half.hpp

Go to the documentation of this file.

// half - IEEE 754-based half-precision floating-point library.
//
// Copyright (c) 2012-2021 Christian Rau <rauy@users.sourceforge.net>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
// documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
// Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
// Version 2.2.0
 
 
#ifndef HALF_HALF_HPP
#define HALF_HALF_HPP
 
#define HALF_GCC_VERSION (__GNUC__ * 100 + __GNUC_MINOR__)
 
#if defined(__INTEL_COMPILER)
#define HALF_ICC_VERSION __INTEL_COMPILER
#elif defined(__ICC)
#define HALF_ICC_VERSION __ICC
#elif defined(__ICL)
#define HALF_ICC_VERSION __ICL
#else
#define HALF_ICC_VERSION 0
#endif
 
// check C++11 language features
#if defined(__clang__) // clang
#if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if __has_feature(cxx_thread_local) && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
#endif
#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#elif HALF_ICC_VERSION && defined(__INTEL_CXX11_MODE__) // Intel C++
#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
#endif
#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#elif defined(__GNUC__) // gcc
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
#if HALF_GCC_VERSION >= 408 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
#endif
#if HALF_GCC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#endif
#define HALF_TWOS_COMPLEMENT_INT 1
#elif defined(_MSC_VER) // Visual C++
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#define HALF_TWOS_COMPLEMENT_INT 1
#define HALF_POP_WARNINGS 1
#pragma warning(push)
#pragma warning(disable : 4099 4127 4146) // struct vs class, constant in if, negative unsigned
#endif
 
// check C++11 library features
#include <utility>
#if defined(_LIBCPP_VERSION) // libc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#ifndef HALF_ENABLE_CPP11_CSTDINT
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#ifndef HALF_ENABLE_CPP11_CMATH
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#ifndef HALF_ENABLE_CPP11_HASH
#define HALF_ENABLE_CPP11_HASH 1
#endif
#ifndef HALF_ENABLE_CPP11_CFENV
#define HALF_ENABLE_CPP11_CFENV 1
#endif
#endif
#elif defined(__GLIBCXX__) // libstdc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifdef __clang__
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CFENV)
#define HALF_ENABLE_CPP11_CFENV 1
#endif
#else
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CFENV)
#define HALF_ENABLE_CPP11_CFENV 1
#endif
#endif
#endif
#elif defined(_CPPLIB_VER) // Dinkumware/Visual C++
#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CFENV)
#define HALF_ENABLE_CPP11_CFENV 1
#endif
#endif
#undef HALF_GCC_VERSION
#undef HALF_ICC_VERSION
 
// any error throwing C++ exceptions?
#if defined(HALF_ERRHANDLING_THROW_INVALID) || defined(HALF_ERRHANDLING_THROW_DIVBYZERO) ||                            \
    defined(HALF_ERRHANDLING_THROW_OVERFLOW) || defined(HALF_ERRHANDLING_THROW_UNDERFLOW) ||                           \
    defined(HALF_ERRHANDLING_THROW_INEXACT)
#define HALF_ERRHANDLING_THROWS 1
#endif
 
// any error handling enabled?
#define HALF_ERRHANDLING                                                                                               \
    (HALF_ERRHANDLING_FLAGS || HALF_ERRHANDLING_ERRNO || HALF_ERRHANDLING_FENV || HALF_ERRHANDLING_THROWS)
 
#if HALF_ERRHANDLING
#define HALF_UNUSED_NOERR(name) name
#else
#define HALF_UNUSED_NOERR(name)
#endif
 
// support constexpr
#if HALF_ENABLE_CPP11_CONSTEXPR
#define HALF_CONSTEXPR constexpr
#define HALF_CONSTEXPR_CONST constexpr
#if HALF_ERRHANDLING
#define HALF_CONSTEXPR_NOERR
#else
#define HALF_CONSTEXPR_NOERR constexpr
#endif
#else
#define HALF_CONSTEXPR
#define HALF_CONSTEXPR_CONST const
#define HALF_CONSTEXPR_NOERR
#endif
 
// support noexcept
#if HALF_ENABLE_CPP11_NOEXCEPT
#define HALF_NOEXCEPT noexcept
#define HALF_NOTHROW noexcept
#else
#define HALF_NOEXCEPT
#define HALF_NOTHROW throw()
#endif
 
// support thread storage
#if HALF_ENABLE_CPP11_THREAD_LOCAL
#define HALF_THREAD_LOCAL thread_local
#else
#define HALF_THREAD_LOCAL static
#endif
 
#include <algorithm>
#include <climits>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <istream>
#include <limits>
#include <ostream>
#include <stdexcept>
#include <utility>
#if HALF_ENABLE_CPP11_TYPE_TRAITS
#include <type_traits>
#endif
#if HALF_ENABLE_CPP11_CSTDINT
#include <cstdint>
#endif
#if HALF_ERRHANDLING_ERRNO
#include <cerrno>
#endif
#if HALF_ENABLE_CPP11_CFENV
#include <cfenv>
#endif
#if HALF_ENABLE_CPP11_HASH
#include <functional>
#endif
 
#ifndef HALF_ENABLE_F16C_INTRINSICS
#define HALF_ENABLE_F16C_INTRINSICS __F16C__
#endif
#if HALF_ENABLE_F16C_INTRINSICS
#include <immintrin.h>
#endif
 
#ifdef HALF_DOXYGEN_ONLY
#define HALF_ARITHMETIC_TYPE (undefined)
 
#define HALF_ERRHANDLING_FLAGS 0
 
#define HALF_ERRHANDLING_ERRNO 0
 
#define HALF_ERRHANDLING_FENV 0
 
#define HALF_ERRHANDLING_THROW_INVALID (undefined)
 
#define HALF_ERRHANDLING_THROW_DIVBYZERO (undefined)
 
#define HALF_ERRHANDLING_THROW_OVERFLOW (undefined)
 
#define HALF_ERRHANDLING_THROW_UNDERFLOW (undefined)
 
#define HALF_ERRHANDLING_THROW_INEXACT (undefined)
#endif
 
#ifndef HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
#define HALF_ERRHANDLING_OVERFLOW_TO_INEXACT 1
#endif
 
#ifndef HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
#define HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT 1
#endif
 
#ifndef HALF_ROUND_STYLE
#define HALF_ROUND_STYLE 1 // = std::round_to_nearest
#endif
 
#define HUGE_VALH std::numeric_limits<half_float::half>::infinity()
 
#define FP_FAST_FMAH 1
 
#define HLF_ROUNDS HALF_ROUND_STYLE
 
#ifndef FP_ILOGB0
#define FP_ILOGB0 INT_MIN
#endif
#ifndef FP_ILOGBNAN
#define FP_ILOGBNAN INT_MAX
#endif
#ifndef FP_SUBNORMAL
#define FP_SUBNORMAL 0
#endif
#ifndef FP_ZERO
#define FP_ZERO 1
#endif
#ifndef FP_NAN
#define FP_NAN 2
#endif
#ifndef FP_INFINITE
#define FP_INFINITE 3
#endif
#ifndef FP_NORMAL
#define FP_NORMAL 4
#endif
 
#if !HALF_ENABLE_CPP11_CFENV && !defined(FE_ALL_EXCEPT)
#define FE_INVALID 0x10
#define FE_DIVBYZERO 0x08
#define FE_OVERFLOW 0x04
#define FE_UNDERFLOW 0x02
#define FE_INEXACT 0x01
#define FE_ALL_EXCEPT (FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW | FE_INEXACT)
#endif
 
namespace half_float {
class half;
 
#if HALF_ENABLE_CPP11_USER_LITERALS
namespace literal {
    half operator"" _h(long double);
}
#endif
 
namespace detail {
#if HALF_ENABLE_CPP11_TYPE_TRAITS
    template <bool B, typename T, typename F> struct conditional : std::conditional<B, T, F> {
    };
 
    template <bool B> struct bool_type : std::integral_constant<bool, B> {
    };
    using std::false_type;
    using std::true_type;
 
    template <typename T> struct is_float : std::is_floating_point<T> {
    };
#else
    template <bool, typename T, typename> struct conditional {
        typedef T type;
    };
    template <typename T, typename F> struct conditional<false, T, F> {
        typedef F type;
    };
 
    template <bool> struct bool_type {
    };
    typedef bool_type<true> true_type;
    typedef bool_type<false> false_type;
 
    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
 
    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
    typedef std::uint_least16_t uint16;
 
    typedef std::uint_fast32_t uint32;
 
    typedef std::int_fast32_t int32;
 
    template <> struct bits<float> {
        typedef std::uint_least32_t type;
    };
 
    template <> struct bits<double> {
        typedef std::uint_least64_t type;
    };
#else
    typedef unsigned short uint16;
 
    typedef unsigned long uint32;
 
    typedef long int32;
 
    template <>
    struct bits<float> : conditional<std::numeric_limits<unsigned int>::digits >= 32, unsigned int, unsigned long> {
    };
 
#if HALF_ENABLE_CPP11_LONG_LONG
    template <>
    struct bits<double>
        : conditional<std::numeric_limits<unsigned long>::digits >= 64, unsigned long, unsigned long long> {
    };
#else
    template <> struct bits<double> {
        typedef unsigned long type;
    };
#endif
#endif
 
#ifdef HALF_ARITHMETIC_TYPE
    typedef HALF_ARITHMETIC_TYPE internal_t;
#endif
 
    struct binary_t {};
 
    HALF_CONSTEXPR_CONST binary_t binary = binary_t();
 
 
    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
    }
 
    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
    }
 
    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
    }
 
    inline uint32 sign_mask(uint32 arg)
    {
        static const int N = std::numeric_limits<uint32>::digits - 1;
#if HALF_TWOS_COMPLEMENT_INT
        return static_cast<int32>(arg) >> N;
#else
        return -((arg >> N) & 1);
#endif
    }
 
    inline uint32 arithmetic_shift(uint32 arg, int i)
    {
#if HALF_TWOS_COMPLEMENT_INT
        return static_cast<int32>(arg) >> i;
#else
        return static_cast<int32>(arg) / (static_cast<int32>(1) << i) -
            ((arg >> (std::numeric_limits<uint32>::digits - 1)) & 1);
#endif
    }
 
 
    inline int& errflags()
    {
        HALF_THREAD_LOCAL int flags = 0;
        return flags;
    }
 
    inline void raise(int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond) = true)
    {
#if HALF_ERRHANDLING
        if (!cond)
            return;
#if HALF_ERRHANDLING_FLAGS
        errflags() |= flags;
#endif
#if HALF_ERRHANDLING_ERRNO
        if (flags & FE_INVALID)
            errno = EDOM;
        else if (flags & (FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW))
            errno = ERANGE;
#endif
#if HALF_ERRHANDLING_FENV && HALF_ENABLE_CPP11_CFENV
        std::feraiseexcept(flags);
#endif
#ifdef HALF_ERRHANDLING_THROW_INVALID
        if (flags & FE_INVALID)
            throw std::domain_error(HALF_ERRHANDLING_THROW_INVALID);
#endif
#ifdef HALF_ERRHANDLING_THROW_DIVBYZERO
        if (flags & FE_DIVBYZERO)
            throw std::domain_error(HALF_ERRHANDLING_THROW_DIVBYZERO);
#endif
#ifdef HALF_ERRHANDLING_THROW_OVERFLOW
        if (flags & FE_OVERFLOW)
            throw std::overflow_error(HALF_ERRHANDLING_THROW_OVERFLOW);
#endif
#ifdef HALF_ERRHANDLING_THROW_UNDERFLOW
        if (flags & FE_UNDERFLOW)
            throw std::underflow_error(HALF_ERRHANDLING_THROW_UNDERFLOW);
#endif
#ifdef HALF_ERRHANDLING_THROW_INEXACT
        if (flags & FE_INEXACT)
            throw std::range_error(HALF_ERRHANDLING_THROW_INEXACT);
#endif
#if HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
        if ((flags & FE_UNDERFLOW) && !(flags & FE_INEXACT))
            raise(FE_INEXACT);
#endif
#if HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
        if ((flags & FE_OVERFLOW) && !(flags & FE_INEXACT))
            raise(FE_INEXACT);
#endif
#endif
    }
 
    inline HALF_CONSTEXPR_NOERR bool compsignal(unsigned int x, unsigned int y)
    {
#if HALF_ERRHANDLING
        raise(FE_INVALID, (x & 0x7FFF) > 0x7C00 || (y & 0x7FFF) > 0x7C00);
#endif
        return (x & 0x7FFF) > 0x7C00 || (y & 0x7FFF) > 0x7C00;
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int nan)
    {
#if HALF_ERRHANDLING
        raise(FE_INVALID, !(nan & 0x200));
#endif
        return nan | 0x200;
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y)
    {
#if HALF_ERRHANDLING
        raise(FE_INVALID, ((x & 0x7FFF) > 0x7C00 && !(x & 0x200)) || ((y & 0x7FFF) > 0x7C00 && !(y & 0x200)));
#endif
        return ((x & 0x7FFF) > 0x7C00) ? (x | 0x200) : (y | 0x200);
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y, unsigned int z)
    {
#if HALF_ERRHANDLING
        raise(FE_INVALID,
            ((x & 0x7FFF) > 0x7C00 && !(x & 0x200)) || ((y & 0x7FFF) > 0x7C00 && !(y & 0x200)) ||
                ((z & 0x7FFF) > 0x7C00 && !(z & 0x200)));
#endif
        return ((x & 0x7FFF) > 0x7C00) ? (x | 0x200) : ((y & 0x7FFF) > 0x7C00) ? (y | 0x200) : (z | 0x200);
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int select(unsigned int x, unsigned int HALF_UNUSED_NOERR(y))
    {
#if HALF_ERRHANDLING
        return (((y & 0x7FFF) > 0x7C00) && !(y & 0x200)) ? signal(y) : x;
#else
        return x;
#endif
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int invalid()
    {
#if HALF_ERRHANDLING
        raise(FE_INVALID);
#endif
        return 0x7FFF;
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int pole(unsigned int sign = 0)
    {
#if HALF_ERRHANDLING
        raise(FE_DIVBYZERO);
#endif
        return sign | 0x7C00;
    }
 
    inline HALF_CONSTEXPR_NOERR unsigned int check_underflow(unsigned int arg)
    {
#if HALF_ERRHANDLING && !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
        raise(FE_UNDERFLOW, !(arg & 0x7C00));
#endif
        return arg;
    }
 
 
    template <std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int overflow(unsigned int sign = 0)
    {
#if HALF_ERRHANDLING
        raise(FE_OVERFLOW);
#endif
        return (R == std::round_toward_infinity)    ? (sign + 0x7C00 - (sign >> 15))
            : (R == std::round_toward_neg_infinity) ? (sign + 0x7BFF + (sign >> 15))
            : (R == std::round_toward_zero)         ? (sign | 0x7BFF)
                                                    : (sign | 0x7C00);
    }
 
    template <std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int underflow(unsigned int sign = 0)
    {
#if HALF_ERRHANDLING
        raise(FE_UNDERFLOW);
#endif
        return (R == std::round_toward_infinity)    ? (sign + 1 - (sign >> 15))
            : (R == std::round_toward_neg_infinity) ? (sign + (sign >> 15))
                                                    : sign;
    }
 
