From af50cc5e3fe7eb3e75c349292f3ac3621e0b424f Mon Sep 17 00:00:00 2001
From: Chen Feiyue <69809761+chenfeiyue-cfy@users.noreply.github.com>
Date: Sat, 12 Aug 2023 10:04:16 +0800
Subject: [PATCH] Added general Float16 support (#631)

Added Float16 type definition from third-party
Refine float16 bias handlling in conv2d
Refine float16 case in conv2d
Caution: Headers of float16 only be included when build unit_test

Type: New Feature

Signed-off-by: Feiyue Chen <Feiyue.Chen@verisilicon.com>
---
 BUILD                                  |    2 +
 CMakeLists.txt                         |    2 +
 include/tim/vx/ops/conv2d.h            |    3 -
 src/tim/vx/ops/conv2d.cc               |   28 +-
 src/tim/vx/ops/conv2d_test.cc          |  354 +--
 third_party/half/ChangeLog.txt         |  184 ++
 third_party/half/ChangeLog.txt.license |    4 +
 third_party/half/LICENSE.spdx          |    7 +
 third_party/half/LICENSE.txt           |   21 +
 third_party/half/README.txt            |  288 +++
 third_party/half/README.txt.license    |    4 +
 third_party/half/half.hpp              | 3070 ++++++++++++++++++++++++
 12 files changed, 3771 insertions(+), 196 deletions(-)
 create mode 100644 third_party/half/ChangeLog.txt
 create mode 100644 third_party/half/ChangeLog.txt.license
 create mode 100644 third_party/half/LICENSE.spdx
 create mode 100644 third_party/half/LICENSE.txt
 create mode 100644 third_party/half/README.txt
 create mode 100644 third_party/half/README.txt.license
 create mode 100644 third_party/half/half.hpp

diff --git a/BUILD b/BUILD
index 0fcaf9f..368e645 100644
--- a/BUILD
+++ b/BUILD
@@ -134,8 +134,10 @@ cc_binary(
 cc_test (
     name = "unit_test",
     copts = ["-std=c++14", "-Werror"],
+    includes = ["third_party/half"],
     srcs = [
         "src/tim/vx/test_utils.h",
+        "third_party/half/half.hpp"
     ] + glob(["src/tim/**/*_test.cc"]),
     deps = [
         "@gtest//:gtest",
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 72691e6..f77c8c4 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -98,6 +98,8 @@ if(TIM_VX_ENABLE_TEST)
         FetchContent_Populate(googletest)
         add_subdirectory(${googletest_SOURCE_DIR} ${googletest_BINARY_DIR})
     endif()
+
+    include_directories(third_party/half)
 endif()
 
 if(TIM_VX_ENABLE_GRPC)
diff --git a/include/tim/vx/ops/conv2d.h b/include/tim/vx/ops/conv2d.h
index f609960..72b2265 100644
--- a/include/tim/vx/ops/conv2d.h
+++ b/include/tim/vx/ops/conv2d.h
@@ -99,12 +99,9 @@ class Conv2d : public BuiltinOp {
   const int32_t multiplier_;
   const DataLayout kernel_layout_;
 
-#if defined(__clang__) && (__clang_major__ >= 15)
-#define TIM_VX_OPS_CONV2D_WITH_F16BIAS 1
  private:
   void OnBindInputPostProc(const std::shared_ptr<Tensor>& tensor,
                            int32_t input_idx) override;
-#endif
 };
 
 }  // namespace ops
diff --git a/src/tim/vx/ops/conv2d.cc b/src/tim/vx/ops/conv2d.cc
index 4f93b1c..d5130db 100644
--- a/src/tim/vx/ops/conv2d.cc
+++ b/src/tim/vx/ops/conv2d.cc
@@ -42,8 +42,8 @@ Conv2d::Conv2d(Graph* graph, const std::array<uint32_t, 4> pad,
                const std::array<uint32_t, 2>& stride,
                const std::array<uint32_t, 2>& dilation, int32_t multiplier,
                DataLayout input_layout, DataLayout kernel_layout)
-    : Conv2d(graph, 0, PadType::AUTO, {0, 0}, stride, dilation, pad,
-             multiplier, input_layout, kernel_layout) {}
+    : Conv2d(graph, 0, PadType::AUTO, {0, 0}, stride, dilation, pad, multiplier,
+             input_layout, kernel_layout) {}
 
 Conv2d::Conv2d(Graph* graph, int32_t weights, PadType padding,
                const std::array<uint32_t, 2>& ksize,
@@ -88,41 +88,33 @@ std::shared_ptr<Operation> Conv2d::Clone(std::shared_ptr<Graph>& graph) const {
       this->kernel_layout_);
 }
 
-const std::vector<std::shared_ptr<Tensor>> Conv2d::ConstantInputsTensor() const {
-   if (this->IsAllInputsConst()) {
+const std::vector<std::shared_ptr<Tensor>> Conv2d::ConstantInputsTensor()
+    const {
+  if (this->IsAllInputsConst()) {
     return {this->impl_->inputs_tensor_[0]};
   } else {
     return {};
   }
 }
 
-// Handle float16 bias if clang compiler is no less than 15.0.0 version
-#ifdef TIM_VX_OPS_CONV2D_WITH_F16BIAS
+// Handle float16 bias
 void Conv2d::OnBindInputPostProc(const std::shared_ptr<Tensor>& tensor,
                                  int32_t input_idx) {
   if (tensor->GetDataType() == vx::DataType::FLOAT16 &&
       tensor->IsConstTensor() && impl_->inputs_tensor_.size() == 3) {
-    uint32_t bias_size = 1;
-    for (auto i : tensor->GetShape()) {
-      bias_size *= i;
-    }
-    std::vector<_Float16> in(bias_size);
-    tensor->CopyDataFromTensor(in.data());
+    float* float32_bias = tensor->ConvertTensorToFloat32Data();
 
-    std::vector<float> out(bias_size);
-    for (uint i = 0; i < bias_size; i++) {
-      out[i] = static_cast<float>(in[i]);
-    }
     TensorSpec fp32bias_spec(tim::vx::DataType::FLOAT32, tensor->GetShape(),
                              tim::vx::TensorAttribute::CONSTANT);
-    auto out_tensor = impl_->graph_->CreateTensor(fp32bias_spec, out.data());
+
+    auto out_tensor = impl_->graph_->CreateTensor(fp32bias_spec, float32_bias);
+    vsi_nn_Free(float32_bias);
 
     impl_->inputs_tensor_[2] = out_tensor;
     impl_->node()->input.tensors[input_idx] = out_tensor->GetId();
     impl_->graph_->RenewTensorConsumersMap(tensor, out_tensor, this);
   }
 }
-#endif
 
 }  // namespace ops
 }  // namespace vx
diff --git a/src/tim/vx/ops/conv2d_test.cc b/src/tim/vx/ops/conv2d_test.cc
index 77db127..5332cf0 100644
--- a/src/tim/vx/ops/conv2d_test.cc
+++ b/src/tim/vx/ops/conv2d_test.cc
@@ -28,11 +28,12 @@
 #include "tim/vx/context.h"
 #include "tim/vx/graph.h"
 #include "tim/vx/types.h"
+#include "third_party/half/half.hpp"
 
-#ifdef TIM_VX_OPS_CONV2D_WITH_F16BIAS
 TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) {
   auto ctx = tim::vx::Context::Create();
   auto graph = ctx->CreateGraph();
+  using namespace half_float::literal;
 
   tim::vx::ShapeType input_shape({4, 2, 1, 1});   //whcn
   tim::vx::ShapeType weight_shape({2, 2, 1, 3});  //whio
@@ -50,26 +51,29 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) {
                                   tim::vx::TensorAttribute::OUTPUT);
 
   // Input data  nchw
-  std::vector<_Float16> input_data = {
-      1, 1, 1, 1,  // row = 1
-      2, 2, 3, 2   // row = 2
+
+  std::vector<half_float::half> input_data = {
+      1.0_h, 1.0_h, 1.0_h, 1.0_h,  // row = 1
+      2.0_h, 2.0_h, 3.0_h, 2.0_h   // row = 2
   };
 
   // weight data   oihw
-  std::vector<_Float16> weight_data = {
-      1,  2,  3,  4,  //first 2x2 filter
-      -1, 1,  -1, 1,  // second 2x2 filter
-      -1, -1, 1,  1,  // third 2x2 filter
+  std::vector<half_float::half> weight_data = {
+      1.0_h,  2.0_h,  3.0_h,  4.0_h,  //first 2x2 filter
+      -1.0_h, 1.0_h,  -1.0_h, 1.0_h,  // second 2x2 filter
+      -1.0_h, -1.0_h, 1.0_h,  1.0_h,  // third 2x2 filter
   };
 
   // bias data
-  std::vector<_Float16> bias_data = {1, 2, 3};
+  std::vector<half_float::half> bias_data = {1.0_h, 2.0_h, 3.0_h};
 
-  // nchw
-  std::vector<_Float16> golden = {// first channel
-                               18, 22, 21, 8, 7, 9, 8, 3, 2, 3, 1, -1,
-                               // second channel
-                               2, 3, 1, 0, 5, 6, 6, 4, -1, -2, -2, 1};
+  std::vector<half_float::half> golden = {
+      // first channel
+      18.0_h, 22.0_h, 21.0_h, 8.0_h, 7.0_h, 9.0_h, 8.0_h, 3.0_h, 2.0_h, 3.0_h,
+      1.0_h, -1.0_h,
+      // second channel
+      2.0_h, 3.0_h, 1.0_h, 0.0_h, 5.0_h, 6.0_h, 6.0_h, 4.0_h, -1.0_h, -2.0_h,
+      -2.0_h, 1.0_h};
 
   auto input_tensor = graph->CreateTensor(input_spec);
   auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data());
@@ -80,8 +84,8 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -98,11 +102,10 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) {
   for (auto i : output_tensor->GetShape()) {
     output_size *= i;
   }
-  std::vector<_Float16> output(output_size);
+  std::vector<half_float::half> output(output_size);
   EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data()));
-  EXPECT_TRUE(ArraysMatch(golden, output, (_Float16)0.1));
+  EXPECT_TRUE(ArraysMatch(golden, output, (half_float::half)0.1));
 }
-#endif
 
 TEST(Conv2d, shape_4_2_1_1_float32_PaddingTest) {
   auto ctx = tim::vx::Context::Create();
@@ -155,8 +158,8 @@ TEST(Conv2d, shape_4_2_1_1_float32_PaddingTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -224,8 +227,8 @@ TEST(Conv2d, shape_4_2_2_2_float32_PointwiseTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -295,8 +298,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_SimpleTest) {
   std::array<uint32_t, 2> stride({2, 2});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -361,8 +364,8 @@ TEST(Conv2d, shape_4_2_2_2_float32_SimpleChannelsTest) {
   std::array<uint32_t, 2> stride({2, 2});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -432,8 +435,8 @@ TEST(Conv2d, shape_6_3_1_1_float32_SimpleAnisotropicStridesTest) {
   std::array<uint32_t, 2> stride({3, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -497,8 +500,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -562,8 +565,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedConstFilterTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -627,8 +630,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedBiasTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -691,8 +694,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedValidTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -759,8 +762,8 @@ TEST(Conv2d, DISABLED_shape_4_2_2_2_float32_DisabledPointwiseMultifilterTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -827,8 +830,8 @@ TEST(Conv2d, shape_9_9_1_1_float32_SimpleDilationTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({3, 3});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -893,8 +896,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_StrideTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -958,8 +961,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_InputAndFilterSameWidthHeightTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1011,13 +1014,13 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_weight, zero_point_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias,
-                                  zero_point_bias);
+                                     scales_weight, zero_point_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2,
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1047,8 +1050,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) {
 
   std::vector<u_int8_t> input_data =
       Quantize<uint8_t>(input_data_float, scales_input[0], zero_point_input[0]);
-  std::vector<u_int8_t> weight_data =
-      Quantize<uint8_t>(weight_data_float, scales_weight[0], zero_point_input[0]);
+  std::vector<u_int8_t> weight_data = Quantize<uint8_t>(
+      weight_data_float, scales_weight[0], zero_point_input[0]);
   std::vector<int32_t> bias_data =
       Quantize<int32_t>(bias_data_float, scales_bias[0], zero_point_bias[0]);
   std::vector<u_int8_t> golden =
@@ -1062,8 +1065,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) {
   std::array<uint32_t, 2> stride({2, 2});
   std::array<uint32_t, 2> dilation({1, 1});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1094,8 +1097,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) {
   tim::vx::ShapeType output_shape(
       {2, 1, weight_shape[3], input_shape[3]});  //whcn
 
-  float input_min = -128.5, input_max = 128, weight_min = -128.5, weight_max = 128,
-        output_min = -127, output_max = 128;
+  float input_min = -128.5, input_max = 128, weight_min = -128.5,
+        weight_max = 128, output_min = -127, output_max = 128;
 
   std::pair<float, int32_t> scales_zp;
 
@@ -1115,13 +1118,13 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_weight, zero_point_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias,
-                                  zero_point_bias);
+                                     scales_weight, zero_point_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2,
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1151,8 +1154,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) {
 
   std::vector<u_int8_t> input_data =
       Quantize<uint8_t>(input_data_float, scales_input[0], zero_point_input[0]);
-  std::vector<u_int8_t> weight_data =
-      Quantize<uint8_t>(weight_data_float, scales_weight[0], zero_point_input[0]);
+  std::vector<u_int8_t> weight_data = Quantize<uint8_t>(
+      weight_data_float, scales_weight[0], zero_point_input[0]);
   std::vector<int32_t> bias_data =
       Quantize<int32_t>(bias_data_float, scales_bias[0], zero_point_bias[0]);
   std::vector<u_int8_t> golden =
@@ -1167,8 +1170,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) {
   std::array<uint32_t, 2> stride({2, 2});
   std::array<uint32_t, 2> dilation({1, 1});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1220,13 +1223,13 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_weight, zero_point_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias,
-                                  zero_point_bias);
+                                     scales_weight, zero_point_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2,
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1255,8 +1258,8 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) {
 
   std::vector<u_int8_t> input_data =
       Quantize<uint8_t>(input_data_float, scales_input[0], zero_point_input[0]);
-  std::vector<u_int8_t> weight_data =
-      Quantize<uint8_t>(weight_data_float, scales_weight[0], zero_point_input[0]);
+  std::vector<u_int8_t> weight_data = Quantize<uint8_t>(
+      weight_data_float, scales_weight[0], zero_point_input[0]);
   std::vector<int32_t> bias_data =
       Quantize<int32_t>(bias_data_float, scales_bias[0], zero_point_bias[0]);
   std::vector<u_int8_t> golden =
@@ -1271,8 +1274,8 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) {
   std::array<uint32_t, 2> stride({3, 1});
   std::array<uint32_t, 2> dilation({1, 1});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1324,13 +1327,13 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_weight, zero_point_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias,
-                                  zero_point_bias);
+                                     scales_weight, zero_point_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2,
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1362,8 +1365,8 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) {
 
   std::vector<u_int8_t> input_data =
       Quantize<uint8_t>(input_data_float, scales_input[0], zero_point_input[0]);
-  std::vector<u_int8_t> weight_data =
-      Quantize<uint8_t>(weight_data_float, scales_weight[0], zero_point_input[0]);
+  std::vector<u_int8_t> weight_data = Quantize<uint8_t>(
+      weight_data_float, scales_weight[0], zero_point_input[0]);
   std::vector<int32_t> bias_data =
       Quantize<int32_t>(bias_data_float, scales_bias[0], zero_point_bias[0]);
   std::vector<u_int8_t> golden =
@@ -1378,8 +1381,8 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({3, 3});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1431,13 +1434,13 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerTensorTest) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_weight, zero_point_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias,
-                                  zero_point_bias);
+                                     scales_weight, zero_point_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2,
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::INT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1481,8 +1484,8 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerTensorTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({1, 1});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1527,7 +1530,7 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) {
   std::vector<int32_t> zero_point_weight = {0, 0};
 
