text: // half - IEEE 754-based half-precision floating point library.
  //
  // Copyright (c) 2012-2013 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 1.11.0
  
  /// \file
  /// Main header file for half precision functionality.
  
  #ifndef HALF_HALF_HPP
  #define HALF_HALF_HPP
  
  #include <math.h>
  #include <stdio.h>
  
  /// 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 >= 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
  
  // TODO
  // warning: calling a constexpr __host__ function("tgamma") from a
  // __host__ __device__ function("tgamma") is not allowed. The experimental
  // flag '--expt-relaxed-constexpr' can be used to allow this.
  #ifdef __CUDA_ARCH__
  #ifdef HALF_ENABLE_CPP11_CMATH
  #undef HALF_ENABLE_CPP11_CMATH
  #endif
  #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
  
  #ifdef __CUDA_ARCH__
  #include "caffe/util/half.cuh"
  #include "caffe/util/gpu_math_functions.cuh"
  #endif
  
  #if defined(__CUDA_ARCH__)
  #define CAFFE_UTIL_HD __host__ __device__
  #define CAFFE_UTIL_IHD __inline__ __host__ __device__
  #else
  #define CAFFE_UTIL_HD
  #define CAFFE_UTIL_IHD inline
  #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
  #define HALF_ROUND_STYLE 1 // = std::round_to_nearest
  #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;
  
  template <typename T>
  inline CAFFE_UTIL_HD T max(T a, T b) { return a > b ? a : b; }
  
  template <typename T>
  inline CAFFE_UTIL_HD T min(T a, T b) { return a < b ? a : b; }
  
  inline float CAFFE_UTIL_HD float_infinity() { return 1.0F / 0.0F; }
  
  inline float CAFFE_UTIL_HD float_nan() { return 0.0F / 0.0F; }
  
  /// \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::false_type;
  using std::true_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
  
  #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.
  typedef std::uint_least32_t uint32;
  
  /// Fastest signed integer capable of holding all values of type uint16.
  typedef std::int_fast32_t int17;
  #else
  /// Unsigned integer of (at least) 16 bits width.
  typedef unsigned short uint16;
  
  /// Unsigned integer of (at least) 32 bits width.
  typedef conditional<std::numeric_limits<unsigned int>::digits >= 32, unsigned int, unsigned long>::type uint32;
  
  /// Fastest signed integer capable of holding all values of type uint16.
  typedef conditional<std::numeric_limits<int>::digits >= 16, int, long>::type int17;
  #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
  		CAFFE_UTIL_HD
  		expr(float f) : value_(f) {}
  
  	/// Conversion to single-precision.
  	/// \return single precision value representing expression value
  	HALF_CONSTEXPR
  	CAFFE_UTIL_HD
  	operator float() const { 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)
  {
  #if HALF_ENABLE_CPP11_STATIC_ASSERT
  	static_assert(std::numeric_limits<float>::is_iec559, "float to half conversion needs IEEE 754 conformant 'float' type");
  	static_assert(sizeof(uint32) == sizeof(float), "float to half conversion needs unsigned integer type of exactly the size of a 'float'");
  #endif
  	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};
  	uint32 bits; // = *reinterpret_cast<uint32*>(&value);		//violating strict aliasing!
  	std::memcpy(&bits, &value, sizeof(float));
  	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 non-IEEE single-precision to half-precision.
  /// \param value single-precision value
  /// \return binary representation of half-precision value
  template <std::float_round_style R>
  uint16 float2half_impl(float value, false_type)
  {
  	uint16 hbits = builtin_signbit(value) << 15;
  	if (value == 0.0f)
  		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_zero)
  			return hbits | 0x7BFF;
  		else 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 | 0x7C00;
  	}
  	if (exp < -13)
  		value = std::ldexp(value, 24);
  	else
  	{
  		value = std::ldexp(value, 11 - exp);
  		hbits |= ((exp + 14) << 10);
  	}
  	int ival = static_cast<int>(value);
  	hbits |= static_cast<uint16>(std::abs(ival) & 0x3FF);
  	if (R == std::round_to_nearest)
  	{
  		float diff = std::abs(value - static_cast<float>(ival));
  #if HALF_ROUND_TIES_TO_EVEN
  		hbits += (diff > 0.5f) | ((diff == 0.5f) & hbits);
  #else
  		hbits += diff >= 0.5f;
  #endif
  	}
  	else if (R == std::round_toward_infinity)
  		hbits += value > static_cast<float>(ival);
  	else if (R == std::round_toward_neg_infinity)
  		hbits += value < static_cast<float>(ival);
  	return hbits;
  }
  
  /// Convert single-precision to half-precision.
  /// \param value single-precision value
  /// \return binary representation of half-precision value
  template <std::float_round_style R>
  uint16 float2half(float value)
  {
  	return float2half_impl<R>(value, bool_type < std::numeric_limits<float>::is_iec559 && sizeof(uint32) == sizeof(float) > ());
  }
  