    template <std::float_round_style R, bool I>
    HALF_CONSTEXPR_NOERR unsigned int rounded(unsigned int value, int g, int s)
    {
#if HALF_ERRHANDLING
        value += (R == std::round_to_nearest)       ? (g & (s | value))
            : (R == std::round_toward_infinity)     ? (~(value >> 15) & (g | s))
            : (R == std::round_toward_neg_infinity) ? ((value >> 15) & (g | s))
                                                    : 0;
        if ((value & 0x7C00) == 0x7C00)
            raise(FE_OVERFLOW);
        else if (value & 0x7C00)
            raise(FE_INEXACT, I || (g | s) != 0);
        else
            raise(FE_UNDERFLOW, !(HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT) || I || (g | s) != 0);
        return value;
#else
        return (R == std::round_to_nearest)         ? (value + (g & (s | value)))
            : (R == std::round_toward_infinity)     ? (value + (~(value >> 15) & (g | s)))
            : (R == std::round_toward_neg_infinity) ? (value + ((value >> 15) & (g | s)))
                                                    : value;
#endif
    }
 
    template <std::float_round_style R, bool E, bool I> unsigned int integral(unsigned int value)
    {
        unsigned int abs = value & 0x7FFF;
        if (abs < 0x3C00) {
            raise(FE_INEXACT, I);
            return ((R == std::round_to_nearest)               ? (0x3C00 & -static_cast<unsigned>(abs >= (0x3800 + E)))
                           : (R == std::round_toward_infinity) ? (0x3C00 & -(~(value >> 15) & (abs != 0)))
                           : (R == std::round_toward_neg_infinity) ? (0x3C00 & -static_cast<unsigned>(value > 0x8000))
                                                                   : 0) |
                (value & 0x8000);
        }
        if (abs >= 0x6400)
            return (abs > 0x7C00) ? signal(value) : value;
        unsigned int exp = 25 - (abs >> 10), mask = (1 << exp) - 1;
        raise(FE_INEXACT, I && (value & mask));
        return (((R == std::round_to_nearest)                   ? ((1 << (exp - 1)) - (~(value >> exp) & E))
                        : (R == std::round_toward_infinity)     ? (mask & ((value >> 15) - 1))
                        : (R == std::round_toward_neg_infinity) ? (mask & -(value >> 15))
                                                                : 0) +
                   value) &
            ~mask;
    }
 
    template <std::float_round_style R, unsigned int F, bool S, bool N, bool I>
    unsigned int fixed2half(uint32 m, int exp = 14, unsigned int sign = 0, int s = 0)
    {
        if (S) {
            uint32 msign = sign_mask(m);
            m = (m ^ msign) - msign;
            sign = msign & 0x8000;
        }
        if (N)
            for (; m < (static_cast<uint32>(1) << F) && exp; m <<= 1, --exp)
                ;
        else if (exp < 0)
            return rounded<R, I>(sign + (m >> (F - 10 - exp)), (m >> (F - 11 - exp)) & 1,
                s | ((m & ((static_cast<uint32>(1) << (F - 11 - exp)) - 1)) != 0));
        return rounded<R, I>(sign + (exp << 10) + (m >> (F - 10)), (m >> (F - 11)) & 1,
            s | ((m & ((static_cast<uint32>(1) << (F - 11)) - 1)) != 0));
    }
 
    template <std::float_round_style R> unsigned int float2half_impl(float value, true_type)
    {
#if HALF_ENABLE_F16C_INTRINSICS
        return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_set_ss(value),
            (R == std::round_to_nearest)                ? _MM_FROUND_TO_NEAREST_INT
                : (R == std::round_toward_zero)         ? _MM_FROUND_TO_ZERO
                : (R == std::round_toward_infinity)     ? _MM_FROUND_TO_POS_INF
                : (R == std::round_toward_neg_infinity) ? _MM_FROUND_TO_NEG_INF
                                                        : _MM_FROUND_CUR_DIRECTION));
#else
        bits<float>::type fbits;
        std::memcpy(&fbits, &value, sizeof(float));
#if 1
        unsigned int sign = (fbits >> 16) & 0x8000;
        fbits &= 0x7FFFFFFF;
        if (fbits >= 0x7F800000)
            return sign | 0x7C00 | ((fbits > 0x7F800000) ? (0x200 | ((fbits >> 13) & 0x3FF)) : 0);
        if (fbits >= 0x47800000)
            return overflow<R>(sign);
        if (fbits >= 0x38800000)
            return rounded<R, false>(sign | (((fbits >> 23) - 112) << 10) | ((fbits >> 13) & 0x3FF), (fbits >> 12) & 1,
                (fbits & 0xFFF) != 0);
        if (fbits >= 0x33000000) {
            int i = 125 - (fbits >> 23);
            fbits = (fbits & 0x7FFFFF) | 0x800000;
            return rounded<R, false>(
                sign | (fbits >> (i + 1)), (fbits >> i) & 1, (fbits & ((static_cast<uint32>(1) << i) - 1)) != 0);
        }
        if (fbits != 0)
            return underflow<R>(sign);
        return sign;
#else
        static const uint16 base_table[512] = { 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
            0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, 0x0200,
            0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400,
            0x3800, 0x3C00, 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800,
            0x6C00, 0x7000, 0x7400, 0x7800, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF,
            0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7C00,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
            0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001,
            0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000,
            0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 0xC000, 0xC400,
            0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF,
            0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFC00 };
        static const unsigned char shift_table[256] = { 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
            25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
            25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
            25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
            25, 25, 25, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
            13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24,
            24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
            24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
            24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
            24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
        int sexp = fbits >> 23, exp = sexp & 0xFF, i = shift_table[exp];
        fbits &= 0x7FFFFF;
        uint32 m = (fbits | ((exp != 0) << 23)) & -static_cast<uint32>(exp != 0xFF);
        return rounded<R, false>(
            base_table[sexp] + (fbits >> i), (m >> (i - 1)) & 1, (((static_cast<uint32>(1) << (i - 1)) - 1) & m) != 0);
#endif
#endif
    }
 
    template <std::float_round_style R> unsigned int float2half_impl(double value, true_type)
    {
#if HALF_ENABLE_F16C_INTRINSICS
        if (R == std::round_indeterminate)
            return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_cvtpd_ps(_mm_set_sd(value)), _MM_FROUND_CUR_DIRECTION));
#endif
        bits<double>::type dbits;
        std::memcpy(&dbits, &value, sizeof(double));
        uint32 hi = dbits >> 32, lo = dbits & 0xFFFFFFFF;
        unsigned int sign = (hi >> 16) & 0x8000;
        hi &= 0x7FFFFFFF;
        if (hi >= 0x7FF00000)
            return sign | 0x7C00 | ((dbits & 0xFFFFFFFFFFFFF) ? (0x200 | ((hi >> 10) & 0x3FF)) : 0);
        if (hi >= 0x40F00000)
            return overflow<R>(sign);
        if (hi >= 0x3F100000)
            return rounded<R, false>(
                sign | (((hi >> 20) - 1008) << 10) | ((hi >> 10) & 0x3FF), (hi >> 9) & 1, ((hi & 0x1FF) | lo) != 0);
        if (hi >= 0x3E600000) {
            int i = 1018 - (hi >> 20);
            hi = (hi & 0xFFFFF) | 0x100000;
            return rounded<R, false>(
                sign | (hi >> (i + 1)), (hi >> i) & 1, ((hi & ((static_cast<uint32>(1) << i) - 1)) | lo) != 0);
        }
        if ((hi | lo) != 0)
            return underflow<R>(sign);
        return sign;
    }
 
    template <std::float_round_style R, typename T> unsigned int float2half_impl(T value, ...)
    {
        unsigned int hbits = static_cast<unsigned>(builtin_signbit(value)) << 15;
        if (value == T())
            return hbits;
        if (builtin_isnan(value))
            return hbits | 0x7FFF;
        if (builtin_isinf(value))
            return hbits | 0x7C00;
        int exp;
        std::frexp(value, &exp);
        if (exp > 16)
            return overflow<R>(hbits);
        if (exp < -13)
            value = std::ldexp(value, 25);
        else {
            value = std::ldexp(value, 12 - exp);
            hbits |= ((exp + 13) << 10);
        }
        T ival, frac = std::modf(value, &ival);
        int m = std::abs(static_cast<int>(ival));
        return rounded<R, false>(hbits + (m >> 1), m & 1, frac != T());
    }
 
    template <std::float_round_style R, typename T> unsigned int float2half(T value)
    {
        return float2half_impl<R>(
            value, bool_type < std::numeric_limits<T>::is_iec559 && sizeof(typename bits<T>::type) == sizeof(T) > ());
    }
 
    template <std::float_round_style R, typename T> unsigned int int2half(T value)
    {
        unsigned int bits = static_cast<unsigned>(value < 0) << 15;
        if (!value)
            return bits;
        if (bits)
            value = -value;
        if (value > 0xFFFF)
            return overflow<R>(bits);
        unsigned int m = static_cast<unsigned int>(value), exp = 24;
        for (; m < 0x400; m <<= 1, --exp)
            ;
        for (; m > 0x7FF; m >>= 1, ++exp)
            ;
        bits |= (exp << 10) + m;
        return (exp > 24) ? rounded<R, false>(bits, (value >> (exp - 25)) & 1, (((1 << (exp - 25)) - 1) & value) != 0)
                          : bits;
    }
 
    inline float half2float_impl(unsigned int value, float, true_type)
    {
#if HALF_ENABLE_F16C_INTRINSICS
        return _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(value)));
#else
#if 0
            bits<float>::type fbits = static_cast<bits<float>::type>(value&0x8000) << 16;
            int abs = value & 0x7FFF;
            if(abs)
            {
                fbits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);
                for(; abs<0x400; abs<<=1,fbits-=0x800000) ;
                fbits += static_cast<bits<float>::type>(abs) << 13;
            }
#else
        static const bits<float>::type mantissa_table[2048] = { 0x00000000, 0x33800000, 0x34000000, 0x34400000,
            0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000,
            0x35500000, 0x35600000, 0x35700000, 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000,
            0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000,
            0x35F80000, 0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000,
            0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 0x36400000,
            0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000,
            0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 0x36800000, 0x36820000, 0x36840000,
            0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000,
            0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000,
            0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000,
            0x36BC0000, 0x36BE0000, 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000,
            0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
            0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000,
            0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, 0x37000000, 0x37010000,
            0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000,
            0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 0x37100000, 0x37110000, 0x37120000, 0x37130000,
            0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000,
            0x371D0000, 0x371E0000, 0x371F0000, 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000,
            0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000,
            0x372F0000, 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000,
            0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, 0x37400000,
            0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000,
            0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 0x37500000, 0x37510000, 0x37520000,
            0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000,
            0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000,
            0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000,
            0x376E0000, 0x376F0000, 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000,
            0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
            0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000,
            0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 0x37880000, 0x37888000,
            0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000,
            0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, 0x37900000, 0x37908000, 0x37910000, 0x37918000,
            0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000,
            0x37968000, 0x37970000, 0x37978000, 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000,
            0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000,
            0x379F8000, 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000,
            0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, 0x37A80000,
            0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000,
            0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 0x37B00000, 0x37B08000, 0x37B10000,
            0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000,
            0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000,
            0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000,
            0x37BF0000, 0x37BF8000, 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000,
            0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
            0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000,
            0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, 0x37D00000, 0x37D08000,
            0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000,
            0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000,
            0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000,
            0x37DE8000, 0x37DF0000, 0x37DF8000, 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000,
            0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000,
            0x37E78000, 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000,
            0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, 0x37F00000,
            0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000,
            0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 0x37F80000, 0x37F88000, 0x37F90000,
            0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000,
            0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000,
            0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000,
            0x38038000, 0x3803C000, 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000,
            0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
            0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000,
            0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, 0x380C0000, 0x380C4000,
            0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000,
            0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, 0x38100000, 0x38104000, 0x38108000, 0x3810C000,
            0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000,
            0x38134000, 0x38138000, 0x3813C000, 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000,
            0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000,
            0x3817C000, 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000,
            0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, 0x381C0000,
            0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000,
            0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, 0x38200000, 0x38204000, 0x38208000,
            0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000,
            0x38230000, 0x38234000, 0x38238000, 0x3823C000, 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000,
            0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000,
            0x38278000, 0x3827C000, 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000,
            0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
            0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000,
            0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 0x38300000, 0x38304000,
            0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000,
            0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, 0x38340000, 0x38344000, 0x38348000, 0x3834C000,
            0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000,
            0x38374000, 0x38378000, 0x3837C000, 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000,
            0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000,
            0x383BC000, 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000,
            0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, 0x38400000,
            0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000,
            0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 0x38440000, 0x38444000, 0x38448000,
            0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000,
            0x38470000, 0x38474000, 0x38478000, 0x3847C000, 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000,
            0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000,
            0x384B8000, 0x384BC000, 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000,
            0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000,
            0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000,
            0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, 0x38540000, 0x38544000,
            0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000,
            0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, 0x38580000, 0x38584000, 0x38588000, 0x3858C000,
            0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000,
            0x385B4000, 0x385B8000, 0x385BC000, 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000,
            0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000,
            0x385FC000, 0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000,
            0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, 0x38640000,
            0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000,
            0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 0x38680000, 0x38684000, 0x38688000,
            0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000,
            0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000,
            0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000,
            0x386F8000, 0x386FC000, 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000,
            0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000,
            0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000,
            0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, 0x38780000, 0x38784000,
            0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000,
            0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000,
            0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000,
            0x387F4000, 0x387F8000, 0x387FC000, 0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000,
            0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000,
            0x3801E000, 0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000,
            0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, 0x38040000,
            0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000,
            0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, 0x38060000, 0x38062000, 0x38064000,
            0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000,
            0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, 0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000,
            0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000,
            0x3809C000, 0x3809E000, 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000,
            0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000,
            0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000,
            0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, 0x380E0000, 0x380E2000,
            0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000,
            0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, 0x38100000, 0x38102000, 0x38104000, 0x38106000,
            0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000,
            0x3811A000, 0x3811C000, 0x3811E000, 0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000,
            0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000,
            0x3813E000, 0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000,
            0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, 0x38160000,
            0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000,
            0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 0x38180000, 0x38182000, 0x38184000,
            0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000,
            0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000,
            0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000,
            0x381BC000, 0x381BE000, 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000,
            0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000,
            0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000,
            0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, 0x38200000, 0x38202000,
            0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000,
            0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, 0x38220000, 0x38222000, 0x38224000, 0x38226000,
            0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000,
            0x3823A000, 0x3823C000, 0x3823E000, 0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000,
            0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000,
            0x3825E000, 0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000,
            0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 0x38280000,
            0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000,
            0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, 0x382A0000, 0x382A2000, 0x382A4000,
            0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000,
            0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000,
            0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000,
            0x382DC000, 0x382DE000, 0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000,
            0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000,
            0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000,
            0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 0x38320000, 0x38322000,
            0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000,
            0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 0x38340000, 0x38342000, 0x38344000, 0x38346000,
            0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000,
            0x3835A000, 0x3835C000, 0x3835E000, 0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000,
            0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000,
            0x3837E000, 0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000,
            0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 0x383A0000,
            0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000,
            0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 0x383C0000, 0x383C2000, 0x383C4000,
            0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000,
            0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000,
            0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000,
            0x383FC000, 0x383FE000, 0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000,
            0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000,
            0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000,
            0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, 0x38440000, 0x38442000,
            0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000,
            0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 0x38460000, 0x38462000, 0x38464000, 0x38466000,
            0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000,
            0x3847A000, 0x3847C000, 0x3847E000, 0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000,
            0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000,
            0x3849E000, 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000,
            0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, 0x384C0000,
            0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000,
            0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, 0x384E0000, 0x384E2000, 0x384E4000,
            0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000,
            0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000,
            0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000,
            0x3851C000, 0x3851E000, 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000,
            0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000,
            0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000,
            0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 0x38560000, 0x38562000,
            0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000,
            0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 0x38580000, 0x38582000, 0x38584000, 0x38586000,
            0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000,
            0x3859A000, 0x3859C000, 0x3859E000, 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000,
            0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000,
            0x385BE000, 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000,
            0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 0x385E0000,
            0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000,
            0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, 0x38600000, 0x38602000, 0x38604000,
            0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000,
            0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, 0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000,
            0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000,
            0x3863C000, 0x3863E000, 0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000,
            0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
            0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000,
            0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, 0x38680000, 0x38682000,
            0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000,
            0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000,
            0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000,
            0x386BA000, 0x386BC000, 0x386BE000, 0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000,
            0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000,
            0x386DE000, 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000,
            0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, 0x38700000,
            0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000,
            0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 0x38720000, 0x38722000, 0x38724000,
            0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000,
            0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000,
            0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000,
            0x3875C000, 0x3875E000, 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000,
            0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
            0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000,
            0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 0x387A0000, 0x387A2000,
            0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000,
            0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000,
            0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000,
            0x387DA000, 0x387DC000, 0x387DE000, 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000,
            0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000,
            0x387FE000 };
        static const bits<float>::type exponent_table[64] = { 0x00000000, 0x00800000, 0x01000000, 0x01800000,
            0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000,
            0x06800000, 0x07000000, 0x07800000, 0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000,
            0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000,
            0x47800000, 0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000,
            0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, 0x88000000,
            0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000,
            0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
        static const unsigned short offset_table[64] = { 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
            1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
            1024, 1024, 1024, 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
            1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
        bits<float>::type fbits =
            mantissa_table[offset_table[value >> 10] + (value & 0x3FF)] + exponent_table[value >> 10];
#endif
        float out;
        std::memcpy(&out, &fbits, sizeof(float));
        return out;
#endif
    }
 
