -sc.first); break;

+				case 2: sc = std::make_pair(-sc.first, -sc.second); break;

+				case 3: sc = std::make_pair(-sc.second, sc.first); break;

+			}

+			*sin = half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((sc.first^-static_cast<detail::uint32>(sign))+sign));

+			*cos = half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>(sc.second));

+		}

+	#endif

+	}

+

+	/// Sine function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::sin](https://en.cppreference.com/w/cpp/numeric/math/sin).

+	/// \param arg function argument

+	/// \return sine value of \a arg

+	/// \exception FE_INVALID for signaling NaN or infinity

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half sin(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::sin(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, k;

+		if(!abs)

+			return arg;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs < 0x2900)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));

+		if(half::round_style != std::round_to_nearest)

+			switch(abs)

+			{

+				case 0x48B7: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x1D07, 1, 1));

+				case 0x6A64: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x3BFE, 1, 1));

+				case 0x6D8C: return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x0FE6, 1, 1));

+			}

+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);

+		detail::uint32 sign = -static_cast<detail::uint32>(((k>>1)&1)^(arg.data_>>15));

+		return half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((((k&1) ? sc.second : sc.first)^sign) - sign));

+	#endif

+	}

+

+	/// Cosine function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::cos](https://en.cppreference.com/w/cpp/numeric/math/cos).

+	/// \param arg function argument

+	/// \return cosine value of \a arg

+	/// \exception FE_INVALID for signaling NaN or infinity

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half cos(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::cos(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, k;

+		if(!abs)

+			return half(detail::binary, 0x3C00);

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs < 0x2500)

+			return half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));

+		if(half::round_style != std::round_to_nearest && abs == 0x598C)

+			return half(detail::binary, detail::rounded<half::round_style,true>(0x80FC, 1, 1));

+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);

+		detail::uint32 sign = -static_cast<detail::uint32>(((k>>1)^k)&1);

+		return half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((((k&1) ? sc.first : sc.second)^sign) - sign));

+	#endif

+	}

+

+	/// Tangent function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::tan](https://en.cppreference.com/w/cpp/numeric/math/tan).

+	/// \param arg function argument

+	/// \return tangent value of \a arg

+	/// \exception FE_INVALID for signaling NaN or infinity

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half tan(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::tan(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = 13, k;

+		if(!abs)

+			return arg;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs < 0x2700)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));

+		if(half::round_style != std::round_to_nearest)

+			switch(abs)

+			{

+				case 0x658C: return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x07E6, 1, 1));

+				case 0x7330: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x4B62, 1, 1));

+			}

+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 30);

+		if(k & 1)

+			sc = std::make_pair(-sc.second, sc.first);

+		detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second);

+		detail::uint32 my = (sc.first^signy) - signy, mx = (sc.second^signx) - signx;

+		for(; my<0x80000000; my<<=1,--exp) ;

+		for(; mx<0x80000000; mx<<=1,++exp) ;

+		return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp, (signy^signx^arg.data_)&0x8000));

+	#endif

+	}

+

+	/// Arc sine.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::asin](https://en.cppreference.com/w/cpp/numeric/math/asin).

+	/// \param arg function argument

+	/// \return arc sine value of \a arg

+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half asin(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::asin(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;

+		if(!abs)

+			return arg;

+		if(abs >= 0x3C00)

+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() :

+										detail::rounded<half::round_style,true>(sign|0x3E48, 0, 1));

+		if(abs < 0x2900)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));

+		if(half::round_style != std::round_to_nearest && (abs == 0x2B44 || abs == 0x2DC3))

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_+1, 1, 1));

+		std::pair<detail::uint32,detail::uint32> sc = detail::atan2_args(abs);

+		detail::uint32 m = detail::atan2(sc.first, sc.second, (half::round_style==std::round_to_nearest) ? 27 : 26);

+		return half(detail::binary, detail::fixed2half<half::round_style,30,false,true,true>(m, 14, sign));

+	#endif

+	}

+

+	/// Arc cosine function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::acos](https://en.cppreference.com/w/cpp/numeric/math/acos).

+	/// \param arg function argument

+	/// \return arc cosine value of \a arg

+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half acos(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::acos(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15;

+		if(!abs)

+			return half(detail::binary, detail::rounded<half::round_style,true>(0x3E48, 0, 1));

+		if(abs >= 0x3C00)

+			return half(detail::binary,	(abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() :

+										sign ? detail::rounded<half::round_style,true>(0x4248, 0, 1) : 0);

+		std::pair<detail::uint32,detail::uint32> cs = detail::atan2_args(abs);

+		detail::uint32 m = detail::atan2(cs.second, cs.first, 28);

+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,true,true>(sign ? (0xC90FDAA2-m) : m, 15, 0, sign));

+	#endif

+	}

+

+	/// Arc tangent function.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::atan](https://en.cppreference.com/w/cpp/numeric/math/atan).

