merge with a294fd8c

mace/BUILD

@@ -10,7 +10,7 @@ config_setting(
     name = "android_armv7",
     values = {
         "crosstool_top": "//external:android/crosstool",
-        "android_cpu": "armeabi-v7a",
+        "cpu": "armeabi-v7a",
     },
     visibility = ["//visibility:public"],
 )
@@ -19,7 +19,7 @@ config_setting(
     name = "android_arm64",
     values = {
         "crosstool_top": "//external:android/crosstool",
-        "android_cpu": "arm64-v8a",
+        "cpu": "arm64-v8a",
     },
     visibility = ["//visibility:public"],
 )

mace/core/allocator.h

@@ -10,6 +10,7 @@
 #include "mace/core/common.h"
 #include "mace/core/registry.h"
 #include "mace/proto/mace.pb.h"
+#include "mace/core/types.h"
 
 namespace mace {
 
@@ -26,8 +27,14 @@ class Allocator {
   Allocator() {}
   virtual ~Allocator() noexcept {}
   virtual void *New(size_t nbytes) = 0;
+  virtual void *NewImage(const std::vector<size_t> &image_shape,
+                         const DataType dt) = 0;
   virtual void Delete(void *data) = 0;
+  virtual void DeleteImage(void *data) = 0;
   virtual void *Map(void *buffer, size_t nbytes) = 0;
+  virtual void *MapImage(void *buffer,
+                         const std::vector<size_t> &image_shape,
+                         std::vector<size_t> &mapped_image_pitch) = 0;
   virtual void Unmap(void *buffer, void *mapper_ptr) = 0;
   virtual bool OnHost() = 0;
 
@@ -58,8 +65,19 @@ class CPUAllocator : public Allocator {
     return data;
   }
 
+  void *NewImage(const std::vector<size_t> &shape,
+                 const DataType dt) override {
+    return nullptr;
+  }
+
   void Delete(void *data) override { free(data); }
+  void DeleteImage(void *data) override { free(data); };
   void *Map(void *buffer, size_t nbytes) override { return buffer; }
+  void *MapImage(void *buffer,
+                 const std::vector<size_t> &image_shape,
+                 std::vector<size_t> &mapped_image_pitch) override {
+    return buffer;
+  }
   void Unmap(void *buffer, void *mapper_ptr) override {}
   bool OnHost() override { return true; }
 };

mace/core/half.h

+// half - IEEE 754-based half-precision floating point library.
+//
+// Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net>
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation 
+// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, 
+// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the 
+// Software is furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE 
+// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR 
+// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 
+// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+// Version 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>
+#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, 
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+				0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 
+				0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, 
+				0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 
+				0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, 
+				0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, 
+				0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 
+				0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 
+				0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, 
+				0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, 
+				0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 
+				0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 
+				0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, 
+				0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, 
+				0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, 
+				0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, 
+				0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 
+				0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, 
+				0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, 
+				0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, 
+				0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, 
+				0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 
+				0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, 
+				0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, 
+				0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 
+				0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 
+				0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, 
+				0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, 
+				0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 
+				0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, 
+				0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, 
+				0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 
+				0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, 
+				0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, 
+				0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, 
+				0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, 
+				0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, 
+				0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, 
+				0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 
+				0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 
+				0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, 
+				0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, 
+				0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 
+				0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, 
+				0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, 
+				0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
+			static const 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

mace/core/opencl_allocator.cc

@@ -8,6 +8,29 @@
 
 namespace mace {
 
+namespace {
+
+static cl_channel_type DataTypeToCLChannelType(const DataType t) {
+  switch (t) {
+    case DT_HALF:
+    case DT_FLOAT:
+      return CL_FLOAT;
+    case DT_INT8:
+    case DT_INT16:
+    case DT_INT32:
+      return CL_SIGNED_INT32;
+    case DT_UINT8:
+    case DT_UINT16:
+    case DT_UINT32:
+      return CL_UNSIGNED_INT32;
+    default:
+      LOG(FATAL) << "Image doesn't support the data type: " << t;
+      return 0;
+  }
+}
+
+}
+
 OpenCLAllocator::OpenCLAllocator() {}
 
 OpenCLAllocator::~OpenCLAllocator() {}
@@ -21,6 +44,23 @@ void *OpenCLAllocator::New(size_t nbytes) {
   return static_cast<void *>(buffer);
 }
 
+void *OpenCLAllocator::NewImage(const std::vector<size_t> &image_shape,
+                                const DataType dt) {
+  MACE_CHECK(image_shape.size() == 2) << "Image shape's size must equal 2";
+
+  cl::ImageFormat img_format(CL_RGBA, DataTypeToCLChannelType(dt));
+
+  cl_int error;
+  cl::Image2D *cl_image =
+      new cl::Image2D(OpenCLRuntime::Get()->context(),
+                      CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR ,
+                      img_format,
+                      image_shape[0], image_shape[1],
+                      0, nullptr, &error);
+
+  return cl_image;
+}
+
 void OpenCLAllocator::Delete(void *buffer) {
   if (buffer != nullptr) {
     cl::Buffer *cl_buffer = static_cast<cl::Buffer *>(buffer);
@@ -28,6 +68,13 @@ void OpenCLAllocator::Delete(void *buffer) {
   }
 }
 
+void OpenCLAllocator::DeleteImage(void *buffer) {
+  if (buffer != nullptr) {
+    cl::Image2D *cl_image = static_cast<cl::Image2D *>(buffer);
+    delete cl_image;
+  }
+}
+
 void *OpenCLAllocator::Map(void *buffer, size_t nbytes) {
   auto cl_buffer = static_cast<cl::Buffer *>(buffer);
   auto queue = OpenCLRuntime::Get()->command_queue();
@@ -40,6 +87,29 @@ void *OpenCLAllocator::Map(void *buffer, size_t nbytes) {
   return mapped_ptr;
 }
 
+// TODO : there is something wrong with half type.
+void *OpenCLAllocator::MapImage(void *buffer,
+                                const std::vector<size_t> &image_shape,
+                                std::vector<size_t> &mapped_image_pitch) {
+  MACE_CHECK(image_shape.size() == 2) << "Just support map 2d image";
+  auto cl_image = static_cast<cl::Image2D *>(buffer);
+  std::array<size_t, 3> origin = {0, 0, 0};
+  std::array<size_t, 3> region = {image_shape[0], image_shape[1], 1};
+
+  mapped_image_pitch.resize(2);
+  cl_int error;
+  void *mapped_ptr =
+      OpenCLRuntime::Get()->command_queue().enqueueMapImage(*cl_image,
+                                                            CL_TRUE, CL_MAP_READ | CL_MAP_WRITE,
+                                                            origin, region,
+                                                            &mapped_image_pitch[0],
+                                                            &mapped_image_pitch[1],
+                                                            nullptr, nullptr, &error);
+  MACE_CHECK(error == CL_SUCCESS) << error;
+
+  return mapped_ptr;
+}
+
 void OpenCLAllocator::Unmap(void *buffer, void *mapped_ptr) {
   auto cl_buffer = static_cast<cl::Buffer *>(buffer);
   auto queue = OpenCLRuntime::Get()->command_queue();

mace/core/opencl_allocator.h

@@ -17,10 +17,24 @@ class OpenCLAllocator : public Allocator {
 
   void *New(size_t nbytes) override;
 
+  /*
+   * Use Image2D with RGBA (128-bit) format to represent the image.
+   *
+   * @ shape : [depth, ..., height, width ].
+   */
+  void *NewImage(const std::vector<size_t> &image_shape,
+                 const DataType dt) override;
+
   void Delete(void *buffer) override;
 
+  void DeleteImage(void *buffer) override;
+
   void *Map(void *buffer, size_t nbytes) override;
 
+  void *MapImage(void *buffer,
+                 const std::vector<size_t> &image_shape,
+                 std::vector<size_t> &mapped_image_pitch) override;
+
   void Unmap(void *buffer, void *mapped_ptr) override;
 
   bool OnHost() override;

mace/core/runtime/opencl/opencl_runtime.cc

@@ -147,6 +147,7 @@ const std::map<std::string, std::string>
   {"relu", "relu.cl"},
   {"resize_bilinear", "resize_bilinear.cl"},
   {"space_to_batch", "space_to_batch.cl"},
+  {"buffer_to_image", "buffer_to_image.cl"},
 };
 
 void OpenCLRuntime::BuildProgram(const std::string &program_file_name,

mace/core/runtime/opencl/opencl_wrapper.cc

@@ -101,6 +101,18 @@ class OpenCLLibraryImpl final {
                                            const cl_event *,
                                            cl_event *,
                                            cl_int *);
+  using clEnqueueMapImageFunc = void *(*)(cl_command_queue,
+                                          cl_mem,
+                                          cl_bool,
+                                          cl_map_flags,
+                                          const size_t *,
+                                          const size_t *,
+                                          size_t *,
+                                          size_t *,
+                                          cl_uint,
+                                          const cl_event *,
+                                          cl_event *,
+                                          cl_int *);
   using clCreateCommandQueueWithPropertiesFunc =
       cl_command_queue (*)(cl_context /* context */,
                            cl_device_id /* device */,
@@ -153,6 +165,11 @@ class OpenCLLibraryImpl final {
                                                   size_t param_value_size,
                                                   void *param_value,
                                                   size_t *param_value_size_ret);
+  using clGetImageInfoFunc = cl_int (*)(cl_mem,
+                                    cl_image_info,
+                                    size_t,
+                                    void *,
+                                    size_t *);
 