    inline double half2float_impl(unsigned int value, double, true_type)
    {
#if HALF_ENABLE_F16C_INTRINSICS
        return _mm_cvtsd_f64(_mm_cvtps_pd(_mm_cvtph_ps(_mm_cvtsi32_si128(value))));
#else
        uint32 hi = static_cast<uint32>(value & 0x8000) << 16;
        unsigned int abs = value & 0x7FFF;
        if (abs) {
            hi |= 0x3F000000 << static_cast<unsigned>(abs >= 0x7C00);
            for (; abs < 0x400; abs <<= 1, hi -= 0x100000)
                ;
            hi += static_cast<uint32>(abs) << 10;
        }
        bits<double>::type dbits = static_cast<bits<double>::type>(hi) << 32;
        double out;
        std::memcpy(&out, &dbits, sizeof(double));
        return out;
#endif
    }
 
    template <typename T> T half2float_impl(unsigned int value, T, ...)
    {
        T out;
        unsigned int abs = value & 0x7FFF;
        if (abs > 0x7C00)
            out = (std::numeric_limits<T>::has_signaling_NaN && !(abs & 0x200))
                ? std::numeric_limits<T>::signaling_NaN()
                : std::numeric_limits<T>::has_quiet_NaN ? std::numeric_limits<T>::quiet_NaN()
                                                        : T();
        else if (abs == 0x7C00)
            out = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity()
                                                       : std::numeric_limits<T>::max();
        else if (abs > 0x3FF)
            out = std::ldexp(static_cast<T>((abs & 0x3FF) | 0x400), (abs >> 10) - 25);
        else
            out = std::ldexp(static_cast<T>(abs), -24);
        return (value & 0x8000) ? -out : out;
    }
 
    template <typename T> T half2float(unsigned int value)
    {
        return half2float_impl(value, T(),
            bool_type < std::numeric_limits<T>::is_iec559 && sizeof(typename bits<T>::type) == sizeof(T) > ());
    }
 
    template <std::float_round_style R, bool E, bool I, typename T> T half2int(unsigned int value)
    {
        unsigned int abs = value & 0x7FFF;
        if (abs >= 0x7C00) {
            raise(FE_INVALID);
            return (value & 0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
        }
        if (abs < 0x3800) {
            raise(FE_INEXACT, I);
            return (R == std::round_toward_infinity)    ? T(~(value >> 15) & (abs != 0))
                : (R == std::round_toward_neg_infinity) ? -T(value > 0x8000)
                                                        : T();
        }
        int exp = 25 - (abs >> 10);
        unsigned int m = (value & 0x3FF) | 0x400;
        int32 i = static_cast<int32>((exp <= 0)
                ? (m << -exp)
                : ((m +
                       ((R == std::round_to_nearest)                   ? ((1 << (exp - 1)) - (~(m >> exp) & E))
                               : (R == std::round_toward_infinity)     ? (((1 << exp) - 1) & ((value >> 15) - 1))
                               : (R == std::round_toward_neg_infinity) ? (((1 << exp) - 1) & -(value >> 15))
                                                                       : 0)) >>
                      exp));
        if ((!std::numeric_limits<T>::is_signed && (value & 0x8000)) ||
            (std::numeric_limits<T>::digits < 16 &&
                ((value & 0x8000) ? (-i < std::numeric_limits<T>::min()) : (i > std::numeric_limits<T>::max()))))
            raise(FE_INVALID);
        else if (I && exp > 0 && (m & ((1 << exp) - 1)))
            raise(FE_INEXACT);
        return static_cast<T>((value & 0x8000) ? -i : i);
    }
 
 
    template <std::float_round_style R> uint32 mulhi(uint32 x, uint32 y)
    {
        uint32 xy = (x >> 16) * (y & 0xFFFF), yx = (x & 0xFFFF) * (y >> 16),
               c = (xy & 0xFFFF) + (yx & 0xFFFF) + (((x & 0xFFFF) * (y & 0xFFFF)) >> 16);
        return (x >> 16) * (y >> 16) + (xy >> 16) + (yx >> 16) + (c >> 16) +
            ((R == std::round_to_nearest)               ? ((c >> 15) & 1)
                    : (R == std::round_toward_infinity) ? ((c & 0xFFFF) != 0)
                                                        : 0);
    }
 
    inline uint32 multiply64(uint32 x, uint32 y)
    {
#if HALF_ENABLE_CPP11_LONG_LONG
        return static_cast<uint32>(
            (static_cast<unsigned long long>(x) * static_cast<unsigned long long>(y) + 0x80000000) >> 32);
#else
        return mulhi<std::round_to_nearest>(x, y);
#endif
    }
 
    inline uint32 divide64(uint32 x, uint32 y, int& s)
    {
#if HALF_ENABLE_CPP11_LONG_LONG
        unsigned long long xx = static_cast<unsigned long long>(x) << 32;
        return s = (xx % y != 0), static_cast<uint32>(xx / y);
#else
        y >>= 1;
        uint32 rem = x, div = 0;
        for (unsigned int i = 0; i < 32; ++i) {
            div <<= 1;
            if (rem >= y) {
                rem -= y;
                div |= 1;
            }
            rem <<= 1;
        }
        return s = rem > 1, div;
#endif
    }
 
    template <bool Q, bool R> unsigned int mod(unsigned int x, unsigned int y, int* quo = NULL)
    {
        unsigned int q = 0;
        if (x > y) {
            int absx = x, absy = y, expx = 0, expy = 0;
            for (; absx < 0x400; absx <<= 1, --expx)
                ;
            for (; absy < 0x400; absy <<= 1, --expy)
                ;
            expx += absx >> 10;
            expy += absy >> 10;
            int mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400;
            for (int d = expx - expy; d; --d) {
                if (!Q && mx == my)
                    return 0;
                if (mx >= my) {
                    mx -= my;
                    q += Q;
                }
                mx <<= 1;
                q <<= static_cast<int>(Q);
            }
            if (!Q && mx == my)
                return 0;
            if (mx >= my) {
                mx -= my;
                ++q;
            }
            if (Q) {
                q &= (1 << (std::numeric_limits<int>::digits - 1)) - 1;
                if (!mx)
                    return *quo = q, 0;
            }
            for (; mx < 0x400; mx <<= 1, --expy)
                ;
            x = (expy > 0) ? ((expy << 10) | (mx & 0x3FF)) : (mx >> (1 - expy));
        }
        if (R) {
            unsigned int a, b;
            if (y < 0x800) {
                a = (x < 0x400) ? (x << 1) : (x + 0x400);
                b = y;
            } else {
                a = x;
                b = y - 0x400;
            }
            if (a > b || (a == b && (q & 1))) {
                int exp = (y >> 10) + (y <= 0x3FF), d = exp - (x >> 10) - (x <= 0x3FF);
                int m = (((y & 0x3FF) | ((y > 0x3FF) << 10)) << 1) - (((x & 0x3FF) | ((x > 0x3FF) << 10)) << (1 - d));
                for (; m < 0x800 && exp > 1; m <<= 1, --exp)
                    ;
                x = 0x8000 + ((exp - 1) << 10) + (m >> 1);
                q += Q;
            }
        }
        if (Q)
            *quo = q;
        return x;
    }
 
    template <unsigned int F> uint32 sqrt(uint32& r, int& exp)
    {
        int i = exp & 1;
        r <<= i;
        exp = (exp - i) / 2;
        uint32 m = 0;
        for (uint32 bit = static_cast<uint32>(1) << F; bit; bit >>= 2) {
            if (r < m + bit)
                m >>= 1;
            else {
                r -= m + bit;
                m = (m >> 1) + bit;
            }
        }
        return m;
    }
 
    inline uint32 exp2(uint32 m, unsigned int n = 32)
    {
        static const uint32 logs[] = { 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD,
            0x02DCF2D1, 0x016FE50B, 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3,
            0x00017153, 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
            0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
        if (!m)
            return 0x80000000;
        uint32 mx = 0x80000000, my = 0;
        for (unsigned int i = 1; i < n; ++i) {
            uint32 mz = my + logs[i];
            if (mz <= m) {
                my = mz;
                mx += mx >> i;
            }
        }
        return mx;
    }
 
    inline uint32 log2(uint32 m, unsigned int n = 32)
    {
        static const uint32 logs[] = { 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD,
            0x02DCF2D1, 0x016FE50B, 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3,
            0x00017153, 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
            0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
        if (m == 0x40000000)
            return 0;
        uint32 mx = 0x40000000, my = 0;
        for (unsigned int i = 1; i < n; ++i) {
            uint32 mz = mx + (mx >> i);
            if (mz <= m) {
                mx = mz;
                my += logs[i];
            }
        }
        return my;
    }
 
    inline std::pair<uint32, uint32> sincos(uint32 mz, unsigned int n = 31)
    {
        static const uint32 angles[] = { 0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C,
            0x00FFFAAB, 0x007FFF55, 0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000,
            0x00008000, 0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,
            0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };
        uint32 mx = 0x26DD3B6A, my = 0;
        for (unsigned int i = 0; i < n; ++i) {
            uint32 sign = sign_mask(mz);
            uint32 tx = mx - (arithmetic_shift(my, i) ^ sign) + sign;
            uint32 ty = my + (arithmetic_shift(mx, i) ^ sign) - sign;
            mx = tx;
            my = ty;
            mz -= (angles[i] ^ sign) - sign;
        }
        return std::make_pair(my, mx);
    }
 
    inline uint32 atan2(uint32 my, uint32 mx, unsigned int n = 31)
    {
        static const uint32 angles[] = { 0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C,
            0x00FFFAAB, 0x007FFF55, 0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000,
            0x00008000, 0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,
            0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };
        uint32 mz = 0;
        for (unsigned int i = 0; i < n; ++i) {
            uint32 sign = sign_mask(my);
            uint32 tx = mx + (arithmetic_shift(my, i) ^ sign) - sign;
            uint32 ty = my - (arithmetic_shift(mx, i) ^ sign) + sign;
            mx = tx;
            my = ty;
            mz += (angles[i] ^ sign) - sign;
        }
        return mz;
    }
 
    inline uint32 angle_arg(unsigned int abs, int& k)
    {
        uint32 m = (abs & 0x3FF) | ((abs > 0x3FF) << 10);
        int exp = (abs >> 10) + (abs <= 0x3FF) - 15;
        if (abs < 0x3A48)
            return k = 0, m << (exp + 20);
#if HALF_ENABLE_CPP11_LONG_LONG
        unsigned long long y = m * 0xA2F9836E4E442, mask = (1ULL << (62 - exp)) - 1, yi = (y + (mask >> 1)) & ~mask,
                           f = y - yi;
        uint32 sign = -static_cast<uint32>(f >> 63);
        k = static_cast<int>(yi >> (62 - exp));
        return (multiply64(static_cast<uint32>((sign ? -f : f) >> (31 - exp)), 0xC90FDAA2) ^ sign) - sign;
#else
        uint32 yh = m * 0xA2F98 + mulhi<std::round_toward_zero>(m, 0x36E4E442), yl = (m * 0x36E4E442) & 0xFFFFFFFF;
        uint32 mask = (static_cast<uint32>(1) << (30 - exp)) - 1, yi = (yh + (mask >> 1)) & ~mask,
               sign = -static_cast<uint32>(yi > yh);
        k = static_cast<int>(yi >> (30 - exp));
        uint32 fh = (yh ^ sign) + (yi ^ ~sign) - ~sign, fl = (yl ^ sign) - sign;
        return (multiply64((exp > -1) ? (((fh << (1 + exp)) & 0xFFFFFFFF) | ((fl & 0xFFFFFFFF) >> (31 - exp))) : fh,
                    0xC90FDAA2) ^
                   sign) -
            sign;
#endif
    }
 
    inline std::pair<uint32, uint32> atan2_args(unsigned int abs)
    {
        int exp = -15;
        for (; abs < 0x400; abs <<= 1, --exp)
            ;
        exp += abs >> 10;
        uint32 my = ((abs & 0x3FF) | 0x400) << 5, r = my * my;
        int rexp = 2 * exp;
        r = 0x40000000 - ((rexp > -31) ? ((r >> -rexp) | ((r & ((static_cast<uint32>(1) << -rexp) - 1)) != 0)) : 1);
        for (rexp = 0; r < 0x40000000; r <<= 1, --rexp)
            ;
        uint32 mx = sqrt<30>(r, rexp);
        int d = exp - rexp;
        if (d < 0)
            return std::make_pair((d < -14) ? ((my >> (-d - 14)) + ((my >> (-d - 15)) & 1)) : (my << (14 + d)),
                (mx << 14) + (r << 13) / mx);
        if (d > 0)
            return std::make_pair(my << 14,
                (d > 14) ? ((mx >> (d - 14)) + ((mx >> (d - 15)) & 1))
                         : ((d == 14) ? mx : ((mx << (14 - d)) + (r << (13 - d)) / mx)));
        return std::make_pair(my << 13, (mx << 13) + (r << 12) / mx);
    }
 
    inline std::pair<uint32, uint32> hyperbolic_args(unsigned int abs, int& exp, unsigned int n = 32)
    {
        uint32 mx = detail::multiply64(static_cast<uint32>((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, 0xB8AA3B29),
               my;
        int e = (abs >> 10) + (abs <= 0x3FF);
        if (e < 14) {
            exp = 0;
            mx >>= 14 - e;
        } else {
            exp = mx >> (45 - e);
            mx = (mx << (e - 14)) & 0x7FFFFFFF;
        }
        mx = exp2(mx, n);
        int d = exp << 1, s;
        if (mx > 0x80000000) {
            my = divide64(0x80000000, mx, s);
            my |= s;
            ++d;
        } else
            my = mx;
        return std::make_pair(mx, (d < 31) ? ((my >> d) | ((my & ((static_cast<uint32>(1) << d) - 1)) != 0)) : 1);
    }
 
