half.hpp

// half - IEEE 754-based half-precision floating point library.
//
// Copyright (c) 2012-2013 Christian Rau <rauy@users.sourceforge.net>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation 
// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, 
// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the 
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE 
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR 
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

// Version 1.11.0

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

#ifndef HALF_HALF_HPP
#define HALF_HALF_HPP

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

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

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

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

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

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


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

/// Tie-breaking behaviour for round to nearest.
/// This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is 
/// defined to `0` resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and 
/// thus equal to the round() function), but can be redefined to `1` (before including half.hpp) if more IEEE-conformant 
/// behaviour is needed.
#ifndef HALF_ROUND_TIES_TO_EVEN
	#define HALF_ROUND_TIES_TO_EVEN	0		// ties away from zero
#endif

/// Value signaling overflow.
/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to a positive value signaling the overflow of an 
/// operation, in particular it just evaluates to positive infinity.
#define HUGE_VALH	std::numeric_limits<half_float::half>::infinity()

/// Fast half-precision fma function.
/// This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate 
/// half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all 
/// arithmetic operations, this is in fact always the case.
#define FP_FAST_FMAH	1

#ifndef FP_ILOGB0
	#define FP_ILOGB0		INT_MIN
#endif
#ifndef FP_ILOGBNAN
	#define FP_ILOGBNAN		INT_MAX
#endif
#ifndef FP_SUBNORMAL
	#define FP_SUBNORMAL	0
#endif
#ifndef FP_ZERO
	#define FP_ZERO			1
#endif
#ifndef FP_NAN
	#define FP_NAN			2
#endif
#ifndef FP_INFINITE
	#define FP_INFINITE		3
#endif
#ifndef FP_NORMAL
	#define FP_NORMAL		4
#endif


/// Main namespace for half precision functionality.
/// This namespace contains all the functionality provided by the library.
namespace half_float
{
	class half;

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

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

		/// Type traits for floating point types.
		template<typename T> struct is_float : std::is_floating_point<T> {};
	#else
		/// Conditional type.
		template<bool,typename T,typename> struct conditional { typedef T type; };
		template<typename T,typename F> struct conditional<false,T,F> { typedef F type; };

		/// Helper for tag dispatching.
		template<bool> struct bool_type {};
		typedef bool_type<true> true_type;
		typedef bool_type<false> false_type;

		/// Type traits for floating point types.
		template<typename> struct is_float : false_type {};
		template<typename T> struct is_float<const T> : is_float<T> {};
		template<typename T> struct is_float<volatile T> : is_float<T> {};
		template<typename T> struct is_float<const volatile T> : is_float<T> {};
		template<> struct is_float<float> : true_type {};
		template<> struct is_float<double> : true_type {};
		template<> struct is_float<long double> : true_type {};
	#endif

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

		/// Unsigned integer of (at least) 32 bits width.
		typedef std::uint_least32_t uint32;

		/// Fastest signed integer capable of holding all values of type uint16.
		typedef std::int_fast32_t int17;
	#else
		/// Unsigned integer of (at least) 16 bits width.
		typedef unsigned short uint16;

		/// Unsigned integer of (at least) 32 bits width.
		typedef conditional<std::numeric_limits<unsigned int>::digits>=32,unsigned int,unsigned long>::type uint32;

		/// Fastest signed integer capable of holding all values of type uint16.
		typedef conditional<std::numeric_limits<int>::digits>=16,int,long>::type int17;
	#endif