 #define DEFINE_FUNC_PTR(func) func##Func func = nullptr
 
@@ -177,6 +194,7 @@ class OpenCLLibraryImpl final {
   DEFINE_FUNC_PTR(clCreateCommandQueueWithProperties);
   DEFINE_FUNC_PTR(clReleaseCommandQueue);
   DEFINE_FUNC_PTR(clEnqueueMapBuffer);
+  DEFINE_FUNC_PTR(clEnqueueMapImage);
   DEFINE_FUNC_PTR(clRetainProgram);
   DEFINE_FUNC_PTR(clGetProgramBuildInfo);
   DEFINE_FUNC_PTR(clEnqueueReadBuffer);
@@ -197,6 +215,7 @@ class OpenCLLibraryImpl final {
   DEFINE_FUNC_PTR(clRetainEvent);
   DEFINE_FUNC_PTR(clGetKernelWorkGroupInfo);
   DEFINE_FUNC_PTR(clGetEventProfilingInfo);
+  DEFINE_FUNC_PTR(clGetImageInfo);
 
 #undef DEFINE_FUNC_PTR
 
@@ -300,6 +319,7 @@ void *OpenCLLibraryImpl::LoadFromPath(const std::string &path) {
   ASSIGN_FROM_DLSYM(clCreateCommandQueueWithProperties);
   ASSIGN_FROM_DLSYM(clReleaseCommandQueue);
   ASSIGN_FROM_DLSYM(clEnqueueMapBuffer);
+  ASSIGN_FROM_DLSYM(clEnqueueMapImage);
   ASSIGN_FROM_DLSYM(clRetainProgram);
   ASSIGN_FROM_DLSYM(clGetProgramBuildInfo);
   ASSIGN_FROM_DLSYM(clEnqueueReadBuffer);
@@ -320,6 +340,7 @@ void *OpenCLLibraryImpl::LoadFromPath(const std::string &path) {
   ASSIGN_FROM_DLSYM(clRetainEvent);
   ASSIGN_FROM_DLSYM(clGetKernelWorkGroupInfo);
   ASSIGN_FROM_DLSYM(clGetEventProfilingInfo);
+  ASSIGN_FROM_DLSYM(clGetImageInfo);
 
 #undef ASSIGN_FROM_DLSYM
 
@@ -584,6 +605,31 @@ void *clEnqueueMapBuffer(cl_command_queue command_queue,
     return nullptr;
   }
 }
+
+void *clEnqueueMapImage(cl_command_queue command_queue,
+                        cl_mem image,
+                        cl_bool blocking_map,
+                        cl_map_flags map_flags,
+                        const size_t origin[3],
+                        const size_t region[3],
+                        size_t *image_row_pitch,
+                        size_t *image_slice_pitch,
+                        cl_uint num_events_in_wait_list,
+                        const cl_event *event_wait_list,
+                        cl_event *event,
+                        cl_int *errcode_ret) {
+  auto func = mace::OpenCLLibraryImpl::Get().clEnqueueMapImage;
+  if (func != nullptr) {
+    return func(command_queue, image, blocking_map, map_flags, origin, region,
+                image_row_pitch, image_slice_pitch,
+                num_events_in_wait_list, event_wait_list, event, errcode_ret);
+  } else {
+    if (errcode_ret != nullptr) {
+      *errcode_ret = CL_OUT_OF_RESOURCES;
+    }
+    return nullptr;
+  }
+}
 cl_command_queue clCreateCommandQueueWithProperties(
     cl_context context,
     cl_device_id device,
@@ -853,3 +899,18 @@ cl_int clGetEventProfilingInfo(cl_event event,
     return CL_OUT_OF_RESOURCES;
   }
 }
+
+cl_int clGetImageInfo(cl_mem image,
+                      cl_image_info param_name,
+                      size_t param_value_size,
+                      void *param_value,
+                      size_t *param_value_size_ret) {
+  auto func = mace::OpenCLLibraryImpl::Get().clGetImageInfo;
+  if (func != nullptr) {
+    return func(image, param_name, param_value_size, param_value,
+                param_value_size_ret);
+  } else {
+    return CL_OUT_OF_RESOURCES;
+  }
+}
+

mace/core/tensor.h

@@ -23,6 +23,7 @@ namespace mace {
 
 #define CASES_WITH_DEFAULT(TYPE_ENUM, STMTS, INVALID, DEFAULT) \
   switch (TYPE_ENUM) {                                         \
+    CASE(half, SINGLE_ARG(STMTS))                              \
     CASE(float, SINGLE_ARG(STMTS))                             \
     CASE(double, SINGLE_ARG(STMTS))                            \
     CASE(int32_t, SINGLE_ARG(STMTS))                           \
@@ -68,20 +69,26 @@ class Tensor {
         size_(0),
         dtype_(DT_FLOAT),
         buffer_(nullptr),
-        data_(nullptr){};
+        data_(nullptr),
+        is_image_(false){};
 
   Tensor(Allocator *alloc, DataType type)
       : alloc_(alloc),
         size_(0),
         dtype_(type),
         buffer_(nullptr),
-        data_(nullptr){};
+        data_(nullptr),
+        is_image_(false){};
 
   ~Tensor() {
     MACE_CHECK(data_ == nullptr, "Buffer must be unmapped before destroy");
     if (buffer_ != nullptr) {
       MACE_CHECK_NOTNULL(alloc_);
-      alloc_->Delete(buffer_);
+      if (is_image_) {
+        alloc_->DeleteImage(buffer_);
+      } else {
+        alloc_->Delete(buffer_);
+      }
     }
   }
 
@@ -91,6 +98,10 @@ class Tensor {
 
   inline const vector<index_t> &shape() const { return shape_; }
 
+  inline const vector<size_t> &image_shape() const { return image_shape_; }
+
+  inline const bool is_image() const { return is_image_; }
+
   inline index_t dim_size() const { return shape_.size(); }
 
   inline index_t dim(unsigned int index) const {
@@ -120,6 +131,11 @@ class Tensor {
     }
   }
 
+  inline void MapImage(std::vector<size_t> &mapped_image_pitch) const {
+    MACE_CHECK(!OnHost() && buffer_ != nullptr && data_ == nullptr);
+    data_ = alloc_->MapImage(buffer_, image_shape_, mapped_image_pitch);
+  }
+
   /*
    *  Unmap the device buffer
    */
@@ -162,17 +178,53 @@ class Tensor {
   inline void Resize(const vector<index_t> &shape) {
     shape_ = shape;
     index_t size = NumElements();
-    if (size_ != size) {
+    if (size_ != size || is_image_) {
       size_ = size;
       MACE_CHECK(data_ == nullptr, "Buffer must be unmapped before resize");
-      alloc_->Delete(buffer_);
+      if (is_image_) {
+        alloc_->DeleteImage(buffer_);
+      } else {
+        alloc_->Delete(buffer_);
+      }
+      is_image_ = false;
       CASES(dtype_, buffer_ = alloc_->New(size_ * sizeof(T)));
     }
   }
 
-  inline void ResizeLike(const Tensor &other) { Resize(other.shape()); }
+  inline void ResizeImage(const vector<index_t> &shape,
+                          const std::vector<size_t> &image_shape) {
+    shape_ = shape;
+    index_t size = NumElements();
+    if (size_ != size || !is_image_) {
+      size_ = size;
+      MACE_CHECK(data_ == nullptr, "Buffer must be unmapped before resize");
+
+      if (is_image_) {
+        alloc_->DeleteImage(buffer_);
+      } else {
+        alloc_->Delete(buffer_);
+      }
+      is_image_ = true;
+      image_shape_ = image_shape;
+      buffer_ = alloc_->NewImage(image_shape, dtype_);
+    }
+  }
+
+  inline void ResizeLike(const Tensor &other) {
+    if (other.is_image()) {
+      ResizeImage(other.shape(), other.image_shape());
+    } else {
+      Resize(other.shape());
+    }
+  }
 