    template <std::float_round_style R>
    unsigned int exp2_post(uint32 m, int exp, bool esign, unsigned int sign = 0, unsigned int n = 32)
    {
        if (esign) {
            exp = -exp - (m != 0);
            if (exp < -25)
                return underflow<R>(sign);
            else if (exp == -25)
                return rounded<R, false>(sign, 1, m != 0);
        } else if (exp > 15)
            return overflow<R>(sign);
        if (!m)
            return sign | (((exp += 15) > 0) ? (exp << 10) : check_underflow(0x200 >> -exp));
        m = exp2(m, n);
        int s = 0;
        if (esign)
            m = divide64(0x80000000, m, s);
        return fixed2half<R, 31, false, false, true>(m, exp + 14, sign, s);
    }
 
    template <std::float_round_style R, uint32 L>
    unsigned int log2_post(uint32 m, int ilog, int exp, unsigned int sign = 0)
    {
        uint32 msign = sign_mask(ilog);
        m = (((static_cast<uint32>(ilog) << 27) + (m >> 4)) ^ msign) - msign;
        if (!m)
            return 0;
        for (; m < 0x80000000; m <<= 1, --exp)
            ;
        int i = m >= L, s;
        exp += i;
        m >>= 1 + i;
        sign ^= msign & 0x8000;
        if (exp < -11)
            return underflow<R>(sign);
        m = divide64(m, L, s);
        return fixed2half<R, 30, false, false, true>(m, exp, sign, 1);
    }
 
    template <std::float_round_style R> unsigned int hypot_post(uint32 r, int exp)
    {
        int i = r >> 31;
        if ((exp += i) > 46)
            return overflow<R>();
        if (exp < -34)
            return underflow<R>();
        r = (r >> i) | (r & i);
        uint32 m = sqrt<30>(r, exp += 15);
        return fixed2half<R, 15, false, false, false>(m, exp - 1, 0, r != 0);
    }
 
    template <std::float_round_style R> unsigned int tangent_post(uint32 my, uint32 mx, int exp, unsigned int sign = 0)
    {
        int i = my >= mx, s;
        exp += i;
        if (exp > 29)
            return overflow<R>(sign);
        if (exp < -11)
            return underflow<R>(sign);
        uint32 m = divide64(my >> (i + 1), mx, s);
        return fixed2half<R, 30, false, false, true>(m, exp, sign, s);
    }
 
    template <std::float_round_style R, bool S> unsigned int area(unsigned int arg)
    {
        int abs = arg & 0x7FFF, expx = (abs >> 10) + (abs <= 0x3FF) - 15, expy = -15, ilog, i;
        uint32 mx = static_cast<uint32>((abs & 0x3FF) | ((abs > 0x3FF) << 10)) << 20, my, r;
        for (; abs < 0x400; abs <<= 1, --expy)
            ;
        expy += abs >> 10;
        r = ((abs & 0x3FF) | 0x400) << 5;
        r *= r;
        i = r >> 31;
        expy = 2 * expy + i;
        r >>= i;
        if (S) {
            if (expy < 0) {
                r = 0x40000000 +
                    ((expy > -30) ? ((r >> -expy) | ((r & ((static_cast<uint32>(1) << -expy) - 1)) != 0)) : 1);
                expy = 0;
            } else {
                r += 0x40000000 >> expy;
                i = r >> 31;
                r = (r >> i) | (r & i);
                expy += i;
            }
        } else {
            r -= 0x40000000 >> expy;
            for (; r < 0x40000000; r <<= 1, --expy)
                ;
        }
        my = sqrt<30>(r, expy);
        my = (my << 15) + (r << 14) / my;
        if (S) {
            mx >>= expy - expx;
            ilog = expy;
        } else {
            my >>= expx - expy;
            ilog = expx;
        }
        my += mx;
        i = my >> 31;
        static const int G = S && (R == std::round_to_nearest);
        return log2_post<R, 0xB8AA3B2A>(
            log2(my >> i, 26 + S + G) + (G << 3), ilog + i, 17, arg & (static_cast<unsigned>(S) << 15));
    }
 
    struct f31 {
        HALF_CONSTEXPR f31(uint32 mant, int e)
            : m(mant)
            , exp(e)
        {
        }
 
        f31(unsigned int abs)
            : exp(-15)
        {
            for (; abs < 0x400; abs <<= 1, --exp)
                ;
            m = static_cast<uint32>((abs & 0x3FF) | 0x400) << 21;
            exp += (abs >> 10);
        }
 
        friend f31 operator+(f31 a, f31 b)
        {
            if (b.exp > a.exp)
                std::swap(a, b);
            int d = a.exp - b.exp;
            uint32 m = a.m + ((d < 32) ? (b.m >> d) : 0);
            int i = (m & 0xFFFFFFFF) < a.m;
            return f31(((m + i) >> i) | 0x80000000, a.exp + i);
        }
 
        friend f31 operator-(f31 a, f31 b)
        {
            int d = a.exp - b.exp, exp = a.exp;
            uint32 m = a.m - ((d < 32) ? (b.m >> d) : 0);
            if (!m)
                return f31(0, -32);
            for (; m < 0x80000000; m <<= 1, --exp)
                ;
            return f31(m, exp);
        }
 
        friend f31 operator*(f31 a, f31 b)
        {
            uint32 m = multiply64(a.m, b.m);
            int i = m >> 31;
            return f31(m << (1 - i), a.exp + b.exp + i);
        }
 
        friend f31 operator/(f31 a, f31 b)
        {
            int i = a.m >= b.m, s;
            uint32 m = divide64((a.m + i) >> i, b.m, s);
            return f31(m, a.exp - b.exp + i - 1);
        }
 
        uint32 m; 
        int exp; 
    };
 
    template <std::float_round_style R, bool C> unsigned int erf(unsigned int arg)
    {
        unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
        f31 x(abs), x2 = x * x * f31(0xB8AA3B29, 0),
                    t = f31(0x80000000, 0) / (f31(0x80000000, 0) + f31(0xA7BA054A, -2) * x), t2 = t * t;
        f31 e = ((f31(0x87DC2213, 0) * t2 + f31(0xB5F0E2AE, 0)) * t2 + f31(0x82790637, -2) -
                    (f31(0xBA00E2B8, 0) * t2 + f31(0x91A98E62, -2)) * t) *
            t /
            ((x2.exp < 0) ? f31(exp2((x2.exp > -32) ? (x2.m >> -x2.exp) : 0, 30), 0)
                          : f31(exp2((x2.m << x2.exp) & 0x7FFFFFFF, 22), x2.m >> (31 - x2.exp)));
        return (!C || sign)
            ? fixed2half<R, 31, false, true, true>(0x80000000 - (e.m >> (C - e.exp)), 14 + C, sign & (C - 1U))
            : (e.exp < -25) ? underflow<R>()
                            : fixed2half<R, 30, false, false, true>(e.m >> 1, e.exp + 14, 0, e.m & 1);
    }
 
    template <std::float_round_style R, bool L> unsigned int gamma(unsigned int arg)
    {
        /*          static const double p[] ={ 2.50662827563479526904, 225.525584619175212544,
           -268.295973841304927459, 80.9030806934622512966, -5.00757863970517583837, 0.0114684895434781459556 }; double
           t = arg + 4.65, s = p[0]; for(unsigned int i=0; i<5; ++i) s += p[i+1] / (arg+i); return std::log(s) +
           (arg-0.5)*std::log(t) - t;
        */
        static const f31 pi(0xC90FDAA2, 1), lbe(0xB8AA3B29, 0);
        unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
        bool bsign = sign != 0;
        f31 z(abs), x = sign ? (z + f31(0x80000000, 0)) : z, t = x + f31(0x94CCCCCD, 2),
                    s = f31(0xA06C9901, 1) + f31(0xBBE654E2, -7) / (x + f31(0x80000000, 2)) +
            f31(0xA1CE6098, 6) / (x + f31(0x80000000, 1)) + f31(0xE1868CB7, 7) / x -
            f31(0x8625E279, 8) / (x + f31(0x80000000, 0)) - f31(0xA03E158F, 2) / (x + f31(0xC0000000, 1));
        int i = (s.exp >= 2) + (s.exp >= 4) + (s.exp >= 8) + (s.exp >= 16);
        s = f31((static_cast<uint32>(s.exp) << (31 - i)) + (log2(s.m >> 1, 28) >> i), i) / lbe;
        if (x.exp != -1 || x.m != 0x80000000) {
            i = (t.exp >= 2) + (t.exp >= 4) + (t.exp >= 8);
            f31 l = f31((static_cast<uint32>(t.exp) << (31 - i)) + (log2(t.m >> 1, 30) >> i), i) / lbe;
            s = (x.exp < -1) ? (s - (f31(0x80000000, -1) - x) * l) : (s + (x - f31(0x80000000, -1)) * l);
        }
        s = x.exp ? (s - t) : (t - s);
        if (bsign) {
            if (z.exp >= 0) {
                sign &= (L | ((z.m >> (31 - z.exp)) & 1)) - 1;
                for (z = f31((z.m << (1 + z.exp)) & 0xFFFFFFFF, -1); z.m < 0x80000000; z.m <<= 1, --z.exp)
                    ;
            }
            if (z.exp == -1)
                z = f31(0x80000000, 0) - z;
            if (z.exp < -1) {
                z = z * pi;
                z.m = sincos(z.m >> (1 - z.exp), 30).first;
                for (z.exp = 1; z.m < 0x80000000; z.m <<= 1, --z.exp)
                    ;
            } else
                z = f31(0x80000000, 0);
        }
        if (L) {
            if (bsign) {
                f31 l(0x92868247, 0);
                if (z.exp < 0) {
                    uint32 m = log2((z.m + 1) >> 1, 27);
                    z = f31(-((static_cast<uint32>(z.exp) << 26) + (m >> 5)), 5);
                    for (; z.m < 0x80000000; z.m <<= 1, --z.exp)
                        ;
                    l = l + z / lbe;
                }
                sign = static_cast<unsigned>(x.exp && (l.exp < s.exp || (l.exp == s.exp && l.m < s.m))) << 15;
                s = sign ? (s - l) : x.exp ? (l - s) : (l + s);
            } else {
                sign = static_cast<unsigned>(x.exp == 0) << 15;
                if (s.exp < -24)
                    return underflow<R>(sign);
                if (s.exp > 15)
                    return overflow<R>(sign);
            }
        } else {
            s = s * lbe;
            uint32 m;
            if (s.exp < 0) {
                m = s.m >> -s.exp;
                s.exp = 0;
            } else {
                m = (s.m << s.exp) & 0x7FFFFFFF;
                s.exp = (s.m >> (31 - s.exp));
            }
            s.m = exp2(m, 27);
            if (!x.exp)
                s = f31(0x80000000, 0) / s;
            if (bsign) {
                if (z.exp < 0)
                    s = s * z;
                s = pi / s;
                if (s.exp < -24)
                    return underflow<R>(sign);
            } else if (z.exp > 0 && !(z.m & ((1 << (31 - z.exp)) - 1)))
                return ((s.exp + 14) << 10) + (s.m >> 21);
            if (s.exp > 15)
                return overflow<R>(sign);
        }
        return fixed2half<R, 31, false, false, true>(s.m, s.exp + 14, sign);
    }
 
    template <typename, typename, std::float_round_style> struct half_caster;
} // namespace detail
 
class half {
public:
 
    HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}
 
    explicit half(float rhs)
        : data_(static_cast<detail::uint16>(detail::float2half<round_style>(rhs)))
    {
    }
 
    operator float() const { return detail::half2float<float>(data_); }
 
    half& operator=(float rhs)
    {
        data_ = static_cast<detail::uint16>(detail::float2half<round_style>(rhs));
        return *this;
    }
 
 
    half& operator+=(half rhs) { return *this = *this + rhs; }
 
    half& operator-=(half rhs) { return *this = *this - rhs; }
 
    half& operator*=(half rhs) { return *this = *this * rhs; }
 
    half& operator/=(half rhs) { return *this = *this / rhs; }
 
    half& operator+=(float rhs) { return *this = *this + rhs; }
 
    half& operator-=(float rhs) { return *this = *this - rhs; }
 
    half& operator*=(float rhs) { return *this = *this * rhs; }
 
    half& operator/=(float rhs) { return *this = *this / rhs; }
 
 
    half& operator++() { return *this = *this + half(detail::binary, 0x3C00); }
 
    half& operator--() { return *this = *this + half(detail::binary, 0xBC00); }
 
    half operator++(int)
    {
        half out(*this);
        ++*this;
        return out;
    }
 
    half operator--(int)
    {
        half out(*this);
        --*this;
        return out;
    }
 
private:
    static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
 
    HALF_CONSTEXPR half(detail::binary_t, unsigned int bits) HALF_NOEXCEPT : data_(static_cast<detail::uint16>(bits)) {}
 
    detail::uint16 data_;
 
#ifndef HALF_DOXYGEN_ONLY
    friend HALF_CONSTEXPR_NOERR bool operator==(half, half);
    friend HALF_CONSTEXPR_NOERR bool operator!=(half, half);
    friend HALF_CONSTEXPR_NOERR bool operator<(half, half);
    friend HALF_CONSTEXPR_NOERR bool operator>(half, half);
    friend HALF_CONSTEXPR_NOERR bool operator<=(half, half);
    friend HALF_CONSTEXPR_NOERR bool operator>=(half, half);
    friend HALF_CONSTEXPR half operator-(half);
    friend half operator+(half, half);
    friend half operator-(half, half);
    friend half operator*(half, half);
    friend half operator/(half, half);
    template <typename charT, typename traits>
    friend std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>&, half);
    template <typename charT, typename traits>
    friend std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>&, half&);
    friend HALF_CONSTEXPR half fabs(half);
    friend half fmod(half, half);
    friend half remainder(half, half);
    friend half remquo(half, half, int*);
    friend half fma(half, half, half);
    friend HALF_CONSTEXPR_NOERR half fmax(half, half);
    friend HALF_CONSTEXPR_NOERR half fmin(half, half);
    friend half fdim(half, half);
    friend half nanh(const char*);
    friend half exp(half);
    friend half exp2(half);
    friend half expm1(half);
    friend half log(half);
    friend half log10(half);
    friend half log2(half);
    friend half log1p(half);
    friend half sqrt(half);
    friend half rsqrt(half);
    friend half cbrt(half);
    friend half hypot(half, half);
    friend half hypot(half, half, half);
    friend half pow(half, half);
    friend void sincos(half, half*, half*);
    friend half sin(half);
    friend half cos(half);
    friend half tan(half);
    friend half asin(half);
    friend half acos(half);
    friend half atan(half);
    friend half atan2(half, half);
    friend half sinh(half);
    friend half cosh(half);
    friend half tanh(half);
    friend half asinh(half);
    friend half acosh(half);
    friend half atanh(half);
    friend half erf(half);
    friend half erfc(half);
    friend half lgamma(half);
    friend half tgamma(half);
    friend half ceil(half);
    friend half floor(half);
    friend half trunc(half);
    friend half round(half);
    friend long lround(half);
    friend half rint(half);
    friend long lrint(half);
    friend half nearbyint(half);
#ifdef HALF_ENABLE_CPP11_LONG_LONG
    friend long long llround(half);
    friend long long llrint(half);
#endif
    friend half frexp(half, int*);
    friend half scalbln(half, long);
    friend half modf(half, half*);
    friend int ilogb(half);
    friend half logb(half);
    friend half nextafter(half, half);
    friend half nexttoward(half, long double);
    friend HALF_CONSTEXPR half copysign(half, half);
    friend HALF_CONSTEXPR int fpclassify(half);
    friend HALF_CONSTEXPR bool isfinite(half);
    friend HALF_CONSTEXPR bool isinf(half);
    friend HALF_CONSTEXPR bool isnan(half);
    friend HALF_CONSTEXPR bool isnormal(half);
    friend HALF_CONSTEXPR bool signbit(half);
    friend HALF_CONSTEXPR bool isgreater(half, half);
    friend HALF_CONSTEXPR bool isgreaterequal(half, half);
    friend HALF_CONSTEXPR bool isless(half, half);
    friend HALF_CONSTEXPR bool islessequal(half, half);
    friend HALF_CONSTEXPR bool islessgreater(half, half);
    template <typename, typename, std::float_round_style> friend struct detail::half_caster;
    friend class std::numeric_limits<half>;
#if HALF_ENABLE_CPP11_HASH
    friend struct std::hash<half>;
#endif
#if HALF_ENABLE_CPP11_USER_LITERALS
    friend half literal::operator"" _h(long double);
#endif
#endif
};
 