+	/// \param arg function argument

+	/// \return arc tangent value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half atan(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::atan(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;

+		if(!abs)

+			return arg;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? detail::rounded<half::round_style,true>(sign|0x3E48, 0, 1) : detail::signal(arg.data_));

+		if(abs <= 0x2700)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));

+		int exp = (abs>>10) + (abs<=0x3FF);

+		detail::uint32 my = (abs&0x3FF) | ((abs>0x3FF)<<10);

+		detail::uint32 m = (exp>15) ?	detail::atan2(my<<19, 0x20000000>>(exp-15), (half::round_style==std::round_to_nearest) ? 26 : 24) :

+										detail::atan2(my<<(exp+4), 0x20000000, (half::round_style==std::round_to_nearest) ? 30 : 28);

+		return half(detail::binary, detail::fixed2half<half::round_style,30,false,true,true>(m, 14, sign));

+	#endif

+	}

+

+	/// Arc tangent function.

+	/// This function may be 1 ULP off the correctly rounded exact result in ~0.005% of inputs for `std::round_to_nearest`, 

+	/// in ~0.1% of inputs for `std::round_toward_zero` and in ~0.02% of inputs for any other rounding mode.

+	///

+	/// **See also:** Documentation for [std::atan2](https://en.cppreference.com/w/cpp/numeric/math/atan2).

+	/// \param y numerator

+	/// \param x denominator

+	/// \return arc tangent value

+	/// \exception FE_INVALID if \a x or \a y is signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half atan2(half y, half x)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::atan2(detail::half2float<detail::internal_t>(y.data_), detail::half2float<detail::internal_t>(x.data_))));

+	#else

+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, signx = x.data_ >> 15, signy = y.data_ & 0x8000;

+		if(absx >= 0x7C00 || absy >= 0x7C00)

+		{

+			if(absx > 0x7C00 || absy > 0x7C00)

+				return half(detail::binary, detail::signal(x.data_, y.data_));

+			if(absy == 0x7C00)

+				return half(detail::binary, (absx<0x7C00) ?	detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1) :

+													signx ?	detail::rounded<half::round_style,true>(signy|0x40B6, 0, 1) :

+															detail::rounded<half::round_style,true>(signy|0x3A48, 0, 1));

+			return (x.data_==0x7C00) ? half(detail::binary, signy) : half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1));

+		}

+		if(!absy)

+			return signx ? half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1)) : y;

+		if(!absx)

+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1));

+		int d = (absy>>10) + (absy<=0x3FF) - (absx>>10) - (absx<=0x3FF);

+		if(d > (signx ? 18 : 12))

+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1));

+		if(signx && d < -11)

+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1));

+		if(!signx && d < ((half::round_style==std::round_toward_zero) ? -15 : -9))

+		{

+			for(; absy<0x400; absy<<=1,--d) ;

+			detail::uint32 mx = ((absx<<1)&0x7FF) | 0x800, my = ((absy<<1)&0x7FF) | 0x800;

+			int i = my < mx;

+			d -= i;

+			if(d < -25)

+				return half(detail::binary, detail::underflow<half::round_style>(signy));

+			my <<= 11 + i;

+			return half(detail::binary, detail::fixed2half<half::round_style,11,false,false,true>(my/mx, d+14, signy, my%mx!=0));

+		}

+		detail::uint32 m = detail::atan2(	((absy&0x3FF)|((absy>0x3FF)<<10))<<(19+((d<0) ? d : (d>0) ? 0 : -1)),

+											((absx&0x3FF)|((absx>0x3FF)<<10))<<(19-((d>0) ? d : (d<0) ? 0 : 1)));

+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,true,true>(signx ? (0xC90FDAA2-m) : m, 15, signy, signx));

+	#endif

+	}

+

+	/// \}

+	/// \anchor hyperbolic

+	/// \name Hyperbolic functions

+	/// \{

+

+	/// Hyperbolic sine.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::sinh](https://en.cppreference.com/w/cpp/numeric/math/sinh).

+	/// \param arg function argument

+	/// \return hyperbolic sine value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half sinh(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::sinh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp;

+		if(!abs || abs >= 0x7C00)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		if(abs <= 0x2900)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));

+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 29 : 27);

+		detail::uint32 m = mm.first - mm.second;

+		for(exp+=13; m<0x80000000 && exp; m<<=1,--exp) ;

+		unsigned int sign = arg.data_ & 0x8000;

+		if(exp > 29)

+			return half(detail::binary, detail::overflow<half::round_style>(sign));

+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,true>(m, exp, sign));

+	#endif

+	}

+

+	/// Hyperbolic cosine.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::cosh](https://en.cppreference.com/w/cpp/numeric/math/cosh).

+	/// \param arg function argument

+	/// \return hyperbolic cosine value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half cosh(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::cosh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp;

+		if(!abs)

+			return half(detail::binary, 0x3C00);

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : 0x7C00);

+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 23 : 26);

+		detail::uint32 m = mm.first + mm.second, i = (~m&0xFFFFFFFF) >> 31;

+		m = (m>>i) | (m&i) | 0x80000000;

+		if((exp+=13+i) > 29)

+			return half(detail::binary, detail::overflow<half::round_style>());

+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,true>(m, exp));

+	#endif

+	}

+

+	/// Hyperbolic tangent.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::tanh](https://en.cppreference.com/w/cpp/numeric/math/tanh).