   std::vector<float> scales_bias = {scales_input[0] * scales_weight[0],
-                                   scales_input[0] * scales_weight[1]};
+                                    scales_input[0] * scales_weight[1]};
   std::vector<int32_t> zero_point_bias = {0, 0};
 
   scales_zp = QuantizationParams<int8_t>(output_min, output_max);
@@ -1535,13 +1538,13 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) {
   std::vector<int32_t> zero_point_output = {scales_zp.second};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL,
-                                    3, scales_weight, zero_point_weight);
+                                     3, scales_weight, zero_point_weight);
   tim::vx::Quantization quant_bias(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, 0,
-                                  scales_bias, zero_point_bias);
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   tim::vx::TensorSpec input_spec(tim::vx::DataType::INT8, input_shape,
                                  tim::vx::TensorAttribute::INPUT, quant_input);
@@ -1583,8 +1586,8 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({1, 1});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1609,12 +1612,12 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) {
 TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) {
   std::map<uint32_t, std::vector<uint32_t>> input_shape_list;
   input_shape_list[32] = {18, 20, 22, 26, 28, 30, 34, 36, 38,
-                        42, 44, 46, 50, 52, 54, 58, 60, 62};
+                          42, 44, 46, 50, 52, 54, 58, 60, 62};
   input_shape_list[63] = {18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62};
   input_shape_list[95] = {18, 20, 22, 26, 28, 30, 34, 36, 38,
-                        42, 44, 46, 50, 52, 54, 58, 60, 62};
+                          42, 44, 46, 50, 52, 54, 58, 60, 62};
   input_shape_list[96] = {18, 20, 22, 26, 28, 30, 34, 36, 38,
-                        42, 44, 46, 50, 52, 54, 58, 60, 62};
+                          42, 44, 46, 50, 52, 54, 58, 60, 62};
   tim::vx::ShapeType input_shape({2, 2, 128, 1});     //whcn
   tim::vx::ShapeType weight_shape({1, 1, 128, 256});  //whio
   tim::vx::ShapeType bias_shape({weight_shape[3]});
@@ -1642,13 +1645,13 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) {
   std::vector<int32_t> zero_point_output = {-1};
 
   tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2,
-                                   scales_input, zero_point_input);
+                                    scales_input, zero_point_input);
   tim::vx::Quantization quant_weight(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL,
-                                    3, scales_weight, zero_point_weight);
+                                     3, scales_weight, zero_point_weight);
   tim::vx::Quantization quant_bias(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, 0,
-                                  scales_bias, zero_point_bias);
+                                   scales_bias, zero_point_bias);
   tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2,
-                                    scales_output, zero_point_output);
+                                     scales_output, zero_point_output);
 
   uint32_t weight_size =
       weight_shape[0] * weight_shape[1] * weight_shape[2] * weight_shape[3];
@@ -1699,8 +1702,8 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) {
       for (uint32_t i = 0; i < golden_size; i++) {
         golden_float[i] = 129;
       }
-      std::vector<int8_t> golden =
-          Quantize<int8_t>(golden_float, scales_output[0], zero_point_output[0]);
+      std::vector<int8_t> golden = Quantize<int8_t>(
+          golden_float, scales_output[0], zero_point_output[0]);
 
       auto ctx = tim::vx::Context::Create();
       auto graph = ctx->CreateGraph();
@@ -1738,28 +1741,30 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) {
   }
 }
 
-TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){
+TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest) {
   auto ctx = tim::vx::Context::Create();
-  if(ctx->isClOnly()) GTEST_SKIP();
+  if (ctx->isClOnly()) GTEST_SKIP();
   auto graph = ctx->CreateGraph();
   tim::vx::ShapeType input_shape({4, 2, 2, 2});   //whcn
   tim::vx::ShapeType weight_shape({1, 1, 2, 1});  //whio
   tim::vx::ShapeType bias_shape({weight_shape[3]});
   tim::vx::ShapeType output_shape(
       {4, 2, weight_shape[3], input_shape[3]});  //whcn
-  int8_t fl_input = 9, fl_weight= 8,  fl_output = 8;
-  tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_input);
-  tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_weight);
-  tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_output);
+  int8_t fl_input = 9, fl_weight = 8, fl_output = 8;
+  tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                    fl_input);
+  tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                     fl_weight);
+  tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                     fl_output);
   tim::vx::TensorSpec input_spec(tim::vx::DataType::INT16, input_shape,
-                                     tim::vx::TensorAttribute::INPUT,
-                                     quant_input);
+                                 tim::vx::TensorAttribute::INPUT, quant_input);
   tim::vx::TensorSpec weight_spec(tim::vx::DataType::INT16, weight_shape,
-                                      tim::vx::TensorAttribute::CONSTANT,
-                                      quant_weight);
+                                  tim::vx::TensorAttribute::CONSTANT,
+                                  quant_weight);
   tim::vx::TensorSpec output_spec(tim::vx::DataType::INT16, output_shape,
-                                      tim::vx::TensorAttribute::OUTPUT,
-                                      quant_output);
+                                  tim::vx::TensorAttribute::OUTPUT,
+                                  quant_output);
 
   // Input data  float
   std::vector<float> input_data_float = {
@@ -1767,25 +1772,23 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){
       0.5, 1,   1.5, 2,   0.5, 1, 1.5, 2, 0.5, 1,   1.5, 2,   0.5, 1, 1.5, 2};
 
   // weight data   float
-  std::vector<float> weight_data_float= {
+  std::vector<float> weight_data_float = {
       1, 2  // first filter
   };
   //input data(dfp16)
-  std::vector<int16_t> input_data = {
-      256,256,256,256, 512,512,512,512, 256,256,256,256,512,512,512,512,
-      256,512,768,1024,256,512,768,1024,256,512,768,1024,256,512,768,1024
-  };
+  std::vector<int16_t> input_data = {256, 256, 256, 256,  512, 512, 512, 512,
+                                     256, 256, 256, 256,  512, 512, 512, 512,
+                                     256, 512, 768, 1024, 256, 512, 768, 1024,
+                                     256, 512, 768, 1024, 256, 512, 768, 1024};
   //weight data(dfp16)
-  std::vector<int16_t> weight_data = {
-      256,512
-  };
+  std::vector<int16_t> weight_data = {256, 512};
   // bias data
   std::vector<int64_t> bias_data = {0};
   //golden
   std::vector<float> golden = {1.5, 1.5, 1.5, 1.5, 3,   3, 3,   3,
                                1.5, 3,   4.5, 6,   1.5, 3, 4.5, 6};
 
-  auto input_tensor = graph->CreateTensor(input_spec,input_data.data());
+  auto input_tensor = graph->CreateTensor(input_spec, input_data.data());
   auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data());
   auto output_tensor = graph->CreateTensor(output_spec);
 
@@ -1793,8 +1796,8 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1812,16 +1815,16 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){
   }
   std::vector<int16_t> output(output_size);
   EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data()));
- //transform output(int16) to fp
+  //transform output(int16) to fp
   std::vector<float> f;
-  for(const auto& q : output){
-    f.push_back( q / (float)((int64_t)1 << fl_output));
+  for (const auto& q : output) {
+    f.push_back(q / (float)((int64_t)1 << fl_output));
   }
   EXPECT_EQ(golden, f);
 }
 TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) {
   auto ctx = tim::vx::Context::Create();
-  if(ctx->isClOnly()) GTEST_SKIP();
+  if (ctx->isClOnly()) GTEST_SKIP();
   auto graph = ctx->CreateGraph();
 
   tim::vx::ShapeType input_shape({4, 2, 1, 1});   //whcn
@@ -1829,32 +1832,34 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) {
   tim::vx::ShapeType bias_shape({weight_shape[3]});
   tim::vx::ShapeType output_shape(
       {4, 2, weight_shape[3], input_shape[3]});  //whcn
-  int8_t fl_input = 9, fl_weight = 8, fl_bias = 17,fl_output = 8;
+  int8_t fl_input = 9, fl_weight = 8, fl_bias = 17, fl_output = 8;
 
-  tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_input);
-  tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_weight);
-  tim::vx::Quantization quant_bias(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_bias);
-  tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_output);
+  tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                    fl_input);
+  tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                     fl_weight);
+  tim::vx::Quantization quant_bias(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                   fl_bias);
+  tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT,
+                                     fl_output);
   tim::vx::TensorSpec input_spec(tim::vx::DataType::INT16, input_shape,
-                                     tim::vx::TensorAttribute::INPUT,
-                                     quant_input);
+                                 tim::vx::TensorAttribute::INPUT, quant_input);
   tim::vx::TensorSpec weight_spec(tim::vx::DataType::INT16, weight_shape,
-                                      tim::vx::TensorAttribute::CONSTANT,
-                                      quant_weight);
+                                  tim::vx::TensorAttribute::CONSTANT,
+                                  quant_weight);
   tim::vx::TensorSpec bias_spec(tim::vx::DataType::INT64, bias_shape,
-                                      tim::vx::TensorAttribute::CONSTANT,
-                                      quant_bias);
+                                tim::vx::TensorAttribute::CONSTANT, quant_bias);
   tim::vx::TensorSpec output_spec(tim::vx::DataType::INT16, output_shape,
-                                      tim::vx::TensorAttribute::OUTPUT,
-                                      quant_output);
+                                  tim::vx::TensorAttribute::OUTPUT,
+                                  quant_output);
   // Input data  nchw
-  std::vector<float> input_data_float= {
+  std::vector<float> input_data_float = {
       1, 1, 1, 1,  // row = 1
       2, 2, 3, 2   // row = 2
   };
 
   // weight data   oihw
-  std::vector<float> weight_data_float= {
+  std::vector<float> weight_data_float = {
       1,  2,  3,  4,  //first 2x2 filter
       -1, 1,  -1, 1,  // second 2x2 filter
       -1, -1, 1,  1,  // third 2x2 filter
@@ -1865,24 +1870,18 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) {
 
   // nchw
   std::vector<float> golden = {// first channel
-                               18, 22, 21, 8,  7, 9, 8, 3,
+                               18, 22, 21, 8, 7, 9, 8, 3,
                                // second channel
-                               2,  3,  1,  -1, 2, 3, 1, 0,
+                               2, 3, 1, -1, 2, 3, 1, 0,
                                // third channel
-                               5,  6,  6,  4, -1, -2, -2, 1};
+                               5, 6, 6, 4, -1, -2, -2, 1};
 
-  std::vector<int16_t> input_data = {
-    512, 512, 512, 512,
-    1024,1024,1536,1024
-  };
-  std::vector<int16_t> weight_data = {
-    256,512,768,1024,
-    -256,256,-256,256,
-    -256,-256,256,256
-  };
-  std::vector<int64_t> bias_data = {
-    1<<fl_bias, 2*(1<<fl_bias),3*(1<<fl_bias)
-  };
+  std::vector<int16_t> input_data = {512,  512,  512,  512,
+                                     1024, 1024, 1536, 1024};
+  std::vector<int16_t> weight_data = {256,  512, 768,  1024, -256, 256,
+                                      -256, 256, -256, -256, 256,  256};
+  std::vector<int64_t> bias_data = {1 << fl_bias, 2 * (1 << fl_bias),
+                                    3 * (1 << fl_bias)};
 
   auto input_tensor = graph->CreateTensor(input_spec, input_data.data());
   auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data());
@@ -1894,8 +1893,8 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) {
   std::array<uint32_t, 2> stride({1, 1});
   std::array<uint32_t, 2> dilation({0, 0});
 
-  auto conv2d = graph->CreateOperation<tim::vx::ops::Conv2d>(
-      padding, stride, dilation);
+  auto conv2d =
+      graph->CreateOperation<tim::vx::ops::Conv2d>(padding, stride, dilation);
   (*conv2d)
       .BindInput(input_tensor)
       .BindInput(weight_tensor)
@@ -1916,8 +1915,8 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) {
   EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data()));
   //transform output(int16) to fp
   std::vector<float> f;
-  for(const auto& q : output){
-    f.push_back( q / (float)((int64_t)1 << fl_output));
+  for (const auto& q : output) {
+    f.push_back(q / (float)((int64_t)1 << fl_output));
   }
   EXPECT_EQ(golden, f);
 }
@@ -1926,7 +1925,7 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) {
   auto ctx = tim::vx::Context::Create();
   auto graph = ctx->CreateGraph();
 
-  tim::vx::ShapeType input_shape({2, 3, 1, 1});  //whcn
+  tim::vx::ShapeType input_shape({2, 3, 1, 1});   //whcn
   tim::vx::ShapeType kernel_shape({3, 2, 1, 1});  //whio
   tim::vx::ShapeType bias_shape({1});
   tim::vx::ShapeType output_shape({2, 3, 1, 1});
@@ -1939,13 +1938,16 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) {
   tim::vx::TensorSpec output_spec(tim::vx::DataType::FLOAT32, output_shape,
                                   tim::vx::TensorAttribute::OUTPUT);
 
-  std::vector<float> input_data = {1.0f, 3.0f, 4.0f, 2.0f, 2.0f, 3.0f,
-                                };
-  std::vector<float> weight = {100.0f, 20.0f, 1.0f, 200.0f, 10.0f, 2.0f,
-                               };
+  std::vector<float> input_data = {
+      1.0f, 3.0f, 4.0f, 2.0f, 2.0f, 3.0f,
+  };
+  std::vector<float> weight = {
+      100.0f, 20.0f, 1.0f, 200.0f, 10.0f, 2.0f,
+  };
   std::vector<float> bias = {500.0f};
-  std::vector<float> golden = {567.0f,  1480.0f, 608.0f,  1370.0f,
-                               543.0f,  760.0f, };
+  std::vector<float> golden = {
+      567.0f, 1480.0f, 608.0f, 1370.0f, 543.0f, 760.0f,
+  };
   auto input_tensor = graph->CreateTensor(input_spec);
   auto weight_tensor = graph->CreateTensor(kernel_spec, weight.data());
   auto bias_tensor = graph->CreateTensor(bias_spec, bias.data());
@@ -1956,7 +1958,9 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) {
   auto op = graph->CreateOperation<tim::vx::ops::Conv2d>(
       tim::vx::PadType::SAME, strides, dilations, 0, tim::vx::DataLayout::WHCN,
       tim::vx::DataLayout::IcWHOc);
-  (*op).BindInputs({input_tensor, weight_tensor, bias_tensor}).BindOutputs({output_tensor});
+  (*op)
+      .BindInputs({input_tensor, weight_tensor, bias_tensor})
+      .BindOutputs({output_tensor});
 