  /// 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 (S)
  		value = -value;
  	uint16 bits = S << 15;
  	if (value > 65504)
  	{
  		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 = 25;
  		for (; m < 0x400; m <<= 1, --exp)
  			;
  		for (; m > 0x7FF; m >>= 1, ++exp)
  			;
  		bits |= (exp << 10) | (m & 0x3FF);
  		if (exp > 25)
  		{
  			if (R == std::round_to_nearest)
  				bits += (value >> (exp - 26)) & 1
  #if HALF_ROUND_TIES_TO_EVEN
  						& (((((1 << (exp - 26)) - 1) & value) != 0) | bits)
  #endif
  					;
  			else if (R == std::round_toward_infinity)
  				bits += ((value & ((1 << (exp - 25)) - 1)) != 0) & !S;
  			else if (R == std::round_toward_neg_infinity)
  				bits += ((value & ((1 << (exp - 25)) - 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, true_type)
  {
  #if HALF_ENABLE_CPP11_STATIC_ASSERT
  	static_assert(std::numeric_limits<float>::is_iec559, "half to float conversion needs IEEE 754 conformant 'float' type");
  	static_assert(sizeof(uint32) == sizeof(float), "half to float conversion needs unsigned integer type of exactly the size of a 'float'");
  #endif
  	static const uint32 mantissa_table[2048] = {
  		0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000,
  		0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000,
  		0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
  		0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000,
  		0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000,
  		0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
  		0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
  		0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000,
  		0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
  		0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000,
  		0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000,
  		0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
  		0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000,
  		0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000,
  		0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
  		0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
  		0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000,
  		0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
  		0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000,
  		0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000,
  		0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
  		0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000,
  		0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000,
  		0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
  		0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
  		0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000,
  		0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
  		0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000,
  		0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000,
  		0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
  		0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000,
  		0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000,
  		0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
  		0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
  		0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000,
  		0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
  		0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000,
  		0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000,
  		0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
  		0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000,
  		0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000,
  		0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
  		0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
  		0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000,
  		0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
  		0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000,
  		0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000,
  		0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
  		0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000,
  		0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000,
  		0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000,
  		0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000,
  		0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000,
  		0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000,
  		0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000,
  		0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000,
  		0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000,
  		0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000,
  		0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000,
  		0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000,
  		0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000,
  		0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000,
  		0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000,
  		0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000,
  		0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000,
  		0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000,
  		0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000,
  		0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000,
  		0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000,
  		0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000,
  		0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000,
  		0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000,
  		0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000,
  		0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000,
  		0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000,
  		0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000,
  		0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000,
  		0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000,
  		0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000,
  		0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000,
  		0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000,
  		0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000,
  		0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000,
  		0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000,
  		0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000,
  		0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000,
  		0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000,
  		0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000,
  		0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000,
  		0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000,
  		0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000,
  		0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000,
  		0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000,
  		0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000,
  		0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000,
  		0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000,
  		0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000,
  		0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000,
  		0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000,
  		0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000,
  		0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000,
  		0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000,
  		0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000,
  		0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000,
  		0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000,
  		0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000,
  		0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000,
  		0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000,
  		0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000,
  		0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000,
  		0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000,
  		0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000,
  		0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000,
  		0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000,
  		0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
  		0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000,
  		0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000,
  		0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000,
  		0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000,
  		0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000,
  		0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000,
  		0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000,
  		0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000,
  		0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
  		0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000,
  		0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000,
  		0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000,
  		0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000};
  	static const 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];
  	//			uint32 bits = mantissa_table[(((value&0x7C00)!=0)<<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 non-IEEE single-precision.
  /// \param value binary representation of half-precision value
  /// \return single-precision value
  inline float half2float_impl(uint16 value, false_type)
  {
  	float out;
  	int abs = value & 0x7FFF;
  	if (abs > 0x7C00)
  		out = std::numeric_limits<float>::has_quiet_NaN ? std::numeric_limits<float>::quiet_NaN() : 0.0f;
  	else if (abs == 0x7C00)
  		out = std::numeric_limits<float>::has_infinity ? std::numeric_limits<float>::infinity() : std::numeric_limits<float>::max();
  	else if (abs > 0x3FF)
  		out = std::ldexp(static_cast<float>((value & 0x3FF) | 0x400), (abs >> 10) - 25);
  	else
  		out = std::ldexp(static_cast<float>(abs), -24);
  	return (value & 0x8000) ? -out : out;
  }
  
  /// Convert half-precision to single-precision.
  /// \param value binary representation of half-precision value
  /// \return single-precision value
  inline float half2float(uint16 value)
  {
  	return half2float_impl(value, bool_type < std::numeric_limits<float>::is_iec559 && sizeof(uint32) == sizeof(float) > ());
  }
  
  /// 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)
  {
  	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();
  	}
  	int17 m = (value & 0x3FF) | 0x400;
  	e >>= 10;
  	if (e < 25)
  	{
  		if (R == std::round_indeterminate || R == std::round_toward_zero)
  			m >>= 25 - e;
  		else
  		{
  			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;
  	//			if(std::numeric_limits<T>::digits < 16)
  	//				return std::min(std::max(m, static_cast<int17>(std::numeric_limits<T>::min())), static_cast<int17>(std::numeric_limits<T>::max()));
  	return static_cast<T>((value & 0x8000) ? -m : 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 CAFFE_UTIL_HD 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;
  } // namespace detail
  
  /// 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 truncation (round towards zero), 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
  
  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
  	CAFFE_UTIL_HD
  	half() : data_() {}
  
  	template <typename H>
  	CAFFE_UTIL_HD const H *gethp() const
  	{
  		return reinterpret_cast<const H *>(&data_);
  	}
  
  	template <typename H>
  	CAFFE_UTIL_HD
  		H *
  		gethp()
  	{
  		return reinterpret_cast<H *>(&data_);
  	}
  