+	/// \param arg function argument

+	/// \return hyperbolic tangent value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half tanh(half arg)

+	{

+	#ifdef HALF_ARITHMETIC_TYPE

+		return half(detail::binary, detail::float2half<half::round_style>(std::tanh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp;

+		if(!abs)

+			return arg;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_-0x4000));

+		if(abs >= 0x4500)

+			return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));

+		if(abs < 0x2700)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));

+		if(half::round_style != std::round_to_nearest && abs == 0x2D3F)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-3, 0, 1));

+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, 27);

+		detail::uint32 my = mm.first - mm.second - (half::round_style!=std::round_to_nearest), mx = mm.first + mm.second, i = (~mx&0xFFFFFFFF) >> 31;

+		for(exp=13; my<0x80000000; my<<=1,--exp) ;

+		mx = (mx>>i) | 0x80000000;

+		return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp-i, arg.data_&0x8000));

+	#endif

+	}

+

+	/// Hyperbolic area sine.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::asinh](https://en.cppreference.com/w/cpp/numeric/math/asinh).

+	/// \param arg function argument

+	/// \return area sine value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half asinh(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::asinh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF;

+		if(!abs || abs >= 0x7C00)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		if(abs <= 0x2900)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));

+		if(half::round_style != std::round_to_nearest)

+			switch(abs)

+			{

+				case 0x32D4: return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-13, 1, 1));

+				case 0x3B5B: return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-197, 1, 1));

+			}

+		return half(detail::binary, detail::area<half::round_style,true>(arg.data_));

+	#endif

+	}

+

+	/// Hyperbolic area cosine.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::acosh](https://en.cppreference.com/w/cpp/numeric/math/acosh).

+	/// \param arg function argument

+	/// \return area cosine value of \a arg

+	/// \exception FE_INVALID for signaling NaN or arguments <1

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half acosh(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::acosh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF;

+		if((arg.data_&0x8000) || abs < 0x3C00)

+			return half(detail::binary, (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs == 0x3C00)

+			return half(detail::binary, 0);

+		if(arg.data_ >= 0x7C00)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		return half(detail::binary, detail::area<half::round_style,false>(arg.data_));

+	#endif

+	}

+

+	/// Hyperbolic area tangent.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::atanh](https://en.cppreference.com/w/cpp/numeric/math/atanh).

+	/// \param arg function argument

+	/// \return area tangent value of \a arg

+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1

+	/// \exception FE_DIVBYZERO for +/-1

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half atanh(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::atanh(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF, exp = 0;

+		if(!abs)

+			return arg;

+		if(abs >= 0x3C00)

+			return half(detail::binary, (abs==0x3C00) ? detail::pole(arg.data_&0x8000) : (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_));

+		if(abs < 0x2700)

+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));

+		detail::uint32 m = static_cast<detail::uint32>((abs&0x3FF)|((abs>0x3FF)<<10)) << ((abs>>10)+(abs<=0x3FF)+6), my = 0x80000000 + m, mx = 0x80000000 - m;

+		for(; mx<0x80000000; mx<<=1,++exp) ;

+		int i = my >= mx, s;

+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(detail::log2(

+			(detail::divide64(my>>i, mx, s)+1)>>1, 27)+0x10, exp+i-1, 16, arg.data_&0x8000));

+	#endif

+	}

+

+	/// \}

+	/// \anchor special

+	/// \name Error and gamma functions

+	/// \{

+

+	/// Error function.

+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.

+	///

+	/// **See also:** Documentation for [std::erf](https://en.cppreference.com/w/cpp/numeric/math/erf).

+	/// \param arg function argument

+	/// \return error function value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half erf(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::erf(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF;

+		if(!abs || abs >= 0x7C00)

+			return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (arg.data_-0x4000) : detail::signal(arg.data_)) : arg;

+		if(abs >= 0x4200)

+			return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));

+		return half(detail::binary, detail::erf<half::round_style,false>(arg.data_));

+	#endif

+	}

+

+	/// Complementary error function.

+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.

+	///

+	/// **See also:** Documentation for [std::erfc](https://en.cppreference.com/w/cpp/numeric/math/erfc).

+	/// \param arg function argument

+	/// \return 1 minus error function value of \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half erfc(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::erfc(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;

+		if(abs >= 0x7C00)

+			return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (sign>>1) : detail::signal(arg.data_)) : arg;

+		if(!abs)

+			return half(detail::binary, 0x3C00);

+		if(abs >= 0x4400)

+			return half(detail::binary, detail::rounded<half::round_style,true>((sign>>1)-(sign>>15), sign>>15, 1));

+		return half(detail::binary, detail::erf<half::round_style,true>(arg.data_));

+	#endif

+	}

+

+	/// Natural logarithm of gamma function.

+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.025% of inputs.

+	///

+	/// **See also:** Documentation for [std::lgamma](https://en.cppreference.com/w/cpp/numeric/math/lgamma).

