half.h

// half - IEEE 754-based half-precision floating point library.
//
// Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
// documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
// Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

/*
 * Copyright (c) 2020, NVIDIA CORPORATION. All rights reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

// Version 1.12.0

/// \file
/// Main header file for half precision functionality.

#ifndef HALF_HALF_HPP
#define HALF_HALF_HPP

/// Combined gcc version number.
#define HALF_GNUC_VERSION (__GNUC__ * 100 + __GNUC_MINOR__)

// check C++11 language features
#if defined(__clang__) // clang
#if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
/*#elif defined(__INTEL_COMPILER)								//Intel C++
    #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)		????????
        #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
    #endif
    #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)			????????
        #define HALF_ENABLE_CPP11_CONSTEXPR 1
    #endif
    #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)			????????
        #define HALF_ENABLE_CPP11_NOEXCEPT 1
    #endif
    #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG)			????????
        #define HALF_ENABLE_CPP11_LONG_LONG 1
    #endif*/
#elif defined(__GNUC__) // gcc
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#endif
#elif defined(_MSC_VER) // Visual C++
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#define HALF_POP_WARNINGS 1
#pragma warning(push)
#pragma warning(disable : 4099 4127 4146) // struct vs class, constant in if, negative unsigned
#endif

// check C++11 library features
#include <utility>
#if defined(_LIBCPP_VERSION) // libc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#ifndef HALF_ENABLE_CPP11_CSTDINT
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#ifndef HALF_ENABLE_CPP11_CMATH
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#ifndef HALF_ENABLE_CPP11_HASH
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#elif defined(__GLIBCXX__) // libstdc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifdef __clang__
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#else
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#endif
#elif defined(_CPPLIB_VER) // Dinkumware/Visual C++
#if _CPPLIB_VER >= 520
#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#ifndef HALF_ENABLE_CPP11_CSTDINT
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#ifndef HALF_ENABLE_CPP11_HASH
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#if _CPPLIB_VER >= 610
#ifndef HALF_ENABLE_CPP11_CMATH
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#endif
#endif
#undef HALF_GNUC_VERSION

// support constexpr
#if HALF_ENABLE_CPP11_CONSTEXPR
#define HALF_CONSTEXPR constexpr
#define HALF_CONSTEXPR_CONST constexpr
#else
#define HALF_CONSTEXPR
#define HALF_CONSTEXPR_CONST const
#endif

// support noexcept
#if HALF_ENABLE_CPP11_NOEXCEPT
#define HALF_NOEXCEPT noexcept
#define HALF_NOTHROW noexcept
#else
#define HALF_NOEXCEPT
#define HALF_NOTHROW throw()
#endif

#include <algorithm>
#include <climits>
#include <cmath>
#include <cstring>
#include <iostream>
#include <limits>
#if HALF_ENABLE_CPP11_TYPE_TRAITS
#include <type_traits>
#endif
#if HALF_ENABLE_CPP11_CSTDINT
#include <cstdint>
#endif
#if HALF_ENABLE_CPP11_HASH
#include <functional>
#endif

/// Default rounding mode.
/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and `float`s as
/// well as for the half_cast() if not specifying a rounding mode explicitly. It can be redefined (before including
/// half.hpp) to one of the standard rounding modes using their respective constants or the equivalent values of
/// `std::float_round_style`:
///
/// `std::float_round_style`         | value | rounding
/// ---------------------------------|-------|-------------------------
/// `std::round_indeterminate`       | -1    | fastest (default)
/// `std::round_toward_zero`         | 0     | toward zero
/// `std::round_to_nearest`          | 1     | to nearest
/// `std::round_toward_infinity`     | 2     | toward positive infinity
/// `std::round_toward_neg_infinity` | 3     | toward negative infinity
///
/// By default this is set to `-1` (`std::round_indeterminate`), which uses truncation (round toward zero, but with
/// overflows set to infinity) and is the fastest rounding mode possible. It can even be set to
/// `std::numeric_limits<float>::round_style` to synchronize the rounding mode with that of the underlying
/// single-precision implementation. For TRT-1275, changing it to 1 (to nearest)
#ifndef HALF_ROUND_STYLE
#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;

#if HALF_ENABLE_CPP11_USER_LITERALS
/// Library-defined half-precision literals.
/// Import this namespace to enable half-precision floating point literals:
/// ~~~~{.cpp}
/// using namespace half_float::literal;
/// half_float::half = 4.2_h;
/// ~~~~
namespace literal
{
half operator"" _h(long double);
}
#endif

/// \internal
/// \brief Implementation details.
namespace detail
{
#if HALF_ENABLE_CPP11_TYPE_TRAITS
/// Conditional type.
template <bool B, typename T, typename F>
struct conditional : std::conditional<B, T, F>
{
};

/// Helper for tag dispatching.
template <bool B>
struct bool_type : std::integral_constant<bool, B>
{
};
using std::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

/// Type traits for floating point bits.
template <typename T>
struct bits
{
    typedef unsigned char type;
};
template <typename T>
struct bits<const T> : bits<T>
{
};
template <typename T>
struct bits<volatile T> : bits<T>
{
};
template <typename T>
struct bits<const volatile T> : bits<T>
{
};

#if HALF_ENABLE_CPP11_CSTDINT
/// Unsigned integer of (at least) 16 bits width.
typedef std::uint_least16_t uint16;

/// Unsigned integer of (at least) 32 bits width.
template <>
struct bits<float>
{
    typedef std::uint_least32_t type;
};

/// Unsigned integer of (at least) 64 bits width.
template <>
struct bits<double>
{
    typedef std::uint_least64_t type;
};
#else
/// Unsigned integer of (at least) 16 bits width.
typedef unsigned short uint16;

/// Unsigned integer of (at least) 32 bits width.
template <>
struct bits<float> : conditional<std::numeric_limits<unsigned int>::digits >= 32, unsigned int, unsigned long>
{
};

#if HALF_ENABLE_CPP11_LONG_LONG
/// Unsigned integer of (at least) 64 bits width.
template <>
struct bits<double> : conditional<std::numeric_limits<unsigned long>::digits >= 64, unsigned long, unsigned long long>
{
};
#else
/// Unsigned integer of (at least) 64 bits width.
template <>
struct bits<double>
{
    typedef unsigned long type;
};
#endif
#endif

/// Tag type for binary construction.
struct binary_t
{
};

/// Tag for binary construction.
HALF_CONSTEXPR_CONST binary_t binary = binary_t();

/// Temporary half-precision expression.
/// This class represents a half-precision expression which just stores a single-precision value internally.
struct expr
{
    /// Conversion constructor.
    /// \param f single-precision value to convert
    explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {}

    /// Conversion to single-precision.
    /// \return single precision value representing expression value
    HALF_CONSTEXPR operator float() const HALF_NOEXCEPT
    {
        return value_;
    }

private:
    /// Internal expression value stored in single-precision.
    float value_;
};

/// SFINAE helper for generic half-precision functions.
/// This class template has to be specialized for each valid combination of argument types to provide a corresponding
/// `type` member equivalent to \a T.
/// \tparam T type to return
template <typename T, typename, typename = void, typename = void>
struct enable
{
};
template <typename T>
struct enable<T, half, void, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, void, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, half, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, expr, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, half, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, expr, void>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, half, half>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, half, expr>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, expr, half>
{
    typedef T type;
};
template <typename T>
struct enable<T, half, expr, expr>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, half, half>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, half, expr>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, expr, half>
{
    typedef T type;
};
template <typename T>
struct enable<T, expr, expr, expr>
{
    typedef T type;
};

/// Return type for specialized generic 2-argument half-precision functions.
/// This class template has to be specialized for each valid combination of argument types to provide a corresponding
/// `type` member denoting the appropriate return type.
/// \tparam T first argument type
/// \tparam U first argument type
template <typename T, typename U>
struct result : enable<expr, T, U>
{
};
template <>
struct result<half, half>
{
    typedef half type;
};

/// \name Classification helpers
/// \{

/// Check for infinity.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if infinity
/// \retval false else
template <typename T>
bool builtin_isinf(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
    return std::isinf(arg);
#elif defined(_MSC_VER)
    return !::_finite(static_cast<double>(arg)) && !::_isnan(static_cast<double>(arg));
#else
    return arg == std::numeric_limits<T>::infinity() || arg == -std::numeric_limits<T>::infinity();
#endif
}

/// Check for NaN.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if not a number
/// \retval false else
template <typename T>
bool builtin_isnan(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
    return std::isnan(arg);
#elif defined(_MSC_VER)
    return ::_isnan(static_cast<double>(arg)) != 0;
#else
    return arg != arg;
#endif
}

/// Check sign.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if signbit set
/// \retval false else
template <typename T>
bool builtin_signbit(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
    return std::signbit(arg);
#else
    return arg < T() || (arg == T() && T(1) / arg < T());
#endif
}

/// \}
/// \name Conversion
/// \{

/// Convert IEEE single-precision to half-precision.
/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \param value single-precision value
/// \return binary representation of half-precision value
template <std::float_round_style R>
uint16 float2half_impl(float value, true_type)
{
    typedef bits<float>::type uint32;
    uint32 bits; // = *reinterpret_cast<uint32*>(&value);		//violating strict aliasing!
    std::memcpy(&bits, &value, sizeof(float));
    /*			uint16 hbits = (bits>>16) & 0x8000;
                bits &= 0x7FFFFFFF;
                int exp = bits >> 23;
                if(exp == 255)
                    return hbits | 0x7C00 | (0x3FF&-static_cast<unsigned>((bits&0x7FFFFF)!=0));
                if(exp > 142)
                {
                    if(R == std::round_toward_infinity)
                        return hbits | 0x7C00 - (hbits>>15);
                    if(R == std::round_toward_neg_infinity)
                        return hbits | 0x7BFF + (hbits>>15);
                    return hbits | 0x7BFF + (R!=std::round_toward_zero);
                }
                int g, s;
                if(exp > 112)
                {
                    g = (bits>>12) & 1;
                    s = (bits&0xFFF) != 0;
                    hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF);
                }
                else if(exp > 101)
                {
                    int i = 125 - exp;
                    bits = (bits&0x7FFFFF) | 0x800000;
                    g = (bits>>i) & 1;
                    s = (bits&((1L<<i)-1)) != 0;
                    hbits |= bits >> (i+1);
                }
                else
                {
                    g = 0;
                    s = bits != 0;
                }
                if(R == std::round_to_nearest)
                    #if HALF_ROUND_TIES_TO_EVEN
                        hbits += g & (s|hbits);
                    #else
                        hbits += g;
                    #endif
                else if(R == std::round_toward_infinity)
                    hbits += ~(hbits>>15) & (s|g);
                else if(R == std::round_toward_neg_infinity)
                    hbits += (hbits>>15) & (g|s);
    */
    static const uint16 base_table[512] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
        0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008,
        0x0010, 0x0020, 0x0040, 0x0080, 0x0100, 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000,
        0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800,
        0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
        0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
        0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000,
        0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 0xC000, 0xC400, 0xC800,
        0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
        0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00};
    static const unsigned char shift_table[512] = {24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
        13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
        13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
        24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13};
    uint16 hbits = base_table[bits >> 23] + static_cast<uint16>((bits & 0x7FFFFF) >> shift_table[bits >> 23]);
    if (R == std::round_to_nearest)
        hbits += (((bits & 0x7FFFFF) >> (shift_table[bits >> 23] - 1)) | (((bits >> 23) & 0xFF) == 102))
            & ((hbits & 0x7C00) != 0x7C00)
#if HALF_ROUND_TIES_TO_EVEN
            & (((((static_cast<uint32>(1) << (shift_table[bits >> 23] - 1)) - 1) & bits) != 0) | hbits)
#endif
            ;
    else if (R == std::round_toward_zero)
        hbits -= ((hbits & 0x7FFF) == 0x7C00) & ~shift_table[bits >> 23];
    else if (R == std::round_toward_infinity)
        hbits += ((((bits & 0x7FFFFF & ((static_cast<uint32>(1) << (shift_table[bits >> 23])) - 1)) != 0)
                      | (((bits >> 23) <= 102) & ((bits >> 23) != 0)))
                     & (hbits < 0x7C00))
            - ((hbits == 0xFC00) & ((bits >> 23) != 511));
    else if (R == std::round_toward_neg_infinity)
        hbits += ((((bits & 0x7FFFFF & ((static_cast<uint32>(1) << (shift_table[bits >> 23])) - 1)) != 0)
                      | (((bits >> 23) <= 358) & ((bits >> 23) != 256)))
                     & (hbits < 0xFC00) & (hbits >> 15))
            - ((hbits == 0x7C00) & ((bits >> 23) != 255));
    return hbits;
}