-  inline void ResizeLike(const Tensor *other) { Resize(other->shape()); }
+  inline void ResizeLike(const Tensor *other) {
+    if (other->is_image()) {
+      ResizeImage(other->shape(), other->image_shape());
+    } else {
+      Resize(other->shape());
+    }
+  }
 
   template <typename T>
   inline void Copy(const T *src, index_t size) {
@@ -202,8 +254,6 @@ class Tensor {
     for (int i : shape_) {
       os << i << ", ";
     }
-    LOG(INFO) << "Tensor shape: " << os.str()
-              << " type: " << DataType_Name(dtype_);
 
     os.str("");
     os.clear();
@@ -212,7 +262,7 @@ class Tensor {
       if ( i != 0 && i % shape_[3] == 0) {
         os << "\n";
       }
-      CASES(dtype_, (os << this->data<T>()[i]) << ", ");
+      CASES(dtype_, (os << (this->data<T>()[i]) << ", "));
     }
     LOG(INFO) << os.str();
   }
@@ -228,20 +278,33 @@ class Tensor {
     dtype_ = other.dtype_;
     ResizeLike(other);
     MappingGuard map_other(&other);
-    CopyBytes(other.raw_data(), size_ * SizeOfType());
+    if (is_image_) {
+      LOG(FATAL) << "Not support copy image tensor, please use Copy API.";
+    } else {
+      CopyBytes(other.raw_data(), size_ * SizeOfType());
+    }
   }
 
   class MappingGuard {
    public:
     MappingGuard(const Tensor *tensor) : tensor_(tensor) {
-      if (tensor_ != nullptr) tensor_->Map();
+      if (tensor_ != nullptr) {
+        if (tensor_->is_image()) {
+          tensor_->MapImage(mapped_image_pitch_);
+        } else {
+          tensor_->Map();
+        }
+      }
     }
     ~MappingGuard() {
       if (tensor_ != nullptr) tensor_->Unmap();
     }
 
+    inline const vector<size_t> &mapped_image_pitch() const { return mapped_image_pitch_; }
+
    private:
     const Tensor *tensor_;
+    std::vector<size_t> mapped_image_pitch_;
   };
 
  private:
@@ -261,6 +324,9 @@ class Tensor {
   // Mapped buffer
   mutable void *data_;
   vector<index_t> shape_;
+  // Image for opencl
+  bool is_image_;
+  std::vector<size_t> image_shape_;
 
   DISABLE_COPY_AND_ASSIGN(Tensor);
 };

mace/core/types.cc

@@ -24,31 +24,32 @@ bool DataTypeCanUseMemcpy(DataType dt) {
   }
 }
 
-std::string DataTypeToCLType(const DataType dt) {
+
+size_t GetEnumTypeSize(const DataType dt) {
   switch (dt) {
     case DT_FLOAT:
-      return "float";
+      return sizeof(float);
     case DT_HALF:
-      return "half";
+      return sizeof(half);
     case DT_UINT8:
-      return "uchar";
+      return sizeof(uint8_t);
     case DT_INT8:
-      return "char";
+      return sizeof(int8_t);
     case DT_DOUBLE:
-      return "double";
+      return sizeof(double);
     case DT_INT32:
-      return "int";
+      return sizeof(int32_t);
     case DT_UINT32:
-      return "int";
+      return sizeof(uint32_t);
     case DT_UINT16:
-      return "ushort";
+      return sizeof(uint16_t);
     case DT_INT16:
-      return "short";
+      return sizeof(int16_t);
     case DT_INT64:
-      return "long";
+      return sizeof(int64_t);
     default:
       LOG(FATAL) << "Unsupported data type";
-      return "";
+      return 0;
   }
 }
 

mace/core/types.h

@@ -7,12 +7,16 @@
 
 #include "mace/core/common.h"
 #include "mace/proto/mace.pb.h"
+#include "mace/core/half.h"
+
 
 namespace mace {
 
+using half = half_float::half;
+
 bool DataTypeCanUseMemcpy(DataType dt);
 
-std::string DataTypeToCLType(const DataType dt);
+size_t GetEnumTypeSize(const DataType dt);
 
 template <class T>
 struct IsValidDataType;
@@ -43,6 +47,7 @@ struct EnumToDataType {};  // Specializations below
     typedef TYPE Type;                      \
   }
 
+MATCH_TYPE_AND_ENUM(half, DT_HALF);
 MATCH_TYPE_AND_ENUM(float, DT_FLOAT);
 MATCH_TYPE_AND_ENUM(double, DT_DOUBLE);
 MATCH_TYPE_AND_ENUM(int32_t, DT_INT32);

mace/kernels/BUILD

@@ -13,7 +13,7 @@ load("//mace:mace.bzl", "if_android_arm64")
 cc_library(
     name = "kernels",
     srcs = glob(["*.cc"]) + if_android(glob(["opencl/*.cc"])) + if_android_arm64(glob(["neon/*.cc"])),
-    hdrs = glob(["*.h"]) + if_android(glob(["opencl/*.cc"])) + if_android_arm64(glob(["neon/*.cc"])),
+    hdrs = glob(["*.h"]) + if_android(glob(["opencl/*.h"])) + if_android_arm64(glob(["neon/*.h"])),
     copts = [
         "-std=c++11",
         "-fopenmp",

mace/kernels/buffer_to_image.h

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#ifndef MACE_KERNELS_BATCH_NORM_H_
+#define MACE_KERNELS_BATCH_NORM_H_
+
+#include "mace/core/tensor.h"
+#include "mace/kernels/opencl/helper.h"
+
+namespace mace {
+namespace kernels {
+
+struct BufferToImageFunctorBase {
+  BufferToImageFunctorBase(bool i2b) : i2b_(i2b) {}
+  bool i2b_;
+};
+
+template<DeviceType D, typename T>
+struct BufferToImageFunctor : BufferToImageFunctorBase{
+  BufferToImageFunctor(bool i2b = false) :
+      BufferToImageFunctorBase(i2b) {}
+  void operator()(Tensor *input,
+                  const BufferType type,
+                  Tensor *output) {
+    MACE_NOT_IMPLEMENTED;
+  }
+  bool i2b_;
+};
+
+template<typename T>
+struct BufferToImageFunctor<DeviceType::OPENCL, T> : BufferToImageFunctorBase{
+  BufferToImageFunctor(bool i2b = false) :
+      BufferToImageFunctorBase(i2b) {}
+  void operator()(Tensor *input,
+                  const BufferType type,
+                  Tensor *output);
+};
+
+}  //  namepsace kernels
+}  //  namespace mace
+
+#endif  //  MACE_KERNELS_BATCH_NORM_H_

mace/kernels/conv_2d.h

@@ -15,9 +15,9 @@ template <DeviceType D, typename T>
 struct Conv2dFunctor {
   Conv2dFunctor() {}
   Conv2dFunctor(const int *strides,
-                const std::vector<int> &paddings,
+                const Padding &paddings,
                 const int *dilations)
-      : strides_(strides), paddings_(paddings), dilations_(dilations) {}
+      : strides_(strides), dilations_(dilations), paddings_(paddings)  {}
 
   void operator()(const Tensor *input,
                   const Tensor *filter,
@@ -27,6 +27,13 @@ struct Conv2dFunctor {
     MACE_CHECK_NOTNULL(filter);
     MACE_CHECK_NOTNULL(output);
 
+    std::vector<index_t> output_shape(4);
+    std::vector<int> paddings(2);
+    kernels::CalcPaddingAndOutputSize(
+        input->shape().data(), filter->shape().data(), dilations_,
+        strides_, paddings_, output_shape.data(), paddings.data());
+    output->Resize(output_shape);
+
     index_t batch = output->dim(0);
     index_t channels = output->dim(1);
     index_t height = output->dim(2);
@@ -49,10 +56,10 @@ struct Conv2dFunctor {
     MACE_CHECK(batch == input_batch, "Input/Output batch size mismatch");
 
     // The left-upper most offset of the padded input
-    int padded_h_start = 0 - paddings_[0] / 2;
-    int padded_w_start = 0 - paddings_[1] / 2;
-    index_t padded_h_stop = input_height + paddings_[0] - paddings_[0] / 2;
-    index_t padded_w_stop = input_width + paddings_[1] - paddings_[1] / 2;
+    int padded_h_start = 0 - paddings[0] / 2;
+    int padded_w_start = 0 - paddings[1] / 2;
+    index_t padded_h_stop = input_height + paddings[0] - paddings[0] / 2;
+    index_t padded_w_stop = input_width + paddings[1] - paddings[1] / 2;
 
     index_t kernel_size = input_channels * kernel_h * kernel_w;
 