#if HALF_ENABLE_CPP11_USER_LITERALS
namespace literal {
    inline half operator"" _h(long double value)
    {
        return half(detail::binary, detail::float2half<half::round_style>(value));
    }
} // namespace literal
#endif
 
namespace detail {
    template <typename T, typename U, std::float_round_style R = (std::float_round_style)(HALF_ROUND_STYLE)>
    struct half_caster {
    };
    template <typename U, std::float_round_style R> struct half_caster<half, U, R> {
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
        static_assert(std::is_arithmetic<U>::value, "half_cast from non-arithmetic type unsupported");
#endif
 
        static half cast(U arg) { return cast_impl(arg, is_float<U>()); };
 
    private:
        static half cast_impl(U arg, true_type) { return half(binary, float2half<R>(arg)); }
        static half cast_impl(U arg, false_type) { return half(binary, int2half<R>(arg)); }
    };
    template <typename T, std::float_round_style R> struct half_caster<T, half, R> {
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
        static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");
#endif
 
        static T cast(half arg) { return cast_impl(arg, is_float<T>()); }
 
    private:
        static T cast_impl(half arg, true_type) { return half2float<T>(arg.data_); }
        static T cast_impl(half arg, false_type) { return half2int<R, true, true, T>(arg.data_); }
    };
    template <std::float_round_style R> struct half_caster<half, half, R> {
        static half cast(half arg) { return arg; }
    };
} // namespace detail
} // namespace half_float
 
namespace std {
template <> class numeric_limits<half_float::half> {
public:
    static HALF_CONSTEXPR_CONST bool is_specialized = true;
 
    static HALF_CONSTEXPR_CONST bool is_signed = true;
 
    static HALF_CONSTEXPR_CONST bool is_integer = false;
 
    static HALF_CONSTEXPR_CONST bool is_exact = false;
 
    static HALF_CONSTEXPR_CONST bool is_modulo = false;
 
    static HALF_CONSTEXPR_CONST bool is_bounded = true;
 
    static HALF_CONSTEXPR_CONST bool is_iec559 = true;
 
    static HALF_CONSTEXPR_CONST bool has_infinity = true;
 
    static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;
 
    static HALF_CONSTEXPR_CONST bool has_signaling_NaN = true;
 
    static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
 
    static HALF_CONSTEXPR_CONST bool has_denorm_loss = false;
 
#if HALF_ERRHANDLING_THROWS
    static HALF_CONSTEXPR_CONST bool traps = true;
#else
    static HALF_CONSTEXPR_CONST bool traps = false;
#endif
 
    static HALF_CONSTEXPR_CONST bool tinyness_before = false;
 
    static HALF_CONSTEXPR_CONST float_round_style round_style = half_float::half::round_style;
 
    static HALF_CONSTEXPR_CONST int digits = 11;
 
    static HALF_CONSTEXPR_CONST int digits10 = 3;
 
    static HALF_CONSTEXPR_CONST int max_digits10 = 5;
 
    static HALF_CONSTEXPR_CONST int radix = 2;
 
    static HALF_CONSTEXPR_CONST int min_exponent = -13;
 
    static HALF_CONSTEXPR_CONST int min_exponent10 = -4;
 
    static HALF_CONSTEXPR_CONST int max_exponent = 16;
 
    static HALF_CONSTEXPR_CONST int max_exponent10 = 4;
 
    static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x0400);
    }
 
    static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0xFBFF);
    }
 
    static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7BFF);
    }
 
    static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x1400);
    }
 
    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);
    }
 
    static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7C00);
    }
 
    static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7FFF);
    }
 
    static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x7DFF);
    }
 
    static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW
    {
        return half_float::half(half_float::detail::binary, 0x0001);
    }
};
 
#if HALF_ENABLE_CPP11_HASH
template <> struct hash<half_float::half> {
    typedef half_float::half argument_type;
 
    typedef size_t result_type;
 
    result_type operator()(argument_type arg) const
    {
        return hash<half_float::detail::uint16>()(arg.data_ & -static_cast<unsigned>(arg.data_ != 0x8000));
    }
};
#endif
} // namespace std
 
namespace half_float {
 
inline HALF_CONSTEXPR_NOERR bool operator==(half x, half y)
{
    return !detail::compsignal(x.data_, y.data_) && (x.data_ == y.data_ || !((x.data_ | y.data_) & 0x7FFF));
}
 
inline HALF_CONSTEXPR_NOERR bool operator!=(half x, half y)
{
    return detail::compsignal(x.data_, y.data_) || (x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF));
}
 
inline HALF_CONSTEXPR_NOERR bool operator<(half x, half y)
{
    return !detail::compsignal(x.data_, y.data_) &&
        ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15));
}
 
inline HALF_CONSTEXPR_NOERR bool operator>(half x, half y)
{
    return !detail::compsignal(x.data_, y.data_) &&
        ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15));
}
 
inline HALF_CONSTEXPR_NOERR bool operator<=(half x, half y)
{
    return !detail::compsignal(x.data_, y.data_) &&
        ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <=
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15));
}
 
inline HALF_CONSTEXPR_NOERR bool operator>=(half x, half y)
{
    return !detail::compsignal(x.data_, y.data_) &&
        ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >=
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15));
}
 
 
inline HALF_CONSTEXPR half operator+(half arg) { return arg; }
 
inline HALF_CONSTEXPR half operator-(half arg) { return half(detail::binary, arg.data_ ^ 0x8000); }
 
inline half operator+(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(
            detail::half2float<detail::internal_t>(x.data_) + detail::half2float<detail::internal_t>(y.data_)));
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF;
    bool sub = ((x.data_ ^ y.data_) & 0x8000) != 0;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absy != 0x7C00)           ? x.data_
                : (sub && absx == 0x7C00)    ? detail::invalid()
                                             : y.data_);
    if (!absx)
        return absy
            ? y
            : half(detail::binary,
                  (half::round_style == std::round_toward_neg_infinity) ? (x.data_ | y.data_) : (x.data_ & y.data_));
    if (!absy)
        return x;
    unsigned int sign = ((sub && absy > absx) ? y.data_ : x.data_) & 0x8000;
    if (absy > absx)
        std::swap(absx, absy);
    int exp = (absx >> 10) + (absx <= 0x3FF), d = exp - (absy >> 10) - (absy <= 0x3FF),
        mx = ((absx & 0x3FF) | ((absx > 0x3FF) << 10)) << 3, my;
    if (d < 13) {
        my = ((absy & 0x3FF) | ((absy > 0x3FF) << 10)) << 3;
        my = (my >> d) | ((my & ((1 << d) - 1)) != 0);
    } else
        my = 1;
    if (sub) {
        if (!(mx -= my))
            return half(
                detail::binary, static_cast<unsigned>(half::round_style == std::round_toward_neg_infinity) << 15);
        for (; mx < 0x2000 && exp > 1; mx <<= 1, --exp)
            ;
    } else {
        mx += my;
        int i = mx >> 14;
        if ((exp += i) > 30)
            return half(detail::binary, detail::overflow<half::round_style>(sign));
        mx = (mx >> i) | (mx & i);
    }
    return half(detail::binary,
        detail::rounded<half::round_style, false>(
            sign + ((exp - 1) << 10) + (mx >> 3), (mx >> 2) & 1, (mx & 0x3) != 0));
#endif
}
 
inline half operator-(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(
            detail::half2float<detail::internal_t>(x.data_) - detail::half2float<detail::internal_t>(y.data_)));
#else
    return x + -y;
#endif
}
 
inline half operator*(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(
            detail::half2float<detail::internal_t>(x.data_) * detail::half2float<detail::internal_t>(y.data_)));
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -16;
    unsigned int sign = (x.data_ ^ y.data_) & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00)                               ? detail::signal(x.data_, y.data_)
                : ((absx == 0x7C00 && !absy) || (absy == 0x7C00 && !absx)) ? detail::invalid()
                                                                           : (sign | 0x7C00));
    if (!absx || !absy)
        return half(detail::binary, sign);
    for (; absx < 0x400; absx <<= 1, --exp)
        ;
    for (; absy < 0x400; absy <<= 1, --exp)
        ;
    detail::uint32 m =
        static_cast<detail::uint32>((absx & 0x3FF) | 0x400) * static_cast<detail::uint32>((absy & 0x3FF) | 0x400);
    int i = m >> 21, s = m & i;
    exp += (absx >> 10) + (absy >> 10) + i;
    if (exp > 29)
        return half(detail::binary, detail::overflow<half::round_style>(sign));
    else if (exp < -11)
        return half(detail::binary, detail::underflow<half::round_style>(sign));
    return half(detail::binary, detail::fixed2half<half::round_style, 20, false, false, false>(m >> i, exp, sign, s));
#endif
}
 
inline half operator/(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(
            detail::half2float<detail::internal_t>(x.data_) / detail::half2float<detail::internal_t>(y.data_)));
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = 14;
    unsigned int sign = (x.data_ ^ y.data_) & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absx == absy)             ? detail::invalid()
                                             : (sign | ((absx == 0x7C00) ? 0x7C00 : 0)));
    if (!absx)
        return half(detail::binary, absy ? sign : detail::invalid());
    if (!absy)
        return half(detail::binary, detail::pole(sign));
    for (; absx < 0x400; absx <<= 1, --exp)
        ;
    for (; absy < 0x400; absy <<= 1, ++exp)
        ;
    detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400;
    int i = mx < my;
    exp += (absx >> 10) - (absy >> 10) - i;
    if (exp > 29)
        return half(detail::binary, detail::overflow<half::round_style>(sign));
    else if (exp < -11)
        return half(detail::binary, detail::underflow<half::round_style>(sign));
    mx <<= 12 + i;
    my <<= 1;
    return half(detail::binary,
        detail::fixed2half<half::round_style, 11, false, false, false>(mx / my, exp, sign, mx % my != 0));
#endif
}
 
 
template <typename charT, typename traits>
std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& out, half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return out << detail::half2float<detail::internal_t>(arg.data_);
#else
    return out << detail::half2float<float>(arg.data_);
#endif
}
 
template <typename charT, typename traits>
std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& in, half& arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    detail::internal_t f;
#else
    double f;
#endif
    if (in >> f)
        arg.data_ = detail::float2half<half::round_style>(f);
    return in;
}
 
 
inline HALF_CONSTEXPR half fabs(half arg) { return half(detail::binary, arg.data_ & 0x7FFF); }
 
inline HALF_CONSTEXPR half abs(half arg) { return fabs(arg); }
 
inline half fmod(half x, half y)
{
    unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absx == 0x7C00)           ? detail::invalid()
                                             : x.data_);
    if (!absy)
        return half(detail::binary, detail::invalid());
    if (!absx)
        return x;
    if (absx == absy)
        return half(detail::binary, sign);
    return half(detail::binary, sign | detail::mod<false, false>(absx, absy));
}
 
inline half remainder(half x, half y)
{
    unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absx == 0x7C00)           ? detail::invalid()
                                             : x.data_);
    if (!absy)
        return half(detail::binary, detail::invalid());
    if (absx == absy)
        return half(detail::binary, sign);
    return half(detail::binary, sign ^ detail::mod<false, true>(absx, absy));
}
 
inline half remquo(half x, half y, int* quo)
{
    unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, value = x.data_ & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absx == 0x7C00)           ? detail::invalid()
                                             : (*quo = 0, x.data_));
    if (!absy)
        return half(detail::binary, detail::invalid());
    bool qsign = ((value ^ y.data_) & 0x8000) != 0;
    int q = 1;
    if (absx != absy)
        value ^= detail::mod<true, true>(absx, absy, &q);
    return *quo = qsign ? -q : q, half(detail::binary, value);
}
 
inline half fma(half x, half y, half z)
{
#ifdef HALF_ARITHMETIC_TYPE
    detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_),
                       fy = detail::half2float<detail::internal_t>(y.data_),
                       fz = detail::half2float<detail::internal_t>(z.data_);
#if HALF_ENABLE_CPP11_CMATH && FP_FAST_FMA
    return half(detail::binary, detail::float2half<half::round_style>(std::fma(fx, fy, fz)));
#else
    return half(detail::binary, detail::float2half<half::round_style>(fx * fy + fz));
#endif
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, exp = -15;
    unsigned int sign = (x.data_ ^ y.data_) & 0x8000;
    bool sub = ((sign ^ z.data_) & 0x8000) != 0;
    if (absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)
        return (absx > 0x7C00 || absy > 0x7C00 || absz > 0x7C00)
            ? half(detail::binary, detail::signal(x.data_, y.data_, z.data_))
            : (absx == 0x7C00)
            ? half(detail::binary, (!absy || (sub && absz == 0x7C00)) ? detail::invalid() : (sign | 0x7C00))
            : (absy == 0x7C00)
            ? half(detail::binary, (!absx || (sub && absz == 0x7C00)) ? detail::invalid() : (sign | 0x7C00))
            : z;
    if (!absx || !absy)
        return absz ? z
                    : half(detail::binary,
                          (half::round_style == std::round_toward_neg_infinity) ? (z.data_ | sign) : (z.data_ & sign));
    for (; absx < 0x400; absx <<= 1, --exp)
        ;
    for (; absy < 0x400; absy <<= 1, --exp)
        ;
    detail::uint32 m =
        static_cast<detail::uint32>((absx & 0x3FF) | 0x400) * static_cast<detail::uint32>((absy & 0x3FF) | 0x400);
    int i = m >> 21;
    exp += (absx >> 10) + (absy >> 10) + i;
    m <<= 3 - i;
    if (absz) {
        int expz = 0;
        for (; absz < 0x400; absz <<= 1, --expz)
            ;
        expz += absz >> 10;
        detail::uint32 mz = static_cast<detail::uint32>((absz & 0x3FF) | 0x400) << 13;
        if (expz > exp || (expz == exp && mz > m)) {
            std::swap(m, mz);
            std::swap(exp, expz);
            if (sub)
                sign = z.data_ & 0x8000;
        }
        int d = exp - expz;
        mz = (d < 23) ? ((mz >> d) | ((mz & ((static_cast<detail::uint32>(1) << d) - 1)) != 0)) : 1;
        if (sub) {
            m = m - mz;
            if (!m)
                return half(
                    detail::binary, static_cast<unsigned>(half::round_style == std::round_toward_neg_infinity) << 15);
            for (; m < 0x800000; m <<= 1, --exp)
                ;
        } else {
            m += mz;
            i = m >> 24;
            m = (m >> i) | (m & i);
            exp += i;
        }
    }
    if (exp > 30)
        return half(detail::binary, detail::overflow<half::round_style>(sign));
    else if (exp < -10)
        return half(detail::binary, detail::underflow<half::round_style>(sign));
    return half(detail::binary, detail::fixed2half<half::round_style, 23, false, false, false>(m, exp - 1, sign));
#endif
}
 