/// Convert IEEE double-precision to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \param value double-precision value
/// \return binary representation of half-precision value
template <std::float_round_style R>
uint16 float2half_impl(double value, true_type)
{
    typedef bits<float>::type uint32;
    typedef bits<double>::type uint64;
    uint64 bits; // = *reinterpret_cast<uint64*>(&value);		//violating strict aliasing!
    std::memcpy(&bits, &value, sizeof(double));
    uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF;
    uint16 hbits = (hi >> 16) & 0x8000;
    hi &= 0x7FFFFFFF;
    int exp = hi >> 20;
    if (exp == 2047)
        return hbits | 0x7C00 | (0x3FF & -static_cast<unsigned>((bits & 0xFFFFFFFFFFFFF) != 0));
    if (exp > 1038)
    {
        if (R == std::round_toward_infinity)
            return hbits | 0x7C00 - (hbits >> 15);
        if (R == std::round_toward_neg_infinity)
            return hbits | 0x7BFF + (hbits >> 15);
        return hbits | 0x7BFF + (R != std::round_toward_zero);
    }
    int g, s = lo != 0;
    if (exp > 1008)
    {
        g = (hi >> 9) & 1;
        s |= (hi & 0x1FF) != 0;
        hbits |= ((exp - 1008) << 10) | ((hi >> 10) & 0x3FF);
    }
    else if (exp > 997)
    {
        int i = 1018 - exp;
        hi = (hi & 0xFFFFF) | 0x100000;
        g = (hi >> i) & 1;
        s |= (hi & ((1L << i) - 1)) != 0;
        hbits |= hi >> (i + 1);
    }
    else
    {
        g = 0;
        s |= hi != 0;
    }
    if (R == std::round_to_nearest)
#if HALF_ROUND_TIES_TO_EVEN
        hbits += g & (s | hbits);
#else
        hbits += g;
#endif
    else if (R == std::round_toward_infinity)
        hbits += ~(hbits >> 15) & (s | g);
    else if (R == std::round_toward_neg_infinity)
        hbits += (hbits >> 15) & (g | s);
    return hbits;
}

/// Convert non-IEEE floating point to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T source type (builtin floating point type)
/// \param value floating point value
/// \return binary representation of half-precision value
template <std::float_round_style R, typename T>
uint16 float2half_impl(T value, ...)
{
    uint16 hbits = static_cast<unsigned>(builtin_signbit(value)) << 15;
    if (value == T())
        return hbits;
    if (builtin_isnan(value))
        return hbits | 0x7FFF;
    if (builtin_isinf(value))
        return hbits | 0x7C00;
    int exp;
    std::frexp(value, &exp);
    if (exp > 16)
    {
        if (R == std::round_toward_infinity)
            return hbits | (0x7C00 - (hbits >> 15));
        else if (R == std::round_toward_neg_infinity)
            return hbits | (0x7BFF + (hbits >> 15));
        return hbits | (0x7BFF + (R != std::round_toward_zero));
    }
    if (exp < -13)
        value = std::ldexp(value, 24);
    else
    {
        value = std::ldexp(value, 11 - exp);
        hbits |= ((exp + 13) << 10);
    }
    T ival, frac = std::modf(value, &ival);
    hbits += static_cast<uint16>(std::abs(static_cast<int>(ival)));
    if (R == std::round_to_nearest)
    {
        frac = std::abs(frac);
#if HALF_ROUND_TIES_TO_EVEN
        hbits += (frac > T(0.5)) | ((frac == T(0.5)) & hbits);
#else
        hbits += frac >= T(0.5);
#endif
    }
    else if (R == std::round_toward_infinity)
        hbits += frac > T();
    else if (R == std::round_toward_neg_infinity)
        hbits += frac < T();
    return hbits;
}

/// Convert floating point to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T source type (builtin floating point type)
/// \param value floating point value
/// \return binary representation of half-precision value
template <std::float_round_style R, typename T>
uint16 float2half(T value)
{
    return float2half_impl<R>(
        value, bool_type < std::numeric_limits<T>::is_iec559 && sizeof(typename bits<T>::type) == sizeof(T) > ());
}

/// Convert integer to half-precision floating point.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam S `true` if value negative, `false` else
/// \tparam T type to convert (builtin integer type)
/// \param value non-negative integral value
/// \return binary representation of half-precision value
template <std::float_round_style R, bool S, typename T>
uint16 int2half_impl(T value)
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
    static_assert(std::is_integral<T>::value, "int to half conversion only supports builtin integer types");
#endif
    if (S)
        value = -value;
    uint16 bits = S << 15;
    if (value > 0xFFFF)
    {
        if (R == std::round_toward_infinity)
            bits |= 0x7C00 - S;
        else if (R == std::round_toward_neg_infinity)
            bits |= 0x7BFF + S;
        else
            bits |= 0x7BFF + (R != std::round_toward_zero);
    }
    else if (value)
    {
        unsigned int m = value, exp = 24;
        for (; m < 0x400; m <<= 1, --exp)
            ;
        for (; m > 0x7FF; m >>= 1, ++exp)
            ;
        bits |= (exp << 10) + m;
        if (exp > 24)
        {
            if (R == std::round_to_nearest)
                bits += (value >> (exp - 25)) & 1
#if HALF_ROUND_TIES_TO_EVEN
                    & (((((1 << (exp - 25)) - 1) & value) != 0) | bits)
#endif
                    ;
            else if (R == std::round_toward_infinity)
                bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & !S;
            else if (R == std::round_toward_neg_infinity)
                bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & S;
        }
    }
    return bits;
}

/// Convert integer to half-precision floating point.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T type to convert (builtin integer type)
/// \param value integral value
/// \return binary representation of half-precision value
template <std::float_round_style R, typename T>
uint16 int2half(T value)
{
    return (value < 0) ? int2half_impl<R, true>(value) : int2half_impl<R, false>(value);
}

/// Convert half-precision to IEEE single-precision.
/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
/// \param value binary representation of half-precision value
/// \return single-precision value
inline float half2float_impl(uint16 value, float, true_type)
{
    typedef bits<float>::type uint32;
    /*			uint32 bits = static_cast<uint32>(value&0x8000) << 16;
                int abs = value & 0x7FFF;
                if(abs)
                {
                    bits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);
                    for(; abs<0x400; abs<<=1,bits-=0x800000) ;
                    bits += static_cast<uint32>(abs) << 13;
                }
    */
    static const uint32 mantissa_table[2048] = {0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000,
        0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000,
        0x35700000, 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000,
        0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, 0x36000000,
        0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000,
        0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 0x36400000, 0x36440000, 0x36480000,
        0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000,
        0x36700000, 0x36740000, 0x36780000, 0x367C0000, 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000,
        0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000,
        0x369C0000, 0x369E0000, 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000,
        0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
        0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000,
        0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, 0x36E00000, 0x36E20000,
        0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000,
        0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, 0x37000000, 0x37010000, 0x37020000, 0x37030000,
        0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000,
        0x370D0000, 0x370E0000, 0x370F0000, 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000,
        0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000,
        0x371F0000, 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000,
        0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, 0x37300000,
        0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000,
        0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, 0x37400000, 0x37410000, 0x37420000,
        0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000,
        0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000,
        0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000,
        0x375E0000, 0x375F0000, 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000,
        0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
        0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000,
        0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 0x37800000, 0x37808000,
        0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000,
        0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 0x37880000, 0x37888000, 0x37890000, 0x37898000,
        0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000,
        0x378E8000, 0x378F0000, 0x378F8000, 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000,
        0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000,
        0x37978000, 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000,
        0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, 0x37A00000,
        0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000,
        0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, 0x37A80000, 0x37A88000, 0x37A90000,
        0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000,
        0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000,
        0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000,
        0x37B70000, 0x37B78000, 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000,
        0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
        0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000,
        0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, 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];
    //			return *reinterpret_cast<float*>(&bits);			//violating strict aliasing!
    float out;
    std::memcpy(&out, &bits, sizeof(float));
    return out;
}

/// Convert half-precision to IEEE double-precision.
/// \param value binary representation of half-precision value
/// \return double-precision value
inline double half2float_impl(uint16 value, double, true_type)
{
    typedef bits<float>::type uint32;
    typedef bits<double>::type uint64;
    uint32 hi = static_cast<uint32>(value & 0x8000) << 16;
    int abs = value & 0x7FFF;
    if (abs)
    {
        hi |= 0x3F000000 << static_cast<unsigned>(abs >= 0x7C00);
        for (; abs < 0x400; abs <<= 1, hi -= 0x100000)
            ;
        hi += static_cast<uint32>(abs) << 10;
    }
    uint64 bits = static_cast<uint64>(hi) << 32;
    //			return *reinterpret_cast<double*>(&bits);			//violating strict aliasing!
    double out;
    std::memcpy(&out, &bits, sizeof(double));
    return out;
}

/// Convert half-precision to non-IEEE floating point.
/// \tparam T type to convert to (builtin integer type)
/// \param value binary representation of half-precision value
/// \return floating point value
template <typename T>
T half2float_impl(uint16 value, T, ...)
{
    T out;
    int abs = value & 0x7FFF;
    if (abs > 0x7C00)
        out = std::numeric_limits<T>::has_quiet_NaN ? std::numeric_limits<T>::quiet_NaN() : T();
    else if (abs == 0x7C00)
        out = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : std::numeric_limits<T>::max();
    else if (abs > 0x3FF)
        out = std::ldexp(static_cast<T>((abs & 0x3FF) | 0x400), (abs >> 10) - 25);
    else
        out = std::ldexp(static_cast<T>(abs), -24);
    return (value & 0x8000) ? -out : out;
}

/// Convert half-precision to floating point.
/// \tparam T type to convert to (builtin integer type)
/// \param value binary representation of half-precision value
/// \return floating point value
template <typename T>
T half2float(uint16 value)
{
    return half2float_impl(
        value, T(), bool_type < std::numeric_limits<T>::is_iec559 && sizeof(typename bits<T>::type) == sizeof(T) > ());
}