  	CAFFE_UTIL_HD
  	unsigned short getx() const
  	{
  		return data_;
  	}
  
  	CAFFE_UTIL_HD
  	half &setx(unsigned short x)
  	{
  		data_ = x;
  		return *this;
  	}
  
  	/// Copy constructor.
  	/// \tparam T type of concrete half expression
  	/// \param rhs half expression to copy from
  	CAFFE_UTIL_HD
  	half(detail::expr rhs)
  	{
  		assign(rhs);
  	}
  
  	/// Conversion constructor.
  	/// \param rhs float to convert
  	template <typename T>
  	CAFFE_UTIL_HD
  	half(const T &rhs)
  	{
  		assign(static_cast<float>(rhs));
  	}
  
  	// Copy constructor overriding the one above
  	// It avoids half->float->half path
  	CAFFE_UTIL_HD
  	half(const half &rhs) : data_(rhs.data_) {}
  
  	//		explicit half(float rhs) : data_(detail::float2half<round_style>(rhs)) {}
  	CAFFE_UTIL_HD
  	explicit half(float rhs)
  	{
  		assign(rhs);
  	}
  
  	/// Conversion to single-precision.
  	/// \return single precision value representing expression value
  	//		operator float() const { return detail::half2float(data_); }
  	CAFFE_UTIL_HD operator float() const
  	{
  #ifdef __CUDA_ARCH__
  		::half h;
  		h.setx(data_);
  		return __half2float(h);
  #else
  		return detail::half2float(data_);
  #endif
  	}
  
  	CAFFE_UTIL_HD void assign(float rhs)
  	{
  #ifdef __CUDA_ARCH__
  		data_ = float2half_clip(rhs).x();
  #else
  		data_ = detail::float2half<round_style>(rhs);
  #endif
  	}
  
  	template <class T>
  	CAFFE_UTIL_IHD half &operator=(const T &rhs)
  	{
  		assign(static_cast<float>(rhs));
  		return *this;
  	}
  
  	/// Assignment operator.
  	/// \tparam T type of concrete half expression
  	/// \param rhs half expression to copy from
  	/// \return reference to this half
  	CAFFE_UTIL_HD
  	half &operator=(detail::expr rhs) { return *this = static_cast<float>(rhs); }
  
  	CAFFE_UTIL_HD
  	half &operator=(const half &rhs)
  	{
  		data_ = rhs.data_;
  		return *this;
  	}
  
  	/// Arithmetic assignment.
  	/// \tparam T type of concrete half expression
  	/// \param rhs half expression to add
  	/// \return reference to this half
  	template <typename T>
  	CAFFE_UTIL_HD
  		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>
  	CAFFE_UTIL_HD
  		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>
  	CAFFE_UTIL_HD
  		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>
  	CAFFE_UTIL_HD
  		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
  	CAFFE_UTIL_HD
  	half &operator=(float rhs)
  	{
  		assign(rhs);
  		return *this;
  	}
  
  	/// Arithmetic assignment.
  	/// \param rhs single-precision value to add
  	/// \return reference to this half
  	CAFFE_UTIL_HD
  	half &operator+=(float rhs)
  	{
  		assign(static_cast<float>(*this) + rhs);
  		return *this;
  	}
  
  	/// Arithmetic assignment.
  	/// \param rhs single-precision value to subtract
  	/// \return reference to this half
  	CAFFE_UTIL_HD
  	half &operator-=(float rhs)
  	{
  #ifdef DEBUG_PRECISION
  		float before = static_cast<float>(*this);
  		assign(before - rhs);
  		float after = static_cast<float>(*this);
  		if (before == after && before != 0.f && rhs != 0.f)
  		{
  #ifdef __CUDA_ARCH__
  			printf("GPU PRECISION LOSS: %g -= %g\n", before, rhs);
  #else
  			printf("CPU PRECISION LOSS: %g -= %g\n", before, rhs);
  #endif
  		}
  #else
  		assign(static_cast<float>(*this) - rhs);
  #endif
  		return *this;
  	}
  
  	/// Arithmetic assignment.
  	/// \param rhs single-precision value to multiply with
  	/// \return reference to this half
  	CAFFE_UTIL_HD
  	half &operator*=(float rhs)
  	{
  		assign(static_cast<float>(*this) * rhs);
  		return *this;
  	}
  
  	/// Arithmetic assignment.
  	/// \param rhs single-precision value to divide by
  	/// \return reference to this half
  	CAFFE_UTIL_HD
  	half &operator/=(float rhs)
  	{
  		assign(static_cast<float>(*this) / rhs);
  		return *this;
  	}
  
  	/// Prefix increment.
  	/// \return incremented half value
  	CAFFE_UTIL_HD
  	half &operator++() { return *this += 1.0f; }
  
  	/// Prefix decrement.
  	/// \return decremented half value
  	CAFFE_UTIL_HD
  	half &operator--() { return *this -= 1.0f; }
  
  	/// Postfix increment.
  	/// \return non-incremented half value
  	CAFFE_UTIL_HD
  	half operator++(int)
  	{
  		half out(*this);
  		++*this;
  		return out;
  	}
  