@@ -108,8 +115,8 @@ struct Conv2dFunctor {
   }
 
   const int *strides_;         // [stride_h, stride_w]
-  std::vector<int> paddings_;  // [padding_h, padding_w]
   const int *dilations_;       // [dilation_h, dilation_w]
+  Padding paddings_;
 };
 
 template <>

mace/kernels/neon/conv_2d_neon.cc

@@ -49,6 +49,14 @@ void Conv2dFunctor<DeviceType::NEON, float>::operator()(const Tensor *input,
   MACE_CHECK_NOTNULL(filter);
   MACE_CHECK_NOTNULL(output);
 
+
+  std::vector<index_t> output_shape_vec(4);
+  std::vector<int> paddings(2);
+  kernels::CalcPaddingAndOutputSize(
+      input->shape().data(), filter->shape().data(), dilations_,
+      strides_, paddings_, output_shape_vec.data(), paddings.data());
+  output->Resize(output_shape_vec);
+
   typedef void (*Conv2dNeonFunction)(
       const float *input, const index_t *input_shape, const float *filter,
       const index_t *filter_shape, const float *bias, float *output,
@@ -77,8 +85,8 @@ void Conv2dFunctor<DeviceType::NEON, float>::operator()(const Tensor *input,
 
   Tensor padded_input;
   // Keep this alive during kernel execution
-  if (paddings_[0] > 0 || paddings_[1] > 0) {
-    ConstructInputWithPadding(input, paddings_.data(), &padded_input);
+  if (paddings[0] > 0 || paddings[1] > 0) {
+    ConstructInputWithPadding(input, paddings.data(), &padded_input);
     input = &padded_input;
   }
   Tensor::MappingGuard input_mapper(input);

mace/kernels/opencl/addn.cc

@@ -4,6 +4,7 @@
 
 #include "mace/kernels/addn.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/batch_norm_opencl.cc

@@ -6,6 +6,7 @@
 #include "mace/core/runtime/opencl/cl2_header.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/utils/tuner.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/buffer_to_image.cc

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#include "mace/kernels/buffer_to_image.h"
+#include "mace/core/runtime/opencl/cl2_header.h"
+#include "mace/core/runtime/opencl/opencl_runtime.h"
+
+namespace mace {
+namespace kernels {
+
+template<typename T>
+void BufferToImageFunctor<DeviceType::OPENCL, T>::operator()(Tensor *buffer,
+                                                             const BufferType type,
+                                                             Tensor *image) {
+  MACE_CHECK(!buffer->is_image()) << "buffer must be buffer-type";
+  std::vector<size_t> image_shape;
+  if (!i2b_) {
+    CalImage2DShape(buffer->shape(), type, image_shape);
+    image->ResizeImage(buffer->shape(), image_shape);
+  } else {
+    image_shape = image->image_shape();
+    buffer->Resize(image->shape());
+  }
+
+  std::set<std::string> built_options;
+  built_options.emplace("-DDATA_TYPE=" + DataTypeToCLType(image->dtype()));
+  built_options.emplace("-DCMD_DATA_TYPE=" + DataTypeToOpenclCMDDataType(image->dtype()));
+  auto runtime = OpenCLRuntime::Get();
+  string kernel_name;
+  switch (type) {
+    case FILTER:
+      kernel_name = i2b_ ? "filter_image_to_buffer" : "filter_buffer_to_image";
+      break;
+    case IN_OUT:
+      kernel_name = i2b_ ? "in_out_image_to_buffer" : "in_out_buffer_to_image";
+      break;
+    case ARGUMENT:
+      kernel_name = i2b_ ? "arg_image_to_buffer" : "arg_buffer_to_image";
+      break;
+  }
+  auto b2f_kernel = runtime->BuildKernel("buffer_to_image",
+                                         kernel_name,
+                                         built_options);
+
+  uint32_t idx = 0;
+  b2f_kernel.setArg(idx++, *(static_cast<const cl::Image2D *>(buffer->buffer())));
+  if (type == ARGUMENT) {
+    b2f_kernel.setArg(idx++, static_cast<uint32_t>(buffer->dim(0)));
+  } else {
+    b2f_kernel.setArg(idx++, static_cast<uint32_t>(buffer->dim(1)));
+    b2f_kernel.setArg(idx++, static_cast<uint32_t>(buffer->dim(2)));
+    b2f_kernel.setArg(idx++, static_cast<uint32_t>(buffer->dim(3)));
+  }
+  b2f_kernel.setArg(idx++, *(static_cast<cl::Image2D *>(image->buffer())));
+
+  const size_t gws[3] = {image_shape[0],
+                         image_shape[1],
+                         1};
+  const uint32_t kwg_size = runtime->GetKernelMaxWorkGroupSize(b2f_kernel);
+  const std::vector<uint32_t> lws = {kwg_size, 1, 1};
+  cl_int error = runtime->command_queue().enqueueNDRangeKernel(
+      b2f_kernel, cl::NullRange,
+      cl::NDRange(gws[0], gws[1], gws[2]),
+      cl::NDRange(lws[0], lws[1], lws[2]));
+
+  MACE_CHECK(error == CL_SUCCESS) << "Error code: " << error;
+}
+
+template struct BufferToImageFunctor<DeviceType::OPENCL, float>;
+template struct BufferToImageFunctor<DeviceType::OPENCL, half>;
+
+}  // namespace kernels
+}  // namespace mace

mace/kernels/opencl/cl/buffer_to_image.cl

+#include <common.h>
+
+__kernel void filter_buffer_to_image(__global const DATA_TYPE *input, /* h, w, ic, oc */
+                                     __private const int filter_w,
+                                     __private const int in_channel,
+                                     __private const int out_channel,
+                                     __write_only image2d_t output) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int out_channel_idx = h * 4;
+  const int hw_idx = w / in_channel;
+  int in_channel_idx = w % in_channel;
+  const int h_idx = hw_idx / filter_w;
+  const int w_idx = hw_idx % filter_w;
+  const int offset = ((h_idx * filter_w + w_idx) * in_channel + in_channel_idx) * out_channel
+                           + out_channel_idx;
+
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = vload4(0, input + offset);
+  int2 coord = (int2)(w, h);
+  CMD_TYPE(write_image, CMD_DATA_TYPE)(output, coord, values);
+}
+
+__kernel void filter_image_to_buffer(__global DATA_TYPE *output, /* h, w, ic, oc */
+                                     __private const int filter_w,
+                                     __private const int in_channel,
+                                     __private const int out_channel,
+                                     __read_only image2d_t input) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int out_channel_idx = h * 4;
+  const int hw_idx = w / in_channel;
+  int in_channel_idx = w % in_channel;
+  const int h_idx = hw_idx / filter_w;
+  const int w_idx = hw_idx % filter_w;
+  const int offset = ((h_idx * filter_w + w_idx) * in_channel + in_channel_idx) * out_channel
+                           + out_channel_idx;
+
+  const sampler_t sampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP | CLK_FILTER_NEAREST;
+  int2 coord = (int2)(w, h);
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = CMD_TYPE(read_image, CMD_DATA_TYPE)(input, sampler, coord);
+  if (out_channel_idx + 4 > out_channel) {
+    const int diff = in_channel - in_channel_idx;
+    output[offset] = values.s0;
+    if (diff == 2) {
+      output[offset+1] = values.s1;
+    } else {
+      output[offset+1] = values.s1;
+      output[offset+2] = values.s2;
+    }
+  } else {
+    vstore4(values, 0, output + offset);
+  }
+}
+
+__kernel void in_out_buffer_to_image(__global const DATA_TYPE *input, /* nhwc */
+                                     __private const int height,
+                                     __private const int width,
+                                     __private const int channels,
+                                     __write_only image2d_t output) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int batch_idx = h / height;
+  const int height_idx = h % height;
+  const int width_idx = w % width;
+  const int channel_idx = w / width * 4;
+  const int offset = ((batch_idx * height + height_idx) * width + width_idx) * channels
+                           + channel_idx;
+
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = vload4(0, input + offset);
+  int2 coord = (int2)(w, h);
+  CMD_TYPE(write_image, CMD_DATA_TYPE)(output, coord, values);
+}
+
+__kernel void in_out_image_to_buffer(__global DATA_TYPE *output, /* nhwc */
+                                     __private const int height,
+                                     __private const int width,
+                                     __private const int channels,
+                                     __read_only image2d_t input) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int batch_idx = h / height;
+  const int height_idx = h % height;
+  const int width_idx = w % width;
+  const int channel_idx = w / width * 4;
+  const int offset = ((batch_idx * height + height_idx) * width + width_idx) * channels
+                           + channel_idx;
+
+  const sampler_t sampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP | CLK_FILTER_NEAREST;
+  int2 coord = (int2)(w, h);
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = CMD_TYPE(read_image, CMD_DATA_TYPE)(input, sampler, coord);
+  if (channel_idx + 4 > channels) {
+    const int diff = channels - channel_idx;
+    output[offset] = values.s0;
+    if (diff == 2) {
+      output[offset+1] = values.s1;
+    } else {
+      output[offset+1] = values.s1;
+      output[offset+2] = values.s2;
+    }
+  } else {
+    vstore4(values, 0, output + offset);
+  }
+}
+
+__kernel void arg_buffer_to_image(__global const DATA_TYPE *input, /* nhwc */
+                                  __private const int count,
+                                  __write_only image2d_t output) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int offset = w * 4;
+
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = vload4(0, input + offset);
+  int2 coord = (int2)(w, h);
+  CMD_TYPE(write_image, CMD_DATA_TYPE)(output, coord, values);
+}
+
+__kernel void arg_image_to_buffer(__global DATA_TYPE *output, /* nhwc */
+                                  __private const int count,
+                                  __read_only image2d_t input) {
+  int w = get_global_id(0);
+  int h = get_global_id(1);
+  const int offset = w * 4;
+
+  const sampler_t sampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP | CLK_FILTER_NEAREST;
+  int2 coord = (int2)(w, h);
+  VEC_DATA_TYPE(DATA_TYPE, 4) values = CMD_TYPE(read_image, CMD_DATA_TYPE)(input, sampler, coord);
+  if (offset + 4 > count) {
+    const int diff = count - offset;
+    output[offset] = values.s0;
+    if (diff == 2) {
+      output[offset+1] = values.s1;
+    } else {
+      output[offset+1] = values.s1;
+      output[offset+2] = values.s2;
+    }
+  } else {
+    vstore4(values, 0, output + offset);
+  }
+}