   EXPECT_TRUE(graph->Compile());
 
diff --git a/third_party/half/ChangeLog.txt b/third_party/half/ChangeLog.txt
new file mode 100644
index 0000000..9100b6a
--- /dev/null
+++ b/third_party/half/ChangeLog.txt
@@ -0,0 +1,184 @@
+Release Notes											{#changelog}
+=============
+
+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/ChangeLog.txt.license b/third_party/half/ChangeLog.txt.license
new file mode 100644
index 0000000..771b79e
--- /dev/null
+++ b/third_party/half/ChangeLog.txt.license
@@ -0,0 +1,4 @@
+#
+# Copyright (c) 2012-2017 Christian Rau
+# SPDX-License-Identifier: MIT
+#
diff --git a/third_party/half/LICENSE.spdx b/third_party/half/LICENSE.spdx
new file mode 100644
index 0000000..d71fa7d
--- /dev/null
+++ b/third_party/half/LICENSE.spdx
@@ -0,0 +1,7 @@
+PackageName: half
+SPDXID: SPDXRef-half
+FilesAnalyzed: true
+PackageLicenseConcluded: MIT
+PackageLicenseInfoFromFiles: MIT
+PackageLicenseDeclared: MIT
+PackageCopyrightText:<text>Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net></text>
diff --git a/third_party/half/LICENSE.txt b/third_party/half/LICENSE.txt
new file mode 100644
index 0000000..9e4618b
--- /dev/null
+++ b/third_party/half/LICENSE.txt
@@ -0,0 +1,21 @@
+The MIT License
+
+Copyright (c) 2012-2017 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..3a0960c
--- /dev/null
+++ b/third_party/half/README.txt
@@ -0,0 +1,288 @@
+HALF-PRECISION FLOATING POINT LIBRARY (Version 1.12.0)
+------------------------------------------------------
+
+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 
+builtin floating point types at the best performance possible.
+
+
+INSTALLATION AND REQUIREMENTS
+-----------------------------
+
+Comfortably enough, 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 
+defining the corresponding preprocessor symbols to either 1 or 0 yourself. 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 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 and newer, overridable with 'HALF_ENABLE_CPP11_STATIC_ASSERT').
+
+  - Generalized constant expressions (enabled for VC++ 2015, gcc 4.6, clang 3.1 
+    and newer, overridable with 'HALF_ENABLE_CPP11_CONSTEXPR').
+
+  - noexcept exception specifications (enabled for VC++ 2015, gcc 4.6, clang 3.0 
+    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 and newer, overridable with 
+    'HALF_ENABLE_CPP11_USER_LITERALS').
+
+  - 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 
+    an improved implementation of their half-precision counterparts to work 
+    (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with 
+    'HALF_ENABLE_CPP11_CMATH').
+
+  - 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 4.4-4.8 
+and clang 3.1. Please contact me if you have any problems, suggestions or even 
+just success testing it on other platforms.
+
+
+DOCUMENTATION
+-------------
+
+Here follow some general words about the usage of the library and its 
+implementation. For a complete documentation of its iterface look at 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 (for 
+reasons described below).
+
+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. This 
+type behaves like the builtin 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 from float to half uses truncation 
+(round toward zero, but mapping overflows to infinity) for rounding values not 
+representable exactly in half-precision. This is the fastest rounding possible 
+and is usually sufficient. But by redefining the 'HALF_ROUND_STYLE' 
+preprocessor symbol (before including half.hpp) 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 underlying single-precision implementation by defining it 
+to 'std::numeric_limits<float>::round_style'):
+
+  - 'std::round_indeterminate' or -1 for the fastest rounding (default).
+
+  - 'std::round_toward_zero' or 0 for rounding toward zero.
+
+  - std::round_to_nearest' or 1 for rounding to the nearest value.
+
+  - std::round_toward_infinity' or 2 for rounding toward positive infinity.
+
+  - std::round_toward_neg_infinity' or 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 );
+
+When using round to nearest (either as default or through 'half_cast') ties are 
+by default resolved by rounding them away from zero (and thus equal to the 
+behaviour of the 'round' function). But by redefining the 
+'HALF_ROUND_TIES_TO_EVEN' preprocessor symbol to 1 (before including half.hpp) 
+this default can be changed to the slightly slower but less biased and more 
+IEEE-conformant behaviour of rounding half-way cases to the nearest even value.
+
+    #define HALF_ROUND_TIES_TO_EVEN 1
+    #include <half.hpp>
+    ...
+    assert( half_cast<int,std::round_to_nearest>(3.5_h) 
+         == half_cast<int,std::round_to_nearest>(4.5_h) );
+
+IMPLEMENTATION
+
+For performance reasons (and ease of implementation) many of the mathematical 
+functions provided by the library as well as all arithmetic operations are 
+actually carried out in single-precision under the hood, calling to the C++ 
+standard library implementations of those functions whenever appropriate, 
+meaning the arguments are converted to floats and the result back to half. But 
+to reduce the conversion overhead as much as possible any temporary values 
+inside of lengthy expressions are kept in single-precision as long as possible, 
+while still maintaining a strong half-precision type to the outside world. Only 
+when finally assigning the value to a half or calling a function that works 
+directly on halfs is the actual conversion done (or never, when further 
+converting the result to float.
+
+This approach has two implications. First of all you have to treat the 
+library's documentation at http://half.sourceforge.net as a simplified version, 
+describing the behaviour of the library as if implemented this way. The actual 
+argument and return types of functions and operators may involve other internal 
+types (feel free to generate the exact developer documentation from the Doxygen 
+comments in the library's header file if you really need to). But nevertheless 
+the behaviour is exactly like specified in the documentation. The other 
+implication is, that in the presence of rounding errors or over-/underflows 
+arithmetic expressions may produce different results when compared to 
+converting to half-precision after each individual operation:
+
+    half a = std::numeric_limits<half>::max() * 2.0_h / 2.0_h;       // a = MAX
+    half b = half(std::numeric_limits<half>::max() * 2.0_h) / 2.0_h; // b = INF
+    assert( a != b );
+
+But this should only be a problem in very few cases. One last word has to be 
+said when talking about performance. Even with its efforts in reducing 
+conversion overhead as much as possible, the software half-precision 
+implementation can most probably not beat the direct use of single-precision 
+computations. Usually using actual float values for all computations and 
+temproraries and using halfs only for storage is the recommended way. On the 
+one hand this somehow makes the provided mathematical functions obsolete 
+(especially in light of the implicit conversion from half to float), but 
+nevertheless the goal of this library was to provide a complete and 
+conceptually clean half-precision implementation, to which the standard 
+mathematical functions belong, even if usually not needed.
+
+IEEE CONFORMANCE
+
+The half type uses the standard IEEE representation with 1 sign bit, 5 exponent 
+bits and 10 mantissa bits (11 when counting the hidden bit). It supports all 
+types of special values, like subnormal values, infinity and NaNs. But there 
+are some limitations to the complete conformance to the IEEE 754 standard:
+
+  - The implementation does not differentiate between signalling and quiet 
+    NaNs, this means operations on halfs are not specified to trap on 
+    signalling NaNs (though they may, see last point).
+
+  - Though arithmetic operations are internally rounded to single-precision 
+    using the underlying single-precision implementation's current rounding 
+    mode, those values are then converted to half-precision using the default 
+    half-precision rounding mode (changed by defining 'HALF_ROUND_STYLE' 
+    accordingly). This mixture of rounding modes is also the reason why 
+    'std::numeric_limits<half>::round_style' may actually return 
+    'std::round_indeterminate' when half- and single-precision rounding modes 
+    don't match.
+
+  - Because of internal truncation it may also be that certain single-precision 
+    NaNs will be wrongly converted to half-precision infinity, though this is 
+    very unlikely to happen, since most single-precision implementations don't 
+    tend to only set the lowest bits of a NaN mantissa.
+
+  - The implementation does not provide any floating point exceptions, thus 
+    arithmetic operations or mathematical functions are not specified to invoke 
+    proper floating point exceptions. But due to many functions implemented in 
+    single-precision, those may still invoke floating point exceptions of the 
+    underlying single-precision implementation.
+
+Some of those points could have been circumvented by controlling the floating 
+point environment using <cfenv> or implementing a similar exception mechanism. 
+But this would have required excessive runtime checks giving two high an impact 
+on performance for something that is rarely ever needed. If you really need to 
+rely on proper floating point exceptions, it is recommended to explicitly 
+perform computations using the built-in floating point types to be on the safe 
+side. In the same way, if you really need to rely on a particular rounding 
+behaviour, it is recommended to either use single-precision computations and 
+explicitly convert the result to half-precision using 'half_cast' and 
+specifying the desired rounding mode, or synchronize the default half-precision 
+rounding mode to the rounding mode of the single-precision implementation (most 
+likely 'HALF_ROUND_STYLE=1', 'HALF_ROUND_TIES_TO_EVEN=1'). But this is really 
+considered an expert-scenario that should be used only when necessary, since 
+actually working with half-precision usually comes with a certain 
+tolerance/ignorance of exactness considerations and proper rounding comes with 
+a certain performance cost.
+
+
+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/README.txt.license b/third_party/half/README.txt.license
new file mode 100644
index 0000000..771b79e
--- /dev/null
+++ b/third_party/half/README.txt.license
@@ -0,0 +1,4 @@
+#
+# Copyright (c) 2012-2017 Christian Rau
+# SPDX-License-Identifier: MIT
+#
diff --git a/third_party/half/half.hpp b/third_party/half/half.hpp
new file mode 100644
index 0000000..4e432b9
--- /dev/null
+++ b/third_party/half/half.hpp
@@ -0,0 +1,3070 @@
+// half - IEEE 754-based half-precision floating point library.
+//
+// Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net>
+//
+// SPDX-License-Identifier: MIT
+//
+// 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 1.12.0
+
+/// \file
+/// Main header file for half precision functionality.
+
+#ifndef HALF_HALF_HPP
+#define HALF_HALF_HPP
+
+/// Combined gcc version number.
+#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__)
+
+//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 (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+		#define HALF_ENABLE_CPP11_LONG_LONG 1
+	#endif
+/*#elif defined(__INTEL_COMPILER)								//Intel C++
+	#if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)		????????
+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+	#endif
+	#if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)			????????
+		#define HALF_ENABLE_CPP11_CONSTEXPR 1
+	#endif
+	#if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)			????????
+		#define HALF_ENABLE_CPP11_NOEXCEPT 1
+	#endif
+	#if __INTEL_COMPILER >= 1100 && !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_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+			#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+		#endif
+		#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+			#define HALF_ENABLE_CPP11_CONSTEXPR 1
+		#endif
+		#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+			#define HALF_ENABLE_CPP11_NOEXCEPT 1
+		#endif
+		#if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+			#define HALF_ENABLE_CPP11_USER_LITERALS 1
+		#endif
+		#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
+			#define HALF_ENABLE_CPP11_LONG_LONG 1
+		#endif
+	#endif
+#elif defined(_MSC_VER)										//Visual C++
+	#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 >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+		#define HALF_ENABLE_CPP11_USER_LITERALS 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_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
+	#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
+		#else
+			#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+				#define HALF_ENABLE_CPP11_CSTDINT 1
+			#endif
+			#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
+				#define HALF_ENABLE_CPP11_CMATH 1
+			#endif
+			#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
+				#define HALF_ENABLE_CPP11_HASH 1
+			#endif
+		#endif
+	#endif
+#elif defined(_CPPLIB_VER)									//Dinkumware/Visual C++
+	#if _CPPLIB_VER >= 520
+		#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_HASH
+			#define HALF_ENABLE_CPP11_HASH 1
+		#endif
+	#endif
+	#if _CPPLIB_VER >= 610
+		#ifndef HALF_ENABLE_CPP11_CMATH
+			#define HALF_ENABLE_CPP11_CMATH 1
+		#endif
+	#endif
+#endif
+#undef HALF_GNUC_VERSION
+
+//support constexpr
+#if HALF_ENABLE_CPP11_CONSTEXPR
+	#define HALF_CONSTEXPR			constexpr
+	#define HALF_CONSTEXPR_CONST	constexpr
+#else
+	#define HALF_CONSTEXPR
+	#define HALF_CONSTEXPR_CONST	const
+#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
+
+#include <algorithm>
+#include <iostream>
+#include <limits>
+#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_ENABLE_CPP11_HASH
+	#include <functional>
+#endif
+
+
+/// Default rounding mode.
+/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and `float`s as well as
+/// for the half_cast() if not specifying a rounding mode explicitly. 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`:
+///
+/// `std::float_round_style`         | value | rounding
+/// ---------------------------------|-------|-------------------------
+/// `std::round_indeterminate`       | -1    | fastest (default)
+/// `std::round_toward_zero`         | 0     | toward zero
+/// `std::round_to_nearest`          | 1     | to nearest
+/// `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_indeterminate`), which uses truncation (round toward zero, but with overflows
+/// set to infinity) and is the fastest rounding mode possible. It can even be set to `std::numeric_limits<float>::round_style`
+/// to synchronize the rounding mode with that of the underlying single-precision implementation.
+#ifndef HALF_ROUND_STYLE
+	#define HALF_ROUND_STYLE	-1			// = std::round_indeterminate
+#endif
+
+/// Tie-breaking behaviour for round to nearest.
+/// This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is
+/// defined to `0` resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and
+/// thus equal to the round() function), but can be redefined to `1` (before including half.hpp) if more IEEE-conformant
+/// behaviour is needed.
+#ifndef HALF_ROUND_TIES_TO_EVEN
+	#define HALF_ROUND_TIES_TO_EVEN	0		// ties away from zero
+#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.
+#define HUGE_VALH	std::numeric_limits<half_float::half>::infinity()
+
+/// Fast half-precision fma function.
+/// This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate
+/// half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all
+/// arithmetic operations, this is in fact always the case.
+#define FP_FAST_FMAH	1
+
+#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
+
+
+/// 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;
+
+		/// 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;
+
+		/// 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
+
+		/// Tag type for binary construction.
+		struct binary_t {};
+
+		/// Tag for binary construction.
+		HALF_CONSTEXPR_CONST binary_t binary = binary_t();
+
+		/// Temporary half-precision expression.
+		/// This class represents a half-precision expression which just stores a single-precision value internally.
+		struct expr
+		{
+			/// Conversion constructor.
+			/// \param f single-precision value to convert
+			explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {}
+
+			/// Conversion to single-precision.
+			/// \return single precision value representing expression value
+			HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; }
+
+		private:
+			/// Internal expression value stored in single-precision.
+			float value_;
+		};
+
+		/// SFINAE helper for generic half-precision functions.
+		/// This class template has to be specialized for each valid combination of argument types to provide a corresponding