/// Convert half-precision floating point to integer.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam E `true` for round to even, `false` for round away from zero
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign
/// bits) \param value binary representation of half-precision value \return integral value
template <std::float_round_style R, bool E, typename T>
T half2int_impl(uint16 value)
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
    static_assert(std::is_integral<T>::value, "half to int conversion only supports builtin integer types");
#endif
    unsigned int e = value & 0x7FFF;
    if (e >= 0x7C00)
        return (value & 0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
    if (e < 0x3800)
    {
        if (R == std::round_toward_infinity)
            return T(~(value >> 15) & (e != 0));
        else if (R == std::round_toward_neg_infinity)
            return -T(value > 0x8000);
        return T();
    }
    unsigned int m = (value & 0x3FF) | 0x400;
    e >>= 10;
    if (e < 25)
    {
        if (R == std::round_to_nearest)
            m += (1 << (24 - e)) - (~(m >> (25 - e)) & E);
        else if (R == std::round_toward_infinity)
            m += ((value >> 15) - 1) & ((1 << (25 - e)) - 1U);
        else if (R == std::round_toward_neg_infinity)
            m += -(value >> 15) & ((1 << (25 - e)) - 1U);
        m >>= 25 - e;
    }
    else
        m <<= e - 25;
    return (value & 0x8000) ? -static_cast<T>(m) : static_cast<T>(m);
}

/// Convert half-precision floating point to integer.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign
/// bits) \param value binary representation of half-precision value \return integral value
template <std::float_round_style R, typename T>
T half2int(uint16 value)
{
    return half2int_impl<R, HALF_ROUND_TIES_TO_EVEN, T>(value);
}

/// Convert half-precision floating point to integer using round-to-nearest-away-from-zero.
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign
/// bits) \param value binary representation of half-precision value \return integral value
template <typename T>
T half2int_up(uint16 value)
{
    return half2int_impl<std::round_to_nearest, 0, T>(value);
}

/// Round half-precision number to nearest integer value.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam E `true` for round to even, `false` for round away from zero
/// \param value binary representation of half-precision value
/// \return half-precision bits for nearest integral value
template <std::float_round_style R, bool E>
uint16 round_half_impl(uint16 value)
{
    unsigned int e = value & 0x7FFF;
    uint16 result = value;
    if (e < 0x3C00)
    {
        result &= 0x8000;
        if (R == std::round_to_nearest)
            result |= 0x3C00U & -(e >= (0x3800 + E));
        else if (R == std::round_toward_infinity)
            result |= 0x3C00U & -(~(value >> 15) & (e != 0));
        else if (R == std::round_toward_neg_infinity)
            result |= 0x3C00U & -(value > 0x8000);
    }
    else if (e < 0x6400)
    {
        e = 25 - (e >> 10);
        unsigned int mask = (1 << e) - 1;
        if (R == std::round_to_nearest)
            result += (1 << (e - 1)) - (~(result >> e) & E);
        else if (R == std::round_toward_infinity)
            result += mask & ((value >> 15) - 1);
        else if (R == std::round_toward_neg_infinity)
            result += mask & -(value >> 15);
        result &= ~mask;
    }
    return result;
}

/// Round half-precision number to nearest integer value.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \param value binary representation of half-precision value
/// \return half-precision bits for nearest integral value
template <std::float_round_style R>
uint16 round_half(uint16 value)
{
    return round_half_impl<R, HALF_ROUND_TIES_TO_EVEN>(value);
}

/// Round half-precision number to nearest integer value using round-to-nearest-away-from-zero.
/// \param value binary representation of half-precision value
/// \return half-precision bits for nearest integral value
inline uint16 round_half_up(uint16 value)
{
    return round_half_impl<std::round_to_nearest, 0>(value);
}
/// \}

struct functions;
template <typename>
struct unary_specialized;
template <typename, typename>
struct binary_specialized;
template <typename, typename, std::float_round_style>
struct half_caster;
} // 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 the library's default rounding mode, but temporary results inside chained arithmetic
/// expressions are kept in single-precision as long as possible (while of course still maintaining a strong
/// half-precision type).
///
/// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and
/// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which
/// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the
/// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be
/// of exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will
/// most probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying
/// 16-bit IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16
/// bits if your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the
/// case on nearly any reasonable platform.
///
/// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable
/// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.
class half
{
    friend struct detail::functions;
    friend struct detail::unary_specialized<half>;
    friend struct detail::binary_specialized<half, half>;
    template <typename, typename, std::float_round_style>
    friend struct detail::half_caster;
    friend class std::numeric_limits<half>;
#if HALF_ENABLE_CPP11_HASH
    friend struct std::hash<half>;
#endif
#if HALF_ENABLE_CPP11_USER_LITERALS
    friend half literal::operator"" _h(long double);
#endif

public:
    /// Default constructor.
    /// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics
    /// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.
    HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}

    /// Copy constructor.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to copy from
    half(detail::expr rhs)
        : data_(detail::float2half<round_style>(static_cast<float>(rhs)))
    {
    }

    /// Conversion constructor.
    /// \param rhs float to convert
    explicit half(float rhs)
        : data_(detail::float2half<round_style>(rhs))
    {
    }

    /// Conversion to single-precision.
    /// \return single precision value representing expression value
    operator float() const
    {
        return detail::half2float<float>(data_);
    }

    /// Assignment operator.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to copy from
    /// \return reference to this half
    half& operator=(detail::expr rhs)
    {
        return *this = static_cast<float>(rhs);
    }

    /// Arithmetic assignment.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to add
    /// \return reference to this half
    template <typename T>
    typename detail::enable<half&, T>::type operator+=(T rhs)
    {
        return *this += static_cast<float>(rhs);
    }

    /// Arithmetic assignment.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to subtract
    /// \return reference to this half
    template <typename T>
    typename detail::enable<half&, T>::type operator-=(T rhs)
    {
        return *this -= static_cast<float>(rhs);
    }

    /// Arithmetic assignment.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to multiply with
    /// \return reference to this half
    template <typename T>
    typename detail::enable<half&, T>::type operator*=(T rhs)
    {
        return *this *= static_cast<float>(rhs);
    }

    /// Arithmetic assignment.
    /// \tparam T type of concrete half expression
    /// \param rhs half expression to divide by
    /// \return reference to this half
    template <typename T>
    typename detail::enable<half&, T>::type operator/=(T rhs)
    {
        return *this /= static_cast<float>(rhs);
    }

    /// Assignment operator.
    /// \param rhs single-precision value to copy from
    /// \return reference to this half
    half& operator=(float rhs)
    {
        data_ = detail::float2half<round_style>(rhs);
        return *this;
    }

    /// Arithmetic assignment.
    /// \param rhs single-precision value to add
    /// \return reference to this half
    half& operator+=(float rhs)
    {
        data_ = detail::float2half<round_style>(detail::half2float<float>(data_) + rhs);
        return *this;
    }

    /// Arithmetic assignment.
    /// \param rhs single-precision value to subtract
    /// \return reference to this half
    half& operator-=(float rhs)
    {
        data_ = detail::float2half<round_style>(detail::half2float<float>(data_) - rhs);
        return *this;
    }

    /// Arithmetic assignment.
    /// \param rhs single-precision value to multiply with
    /// \return reference to this half
    half& operator*=(float rhs)
    {
        data_ = detail::float2half<round_style>(detail::half2float<float>(data_) * rhs);
        return *this;
    }

    /// Arithmetic assignment.
    /// \param rhs single-precision value to divide by
    /// \return reference to this half
    half& operator/=(float rhs)
    {
        data_ = detail::float2half<round_style>(detail::half2float<float>(data_) / rhs);
        return *this;
    }

    /// Prefix increment.
    /// \return incremented half value
    half& operator++()
    {
        return *this += 1.0f;
    }

    /// Prefix decrement.
    /// \return decremented half value
    half& operator--()
    {
        return *this -= 1.0f;
    }

    /// Postfix increment.
    /// \return non-incremented half value
    half operator++(int)
    {
        half out(*this);
        ++*this;
        return out;
    }

    /// Postfix decrement.
    /// \return non-decremented half value
    half operator--(int)
    {
        half out(*this);
        --*this;
        return out;
    }

private:
    /// Rounding mode to use
    static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);

    /// Constructor.
    /// \param bits binary representation to set half to
    HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) HALF_NOEXCEPT : data_(bits) {}

    /// Internal binary representation
    detail::uint16 data_;
};

#if HALF_ENABLE_CPP11_USER_LITERALS
namespace literal
{
/// Half literal.
/// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due
/// to rather involved conversions.
/// \param value literal value
/// \return half with given value (if representable)
inline half operator"" _h(long double value)
{
    return half(detail::binary, detail::float2half<half::round_style>(value));
}
} // 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 expr plus(float x, float y)
    {
        return expr(x + y);
    }

    /// Subtraction implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Half-precision difference stored in single-precision
    static expr minus(float x, float y)
    {
        return expr(x - y);
    }

    /// Multiplication implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Half-precision product stored in single-precision
    static expr multiplies(float x, float y)
    {
        return expr(x * y);
    }

    /// Division implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Half-precision quotient stored in single-precision
    static expr divides(float x, float y)
    {
        return expr(x / y);
    }

    /// Output implementation.
    /// \param out stream to write to
    /// \param arg value to write
    /// \return reference to stream
    template <typename charT, typename traits>
    static std::basic_ostream<charT, traits>& write(std::basic_ostream<charT, traits>& out, float arg)
    {
        return out << arg;
    }

    /// Input implementation.
    /// \param in stream to read from
    /// \param arg half to read into
    /// \return reference to stream
    template <typename charT, typename traits>
    static std::basic_istream<charT, traits>& read(std::basic_istream<charT, traits>& in, half& arg)
    {
        float f;
        if (in >> f)
            arg = f;
        return in;
    }

    /// Modulo implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Half-precision division remainder stored in single-precision
    static expr fmod(float x, float y)
    {
        return expr(std::fmod(x, y));
    }

    /// Remainder implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Half-precision division remainder stored in single-precision
    static expr remainder(float x, float y)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::remainder(x, y));
#else
        if (builtin_isnan(x) || builtin_isnan(y))
            return expr(std::numeric_limits<float>::quiet_NaN());
        float ax = std::fabs(x), ay = std::fabs(y);
        if (ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
            return expr(std::numeric_limits<float>::quiet_NaN());
        if (ay >= 65536.0f)
            return expr(x);
        if (ax == ay)
            return expr(builtin_signbit(x) ? -0.0f : 0.0f);
        ax = std::fmod(ax, ay + ay);
        float y2 = 0.5f * ay;
        if (ax > y2)
        {
            ax -= ay;
            if (ax >= y2)
                ax -= ay;
        }
        return expr(builtin_signbit(x) ? -ax : ax);
#endif
    }

    /// Remainder implementation.
    /// \param x first operand
    /// \param y second operand
    /// \param quo address to store quotient bits at
    /// \return Half-precision division remainder stored in single-precision
    static expr remquo(float x, float y, int* quo)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::remquo(x, y, quo));
#else
        if (builtin_isnan(x) || builtin_isnan(y))
            return expr(std::numeric_limits<float>::quiet_NaN());
        bool sign = builtin_signbit(x), qsign = static_cast<bool>(sign ^ builtin_signbit(y));
        float ax = std::fabs(x), ay = std::fabs(y);
        if (ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
            return expr(std::numeric_limits<float>::quiet_NaN());
        if (ay >= 65536.0f)
            return expr(x);
        if (ax == ay)
            return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f);
        ax = std::fmod(ax, 8.0f * ay);
        int cquo = 0;
        if (ax >= 4.0f * ay)
        {
            ax -= 4.0f * ay;
            cquo += 4;
        }
        if (ax >= 2.0f * ay)
        {
            ax -= 2.0f * ay;
            cquo += 2;
        }
        float y2 = 0.5f * ay;
        if (ax > y2)
        {
            ax -= ay;
            ++cquo;
            if (ax >= y2)
            {
                ax -= ay;
                ++cquo;
            }
        }
        return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax);
#endif
    }