mace/kernels/opencl/cl/common.h

@@ -11,4 +11,7 @@
 #define VEC_DATA_TYPE_STR(data_type, size) data_type##size
 #define VEC_DATA_TYPE(data_type, size) VEC_DATA_TYPE_STR(data_type, size)
 
+#define CMD_TYPE_STR(cmd, type) cmd##type
+#define CMD_TYPE(cmd, type) CMD_TYPE_STR(cmd, type)
+
 #endif  // MACE_KERNELS_OPENCL_CL_COMMON_H_

mace/kernels/opencl/cl/conv_2d_1x1.cl

 #include <common.h>
 
-__kernel void conv_2d_1x1_naive(__global const float *input, /* n, c, h, w */
-                                __global const float *filter, /* o, i, kh, kw */
-                                __global const float *bias, /* o */
-                                __global float *output, /* n, c, h, w */
-                                __private const int in_chan_num) {
-  const int batch = get_global_id(0);
-  const int channel = get_global_id(1);
-  const int channels = get_global_size(1);
-  const int pixel = get_global_id(2);
-  const int pixels = get_global_size(2);
-
-  float *output_ptr = output + (batch * channels + channel) * pixels;
-  output_ptr[pixel] = bias[channel];
-
-  for (int inc = 0; inc < in_chan_num; ++inc) {
-    const float *input_ptr = input + (batch * in_chan_num + inc) * pixels + pixel;
-    const float weights = filter[channel * in_chan_num + inc];
-    float in = input_ptr[0];
-    float out = output_ptr[0];
-    out += in * weights;
-    output_ptr[0] = out;
-  }
-}
-
 #define vec_conv_2d_1x1_s1                    \
   VEC_DATA_TYPE(DATA_TYPE,4) in0 = vload4(0, input_ptr);                   \
   VEC_DATA_TYPE(DATA_TYPE,4) in1 = vload4(0, input_ptr + in_pixel);        \
@@ -165,47 +141,85 @@ __kernel void conv_2d_1x1_v2(__global const DATA_TYPE *input, /* n, c, h, w */
   }
 }
 
-/* FIXME this is incomplete */
-__kernel void conv_2d_1x1_v3(__read_only image3d_t input, /* n, c/4, h, w, 4 */
-                             __global const float *filter, /* o, i, kh, kw */
-                             __global const float *bias, /* o */
-                             __write_only image3d_t output, /* n, c/4, h, w, 4 */
-                             __private const int batch_num,
-                             __private const int in_chan_num,
-                             __private const int out_chan_num,
-                             __private const int height,
-                             __private const int width) {
-  int out_chan_blk = get_global_id(0);
-  int h = get_global_id(1);
-  int w = get_global_id(2);
+// TODO : validation
+__kernel void conv_2d_1x1(__read_only image2d_t input, /* [c%4 * w * c/4, h * b] */
+                          __read_only image2d_t filter, /* cout%4 * cin, cout/4 */
+                          __read_only image2d_t bias, /* cout%4 * cout/4 */
+                          __write_only image2d_t output,
+                          __private const int in_ch_blks,
+                          __private const int width) {
+  const int out_ch_blk = get_global_id(0);
+  const int out_w_blk = get_global_id(1);
+  const int out_w_blks = get_global_size(1);
+  const int out_hb = get_global_id(2);
 
+  const sampler_t sampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP | CLK_FILTER_NEAREST;
 
-  int in_chan_blk_num = (in_chan_num + 3) / 4;
-  int out_chan_blk_num = (out_chan_num + 3) / 4;
+  half4 bias_value = read_imageh(bias, sampler, (int2)(out_w_blk, 1));
+  half4 out0 = (half4)(bias_value.x, bias_value.x, bias_value.x, bias_value.x);
+  half4 out1 = (half4)(bias_value.y, bias_value.y, bias_value.y, bias_value.y);
+  half4 out2 = (half4)(bias_value.z, bias_value.z, bias_value.z, bias_value.z);
+  half4 out3 = (half4)(bias_value.w, bias_value.w, bias_value.w, bias_value.w);
+
+  // Unrolling this loop hurt perfmance
+  int in_x_base = 0;
+  for (int in_ch_blk = 0; in_ch_blk < in_ch_blks; ++in_ch_blk) {
+    const int in_x0 = in_x_base + out_w_blk;;
+    const int in_x1 = in_x0 + out_w_blks;
+    const int in_x2 = in_x1 + out_w_blks;
+    const int in_x3 = in_x2 + out_w_blks;
+    in_x_base += width;
+
+    const half4 in0 = read_imageh(input, sampler, (int2)(in_x0, out_hb));
+    const half4 in1 = read_imageh(input, sampler, (int2)(in_x1, out_hb));
+    const half4 in2 = read_imageh(input, sampler, (int2)(in_x2, out_hb));
+    const half4 in3 = read_imageh(input, sampler, (int2)(in_x3, out_hb));
+
+    // The order matters, load input first then load filter, why?
+    const int filter_x0 = in_ch_blk << 2;
+    const half4 weights0 = read_imageh(filter, sampler, (int2)(filter_x0, out_ch_blk));
+    const half4 weights1 = read_imageh(filter, sampler, (int2)(filter_x0 + 1, out_ch_blk));
+    const half4 weights2 = read_imageh(filter, sampler, (int2)(filter_x0 + 2, out_ch_blk));
+    const half4 weights3 = read_imageh(filter, sampler, (int2)(filter_x0 + 3, out_ch_blk));
+    // Will prefetch L2 improve performance? How to pretch image data?
+
+    // Interleaving load and mul does not improve performance as expected
+    out0 += in0.x * weights0;
+    out1 += in1.x * weights0;
+    out2 += in2.x * weights0;
+    out3 += in3.x * weights0;
+
+    out0 += in0.y * weights1;
+    out1 += in1.y * weights1;
+    out2 += in2.y * weights1;
+    out3 += in3.y * weights1;
+
+    out0 += in0.z * weights2;
+    out1 += in1.z * weights2;
+    out2 += in2.z * weights2;
+    out3 += in3.z * weights2;
+
+    out0 += in0.w * weights3;
+    out1 += in1.w * weights3;
+    out2 += in2.w * weights3;
+    out3 += in3.w * weights3;
+  }
 
-  const sampler_t sampler = CLK_NORMALIZED_COORDS_FALSE | CLK_ADDRESS_CLAMP | CLK_FILTER_NEAREST;
+  const int out_x_offset = out_ch_blk * width;
+  const int w0 = out_w_blk;
+  write_imageh(output, (int2)(out_x_offset + w0, out_hb), out0);
 