  	/// Postfix decrement.
  	/// \return non-decremented half value
  	CAFFE_UTIL_HD
  	half operator--(int)
  	{
  		half out(*this);
  		--*this;
  		return out;
  	}
  
  private:
  	/// Rounding mode to use (always `std::round_indeterminate`)
  	static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
  
  	/// Constructor.
  	/// \param bits binary representation to set half to
  	CAFFE_UTIL_HD
  	HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) : data_(bits) {}
  
  	/// Internal binary representation
  	detail::uint16 data_;
  };
  
  template <>
  CAFFE_UTIL_IHD half &half::operator=<half>(const half &rhs)
  {
  	data_ = rhs.data_;
  	return *this;
  }
  
  #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 literal.
  /// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due
  /// to rather involved single-to-half conversion.
  /// \param value literal value
  /// \return half with given value (if representable)
  inline half operator"" _h(long double value) { return half(static_cast<float>(value)); }
  } // namespace literal
  #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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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(float_nan() /*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(float_nan() /*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 CAFFE_UTIL_HD 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(float_nan() /*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(float_nan() /*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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half nanh(const char *) { return half(binary, 0x7FFF); }
  
  	/// Exponential implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr exp(float arg) { return expr(std::exp(arg)); }
  
  	/// Exponential implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr log(float arg) { return expr(std::log(arg)); }
  
  	/// Common logarithm implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr log10(float arg) { return expr(std::log10(arg)); }
  
  	/// Logarithm implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sqrt(float arg) { return expr(std::sqrt(arg)); }
  
  	/// Cubic root implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD 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(std::fabs(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 CAFFE_UTIL_HD 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)) ? float_infinity() /*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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sin(float arg) { return expr(std::sin(arg)); }
  
  	/// Cosine implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr cos(float arg) { return expr(std::cos(arg)); }
  
  	/// Tan implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr tan(float arg) { return expr(std::tan(arg)); }
  
  	/// Arc sine implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr asin(float arg) { return expr(std::asin(arg)); }
  
  	/// Arc cosine implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr acos(float arg) { return expr(std::acos(arg)); }
  
  	/// Arc tangent implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sinh(float arg) { return expr(std::sinh(arg)); }
  
  	/// Hyperbolic cosine implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr cosh(float arg) { return expr(std::cosh(arg)); }
  
  	/// Hyperbolic tangent implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr asinh(float arg)
  	{
  #if HALF_ENABLE_CPP11_CMATH
  		return expr(std::asinh(arg));
  #else
  		return expr((arg == -float_infinity() /*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 CAFFE_UTIL_HD expr acosh(float arg)
  	{
  #if HALF_ENABLE_CPP11_CMATH
  		return expr(std::acosh(arg));
  #else
  		return expr((arg < -1.0f) ? float_nan() /*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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr lgamma(float arg)
  	{
  #if HALF_ENABLE_CPP11_CMATH
  		return expr(std::lgamma(arg));
  #else
  		if (builtin_isinf(arg))
  			return expr(float_infinity() /*std::numeric_limits<float>::infinity()*/);
  		double z = static_cast<double>(arg);
  		if (z < 0)
  		{
  			double i, f = std::modf(-z, &i);
  			if (f == 0.0)
  				return expr(float_infinity() /*std::numeric_limits<float>::infinity()*/);
  			return expr(static_cast<float>(1.1447298858494001741434273513531 - std::log(std::abs(std::sin(3.1415926535897932384626433832795 * f))) - lgamma(1.0 - z)));
  		}
  		//				if(z < 8.0)
  		//					return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
  		return expr(static_cast<float>(0.5 * (1.8378770664093454835606594728112 - std::log(z)) + z * (std::log(z + 1.0 / (12.0 * z - 1.0 / (10.0 * z) - 1.0)) - 1.0)));
  #endif
  	}
  
  	/// Gamma implementation.
  	/// \param arg function argument
  	/// \return function value stored in single-preicision
  	static CAFFE_UTIL_HD expr tgamma(float arg)
  	{
  #if HALF_ENABLE_CPP11_CMATH
  		return expr(std::tgamma(arg));
  #else
  		double z = static_cast<double>(arg);
  		if (z == 0.0)
  			return builtin_signbit(z) ? expr(-float_infinity() /*std::numeric_limits<float>::infinity()*/) : expr(float_infinity() /*std::numeric_limits<float>::infinity()*/);
  		if (z < 0.0)
  		{
  			double i, f = std::modf(-z, &i);
  			if (f == 0.0)
  				return expr(float_nan() /*std::numeric_limits<float>::quiet_NaN()*/);
  			double sign = (std::fmod(i, 2.0) == 0.0) ? -1.0 : 1.0;
  			return expr(static_cast<float>(sign * 3.1415926535897932384626433832795 / (std::sin(3.1415926535897932384626433832795 * f) * std::exp(lgamma(1.0 - z)))));
  		}
  		if (builtin_isinf(arg))
  			return expr(arg);
  		//				if(arg < 8.0f)
  		//					return expr(static_cast<float>(std::exp(lgamma(z))));
  		return expr(static_cast<float>(std::sqrt(6.283185307179586476925286766559 / z) * std::pow(0.36787944117144232159552377016146 * (z + 1.0 / (12.0 * z - 1.0 / (10.0 * z))), z)));
  #endif
  	}
  
  	/// Floor implementation.
  	/// \param arg value to round
  	/// \return rounded value
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half round(half arg) { return half(binary, round_half_up(arg.data_)); }
  