+		/// `type` member equivalent to \a T.
+		/// \tparam T type to return
+		template<typename T,typename,typename=void,typename=void> struct enable {};
+		template<typename T> struct enable<T,half,void,void> { typedef T type; };
+		template<typename T> struct enable<T,expr,void,void> { typedef T type; };
+		template<typename T> struct enable<T,half,half,void> { typedef T type; };
+		template<typename T> struct enable<T,half,expr,void> { typedef T type; };
+		template<typename T> struct enable<T,expr,half,void> { typedef T type; };
+		template<typename T> struct enable<T,expr,expr,void> { typedef T type; };
+		template<typename T> struct enable<T,half,half,half> { typedef T type; };
+		template<typename T> struct enable<T,half,half,expr> { typedef T type; };
+		template<typename T> struct enable<T,half,expr,half> { typedef T type; };
+		template<typename T> struct enable<T,half,expr,expr> { typedef T type; };
+		template<typename T> struct enable<T,expr,half,half> { typedef T type; };
+		template<typename T> struct enable<T,expr,half,expr> { typedef T type; };
+		template<typename T> struct enable<T,expr,expr,half> { typedef T type; };
+		template<typename T> struct enable<T,expr,expr,expr> { typedef T type; };
+
+		/// Return type for specialized generic 2-argument half-precision functions.
+		/// This class template has to be specialized for each valid combination of argument types to provide a corresponding 
+		/// `type` member denoting the appropriate return type.
+		/// \tparam T first argument type
+		/// \tparam U first argument type
+		template<typename T,typename U> struct result : enable<expr,T,U> {};
+		template<> struct result<half,half> { typedef half type; };
+
+		/// \name Classification helpers
+		/// \{
+
+		/// 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
+		}
+
+		/// \}
+		/// \name Conversion
+		/// \{
+
+		/// 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, `std::round_indeterminate` for fastest rounding
+		/// \param value single-precision value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R> uint16 float2half_impl(float value, true_type)
+		{
+			typedef bits<float>::type uint32;
+			uint32 bits;// = *reinterpret_cast<uint32*>(&value);		//violating strict aliasing!
+			std::memcpy(&bits, &value, sizeof(float));
+/*			uint16 hbits = (bits>>16) & 0x8000;
+			bits &= 0x7FFFFFFF;
+			int exp = bits >> 23;
+			if(exp == 255)
+				return hbits | 0x7C00 | (0x3FF&-static_cast<unsigned>((bits&0x7FFFFF)!=0));
+			if(exp > 142)
+			{
+				if(R == std::round_toward_infinity)
+					return hbits | 0x7C00 - (hbits>>15);
+				if(R == std::round_toward_neg_infinity)
+					return hbits | 0x7BFF + (hbits>>15);
+				return hbits | 0x7BFF + (R!=std::round_toward_zero);
+			}
+			int g, s;
+			if(exp > 112)
+			{
+				g = (bits>>12) & 1;
+				s = (bits&0xFFF) != 0;
+				hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF);
+			}
+			else if(exp > 101)
+			{
+				int i = 125 - exp;
+				bits = (bits&0x7FFFFF) | 0x800000;
+				g = (bits>>i) & 1;
+				s = (bits&((1L<<i)-1)) != 0;
+				hbits |= bits >> (i+1);
+			}
+			else
+			{
+				g = 0;
+				s = bits != 0;
+			}
+			if(R == std::round_to_nearest)
+				#if HALF_ROUND_TIES_TO_EVEN
+					hbits += g & (s|hbits);
+				#else
+					hbits += g;
+				#endif
+			else if(R == std::round_toward_infinity)
+				hbits += ~(hbits>>15) & (s|g);
+			else if(R == std::round_toward_neg_infinity)
+				hbits += (hbits>>15) & (g|s);
+*/			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, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
+				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 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, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
+				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 };
+			static const unsigned char shift_table[512] = { 
+				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, 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, 
+				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, 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 };
+			uint16 hbits = base_table[bits>>23] + static_cast<uint16>((bits&0x7FFFFF)>>shift_table[bits>>23]);
+			if(R == std::round_to_nearest)
+				hbits += (((bits&0x7FFFFF)>>(shift_table[bits>>23]-1))|(((bits>>23)&0xFF)==102)) & ((hbits&0x7C00)!=0x7C00)
+				#if HALF_ROUND_TIES_TO_EVEN
+					& (((((static_cast<uint32>(1)<<(shift_table[bits>>23]-1))-1)&bits)!=0)|hbits)
+				#endif
+				;
+			else if(R == std::round_toward_zero)
+				hbits -= ((hbits&0x7FFF)==0x7C00) & ~shift_table[bits>>23];
+			else if(R == std::round_toward_infinity)
+				hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=102)&
+					((bits>>23)!=0)))&(hbits<0x7C00)) - ((hbits==0xFC00)&((bits>>23)!=511));
+			else if(R == std::round_toward_neg_infinity)
+				hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=358)&
+					((bits>>23)!=256)))&(hbits<0xFC00)&(hbits>>15)) - ((hbits==0x7C00)&((bits>>23)!=255));
+			return hbits;
+		}
+
+		/// Convert IEEE double-precision to half-precision.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \param value double-precision value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R> uint16 float2half_impl(double value, true_type)
+		{
+			typedef bits<float>::type uint32;
+			typedef bits<double>::type uint64;
+			uint64 bits;// = *reinterpret_cast<uint64*>(&value);		//violating strict aliasing!
+			std::memcpy(&bits, &value, sizeof(double));
+			uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF;
+			uint16 hbits = (hi>>16) & 0x8000;
+			hi &= 0x7FFFFFFF;
+			int exp = hi >> 20;
+			if(exp == 2047)
+				return hbits | 0x7C00 | (0x3FF&-static_cast<unsigned>((bits&0xFFFFFFFFFFFFF)!=0));
+			if(exp > 1038)
+			{
+				if(R == std::round_toward_infinity)
+					return hbits | 0x7C00 - (hbits>>15);
+				if(R == std::round_toward_neg_infinity)
+					return hbits | 0x7BFF + (hbits>>15);
+				return hbits | 0x7BFF + (R!=std::round_toward_zero);
+			}
+			int g, s = lo != 0;
+			if(exp > 1008)
+			{
+				g = (hi>>9) & 1;
+				s |= (hi&0x1FF) != 0;
+				hbits |= ((exp-1008)<<10) | ((hi>>10)&0x3FF);
+			}
+			else if(exp > 997)
+			{
+				int i = 1018 - exp;
+				hi = (hi&0xFFFFF) | 0x100000;
+				g = (hi>>i) & 1;
+				s |= (hi&((1L<<i)-1)) != 0;
+				hbits |= hi >> (i+1);
+			}
+			else
+			{
+				g = 0;
+				s |= hi != 0;
+			}
+			if(R == std::round_to_nearest)
+				#if HALF_ROUND_TIES_TO_EVEN
+					hbits += g & (s|hbits);
+				#else
+					hbits += g;
+				#endif
+			else if(R == std::round_toward_infinity)
+				hbits += ~(hbits>>15) & (s|g);
+			else if(R == std::round_toward_neg_infinity)
+				hbits += (hbits>>15) & (g|s);
+			return hbits;
+		}
+
+		/// Convert non-IEEE floating point to half-precision.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \tparam T source type (builtin floating point type)
+		/// \param value floating point value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R,typename T> uint16 float2half_impl(T value, ...)
+		{
+			uint16 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)
+			{
+				if(R == std::round_toward_infinity)
+					return hbits | (0x7C00-(hbits>>15));
+				else if(R == std::round_toward_neg_infinity)
+					return hbits | (0x7BFF+(hbits>>15));
+				return hbits | (0x7BFF+(R!=std::round_toward_zero));
+			}
+			if(exp < -13)
+				value = std::ldexp(value, 24);
+			else
+			{
+				value = std::ldexp(value, 11-exp);
+				hbits |= ((exp+13)<<10);
+			}
+			T ival, frac = std::modf(value, &ival);
+			hbits += static_cast<uint16>(std::abs(static_cast<int>(ival)));
+			if(R == std::round_to_nearest)
+			{
+				frac = std::abs(frac);
+				#if HALF_ROUND_TIES_TO_EVEN
+					hbits += (frac>T(0.5)) | ((frac==T(0.5))&hbits);
+				#else
+					hbits += frac >= T(0.5);
+				#endif
+			}
+			else if(R == std::round_toward_infinity)
+				hbits += frac > T();
+			else if(R == std::round_toward_neg_infinity)
+				hbits += frac < T();
+			return hbits;
+		}
+
+		/// Convert floating point to half-precision.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \tparam T source type (builtin floating point type)
+		/// \param value floating point value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R,typename T> uint16 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, `std::round_indeterminate` for fastest rounding
+		/// \tparam S `true` if value negative, `false` else
+		/// \tparam T type to convert (builtin integer type)
+		/// \param value non-negative integral value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R,bool S,typename T> uint16 int2half_impl(T value)
+		{
+		#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+			static_assert(std::is_integral<T>::value, "int to half conversion only supports builtin integer types");
+		#endif
+			if(S)
+				value = -value;
+			uint16 bits = S << 15;
+			if(value > 0xFFFF)
+			{
+				if(R == std::round_toward_infinity)
+					bits |= 0x7C00 - S;
+				else if(R == std::round_toward_neg_infinity)
+					bits |= 0x7BFF + S;
+				else
+					bits |= 0x7BFF + (R!=std::round_toward_zero);
+			}
+			else if(value)
+			{
+				unsigned int m = value, exp = 24;
+				for(; m<0x400; m<<=1,--exp) ;
+				for(; m>0x7FF; m>>=1,++exp) ;
+				bits |= (exp<<10) + m;
+				if(exp > 24)
+				{
+					if(R == std::round_to_nearest)
+						bits += (value>>(exp-25)) & 1
+						#if HALF_ROUND_TIES_TO_EVEN
+							& (((((1<<(exp-25))-1)&value)!=0)|bits)
+						#endif
+						;
+					else if(R == std::round_toward_infinity)
+						bits += ((value&((1<<(exp-24))-1))!=0) & !S;
+					else if(R == std::round_toward_neg_infinity)
+						bits += ((value&((1<<(exp-24))-1))!=0) & S;
+				}
+			}
+			return bits;
+		}
+
+		/// Convert integer to half-precision floating point.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \tparam T type to convert (builtin integer type)
+		/// \param value integral value
+		/// \return binary representation of half-precision value
+		template<std::float_round_style R,typename T> uint16 int2half(T value)
+		{
+			return (value<0) ? int2half_impl<R,true>(value) : int2half_impl<R,false>(value);
+		}
+
+		/// 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 binary representation of half-precision value
+		/// \return single-precision value
+		inline float half2float_impl(uint16 value, float, true_type)
+		{
+			typedef bits<float>::type uint32;
+/*			uint32 bits = static_cast<uint32>(value&0x8000) << 16;
+			int abs = value & 0x7FFF;
+			if(abs)
+			{
+				bits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);
+				for(; abs<0x400; abs<<=1,bits-=0x800000) ;
+				bits += static_cast<uint32>(abs) << 13;
+			}
+*/			static const uint32 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, 
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+				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 uint32 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 };
+			uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
+//			return *reinterpret_cast<float*>(&bits);			//violating strict aliasing!
+			float out;
+			std::memcpy(&out, &bits, sizeof(float));
+			return out;
+		}
+
+		/// Convert half-precision to IEEE double-precision.
+		/// \param value binary representation of half-precision value
+		/// \return double-precision value
+		inline double half2float_impl(uint16 value, double, true_type)
+		{
+			typedef bits<float>::type uint32;
+			typedef bits<double>::type uint64;
+			uint32 hi = static_cast<uint32>(value&0x8000) << 16;
+			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;
+			}
+			uint64 bits = static_cast<uint64>(hi) << 32;
+//			return *reinterpret_cast<double*>(&bits);			//violating strict aliasing!
+			double out;
+			std::memcpy(&out, &bits, sizeof(double));
+			return out;
+		}
+
+		/// Convert half-precision to non-IEEE floating point.
+		/// \tparam T type to convert to (builtin integer type)
+		/// \param value binary representation of half-precision value
+		/// \return floating point value
+		template<typename T> T half2float_impl(uint16 value, T, ...)
+		{
+			T out;
+			int abs = value & 0x7FFF;
+			if(abs > 0x7C00)
+				out = 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 binary representation of half-precision value
+		/// \return floating point value
+		template<typename T> T half2float(uint16 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, `std::round_indeterminate` for fastest rounding
+		/// \tparam E `true` for round to even, `false` for round away from zero
+		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
+		/// \param value binary representation of half-precision value
+		/// \return integral value
+		template<std::float_round_style R,bool E,typename T> T half2int_impl(uint16 value)
+		{
+		#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+			static_assert(std::is_integral<T>::value, "half to int conversion only supports builtin integer types");
+		#endif
+			unsigned int e = value & 0x7FFF;
+			if(e >= 0x7C00)
+				return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
+			if(e < 0x3800)
+			{
+				if(R == std::round_toward_infinity)
+					return T(~(value>>15)&(e!=0));
+				else if(R == std::round_toward_neg_infinity)
+					return -T(value>0x8000);
+				return T();
+			}
+			unsigned int m = (value&0x3FF) | 0x400;
+			e >>= 10;
+			if(e < 25)
+			{
+				if(R == std::round_to_nearest)
+					m += (1<<(24-e)) - (~(m>>(25-e))&E);
+				else if(R == std::round_toward_infinity)
+					m += ((value>>15)-1) & ((1<<(25-e))-1U);
+				else if(R == std::round_toward_neg_infinity)
+					m += -(value>>15) & ((1<<(25-e))-1U);
+				m >>= 25 - e;
+			}
+			else
+				m <<= e - 25;
+			return (value&0x8000) ? -static_cast<T>(m) : static_cast<T>(m);
+		}
+
+		/// Convert half-precision floating point to integer.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
+		/// \param value binary representation of half-precision value
+		/// \return integral value
+		template<std::float_round_style R,typename T> T half2int(uint16 value) { return half2int_impl<R,HALF_ROUND_TIES_TO_EVEN,T>(value); }
+
+		/// Convert half-precision floating point to integer using round-to-nearest-away-from-zero.
+		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
+		/// \param value binary representation of half-precision value
+		/// \return integral value
+		template<typename T> T half2int_up(uint16 value) { return half2int_impl<std::round_to_nearest,0,T>(value); }
+
+		/// Round half-precision number to nearest integer value.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \tparam E `true` for round to even, `false` for round away from zero
+		/// \param value binary representation of half-precision value
+		/// \return half-precision bits for nearest integral value
+		template<std::float_round_style R,bool E> uint16 round_half_impl(uint16 value)
+		{
+			unsigned int e = value & 0x7FFF;
+			uint16 result = value;
+			if(e < 0x3C00)
+			{
+				result &= 0x8000;
+				if(R == std::round_to_nearest)
+					result |= 0x3C00U & -(e>=(0x3800+E));
+				else if(R == std::round_toward_infinity)
+					result |= 0x3C00U & -(~(value>>15)&(e!=0));
+				else if(R == std::round_toward_neg_infinity)
+					result |= 0x3C00U & -(value>0x8000);
+			}
+			else if(e < 0x6400)
+			{
+				e = 25 - (e>>10);
+				unsigned int mask = (1<<e) - 1;
+				if(R == std::round_to_nearest)
+					result += (1<<(e-1)) - (~(result>>e)&E);
+				else if(R == std::round_toward_infinity)
+					result += mask & ((value>>15)-1);
+				else if(R == std::round_toward_neg_infinity)
+					result += mask & -(value>>15);
+				result &= ~mask;
+			}
+			return result;
+		}
+
+		/// Round half-precision number to nearest integer value.
+		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
+		/// \param value binary representation of half-precision value
+		/// \return half-precision bits for nearest integral value
+		template<std::float_round_style R> uint16 round_half(uint16 value) { return round_half_impl<R,HALF_ROUND_TIES_TO_EVEN>(value); }
+
+		/// Round half-precision number to nearest integer value using round-to-nearest-away-from-zero.
+		/// \param value binary representation of half-precision value
+		/// \return half-precision bits for nearest integral value
+		inline uint16 round_half_up(uint16 value) { return round_half_impl<std::round_to_nearest,0>(value); }
+		/// \}
+
+		struct functions;
+		template<typename> struct unary_specialized;
+		template<typename,typename> struct binary_specialized;
+		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. Additionally all arithmetic operations 
+	/// (and many mathematical functions) are carried out in single-precision internally. All conversions from single- to 
+	/// half-precision are done using the library's default rounding mode, but temporary results inside chained arithmetic 
+	/// expressions are kept in single-precision as long as possible (while of course still maintaining a strong half-precision 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
+	{
+		friend struct detail::functions;
+		friend struct detail::unary_specialized<half>;