    /// Positive difference implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return Positive difference stored in single-precision
    static expr fdim(float x, float y)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::fdim(x, y));
#else
        return expr((x <= y) ? 0.0f : (x - y));
#endif
    }

    /// Fused multiply-add implementation.
    /// \param x first operand
    /// \param y second operand
    /// \param z third operand
    /// \return \a x * \a y + \a z stored in single-precision
    static expr fma(float x, float y, float z)
    {
#if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF)
        return expr(std::fma(x, y, z));
#else
        return expr(x * y + z);
#endif
    }

    /// Get NaN.
    /// \return Half-precision quiet NaN
    static half nanh()
    {
        return half(binary, 0x7FFF);
    }

    /// Exponential implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr exp(float arg)
    {
        return expr(std::exp(arg));
    }

    /// Exponential implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr expm1(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::expm1(arg));
#else
        return expr(static_cast<float>(std::exp(static_cast<double>(arg)) - 1.0));
#endif
    }

    /// Binary exponential implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr exp2(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::exp2(arg));
#else
        return expr(static_cast<float>(std::exp(arg * 0.69314718055994530941723212145818)));
#endif
    }

    /// Logarithm implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr log(float arg)
    {
        return expr(std::log(arg));
    }

    /// Common logarithm implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr log10(float arg)
    {
        return expr(std::log10(arg));
    }

    /// Logarithm implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr log1p(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::log1p(arg));
#else
        return expr(static_cast<float>(std::log(1.0 + arg)));
#endif
    }

    /// Binary logarithm implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr log2(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::log2(arg));
#else
        return expr(static_cast<float>(std::log(static_cast<double>(arg)) * 1.4426950408889634073599246810019));
#endif
    }

    /// Square root implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr sqrt(float arg)
    {
        return expr(std::sqrt(arg));
    }

    /// Cubic root implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr cbrt(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::cbrt(arg));
#else
        if (builtin_isnan(arg) || builtin_isinf(arg))
            return expr(arg);
        return expr(builtin_signbit(arg) ? -static_cast<float>(std::pow(-static_cast<double>(arg), 1.0 / 3.0))
                                         : static_cast<float>(std::pow(static_cast<double>(arg), 1.0 / 3.0)));
#endif
    }

    /// Hypotenuse implementation.
    /// \param x first argument
    /// \param y second argument
    /// \return function value stored in single-preicision
    static expr hypot(float x, float y)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::hypot(x, y));
#else
        return expr((builtin_isinf(x) || builtin_isinf(y))
                ? std::numeric_limits<float>::infinity()
                : static_cast<float>(std::sqrt(static_cast<double>(x) * x + static_cast<double>(y) * y)));
#endif
    }

    /// Power implementation.
    /// \param base value to exponentiate
    /// \param exp power to expontiate to
    /// \return function value stored in single-preicision
    static expr pow(float base, float exp)
    {
        return expr(std::pow(base, exp));
    }

    /// Sine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr sin(float arg)
    {
        return expr(std::sin(arg));
    }

    /// Cosine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr cos(float arg)
    {
        return expr(std::cos(arg));
    }

    /// Tan implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr tan(float arg)
    {
        return expr(std::tan(arg));
    }

    /// Arc sine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr asin(float arg)
    {
        return expr(std::asin(arg));
    }

    /// Arc cosine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr acos(float arg)
    {
        return expr(std::acos(arg));
    }

    /// Arc tangent implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr atan(float arg)
    {
        return expr(std::atan(arg));
    }

    /// Arc tangent implementation.
    /// \param x first argument
    /// \param y second argument
    /// \return function value stored in single-preicision
    static expr atan2(float x, float y)
    {
        return expr(std::atan2(x, y));
    }

    /// Hyperbolic sine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr sinh(float arg)
    {
        return expr(std::sinh(arg));
    }

    /// Hyperbolic cosine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr cosh(float arg)
    {
        return expr(std::cosh(arg));
    }

    /// Hyperbolic tangent implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr tanh(float arg)
    {
        return expr(std::tanh(arg));
    }

    /// Hyperbolic area sine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr asinh(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::asinh(arg));
#else
        return expr((arg == -std::numeric_limits<float>::infinity())
                ? arg
                : static_cast<float>(std::log(arg + std::sqrt(arg * arg + 1.0))));
#endif
    }

    /// Hyperbolic area cosine implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr acosh(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::acosh(arg));
#else
        return expr((arg < -1.0f) ? std::numeric_limits<float>::quiet_NaN()
                                  : static_cast<float>(std::log(arg + std::sqrt(arg * arg - 1.0))));
#endif
    }

    /// Hyperbolic area tangent implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr atanh(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::atanh(arg));
#else
        return expr(static_cast<float>(0.5 * std::log((1.0 + arg) / (1.0 - arg))));
#endif
    }

    /// Error function implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr erf(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::erf(arg));
#else
        return expr(static_cast<float>(erf(static_cast<double>(arg))));
#endif
    }

    /// Complementary implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr erfc(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::erfc(arg));
#else
        return expr(static_cast<float>(1.0 - erf(static_cast<double>(arg))));
#endif
    }

    /// Gamma logarithm implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr lgamma(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::lgamma(arg));
#else
        if (builtin_isinf(arg))
            return expr(std::numeric_limits<float>::infinity());
        if (arg < 0.0f)
        {
            float i, f = std::modf(-arg, &i);
            if (f == 0.0f)
                return expr(std::numeric_limits<float>::infinity());
            return expr(static_cast<float>(1.1447298858494001741434273513531
                - std::log(std::abs(std::sin(3.1415926535897932384626433832795 * f))) - lgamma(1.0 - arg)));
        }
        return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
#endif
    }

    /// Gamma implementation.
    /// \param arg function argument
    /// \return function value stored in single-preicision
    static expr tgamma(float arg)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::tgamma(arg));
#else
        if (arg == 0.0f)
            return builtin_signbit(arg) ? expr(-std::numeric_limits<float>::infinity())
                                        : expr(std::numeric_limits<float>::infinity());
        if (arg < 0.0f)
        {
            float i, f = std::modf(-arg, &i);
            if (f == 0.0f)
                return expr(std::numeric_limits<float>::quiet_NaN());
            double value = 3.1415926535897932384626433832795
                / (std::sin(3.1415926535897932384626433832795 * f) * std::exp(lgamma(1.0 - arg)));
            return expr(static_cast<float>((std::fmod(i, 2.0f) == 0.0f) ? -value : value));
        }
        if (builtin_isinf(arg))
            return expr(arg);
        return expr(static_cast<float>(std::exp(lgamma(static_cast<double>(arg)))));
#endif
    }

    /// Floor implementation.
    /// \param arg value to round
    /// \return rounded value
    static half floor(half arg)
    {
        return half(binary, round_half<std::round_toward_neg_infinity>(arg.data_));
    }

    /// Ceiling implementation.
    /// \param arg value to round
    /// \return rounded value
    static half ceil(half arg)
    {
        return half(binary, round_half<std::round_toward_infinity>(arg.data_));
    }

    /// Truncation implementation.
    /// \param arg value to round
    /// \return rounded value
    static half trunc(half arg)
    {
        return half(binary, round_half<std::round_toward_zero>(arg.data_));
    }

    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static half round(half arg)
    {
        return half(binary, round_half_up(arg.data_));
    }

    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static long lround(half arg)
    {
        return detail::half2int_up<long>(arg.data_);
    }

    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static half rint(half arg)
    {
        return half(binary, round_half<half::round_style>(arg.data_));
    }

    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static long lrint(half arg)
    {
        return detail::half2int<half::round_style, long>(arg.data_);
    }

#if HALF_ENABLE_CPP11_LONG_LONG
    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static long long llround(half arg)
    {
        return detail::half2int_up<long long>(arg.data_);
    }

    /// Nearest integer implementation.
    /// \param arg value to round
    /// \return rounded value
    static long long llrint(half arg)
    {
        return detail::half2int<half::round_style, long long>(arg.data_);
    }
#endif

    /// Decompression implementation.
    /// \param arg number to decompress
    /// \param exp address to store exponent at
    /// \return normalized significant
    static half frexp(half arg, int* exp)
    {
        int m = arg.data_ & 0x7FFF, e = -14;
        if (m >= 0x7C00 || !m)
            return *exp = 0, arg;
        for (; m < 0x400; m <<= 1, --e)
            ;
        return *exp = e + (m >> 10), half(binary, (arg.data_ & 0x8000) | 0x3800 | (m & 0x3FF));
    }

    /// Decompression implementation.
    /// \param arg number to decompress
    /// \param iptr address to store integer part at
    /// \return fractional part
    static half modf(half arg, half* iptr)
    {
        unsigned int e = arg.data_ & 0x7FFF;
        if (e >= 0x6400)
            return *iptr = arg, half(binary, arg.data_ & (0x8000U | -(e > 0x7C00)));
        if (e < 0x3C00)
            return iptr->data_ = arg.data_ & 0x8000, arg;
        e >>= 10;
        unsigned int mask = (1 << (25 - e)) - 1, m = arg.data_ & mask;
        iptr->data_ = arg.data_ & ~mask;
        if (!m)
            return half(binary, arg.data_ & 0x8000);
        for (; m < 0x400; m <<= 1, --e)
            ;
        return half(binary, static_cast<uint16>((arg.data_ & 0x8000) | (e << 10) | (m & 0x3FF)));
    }

    /// Scaling implementation.
    /// \param arg number to scale
    /// \param exp power of two to scale by
    /// \return scaled number
    static half scalbln(half arg, long exp)
    {
        unsigned int m = arg.data_ & 0x7FFF;
        if (m >= 0x7C00 || !m)
            return arg;
        for (; m < 0x400; m <<= 1, --exp)
            ;
        exp += m >> 10;
        uint16 value = arg.data_ & 0x8000;
        if (exp > 30)
        {
            if (half::round_style == std::round_toward_zero)
                value |= 0x7BFF;
            else if (half::round_style == std::round_toward_infinity)
                value |= 0x7C00 - (value >> 15);
            else if (half::round_style == std::round_toward_neg_infinity)
                value |= 0x7BFF + (value >> 15);
            else
                value |= 0x7C00;
        }
        else if (exp > 0)
            value |= (exp << 10) | (m & 0x3FF);
        else if (exp > -11)
        {
            m = (m & 0x3FF) | 0x400;
            if (half::round_style == std::round_to_nearest)
            {
                m += 1 << -exp;
#if HALF_ROUND_TIES_TO_EVEN
                m -= (m >> (1 - exp)) & 1;
#endif
            }
            else if (half::round_style == std::round_toward_infinity)
                m += ((value >> 15) - 1) & ((1 << (1 - exp)) - 1U);
            else if (half::round_style == std::round_toward_neg_infinity)
                m += -(value >> 15) & ((1 << (1 - exp)) - 1U);
            value |= m >> (1 - exp);
        }
        else if (half::round_style == std::round_toward_infinity)
            value -= (value >> 15) - 1;
        else if (half::round_style == std::round_toward_neg_infinity)
            value += value >> 15;
        return half(binary, value);
    }

    /// Exponent implementation.
    /// \param arg number to query
    /// \return floating point exponent
    static int ilogb(half arg)
    {
        int abs = arg.data_ & 0x7FFF;
        if (!abs)
            return FP_ILOGB0;
        if (abs < 0x7C00)
        {
            int exp = (abs >> 10) - 15;
            if (abs < 0x400)
                for (; abs < 0x200; abs <<= 1, --exp)
                    ;
            return exp;
        }
        if (abs > 0x7C00)
            return FP_ILOGBNAN;
        return INT_MAX;
    }