  	/// Nearest integer implementation.
  	/// \param arg value to round
  	/// \return rounded value
  	static CAFFE_UTIL_HD long lround(half arg) { return detail::half2int_up<long>(arg.data_); }
  
  	/// Nearest integer implementation.
  	/// \param arg value to round
  	/// \return rounded value
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half frexp(half arg, int *exp)
  	{
  		unsigned int m = arg.data_ & 0x7FFF;
  		if (m >= 0x7C00 || !m)
  			return *exp = 0, arg;
  		int e = m >> 10;
  		if (!e)
  			for (m <<= 1; m < 0x400; m <<= 1, --e)
  				;
  		return *exp = e - 14, half(binary, static_cast<uint16>((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 CAFFE_UTIL_HD half modf(half arg, half *iptr)
  	{
  		unsigned int e = arg.data_ & 0x7C00;
  		if (e > 0x6000)
  			return *iptr = arg, (e == 0x7C00 && (arg.data_ & 0x3FF)) ? arg : half(binary, arg.data_ & 0x8000);
  		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 CAFFE_UTIL_HD half scalbln(half arg, long exp)
  	{
  		long e = arg.data_ & 0x7C00;
  		if (e == 0x7C00)
  			return arg;
  		unsigned int m = arg.data_ & 0x3FF;
  		if (e >>= 10)
  			m |= 0x400;
  		else
  		{
  			if (!m)
  				return arg;
  			for (m <<= 1; m < 0x400; m <<= 1, --e)
  				;
  		}
  		e += exp;
  		uint16 value = arg.data_ & 0x8000;
  		if (e > 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 (e > 0)
  			value |= (e << 10) | (m & 0x3FF);
  		else if (e > -11)
  		{
  			if (half::round_style == std::round_to_nearest)
  			{
  				m += 1 << -e;
  #if HALF_ROUND_TIES_TO_EVEN
  				m -= (m >> (1 - e)) & 1;
  #endif
  			}
  			else if (half::round_style == std::round_toward_infinity)
  				m += ((value >> 15) - 1) & ((1 << (1 - e)) - 1U);
  			else if (half::round_style == std::round_toward_neg_infinity)
  				m += -(value >> 15) & ((1 << (1 - e)) - 1U);
  			value |= m >> (1 - e);
  		}
  		else if (half::round_style == std::round_toward_infinity)
  			value |= ((value >> 15) - 1) & 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 CAFFE_UTIL_HD int ilogb(half arg)
  	{
  		int exp = arg.data_ & 0x7FFF;
  		if (!exp)
  			return FP_ILOGB0;
  		if (exp < 0x7C00)
  		{
  			if (!(exp >>= 10))
  				for (unsigned int m = (arg.data_ & 0x3FF); m < 0x200; m <<= 1, --exp)
  					;
  			return exp - 15;
  		}
  		if (exp > 0x7C00)
  			return FP_ILOGBNAN;
  		return INT_MAX;
  	}
  
  	/// Exponent implementation.
  	/// \param arg number to query
  	/// \return floating point exponent
  	static CAFFE_UTIL_HD half logb(half arg)
  	{
  		int exp = arg.data_ & 0x7FFF;
  		if (!exp)
  			return half(binary, 0xFC00);
  		if (exp < 0x7C00)
  		{
  			if (!(exp >>= 10))
  				for (unsigned int m = (arg.data_ & 0x3FF); m < 0x200; m <<= 1, --exp)
  					;
  			return half(static_cast<float>(exp - 15));
  		}
  		if (exp > 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 CAFFE_UTIL_HD 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 = (signbit(from) ? (static_cast<int17>(0x8000) - from.data_) : static_cast<int17>(from.data_)) <
  				  (signbit(to) ? (static_cast<int17>(0x8000) - to.data_) : static_cast<int17>(to.data_));
  		return half(binary, from.data_ + (((from.data_ >> 15) ^ static_cast<uint16>(lt)) << 1) - 1);
  	}
  
  	/// Enumeration implementation.
  	/// \param from number to increase/decrease
  	/// \param to direction to enumerate into
  	/// \return next representable number
  	static CAFFE_UTIL_HD half nexttoward(half from, double to)
  	{
  		if (isnan(from))
  			return from;
  		double lfrom = static_cast<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<uint16>(lfrom < to)) << 1) - 1);
  	}
  
  	/// Sign implementation
  	/// \param x first operand
  	/// \param y second operand
  	/// \return composed value
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD int fpclassify(half arg)
  	{
  		unsigned int abs = arg.data_ & 0x7FFF;
  		if (abs > 0x7C00)
  			return FP_NAN;
  		if (abs == 0x7C00)
  			return FP_INFINITE;
  		if (abs > 0x3FF)
  			return FP_NORMAL;
  		return abs ? FP_SUBNORMAL : FP_ZERO;
  	}
  
  	/// Classification implementation.
  	/// \param arg value to classify
  	/// \retval true if finite number
  	/// \retval false else
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isgreater(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) > (signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_))); }
  
  	/// Comparison implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \retval true if \a x >= \a y
  	/// \retval false else
  	static CAFFE_UTIL_HD bool isgreaterequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) >= (signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_))); }
  
  	/// Comparison implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \retval true if \a x < \a y
  	/// \retval false else
  	static CAFFE_UTIL_HD bool isless(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) < (signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_))); }
  