+		friend struct detail::binary_specialized<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
+
+	public:
+		/// 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_() {}
+
+		/// Copy constructor.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to copy from
+		half(detail::expr rhs) : data_(detail::float2half<round_style>(static_cast<float>(rhs))) {}
+
+		/// Conversion constructor.
+		/// \param rhs float to convert
+		explicit half(float rhs) : data_(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.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to copy from
+		/// \return reference to this half
+		half& operator=(detail::expr rhs) { return *this = static_cast<float>(rhs); }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to add
+		/// \return reference to this half
+		template<typename T> typename detail::enable<half&,T>::type operator+=(T rhs) { return *this += static_cast<float>(rhs); }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to subtract
+		/// \return reference to this half
+		template<typename T> typename detail::enable<half&,T>::type operator-=(T rhs) { return *this -= static_cast<float>(rhs); }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to multiply with
+		/// \return reference to this half
+		template<typename T> typename detail::enable<half&,T>::type operator*=(T rhs) { return *this *= static_cast<float>(rhs); }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to divide by
+		/// \return reference to this half
+		template<typename T> typename detail::enable<half&,T>::type operator/=(T rhs) { return *this /= static_cast<float>(rhs); }
+
+		/// Assignment operator.
+		/// \param rhs single-precision value to copy from
+		/// \return reference to this half
+		half& operator=(float rhs) { data_ = detail::float2half<round_style>(rhs); return *this; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to add
+		/// \return reference to this half
+		half& operator+=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float<float>(data_)+rhs); return *this; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to subtract
+		/// \return reference to this half
+		half& operator-=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float<float>(data_)-rhs); return *this; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to multiply with
+		/// \return reference to this half
+		half& operator*=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float<float>(data_)*rhs); return *this; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to divide by
+		/// \return reference to this half
+		half& operator/=(float rhs) { data_ = detail::float2half<round_style>(detail::half2float<float>(data_)/rhs); return *this; }
+
+		/// Prefix increment.
+		/// \return incremented half value
+		half& operator++() { return *this += 1.0f; }
+
+		/// Prefix decrement.
+		/// \return decremented half value
+		half& operator--() { return *this -= 1.0f; }
+
+		/// Postfix increment.
+		/// \return non-incremented half value
+		half operator++(int) { half out(*this); ++*this; return out; }
+
+		/// Postfix decrement.
+		/// \return non-decremented half value
+		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, detail::uint16 bits) HALF_NOEXCEPT : data_(bits) {}
+
+		/// Internal binary representation
+		detail::uint16 data_;
+	};
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+	namespace literal
+	{
+		/// Half literal.
+		/// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due 
+		/// to rather involved conversions.
+		/// \param value literal value
+		/// \return half with given value (if representable)
+		inline half operator""_h(long double value) { return half(detail::binary, detail::float2half<half::round_style>(value)); }
+	}
+#endif
+
+	namespace detail
+	{
+		/// Wrapper implementing unspecialized half-precision functions.
+		struct functions
+		{
+			/// Addition implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision sum stored in single-precision
+			static expr plus(float x, float y) { return expr(x+y); }
+
+			/// Subtraction implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision difference stored in single-precision
+			static expr minus(float x, float y) { return expr(x-y); }
+
+			/// Multiplication implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision product stored in single-precision
+			static expr multiplies(float x, float y) { return expr(x*y); }
+
+			/// Division implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision quotient stored in single-precision
+			static expr divides(float x, float y) { return expr(x/y); }
+
+			/// Output implementation.
+			/// \param out stream to write to
+			/// \param arg value to write
+			/// \return reference to stream
+			template<typename charT,typename traits> static std::basic_ostream<charT,traits>& write(std::basic_ostream<charT,traits> &out, float arg) { return out << arg; }
+
+			/// Input implementation.
+			/// \param in stream to read from
+			/// \param arg half to read into
+			/// \return reference to stream
+			template<typename charT,typename traits> static std::basic_istream<charT,traits>& read(std::basic_istream<charT,traits> &in, half &arg)
+			{
+				float f;
+				if(in >> f)
+					arg = f;
+				return in;
+			}
+
+			/// Modulo implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision division remainder stored in single-precision
+			static expr fmod(float x, float y) { return expr(std::fmod(x, y)); }
+
+			/// Remainder implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Half-precision division remainder stored in single-precision
+			static expr remainder(float x, float y)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::remainder(x, y));
+			#else
+				if(builtin_isnan(x) || builtin_isnan(y))
+					return expr(std::numeric_limits<float>::quiet_NaN());
+				float ax = std::fabs(x), ay = std::fabs(y);
+				if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
+					return expr(std::numeric_limits<float>::quiet_NaN());
+				if(ay >= 65536.0f)
+					return expr(x);
+				if(ax == ay)
+					return expr(builtin_signbit(x) ? -0.0f : 0.0f);
+				ax = std::fmod(ax, ay+ay);
+				float y2 = 0.5f * ay;
+				if(ax > y2)
+				{
+					ax -= ay;
+					if(ax >= y2)
+						ax -= ay;
+				}
+				return expr(builtin_signbit(x) ? -ax : ax);
+			#endif
+			}
+
+			/// Remainder implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \param quo address to store quotient bits at
+			/// \return Half-precision division remainder stored in single-precision
+			static expr remquo(float x, float y, int *quo)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::remquo(x, y, quo));
+			#else
+				if(builtin_isnan(x) || builtin_isnan(y))
+					return expr(std::numeric_limits<float>::quiet_NaN());
+				bool sign = builtin_signbit(x), qsign = static_cast<bool>(sign^builtin_signbit(y));
+				float ax = std::fabs(x), ay = std::fabs(y);
+				if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
+					return expr(std::numeric_limits<float>::quiet_NaN());
+				if(ay >= 65536.0f)
+					return expr(x);
+				if(ax == ay)
+					return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f);
+				ax = std::fmod(ax, 8.0f*ay);
+				int cquo = 0;
+				if(ax >= 4.0f * ay)
+				{
+					ax -= 4.0f * ay;
+					cquo += 4;
+				}
+				if(ax >= 2.0f * ay)
+				{
+					ax -= 2.0f * ay;
+					cquo += 2;
+				}
+				float y2 = 0.5f * ay;
+				if(ax > y2)
+				{
+					ax -= ay;
+					++cquo;
+					if(ax >= y2)
+					{
+						ax -= ay;
+						++cquo;
+					}
+				}
+				return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax);
+			#endif
+			}
+
+			/// Positive difference implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return Positive difference stored in single-precision
+			static expr fdim(float x, float y)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::fdim(x, y));
+			#else
+				return expr((x<=y) ? 0.0f : (x-y));
+			#endif
+			}
+
+			/// Fused multiply-add implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \param z third operand
+			/// \return \a x * \a y + \a z stored in single-precision
+			static expr fma(float x, float y, float z)
+			{
+			#if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF)
+				return expr(std::fma(x, y, z));
+			#else
+				return expr(x*y+z);
+			#endif
+			}
+
+			/// Get NaN.
+			/// \return Half-precision quiet NaN
+			static half nanh() { return half(binary, 0x7FFF); }
+
+			/// Exponential implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr exp(float arg) { return expr(std::exp(arg)); }
+
+			/// Exponential implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr expm1(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::expm1(arg));
+			#else
+				return expr(static_cast<float>(std::exp(static_cast<double>(arg))-1.0));
+			#endif
+			}
+
+			/// Binary exponential implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr exp2(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::exp2(arg));
+			#else
+				return expr(static_cast<float>(std::exp(arg*0.69314718055994530941723212145818)));
+			#endif
+			}
+
+			/// Logarithm implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr log(float arg) { return expr(std::log(arg)); }
+
+			/// Common logarithm implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr log10(float arg) { return expr(std::log10(arg)); }
+
+			/// Logarithm implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr log1p(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::log1p(arg));
+			#else
+				return expr(static_cast<float>(std::log(1.0+arg)));
+			#endif
+			}
+
+			/// Binary logarithm implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr log2(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::log2(arg));
+			#else
+				return expr(static_cast<float>(std::log(static_cast<double>(arg))*1.4426950408889634073599246810019));
+			#endif
+			}
+
+			/// Square root implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr sqrt(float arg) { return expr(std::sqrt(arg)); }
+
+			/// Cubic root implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr cbrt(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::cbrt(arg));
+			#else
+				if(builtin_isnan(arg) || builtin_isinf(arg))
+					return expr(arg);
+				return expr(builtin_signbit(arg) ? -static_cast<float>(std::pow(-static_cast<double>(arg), 1.0/3.0)) : 
+					static_cast<float>(std::pow(static_cast<double>(arg), 1.0/3.0)));
+			#endif
+			}
+
+			/// Hypotenuse implementation.
+			/// \param x first argument
+			/// \param y second argument
+			/// \return function value stored in single-preicision
+			static expr hypot(float x, float y)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::hypot(x, y));
+			#else
+				return expr((builtin_isinf(x) || builtin_isinf(y)) ? std::numeric_limits<float>::infinity() : 
+					static_cast<float>(std::sqrt(static_cast<double>(x)*x+static_cast<double>(y)*y)));
+			#endif
+			}
+
+			/// Power implementation.
+			/// \param base value to exponentiate
+			/// \param exp power to expontiate to
+			/// \return function value stored in single-preicision
+			static expr pow(float base, float exp) { return expr(std::pow(base, exp)); }
+
+			/// Sine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr sin(float arg) { return expr(std::sin(arg)); }
+
+			/// Cosine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr cos(float arg) { return expr(std::cos(arg)); }
+
+			/// Tan implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr tan(float arg) { return expr(std::tan(arg)); }
+
+			/// Arc sine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr asin(float arg) { return expr(std::asin(arg)); }
+
+			/// Arc cosine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr acos(float arg) { return expr(std::acos(arg)); }
+
+			/// Arc tangent implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr atan(float arg) { return expr(std::atan(arg)); }
+
+			/// Arc tangent implementation.
+			/// \param x first argument
+			/// \param y second argument
+			/// \return function value stored in single-preicision
+			static expr atan2(float x, float y) { return expr(std::atan2(x, y)); }
+
+			/// Hyperbolic sine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr sinh(float arg) { return expr(std::sinh(arg)); }
+
+			/// Hyperbolic cosine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr cosh(float arg) { return expr(std::cosh(arg)); }
+
+			/// Hyperbolic tangent implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr tanh(float arg) { return expr(std::tanh(arg)); }
+
+			/// Hyperbolic area sine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr asinh(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::asinh(arg));
+			#else
+				return expr((arg==-std::numeric_limits<float>::infinity()) ? arg : static_cast<float>(std::log(arg+std::sqrt(arg*arg+1.0))));
+			#endif
+			}
+
+			/// Hyperbolic area cosine implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr acosh(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::acosh(arg));
+			#else
+				return expr((arg<-1.0f) ? std::numeric_limits<float>::quiet_NaN() : static_cast<float>(std::log(arg+std::sqrt(arg*arg-1.0))));
+			#endif
+			}
+
+			/// Hyperbolic area tangent implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr atanh(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::atanh(arg));
+			#else
+				return expr(static_cast<float>(0.5*std::log((1.0+arg)/(1.0-arg))));
+			#endif
+			}
+
+			/// Error function implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr erf(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::erf(arg));
+			#else
+				return expr(static_cast<float>(erf(static_cast<double>(arg))));
+			#endif
+			}
+
+			/// Complementary implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr erfc(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::erfc(arg));
+			#else
+				return expr(static_cast<float>(1.0-erf(static_cast<double>(arg))));
+			#endif
+			}
+
+			/// Gamma logarithm implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr lgamma(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::lgamma(arg));
+			#else
+				if(builtin_isinf(arg))
+					return expr(std::numeric_limits<float>::infinity());
+				if(arg < 0.0f)
+				{
+					float i, f = std::modf(-arg, &i);
+					if(f == 0.0f)
+						return expr(std::numeric_limits<float>::infinity());
+					return expr(static_cast<float>(1.1447298858494001741434273513531-
+						std::log(std::abs(std::sin(3.1415926535897932384626433832795*f)))-lgamma(1.0-arg)));
+				}
+				return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
+			#endif
+			}
+
+			/// Gamma implementation.
+			/// \param arg function argument
+			/// \return function value stored in single-preicision
+			static expr tgamma(float arg)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::tgamma(arg));
+			#else
+				if(arg == 0.0f)
+					return builtin_signbit(arg) ? expr(-std::numeric_limits<float>::infinity()) : expr(std::numeric_limits<float>::infinity());
+				if(arg < 0.0f)
+				{
+					float i, f = std::modf(-arg, &i);
+					if(f == 0.0f)
+						return expr(std::numeric_limits<float>::quiet_NaN());
+					double value = 3.1415926535897932384626433832795 / (std::sin(3.1415926535897932384626433832795*f)*std::exp(lgamma(1.0-arg)));
+					return expr(static_cast<float>((std::fmod(i, 2.0f)==0.0f) ? -value : value));
+				}
+				if(builtin_isinf(arg))
+					return expr(arg);
+				return expr(static_cast<float>(std::exp(lgamma(static_cast<double>(arg)))));
+			#endif
+			}
+
+			/// Floor implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static half floor(half arg) { return half(binary, round_half<std::round_toward_neg_infinity>(arg.data_)); }
+
+			/// Ceiling implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static half ceil(half arg) { return half(binary, round_half<std::round_toward_infinity>(arg.data_)); }
+
+			/// Truncation implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static half trunc(half arg) { return half(binary, round_half<std::round_toward_zero>(arg.data_)); }
+
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static half round(half arg) { return half(binary, round_half_up(arg.data_)); }
+
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static long lround(half arg) { return detail::half2int_up<long>(arg.data_); }
+
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static half rint(half arg) { return half(binary, round_half<half::round_style>(arg.data_)); }
+
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static long lrint(half arg) { return detail::half2int<half::round_style,long>(arg.data_); }
+
+		#if HALF_ENABLE_CPP11_LONG_LONG
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static long long llround(half arg) { return detail::half2int_up<long long>(arg.data_); }
+
+			/// Nearest integer implementation.
+			/// \param arg value to round
+			/// \return rounded value
+			static long long llrint(half arg) { return detail::half2int<half::round_style,long long>(arg.data_); }