inline HALF_CONSTEXPR_NOERR half fmax(half x, half y)
{
    return half(detail::binary,
        (!isnan(y) &&
            (isnan(x) ||
                (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) < (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15))))))
            ? detail::select(y.data_, x.data_)
            : detail::select(x.data_, y.data_));
}
 
inline HALF_CONSTEXPR_NOERR half fmin(half x, half y)
{
    return half(detail::binary,
        (!isnan(y) &&
            (isnan(x) ||
                (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) > (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15))))))
            ? detail::select(y.data_, x.data_)
            : detail::select(x.data_, y.data_));
}
 
inline half fdim(half x, half y)
{
    if (isnan(x) || isnan(y))
        return half(detail::binary, detail::signal(x.data_, y.data_));
    return (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) <= (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15))))
        ? half(detail::binary, 0)
        : (x - y);
}
 
inline half nanh(const char* arg)
{
    unsigned int value = 0x7FFF;
    while (*arg)
        value ^= static_cast<unsigned>(*arg++) & 0xFF;
    return half(detail::binary, value);
}
 
 
inline half exp(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::exp(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, e = (abs >> 10) + (abs <= 0x3FF), exp;
    if (!abs)
        return half(detail::binary, 0x3C00);
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? (0x7C00 & ((arg.data_ >> 15) - 1U)) : detail::signal(arg.data_));
    if (abs >= 0x4C80)
        return half(detail::binary,
            (arg.data_ & 0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());
    detail::uint32 m =
        detail::multiply64(static_cast<detail::uint32>((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, 0xB8AA3B29);
    if (e < 14) {
        exp = 0;
        m >>= 14 - e;
    } else {
        exp = m >> (45 - e);
        m = (m << (e - 14)) & 0x7FFFFFFF;
    }
    return half(detail::binary, detail::exp2_post<half::round_style>(m, exp, (arg.data_ & 0x8000) != 0, 0, 26));
#endif
}
 
inline half exp2(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::exp2(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, e = (abs >> 10) + (abs <= 0x3FF), exp = (abs & 0x3FF) + ((abs > 0x3FF) << 10);
    if (!abs)
        return half(detail::binary, 0x3C00);
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? (0x7C00 & ((arg.data_ >> 15) - 1U)) : detail::signal(arg.data_));
    if (abs >= 0x4E40)
        return half(detail::binary,
            (arg.data_ & 0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());
    return half(detail::binary,
        detail::exp2_post<half::round_style>((static_cast<detail::uint32>(exp) << (6 + e)) & 0x7FFFFFFF,
            exp >> (25 - e), (arg.data_ & 0x8000) != 0, 0, 28));
#endif
}
 
inline half expm1(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::expm1(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000, e = (abs >> 10) + (abs <= 0x3FF), exp;
    if (!abs)
        return arg;
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? (0x7C00 + (sign >> 1)) : detail::signal(arg.data_));
    if (abs >= 0x4A00)
        return half(detail::binary,
            (arg.data_ & 0x8000) ? detail::rounded<half::round_style, true>(0xBBFF, 1, 1)
                                 : detail::overflow<half::round_style>());
    detail::uint32 m =
        detail::multiply64(static_cast<detail::uint32>((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, 0xB8AA3B29);
    if (e < 14) {
        exp = 0;
        m >>= 14 - e;
    } else {
        exp = m >> (45 - e);
        m = (m << (e - 14)) & 0x7FFFFFFF;
    }
    m = detail::exp2(m);
    if (sign) {
        int s = 0;
        if (m > 0x80000000) {
            ++exp;
            m = detail::divide64(0x80000000, m, s);
        }
        m = 0x80000000 - ((m >> exp) | ((m & ((static_cast<detail::uint32>(1) << exp) - 1)) != 0) | s);
        exp = 0;
    } else
        m -= (exp < 31) ? (0x80000000 >> exp) : 1;
    for (exp += 14; m < 0x80000000 && exp; m <<= 1, --exp)
        ;
    if (exp > 29)
        return half(detail::binary, detail::overflow<half::round_style>());
    return half(detail::binary,
        detail::rounded<half::round_style, true>(sign + (exp << 10) + (m >> 21), (m >> 20) & 1, (m & 0xFFFFF) != 0));
#endif
}
 
inline half log(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::log(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = -15;
    if (!abs)
        return half(detail::binary, detail::pole(0x8000));
    if (arg.data_ & 0x8000)
        return half(detail::binary, (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs >= 0x7C00)
        return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    exp += abs >> 10;
    return half(detail::binary,
        detail::log2_post<half::round_style, 0xB8AA3B2A>(
            detail::log2(static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 20, 27) + 8, exp, 17));
#endif
}
 
inline half log10(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::log10(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = -15;
    if (!abs)
        return half(detail::binary, detail::pole(0x8000));
    if (arg.data_ & 0x8000)
        return half(detail::binary, (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs >= 0x7C00)
        return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
    switch (abs) {
    case 0x4900:
        return half(detail::binary, 0x3C00);
    case 0x5640:
        return half(detail::binary, 0x4000);
    case 0x63D0:
        return half(detail::binary, 0x4200);
    case 0x70E2:
        return half(detail::binary, 0x4400);
    }
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    exp += abs >> 10;
    return half(detail::binary,
        detail::log2_post<half::round_style, 0xD49A784C>(
            detail::log2(static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 20, 27) + 8, exp, 16));
#endif
}
 
inline half log2(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::log2(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = -15, s = 0;
    if (!abs)
        return half(detail::binary, detail::pole(0x8000));
    if (arg.data_ & 0x8000)
        return half(detail::binary, (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs >= 0x7C00)
        return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
    if (abs == 0x3C00)
        return half(detail::binary, 0);
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    exp += (abs >> 10);
    if (!(abs & 0x3FF)) {
        unsigned int value = static_cast<unsigned>(exp < 0) << 15, m = std::abs(exp) << 6;
        for (exp = 18; m < 0x400; m <<= 1, --exp)
            ;
        return half(detail::binary, value + (exp << 10) + m);
    }
    detail::uint32 ilog = exp, sign = detail::sign_mask(ilog),
                   m = (((ilog << 27) +
                            (detail::log2(static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 20, 28) >> 4)) ^
                           sign) -
        sign;
    if (!m)
        return half(detail::binary, 0);
    for (exp = 14; m < 0x8000000 && exp; m <<= 1, --exp)
        ;
    for (; m > 0xFFFFFFF; m >>= 1, ++exp)
        s |= m & 1;
    return half(
        detail::binary, detail::fixed2half<half::round_style, 27, false, false, true>(m, exp, sign & 0x8000, s));
#endif
}
 
inline half log1p(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::log1p(detail::half2float<detail::internal_t>(arg.data_))));
#else
    if (arg.data_ >= 0xBC00)
        return half(detail::binary,
            (arg.data_ == 0xBC00)       ? detail::pole(0x8000)
                : (arg.data_ <= 0xFC00) ? detail::invalid()
                                        : detail::signal(arg.data_));
    int abs = arg.data_ & 0x7FFF, exp = -15;
    if (!abs || abs >= 0x7C00)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    exp += abs >> 10;
    detail::uint32 m = static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 20;
    if (arg.data_ & 0x8000) {
        m = 0x40000000 - (m >> -exp);
        for (exp = 0; m < 0x40000000; m <<= 1, --exp)
            ;
    } else {
        if (exp < 0) {
            m = 0x40000000 + (m >> -exp);
            exp = 0;
        } else {
            m += 0x40000000 >> exp;
            int i = m >> 31;
            m >>= i;
            exp += i;
        }
    }
    return half(detail::binary, detail::log2_post<half::round_style, 0xB8AA3B2A>(detail::log2(m), exp, 17));
#endif
}
 
 
inline half sqrt(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::sqrt(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = 15;
    if (!abs || arg.data_ >= 0x7C00)
        return half(detail::binary,
            (abs > 0x7C00)             ? detail::signal(arg.data_)
                : (arg.data_ > 0x8000) ? detail::invalid()
                                       : arg.data_);
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    detail::uint32 r = static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 10,
                   m = detail::sqrt<20>(r, exp += abs >> 10);
    return half(detail::binary, detail::rounded<half::round_style, false>((exp << 10) + (m & 0x3FF), r > m, r != 0));
#endif
}
 
inline half rsqrt(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(
            detail::internal_t(1) / std::sqrt(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, bias = 0x4000;
    if (!abs || arg.data_ >= 0x7C00)
        return half(detail::binary,
            (abs > 0x7C00)             ? detail::signal(arg.data_)
                : (arg.data_ > 0x8000) ? detail::invalid()
                : !abs                 ? detail::pole(arg.data_ & 0x8000)
                                       : 0);
    for (; abs < 0x400; abs <<= 1, bias -= 0x400)
        ;
    unsigned int frac = (abs += bias) & 0x7FF;
    if (frac == 0x400)
        return half(detail::binary, 0x7A00 - (abs >> 1));
    if ((half::round_style == std::round_to_nearest && (frac == 0x3FE || frac == 0x76C)) ||
        (half::round_style != std::round_to_nearest &&
            (frac == 0x15A || frac == 0x3FC || frac == 0x401 || frac == 0x402 || frac == 0x67B)))
        return pow(arg, half(detail::binary, 0xB800));
    detail::uint32 f = 0x17376 - abs, mx = (abs & 0x3FF) | 0x400, my = ((f >> 1) & 0x3FF) | 0x400, mz = my * my;
    int expy = (f >> 11) - 31, expx = 32 - (abs >> 10), i = mz >> 21;
    for (mz = 0x60000000 - (((mz >> i) * mx) >> (expx - 2 * expy - i)); mz < 0x40000000; mz <<= 1, --expy)
        ;
    i = (my *= mz >> 10) >> 31;
    expy += i;
    my = (my >> (20 + i)) + 1;
    i = (mz = my * my) >> 21;
    for (mz = 0x60000000 - (((mz >> i) * mx) >> (expx - 2 * expy - i)); mz < 0x40000000; mz <<= 1, --expy)
        ;
    i = (my *= (mz >> 10) + 1) >> 31;
    return half(detail::binary, detail::fixed2half<half::round_style, 30, false, false, true>(my >> i, expy + i + 14));
#endif
}
 
inline half cbrt(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::cbrt(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = -15;
    if (!abs || abs == 0x3C00 || abs >= 0x7C00)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    detail::uint32 ilog = exp + (abs >> 10), sign = detail::sign_mask(ilog), f,
                   m = (((ilog << 27) +
                            (detail::log2(static_cast<detail::uint32>((abs & 0x3FF) | 0x400) << 20, 24) >> 4)) ^
                           sign) -
        sign;
    for (exp = 2; m < 0x80000000; m <<= 1, --exp)
        ;
    m = detail::multiply64(m, 0xAAAAAAAB);
    int i = m >> 31, s;
    exp += i;
    m <<= 1 - i;
    if (exp < 0) {
        f = m >> -exp;
        exp = 0;
    } else {
        f = (m << exp) & 0x7FFFFFFF;
        exp = m >> (31 - exp);
    }
    m = detail::exp2(f, (half::round_style == std::round_to_nearest) ? 29 : 26);
    if (sign) {
        if (m > 0x80000000) {
            m = detail::divide64(0x80000000, m, s);
            ++exp;
        }
        exp = -exp;
    }
    return half(detail::binary,
        (half::round_style == std::round_to_nearest)
            ? detail::fixed2half<half::round_style, 31, false, false, false>(m, exp + 14, arg.data_ & 0x8000)
            : detail::fixed2half<half::round_style, 23, false, false, false>(
                  (m + 0x80) >> 8, exp + 14, arg.data_ & 0x8000));
#endif
}
 
inline half hypot(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_),
                       fy = detail::half2float<detail::internal_t>(y.data_);
#if HALF_ENABLE_CPP11_CMATH
    return half(detail::binary, detail::float2half<half::round_style>(std::hypot(fx, fy)));
#else
    return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx * fx + fy * fy)));
#endif
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0;
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx == 0x7C00)       ? detail::select(0x7C00, y.data_)
                : (absy == 0x7C00) ? detail::select(0x7C00, x.data_)
                                   : detail::signal(x.data_, y.data_));
    if (!absx)
        return half(detail::binary, absy ? detail::check_underflow(absy) : 0);
    if (!absy)
        return half(detail::binary, detail::check_underflow(absx));
    if (absy > absx)
        std::swap(absx, absy);
    for (; absx < 0x400; absx <<= 1, --expx)
        ;
    for (; absy < 0x400; absy <<= 1, --expy)
        ;
    detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400;
    mx *= mx;
    my *= my;
    int ix = mx >> 21, iy = my >> 21;
    expx = 2 * (expx + (absx >> 10)) - 15 + ix;
    expy = 2 * (expy + (absy >> 10)) - 15 + iy;
    mx <<= 10 - ix;
    my <<= 10 - iy;
    int d = expx - expy;
    my = (d < 30) ? ((my >> d) | ((my & ((static_cast<detail::uint32>(1) << d) - 1)) != 0)) : 1;
    return half(detail::binary, detail::hypot_post<half::round_style>(mx + my, expx));
#endif
}
 
inline half hypot(half x, half y, half z)
{
#ifdef HALF_ARITHMETIC_TYPE
    detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_),
                       fy = detail::half2float<detail::internal_t>(y.data_),
                       fz = detail::half2float<detail::internal_t>(z.data_);
    return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx * fx + fy * fy + fz * fz)));
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, expx = 0, expy = 0, expz = 0;
    if (!absx)
        return hypot(y, z);
    if (!absy)
        return hypot(x, z);
    if (!absz)
        return hypot(x, y);
    if (absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)
        return half(detail::binary,
            (absx == 0x7C00)       ? detail::select(0x7C00, detail::select(y.data_, z.data_))
                : (absy == 0x7C00) ? detail::select(0x7C00, detail::select(x.data_, z.data_))
                : (absz == 0x7C00) ? detail::select(0x7C00, detail::select(x.data_, y.data_))
                                   : detail::signal(x.data_, y.data_, z.data_));
    if (absz > absy)
        std::swap(absy, absz);
    if (absy > absx)
        std::swap(absx, absy);
    if (absz > absy)
        std::swap(absy, absz);
    for (; absx < 0x400; absx <<= 1, --expx)
        ;
    for (; absy < 0x400; absy <<= 1, --expy)
        ;
    for (; absz < 0x400; absz <<= 1, --expz)
        ;
    detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400, mz = (absz & 0x3FF) | 0x400;
    mx *= mx;
    my *= my;
    mz *= mz;
    int ix = mx >> 21, iy = my >> 21, iz = mz >> 21;
    expx = 2 * (expx + (absx >> 10)) - 15 + ix;
    expy = 2 * (expy + (absy >> 10)) - 15 + iy;
    expz = 2 * (expz + (absz >> 10)) - 15 + iz;
    mx <<= 10 - ix;
    my <<= 10 - iy;
    mz <<= 10 - iz;
    int d = expy - expz;
    mz = (d < 30) ? ((mz >> d) | ((mz & ((static_cast<detail::uint32>(1) << d) - 1)) != 0)) : 1;
    my += mz;
    if (my & 0x80000000) {
        my = (my >> 1) | (my & 1);
        if (++expy > expx) {
            std::swap(mx, my);
            std::swap(expx, expy);
        }
    }
    d = expx - expy;
    my = (d < 30) ? ((my >> d) | ((my & ((static_cast<detail::uint32>(1) << d) - 1)) != 0)) : 1;
    return half(detail::binary, detail::hypot_post<half::round_style>(mx + my, expx));
#endif
}
 