    /// Exponent implementation.
    /// \param arg number to query
    /// \return floating point exponent
    static half logb(half arg)
    {
        int abs = arg.data_ & 0x7FFF;
        if (!abs)
            return half(binary, 0xFC00);
        if (abs < 0x7C00)
        {
            int exp = (abs >> 10) - 15;
            if (abs < 0x400)
                for (; abs < 0x200; abs <<= 1, --exp)
                    ;
            uint16 bits = (exp < 0) << 15;
            if (exp)
            {
                unsigned int m = std::abs(exp) << 6, e = 18;
                for (; m < 0x400; m <<= 1, --e)
                    ;
                bits |= (e << 10) + m;
            }
            return half(binary, bits);
        }
        if (abs > 0x7C00)
            return arg;
        return half(binary, 0x7C00);
    }

    /// Enumeration implementation.
    /// \param from number to increase/decrease
    /// \param to direction to enumerate into
    /// \return next representable number
    static half nextafter(half from, half to)
    {
        uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
        if (fabs > 0x7C00)
            return from;
        if (tabs > 0x7C00 || from.data_ == to.data_ || !(fabs | tabs))
            return to;
        if (!fabs)
            return half(binary, (to.data_ & 0x8000) + 1);
        bool lt = ((fabs == from.data_) ? static_cast<int>(fabs) : -static_cast<int>(fabs))
            < ((tabs == to.data_) ? static_cast<int>(tabs) : -static_cast<int>(tabs));
        return half(binary, from.data_ + (((from.data_ >> 15) ^ static_cast<unsigned>(lt)) << 1) - 1);
    }

    /// Enumeration implementation.
    /// \param from number to increase/decrease
    /// \param to direction to enumerate into
    /// \return next representable number
    static half nexttoward(half from, long double to)
    {
        if (isnan(from))
            return from;
        long double lfrom = static_cast<long double>(from);
        if (builtin_isnan(to) || lfrom == to)
            return half(static_cast<float>(to));
        if (!(from.data_ & 0x7FFF))
            return half(binary, (static_cast<detail::uint16>(builtin_signbit(to)) << 15) + 1);
        return half(binary, from.data_ + (((from.data_ >> 15) ^ static_cast<unsigned>(lfrom < to)) << 1) - 1);
    }

    /// Sign implementation
    /// \param x first operand
    /// \param y second operand
    /// \return composed value
    static half copysign(half x, half y)
    {
        return half(binary, x.data_ ^ ((x.data_ ^ y.data_) & 0x8000));
    }

    /// Classification implementation.
    /// \param arg value to classify
    /// \retval true if infinite number
    /// \retval false else
    static int fpclassify(half arg)
    {
        unsigned int abs = arg.data_ & 0x7FFF;
        return abs
            ? ((abs > 0x3FF) ? ((abs >= 0x7C00) ? ((abs > 0x7C00) ? FP_NAN : FP_INFINITE) : FP_NORMAL) : FP_SUBNORMAL)
            : FP_ZERO;
    }

    /// Classification implementation.
    /// \param arg value to classify
    /// \retval true if finite number
    /// \retval false else
    static bool isfinite(half arg)
    {
        return (arg.data_ & 0x7C00) != 0x7C00;
    }

    /// Classification implementation.
    /// \param arg value to classify
    /// \retval true if infinite number
    /// \retval false else
    static bool isinf(half arg)
    {
        return (arg.data_ & 0x7FFF) == 0x7C00;
    }

    /// Classification implementation.
    /// \param arg value to classify
    /// \retval true if not a number
    /// \retval false else
    static bool isnan(half arg)
    {
        return (arg.data_ & 0x7FFF) > 0x7C00;
    }

    /// Classification implementation.
    /// \param arg value to classify
    /// \retval true if normal number
    /// \retval false else
    static bool isnormal(half arg)
    {
        return ((arg.data_ & 0x7C00) != 0) & ((arg.data_ & 0x7C00) != 0x7C00);
    }

    /// Sign bit implementation.
    /// \param arg value to check
    /// \retval true if signed
    /// \retval false if unsigned
    static bool signbit(half arg)
    {
        return (arg.data_ & 0x8000) != 0;
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if operands equal
    /// \retval false else
    static bool isequal(half x, half y)
    {
        return (x.data_ == y.data_ || !((x.data_ | y.data_) & 0x7FFF)) && !isnan(x);
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if operands not equal
    /// \retval false else
    static bool isnotequal(half x, half y)
    {
        return (x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF)) || isnan(x);
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if \a x > \a y
    /// \retval false else
    static bool isgreater(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        return xabs <= 0x7C00 && yabs <= 0x7C00
            && (((xabs == x.data_) ? xabs : -xabs) > ((yabs == y.data_) ? yabs : -yabs));
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if \a x >= \a y
    /// \retval false else
    static bool isgreaterequal(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        return xabs <= 0x7C00 && yabs <= 0x7C00
            && (((xabs == x.data_) ? xabs : -xabs) >= ((yabs == y.data_) ? yabs : -yabs));
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if \a x < \a y
    /// \retval false else
    static bool isless(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        return xabs <= 0x7C00 && yabs <= 0x7C00
            && (((xabs == x.data_) ? xabs : -xabs) < ((yabs == y.data_) ? yabs : -yabs));
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if \a x <= \a y
    /// \retval false else
    static bool islessequal(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        return xabs <= 0x7C00 && yabs <= 0x7C00
            && (((xabs == x.data_) ? xabs : -xabs) <= ((yabs == y.data_) ? yabs : -yabs));
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if either \a x > \a y nor \a x < \a y
    /// \retval false else
    static bool islessgreater(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        if (xabs > 0x7C00 || yabs > 0x7C00)
            return false;
        int a = (xabs == x.data_) ? xabs : -xabs, b = (yabs == y.data_) ? yabs : -yabs;
        return a < b || a > b;
    }

    /// Comparison implementation.
    /// \param x first operand
    /// \param y second operand
    /// \retval true if operand unordered
    /// \retval false else
    static bool isunordered(half x, half y)
    {
        return isnan(x) || isnan(y);
    }

private:
    static double erf(double arg)
    {
        if (builtin_isinf(arg))
            return (arg < 0.0) ? -1.0 : 1.0;
        double x2 = arg * arg, ax2 = 0.147 * x2,
               value = std::sqrt(1.0 - std::exp(-x2 * (1.2732395447351626861510701069801 + ax2) / (1.0 + ax2)));
        return builtin_signbit(arg) ? -value : value;
    }

    static double lgamma(double arg)
    {
        double v = 1.0;
        for (; arg < 8.0; ++arg)
            v *= arg;
        double w = 1.0 / (arg * arg);
        return (((((((-0.02955065359477124183006535947712 * w + 0.00641025641025641025641025641026) * w
                        + -0.00191752691752691752691752691753)
                           * w
                       + 8.4175084175084175084175084175084e-4)
                          * w
                      + -5.952380952380952380952380952381e-4)
                         * w
                     + 7.9365079365079365079365079365079e-4)
                        * w
                    + -0.00277777777777777777777777777778)
                       * w
                   + 0.08333333333333333333333333333333)
            / arg
            + 0.91893853320467274178032973640562 - std::log(v) - arg + (arg - 0.5) * std::log(arg);
    }
};

/// Wrapper for unary half-precision functions needing specialization for individual argument types.
/// \tparam T argument type
template <typename T>
struct unary_specialized
{
    /// Negation implementation.
    /// \param arg value to negate
    /// \return negated value
    static HALF_CONSTEXPR half negate(half arg)
    {
        return half(binary, arg.data_ ^ 0x8000);
    }

    /// Absolute value implementation.
    /// \param arg function argument
    /// \return absolute value
    static half fabs(half arg)
    {
        return half(binary, arg.data_ & 0x7FFF);
    }
};
template <>
struct unary_specialized<expr>
{
    static HALF_CONSTEXPR expr negate(float arg)
    {
        return expr(-arg);
    }
    static expr fabs(float arg)
    {
        return expr(std::fabs(arg));
    }
};

/// Wrapper for binary half-precision functions needing specialization for individual argument types.
/// \tparam T first argument type
/// \tparam U first argument type
template <typename T, typename U>
struct binary_specialized
{
    /// Minimum implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return minimum value
    static expr fmin(float x, float y)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::fmin(x, y));
#else
        if (builtin_isnan(x))
            return expr(y);
        if (builtin_isnan(y))
            return expr(x);
        return expr(std::min(x, y));
#endif
    }

    /// Maximum implementation.
    /// \param x first operand
    /// \param y second operand
    /// \return maximum value
    static expr fmax(float x, float y)
    {
#if HALF_ENABLE_CPP11_CMATH
        return expr(std::fmax(x, y));
#else
        if (builtin_isnan(x))
            return expr(y);
        if (builtin_isnan(y))
            return expr(x);
        return expr(std::max(x, y));
#endif
    }
};
template <>
struct binary_specialized<half, half>
{
    static half fmin(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        if (xabs > 0x7C00)
            return y;
        if (yabs > 0x7C00)
            return x;
        return (((xabs == x.data_) ? xabs : -xabs) > ((yabs == y.data_) ? yabs : -yabs)) ? y : x;
    }
    static half fmax(half x, half y)
    {
        int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
        if (xabs > 0x7C00)
            return y;
        if (yabs > 0x7C00)
            return x;
        return (((xabs == x.data_) ? xabs : -xabs) < ((yabs == y.data_) ? yabs : -yabs)) ? y : x;
    }
};

/// Helper class for half casts.
/// This class template has to be specialized for all valid cast argument to define an appropriate static `cast` member
/// function and a corresponding `type` member denoting its return type.
/// \tparam T destination type
/// \tparam U source type
/// \tparam R rounding mode to use
template <typename T, typename U, std::float_round_style R = (std::float_round_style)(HALF_ROUND_STYLE)>
struct half_caster
{
};
template <typename U, std::float_round_style R>
struct half_caster<half, U, R>
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
    static_assert(std::is_arithmetic<U>::value, "half_cast from non-arithmetic type unsupported");
#endif

    static half cast(U arg)
    {
        return cast_impl(arg, is_float<U>());
    };

private:
    static half cast_impl(U arg, true_type)
    {
        return half(binary, float2half<R>(arg));
    }
    static half cast_impl(U arg, false_type)
    {
        return half(binary, int2half<R>(arg));
    }
};
template <typename T, std::float_round_style R>
struct half_caster<T, half, R>
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
    static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");
#endif

    static T cast(half arg)
    {
        return cast_impl(arg, is_float<T>());
    }

private:
    static T cast_impl(half arg, true_type)
    {
        return half2float<T>(arg.data_);
    }
    static T cast_impl(half arg, false_type)
    {
        return half2int<R, T>(arg.data_);
    }
};
template <typename T, std::float_round_style R>
struct half_caster<T, expr, R>
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
    static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");
#endif

    static T cast(expr arg)
    {
        return cast_impl(arg, is_float<T>());
    }

private:
    static T cast_impl(float arg, true_type)
    {
        return static_cast<T>(arg);
    }
    static T cast_impl(half arg, false_type)
    {
        return half2int<R, T>(arg.data_);
    }
};
template <std::float_round_style R>
struct half_caster<half, half, R>
{
    static half cast(half arg)
    {
        return arg;
    }
};
template <std::float_round_style R>
struct half_caster<half, expr, R> : half_caster<half, half, R>
{
};

/// \name Comparison operators
/// \{

/// Comparison for equality.
/// \param x first operand
/// \param y second operand
/// \retval true if operands equal
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator==(T x, U y)
{
    return functions::isequal(x, y);
}