+		#endif
+
+			/// Decompression implementation.
+			/// \param arg number to decompress
+			/// \param exp address to store exponent at
+			/// \return normalized significant
+			static half frexp(half arg, int *exp)
+			{
+				int m = arg.data_ & 0x7FFF, e = -14;
+				if(m >= 0x7C00 || !m)
+					return *exp = 0, arg;
+				for(; m<0x400; m<<=1,--e) ;
+				return *exp = e+(m>>10), half(binary, (arg.data_&0x8000)|0x3800|(m&0x3FF));
+			}
+
+			/// Decompression implementation.
+			/// \param arg number to decompress
+			/// \param iptr address to store integer part at
+			/// \return fractional part
+			static half modf(half arg, half *iptr)
+			{
+				unsigned int e = arg.data_ & 0x7FFF;
+				if(e >= 0x6400)
+					return *iptr = arg, half(binary, arg.data_&(0x8000U|-(e>0x7C00)));
+				if(e < 0x3C00)
+					return iptr->data_ = arg.data_ & 0x8000, arg;
+				e >>= 10;
+				unsigned int mask = (1<<(25-e)) - 1, m = arg.data_ & mask;
+				iptr->data_ = arg.data_ & ~mask;
+				if(!m)
+					return half(binary, arg.data_&0x8000);
+				for(; m<0x400; m<<=1,--e) ;
+				return half(binary, static_cast<uint16>((arg.data_&0x8000)|(e<<10)|(m&0x3FF)));
+			}
+
+			/// Scaling implementation.
+			/// \param arg number to scale
+			/// \param exp power of two to scale by
+			/// \return scaled number
+			static half scalbln(half arg, long exp)
+			{
+				unsigned int m = arg.data_ & 0x7FFF;
+				if(m >= 0x7C00 || !m)
+					return arg;
+				for(; m<0x400; m<<=1,--exp) ;
+				exp += m >> 10;
+				uint16 value = arg.data_ & 0x8000;
+				if(exp > 30)
+				{
+					if(half::round_style == std::round_toward_zero)
+						value |= 0x7BFF;
+					else if(half::round_style == std::round_toward_infinity)
+						value |= 0x7C00 - (value>>15);
+					else if(half::round_style == std::round_toward_neg_infinity)
+						value |= 0x7BFF + (value>>15);
+					else
+						value |= 0x7C00;
+				}
+				else if(exp > 0)
+					value |= (exp<<10) | (m&0x3FF);
+				else if(exp > -11)
+				{
+					m = (m&0x3FF) | 0x400;
+					if(half::round_style == std::round_to_nearest)
+					{
+						m += 1 << -exp;
+					#if HALF_ROUND_TIES_TO_EVEN
+						m -= (m>>(1-exp)) & 1;
+					#endif
+					}
+					else if(half::round_style == std::round_toward_infinity)
+						m += ((value>>15)-1) & ((1<<(1-exp))-1U);
+					else if(half::round_style == std::round_toward_neg_infinity)
+						m += -(value>>15) & ((1<<(1-exp))-1U);
+					value |= m >> (1-exp);
+				}
+				else if(half::round_style == std::round_toward_infinity)
+					value -= (value>>15) - 1;
+				else if(half::round_style == std::round_toward_neg_infinity)
+					value += value >> 15;
+				return half(binary, value);
+			}
+
+			/// Exponent implementation.
+			/// \param arg number to query
+			/// \return floating point exponent
+			static int ilogb(half arg)
+			{
+				int abs = arg.data_ & 0x7FFF;
+				if(!abs)
+					return FP_ILOGB0;
+				if(abs < 0x7C00)
+				{
+					int exp = (abs>>10) - 15;
+					if(abs < 0x400)
+						for(; abs<0x200; abs<<=1,--exp) ;
+					return exp;
+				}
+				if(abs > 0x7C00)
+					return FP_ILOGBNAN;
+				return INT_MAX;
+			}
+
+			/// Exponent implementation.
+			/// \param arg number to query
+			/// \return floating point exponent
+			static half logb(half arg)
+			{
+				int abs = arg.data_ & 0x7FFF;
+				if(!abs)
+					return half(binary, 0xFC00);
+				if(abs < 0x7C00)
+				{
+					int exp = (abs>>10) - 15;
+					if(abs < 0x400)
+						for(; abs<0x200; abs<<=1,--exp) ;
+					uint16 bits = (exp<0) << 15;
+					if(exp)
+					{
+						unsigned int m = std::abs(exp) << 6, e = 18;
+						for(; m<0x400; m<<=1,--e) ;
+						bits |= (e<<10) + m;
+					}
+					return half(binary, bits);
+				}
+				if(abs > 0x7C00)
+					return arg;
+				return half(binary, 0x7C00);
+			}
+
+			/// Enumeration implementation.
+			/// \param from number to increase/decrease
+			/// \param to direction to enumerate into
+			/// \return next representable number
+			static half nextafter(half from, half to)
+			{
+				uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
+				if(fabs > 0x7C00)
+					return from;
+				if(tabs > 0x7C00 || from.data_ == to.data_ || !(fabs|tabs))
+					return to;
+				if(!fabs)
+					return half(binary, (to.data_&0x8000)+1);
+				bool lt = ((fabs==from.data_) ? static_cast<int>(fabs) : -static_cast<int>(fabs)) < 
+					((tabs==to.data_) ? static_cast<int>(tabs) : -static_cast<int>(tabs));
+				return half(binary, from.data_+(((from.data_>>15)^static_cast<unsigned>(lt))<<1)-1);
+			}
+
+			/// Enumeration implementation.
+			/// \param from number to increase/decrease
+			/// \param to direction to enumerate into
+			/// \return next representable number
+			static half nexttoward(half from, long double to)
+			{
+				if(isnan(from))
+					return from;
+				long double lfrom = static_cast<long double>(from);
+				if(builtin_isnan(to) || lfrom == to)
+					return half(static_cast<float>(to));
+				if(!(from.data_&0x7FFF))
+					return half(binary, (static_cast<detail::uint16>(builtin_signbit(to))<<15)+1);
+				return half(binary, from.data_+(((from.data_>>15)^static_cast<unsigned>(lfrom<to))<<1)-1);
+			}
+
+			/// Sign implementation
+			/// \param x first operand
+			/// \param y second operand
+			/// \return composed value
+			static half copysign(half x, half y) { return half(binary, x.data_^((x.data_^y.data_)&0x8000)); }
+
+			/// Classification implementation.
+			/// \param arg value to classify
+			/// \retval true if infinite number
+			/// \retval false else
+			static int fpclassify(half arg)
+			{
+				unsigned int abs = arg.data_ & 0x7FFF;
+				return abs ? ((abs>0x3FF) ? ((abs>=0x7C00) ? ((abs>0x7C00) ? FP_NAN : FP_INFINITE) : FP_NORMAL) :FP_SUBNORMAL) : FP_ZERO;
+			}
+
+			/// Classification implementation.
+			/// \param arg value to classify
+			/// \retval true if finite number
+			/// \retval false else
+			static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }
+
+			/// Classification implementation.
+			/// \param arg value to classify
+			/// \retval true if infinite number
+			/// \retval false else
+			static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }
+
+			/// Classification implementation.
+			/// \param arg value to classify
+			/// \retval true if not a number
+			/// \retval false else
+			static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }
+
+			/// Classification implementation.
+			/// \param arg value to classify
+			/// \retval true if normal number
+			/// \retval false else
+			static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }
+
+			/// Sign bit implementation.
+			/// \param arg value to check
+			/// \retval true if signed
+			/// \retval false if unsigned
+			static bool signbit(half arg) { return (arg.data_&0x8000) != 0; }
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if operands equal
+			/// \retval false else
+			static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); }
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if operands not equal
+			/// \retval false else
+			static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); }
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if \a x > \a y
+			/// \retval false else
+			static bool isgreater(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) > ((yabs==y.data_) ? yabs : -yabs));
+			}
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if \a x >= \a y
+			/// \retval false else
+			static bool isgreaterequal(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) >= ((yabs==y.data_) ? yabs : -yabs));
+			}
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if \a x < \a y
+			/// \retval false else
+			static bool isless(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) < ((yabs==y.data_) ? yabs : -yabs));
+			}
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if \a x <= \a y
+			/// \retval false else
+			static bool islessequal(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) <= ((yabs==y.data_) ? yabs : -yabs));
+			}
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if either \a x > \a y nor \a x < \a y
+			/// \retval false else
+			static bool islessgreater(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				if(xabs > 0x7C00 || yabs > 0x7C00)
+					return false;
+				int a = (xabs==x.data_) ? xabs : -xabs, b = (yabs==y.data_) ? yabs : -yabs;
+				return a < b || a > b;
+			}
+
+			/// Comparison implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \retval true if operand unordered
+			/// \retval false else
+			static bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
+
+		private:
+			static double erf(double arg)
+			{
+				if(builtin_isinf(arg))
+					return (arg<0.0) ? -1.0 : 1.0;
+				double x2 = arg * arg, ax2 = 0.147 * x2, value = std::sqrt(1.0-std::exp(-x2*(1.2732395447351626861510701069801+ax2)/(1.0+ax2)));
+				return builtin_signbit(arg) ? -value : value;
+			}
+
+			static double lgamma(double arg)
+			{
+				double v = 1.0;
+				for(; arg<8.0; ++arg) v *= arg;
+				double w = 1.0 / (arg*arg);
+				return (((((((-0.02955065359477124183006535947712*w+0.00641025641025641025641025641026)*w+
+					-0.00191752691752691752691752691753)*w+8.4175084175084175084175084175084e-4)*w+
+					-5.952380952380952380952380952381e-4)*w+7.9365079365079365079365079365079e-4)*w+
+					-0.00277777777777777777777777777778)*w+0.08333333333333333333333333333333)/arg + 
+					0.91893853320467274178032973640562 - std::log(v) - arg + (arg-0.5) * std::log(arg);
+			}
+		};
+
+		/// Wrapper for unary half-precision functions needing specialization for individual argument types.
+		/// \tparam T argument type
+		template<typename T> struct unary_specialized
+		{
+			/// Negation implementation.
+			/// \param arg value to negate
+			/// \return negated value
+			static HALF_CONSTEXPR half negate(half arg) { return half(binary, arg.data_^0x8000); }
+
+			/// Absolute value implementation.
+			/// \param arg function argument
+			/// \return absolute value
+			static half fabs(half arg) { return half(binary, arg.data_&0x7FFF); }
+		};
+		template<> struct unary_specialized<expr>
+		{
+			static HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); }
+			static expr fabs(float arg) { return expr(std::fabs(arg)); }
+		};
+
+		/// Wrapper for binary half-precision functions needing specialization for individual argument types.
+		/// \tparam T first argument type
+		/// \tparam U first argument type
+		template<typename T,typename U> struct binary_specialized
+		{
+			/// Minimum implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return minimum value
+			static expr fmin(float x, float y)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::fmin(x, y));
+			#else
+				if(builtin_isnan(x))
+					return expr(y);
+				if(builtin_isnan(y))
+					return expr(x);
+				return expr(std::min(x, y));
+			#endif
+			}
+
+			/// Maximum implementation.
+			/// \param x first operand
+			/// \param y second operand
+			/// \return maximum value
+			static expr fmax(float x, float y)
+			{
+			#if HALF_ENABLE_CPP11_CMATH
+				return expr(std::fmax(x, y));
+			#else
+				if(builtin_isnan(x))
+					return expr(y);
+				if(builtin_isnan(y))
+					return expr(x);
+				return expr(std::max(x, y));
+			#endif
+			}
+		};
+		template<> struct binary_specialized<half,half>
+		{
+			static half fmin(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				if(xabs > 0x7C00)
+					return y;
+				if(yabs > 0x7C00)
+					return x;
+				return (((xabs==x.data_) ? xabs : -xabs) > ((yabs==y.data_) ? yabs : -yabs)) ? y : x;
+			}
+			static half fmax(half x, half y)
+			{
+				int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+				if(xabs > 0x7C00)
+					return y;
+				if(yabs > 0x7C00)
+					return x;
+				return (((xabs==x.data_) ? xabs : -xabs) < ((yabs==y.data_) ? yabs : -yabs)) ? y : x;
+			}
+		};
+
+		/// Helper class for half casts.
+		/// This class template has to be specialized for all valid cast argument 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,T>(arg.data_); }
+		};
+		template<typename T,std::float_round_style R> struct half_caster<T,expr,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(expr arg) { return cast_impl(arg, is_float<T>()); }
+
+		private:
+			static T cast_impl(float arg, true_type) { return static_cast<T>(arg); }
+			static T cast_impl(half arg, false_type) { return half2int<R,T>(arg.data_); }
+		};
+		template<std::float_round_style R> struct half_caster<half,half,R>
+		{
+			static half cast(half arg) { return arg; }
+		};
+		template<std::float_round_style R> struct half_caster<half,expr,R> : half_caster<half,half,R> {};
+
+		/// \name Comparison operators
+		/// \{
+
+		/// Comparison for equality.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if operands equal
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator==(T x, U y) { return functions::isequal(x, y); }
+
+		/// Comparison for inequality.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if operands not equal
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator!=(T x, U y) { return functions::isnotequal(x, y); }
+
+		/// Comparison for less than.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x less than \a y
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator<(T x, U y) { return functions::isless(x, y); }
+
+		/// Comparison for greater than.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x greater than \a y
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator>(T x, U y) { return functions::isgreater(x, y); }
+
+		/// Comparison for less equal.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x less equal \a y
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator<=(T x, U y) { return functions::islessequal(x, y); }
+
+		/// Comparison for greater equal.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x greater equal \a y
+		/// \retval false else
+		template<typename T,typename U> typename enable<bool,T,U>::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); }
+
+		/// \}
+		/// \name Arithmetic operators
+		/// \{
+
+		/// Add halfs.
+		/// \param x left operand
+		/// \param y right operand
+		/// \return sum of half expressions
+		template<typename T,typename U> typename enable<expr,T,U>::type operator+(T x, U y) { return functions::plus(x, y); }
+
+		/// Subtract halfs.
+		/// \param x left operand
+		/// \param y right operand
+		/// \return difference of half expressions
+		template<typename T,typename U> typename enable<expr,T,U>::type operator-(T x, U y) { return functions::minus(x, y); }
+
+		/// Multiply halfs.
+		/// \param x left operand
+		/// \param y right operand
+		/// \return product of half expressions
+		template<typename T,typename U> typename enable<expr,T,U>::type operator*(T x, U y) { return functions::multiplies(x, y); }
+
+		/// Divide halfs.
+		/// \param x left operand
+		/// \param y right operand
+		/// \return quotient of half expressions
+		template<typename T,typename U> typename enable<expr,T,U>::type operator/(T x, U y) { return functions::divides(x, y); }
+
+		/// Identity.
+		/// \param arg operand
+		/// \return uncahnged operand
+		template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator+(T arg) { return arg; }
+
+		/// Negation.
+		/// \param arg operand
+		/// \return negated operand
+		template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator-(T arg) { return unary_specialized<T>::negate(arg); }
+
+		/// \}
+		/// \name Input and output
+		/// \{
+
+		/// Output operator.
+		/// \param out output stream to write into
+		/// \param arg half expression to write
+		/// \return reference to output stream
+		template<typename T,typename charT,typename traits> typename enable<std::basic_ostream<charT,traits>&,T>::type
+			operator<<(std::basic_ostream<charT,traits> &out, T arg) { return functions::write(out, arg); }
+
+		/// Input operator.
+		/// \param in input stream to read from
+		/// \param arg half to read into
+		/// \return reference to input stream
+		template<typename charT,typename traits> std::basic_istream<charT,traits>&
+			operator>>(std::basic_istream<charT,traits> &in, half &arg) { return functions::read(in, arg); }
+
+		/// \}
+		/// \name Basic mathematical operations
+		/// \{
+
+		/// Absolute value.
+		/// \param arg operand
+		/// \return absolute value of \a arg
+//		template<typename T> typename enable<T,T>::type abs(T arg) { return unary_specialized<T>::fabs(arg); }
+		inline half abs(half arg) { return unary_specialized<half>::fabs(arg); }
+		inline expr abs(expr arg) { return unary_specialized<expr>::fabs(arg); }
+
+		/// Absolute value.
+		/// \param arg operand
+		/// \return absolute value of \a arg
+//		template<typename T> typename enable<T,T>::type fabs(T arg) { return unary_specialized<T>::fabs(arg); }
+		inline half fabs(half arg) { return unary_specialized<half>::fabs(arg); }
+		inline expr fabs(expr arg) { return unary_specialized<expr>::fabs(arg); }
+
+		/// Remainder of division.
+		/// \param x first operand
+		/// \param y second operand
+		/// \return remainder of floating point division.