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

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

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

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

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

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

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

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

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

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

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

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

		/// Convert IEEE single-precision to half-precision.
		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
		/// \param value single-precision value
		/// \return binary representation of half-precision value
		template<std::float_round_style R> uint16 float2half_impl(float value, true_type)
		{
		#if HALF_ENABLE_CPP11_STATIC_ASSERT
			static_assert(std::numeric_limits<float>::is_iec559, "float to half conversion needs IEEE 754 conformant 'float' type");
			static_assert(sizeof(uint32)==sizeof(float), "float to half conversion needs unsigned integer type of exactly the size of a 'float'");
		#endif
			static const uint16 base_table[512] = { 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, 
				0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, 
				0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 
				0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 
				0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 
				0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 };
			static const unsigned char shift_table[512] = { 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 
				13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 
				13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
			uint32 bits;// = *reinterpret_cast<uint32*>(&value);		//violating strict aliasing!
			std::memcpy(&bits, &value, sizeof(float));
			uint16 hbits = base_table[bits>>23] + static_cast<uint16>((bits&0x7FFFFF)>>shift_table[bits>>23]);
			if(R == std::round_to_nearest)
				hbits += (((bits&0x7FFFFF)>>(shift_table[bits>>23]-1))|(((bits>>23)&0xFF)==102)) & ((hbits&0x7C00)!=0x7C00)
				#if HALF_ROUND_TIES_TO_EVEN
					& (((((static_cast<uint32>(1)<<(shift_table[bits>>23]-1))-1)&bits)!=0)|hbits)
				#endif
				;
			else if(R == std::round_toward_zero)
				hbits -= ((hbits&0x7FFF)==0x7C00) & ~shift_table[bits>>23];
			else if(R == std::round_toward_infinity)
				hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=102)&
					((bits>>23)!=0)))&(hbits<0x7C00)) - ((hbits==0xFC00)&((bits>>23)!=511));
			else if(R == std::round_toward_neg_infinity)
				hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=358)&
					((bits>>23)!=256)))&(hbits<0xFC00)&(hbits>>15)) - ((hbits==0x7C00)&((bits>>23)!=255));
			return hbits;
		}

		/// Convert non-IEEE single-precision to half-precision.
		/// \param value single-precision value
		/// \return binary representation of half-precision value
		template<std::float_round_style R> uint16 float2half_impl(float value, false_type)
		{
			uint16 hbits = builtin_signbit(value) << 15;
			if(value == 0.0f)
				return hbits;
			if(builtin_isnan(value))
				return hbits | 0x7FFF;
			if(builtin_isinf(value))
				return hbits | 0x7C00;
			int exp;
			std::frexp(value, &exp);
			if(exp > 16)
			{
				if(R == std::round_toward_zero)
					return hbits | 0x7BFF;
				else if(R == std::round_toward_infinity)
					return hbits | 0x7C00 - (hbits>>15);
				else if(R == std::round_toward_neg_infinity)
					return hbits | 0x7BFF + (hbits>>15);
				return hbits | 0x7C00;
			}
			if(exp < -13)
				value = std::ldexp(value, 24);
			else
			{
				value = std::ldexp(value, 11-exp);
				hbits |= ((exp+14)<<10);
			}
			int ival = static_cast<int>(value);
			hbits |= static_cast<uint16>(std::abs(ival)&0x3FF);
			if(R == std::round_to_nearest)
			{
				float diff = std::abs(value-static_cast<float>(ival));
				#if HALF_ROUND_TIES_TO_EVEN
					hbits += (diff>0.5f) | ((diff==0.5f)&hbits);
				#else
					hbits += diff >= 0.5f;
				#endif
			}
			else if(R == std::round_toward_infinity)
				hbits += value > static_cast<float>(ival);
			else if(R == std::round_toward_neg_infinity)
				hbits += value < static_cast<float>(ival);
			return hbits;
		}

		/// Convert single-precision to half-precision.
		/// \param value single-precision value
		/// \return binary representation of half-precision value
		template<std::float_round_style R> uint16 float2half(float value)
		{
			return float2half_impl<R>(value, bool_type<std::numeric_limits<float>::is_iec559&&sizeof(uint32)==sizeof(float)>());
		}

		/// Convert integer to half-precision floating point.
		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
		/// \tparam S `true` if value negative, `false` else
		/// \tparam T type to convert (builtin integer type)
		/// \param value non-negative integral value
		/// \return binary representation of half-precision value
		template<std::float_round_style R,bool S,typename T> uint16 int2half_impl(T value)
		{
			if(S)
				value = -value;
			uint16 bits = S << 15;
			if(value > 65504)
			{
				if(R == std::round_toward_infinity)
					bits |= 0x7C00 - S;
				else if(R == std::round_toward_neg_infinity)
					bits |= 0x7BFF + S;
				else
					bits |= 0x7BFF + (R!=std::round_toward_zero);
			}
			else if(value)
			{
				unsigned int m = value, exp = 25;
				for(; m<0x400; m<<=1,--exp) ;
				for(; m>0x7FF; m>>=1,++exp) ;
				bits |= (exp<<10) | (m&0x3FF);
				if(exp > 25)
				{
					if(R == std::round_to_nearest)
						bits += (value>>(exp-26)) & 1
						#if HALF_ROUND_TIES_TO_EVEN
							& (((((1<<(exp-26))-1)&value)!=0)|bits)
						#endif
						;
					else if(R == std::round_toward_infinity)
						bits += ((value&((1<<(exp-25))-1))!=0) & !S;
					else if(R == std::round_toward_neg_infinity)
						bits += ((value&((1<<(exp-25))-1))!=0) & S;
				}
			}
			return bits;
		}