  	/// Comparison implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \retval true if \a x <= \a y
  	/// \retval false else
  	static CAFFE_UTIL_HD bool islessequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) <= (signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_))); }
  
  	/// Comparison implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \retval true neither \a x > \a y nor \a x < \a y
  	/// \retval false else
  	static CAFFE_UTIL_HD bool islessgreater(half x, half y)
  	{
  		if (isnan(x) || isnan(y))
  			return false;
  		int17 a = signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_);
  		int17 b = signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_);
  		return a < b || a > b;
  	}
  
  	/// Comparison implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \retval true if operand unordered
  	/// \retval false else
  	static CAFFE_UTIL_HD bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
  
  private:
  	static CAFFE_UTIL_HD double erf(double arg)
  	{
  		if (builtin_isinf(arg))
  			return (arg < 0.0) ? -1.0 : 1.0;
  		double x2 = static_cast<double>(arg) * static_cast<double>(arg), ax2 = 0.147 * x2;
  		double value = std::sqrt(1.0 - std::exp(-x2 * (1.2732395447351626861510701069801 + ax2) / (1.0 + ax2)));
  		return builtin_signbit(arg) ? -value : value;
  	}
  
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half negate(half arg)
  	{
  		half h;
  		h.setx(arg.data_ ^ 0x8000);
  		return h;
  	}
  
  	/// Absolute value implementation.
  	/// \param arg function argument
  	/// \return absolute value
  	static CAFFE_UTIL_HD half fabs(half arg)
  	{
  		half h;
  		h.setx(arg.data_ & 0x7FFF);
  		return h;
  	}
  };
  template <>
  struct unary_specialized<expr>
  {
  	static CAFFE_UTIL_HD HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); }
  	static CAFFE_UTIL_HD 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 CAFFE_UTIL_HD 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(min(x, y));
  #endif
  	}
  
  	/// Maximum implementation.
  	/// \param x first operand
  	/// \param y second operand
  	/// \return maximum value
  	static CAFFE_UTIL_HD 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(max(x, y));
  #endif
  	}
  };
  template <>
  struct binary_specialized<half, half>
  {
  	static CAFFE_UTIL_HD half fmin(half x, half y)
  	{
  		if (functions::isnan(x))
  			return y;
  		if (functions::isnan(y))
  			return x;
  		return ((functions::signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) >
  				(functions::signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_)))
  				   ? y
  				   : x;
  	}
  	static CAFFE_UTIL_HD half fmax(half x, half y)
  	{
  		if (functions::isnan(x))
  			return y;
  		if (functions::isnan(y))
  			return x;
  		return ((functions::signbit(x) ? (static_cast<int17>(0x8000) - x.data_) : static_cast<int17>(x.data_)) <
  				(functions::signbit(y) ? (static_cast<int17>(0x8000) - y.data_) : static_cast<int17>(y.data_)))
  				   ? 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
  
  	typedef half type;
  	static CAFFE_UTIL_HD half cast(U arg) { return cast_impl(arg, is_float<U>()); };
  
  private:
  	static CAFFE_UTIL_HD
  		half
  		cast_impl(U arg, true_type)
  	{
  #ifdef __CUDA_ARCH__
  		return half(binary, float2half_clip(static_cast<float>(arg)));
  #else
  		return half(binary, float2half<R>(static_cast<float>(arg)));
  #endif
  	}
  
  	static CAFFE_UTIL_HD
  		half
  		cast_impl(U arg, false_type)
  	{
  #ifdef __CUDA_ARCH__
  		return half(binary, float2half_clip(static_cast<float>(arg)));
  #else
  		return half(binary, int2half<R>(arg));
  #endif
  	}
  };
  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
  
  	typedef T type;
  	template <typename U>
  	static CAFFE_UTIL_HD T cast(U arg) { return cast_impl(arg, is_float<T>()); }
  
  private:
  	static CAFFE_UTIL_HD T cast_impl(float arg, true_type) { return static_cast<T>(arg); }
  	static CAFFE_UTIL_HD 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> : public half_caster<T, half, R>
  {
  };
  template <std::float_round_style R>
  struct half_caster<half, half, R>
  {
  	typedef half type;
  	static CAFFE_UTIL_HD half cast(half arg) { return arg; }
  };
  template <std::float_round_style R>
  struct half_caster<half, expr, R> : public 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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	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>
  CAFFE_UTIL_HD
  	HALF_CONSTEXPR typename enable<T, T>::type
  	operator+(T arg) { return arg; }
  