/// Comparison for inequality.
/// \param x first operand
/// \param y second operand
/// \retval true if operands not equal
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator!=(T x, U y)
{
    return functions::isnotequal(x, y);
}

/// Comparison for less than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less than \a y
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator<(T x, U y)
{
    return functions::isless(x, y);
}

/// Comparison for greater than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater than \a y
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator>(T x, U y)
{
    return functions::isgreater(x, y);
}

/// Comparison for less equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less equal \a y
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator<=(T x, U y)
{
    return functions::islessequal(x, y);
}

/// Comparison for greater equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater equal \a y
/// \retval false else
template <typename T, typename U>
typename enable<bool, T, U>::type operator>=(T x, U y)
{
    return functions::isgreaterequal(x, y);
}

/// \}
/// \name Arithmetic operators
/// \{

/// Add halfs.
/// \param x left operand
/// \param y right operand
/// \return sum of half expressions
template <typename T, typename U>
typename enable<expr, T, U>::type operator+(T x, U y)
{
    return functions::plus(x, y);
}

/// Subtract halfs.
/// \param x left operand
/// \param y right operand
/// \return difference of half expressions
template <typename T, typename U>
typename enable<expr, T, U>::type operator-(T x, U y)
{
    return functions::minus(x, y);
}

/// Multiply halfs.
/// \param x left operand
/// \param y right operand
/// \return product of half expressions
template <typename T, typename U>
typename enable<expr, T, U>::type operator*(T x, U y)
{
    return functions::multiplies(x, y);
}

/// Divide halfs.
/// \param x left operand
/// \param y right operand
/// \return quotient of half expressions
template <typename T, typename U>
typename enable<expr, T, U>::type operator/(T x, U y)
{
    return functions::divides(x, y);
}

/// Identity.
/// \param arg operand
/// \return uncahnged operand
template <typename T>
HALF_CONSTEXPR typename enable<T, T>::type operator+(T arg)
{
    return arg;
}

/// Negation.
/// \param arg operand
/// \return negated operand
template <typename T>
HALF_CONSTEXPR typename enable<T, T>::type operator-(T arg)
{
    return unary_specialized<T>::negate(arg);
}

/// \}
/// \name Input and output
/// \{

/// Output operator.
/// \param out output stream to write into
/// \param arg half expression to write
/// \return reference to output stream
template <typename T, typename charT, typename traits>
typename enable<std::basic_ostream<charT, traits>&, T>::type operator<<(std::basic_ostream<charT, traits>& out, T arg)
{
    return functions::write(out, arg);
}

/// Input operator.
/// \param in input stream to read from
/// \param arg half to read into
/// \return reference to input stream
template <typename charT, typename traits>
std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& in, half& arg)
{
    return functions::read(in, arg);
}

/// \}
/// \name Basic mathematical operations
/// \{

/// Absolute value.
/// \param arg operand
/// \return absolute value of \a arg
//		template<typename T> typename enable<T,T>::type abs(T arg) { return unary_specialized<T>::fabs(arg); }
inline half abs(half arg)
{
    return unary_specialized<half>::fabs(arg);
}
inline expr abs(expr arg)
{
    return unary_specialized<expr>::fabs(arg);
}

/// Absolute value.
/// \param arg operand
/// \return absolute value of \a arg
//		template<typename T> typename enable<T,T>::type fabs(T arg) { return unary_specialized<T>::fabs(arg); }
inline half fabs(half arg)
{
    return unary_specialized<half>::fabs(arg);
}
inline expr fabs(expr arg)
{
    return unary_specialized<expr>::fabs(arg);
}

/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \return remainder of floating point division.
//		template<typename T,typename U> typename enable<expr,T,U>::type fmod(T x, U y) { return functions::fmod(x, y); }
inline expr fmod(half x, half y)
{
    return functions::fmod(x, y);
}
inline expr fmod(half x, expr y)
{
    return functions::fmod(x, y);
}
inline expr fmod(expr x, half y)
{
    return functions::fmod(x, y);
}
inline expr fmod(expr x, expr y)
{
    return functions::fmod(x, y);
}

/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \return remainder of floating point division.
//		template<typename T,typename U> typename enable<expr,T,U>::type remainder(T x, U y) { return
// functions::remainder(x, y); }
inline expr remainder(half x, half y)
{
    return functions::remainder(x, y);
}
inline expr remainder(half x, expr y)
{
    return functions::remainder(x, y);
}
inline expr remainder(expr x, half y)
{
    return functions::remainder(x, y);
}
inline expr remainder(expr x, expr y)
{
    return functions::remainder(x, y);
}

/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \param quo address to store some bits of quotient at
/// \return remainder of floating point division.
//		template<typename T,typename U> typename enable<expr,T,U>::type remquo(T x, U y, int *quo) { return
// functions::remquo(x, y, quo); }
inline expr remquo(half x, half y, int* quo)
{
    return functions::remquo(x, y, quo);
}
inline expr remquo(half x, expr y, int* quo)
{
    return functions::remquo(x, y, quo);
}
inline expr remquo(expr x, half y, int* quo)
{
    return functions::remquo(x, y, quo);
}
inline expr remquo(expr x, expr y, int* quo)
{
    return functions::remquo(x, y, quo);
}

/// Fused multiply add.
/// \param x first operand
/// \param y second operand
/// \param z third operand
/// \return ( \a x * \a y ) + \a z rounded as one operation.
//		template<typename T,typename U,typename V> typename enable<expr,T,U,V>::type fma(T x, U y, V z) { return
// functions::fma(x, y, z); }
inline expr fma(half x, half y, half z)
{
    return functions::fma(x, y, z);
}
inline expr fma(half x, half y, expr z)
{
    return functions::fma(x, y, z);
}
inline expr fma(half x, expr y, half z)
{
    return functions::fma(x, y, z);
}
inline expr fma(half x, expr y, expr z)
{
    return functions::fma(x, y, z);
}
inline expr fma(expr x, half y, half z)
{
    return functions::fma(x, y, z);
}
inline expr fma(expr x, half y, expr z)
{
    return functions::fma(x, y, z);
}
inline expr fma(expr x, expr y, half z)
{
    return functions::fma(x, y, z);
}
inline expr fma(expr x, expr y, expr z)
{
    return functions::fma(x, y, z);
}

/// Maximum of half expressions.
/// \param x first operand
/// \param y second operand
/// \return maximum of operands
//		template<typename T,typename U> typename result<T,U>::type fmax(T x, U y) { return
// binary_specialized<T,U>::fmax(x, y); }
inline half fmax(half x, half y)
{
    return binary_specialized<half, half>::fmax(x, y);
}
inline expr fmax(half x, expr y)
{
    return binary_specialized<half, expr>::fmax(x, y);
}
inline expr fmax(expr x, half y)
{
    return binary_specialized<expr, half>::fmax(x, y);
}
inline expr fmax(expr x, expr y)
{
    return binary_specialized<expr, expr>::fmax(x, y);
}

/// Minimum of half expressions.
/// \param x first operand
/// \param y second operand
/// \return minimum of operands
//		template<typename T,typename U> typename result<T,U>::type fmin(T x, U y) { return
// binary_specialized<T,U>::fmin(x, y); }
inline half fmin(half x, half y)
{
    return binary_specialized<half, half>::fmin(x, y);
}
inline expr fmin(half x, expr y)
{
    return binary_specialized<half, expr>::fmin(x, y);
}
inline expr fmin(expr x, half y)
{
    return binary_specialized<expr, half>::fmin(x, y);
}
inline expr fmin(expr x, expr y)
{
    return binary_specialized<expr, expr>::fmin(x, y);
}

/// Positive difference.
/// \param x first operand
/// \param y second operand
/// \return \a x - \a y or 0 if difference negative
//		template<typename T,typename U> typename enable<expr,T,U>::type fdim(T x, U y) { return functions::fdim(x, y); }
inline expr fdim(half x, half y)
{
    return functions::fdim(x, y);
}
inline expr fdim(half x, expr y)
{
    return functions::fdim(x, y);
}
inline expr fdim(expr x, half y)
{
    return functions::fdim(x, y);
}
inline expr fdim(expr x, expr y)
{
    return functions::fdim(x, y);
}

/// Get NaN value.
/// \return quiet NaN
inline half nanh(const char*)
{
    return functions::nanh();
}

/// \}
/// \name Exponential functions
/// \{

/// Exponential function.
/// \param arg function argument
/// \return e raised to \a arg
//		template<typename T> typename enable<expr,T>::type exp(T arg) { return functions::exp(arg); }
inline expr exp(half arg)
{
    return functions::exp(arg);
}
inline expr exp(expr arg)
{
    return functions::exp(arg);
}

/// Exponential minus one.
/// \param arg function argument
/// \return e raised to \a arg subtracted by 1
//		template<typename T> typename enable<expr,T>::type expm1(T arg) { return functions::expm1(arg); }
inline expr expm1(half arg)
{
    return functions::expm1(arg);
}
inline expr expm1(expr arg)
{
    return functions::expm1(arg);
}

/// Binary exponential.
/// \param arg function argument
/// \return 2 raised to \a arg
//		template<typename T> typename enable<expr,T>::type exp2(T arg) { return functions::exp2(arg); }
inline expr exp2(half arg)
{
    return functions::exp2(arg);
}
inline expr exp2(expr arg)
{
    return functions::exp2(arg);
}

/// Natural logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base e
//		template<typename T> typename enable<expr,T>::type log(T arg) { return functions::log(arg); }
inline expr log(half arg)
{
    return functions::log(arg);
}
inline expr log(expr arg)
{
    return functions::log(arg);
}

/// Common logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base 10
//		template<typename T> typename enable<expr,T>::type log10(T arg) { return functions::log10(arg); }
inline expr log10(half arg)
{
    return functions::log10(arg);
}
inline expr log10(expr arg)
{
    return functions::log10(arg);
}

/// Natural logorithm.
/// \param arg function argument
/// \return logarithm of \a arg plus 1 to base e
//		template<typename T> typename enable<expr,T>::type log1p(T arg) { return functions::log1p(arg); }
inline expr log1p(half arg)
{
    return functions::log1p(arg);
}
inline expr log1p(expr arg)
{
    return functions::log1p(arg);
}

/// Binary logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base 2
//		template<typename T> typename enable<expr,T>::type log2(T arg) { return functions::log2(arg); }
inline expr log2(half arg)
{
    return functions::log2(arg);
}
inline expr log2(expr arg)
{
    return functions::log2(arg);
}

/// \}
/// \name Power functions
/// \{

/// Square root.
/// \param arg function argument
/// \return square root of \a arg
//		template<typename T> typename enable<expr,T>::type sqrt(T arg) { return functions::sqrt(arg); }
inline expr sqrt(half arg)
{
    return functions::sqrt(arg);
}
inline expr sqrt(expr arg)
{
    return functions::sqrt(arg);
}

/// Cubic root.
/// \param arg function argument
/// \return cubic root of \a arg
//		template<typename T> typename enable<expr,T>::type cbrt(T arg) { return functions::cbrt(arg); }
inline expr cbrt(half arg)
{
    return functions::cbrt(arg);
}
inline expr cbrt(expr arg)
{
    return functions::cbrt(arg);
}

/// Hypotenuse function.
/// \param x first argument
/// \param y second argument
/// \return square root of sum of squares without internal over- or underflows
//		template<typename T,typename U> typename enable<expr,T,U>::type hypot(T x, U y) { return functions::hypot(x, y);
//}
inline expr hypot(half x, half y)
{
    return functions::hypot(x, y);
}
inline expr hypot(half x, expr y)
{
    return functions::hypot(x, y);
}
inline expr hypot(expr x, half y)
{
    return functions::hypot(x, y);
}
inline expr hypot(expr x, expr y)
{
    return functions::hypot(x, y);
}