-  for (int batch = 0; batch < batch_num; ++batch) {
-    float4 bias_value = vload4(out_chan_blk, bias);
-    __private float4 out = bias_value;
-
-    for (int in_chan_blk = 0; in_chan_blk < in_chan_blk_num; ++in_chan_blk) {
-      int in_d = batch * in_chan_blk_num + in_chan_blk;
-      float4 in = read_imagef(input, sampler, (int4)(in_d, h, w, 0));
-
-      const float *filter_base = filter + (out_chan_blk << 2) * in_chan_num;
-      float4 weights = vload4(in_chan_blk, filter_base);
-      out.x += dot(in, weights);
-      weights = vload4(in_chan_blk, filter_base + in_chan_num);
-      out.y += dot(in, weights);
-      weights = vload4(in_chan_blk, filter_base + in_chan_num * 2);
-      out.z += dot(in, weights);
-      weights = vload4(in_chan_blk, filter_base + in_chan_num * 3);
-      out.w += dot(in, weights);
-    }
+  const int w1 = w0 + out_w_blks;
+  if (w1 >= width) return;
+  write_imageh(output, (int2)(out_x_offset + w1, out_hb), out1);
 
-    int out_d = batch * out_chan_blk_num + out_chan_blk;
-    int4 out_coord = (int4)(out_d, h, w, 0);
-    write_imagef(output, out_coord, out);
-  }
+  const int w2 = w1 + out_w_blks;
+  if (w2 >= width) return;
+  write_imageh(output, (int2)(out_x_offset + w2, out_hb), out2);
+
+  const int w3 = w2 + out_w_blks;
+  if (w3 >= width) return;
+  write_imageh(output, (int2)(out_x_offset + w3, out_hb), out3);
 }
+
+

mace/kernels/opencl/conv_2d_opencl.cc

@@ -3,6 +3,7 @@
 //
 
 #include "mace/kernels/conv_2d.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {
@@ -47,10 +48,25 @@ void Conv2dFunctor<DeviceType::OPENCL, float>::operator()(const Tensor *input,
         input, filter, bias, output);
     return;
   }
+
+  std::vector<index_t> output_shape(4);
+  std::vector<int> paddings(2);
+  kernels::CalcPaddingAndOutputSize(
+      input->shape().data(), filter->shape().data(), dilations_,
+      strides_, paddings_, output_shape.data(), paddings.data());
+
+  if (input->is_image()) {
+    std::vector<size_t> output_image_shape;
+    CalImage2DShape(output_shape, BufferType::IN_OUT, output_image_shape);
+    output->ResizeImage(output_shape, output_image_shape);
+  } else {
+    output->Resize(output_shape);
+  }
+
   auto conv2d_func = selector[kernel_h - 1][strides_[0] - 1];
-  if (paddings_[0] > 0 || paddings_[1] > 0) {
+  if (paddings[0] > 0 || paddings[1] > 0) {
     Tensor padded_input(GetDeviceAllocator(DeviceType::OPENCL), DataTypeToEnum<float>::v());
-    ConstructInputWithPadding(input, paddings_.data(), &padded_input);
+    ConstructInputWithPadding(input, paddings.data(), &padded_input);
     conv2d_func(&padded_input, filter, bias, output);
   }else {
     conv2d_func(input, filter, bias, output);

mace/kernels/opencl/conv_2d_opencl_1x1.cc

@@ -3,45 +3,14 @@
 //
 
 #include "mace/kernels/conv_2d.h"
-#include "mace/core/common.h"
 #include "mace/core/runtime/opencl/cl2_header.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/utils/utils.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {
 
-void Conv1x1Naive(const Tensor *input,
-                  const Tensor *filter,
-                  const Tensor *bias,
-                  Tensor *output) {
-  const index_t batch = output->dim(0);
-  const index_t channels = output->dim(1);
-  const index_t height = output->dim(2);
-  const index_t width = output->dim(3);
-  const index_t input_channels = input->dim(1);
-
-  auto runtime = OpenCLRuntime::Get();
-  auto program = runtime->program();
-  auto conv_2d =
-      cl::KernelFunctor<cl::Buffer, cl::Buffer, cl::Buffer, cl::Buffer, int,
-                        int>(program, "conv_2d_1x1_naive");
-  const index_t pixels = height * width;
-
-  cl_int error;
-  conv_2d(cl::EnqueueArgs(
-              runtime->command_queue(),
-              cl::NDRange(static_cast<int>(batch), static_cast<int>(channels),
-                          static_cast<int>(pixels)),
-              cl::NDRange(1, 1, 128)),
-          *(static_cast<cl::Buffer *>(input->buffer())),
-          *(static_cast<cl::Buffer *>(filter->buffer())),
-          *(static_cast<cl::Buffer *>(bias->buffer())),
-          *(static_cast<cl::Buffer *>(output->buffer())),
-          static_cast<int>(input_channels), error);
-  MACE_CHECK(error == CL_SUCCESS);
-}
-
 void Conv1x1V2(const Tensor *input,
                const Tensor *filter,
                const Tensor *bias,
@@ -99,85 +68,44 @@ void Conv1x1V3(const Tensor *input,
                const Tensor *filter,
                const Tensor *bias,
                Tensor *output) {
+  
   const index_t batch = output->dim(0);
   const index_t channels = output->dim(1);
   const index_t height = output->dim(2);
   const index_t width = output->dim(3);
   const index_t input_channels = input->dim(1);
 
-  auto runtime = OpenCLRuntime::Get();
-  auto program = runtime->program();
+  const index_t channel_blocks = RoundUpDiv4(channels);
+  const index_t input_channel_blocks = RoundUpDiv4(input_channels);
 
-  const index_t pixels = height * width;
-  const index_t pixel_blocks = (pixels + 3) / 4;
+  std::set<std::string> built_options;
+  built_options.emplace("-DDATA_TYPE=" + DataTypeToCLType(input->dtype()));
+  built_options.emplace("-DSTRIDE_1");
+  built_options.emplace(bias != nullptr ? "-DBIAS" : "");
 
-  const index_t channel_blocks = (channels + 3) / 4;
-  const index_t input_channel_blocks = (input_channels + 3) / 4;
-
-  // FIXME temp hacking
-  static std::map<std::ptrdiff_t, cl::Image3D> input_image_map;
-  static std::map<std::ptrdiff_t, cl::Image3D> output_image_map;
-  cl::Image3D input_image;
-  cl::Image3D output_image;
-  auto input_iter =
-      input_image_map.find(reinterpret_cast<std::ptrdiff_t>(input->buffer()));
-  if (input_iter != input_image_map.end()) {
-    input_image = input_iter->second;
-  } else {
-    // The batch dimension is collapsed with channel
-    cl_int error;
-    cl::Image3D image =
-        cl::Image3D(OpenCLRuntime::Get()->context(),
-                    CL_MEM_READ_ONLY | CL_MEM_ALLOC_HOST_PTR,
-                    cl::ImageFormat(CL_RGBA, CL_FLOAT), height, width,
-                    batch * input_channel_blocks, 0, 0, nullptr, &error);
-    MACE_CHECK(error == CL_SUCCESS);
-    input_image = image;
-    input_image_map.clear();
-    input_image_map.emplace(reinterpret_cast<std::ptrdiff_t>(input->buffer()),
-                            image);
-  }
-  auto output_iter =
-      output_image_map.find(reinterpret_cast<std::ptrdiff_t>(output->buffer()));
-  if (output_iter != output_image_map.end()) {
-    output_image = output_iter->second;
-  } else {
-    cl_int error;
-    cl::Image3D image =
-        cl::Image3D(OpenCLRuntime::Get()->context(),
-                    CL_MEM_WRITE_ONLY | CL_MEM_ALLOC_HOST_PTR,
-                    cl::ImageFormat(CL_RGBA, CL_FLOAT), height, width,
-                    batch * channel_blocks, 0, 0, nullptr, &error);
-    MACE_CHECK(error == CL_SUCCESS);
-    output_image = image;
-    output_image_map.clear();
-    output_image_map.emplace(reinterpret_cast<std::ptrdiff_t>(output->buffer()),
-                             image);
-  }
+  auto runtime = OpenCLRuntime::Get();
+  auto program = runtime->program();
 