  /// Negation.
  /// \param arg operand
  /// \return negated operand
  template <typename T>
  CAFFE_UTIL_HD
  	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); }
  
  inline std::ostream &operator<<(std::ostream &out, const half &arg)
  {
  	return functions::write(out, arg); //return out << (float)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 CAFFE_UTIL_HD half abs(half arg) { return unary_specialized<half>::fabs(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half fabs(half arg) { return unary_specialized<half>::fabs(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr fmod(half x, half y) { return functions::fmod(x, y); }
  inline CAFFE_UTIL_HD expr fmod(half x, expr y) { return functions::fmod(x, y); }
  inline CAFFE_UTIL_HD expr fmod(expr x, half y) { return functions::fmod(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr remainder(half x, half y) { return functions::remainder(x, y); }
  inline CAFFE_UTIL_HD expr remainder(half x, expr y) { return functions::remainder(x, y); }
  inline CAFFE_UTIL_HD expr remainder(expr x, half y) { return functions::remainder(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr remquo(half x, half y, int *quo) { return functions::remquo(x, y, quo); }
  inline CAFFE_UTIL_HD expr remquo(half x, expr y, int *quo) { return functions::remquo(x, y, quo); }
  inline CAFFE_UTIL_HD expr remquo(expr x, half y, int *quo) { return functions::remquo(x, y, quo); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr fma(half x, half y, half z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(half x, half y, expr z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(half x, expr y, half z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(expr x, half y, half z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half fmax(half x, half y) { return binary_specialized<half, half>::fmax(x, y); }
  inline CAFFE_UTIL_HD expr fmax(half x, expr y) { return binary_specialized<half, expr>::fmax(x, y); }
  inline CAFFE_UTIL_HD expr fmax(expr x, half y) { return binary_specialized<expr, half>::fmax(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half fmin(half x, half y) { return binary_specialized<half, half>::fmin(x, y); }
  inline CAFFE_UTIL_HD expr fmin(half x, expr y) { return binary_specialized<half, expr>::fmin(x, y); }
  inline CAFFE_UTIL_HD expr fmin(expr x, half y) { return binary_specialized<expr, half>::fmin(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr fdim(half x, half y) { return functions::fdim(x, y); }
  inline CAFFE_UTIL_HD expr fdim(half x, expr y) { return functions::fdim(x, y); }
  inline CAFFE_UTIL_HD expr fdim(expr x, half y) { return functions::fdim(x, y); }
  inline CAFFE_UTIL_HD expr fdim(expr x, expr y) { return functions::fdim(x, y); }
  
  /// Get NaN value.
  /// \param arg descriptive string (ignored)
  /// \return quiet NaN
  inline CAFFE_UTIL_HD half nanh(const char *arg) { return functions::nanh(arg); }
  
  /// \}
  /// \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 CAFFE_UTIL_HD expr exp(half arg) { return functions::exp(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr expm1(half arg) { return functions::expm1(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr exp2(half arg) { return functions::exp2(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr log(half arg) { return functions::log(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr log10(half arg) { return functions::log10(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr log1p(half arg) { return functions::log1p(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr log2(half arg) { return functions::log2(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sqrt(half arg) { return functions::sqrt(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr cbrt(half arg) { return functions::cbrt(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr hypot(half x, half y) { return functions::hypot(x, y); }
  inline CAFFE_UTIL_HD expr hypot(half x, expr y) { return functions::hypot(x, y); }
  inline CAFFE_UTIL_HD expr hypot(expr x, half y) { return functions::hypot(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr pow(half base, half exp) { return functions::pow(base, exp); }
  inline CAFFE_UTIL_HD expr pow(half base, expr exp) { return functions::pow(base, exp); }
  inline CAFFE_UTIL_HD expr pow(expr base, half exp) { return functions::pow(base, exp); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sin(half arg) { return functions::sin(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr cos(half arg) { return functions::cos(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr tan(half arg) { return functions::tan(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr asin(half arg) { return functions::asin(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr acos(half arg) { return functions::acos(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr atan(half arg) { return functions::atan(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr atan2(half x, half y) { return functions::atan2(x, y); }
  inline CAFFE_UTIL_HD expr atan2(half x, expr y) { return functions::atan2(x, y); }
  inline CAFFE_UTIL_HD expr atan2(expr x, half y) { return functions::atan2(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr sinh(half arg) { return functions::sinh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr cosh(half arg) { return functions::cosh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr tanh(half arg) { return functions::tanh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr asinh(half arg) { return functions::asinh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr acosh(half arg) { return functions::acosh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr atanh(half arg) { return functions::atanh(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr erf(half arg) { return functions::erf(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr erfc(half arg) { return functions::erfc(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr lgamma(half arg) { return functions::lgamma(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD expr tgamma(half arg) { return functions::tgamma(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half ceil(half arg) { return functions::ceil(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half floor(half arg) { return functions::floor(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half trunc(half arg) { return functions::trunc(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half round(half arg) { return functions::round(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD long lround(half arg) { return functions::lround(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half nearbyint(half arg) { return functions::rint(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half rint(half arg) { return functions::rint(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD long lrint(half arg) { return functions::lrint(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD long long llround(half arg) { return functions::llround(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD long long llrint(half arg) { return functions::llrint(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half frexp(half arg, int *exp) { return functions::frexp(arg, exp); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half modf(half arg, half *iptr) { return functions::modf(arg, iptr); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half scalbln(half arg, long exp) { return functions::scalbln(arg, exp); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD int ilogb(half arg) { return functions::ilogb(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half logb(half arg) { return functions::logb(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD half nextafter(half from, half to) { return functions::nextafter(from, to); }
  inline CAFFE_UTIL_HD half nextafter(half from, expr to) { return functions::nextafter(from, to); }
  inline CAFFE_UTIL_HD half nextafter(expr from, half to) { return functions::nextafter(from, to); }
  inline CAFFE_UTIL_HD 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, double to) { return functions::nexttoward(from, to); }
  inline CAFFE_UTIL_HD half nexttoward(half from, double to) { return functions::nexttoward(from, to); }
  inline CAFFE_UTIL_HD half nexttoward(expr from, 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 CAFFE_UTIL_HD half copysign(half x, half y) { return functions::copysign(x, y); }
  inline CAFFE_UTIL_HD half copysign(half x, expr y) { return functions::copysign(x, y); }
  inline CAFFE_UTIL_HD half copysign(expr x, half y) { return functions::copysign(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD int fpclassify(half arg) { return functions::fpclassify(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isfinite(half arg) { return functions::isfinite(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isinf(half arg) { return functions::isinf(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isnan(half arg) { return functions::isnan(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isnormal(half arg) { return functions::isnormal(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool signbit(half arg) { return functions::signbit(arg); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isgreater(half x, half y) { return functions::isgreater(x, y); }
  inline CAFFE_UTIL_HD bool isgreater(half x, expr y) { return functions::isgreater(x, y); }
  inline CAFFE_UTIL_HD bool isgreater(expr x, half y) { return functions::isgreater(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isgreaterequal(half x, half y) { return functions::isgreaterequal(x, y); }
  inline CAFFE_UTIL_HD bool isgreaterequal(half x, expr y) { return functions::isgreaterequal(x, y); }
  inline CAFFE_UTIL_HD bool isgreaterequal(expr x, half y) { return functions::isgreaterequal(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isless(half x, half y) { return functions::isless(x, y); }
  inline CAFFE_UTIL_HD bool isless(half x, expr y) { return functions::isless(x, y); }
  inline CAFFE_UTIL_HD bool isless(expr x, half y) { return functions::isless(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool islessequal(half x, half y) { return functions::islessequal(x, y); }
  inline CAFFE_UTIL_HD bool islessequal(half x, expr y) { return functions::islessequal(x, y); }
  inline CAFFE_UTIL_HD bool islessequal(expr x, half y) { return functions::islessequal(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool islessgreater(half x, half y) { return functions::islessgreater(x, y); }
  inline CAFFE_UTIL_HD bool islessgreater(half x, expr y) { return functions::islessgreater(x, y); }
  inline CAFFE_UTIL_HD bool islessgreater(expr x, half y) { return functions::islessgreater(x, y); }
  inline CAFFE_UTIL_HD 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 CAFFE_UTIL_HD bool isunordered(half x, half y) { return functions::isunordered(x, y); }
  inline CAFFE_UTIL_HD bool isunordered(half x, expr y) { return functions::isunordered(x, y); }
  inline CAFFE_UTIL_HD bool isunordered(expr x, half y) { return functions::isunordered(x, y); }
  inline CAFFE_UTIL_HD 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. Floating point types are
  /// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
  /// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
  /// suppressed. Integer types 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>
  CAFFE_UTIL_HD
  	typename half_caster<T, U>::type
  	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. Floating point types are
  /// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
  /// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
  /// suppressed. Integer types 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>
  CAFFE_UTIL_HD
  	typename half_caster<T, U, R>::type
  	half_cast(U arg)
  {
  	return half_caster<T, U, R>::cast(arg);
  }
  /// \}
  } // namespace detail
  