/// Power function.
/// \param base first argument
/// \param exp second argument
/// \return \a base raised to \a exp
//		template<typename T,typename U> typename enable<expr,T,U>::type pow(T base, U exp) { return functions::pow(base,
// exp); }
inline expr pow(half base, half exp)
{
    return functions::pow(base, exp);
}
inline expr pow(half base, expr exp)
{
    return functions::pow(base, exp);
}
inline expr pow(expr base, half exp)
{
    return functions::pow(base, exp);
}
inline expr pow(expr base, expr exp)
{
    return functions::pow(base, exp);
}

/// \}
/// \name Trigonometric functions
/// \{

/// Sine function.
/// \param arg function argument
/// \return sine value of \a arg
//		template<typename T> typename enable<expr,T>::type sin(T arg) { return functions::sin(arg); }
inline expr sin(half arg)
{
    return functions::sin(arg);
}
inline expr sin(expr arg)
{
    return functions::sin(arg);
}

/// Cosine function.
/// \param arg function argument
/// \return cosine value of \a arg
//		template<typename T> typename enable<expr,T>::type cos(T arg) { return functions::cos(arg); }
inline expr cos(half arg)
{
    return functions::cos(arg);
}
inline expr cos(expr arg)
{
    return functions::cos(arg);
}

/// Tangent function.
/// \param arg function argument
/// \return tangent value of \a arg
//		template<typename T> typename enable<expr,T>::type tan(T arg) { return functions::tan(arg); }
inline expr tan(half arg)
{
    return functions::tan(arg);
}
inline expr tan(expr arg)
{
    return functions::tan(arg);
}

/// Arc sine.
/// \param arg function argument
/// \return arc sine value of \a arg
//		template<typename T> typename enable<expr,T>::type asin(T arg) { return functions::asin(arg); }
inline expr asin(half arg)
{
    return functions::asin(arg);
}
inline expr asin(expr arg)
{
    return functions::asin(arg);
}

/// Arc cosine function.
/// \param arg function argument
/// \return arc cosine value of \a arg
//		template<typename T> typename enable<expr,T>::type acos(T arg) { return functions::acos(arg); }
inline expr acos(half arg)
{
    return functions::acos(arg);
}
inline expr acos(expr arg)
{
    return functions::acos(arg);
}

/// Arc tangent function.
/// \param arg function argument
/// \return arc tangent value of \a arg
//		template<typename T> typename enable<expr,T>::type atan(T arg) { return functions::atan(arg); }
inline expr atan(half arg)
{
    return functions::atan(arg);
}
inline expr atan(expr arg)
{
    return functions::atan(arg);
}

/// Arc tangent function.
/// \param x first argument
/// \param y second argument
/// \return arc tangent value
//		template<typename T,typename U> typename enable<expr,T,U>::type atan2(T x, U y) { return functions::atan2(x, y);
//}
inline expr atan2(half x, half y)
{
    return functions::atan2(x, y);
}
inline expr atan2(half x, expr y)
{
    return functions::atan2(x, y);
}
inline expr atan2(expr x, half y)
{
    return functions::atan2(x, y);
}
inline expr atan2(expr x, expr y)
{
    return functions::atan2(x, y);
}

/// \}
/// \name Hyperbolic functions
/// \{

/// Hyperbolic sine.
/// \param arg function argument
/// \return hyperbolic sine value of \a arg
//		template<typename T> typename enable<expr,T>::type sinh(T arg) { return functions::sinh(arg); }
inline expr sinh(half arg)
{
    return functions::sinh(arg);
}
inline expr sinh(expr arg)
{
    return functions::sinh(arg);
}

/// Hyperbolic cosine.
/// \param arg function argument
/// \return hyperbolic cosine value of \a arg
//		template<typename T> typename enable<expr,T>::type cosh(T arg) { return functions::cosh(arg); }
inline expr cosh(half arg)
{
    return functions::cosh(arg);
}
inline expr cosh(expr arg)
{
    return functions::cosh(arg);
}

/// Hyperbolic tangent.
/// \param arg function argument
/// \return hyperbolic tangent value of \a arg
//		template<typename T> typename enable<expr,T>::type tanh(T arg) { return functions::tanh(arg); }
inline expr tanh(half arg)
{
    return functions::tanh(arg);
}
inline expr tanh(expr arg)
{
    return functions::tanh(arg);
}

/// Hyperbolic area sine.
/// \param arg function argument
/// \return area sine value of \a arg
//		template<typename T> typename enable<expr,T>::type asinh(T arg) { return functions::asinh(arg); }
inline expr asinh(half arg)
{
    return functions::asinh(arg);
}
inline expr asinh(expr arg)
{
    return functions::asinh(arg);
}

/// Hyperbolic area cosine.
/// \param arg function argument
/// \return area cosine value of \a arg
//		template<typename T> typename enable<expr,T>::type acosh(T arg) { return functions::acosh(arg); }
inline expr acosh(half arg)
{
    return functions::acosh(arg);
}
inline expr acosh(expr arg)
{
    return functions::acosh(arg);
}

/// Hyperbolic area tangent.
/// \param arg function argument
/// \return area tangent value of \a arg
//		template<typename T> typename enable<expr,T>::type atanh(T arg) { return functions::atanh(arg); }
inline expr atanh(half arg)
{
    return functions::atanh(arg);
}
inline expr atanh(expr arg)
{
    return functions::atanh(arg);
}

/// \}
/// \name Error and gamma functions
/// \{

/// Error function.
/// \param arg function argument
/// \return error function value of \a arg
//		template<typename T> typename enable<expr,T>::type erf(T arg) { return functions::erf(arg); }
inline expr erf(half arg)
{
    return functions::erf(arg);
}
inline expr erf(expr arg)
{
    return functions::erf(arg);
}

/// Complementary error function.
/// \param arg function argument
/// \return 1 minus error function value of \a arg
//		template<typename T> typename enable<expr,T>::type erfc(T arg) { return functions::erfc(arg); }
inline expr erfc(half arg)
{
    return functions::erfc(arg);
}
inline expr erfc(expr arg)
{
    return functions::erfc(arg);
}

/// Natural logarithm of gamma function.
/// \param arg function argument
/// \return natural logarith of gamma function for \a arg
//		template<typename T> typename enable<expr,T>::type lgamma(T arg) { return functions::lgamma(arg); }
inline expr lgamma(half arg)
{
    return functions::lgamma(arg);
}
inline expr lgamma(expr arg)
{
    return functions::lgamma(arg);
}

/// Gamma function.
/// \param arg function argument
/// \return gamma function value of \a arg
//		template<typename T> typename enable<expr,T>::type tgamma(T arg) { return functions::tgamma(arg); }
inline expr tgamma(half arg)
{
    return functions::tgamma(arg);
}
inline expr tgamma(expr arg)
{
    return functions::tgamma(arg);
}

/// \}
/// \name Rounding
/// \{

/// Nearest integer not less than half value.
/// \param arg half to round
/// \return nearest integer not less than \a arg
//		template<typename T> typename enable<half,T>::type ceil(T arg) { return functions::ceil(arg); }
inline half ceil(half arg)
{
    return functions::ceil(arg);
}
inline half ceil(expr arg)
{
    return functions::ceil(arg);
}

/// Nearest integer not greater than half value.
/// \param arg half to round
/// \return nearest integer not greater than \a arg
//		template<typename T> typename enable<half,T>::type floor(T arg) { return functions::floor(arg); }
inline half floor(half arg)
{
    return functions::floor(arg);
}
inline half floor(expr arg)
{
    return functions::floor(arg);
}

/// Nearest integer not greater in magnitude than half value.
/// \param arg half to round
/// \return nearest integer not greater in magnitude than \a arg
//		template<typename T> typename enable<half,T>::type trunc(T arg) { return functions::trunc(arg); }
inline half trunc(half arg)
{
    return functions::trunc(arg);
}
inline half trunc(expr arg)
{
    return functions::trunc(arg);
}

/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
//		template<typename T> typename enable<half,T>::type round(T arg) { return functions::round(arg); }
inline half round(half arg)
{
    return functions::round(arg);
}
inline half round(expr arg)
{
    return functions::round(arg);
}

/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
//		template<typename T> typename enable<long,T>::type lround(T arg) { return functions::lround(arg); }
inline long lround(half arg)
{
    return functions::lround(arg);
}
inline long lround(expr arg)
{
    return functions::lround(arg);
}

/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
//		template<typename T> typename enable<half,T>::type nearbyint(T arg) { return functions::nearbyint(arg); }
inline half nearbyint(half arg)
{
    return functions::rint(arg);
}
inline half nearbyint(expr arg)
{
    return functions::rint(arg);
}

/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
//		template<typename T> typename enable<half,T>::type rint(T arg) { return functions::rint(arg); }
inline half rint(half arg)
{
    return functions::rint(arg);
}
inline half rint(expr arg)
{
    return functions::rint(arg);
}

/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
//		template<typename T> typename enable<long,T>::type lrint(T arg) { return functions::lrint(arg); }
inline long lrint(half arg)
{
    return functions::lrint(arg);
}
inline long lrint(expr arg)
{
    return functions::lrint(arg);
}
#if HALF_ENABLE_CPP11_LONG_LONG
/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
//		template<typename T> typename enable<long long,T>::type llround(T arg) { return functions::llround(arg); }
inline long long llround(half arg)
{
    return functions::llround(arg);
}
inline long long llround(expr arg)
{
    return functions::llround(arg);
}

/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
//		template<typename T> typename enable<long long,T>::type llrint(T arg) { return functions::llrint(arg); }
inline long long llrint(half arg)
{
    return functions::llrint(arg);
}
inline long long llrint(expr arg)
{
    return functions::llrint(arg);
}
#endif

/// \}
/// \name Floating point manipulation
/// \{

/// Decompress floating point number.
/// \param arg number to decompress
/// \param exp address to store exponent at
/// \return significant in range [0.5, 1)
//		template<typename T> typename enable<half,T>::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); }
inline half frexp(half arg, int* exp)
{
    return functions::frexp(arg, exp);
}
inline half frexp(expr arg, int* exp)
{
    return functions::frexp(arg, exp);
}

/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
//		template<typename T> typename enable<half,T>::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp);
//}
inline half ldexp(half arg, int exp)
{
    return functions::scalbln(arg, exp);
}
inline half ldexp(expr arg, int exp)
{
    return functions::scalbln(arg, exp);
}

/// Extract integer and fractional parts.
/// \param arg number to decompress
/// \param iptr address to store integer part at
/// \return fractional part
//		template<typename T> typename enable<half,T>::type modf(T arg, half *iptr) { return functions::modf(arg, iptr);
//}
inline half modf(half arg, half* iptr)
{
    return functions::modf(arg, iptr);
}
inline half modf(expr arg, half* iptr)
{
    return functions::modf(arg, iptr);
}

/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
//		template<typename T> typename enable<half,T>::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp);
//}
inline half scalbn(half arg, int exp)
{
    return functions::scalbln(arg, exp);
}
inline half scalbn(expr arg, int exp)
{
    return functions::scalbln(arg, exp);
}

/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
//		template<typename T> typename enable<half,T>::type scalbln(T arg, long exp) { return functions::scalbln(arg,
// exp);
//}
inline half scalbln(half arg, long exp)
{
    return functions::scalbln(arg, exp);
}
inline half scalbln(expr arg, long exp)
{
    return functions::scalbln(arg, exp);
}