+	/// \param arg function argument

+	/// \return natural logarith of gamma function for \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_DIVBYZERO for 0 or negative integer arguments

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half lgamma(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::lgamma(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		int abs = arg.data_ & 0x7FFF;

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_));

+		if(!abs || arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1))))

+			return half(detail::binary, detail::pole());

+		if(arg.data_ == 0x3C00 || arg.data_ == 0x4000)

+			return half(detail::binary, 0);

+		return half(detail::binary, detail::gamma<half::round_style,true>(arg.data_));

+	#endif

+	}

+

+	/// Gamma function.

+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.25% of inputs.

+	///

+	/// **See also:** Documentation for [std::tgamma](https://en.cppreference.com/w/cpp/numeric/math/tgamma).

+	/// \param arg function argument

+	/// \return gamma function value of \a arg

+	/// \exception FE_INVALID for signaling NaN, negative infinity or negative integer arguments

+	/// \exception FE_DIVBYZERO for 0

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half tgamma(half arg)

+	{

+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH

+		return half(detail::binary, detail::float2half<half::round_style>(std::tgamma(detail::half2float<detail::internal_t>(arg.data_))));

+	#else

+		unsigned int abs = arg.data_ & 0x7FFF;

+		if(!abs)

+			return half(detail::binary, detail::pole(arg.data_));

+		if(abs >= 0x7C00)

+			return (arg.data_==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));

+		if(arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1))))

+			return half(detail::binary, detail::invalid());

+		if(arg.data_ >= 0xCA80)

+			return half(detail::binary, detail::underflow<half::round_style>((1-((abs>>(25-(abs>>10)))&1))<<15));

+		if(arg.data_ <= 0x100 || (arg.data_ >= 0x4900 && arg.data_ < 0x8000))

+			return half(detail::binary, detail::overflow<half::round_style>());

+		if(arg.data_ == 0x3C00)

+			return arg;

+		return half(detail::binary, detail::gamma<half::round_style,false>(arg.data_));

+	#endif

+	}

+

+	/// \}

+	/// \anchor rounding

+	/// \name Rounding

+	/// \{

+

+	/// Nearest integer not less than half value.

+	/// **See also:** Documentation for [std::ceil](https://en.cppreference.com/w/cpp/numeric/math/ceil).

+	/// \param arg half to round

+	/// \return nearest integer not less than \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT if value had to be rounded

+	inline half ceil(half arg) { return half(detail::binary, detail::integral<std::round_toward_infinity,true,true>(arg.data_)); }

+

+	/// Nearest integer not greater than half value.

+	/// **See also:** Documentation for [std::floor](https://en.cppreference.com/w/cpp/numeric/math/floor).

+	/// \param arg half to round

+	/// \return nearest integer not greater than \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT if value had to be rounded

+	inline half floor(half arg) { return half(detail::binary, detail::integral<std::round_toward_neg_infinity,true,true>(arg.data_)); }

+

+	/// Nearest integer not greater in magnitude than half value.

+	/// **See also:** Documentation for [std::trunc](https://en.cppreference.com/w/cpp/numeric/math/trunc).

+	/// \param arg half to round

+	/// \return nearest integer not greater in magnitude than \a arg

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT if value had to be rounded

+	inline half trunc(half arg) { return half(detail::binary, detail::integral<std::round_toward_zero,true,true>(arg.data_)); }

+

+	/// Nearest integer.

+	/// **See also:** Documentation for [std::round](https://en.cppreference.com/w/cpp/numeric/math/round).

+	/// \param arg half to round

+	/// \return nearest integer, rounded away from zero in half-way cases

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT if value had to be rounded

+	inline half round(half arg) { return half(detail::binary, detail::integral<std::round_to_nearest,false,true>(arg.data_)); }

+

+	/// Nearest integer.

+	/// **See also:** Documentation for [std::lround](https://en.cppreference.com/w/cpp/numeric/math/round).

+	/// \param arg half to round

+	/// \return nearest integer, rounded away from zero in half-way cases

+	/// \exception FE_INVALID if value is not representable as `long`

+	inline long lround(half arg) { return detail::half2int<std::round_to_nearest,false,false,long>(arg.data_); }

+

+	/// Nearest integer using half's internal rounding mode.

+	/// **See also:** Documentation for [std::rint](https://en.cppreference.com/w/cpp/numeric/math/rint).

+	/// \param arg half expression to round

+	/// \return nearest integer using default rounding mode

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_INEXACT if value had to be rounded

+	inline half rint(half arg) { return half(detail::binary, detail::integral<half::round_style,true,true>(arg.data_)); }

+

+	/// Nearest integer using half's internal rounding mode.

+	/// **See also:** Documentation for [std::lrint](https://en.cppreference.com/w/cpp/numeric/math/rint).

+	/// \param arg half expression to round

+	/// \return nearest integer using default rounding mode

+	/// \exception FE_INVALID if value is not representable as `long`

+	/// \exception FE_INEXACT if value had to be rounded

+	inline long lrint(half arg) { return detail::half2int<half::round_style,true,true,long>(arg.data_); }

+

+	/// Nearest integer using half's internal rounding mode.