  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::acos;
  using detail::acosh;
  using detail::asin;
  using detail::asinh;
  using detail::atan;
  using detail::atan2;
  using detail::atanh;
  using detail::cbrt;
  using detail::ceil;
  using detail::cos;
  using detail::cosh;
  using detail::erf;
  using detail::erfc;
  using detail::exp;
  using detail::exp2;
  using detail::expm1;
  using detail::fabs;
  using detail::fdim;
  using detail::floor;
  using detail::fma;
  using detail::fmax;
  using detail::fmin;
  using detail::fmod;
  using detail::hypot;
  using detail::lgamma;
  using detail::log;
  using detail::log10;
  using detail::log1p;
  using detail::log2;
  using detail::lrint;
  using detail::lround;
  using detail::nanh;
  using detail::nearbyint;
  using detail::pow;
  using detail::remainder;
  using detail::remquo;
  using detail::rint;
  using detail::round;
  using detail::sin;
  using detail::sinh;
  using detail::sqrt;
  using detail::tan;
  using detail::tanh;
  using detail::tgamma;
  using detail::trunc;
  #if HALF_ENABLE_CPP11_LONG_LONG
  using detail::llrint;
  using detail::llround;
  #endif
  using detail::copysign;
  using detail::fpclassify;
  using detail::frexp;
  using detail::ilogb;
  using detail::isfinite;
  using detail::isgreater;
  using detail::isgreaterequal;
  using detail::isinf;
  using detail::isless;
  using detail::islessequal;
  using detail::islessgreater;
  using detail::isnan;
  using detail::isnormal;
  using detail::isunordered;
  using detail::ldexp;
  using detail::logb;
  using detail::modf;
  using detail::nextafter;
  using detail::nexttoward;
  using detail::scalbln;
  using detail::scalbn;
  using detail::signbit;
  
  using detail::half_cast;
  } // namespace half_float
  
  /// 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 explicit truncation of the single-to-half conversions, the actual rounding
  	/// mode is indeterminate.
  	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); }
  };
  
  inline bool signbit(const half_float::half &arg) { return half_float::detail::signbit(arg); }
  
  inline half_float::half fabs(half_float::half x)
  {
  	return abs(x);
  }
  
  #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 int>(arg.data_) & -(arg.data_ != 0x8000));
  	}
  };
  #endif
  } // namespace std
  
  #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
  