/// Extract exponent.
/// \param arg number to query
/// \return floating point exponent
/// \retval FP_ILOGB0 for zero
/// \retval FP_ILOGBNAN for NaN
/// \retval MAX_INT for infinity
//		template<typename T> typename enable<int,T>::type ilogb(T arg) { return functions::ilogb(arg); }
inline int ilogb(half arg)
{
    return functions::ilogb(arg);
}
inline int ilogb(expr arg)
{
    return functions::ilogb(arg);
}

/// Extract exponent.
/// \param arg number to query
/// \return floating point exponent
//		template<typename T> typename enable<half,T>::type logb(T arg) { return functions::logb(arg); }
inline half logb(half arg)
{
    return functions::logb(arg);
}
inline half logb(expr arg)
{
    return functions::logb(arg);
}

/// Next representable value.
/// \param from value to compute next representable value for
/// \param to direction towards which to compute next value
/// \return next representable value after \a from in direction towards \a to
//		template<typename T,typename U> typename enable<half,T,U>::type nextafter(T from, U to) { return
// functions::nextafter(from, to); }
inline half nextafter(half from, half to)
{
    return functions::nextafter(from, to);
}
inline half nextafter(half from, expr to)
{
    return functions::nextafter(from, to);
}
inline half nextafter(expr from, half to)
{
    return functions::nextafter(from, to);
}
inline half nextafter(expr from, expr to)
{
    return functions::nextafter(from, to);
}

/// Next representable value.
/// \param from value to compute next representable value for
/// \param to direction towards which to compute next value
/// \return next representable value after \a from in direction towards \a to
//		template<typename T> typename enable<half,T>::type nexttoward(T from, long double to) { return
// functions::nexttoward(from, to); }
inline half nexttoward(half from, long double to)
{
    return functions::nexttoward(from, to);
}
inline half nexttoward(expr from, long double to)
{
    return functions::nexttoward(from, to);
}

/// Take sign.
/// \param x value to change sign for
/// \param y value to take sign from
/// \return value equal to \a x in magnitude and to \a y in sign
//		template<typename T,typename U> typename enable<half,T,U>::type copysign(T x, U y) { return
// functions::copysign(x, y); }
inline half copysign(half x, half y)
{
    return functions::copysign(x, y);
}
inline half copysign(half x, expr y)
{
    return functions::copysign(x, y);
}
inline half copysign(expr x, half y)
{
    return functions::copysign(x, y);
}
inline half copysign(expr x, expr y)
{
    return functions::copysign(x, y);
}

/// \}
/// \name Floating point classification
/// \{

/// Classify floating point value.
/// \param arg number to classify
/// \retval FP_ZERO for positive and negative zero
/// \retval FP_SUBNORMAL for subnormal numbers
/// \retval FP_INFINITY for positive and negative infinity
/// \retval FP_NAN for NaNs
/// \retval FP_NORMAL for all other (normal) values
//		template<typename T> typename enable<int,T>::type fpclassify(T arg) { return functions::fpclassify(arg); }
inline int fpclassify(half arg)
{
    return functions::fpclassify(arg);
}
inline int fpclassify(expr arg)
{
    return functions::fpclassify(arg);
}

/// Check if finite number.
/// \param arg number to check
/// \retval true if neither infinity nor NaN
/// \retval false else
//		template<typename T> typename enable<bool,T>::type isfinite(T arg) { return functions::isfinite(arg); }
inline bool isfinite(half arg)
{
    return functions::isfinite(arg);
}
inline bool isfinite(expr arg)
{
    return functions::isfinite(arg);
}

/// Check for infinity.
/// \param arg number to check
/// \retval true for positive or negative infinity
/// \retval false else
//		template<typename T> typename enable<bool,T>::type isinf(T arg) { return functions::isinf(arg); }
inline bool isinf(half arg)
{
    return functions::isinf(arg);
}
inline bool isinf(expr arg)
{
    return functions::isinf(arg);
}

/// Check for NaN.
/// \param arg number to check
/// \retval true for NaNs
/// \retval false else
//		template<typename T> typename enable<bool,T>::type isnan(T arg) { return functions::isnan(arg); }
inline bool isnan(half arg)
{
    return functions::isnan(arg);
}
inline bool isnan(expr arg)
{
    return functions::isnan(arg);
}

/// Check if normal number.
/// \param arg number to check
/// \retval true if normal number
/// \retval false if either subnormal, zero, infinity or NaN
//		template<typename T> typename enable<bool,T>::type isnormal(T arg) { return functions::isnormal(arg); }
inline bool isnormal(half arg)
{
    return functions::isnormal(arg);
}
inline bool isnormal(expr arg)
{
    return functions::isnormal(arg);
}

/// Check sign.
/// \param arg number to check
/// \retval true for negative number
/// \retval false for positive number
//		template<typename T> typename enable<bool,T>::type signbit(T arg) { return functions::signbit(arg); }
inline bool signbit(half arg)
{
    return functions::signbit(arg);
}
inline bool signbit(expr arg)
{
    return functions::signbit(arg);
}

/// \}
/// \name Comparison
/// \{

/// Comparison for greater than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater than \a y
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type isgreater(T x, U y) { return
// functions::isgreater(x, y); }
inline bool isgreater(half x, half y)
{
    return functions::isgreater(x, y);
}
inline bool isgreater(half x, expr y)
{
    return functions::isgreater(x, y);
}
inline bool isgreater(expr x, half y)
{
    return functions::isgreater(x, y);
}
inline bool isgreater(expr x, expr y)
{
    return functions::isgreater(x, y);
}

/// Comparison for greater equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater equal \a y
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type isgreaterequal(T x, U y) { return
// functions::isgreaterequal(x, y); }
inline bool isgreaterequal(half x, half y)
{
    return functions::isgreaterequal(x, y);
}
inline bool isgreaterequal(half x, expr y)
{
    return functions::isgreaterequal(x, y);
}
inline bool isgreaterequal(expr x, half y)
{
    return functions::isgreaterequal(x, y);
}
inline bool isgreaterequal(expr x, expr y)
{
    return functions::isgreaterequal(x, y);
}

/// Comparison for less than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less than \a y
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type isless(T x, U y) { return functions::isless(x,
// y);
//}
inline bool isless(half x, half y)
{
    return functions::isless(x, y);
}
inline bool isless(half x, expr y)
{
    return functions::isless(x, y);
}
inline bool isless(expr x, half y)
{
    return functions::isless(x, y);
}
inline bool isless(expr x, expr y)
{
    return functions::isless(x, y);
}

/// Comparison for less equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less equal \a y
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type islessequal(T x, U y) { return
// functions::islessequal(x, y); }
inline bool islessequal(half x, half y)
{
    return functions::islessequal(x, y);
}
inline bool islessequal(half x, expr y)
{
    return functions::islessequal(x, y);
}
inline bool islessequal(expr x, half y)
{
    return functions::islessequal(x, y);
}
inline bool islessequal(expr x, expr y)
{
    return functions::islessequal(x, y);
}

/// Comarison for less or greater.
/// \param x first operand
/// \param y second operand
/// \retval true if either less or greater
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type islessgreater(T x, U y) { return
// functions::islessgreater(x, y); }
inline bool islessgreater(half x, half y)
{
    return functions::islessgreater(x, y);
}
inline bool islessgreater(half x, expr y)
{
    return functions::islessgreater(x, y);
}
inline bool islessgreater(expr x, half y)
{
    return functions::islessgreater(x, y);
}
inline bool islessgreater(expr x, expr y)
{
    return functions::islessgreater(x, y);
}

/// Check if unordered.
/// \param x first operand
/// \param y second operand
/// \retval true if unordered (one or two NaN operands)
/// \retval false else
//		template<typename T,typename U> typename enable<bool,T,U>::type isunordered(T x, U y) { return
// functions::isunordered(x, y); }
inline bool isunordered(half x, half y)
{
    return functions::isunordered(x, y);
}
inline bool isunordered(half x, expr y)
{
    return functions::isunordered(x, y);
}
inline bool isunordered(expr x, half y)
{
    return functions::isunordered(x, y);
}
inline bool isunordered(expr x, expr y)
{
    return functions::isunordered(x, y);
}

/// \name Casting
/// \{

/// Cast to or from half-precision floating point number.
/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted
/// directly using the given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.
/// It uses the default rounding mode.
///
/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
/// error and casting between [half](\ref half_float::half)s is just a no-op.
/// \tparam T destination type (half or built-in arithmetic type)
/// \tparam U source type (half or built-in arithmetic type)
/// \param arg value to cast
/// \return \a arg converted to destination type
template <typename T, typename U>
T half_cast(U arg)
{
    return half_caster<T, U>::cast(arg);
}

/// Cast to or from half-precision floating point number.
/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted
/// directly using the given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.
///
/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
/// error and casting between [half](\ref half_float::half)s is just a no-op.
/// \tparam T destination type (half or built-in arithmetic type)
/// \tparam R rounding mode to use.
/// \tparam U source type (half or built-in arithmetic type)
/// \param arg value to cast
/// \return \a arg converted to destination type
template <typename T, std::float_round_style R, typename U>
T half_cast(U arg)
{
    return half_caster<T, U, R>::cast(arg);
}
/// \}
} // 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 the rounding mode of the single-to-half conversions, the actual rounding
    /// mode might be `std::round_indeterminate` if the default half-precision rounding mode doesn't match the
    /// single-precision rounding mode.
    static HALF_CONSTEXPR_CONST float_round_style round_style
        = (std::numeric_limits<float>::round_style == half_float::half::round_style) ? half_float::half::round_style
                                                                                     : round_indeterminate;

    /// Significant digits.
    static HALF_CONSTEXPR_CONST int digits = 11;

    /// Significant decimal digits.
    static HALF_CONSTEXPR_CONST int digits10 = 3;

    /// Required decimal digits to represent all possible values.
    static HALF_CONSTEXPR_CONST int max_digits10 = 5;

    /// Number base.
    static HALF_CONSTEXPR_CONST int radix = 2;

    /// One more than smallest exponent.
    static HALF_CONSTEXPR_CONST int min_exponent = -13;

    /// Smallest normalized representable power of 10.
    static HALF_CONSTEXPR_CONST int min_exponent10 = -4;

    /// One more than largest exponent
    static HALF_CONSTEXPR_CONST int max_exponent = 16;

    /// Largest finitely representable power of 10.
    static HALF_CONSTEXPR_CONST int max_exponent10 = 4;

    /// Smallest positive normal value.
    static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x0400);
    }

    /// Smallest finite value.
    static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0xFBFF);
    }

    /// Largest finite value.
    static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7BFF);
    }

    /// Difference between one and next representable value.
    static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x1400);
    }

    /// Maximum rounding error.
    static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, (round_style == std::round_to_nearest) ? 0x3800 : 0x3C00);
    }

    /// Positive infinity.
    static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7C00);
    }

    /// Quiet NaN.
    static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7FFF);
    }

    /// Signalling NaN.
    static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7DFF);
    }

    /// Smallest positive subnormal value.
    static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x0001);
    }
};

#if HALF_ENABLE_CPP11_HASH
/// Hash function for half-precision floats.
/// This is only defined if C++11 `std::hash` is supported and enabled.
template <>
struct hash<half_float::half> //: unary_function<half_float::half,size_t>
{
    /// Type of function argument.
    typedef half_float::half argument_type;

    /// Function return type.
    typedef size_t result_type;

    /// Compute hash function.
    /// \param arg half to hash
    /// \return hash value
    result_type operator()(argument_type arg) const
    {
        return hash<half_float::detail::uint16>()(static_cast<unsigned>(arg.data_) & -(arg.data_ != 0x8000));
    }
};
#endif
} // 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