+	/// **See also:** Documentation for [std::nearbyint](https://en.cppreference.com/w/cpp/numeric/math/nearbyint).

+	/// \param arg half expression to round

+	/// \return nearest integer using default rounding mode

+	/// \exception FE_INVALID for signaling NaN

+	inline half nearbyint(half arg) { return half(detail::binary, detail::integral<half::round_style,true,false>(arg.data_)); }

+#if HALF_ENABLE_CPP11_LONG_LONG

+	/// Nearest integer.

+	/// **See also:** Documentation for [std::llround](https://en.cppreference.com/w/cpp/numeric/math/round).

+	/// \param arg half to round

+	/// \return nearest integer, rounded away from zero in half-way cases

+	/// \exception FE_INVALID if value is not representable as `long long`

+	inline long long llround(half arg) { return detail::half2int<std::round_to_nearest,false,false,long long>(arg.data_); }

+

+	/// Nearest integer using half's internal rounding mode.

+	/// **See also:** Documentation for [std::llrint](https://en.cppreference.com/w/cpp/numeric/math/rint).

+	/// \param arg half expression to round

+	/// \return nearest integer using default rounding mode

+	/// \exception FE_INVALID if value is not representable as `long long`

+	/// \exception FE_INEXACT if value had to be rounded

+	inline long long llrint(half arg) { return detail::half2int<half::round_style,true,true,long long>(arg.data_); }

+#endif

+

+	/// \}

+	/// \anchor float

+	/// \name Floating point manipulation

+	/// \{

+

+	/// Decompress floating-point number.

+	/// **See also:** Documentation for [std::frexp](https://en.cppreference.com/w/cpp/numeric/math/frexp).

+	/// \param arg number to decompress

+	/// \param exp address to store exponent at

+	/// \return significant in range [0.5, 1)

+	/// \exception FE_INVALID for signaling NaN

+	inline half frexp(half arg, int *exp)

+	{

+		*exp = 0;

+		unsigned int abs = arg.data_ & 0x7FFF;

+		if(abs >= 0x7C00 || !abs)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		for(; abs<0x400; abs<<=1,--*exp) ;

+		*exp += (abs>>10) - 14;

+		return half(detail::binary, (arg.data_&0x8000)|0x3800|(abs&0x3FF));

+	}

+

+	/// Multiply by power of two.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::scalbln](https://en.cppreference.com/w/cpp/numeric/math/scalbn).

+	/// \param arg number to modify

+	/// \param exp power of two to multiply with

+	/// \return \a arg multplied by 2 raised to \a exp

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half scalbln(half arg, long exp)

+	{

+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;

+		if(abs >= 0x7C00 || !abs)

+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;

+		for(; abs<0x400; abs<<=1,--exp) ;

+		exp += abs >> 10;

+		if(exp > 30)

+			return half(detail::binary, detail::overflow<half::round_style>(sign));

+		else if(exp < -10)

+			return half(detail::binary, detail::underflow<half::round_style>(sign));

+		else if(exp > 0)

+			return half(detail::binary, sign|(exp<<10)|(abs&0x3FF));

+		unsigned int m = (abs&0x3FF) | 0x400;

+		return half(detail::binary, detail::rounded<half::round_style,false>(sign|(m>>(1-exp)), (m>>-exp)&1, (m&((1<<-exp)-1))!=0));

+	}

+

+	/// Multiply by power of two.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::scalbn](https://en.cppreference.com/w/cpp/numeric/math/scalbn).

+	/// \param arg number to modify

+	/// \param exp power of two to multiply with

+	/// \return \a arg multplied by 2 raised to \a exp

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half scalbn(half arg, int exp) { return scalbln(arg, exp); }

+

+	/// Multiply by power of two.

+	/// This function is exact to rounding for all rounding modes.

+	///

+	/// **See also:** Documentation for [std::ldexp](https://en.cppreference.com/w/cpp/numeric/math/ldexp).

+	/// \param arg number to modify

+	/// \param exp power of two to multiply with

+	/// \return \a arg multplied by 2 raised to \a exp

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	inline half ldexp(half arg, int exp) { return scalbln(arg, exp); }

+

+	/// Extract integer and fractional parts.

+	/// **See also:** Documentation for [std::modf](https://en.cppreference.com/w/cpp/numeric/math/modf).

+	/// \param arg number to decompress

+	/// \param iptr address to store integer part at

+	/// \return fractional part

+	/// \exception FE_INVALID for signaling NaN

+	inline half modf(half arg, half *iptr)

+	{

+		unsigned int abs = arg.data_ & 0x7FFF;

+		if(abs > 0x7C00)

+		{

+			arg = half(detail::binary, detail::signal(arg.data_));

+			return *iptr = arg, arg;

+		}

+		if(abs >= 0x6400)

+			return *iptr = arg, half(detail::binary, arg.data_&0x8000);

+		if(abs < 0x3C00)

+			return iptr->data_ = arg.data_ & 0x8000, arg;

+		unsigned int exp = abs >> 10, mask = (1<<(25-exp)) - 1, m = arg.data_ & mask;

+		iptr->data_ = arg.data_ & ~mask;

+		if(!m)

+			return half(detail::binary, arg.data_&0x8000);

+		for(; m<0x400; m<<=1,--exp) ;

+		return half(detail::binary, (arg.data_&0x8000)|(exp<<10)|(m&0x3FF));

+	}

+

+	/// Extract exponent.