inline half pow(half x, half y)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::pow(
            detail::half2float<detail::internal_t>(x.data_), detail::half2float<detail::internal_t>(y.data_))));
#else
    int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -15;
    if (!absy || x.data_ == 0x3C00)
        return half(detail::binary, detail::select(0x3C00, (x.data_ == 0x3C00) ? y.data_ : x.data_));
    bool is_int = absy >= 0x6400 || (absy >= 0x3C00 && !(absy & ((1 << (25 - (absy >> 10))) - 1)));
    unsigned int sign =
        x.data_ & (static_cast<unsigned>((absy < 0x6800) && is_int && ((absy >> (25 - (absy >> 10))) & 1)) << 15);
    if (absx >= 0x7C00 || absy >= 0x7C00)
        return half(detail::binary,
            (absx > 0x7C00 || absy > 0x7C00) ? detail::signal(x.data_, y.data_)
                : (absy == 0x7C00)
                ? ((absx == 0x3C00)                      ? 0x3C00
                          : (!absx && y.data_ == 0xFC00) ? detail::pole()
                                                         : (0x7C00 & -((y.data_ >> 15) ^ (absx > 0x3C00))))
                : (sign | (0x7C00 & ((y.data_ >> 15) - 1U))));
    if (!absx)
        return half(detail::binary, (y.data_ & 0x8000) ? detail::pole(sign) : sign);
    if ((x.data_ & 0x8000) && !is_int)
        return half(detail::binary, detail::invalid());
    if (x.data_ == 0xBC00)
        return half(detail::binary, sign | 0x3C00);
    switch (y.data_) {
    case 0x3800:
        return sqrt(x);
    case 0x3C00:
        return half(detail::binary, detail::check_underflow(x.data_));
    case 0x4000:
        return x * x;
    case 0xBC00:
        return half(detail::binary, 0x3C00) / x;
    }
    for (; absx < 0x400; absx <<= 1, --exp)
        ;
    detail::uint32 ilog = exp + (absx >> 10), msign = detail::sign_mask(ilog), f,
                   m = (((ilog << 27) +
                            ((detail::log2(static_cast<detail::uint32>((absx & 0x3FF) | 0x400) << 20) + 8) >> 4)) ^
                           msign) -
        msign;
    for (exp = -11; m < 0x80000000; m <<= 1, --exp)
        ;
    for (; absy < 0x400; absy <<= 1, --exp)
        ;
    m = detail::multiply64(m, static_cast<detail::uint32>((absy & 0x3FF) | 0x400) << 21);
    int i = m >> 31;
    exp += (absy >> 10) + i;
    m <<= 1 - i;
    if (exp < 0) {
        f = m >> -exp;
        exp = 0;
    } else {
        f = (m << exp) & 0x7FFFFFFF;
        exp = m >> (31 - exp);
    }
    return half(
        detail::binary, detail::exp2_post<half::round_style>(f, exp, ((msign & 1) ^ (y.data_ >> 15)) != 0, sign));
#endif
}
 
 
inline void sincos(half arg, half* sin, half* cos)
{
#ifdef HALF_ARITHMETIC_TYPE
    detail::internal_t f = detail::half2float<detail::internal_t>(arg.data_);
    *sin = half(detail::binary, detail::float2half<half::round_style>(std::sin(f)));
    *cos = half(detail::binary, detail::float2half<half::round_style>(std::cos(f)));
#else
    int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15, k;
    if (abs >= 0x7C00)
        *sin = *cos = half(detail::binary, (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_));
    else if (!abs) {
        *sin = arg;
        *cos = half(detail::binary, 0x3C00);
    } else if (abs < 0x2500) {
        *sin = half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 1, 1, 1));
        *cos = half(detail::binary, detail::rounded<half::round_style, true>(0x3BFF, 1, 1));
    } else {
        if (half::round_style != std::round_to_nearest) {
            switch (abs) {
            case 0x48B7:
                *sin = half(
                    detail::binary, detail::rounded<half::round_style, true>((~arg.data_ & 0x8000) | 0x1D07, 1, 1));
                *cos = half(detail::binary, detail::rounded<half::round_style, true>(0xBBFF, 1, 1));
                return;
            case 0x598C:
                *sin =
                    half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x3BFF, 1, 1));
                *cos = half(detail::binary, detail::rounded<half::round_style, true>(0x80FC, 1, 1));
                return;
            case 0x6A64:
                *sin = half(
                    detail::binary, detail::rounded<half::round_style, true>((~arg.data_ & 0x8000) | 0x3BFE, 1, 1));
                *cos = half(detail::binary, detail::rounded<half::round_style, true>(0x27FF, 1, 1));
                return;
            case 0x6D8C:
                *sin =
                    half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x0FE6, 1, 1));
                *cos = half(detail::binary, detail::rounded<half::round_style, true>(0x3BFF, 1, 1));
                return;
            }
        }
        std::pair<detail::uint32, detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
        switch (k & 3) {
        case 1:
            sc = std::make_pair(sc.second, -sc.first);
            break;
        case 2:
            sc = std::make_pair(-sc.first, -sc.second);
            break;
        case 3:
            sc = std::make_pair(-sc.second, sc.first);
            break;
        }
        *sin = half(detail::binary,
            detail::fixed2half<half::round_style, 30, true, true, true>(
                (sc.first ^ -static_cast<detail::uint32>(sign)) + sign));
        *cos = half(detail::binary, detail::fixed2half<half::round_style, 30, true, true, true>(sc.second));
    }
#endif
}
 
inline half sin(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::sin(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, k;
    if (!abs)
        return arg;
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs < 0x2900)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 1, 1, 1));
    if (half::round_style != std::round_to_nearest)
        switch (abs) {
        case 0x48B7:
            return half(detail::binary, detail::rounded<half::round_style, true>((~arg.data_ & 0x8000) | 0x1D07, 1, 1));
        case 0x6A64:
            return half(detail::binary, detail::rounded<half::round_style, true>((~arg.data_ & 0x8000) | 0x3BFE, 1, 1));
        case 0x6D8C:
            return half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x0FE6, 1, 1));
        }
    std::pair<detail::uint32, detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
    detail::uint32 sign = -static_cast<detail::uint32>(((k >> 1) & 1) ^ (arg.data_ >> 15));
    return half(detail::binary,
        detail::fixed2half<half::round_style, 30, true, true, true>((((k & 1) ? sc.second : sc.first) ^ sign) - sign));
#endif
}
 
inline half cos(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::cos(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, k;
    if (!abs)
        return half(detail::binary, 0x3C00);
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs < 0x2500)
        return half(detail::binary, detail::rounded<half::round_style, true>(0x3BFF, 1, 1));
    if (half::round_style != std::round_to_nearest && abs == 0x598C)
        return half(detail::binary, detail::rounded<half::round_style, true>(0x80FC, 1, 1));
    std::pair<detail::uint32, detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
    detail::uint32 sign = -static_cast<detail::uint32>(((k >> 1) ^ k) & 1);
    return half(detail::binary,
        detail::fixed2half<half::round_style, 30, true, true, true>((((k & 1) ? sc.first : sc.second) ^ sign) - sign));
#endif
}
 
inline half tan(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::tan(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = 13, k;
    if (!abs)
        return arg;
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs < 0x2700)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_, 0, 1));
    if (half::round_style != std::round_to_nearest)
        switch (abs) {
        case 0x658C:
            return half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x07E6, 1, 1));
        case 0x7330:
            return half(detail::binary, detail::rounded<half::round_style, true>((~arg.data_ & 0x8000) | 0x4B62, 1, 1));
        }
    std::pair<detail::uint32, detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 30);
    if (k & 1)
        sc = std::make_pair(-sc.second, sc.first);
    detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second);
    detail::uint32 my = (sc.first ^ signy) - signy, mx = (sc.second ^ signx) - signx;
    for (; my < 0x80000000; my <<= 1, --exp)
        ;
    for (; mx < 0x80000000; mx <<= 1, ++exp)
        ;
    return half(
        detail::binary, detail::tangent_post<half::round_style>(my, mx, exp, (signy ^ signx ^ arg.data_) & 0x8000));
#endif
}
 
inline half asin(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::asin(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
    if (!abs)
        return arg;
    if (abs >= 0x3C00)
        return half(detail::binary,
            (abs > 0x7C00)       ? detail::signal(arg.data_)
                : (abs > 0x3C00) ? detail::invalid()
                                 : detail::rounded<half::round_style, true>(sign | 0x3E48, 0, 1));
    if (abs < 0x2900)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_, 0, 1));
    if (half::round_style != std::round_to_nearest && (abs == 0x2B44 || abs == 0x2DC3))
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ + 1, 1, 1));
    std::pair<detail::uint32, detail::uint32> sc = detail::atan2_args(abs);
    detail::uint32 m = detail::atan2(sc.first, sc.second, (half::round_style == std::round_to_nearest) ? 27 : 26);
    return half(detail::binary, detail::fixed2half<half::round_style, 30, false, true, true>(m, 14, sign));
#endif
}
 
inline half acos(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::acos(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15;
    if (!abs)
        return half(detail::binary, detail::rounded<half::round_style, true>(0x3E48, 0, 1));
    if (abs >= 0x3C00)
        return half(detail::binary,
            (abs > 0x7C00)       ? detail::signal(arg.data_)
                : (abs > 0x3C00) ? detail::invalid()
                : sign           ? detail::rounded<half::round_style, true>(0x4248, 0, 1)
                                 : 0);
    std::pair<detail::uint32, detail::uint32> cs = detail::atan2_args(abs);
    detail::uint32 m = detail::atan2(cs.second, cs.first, 28);
    return half(detail::binary,
        detail::fixed2half<half::round_style, 31, false, true, true>(sign ? (0xC90FDAA2 - m) : m, 15, 0, sign));
#endif
}
 
inline half atan(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::atan(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
    if (!abs)
        return arg;
    if (abs >= 0x7C00)
        return half(detail::binary,
            (abs == 0x7C00) ? detail::rounded<half::round_style, true>(sign | 0x3E48, 0, 1)
                            : detail::signal(arg.data_));
    if (abs <= 0x2700)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 1, 1, 1));
    int exp = (abs >> 10) + (abs <= 0x3FF);
    detail::uint32 my = (abs & 0x3FF) | ((abs > 0x3FF) << 10);
    detail::uint32 m = (exp > 15)
        ? detail::atan2(my << 19, 0x20000000 >> (exp - 15), (half::round_style == std::round_to_nearest) ? 26 : 24)
        : detail::atan2(my << (exp + 4), 0x20000000, (half::round_style == std::round_to_nearest) ? 30 : 28);
    return half(detail::binary, detail::fixed2half<half::round_style, 30, false, true, true>(m, 14, sign));
#endif
}
 
inline half atan2(half y, half x)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::atan2(
            detail::half2float<detail::internal_t>(y.data_), detail::half2float<detail::internal_t>(x.data_))));
#else
    unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, signx = x.data_ >> 15, signy = y.data_ & 0x8000;
    if (absx >= 0x7C00 || absy >= 0x7C00) {
        if (absx > 0x7C00 || absy > 0x7C00)
            return half(detail::binary, detail::signal(x.data_, y.data_));
        if (absy == 0x7C00)
            return half(detail::binary,
                (absx < 0x7C00) ? detail::rounded<half::round_style, true>(signy | 0x3E48, 0, 1)
                    : signx     ? detail::rounded<half::round_style, true>(signy | 0x40B6, 0, 1)
                                : detail::rounded<half::round_style, true>(signy | 0x3A48, 0, 1));
        return (x.data_ == 0x7C00)
            ? half(detail::binary, signy)
            : half(detail::binary, detail::rounded<half::round_style, true>(signy | 0x4248, 0, 1));
    }
    if (!absy)
        return signx ? half(detail::binary, detail::rounded<half::round_style, true>(signy | 0x4248, 0, 1)) : y;
    if (!absx)
        return half(detail::binary, detail::rounded<half::round_style, true>(signy | 0x3E48, 0, 1));
    int d = (absy >> 10) + (absy <= 0x3FF) - (absx >> 10) - (absx <= 0x3FF);
    if (d > (signx ? 18 : 12))
        return half(detail::binary, detail::rounded<half::round_style, true>(signy | 0x3E48, 0, 1));
    if (signx && d < -11)
        return half(detail::binary, detail::rounded<half::round_style, true>(signy | 0x4248, 0, 1));
    if (!signx && d < ((half::round_style == std::round_toward_zero) ? -15 : -9)) {
        for (; absy < 0x400; absy <<= 1, --d)
            ;
        detail::uint32 mx = ((absx << 1) & 0x7FF) | 0x800, my = ((absy << 1) & 0x7FF) | 0x800;
        int i = my < mx;
        d -= i;
        if (d < -25)
            return half(detail::binary, detail::underflow<half::round_style>(signy));
        my <<= 11 + i;
        return half(detail::binary,
            detail::fixed2half<half::round_style, 11, false, false, true>(my / mx, d + 14, signy, my % mx != 0));
    }
    detail::uint32 m = detail::atan2(((absy & 0x3FF) | ((absy > 0x3FF) << 10)) << (19 +
                                         ((d < 0)          ? d
                                                 : (d > 0) ? 0
                                                           : -1)),
        ((absx & 0x3FF) | ((absx > 0x3FF) << 10)) << (19 -
            ((d > 0)          ? d
                    : (d < 0) ? 0
                              : 1)));
    return half(detail::binary,
        detail::fixed2half<half::round_style, 31, false, true, true>(signx ? (0xC90FDAA2 - m) : m, 15, signy, signx));
#endif
}
 
 
inline half sinh(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::sinh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp;
    if (!abs || abs >= 0x7C00)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    if (abs <= 0x2900)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_, 0, 1));
    std::pair<detail::uint32, detail::uint32> mm =
        detail::hyperbolic_args(abs, exp, (half::round_style == std::round_to_nearest) ? 29 : 27);
    detail::uint32 m = mm.first - mm.second;
    for (exp += 13; m < 0x80000000 && exp; m <<= 1, --exp)
        ;
    unsigned int sign = arg.data_ & 0x8000;
    if (exp > 29)
        return half(detail::binary, detail::overflow<half::round_style>(sign));
    return half(detail::binary, detail::fixed2half<half::round_style, 31, false, false, true>(m, exp, sign));
#endif
}
 
inline half cosh(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::cosh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp;
    if (!abs)
        return half(detail::binary, 0x3C00);
    if (abs >= 0x7C00)
        return half(detail::binary, (abs > 0x7C00) ? detail::signal(arg.data_) : 0x7C00);
    std::pair<detail::uint32, detail::uint32> mm =
        detail::hyperbolic_args(abs, exp, (half::round_style == std::round_to_nearest) ? 23 : 26);
    detail::uint32 m = mm.first + mm.second, i = (~m & 0xFFFFFFFF) >> 31;
    m = (m >> i) | (m & i) | 0x80000000;
    if ((exp += 13 + i) > 29)
        return half(detail::binary, detail::overflow<half::round_style>());
    return half(detail::binary, detail::fixed2half<half::round_style, 31, false, false, true>(m, exp));
#endif
}
 
inline half tanh(half arg)
{
#ifdef HALF_ARITHMETIC_TYPE
    return half(detail::binary,
        detail::float2half<half::round_style>(std::tanh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp;
    if (!abs)
        return arg;
    if (abs >= 0x7C00)
        return half(detail::binary, (abs > 0x7C00) ? detail::signal(arg.data_) : (arg.data_ - 0x4000));
    if (abs >= 0x4500)
        return half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x3BFF, 1, 1));
    if (abs < 0x2700)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 1, 1, 1));
    if (half::round_style != std::round_to_nearest && abs == 0x2D3F)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 3, 0, 1));
    std::pair<detail::uint32, detail::uint32> mm = detail::hyperbolic_args(abs, exp, 27);
    detail::uint32 my = mm.first - mm.second - (half::round_style != std::round_to_nearest), mx = mm.first + mm.second,
                   i = (~mx & 0xFFFFFFFF) >> 31;
    for (exp = 13; my < 0x80000000; my <<= 1, --exp)
        ;
    mx = (mx >> i) | 0x80000000;
    return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp - i, arg.data_ & 0x8000));
#endif
}
 