-  auto conv_2d_kernel = cl::Kernel(program, "conv_2d_1x1_v3");
+  auto conv_2d_kernel = runtime->BuildKernel("conv_2d_1x1", "conv_2d_1x1", built_options);
   const uint32_t kwg_size = runtime->GetKernelMaxWorkGroupSize(conv_2d_kernel);
 
   uint32_t idx = 0;
-  conv_2d_kernel.setArg(idx++, input_image);
-  conv_2d_kernel.setArg(idx++,
-                        *(static_cast<const cl::Buffer *>(filter->buffer())));
-  conv_2d_kernel.setArg(idx++,
-                        *(static_cast<const cl::Buffer *>(bias->buffer())));
-  conv_2d_kernel.setArg(idx++, output_image);
-  conv_2d_kernel.setArg(idx++, static_cast<int>(batch));
-  conv_2d_kernel.setArg(idx++, static_cast<int>(input_channels));
-  conv_2d_kernel.setArg(idx++, static_cast<int>(channels));
-  conv_2d_kernel.setArg(idx++, static_cast<int>(height));
+  conv_2d_kernel.setArg(idx++, *(static_cast<const cl::Image2D *>(input->buffer())));
+  conv_2d_kernel.setArg(idx++, *(static_cast<const cl::Image2D *>(filter->buffer())));
+  if (bias != nullptr) {
+    conv_2d_kernel.setArg(idx++, *(static_cast<const cl::Image2D *>(bias->buffer())));
+  }
+  conv_2d_kernel.setArg(idx++, *(static_cast<const cl::Image2D *>(output->buffer())));
+  conv_2d_kernel.setArg(idx++, static_cast<int>(input_channel_blocks));
   conv_2d_kernel.setArg(idx++, static_cast<int>(width));
 
   auto command_queue = runtime->command_queue();
   cl_int error;
   error = command_queue.enqueueNDRangeKernel(
       conv_2d_kernel, cl::NullRange,
-      cl::NDRange(static_cast<int>(channel_blocks), static_cast<int>(height),
-                  static_cast<int>(width)),
-      cl::NDRange(1, 2, kwg_size / 2),
+      cl::NDRange(static_cast<uint32_t>(channel_blocks), static_cast<uint32_t>(height),
+                  static_cast<uint32_t>(height * batch)),
+      cl::NDRange(4, 15, 8),
       NULL, OpenCLRuntime::Get()->GetDefaultEvent());
   MACE_CHECK(error == CL_SUCCESS, error);
 }

mace/kernels/opencl/conv_2d_opencl_3x3.cc

@@ -5,6 +5,7 @@
 #include "mace/core/common.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/kernels/conv_2d.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/depthwise_conv_opencl_3x3.cc

@@ -5,6 +5,7 @@
 #include "mace/core/common.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/kernels/conv_2d.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/helper.cc

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#include "mace/kernels/opencl/helper.h"
+#include "mace/utils/utils.h"
+
+namespace mace {
+namespace kernels {
+
+// [(c+3)/4*W, N * H]
+void CalInOutputImageShape(const std::vector<index_t> &shape, /* NHWC */
+                        std::vector<size_t> &image_shape) {
+  MACE_CHECK(shape.size() == 4);
+  image_shape.resize(2);
+  image_shape[0] = RoundUpDiv4(shape[3]) * shape[2];
+  image_shape[1] = shape[0] * shape[1];
+}
+
+// [H * W * Ic, (Oc + 3) / 4]
+void CalFilterImageShape(const std::vector<index_t> &shape, /* HWIO*/
+                         std::vector<size_t> &image_shape) {
+  MACE_CHECK(shape.size() == 4);
+  image_shape.resize(2);
+  image_shape[0] = shape[0] * shape[1] * shape[2];
+  image_shape[1] = RoundUpDiv4(shape.back());
+}
+
+// [(size + 3) / 4, 1]
+void CalArgImageShape(const std::vector<index_t> &shape,
+                      std::vector<size_t> &image_shape) {
+  MACE_CHECK(shape.size() == 1);
+  image_shape.resize(2);
+  image_shape[0] = RoundUpDiv4(shape[0]);
+  image_shape[1] = 1;
+}
+
+void CalImage2DShape(const std::vector<index_t> &shape, /* NHWC */
+                     const BufferType type,
+                     std::vector<size_t> &image_shape) {
+  switch (type) {
+    case FILTER:
+      CalFilterImageShape(shape, image_shape);
+      break;
+    case IN_OUT:
+      CalInOutputImageShape(shape, image_shape);
+      break;
+    case ARGUMENT:
+      CalArgImageShape(shape, image_shape);
+      break;
+    default:
+      LOG(FATAL) << "Mace not supported yet.";
+  }
+}
+
+
+std::string DataTypeToCLType(const DataType dt) {
+  switch (dt) {
+    case DT_FLOAT:
+      return "float";
+    case DT_HALF:
+      return "half";
+    case DT_UINT8:
+      return "uchar";
+    case DT_INT8:
+      return "char";
+    case DT_DOUBLE:
+      return "double";
+    case DT_INT32:
+      return "int";
+    case DT_UINT32:
+      return "int";
+    case DT_UINT16:
+      return "ushort";
+    case DT_INT16:
+      return "short";
+    case DT_INT64:
+      return "long";
+    default:
+      LOG(FATAL) << "Unsupported data type";
+      return "";
+  }
+}
+
+std::string DataTypeToOpenclCMDDataType(const DataType dt) {
+  switch (dt) {
+    case DT_FLOAT:
+      return "f";
+    case DT_HALF:
+      return "h";
+    default:
+      LOG(FATAL) << "Not supported data type for opencl cmd data type";
+      return "";
+  }
+}
+
+}  // namespace kernels
+}  // namespace mace

mace/kernels/opencl/helper.h

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#ifndef MACE_KERNELS_OPENCL_HELPER_H_
+#define MACE_KERNELS_OPENCL_HELPER_H_
+#include "mace/core/types.h"
+
+namespace mace {
+namespace kernels {
+
+enum BufferType {
+  FILTER = 0,
+  IN_OUT= 1,
+  ARGUMENT = 2
+};
+
+void CalImage2DShape(const std::vector<index_t> &shape, /* NHWC */
+                     const BufferType type,
+                     std::vector<size_t> &image_shape);
+
+std::string DataTypeToOpenclCMDDataType(const DataType dt);
+
+std::string DataTypeToCLType(const DataType dt);
+
+
+}  // namespace kernels
+} //  namespace mace
+#endif //  MACE_KERNELS_OPENCL_HELPER_H_

mace/kernels/opencl/pooling_opencl.cc

@@ -5,6 +5,7 @@
 #include "mace/kernels/pooling.h"
 #include "mace/core/runtime/opencl/cl2_header.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/relu_opencl.cc

@@ -5,6 +5,7 @@
 #include "mace/kernels/relu.h"
 #include "mace/core/runtime/opencl/cl2_header.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/resize_bilinear_opencl.cc

@@ -5,6 +5,7 @@
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/core/tensor.h"
 #include "mace/kernels/resize_bilinear.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/kernels/opencl/space_to_batch_opecl.cc

@@ -8,6 +8,7 @@
 #include "mace/core/common.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
 #include "mace/kernels/space_to_batch.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 namespace kernels {

mace/ops/buffer_to_image.cc

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#include "mace/ops/buffer_to_image.h"
+
+namespace mace {
+
+REGISTER_OPENCL_OPERATOR(BufferToImage, BufferToImageOp<DeviceType::OPENCL, float>);
+
+}  //  namespace mace

mace/ops/buffer_to_image.h

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#ifndef MACE_OPS_BUFFER_TO_IMAGE_H_
+#define MACE_OPS_BUFFER_TO_IMAGE_H_
+
+#include "mace/core/operator.h"
+#include "mace/kernels/buffer_to_image.h"
+
+namespace mace {
+
+template <DeviceType D, typename T>
+class BufferToImageOp: public Operator<D, T> {
+ public:
+  BufferToImageOp(const OperatorDef &op_def, Workspace *ws)
+      : Operator<D, T>(op_def, ws)  {}
+
+  bool Run() override {
+    const Tensor *input_tensor = this->Input(INPUT);
+
+    kernels::BufferType type = static_cast<kernels::BufferType>(OperatorBase::GetSingleArgument<int>(
+        "buffer_type", static_cast<int>(kernels::FILTER)));
+    Tensor *output = this->Output(OUTPUT);
+
+    functor_(const_cast<Tensor *>(input_tensor), type, output);
+    return true;
+  }
+
+ private:
+  kernels::BufferToImageFunctor<D, T> functor_;
+
+ protected:
+  OP_INPUT_TAGS(INPUT);
+  OP_OUTPUT_TAGS(OUTPUT);
+};
+
+} //  namespace mace
+#endif //  MACE_OPS_BUFFER_TO_IMAGE_H_