+	/// **See also:** Documentation for [std::ilogb](https://en.cppreference.com/w/cpp/numeric/math/ilogb).

+	/// \param arg number to query

+	/// \return floating-point exponent

+	/// \retval FP_ILOGB0 for zero

+	/// \retval FP_ILOGBNAN for NaN

+	/// \retval INT_MAX for infinity

+	/// \exception FE_INVALID for 0 or infinite values

+	inline int ilogb(half arg)

+	{

+		int abs = arg.data_ & 0x7FFF, exp;

+		if(!abs || abs >= 0x7C00)

+		{

+			detail::raise(FE_INVALID);

+			return !abs ? FP_ILOGB0 : (abs==0x7C00) ? INT_MAX : FP_ILOGBNAN;

+		}

+		for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ;

+		return exp;

+	}

+

+	/// Extract exponent.

+	/// **See also:** Documentation for [std::logb](https://en.cppreference.com/w/cpp/numeric/math/logb).

+	/// \param arg number to query

+	/// \return floating-point exponent

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_DIVBYZERO for 0

+	inline half logb(half arg)

+	{

+		int abs = arg.data_ & 0x7FFF, exp;

+		if(!abs)

+			return half(detail::binary, detail::pole(0x8000));

+		if(abs >= 0x7C00)

+			return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_));

+		for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ;

+		unsigned int value = static_cast<unsigned>(exp<0) << 15;

+		if(exp)

+		{

+			unsigned int m = std::abs(exp) << 6;

+			for(exp=18; m<0x400; m<<=1,--exp) ;

+			value |= (exp<<10) + m;

+		}

+		return half(detail::binary, value);

+	}

+

+	/// Next representable value.

+	/// **See also:** Documentation for [std::nextafter](https://en.cppreference.com/w/cpp/numeric/math/nextafter).

+	/// \param from value to compute next representable value for

+	/// \param to direction towards which to compute next value

+	/// \return next representable value after \a from in direction towards \a to

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW for infinite result from finite argument

+	/// \exception FE_UNDERFLOW for subnormal result

+	inline half nextafter(half from, half to)

+	{

+		int fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;

+		if(fabs > 0x7C00 || tabs > 0x7C00)

+			return half(detail::binary, detail::signal(from.data_, to.data_));

+		if(from.data_ == to.data_ || !(fabs|tabs))

+			return to;

+		if(!fabs)

+		{

+			detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);

+			return half(detail::binary, (to.data_&0x8000)+1);

+		}

+		unsigned int out = from.data_ + (((from.data_>>15)^static_cast<unsigned>(

+			(from.data_^(0x8000|(0x8000-(from.data_>>15))))<(to.data_^(0x8000|(0x8000-(to.data_>>15))))))<<1) - 1;

+		detail::raise(FE_OVERFLOW, fabs<0x7C00 && (out&0x7C00)==0x7C00);

+		detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out&0x7C00)<0x400);

+		return half(detail::binary, out);

+	}

+

+	/// Next representable value.

+	/// **See also:** Documentation for [std::nexttoward](https://en.cppreference.com/w/cpp/numeric/math/nexttoward).

+	/// \param from value to compute next representable value for

+	/// \param to direction towards which to compute next value

+	/// \return next representable value after \a from in direction towards \a to

+	/// \exception FE_INVALID for signaling NaN

+	/// \exception FE_OVERFLOW for infinite result from finite argument

+	/// \exception FE_UNDERFLOW for subnormal result

+	inline half nexttoward(half from, long double to)

+	{

+		int fabs = from.data_ & 0x7FFF;

+		if(fabs > 0x7C00)

+			return half(detail::binary, detail::signal(from.data_));

+		long double lfrom = static_cast<long double>(from);

+		if(detail::builtin_isnan(to) || lfrom == to)

+			return half(static_cast<float>(to));

+		if(!fabs)

+		{

+			detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);

+			return half(detail::binary, (static_cast<unsigned>(detail::builtin_signbit(to))<<15)+1);

+		}

+		unsigned int out = from.data_ + (((from.data_>>15)^static_cast<unsigned>(lfrom<to))<<1) - 1;

+		detail::raise(FE_OVERFLOW, (out&0x7FFF)==0x7C00);

+		detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out&0x7FFF)<0x400);

+		return half(detail::binary, out);

+	}

+

+	/// Take sign.

+	/// **See also:** Documentation for [std::copysign](https://en.cppreference.com/w/cpp/numeric/math/copysign).