+//		template<typename T,typename U> typename enable<expr,T,U>::type fmod(T x, U y) { return functions::fmod(x, y); }
+		inline expr fmod(half x, half y) { return functions::fmod(x, y); }
+		inline expr fmod(half x, expr y) { return functions::fmod(x, y); }
+		inline expr fmod(expr x, half y) { return functions::fmod(x, y); }
+		inline expr fmod(expr x, expr y) { return functions::fmod(x, y); }
+
+		/// Remainder of division.
+		/// \param x first operand
+		/// \param y second operand
+		/// \return remainder of floating point division.
+//		template<typename T,typename U> typename enable<expr,T,U>::type remainder(T x, U y) { return functions::remainder(x, y); }
+		inline expr remainder(half x, half y) { return functions::remainder(x, y); }
+		inline expr remainder(half x, expr y) { return functions::remainder(x, y); }
+		inline expr remainder(expr x, half y) { return functions::remainder(x, y); }
+		inline expr remainder(expr x, expr y) { return functions::remainder(x, y); }
+
+		/// Remainder of division.
+		/// \param x first operand
+		/// \param y second operand
+		/// \param quo address to store some bits of quotient at
+		/// \return remainder of floating point division.
+//		template<typename T,typename U> typename enable<expr,T,U>::type remquo(T x, U y, int *quo) { return functions::remquo(x, y, quo); }
+		inline expr remquo(half x, half y, int *quo) { return functions::remquo(x, y, quo); }
+		inline expr remquo(half x, expr y, int *quo) { return functions::remquo(x, y, quo); }
+		inline expr remquo(expr x, half y, int *quo) { return functions::remquo(x, y, quo); }
+		inline expr remquo(expr x, expr y, int *quo) { return functions::remquo(x, y, quo); }
+
+		/// Fused multiply add.
+		/// \param x first operand
+		/// \param y second operand
+		/// \param z third operand
+		/// \return ( \a x * \a y ) + \a z rounded as one operation.
+//		template<typename T,typename U,typename V> typename enable<expr,T,U,V>::type fma(T x, U y, V z) { return functions::fma(x, y, z); }
+		inline expr fma(half x, half y, half z) { return functions::fma(x, y, z); }
+		inline expr fma(half x, half y, expr z) { return functions::fma(x, y, z); }
+		inline expr fma(half x, expr y, half z) { return functions::fma(x, y, z); }
+		inline expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); }
+		inline expr fma(expr x, half y, half z) { return functions::fma(x, y, z); }
+		inline expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); }
+		inline expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); }
+		inline expr fma(expr x, expr y, expr z) { return functions::fma(x, y, z); }
+
+		/// Maximum of half expressions.
+		/// \param x first operand
+		/// \param y second operand
+		/// \return maximum of operands
+//		template<typename T,typename U> typename result<T,U>::type fmax(T x, U y) { return binary_specialized<T,U>::fmax(x, y); }
+		inline half fmax(half x, half y) { return binary_specialized<half,half>::fmax(x, y); }
+		inline expr fmax(half x, expr y) { return binary_specialized<half,expr>::fmax(x, y); }
+		inline expr fmax(expr x, half y) { return binary_specialized<expr,half>::fmax(x, y); }
+		inline expr fmax(expr x, expr y) { return binary_specialized<expr,expr>::fmax(x, y); }
+
+		/// Minimum of half expressions.
+		/// \param x first operand
+		/// \param y second operand
+		/// \return minimum of operands
+//		template<typename T,typename U> typename result<T,U>::type fmin(T x, U y) { return binary_specialized<T,U>::fmin(x, y); }
+		inline half fmin(half x, half y) { return binary_specialized<half,half>::fmin(x, y); }
+		inline expr fmin(half x, expr y) { return binary_specialized<half,expr>::fmin(x, y); }
+		inline expr fmin(expr x, half y) { return binary_specialized<expr,half>::fmin(x, y); }
+		inline expr fmin(expr x, expr y) { return binary_specialized<expr,expr>::fmin(x, y); }
+
+		/// Positive difference.
+		/// \param x first operand
+		/// \param y second operand
+		/// \return \a x - \a y or 0 if difference negative
+//		template<typename T,typename U> typename enable<expr,T,U>::type fdim(T x, U y) { return functions::fdim(x, y); }
+		inline expr fdim(half x, half y) { return functions::fdim(x, y); }
+		inline expr fdim(half x, expr y) { return functions::fdim(x, y); }
+		inline expr fdim(expr x, half y) { return functions::fdim(x, y); }
+		inline expr fdim(expr x, expr y) { return functions::fdim(x, y); }
+
+		/// Get NaN value.
+		/// \return quiet NaN
+		inline half nanh(const char*) { return functions::nanh(); }
+
+		/// \}
+		/// \name Exponential functions
+		/// \{
+
+		/// Exponential function.
+		/// \param arg function argument
+		/// \return e raised to \a arg
+//		template<typename T> typename enable<expr,T>::type exp(T arg) { return functions::exp(arg); }
+		inline expr exp(half arg) { return functions::exp(arg); }
+		inline expr exp(expr arg) { return functions::exp(arg); }
+
+		/// Exponential minus one.
+		/// \param arg function argument
+		/// \return e raised to \a arg subtracted by 1
+//		template<typename T> typename enable<expr,T>::type expm1(T arg) { return functions::expm1(arg); }
+		inline expr expm1(half arg) { return functions::expm1(arg); }
+		inline expr expm1(expr arg) { return functions::expm1(arg); }
+
+		/// Binary exponential.
+		/// \param arg function argument
+		/// \return 2 raised to \a arg
+//		template<typename T> typename enable<expr,T>::type exp2(T arg) { return functions::exp2(arg); }
+		inline expr exp2(half arg) { return functions::exp2(arg); }
+		inline expr exp2(expr arg) { return functions::exp2(arg); }
+
+		/// Natural logorithm.
+		/// \param arg function argument
+		/// \return logarithm of \a arg to base e
+//		template<typename T> typename enable<expr,T>::type log(T arg) { return functions::log(arg); }
+		inline expr log(half arg) { return functions::log(arg); }
+		inline expr log(expr arg) { return functions::log(arg); }
+
+		/// Common logorithm.
+		/// \param arg function argument
+		/// \return logarithm of \a arg to base 10
+//		template<typename T> typename enable<expr,T>::type log10(T arg) { return functions::log10(arg); }
+		inline expr log10(half arg) { return functions::log10(arg); }
+		inline expr log10(expr arg) { return functions::log10(arg); }
+
+		/// Natural logorithm.
+		/// \param arg function argument
+		/// \return logarithm of \a arg plus 1 to base e
+//		template<typename T> typename enable<expr,T>::type log1p(T arg) { return functions::log1p(arg); }
+		inline expr log1p(half arg) { return functions::log1p(arg); }
+		inline expr log1p(expr arg) { return functions::log1p(arg); }
+
+		/// Binary logorithm.
+		/// \param arg function argument
+		/// \return logarithm of \a arg to base 2
+//		template<typename T> typename enable<expr,T>::type log2(T arg) { return functions::log2(arg); }
+		inline expr log2(half arg) { return functions::log2(arg); }
+		inline expr log2(expr arg) { return functions::log2(arg); }
+
+		/// \}
+		/// \name Power functions
+		/// \{
+
+		/// Square root.
+		/// \param arg function argument
+		/// \return square root of \a arg
+//		template<typename T> typename enable<expr,T>::type sqrt(T arg) { return functions::sqrt(arg); }
+		inline expr sqrt(half arg) { return functions::sqrt(arg); }
+		inline expr sqrt(expr arg) { return functions::sqrt(arg); }
+
+		/// Cubic root.
+		/// \param arg function argument
+		/// \return cubic root of \a arg
+//		template<typename T> typename enable<expr,T>::type cbrt(T arg) { return functions::cbrt(arg); }
+		inline expr cbrt(half arg) { return functions::cbrt(arg); }
+		inline expr cbrt(expr arg) { return functions::cbrt(arg); }
+
+		/// Hypotenuse function.
+		/// \param x first argument
+		/// \param y second argument
+		/// \return square root of sum of squares without internal over- or underflows
+//		template<typename T,typename U> typename enable<expr,T,U>::type hypot(T x, U y) { return functions::hypot(x, y); }
+		inline expr hypot(half x, half y) { return functions::hypot(x, y); }
+		inline expr hypot(half x, expr y) { return functions::hypot(x, y); }
+		inline expr hypot(expr x, half y) { return functions::hypot(x, y); }
+		inline expr hypot(expr x, expr y) { return functions::hypot(x, y); }
+
+		/// Power function.
+		/// \param base first argument
+		/// \param exp second argument
+		/// \return \a base raised to \a exp
+//		template<typename T,typename U> typename enable<expr,T,U>::type pow(T base, U exp) { return functions::pow(base, exp); }
+		inline expr pow(half base, half exp) { return functions::pow(base, exp); }
+		inline expr pow(half base, expr exp) { return functions::pow(base, exp); }
+		inline expr pow(expr base, half exp) { return functions::pow(base, exp); }
+		inline expr pow(expr base, expr exp) { return functions::pow(base, exp); }
+
+		/// \}
+		/// \name Trigonometric functions
+		/// \{
+
+		/// Sine function.
+		/// \param arg function argument
+		/// \return sine value of \a arg
+//		template<typename T> typename enable<expr,T>::type sin(T arg) { return functions::sin(arg); }
+		inline expr sin(half arg) { return functions::sin(arg); }
+		inline expr sin(expr arg) { return functions::sin(arg); }
+
+		/// Cosine function.
+		/// \param arg function argument
+		/// \return cosine value of \a arg
+//		template<typename T> typename enable<expr,T>::type cos(T arg) { return functions::cos(arg); }
+		inline expr cos(half arg) { return functions::cos(arg); }
+		inline expr cos(expr arg) { return functions::cos(arg); }
+
+		/// Tangent function.
+		/// \param arg function argument
+		/// \return tangent value of \a arg
+//		template<typename T> typename enable<expr,T>::type tan(T arg) { return functions::tan(arg); }
+		inline expr tan(half arg) { return functions::tan(arg); }
+		inline expr tan(expr arg) { return functions::tan(arg); }
+
+		/// Arc sine.
+		/// \param arg function argument
+		/// \return arc sine value of \a arg
+//		template<typename T> typename enable<expr,T>::type asin(T arg) { return functions::asin(arg); }
+		inline expr asin(half arg) { return functions::asin(arg); }
+		inline expr asin(expr arg) { return functions::asin(arg); }
+
+		/// Arc cosine function.
+		/// \param arg function argument
+		/// \return arc cosine value of \a arg
+//		template<typename T> typename enable<expr,T>::type acos(T arg) { return functions::acos(arg); }
+		inline expr acos(half arg) { return functions::acos(arg); }
+		inline expr acos(expr arg) { return functions::acos(arg); }
+
+		/// Arc tangent function.
+		/// \param arg function argument
+		/// \return arc tangent value of \a arg
+//		template<typename T> typename enable<expr,T>::type atan(T arg) { return functions::atan(arg); }
+		inline expr atan(half arg) { return functions::atan(arg); }
+		inline expr atan(expr arg) { return functions::atan(arg); }
+
+		/// Arc tangent function.
+		/// \param x first argument
+		/// \param y second argument
+		/// \return arc tangent value
+//		template<typename T,typename U> typename enable<expr,T,U>::type atan2(T x, U y) { return functions::atan2(x, y); }
+		inline expr atan2(half x, half y) { return functions::atan2(x, y); }
+		inline expr atan2(half x, expr y) { return functions::atan2(x, y); }
+		inline expr atan2(expr x, half y) { return functions::atan2(x, y); }
+		inline expr atan2(expr x, expr y) { return functions::atan2(x, y); }
+
+		/// \}
+		/// \name Hyperbolic functions
+		/// \{
+
+		/// Hyperbolic sine.
+		/// \param arg function argument
+		/// \return hyperbolic sine value of \a arg
+//		template<typename T> typename enable<expr,T>::type sinh(T arg) { return functions::sinh(arg); }
+		inline expr sinh(half arg) { return functions::sinh(arg); }
+		inline expr sinh(expr arg) { return functions::sinh(arg); }
+
+		/// Hyperbolic cosine.
+		/// \param arg function argument
+		/// \return hyperbolic cosine value of \a arg
+//		template<typename T> typename enable<expr,T>::type cosh(T arg) { return functions::cosh(arg); }
+		inline expr cosh(half arg) { return functions::cosh(arg); }
+		inline expr cosh(expr arg) { return functions::cosh(arg); }
+
+		/// Hyperbolic tangent.
+		/// \param arg function argument
+		/// \return hyperbolic tangent value of \a arg
+//		template<typename T> typename enable<expr,T>::type tanh(T arg) { return functions::tanh(arg); }
+		inline expr tanh(half arg) { return functions::tanh(arg); }
+		inline expr tanh(expr arg) { return functions::tanh(arg); }
+
+		/// Hyperbolic area sine.
+		/// \param arg function argument
+		/// \return area sine value of \a arg
+//		template<typename T> typename enable<expr,T>::type asinh(T arg) { return functions::asinh(arg); }
+		inline expr asinh(half arg) { return functions::asinh(arg); }
+		inline expr asinh(expr arg) { return functions::asinh(arg); }
+
+		/// Hyperbolic area cosine.
+		/// \param arg function argument
+		/// \return area cosine value of \a arg
+//		template<typename T> typename enable<expr,T>::type acosh(T arg) { return functions::acosh(arg); }
+		inline expr acosh(half arg) { return functions::acosh(arg); }
+		inline expr acosh(expr arg) { return functions::acosh(arg); }
+
+		/// Hyperbolic area tangent.
+		/// \param arg function argument
+		/// \return area tangent value of \a arg
+//		template<typename T> typename enable<expr,T>::type atanh(T arg) { return functions::atanh(arg); }
+		inline expr atanh(half arg) { return functions::atanh(arg); }
+		inline expr atanh(expr arg) { return functions::atanh(arg); }
+
+		/// \}
+		/// \name Error and gamma functions
+		/// \{
+
+		/// Error function.
+		/// \param arg function argument
+		/// \return error function value of \a arg
+//		template<typename T> typename enable<expr,T>::type erf(T arg) { return functions::erf(arg); }
+		inline expr erf(half arg) { return functions::erf(arg); }
+		inline expr erf(expr arg) { return functions::erf(arg); }
+
+		/// Complementary error function.
+		/// \param arg function argument
+		/// \return 1 minus error function value of \a arg
+//		template<typename T> typename enable<expr,T>::type erfc(T arg) { return functions::erfc(arg); }
+		inline expr erfc(half arg) { return functions::erfc(arg); }
+		inline expr erfc(expr arg) { return functions::erfc(arg); }
+
+		/// Natural logarithm of gamma function.
+		/// \param arg function argument
+		/// \return natural logarith of gamma function for \a arg
+//		template<typename T> typename enable<expr,T>::type lgamma(T arg) { return functions::lgamma(arg); }
+		inline expr lgamma(half arg) { return functions::lgamma(arg); }
+		inline expr lgamma(expr arg) { return functions::lgamma(arg); }
+
+		/// Gamma function.
+		/// \param arg function argument
+		/// \return gamma function value of \a arg
+//		template<typename T> typename enable<expr,T>::type tgamma(T arg) { return functions::tgamma(arg); }
+		inline expr tgamma(half arg) { return functions::tgamma(arg); }
+		inline expr tgamma(expr arg) { return functions::tgamma(arg); }
+
+		/// \}
+		/// \name Rounding
+		/// \{
+
+		/// Nearest integer not less than half value.
+		/// \param arg half to round
+		/// \return nearest integer not less than \a arg
+//		template<typename T> typename enable<half,T>::type ceil(T arg) { return functions::ceil(arg); }
+		inline half ceil(half arg) { return functions::ceil(arg); }
+		inline half ceil(expr arg) { return functions::ceil(arg); }
+
+		/// Nearest integer not greater than half value.
+		/// \param arg half to round
+		/// \return nearest integer not greater than \a arg
+//		template<typename T> typename enable<half,T>::type floor(T arg) { return functions::floor(arg); }
+		inline half floor(half arg) { return functions::floor(arg); }
+		inline half floor(expr arg) { return functions::floor(arg); }
+
+		/// Nearest integer not greater in magnitude than half value.
+		/// \param arg half to round
+		/// \return nearest integer not greater in magnitude than \a arg
+//		template<typename T> typename enable<half,T>::type trunc(T arg) { return functions::trunc(arg); }
+		inline half trunc(half arg) { return functions::trunc(arg); }
+		inline half trunc(expr arg) { return functions::trunc(arg); }
+
+		/// Nearest integer.
+		/// \param arg half to round
+		/// \return nearest integer, rounded away from zero in half-way cases
+//		template<typename T> typename enable<half,T>::type round(T arg) { return functions::round(arg); }
+		inline half round(half arg) { return functions::round(arg); }
+		inline half round(expr arg) { return functions::round(arg); }
+
+		/// Nearest integer.
+		/// \param arg half to round
+		/// \return nearest integer, rounded away from zero in half-way cases
+//		template<typename T> typename enable<long,T>::type lround(T arg) { return functions::lround(arg); }
+		inline long lround(half arg) { return functions::lround(arg); }
+		inline long lround(expr arg) { return functions::lround(arg); }
+
+		/// Nearest integer using half's internal rounding mode.
+		/// \param arg half expression to round
+		/// \return nearest integer using default rounding mode