inline half asinh(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::asinh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF;
    if (!abs || abs >= 0x7C00)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    if (abs <= 0x2900)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 1, 1, 1));
    if (half::round_style != std::round_to_nearest)
        switch (abs) {
        case 0x32D4:
            return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 13, 1, 1));
        case 0x3B5B:
            return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_ - 197, 1, 1));
        }
    return half(detail::binary, detail::area<half::round_style, true>(arg.data_));
#endif
}
 
inline half acosh(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::acosh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF;
    if ((arg.data_ & 0x8000) || abs < 0x3C00)
        return half(detail::binary, (abs <= 0x7C00) ? detail::invalid() : detail::signal(arg.data_));
    if (abs == 0x3C00)
        return half(detail::binary, 0);
    if (arg.data_ >= 0x7C00)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    return half(detail::binary, detail::area<half::round_style, false>(arg.data_));
#endif
}
 
inline half atanh(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::atanh(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF, exp = 0;
    if (!abs)
        return arg;
    if (abs >= 0x3C00)
        return half(detail::binary,
            (abs == 0x3C00)       ? detail::pole(arg.data_ & 0x8000)
                : (abs <= 0x7C00) ? detail::invalid()
                                  : detail::signal(arg.data_));
    if (abs < 0x2700)
        return half(detail::binary, detail::rounded<half::round_style, true>(arg.data_, 0, 1));
    detail::uint32 m = static_cast<detail::uint32>((abs & 0x3FF) | ((abs > 0x3FF) << 10))
        << ((abs >> 10) + (abs <= 0x3FF) + 6),
                   my = 0x80000000 + m, mx = 0x80000000 - m;
    for (; mx < 0x80000000; mx <<= 1, ++exp)
        ;
    int i = my >= mx, s;
    return half(detail::binary,
        detail::log2_post<half::round_style, 0xB8AA3B2A>(
            detail::log2((detail::divide64(my >> i, mx, s) + 1) >> 1, 27) + 0x10, exp + i - 1, 16, arg.data_ & 0x8000));
#endif
}
 
 
inline half erf(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::erf(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF;
    if (!abs || abs >= 0x7C00)
        return (abs >= 0x7C00)
            ? half(detail::binary, (abs == 0x7C00) ? (arg.data_ - 0x4000) : detail::signal(arg.data_))
            : arg;
    if (abs >= 0x4200)
        return half(detail::binary, detail::rounded<half::round_style, true>((arg.data_ & 0x8000) | 0x3BFF, 1, 1));
    return half(detail::binary, detail::erf<half::round_style, false>(arg.data_));
#endif
}
 
inline half erfc(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::erfc(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
    if (abs >= 0x7C00)
        return (abs >= 0x7C00) ? half(detail::binary, (abs == 0x7C00) ? (sign >> 1) : detail::signal(arg.data_)) : arg;
    if (!abs)
        return half(detail::binary, 0x3C00);
    if (abs >= 0x4400)
        return half(
            detail::binary, detail::rounded<half::round_style, true>((sign >> 1) - (sign >> 15), sign >> 15, 1));
    return half(detail::binary, detail::erf<half::round_style, true>(arg.data_));
#endif
}
 
inline half lgamma(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::lgamma(detail::half2float<detail::internal_t>(arg.data_))));
#else
    int abs = arg.data_ & 0x7FFF;
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? 0x7C00 : detail::signal(arg.data_));
    if (!abs || arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs & ((1 << (25 - (abs >> 10))) - 1))))
        return half(detail::binary, detail::pole());
    if (arg.data_ == 0x3C00 || arg.data_ == 0x4000)
        return half(detail::binary, 0);
    return half(detail::binary, detail::gamma<half::round_style, true>(arg.data_));
#endif
}
 
inline half tgamma(half arg)
{
#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
    return half(detail::binary,
        detail::float2half<half::round_style>(std::tgamma(detail::half2float<detail::internal_t>(arg.data_))));
#else
    unsigned int abs = arg.data_ & 0x7FFF;
    if (!abs)
        return half(detail::binary, detail::pole(arg.data_));
    if (abs >= 0x7C00)
        return (arg.data_ == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
    if (arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs & ((1 << (25 - (abs >> 10))) - 1))))
        return half(detail::binary, detail::invalid());
    if (arg.data_ >= 0xCA80)
        return half(
            detail::binary, detail::underflow<half::round_style>((1 - ((abs >> (25 - (abs >> 10))) & 1)) << 15));
    if (arg.data_ <= 0x100 || (arg.data_ >= 0x4900 && arg.data_ < 0x8000))
        return half(detail::binary, detail::overflow<half::round_style>());
    if (arg.data_ == 0x3C00)
        return arg;
    return half(detail::binary, detail::gamma<half::round_style, false>(arg.data_));
#endif
}
 
 
inline half ceil(half arg)
{
    return half(detail::binary, detail::integral<std::round_toward_infinity, true, true>(arg.data_));
}
 
inline half floor(half arg)
{
    return half(detail::binary, detail::integral<std::round_toward_neg_infinity, true, true>(arg.data_));
}
 
inline half trunc(half arg)
{
    return half(detail::binary, detail::integral<std::round_toward_zero, true, true>(arg.data_));
}
 
inline half round(half arg)
{
    return half(detail::binary, detail::integral<std::round_to_nearest, false, true>(arg.data_));
}
 
inline long lround(half arg) { return detail::half2int<std::round_to_nearest, false, false, long>(arg.data_); }
 
inline half rint(half arg) { return half(detail::binary, detail::integral<half::round_style, true, true>(arg.data_)); }
 
inline long lrint(half arg) { return detail::half2int<half::round_style, true, true, long>(arg.data_); }
 
inline half nearbyint(half arg)
{
    return half(detail::binary, detail::integral<half::round_style, true, false>(arg.data_));
}
#if HALF_ENABLE_CPP11_LONG_LONG
inline long long llround(half arg)
{
    return detail::half2int<std::round_to_nearest, false, false, long long>(arg.data_);
}
 
inline long long llrint(half arg) { return detail::half2int<half::round_style, true, true, long long>(arg.data_); }
#endif
 
 
inline half frexp(half arg, int* exp)
{
    *exp = 0;
    unsigned int abs = arg.data_ & 0x7FFF;
    if (abs >= 0x7C00 || !abs)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    for (; abs < 0x400; abs <<= 1, --*exp)
        ;
    *exp += (abs >> 10) - 14;
    return half(detail::binary, (arg.data_ & 0x8000) | 0x3800 | (abs & 0x3FF));
}
 
inline half scalbln(half arg, long exp)
{
    unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
    if (abs >= 0x7C00 || !abs)
        return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
    for (; abs < 0x400; abs <<= 1, --exp)
        ;
    exp += abs >> 10;
    if (exp > 30)
        return half(detail::binary, detail::overflow<half::round_style>(sign));
    else if (exp < -10)
        return half(detail::binary, detail::underflow<half::round_style>(sign));
    else if (exp > 0)
        return half(detail::binary, sign | (exp << 10) | (abs & 0x3FF));
    unsigned int m = (abs & 0x3FF) | 0x400;
    return half(detail::binary,
        detail::rounded<half::round_style, false>(
            sign | (m >> (1 - exp)), (m >> -exp) & 1, (m & ((1 << -exp) - 1)) != 0));
}
 
inline half scalbn(half arg, int exp) { return scalbln(arg, exp); }
 
inline half ldexp(half arg, int exp) { return scalbln(arg, exp); }
 
inline half modf(half arg, half* iptr)
{
    unsigned int abs = arg.data_ & 0x7FFF;
    if (abs > 0x7C00) {
        arg = half(detail::binary, detail::signal(arg.data_));
        return *iptr = arg, arg;
    }
    if (abs >= 0x6400)
        return *iptr = arg, half(detail::binary, arg.data_ & 0x8000);
    if (abs < 0x3C00)
        return iptr->data_ = arg.data_ & 0x8000, arg;
    unsigned int exp = abs >> 10, mask = (1 << (25 - exp)) - 1, m = arg.data_ & mask;
    iptr->data_ = arg.data_ & ~mask;
    if (!m)
        return half(detail::binary, arg.data_ & 0x8000);
    for (; m < 0x400; m <<= 1, --exp)
        ;
    return half(detail::binary, (arg.data_ & 0x8000) | (exp << 10) | (m & 0x3FF));
}
 
inline int ilogb(half arg)
{
    int abs = arg.data_ & 0x7FFF, exp;
    if (!abs || abs >= 0x7C00) {
        detail::raise(FE_INVALID);
        return !abs ? FP_ILOGB0 : (abs == 0x7C00) ? INT_MAX : FP_ILOGBNAN;
    }
    for (exp = (abs >> 10) - 15; abs < 0x200; abs <<= 1, --exp)
        ;
    return exp;
}
 
inline half logb(half arg)
{
    int abs = arg.data_ & 0x7FFF, exp;
    if (!abs)
        return half(detail::binary, detail::pole(0x8000));
    if (abs >= 0x7C00)
        return half(detail::binary, (abs == 0x7C00) ? 0x7C00 : detail::signal(arg.data_));
    for (exp = (abs >> 10) - 15; abs < 0x200; abs <<= 1, --exp)
        ;
    unsigned int value = static_cast<unsigned>(exp < 0) << 15;
    if (exp) {
        unsigned int m = std::abs(exp) << 6;
        for (exp = 18; m < 0x400; m <<= 1, --exp)
            ;
        value |= (exp << 10) + m;
    }
    return half(detail::binary, value);
}
 
inline half nextafter(half from, half to)
{
    int fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
    if (fabs > 0x7C00 || tabs > 0x7C00)
        return half(detail::binary, detail::signal(from.data_, to.data_));
    if (from.data_ == to.data_ || !(fabs | tabs))
        return to;
    if (!fabs) {
        detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);
        return half(detail::binary, (to.data_ & 0x8000) + 1);
    }
    unsigned int out = from.data_ +
        (((from.data_ >> 15) ^
             static_cast<unsigned>((from.data_ ^ (0x8000 | (0x8000 - (from.data_ >> 15)))) <
                 (to.data_ ^ (0x8000 | (0x8000 - (to.data_ >> 15))))))
            << 1) -
        1;
    detail::raise(FE_OVERFLOW, fabs < 0x7C00 && (out & 0x7C00) == 0x7C00);
    detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out & 0x7C00) < 0x400);
    return half(detail::binary, out);
}
 
inline half nexttoward(half from, long double to)
{
    int fabs = from.data_ & 0x7FFF;
    if (fabs > 0x7C00)
        return half(detail::binary, detail::signal(from.data_));
    long double lfrom = static_cast<long double>(from);
    if (detail::builtin_isnan(to) || lfrom == to)
        return half(static_cast<float>(to));
    if (!fabs) {
        detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);
        return half(detail::binary, (static_cast<unsigned>(detail::builtin_signbit(to)) << 15) + 1);
    }
    unsigned int out = from.data_ + (((from.data_ >> 15) ^ static_cast<unsigned>(lfrom < to)) << 1) - 1;
    detail::raise(FE_OVERFLOW, (out & 0x7FFF) == 0x7C00);
    detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out & 0x7FFF) < 0x400);
    return half(detail::binary, out);
}
 
inline HALF_CONSTEXPR half copysign(half x, half y)
{
    return half(detail::binary, x.data_ ^ ((x.data_ ^ y.data_) & 0x8000));
}
 
 
inline HALF_CONSTEXPR int fpclassify(half arg)
{
    return !(arg.data_ & 0x7FFF)           ? FP_ZERO
        : ((arg.data_ & 0x7FFF) < 0x400)   ? FP_SUBNORMAL
        : ((arg.data_ & 0x7FFF) < 0x7C00)  ? FP_NORMAL
        : ((arg.data_ & 0x7FFF) == 0x7C00) ? FP_INFINITE
                                           : FP_NAN;
}
 
inline HALF_CONSTEXPR bool isfinite(half arg) { return (arg.data_ & 0x7C00) != 0x7C00; }
 
inline HALF_CONSTEXPR bool isinf(half arg) { return (arg.data_ & 0x7FFF) == 0x7C00; }
 
inline HALF_CONSTEXPR bool isnan(half arg) { return (arg.data_ & 0x7FFF) > 0x7C00; }
 
inline HALF_CONSTEXPR bool isnormal(half arg) { return ((arg.data_ & 0x7C00) != 0) & ((arg.data_ & 0x7C00) != 0x7C00); }
 
inline HALF_CONSTEXPR bool signbit(half arg) { return (arg.data_ & 0x8000) != 0; }
 
 
inline HALF_CONSTEXPR bool isgreater(half x, half y)
{
    return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) &&
        !isnan(x) && !isnan(y);
}
 
inline HALF_CONSTEXPR bool isgreaterequal(half x, half y)
{
    return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >=
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) &&
        !isnan(x) && !isnan(y);
}
 
inline HALF_CONSTEXPR bool isless(half x, half y)
{
    return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) &&
        !isnan(x) && !isnan(y);
}
 
inline HALF_CONSTEXPR bool islessequal(half x, half y)
{
    return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <=
        ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) &&
        !isnan(x) && !isnan(y);
}
 
inline HALF_CONSTEXPR bool islessgreater(half x, half y)
{
    return x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF) && !isnan(x) && !isnan(y);
}
 
inline HALF_CONSTEXPR bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
 
 
template <typename T, typename U> T half_cast(U arg) { return detail::half_caster<T, U>::cast(arg); }
 
template <typename T, std::float_round_style R, typename U> T half_cast(U arg)
{
    return detail::half_caster<T, U, R>::cast(arg);
}
 
 
inline int feclearexcept(int excepts)
{
    detail::errflags() &= ~excepts;
    return 0;
}
 
inline int fetestexcept(int excepts) { return detail::errflags() & excepts; }
 
inline int feraiseexcept(int excepts)
{
    detail::errflags() |= excepts;
    detail::raise(excepts);
    return 0;
}
 
inline int fegetexceptflag(int* flagp, int excepts)
{
    *flagp = detail::errflags() & excepts;
    return 0;
}
 
inline int fesetexceptflag(const int* flagp, int excepts)
{
    detail::errflags() = (detail::errflags() | (*flagp & excepts)) & (*flagp | ~excepts);
    return 0;
}
 
inline void fethrowexcept(int excepts, const char* msg = "")
{
    excepts &= detail::errflags();
    if (excepts & (FE_INVALID | FE_DIVBYZERO))
        throw std::domain_error(msg);
    if (excepts & FE_OVERFLOW)
        throw std::overflow_error(msg);
    if (excepts & FE_UNDERFLOW)
        throw std::underflow_error(msg);
    if (excepts & FE_INEXACT)
        throw std::range_error(msg);
}
} // namespace half_float
 
#undef HALF_UNUSED_NOERR
#undef HALF_CONSTEXPR
#undef HALF_CONSTEXPR_CONST
#undef HALF_CONSTEXPR_NOERR
#undef HALF_NOEXCEPT
#undef HALF_NOTHROW
#undef HALF_THREAD_LOCAL
#undef HALF_TWOS_COMPLEMENT_INT
#ifdef HALF_POP_WARNINGS
#pragma warning(pop)
#undef HALF_POP_WARNINGS
#endif
 
#endif