+	/// \param x value to change sign for

+	/// \param y value to take sign from

+	/// \return value equal to \a x in magnitude and to \a y in sign

+	inline HALF_CONSTEXPR half copysign(half x, half y) { return half(detail::binary, x.data_^((x.data_^y.data_)&0x8000)); }

+

+	/// \}

+	/// \anchor classification

+	/// \name Floating point classification

+	/// \{

+

+	/// Classify floating-point value.

+	/// **See also:** Documentation for [std::fpclassify](https://en.cppreference.com/w/cpp/numeric/math/fpclassify).

+	/// \param arg number to classify

+	/// \retval FP_ZERO for positive and negative zero

+	/// \retval FP_SUBNORMAL for subnormal numbers

+	/// \retval FP_INFINITY for positive and negative infinity

+	/// \retval FP_NAN for NaNs

+	/// \retval FP_NORMAL for all other (normal) values

+	inline HALF_CONSTEXPR int fpclassify(half arg)

+	{

+		return	!(arg.data_&0x7FFF) ? FP_ZERO :

+				((arg.data_&0x7FFF)<0x400) ? FP_SUBNORMAL :

+				((arg.data_&0x7FFF)<0x7C00) ? FP_NORMAL :

+				((arg.data_&0x7FFF)==0x7C00) ? FP_INFINITE :

+				FP_NAN;

+	}

+

+	/// Check if finite number.

+	/// **See also:** Documentation for [std::isfinite](https://en.cppreference.com/w/cpp/numeric/math/isfinite).

+	/// \param arg number to check

+	/// \retval true if neither infinity nor NaN

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }

+

+	/// Check for infinity.

+	/// **See also:** Documentation for [std::isinf](https://en.cppreference.com/w/cpp/numeric/math/isinf).

+	/// \param arg number to check

+	/// \retval true for positive or negative infinity

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }

+

+	/// Check for NaN.

+	/// **See also:** Documentation for [std::isnan](https://en.cppreference.com/w/cpp/numeric/math/isnan).

+	/// \param arg number to check

+	/// \retval true for NaNs

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }

+

+	/// Check if normal number.

+	/// **See also:** Documentation for [std::isnormal](https://en.cppreference.com/w/cpp/numeric/math/isnormal).

+	/// \param arg number to check

+	/// \retval true if normal number

+	/// \retval false if either subnormal, zero, infinity or NaN

+	inline HALF_CONSTEXPR bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }

+

+	/// Check sign.

+	/// **See also:** Documentation for [std::signbit](https://en.cppreference.com/w/cpp/numeric/math/signbit).

+	/// \param arg number to check

+	/// \retval true for negative number

+	/// \retval false for positive number

+	inline HALF_CONSTEXPR bool signbit(half arg) { return (arg.data_&0x8000) != 0; }

+

+	/// \}

+	/// \anchor compfunc

+	/// \name Comparison

+	/// \{

+

+	/// Quiet comparison for greater than.

+	/// **See also:** Documentation for [std::isgreater](https://en.cppreference.com/w/cpp/numeric/math/isgreater).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x greater than \a y

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isgreater(half x, half y)

+	{

+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);

+	}

+

+	/// Quiet comparison for greater equal.

+	/// **See also:** Documentation for [std::isgreaterequal](https://en.cppreference.com/w/cpp/numeric/math/isgreaterequal).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x greater equal \a y

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isgreaterequal(half x, half y)

+	{

+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);

+	}

+

+	/// Quiet comparison for less than.

+	/// **See also:** Documentation for [std::isless](https://en.cppreference.com/w/cpp/numeric/math/isless).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x less than \a y

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isless(half x, half y)

+	{

+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);

+	}

+

+	/// Quiet comparison for less equal.

+	/// **See also:** Documentation for [std::islessequal](https://en.cppreference.com/w/cpp/numeric/math/islessequal).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if \a x less equal \a y

+	/// \retval false else

+	inline HALF_CONSTEXPR bool islessequal(half x, half y)

+	{

+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);

+	}

+

+	/// Quiet comarison for less or greater.

+	/// **See also:** Documentation for [std::islessgreater](https://en.cppreference.com/w/cpp/numeric/math/islessgreater).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if either less or greater

+	/// \retval false else

+	inline HALF_CONSTEXPR bool islessgreater(half x, half y)

+	{

+		return x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF) && !isnan(x) && !isnan(y);

+	}

+

+	/// Quiet check if unordered.

+	/// **See also:** Documentation for [std::isunordered](https://en.cppreference.com/w/cpp/numeric/math/isunordered).

+	/// \param x first operand

+	/// \param y second operand

+	/// \retval true if unordered (one or two NaN operands)

+	/// \retval false else

+	inline HALF_CONSTEXPR bool isunordered(half x, half y) { return isnan(x) || isnan(y); }

+

+	/// \}

+	/// \anchor casting

+	/// \name Casting

+	/// \{

+

+	/// Cast to or from half-precision floating-point number.

+	/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted 

+	/// directly using the default rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.

+	///

+	/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types 

+	/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler 

+	/// error and casting between [half](\ref half_float::half)s returns the argument unmodified.