mace/ops/buffer_to_image_test.cc

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#include "gtest/gtest.h"
+#include "mace/ops/ops_test_util.h"
+#include "mace/kernels/opencl/helper.h"
+
+using namespace mace;
+
+template<DeviceType D, typename T>
+void TestBidirectionTransform(const int type, const std::vector<index_t> &input_shape) {
+  OpsTestNet net;
+  OpDefBuilder("BufferToImage", "BufferToImageTest")
+      .Input("Input")
+      .Output("B2IOutput")
+      .AddIntArg("buffer_type", type)
+      .Finalize(net.NewOperatorDef());
+
+  // Add input data
+  net.AddRandomInput<D, T>("Input", input_shape);
+
+  // Run
+  net.RunOp(D);
+
+  OpDefBuilder("ImageToBuffer", "ImageToBufferTest")
+      .Input("B2IOutput")
+      .Output("I2BOutput")
+      .AddIntArg("buffer_type", type)
+      .Finalize(net.NewOperatorDef());
+
+  // Run
+  net.RunOp(D);
+
+  // Check
+  ExpectTensorNear<T>(*net.GetOutput("Input"), *net.GetOutput("I2BOutput"), 1e-5);
+}
+
+TEST(BufferToImageTest, ArgSmall) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::ARGUMENT, {1});
+}
+
+TEST(BufferToImageTest, ArgMedia) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::ARGUMENT, {11});
+}
+
+TEST(BufferToImageTest, ArgLarge) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::ARGUMENT, {256});
+}
+
+TEST(BufferToImageTest, InputSmallSingleChannel) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::IN_OUT, {1, 2, 3, 1});
+}
+
+TEST(BufferToImageTest, InputSmallMultipleChannel) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::IN_OUT, {1, 2, 3, 3});
+}
+
+TEST(BufferToImageTest, InputSmallMultipleBatchAndChannel) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::IN_OUT, {3, 2, 3, 3});
+}
+
+TEST(BufferToImageTest, InputMedia) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::IN_OUT, {3, 13, 17, 128});
+}
+
+TEST(BufferToImageTest, InputLarge) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::IN_OUT, {3, 64, 64, 256});
+}
+
+TEST(BufferToImageTest, Filter1x1Small) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {1, 1, 3, 5});
+}
+
+TEST(BufferToImageTest, Filter1x1Media) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {1, 1, 13, 17});
+}
+
+TEST(BufferToImageTest, Filter1x1Large) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {1, 1, 128, 512});
+}
+
+TEST(BufferToImageTest, Filter3x3Small) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {3, 3, 3, 5});
+}
+
+TEST(BufferToImageTest, Filter3x3Meida) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {3, 3, 13, 17});
+}
+
+TEST(BufferToImageTest, Filter3x3Large) {
+  TestBidirectionTransform<DeviceType::OPENCL, float>(kernels::FILTER, {3, 3, 128, 256});
+}

mace/ops/conv_2d.h

@@ -17,9 +17,9 @@ template <DeviceType D, typename T>
 class Conv2dOp : public ConvPool2dOpBase<D, T> {
  public:
   Conv2dOp(const OperatorDef &op_def, Workspace *ws)
-      : ConvPool2dOpBase<D, T>(op_def, ws) {
-    functor_.strides_ = this->strides_.data();
-    functor_.dilations_ = this->dilations_.data();
+      : ConvPool2dOpBase<D, T>(op_def, ws),
+        functor_(this->strides_.data(), this->padding_,
+                 this->dilations_.data()) {
   }
 
   bool Run() override {
@@ -28,15 +28,6 @@ class Conv2dOp : public ConvPool2dOpBase<D, T> {
     const Tensor *bias = this->InputSize() >= 3 ? this->Input(BIAS) : nullptr;
     Tensor *output = this->Output(OUTPUT);
 
-    std::vector<index_t> output_shape(4);
-    std::vector<int> paddings(2);
-    kernels::CalcPaddingAndOutputSize(
-        input->shape().data(), filter->shape().data(), this->dilations_.data(),
-        this->strides_.data(), this->padding_, output_shape.data(),
-        paddings.data());
-    output->Resize(output_shape);
-    functor_.paddings_ = paddings;
-
     functor_(input, filter, bias, output);
 
     return true;

mace/ops/image_to_buffer.cc

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#include "mace/ops/image_to_buffer.h"
+
+namespace mace {
+
+REGISTER_OPENCL_OPERATOR(ImageToBuffer, ImageToBufferOp<DeviceType::OPENCL, float>);
+
+}  //  namespace mace

mace/ops/image_to_buffer.h

+//
+// Copyright (c) 2017 XiaoMi All rights reserved.
+//
+
+#ifndef MACE_OPS_BUFFER_TO_IMAGE_H_
+#define MACE_OPS_BUFFER_TO_IMAGE_H_
+
+#include "mace/core/operator.h"
+#include "mace/kernels/buffer_to_image.h"
+
+namespace mace {
+
+template <DeviceType D, typename T>
+class ImageToBufferOp: public Operator<D, T> {
+ public:
+  ImageToBufferOp(const OperatorDef &op_def, Workspace *ws)
+      : Operator<D, T>(op_def, ws), functor_(true)  {}
+
+  bool Run() override {
+    const Tensor *input_tensor = this->Input(INPUT);
+    Tensor *output = this->Output(OUTPUT);
+
+    kernels::BufferType type = static_cast<kernels::BufferType>(OperatorBase::GetSingleArgument<int>(
+        "buffer_type", static_cast<int>(kernels::FILTER)));
+    functor_(output, type, const_cast<Tensor *>(input_tensor));
+    return true;
+  }
+
+ private:
+  kernels::BufferToImageFunctor<D, T> functor_;
+
+ protected:
+  OP_INPUT_TAGS(INPUT);
+  OP_OUTPUT_TAGS(OUTPUT);
+};
+
+} //  namespace mace
+#endif //  MACE_OPS_BUFFER_TO_IMAGE_H_

mace/ops/ops_test_util.h

@@ -12,6 +12,7 @@
 #include "mace/core/net.h"
 #include "mace/core/tensor.h"
 #include "mace/core/runtime/opencl/opencl_runtime.h"
+#include "mace/kernels/opencl/helper.h"
 
 namespace mace {
 
@@ -126,19 +127,26 @@ class OpsTestNet {
         ws_.CreateTensor(name, GetDeviceAllocator(D), DataTypeToEnum<T>::v());
     input->Resize(shape);
     Tensor::MappingGuard input_mapper(input);
-    float *input_data = input->mutable_data<T>();
+    T *input_data = input->mutable_data<T>();
 
     std::random_device rd;
     std::mt19937 gen(rd());
-    std::normal_distribution<T> nd(0, 1);
-
-    std::generate(input_data, input_data + input->size(),
-                  [&gen, &nd, positive] {
-                    return positive ? std::abs(nd(gen)) : nd(gen);
-                  });
+    std::normal_distribution<float> nd(0, 1);
+    if (DataTypeToEnum<T>::value == DT_HALF) {
+      std::generate(input_data, input_data + input->size(),
+                    [&gen, &nd, positive] {
+                      return half_float::half_cast<half>(positive ? std::abs(nd(gen)) : nd(gen));
+                    });
+    } else {
+      std::generate(input_data, input_data + input->size(),
+                    [&gen, &nd, positive] {
+                      return positive ? std::abs(nd(gen)) : nd(gen);
+                    });
+    }
   }
 
   OperatorDef *NewOperatorDef() {
+    op_defs_.clear();
     op_defs_.emplace_back(OperatorDef());
     return &op_defs_[op_defs_.size() - 1];
   }
@@ -258,7 +266,8 @@ inline std::string ShapeToString(const Tensor &x) {
 template <typename T>
 struct is_floating_point_type {
   static const bool value =
-      std::is_same<T, float>::value || std::is_same<T, double>::value;
+      std::is_same<T, float>::value || std::is_same<T, double>::value
+          || std::is_same<T, half>::value;
 };
 
 template <typename T>
@@ -314,6 +323,7 @@ struct Expector<T, true> {
                                        << " index = " << i;
     }
   }
+
 };
 
 template <typename T>
@@ -330,6 +340,7 @@ std::string ToString(const T &input) {
   return ss.str();
 }
 
+
 }  // namespace mace
 
 #endif  //  MACE_OPS_TEST_UTIL_H_

mace/utils/utils.h

@@ -13,6 +13,17 @@ Integer RoundUp(Integer i, Integer factor) {
   return (i + factor - 1) / factor * factor;
 }
 
+template <typename Integer, uint32_t factor>
+Integer RoundUpDiv(Integer i) {
+  return (i + factor - 1) / factor;
+}
+
+// Partial specialization of function templates is not allowed
+template <typename Integer>
+Integer RoundUpDiv4(Integer i) {
+  return (i + 3) >> 2;
+}
+
 template <typename Integer>
 Integer CeilQuotient(Integer a, Integer b) {
   return (a + b - 1) / b;