+//		template<typename T> typename enable<half,T>::type nearbyint(T arg) { return functions::nearbyint(arg); }
+		inline half nearbyint(half arg) { return functions::rint(arg); }
+		inline half nearbyint(expr arg) { return functions::rint(arg); }
+
+		/// Nearest integer using half's internal rounding mode.
+		/// \param arg half expression to round
+		/// \return nearest integer using default rounding mode
+//		template<typename T> typename enable<half,T>::type rint(T arg) { return functions::rint(arg); }
+		inline half rint(half arg) { return functions::rint(arg); }
+		inline half rint(expr arg) { return functions::rint(arg); }
+
+		/// Nearest integer using half's internal rounding mode.
+		/// \param arg half expression to round
+		/// \return nearest integer using default rounding mode
+//		template<typename T> typename enable<long,T>::type lrint(T arg) { return functions::lrint(arg); }
+		inline long lrint(half arg) { return functions::lrint(arg); }
+		inline long lrint(expr arg) { return functions::lrint(arg); }
+	#if HALF_ENABLE_CPP11_LONG_LONG
+		/// Nearest integer.
+		/// \param arg half to round
+		/// \return nearest integer, rounded away from zero in half-way cases
+//		template<typename T> typename enable<long long,T>::type llround(T arg) { return functions::llround(arg); }
+		inline long long llround(half arg) { return functions::llround(arg); }
+		inline long long llround(expr arg) { return functions::llround(arg); }
+
+		/// Nearest integer using half's internal rounding mode.
+		/// \param arg half expression to round
+		/// \return nearest integer using default rounding mode
+//		template<typename T> typename enable<long long,T>::type llrint(T arg) { return functions::llrint(arg); }
+		inline long long llrint(half arg) { return functions::llrint(arg); }
+		inline long long llrint(expr arg) { return functions::llrint(arg); }
+	#endif
+
+		/// \}
+		/// \name Floating point manipulation
+		/// \{
+
+		/// Decompress floating point number.
+		/// \param arg number to decompress
+		/// \param exp address to store exponent at
+		/// \return significant in range [0.5, 1)
+//		template<typename T> typename enable<half,T>::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); }
+		inline half frexp(half arg, int *exp) { return functions::frexp(arg, exp); }
+		inline half frexp(expr arg, int *exp) { return functions::frexp(arg, exp); }
+
+		/// Multiply by power of two.
+		/// \param arg number to modify
+		/// \param exp power of two to multiply with
+		/// \return \a arg multplied by 2 raised to \a exp
+//		template<typename T> typename enable<half,T>::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp); }
+		inline half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); }
+		inline half ldexp(expr arg, int exp) { return functions::scalbln(arg, exp); }
+
+		/// Extract integer and fractional parts.
+		/// \param arg number to decompress
+		/// \param iptr address to store integer part at
+		/// \return fractional part
+//		template<typename T> typename enable<half,T>::type modf(T arg, half *iptr) { return functions::modf(arg, iptr); }
+		inline half modf(half arg, half *iptr) { return functions::modf(arg, iptr); }
+		inline half modf(expr arg, half *iptr) { return functions::modf(arg, iptr); }
+
+		/// Multiply by power of two.
+		/// \param arg number to modify
+		/// \param exp power of two to multiply with
+		/// \return \a arg multplied by 2 raised to \a exp
+//		template<typename T> typename enable<half,T>::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp); }
+		inline half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); }
+		inline half scalbn(expr arg, int exp) { return functions::scalbln(arg, exp); }
+
+		/// Multiply by power of two.
+		/// \param arg number to modify
+		/// \param exp power of two to multiply with
+		/// \return \a arg multplied by 2 raised to \a exp	
+//		template<typename T> typename enable<half,T>::type scalbln(T arg, long exp) { return functions::scalbln(arg, exp); }
+		inline half scalbln(half arg, long exp) { return functions::scalbln(arg, exp); }
+		inline half scalbln(expr arg, long exp) { return functions::scalbln(arg, exp); }
+
+		/// Extract exponent.
+		/// \param arg number to query
+		/// \return floating point exponent
+		/// \retval FP_ILOGB0 for zero
+		/// \retval FP_ILOGBNAN for NaN
+		/// \retval MAX_INT for infinity
+//		template<typename T> typename enable<int,T>::type ilogb(T arg) { return functions::ilogb(arg); }
+		inline int ilogb(half arg) { return functions::ilogb(arg); }
+		inline int ilogb(expr arg) { return functions::ilogb(arg); }
+
+		/// Extract exponent.
+		/// \param arg number to query
+		/// \return floating point exponent
+//		template<typename T> typename enable<half,T>::type logb(T arg) { return functions::logb(arg); }
+		inline half logb(half arg) { return functions::logb(arg); }
+		inline half logb(expr arg) { return functions::logb(arg); }
+
+		/// Next representable value.
+		/// \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
+//		template<typename T,typename U> typename enable<half,T,U>::type nextafter(T from, U to) { return functions::nextafter(from, to); }
+		inline half nextafter(half from, half to) { return functions::nextafter(from, to); }
+		inline half nextafter(half from, expr to) { return functions::nextafter(from, to); }
+		inline half nextafter(expr from, half to) { return functions::nextafter(from, to); }
+		inline half nextafter(expr from, expr to) { return functions::nextafter(from, to); }
+
+		/// Next representable value.
+		/// \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
+//		template<typename T> typename enable<half,T>::type nexttoward(T from, long double to) { return functions::nexttoward(from, to); }
+		inline half nexttoward(half from, long double to) { return functions::nexttoward(from, to); }
+		inline half nexttoward(expr from, long double to) { return functions::nexttoward(from, to); }
+
+		/// Take sign.
+		/// \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
+//		template<typename T,typename U> typename enable<half,T,U>::type copysign(T x, U y) { return functions::copysign(x, y); }
+		inline half copysign(half x, half y) { return functions::copysign(x, y); }
+		inline half copysign(half x, expr y) { return functions::copysign(x, y); }
+		inline half copysign(expr x, half y) { return functions::copysign(x, y); }
+		inline half copysign(expr x, expr y) { return functions::copysign(x, y); }
+
+		/// \}
+		/// \name Floating point classification
+		/// \{
+
+
+		/// Classify floating point value.
+		/// \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
+//		template<typename T> typename enable<int,T>::type fpclassify(T arg) { return functions::fpclassify(arg); }
+		inline int fpclassify(half arg) { return functions::fpclassify(arg); }
+		inline int fpclassify(expr arg) { return functions::fpclassify(arg); }
+
+		/// Check if finite number.
+		/// \param arg number to check
+		/// \retval true if neither infinity nor NaN
+		/// \retval false else
+//		template<typename T> typename enable<bool,T>::type isfinite(T arg) { return functions::isfinite(arg); }
+		inline bool isfinite(half arg) { return functions::isfinite(arg); }
+		inline bool isfinite(expr arg) { return functions::isfinite(arg); }
+
+		/// Check for infinity.
+		/// \param arg number to check
+		/// \retval true for positive or negative infinity
+		/// \retval false else
+//		template<typename T> typename enable<bool,T>::type isinf(T arg) { return functions::isinf(arg); }
+		inline bool isinf(half arg) { return functions::isinf(arg); }
+		inline bool isinf(expr arg) { return functions::isinf(arg); }
+
+		/// Check for NaN.
+		/// \param arg number to check
+		/// \retval true for NaNs
+		/// \retval false else
+//		template<typename T> typename enable<bool,T>::type isnan(T arg) { return functions::isnan(arg); }
+		inline bool isnan(half arg) { return functions::isnan(arg); }
+		inline bool isnan(expr arg) { return functions::isnan(arg); }
+
+		/// Check if normal number.
+		/// \param arg number to check
+		/// \retval true if normal number
+		/// \retval false if either subnormal, zero, infinity or NaN
+//		template<typename T> typename enable<bool,T>::type isnormal(T arg) { return functions::isnormal(arg); }
+		inline bool isnormal(half arg) { return functions::isnormal(arg); }
+		inline bool isnormal(expr arg) { return functions::isnormal(arg); }
+
+		/// Check sign.
+		/// \param arg number to check
+		/// \retval true for negative number
+		/// \retval false for positive number
+//		template<typename T> typename enable<bool,T>::type signbit(T arg) { return functions::signbit(arg); }
+		inline bool signbit(half arg) { return functions::signbit(arg); }
+		inline bool signbit(expr arg) { return functions::signbit(arg); }
+
+		/// \}
+		/// \name Comparison
+		/// \{
+
+		/// Comparison for greater than.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x greater than \a y
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type isgreater(T x, U y) { return functions::isgreater(x, y); }
+		inline bool isgreater(half x, half y) { return functions::isgreater(x, y); }
+		inline bool isgreater(half x, expr y) { return functions::isgreater(x, y); }
+		inline bool isgreater(expr x, half y) { return functions::isgreater(x, y); }
+		inline bool isgreater(expr x, expr y) { return functions::isgreater(x, y); }
+
+		/// Comparison for greater equal.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x greater equal \a y
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type isgreaterequal(T x, U y) { return functions::isgreaterequal(x, y); }
+		inline bool isgreaterequal(half x, half y) { return functions::isgreaterequal(x, y); }
+		inline bool isgreaterequal(half x, expr y) { return functions::isgreaterequal(x, y); }
+		inline bool isgreaterequal(expr x, half y) { return functions::isgreaterequal(x, y); }
+		inline bool isgreaterequal(expr x, expr y) { return functions::isgreaterequal(x, y); }
+
+		/// Comparison for less than.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x less than \a y
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type isless(T x, U y) { return functions::isless(x, y); }
+		inline bool isless(half x, half y) { return functions::isless(x, y); }
+		inline bool isless(half x, expr y) { return functions::isless(x, y); }
+		inline bool isless(expr x, half y) { return functions::isless(x, y); }
+		inline bool isless(expr x, expr y) { return functions::isless(x, y); }
+
+		/// Comparison for less equal.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if \a x less equal \a y
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type islessequal(T x, U y) { return functions::islessequal(x, y); }
+		inline bool islessequal(half x, half y) { return functions::islessequal(x, y); }
+		inline bool islessequal(half x, expr y) { return functions::islessequal(x, y); }
+		inline bool islessequal(expr x, half y) { return functions::islessequal(x, y); }
+		inline bool islessequal(expr x, expr y) { return functions::islessequal(x, y); }
+
+		/// Comarison for less or greater.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if either less or greater
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type islessgreater(T x, U y) { return functions::islessgreater(x, y); }
+		inline bool islessgreater(half x, half y) { return functions::islessgreater(x, y); }
+		inline bool islessgreater(half x, expr y) { return functions::islessgreater(x, y); }
+		inline bool islessgreater(expr x, half y) { return functions::islessgreater(x, y); }
+		inline bool islessgreater(expr x, expr y) { return functions::islessgreater(x, y); }
+
+		/// Check if unordered.
+		/// \param x first operand
+		/// \param y second operand
+		/// \retval true if unordered (one or two NaN operands)
+		/// \retval false else
+//		template<typename T,typename U> typename enable<bool,T,U>::type isunordered(T x, U y) { return functions::isunordered(x, y); }
+		inline bool isunordered(half x, half y) { return functions::isunordered(x, y); }
+		inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); }
+		inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); }
+		inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); }
+
+		/// \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 given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. 
+		/// It uses the default rounding mode.
+		///
+		/// 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 is just a no-op.
+		/// \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
+		template<typename T,typename U> T half_cast(U arg) { return 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 given 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 is just a no-op.
+		/// \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
+		template<typename T,std::float_round_style R,typename U> T half_cast(U arg) { return half_caster<T,U,R>::cast(arg); }
+		/// \}
+	}
+
+	using detail::operator==;
+	using detail::operator!=;
+	using detail::operator<;
+	using detail::operator>;
+	using detail::operator<=;
+	using detail::operator>=;
+	using detail::operator+;
+	using detail::operator-;
+	using detail::operator*;
+	using detail::operator/;
+	using detail::operator<<;
+	using detail::operator>>;
+
+	using detail::abs;
+	using detail::fabs;
+	using detail::fmod;
+	using detail::remainder;
+	using detail::remquo;
+	using detail::fma;
+	using detail::fmax;
+	using detail::fmin;
+	using detail::fdim;
+	using detail::nanh;
+	using detail::exp;
+	using detail::expm1;
+	using detail::exp2;
+	using detail::log;
+	using detail::log10;
+	using detail::log1p;
+	using detail::log2;
+	using detail::sqrt;
+	using detail::cbrt;
+	using detail::hypot;
+	using detail::pow;
+	using detail::sin;
+	using detail::cos;
+	using detail::tan;
+	using detail::asin;
+	using detail::acos;
+	using detail::atan;
+	using detail::atan2;
+	using detail::sinh;
+	using detail::cosh;
+	using detail::tanh;
+	using detail::asinh;
+	using detail::acosh;
+	using detail::atanh;
+	using detail::erf;
+	using detail::erfc;
+	using detail::lgamma;
+	using detail::tgamma;
+	using detail::ceil;
+	using detail::floor;
+	using detail::trunc;
+	using detail::round;
+	using detail::lround;
+	using detail::nearbyint;
+	using detail::rint;
+	using detail::lrint;
+#if HALF_ENABLE_CPP11_LONG_LONG
+	using detail::llround;
+	using detail::llrint;
+#endif
+	using detail::frexp;
+	using detail::ldexp;
+	using detail::modf;
+	using detail::scalbn;
+	using detail::scalbln;
+	using detail::ilogb;
+	using detail::logb;
+	using detail::nextafter;
+	using detail::nexttoward;
+	using detail::copysign;
+	using detail::fpclassify;
+	using detail::isfinite;
+	using detail::isinf;
+	using detail::isnan;
+	using detail::isnormal;
+	using detail::signbit;
+	using detail::isgreater;
+	using detail::isgreaterequal;
+	using detail::isless;
+	using detail::islessequal;
+	using detail::islessgreater;
+	using detail::isunordered;
+
+	using detail::half_cast;
+}
+
+
+/// Extensions to the C++ standard library.
+namespace std
+{
+	/// Numeric limits for half-precision floats.
+	/// Because of the underlying single-precision implementation of many operations, it inherits some properties from 
+	/// `std::numeric_limits<float>`.
+	template<> class numeric_limits<half_float::half> : public numeric_limits<float>
+	{
+	public:
+		/// Supports signed values.
+		static HALF_CONSTEXPR_CONST bool is_signed = true;
+
+		/// Is not exact.
+		static HALF_CONSTEXPR_CONST bool is_exact = false;
+
+		/// Doesn't provide modulo arithmetic.
+		static HALF_CONSTEXPR_CONST bool is_modulo = false;
+
+		/// 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 subnormal values.
+		static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
+
+		/// Rounding mode.
+		/// Due to the mix of internal single-precision computations (using the rounding mode of the underlying 
+		/// single-precision implementation) with the rounding mode of the single-to-half conversions, the actual rounding 
+		/// mode might be `std::round_indeterminate` if the default half-precision rounding mode doesn't match the 
+		/// single-precision rounding mode.
+		static HALF_CONSTEXPR_CONST float_round_style round_style = (std::numeric_limits<float>::round_style==
+			half_float::half::round_style) ? half_float::half::round_style : round_indeterminate;
+
+		/// 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 one 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.
+		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); }
+
+		/// Signalling 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.
+	template<> struct hash<half_float::half> //: unary_function<half_float::half,size_t>
+	{
+		/// 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>()(static_cast<unsigned>(arg.data_)&-(arg.data_!=0x8000)); }
+	};
+#endif
+}
+
+
+#undef HALF_CONSTEXPR
+#undef HALF_CONSTEXPR_CONST
+#undef HALF_NOEXCEPT
+#undef HALF_NOTHROW
+#ifdef HALF_POP_WARNINGS
+	#pragma warning(pop)
+	#undef HALF_POP_WARNINGS
+#endif
+
+#endif