+	/// \tparam T destination type (half or built-in arithmetic type)

+	/// \tparam U source type (half or built-in arithmetic type)

+	/// \param arg value to cast

+	/// \return \a arg converted to destination type

+	/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	template<typename T,typename U> T half_cast(U arg) { return detail::half_caster<T,U>::cast(arg); }

+

+	/// Cast to or from half-precision floating-point number.

+	/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted 

+	/// directly using the specified rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.

+	///

+	/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types 

+	/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler 

+	/// error and casting between [half](\ref half_float::half)s returns the argument unmodified.

+	/// \tparam T destination type (half or built-in arithmetic type)

+	/// \tparam R rounding mode to use.

+	/// \tparam U source type (half or built-in arithmetic type)

+	/// \param arg value to cast

+	/// \return \a arg converted to destination type

+	/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T

+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

+	template<typename T,std::float_round_style R,typename U> T half_cast(U arg) { return detail::half_caster<T,U,R>::cast(arg); }

+	/// \}

+

+	/// \}

+	/// \anchor errors

+	/// \name Error handling

+	/// \{

+

+	/// Clear exception flags.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	///

+	/// **See also:** Documentation for [std::feclearexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feclearexcept).

+	/// \param excepts OR of exceptions to clear

+	/// \retval 0 all selected flags cleared successfully

+	inline int feclearexcept(int excepts) { detail::errflags() &= ~excepts; return 0; }

+

+	/// Test exception flags.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	///

+	/// **See also:** Documentation for [std::fetestexcept](https://en.cppreference.com/w/cpp/numeric/fenv/fetestexcept).

+	/// \param excepts OR of exceptions to test

+	/// \return OR of selected exceptions if raised

+	inline int fetestexcept(int excepts) { return detail::errflags() & excepts; }

+

+	/// Raise exception flags.

+	/// This raises the specified floating point exceptions and also invokes any additional automatic exception handling as 

+	/// configured with the [HALF_ERRHANDLIG_...](\ref HALF_ERRHANDLING_ERRNO) preprocessor symbols.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	///

+	/// **See also:** Documentation for [std::feraiseexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feraiseexcept).

+	/// \param excepts OR of exceptions to raise

+	/// \retval 0 all selected exceptions raised successfully

+	inline int feraiseexcept(int excepts) { detail::errflags() |= excepts; detail::raise(excepts); return 0; }

+

+	/// Save exception flags.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	///

+	/// **See also:** Documentation for [std::fegetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag).

+	/// \param flagp adress to store flag state at

+	/// \param excepts OR of flags to save

+	/// \retval 0 for success

+	inline int fegetexceptflag(int *flagp, int excepts) { *flagp = detail::errflags() & excepts; return 0; }

+

+	/// Restore exception flags.

+	/// This only copies the specified exception state (including unset flags) without incurring any additional exception handling.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	///

+	/// **See also:** Documentation for [std::fesetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag).

+	/// \param flagp adress to take flag state from

+	/// \param excepts OR of flags to restore

+	/// \retval 0 for success

+	inline int fesetexceptflag(const int *flagp, int excepts) { detail::errflags() = (detail::errflags()|(*flagp&excepts)) & (*flagp|~excepts); return 0; }

+

+	/// Throw C++ exceptions based on set exception flags.

+	/// This function manually throws a corresponding C++ exception if one of the specified flags is set, 

+	/// no matter if automatic throwing (via [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID)) is enabled or not.

+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 

+	/// but in that case manual flag management is the only way to raise flags.

+	/// \param excepts OR of exceptions to test

+	/// \param msg error message to use for exception description

+	/// \throw std::domain_error if `FE_INVALID` or `FE_DIVBYZERO` is selected and set

+	/// \throw std::overflow_error if `FE_OVERFLOW` is selected and set

+	/// \throw std::underflow_error if `FE_UNDERFLOW` is selected and set

+	/// \throw std::range_error if `FE_INEXACT` is selected and set

+	inline void fethrowexcept(int excepts, const char *msg = "")

+	{

+		excepts &= detail::errflags();

+		if(excepts & (FE_INVALID|FE_DIVBYZERO))

+			throw std::domain_error(msg);

+		if(excepts & FE_OVERFLOW)

+			throw std::overflow_error(msg);

+		if(excepts & FE_UNDERFLOW)

+			throw std::underflow_error(msg);

+		if(excepts & FE_INEXACT)

+			throw std::range_error(msg);

+	}

+	/// \}

+}

+

+

+#undef HALF_UNUSED_NOERR

+#undef HALF_CONSTEXPR

+#undef HALF_CONSTEXPR_CONST

+#undef HALF_CONSTEXPR_NOERR

+#undef HALF_NOEXCEPT

+#undef HALF_NOTHROW

+#undef HALF_THREAD_LOCAL

+#undef HALF_TWOS_COMPLEMENT_INT

+#ifdef HALF_POP_WARNINGS

+	#pragma warning(pop)

+	#undef HALF_POP_WARNINGS

+#endif

+

+#endif