half.hpp

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// 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 <utility>
#include <algorithm>
#include <istream>
#include <ostream>
#include <limits>
#include <stdexcept>
#include <climits>
#include <cmath>
#include <cstring>
#include <cstdlib>
#if HALF_ENABLE_CPP11_TYPE_TRAITS
    #include <type_traits>
#endif
#if HALF_ENABLE_CPP11_CSTDINT
    #include <cstdint>
#endif
#if HALF_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::true_type;
        using std::false_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;
    }
 
    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)); }
    }
#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 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 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);
    }
}
 
 
#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