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

		/// Convert half-precision to IEEE single-precision.
		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
		/// \param value binary representation of half-precision value
		/// \return single-precision value
		inline float half2float_impl(uint16 value, true_type)
		{
		#if HALF_ENABLE_CPP11_STATIC_ASSERT
			static_assert(std::numeric_limits<float>::is_iec559, "half to float conversion needs IEEE 754 conformant 'float' type");
			static_assert(sizeof(uint32)==sizeof(float), "half to float conversion needs unsigned integer type of exactly the size of a 'float'");
		#endif
			static const uint32 mantissa_table[2048] = { 
				0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000, 
				0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, 
				0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 
				0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 
				0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, 
				0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, 
				0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, 
				0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, 
				0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 
				0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, 
				0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, 
				0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, 
				0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 
				0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, 
				0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000, 
				0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 
				0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 
				0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, 
				0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, 
				0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, 
				0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, 
				0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 
				0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, 
				0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, 
				0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, 
				0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, 
				0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, 
				0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, 
				0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, 
				0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, 
				0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 
				0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, 
				0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, 
				0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 
				0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, 
				0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, 
				0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, 
				0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, 
				0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, 
				0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, 
				0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, 
				0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, 
				0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, 
				0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 
				0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, 
				0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000, 
				0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000, 
				0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, 
				0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 
				0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, 
				0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, 
				0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, 
				0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, 
				0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, 
				0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, 
				0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, 
				0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, 
				0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 
				0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 
				0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, 
				0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000, 
				0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, 
				0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, 
				0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, 
				0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, 
				0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, 
				0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, 
				0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, 
				0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, 
				0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, 
				0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, 
				0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, 
				0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, 
				0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, 
				0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, 
				0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 
				0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, 
				0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000, 
				0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, 
				0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, 
				0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, 
				0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000, 
				0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, 
				0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 
				0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, 
				0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 
				0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, 
				0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, 
				0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 
				0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 
				0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, 
				0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, 
				0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 
				0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 
				0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, 
				0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, 
				0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, 
				0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, 
				0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 
				0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, 
				0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, 
				0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, 
				0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, 
				0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 
				0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, 
				0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, 
				0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 
				0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 
				0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, 
				0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, 
				0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 
				0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, 
				0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, 
				0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 
				0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, 
				0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, 
				0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, 
				0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, 
				0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, 
				0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, 
				0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 
				0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 
				0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, 
				0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, 
				0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 
				0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, 
				0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, 
				0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
			static const uint32 exponent_table[64] = { 
				0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000, 
				0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000, 
				0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, 
				0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
			static const unsigned short offset_table[64] = { 
				   0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 
				   0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
			uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
//			uint32 bits = mantissa_table[(((value&0x7C00)!=0)<<10)+(value&0x3FF)] + exponent_table[value>>10];
//			return *reinterpret_cast<float*>(&bits);			//violating strict aliasing!
			float out;
			std::memcpy(&out, &bits, sizeof(float));
			return out;
		}

		/// Convert half-precision to non-IEEE single-precision.
		/// \param value binary representation of half-precision value
		/// \return single-precision value
		inline float half2float_impl(uint16 value, false_type)
		{
			float out;
			int abs = value & 0x7FFF;
			if(abs > 0x7C00)
				out = std::numeric_limits<float>::has_quiet_NaN ? std::numeric_limits<float>::quiet_NaN() : 0.0f;
			else if(abs == 0x7C00)
				out = std::numeric_limits<float>::has_infinity ? std::numeric_limits<float>::infinity() : std::numeric_limits<float>::max();
			else if(abs > 0x3FF)
				out = std::ldexp(static_cast<float>((value&0x3FF)|0x400), (abs>>10)-25);
			else
				out = std::ldexp(static_cast<float>(abs), -24);
			return (value&0x8000) ? -out : out;
		}

		/// Convert half-precision to single-precision.
		/// \param value binary representation of half-precision value
		/// \return single-precision value
		inline float half2float(uint16 value)
		{
			return half2float_impl(value, bool_type<std::numeric_limits<float>::is_iec559&&sizeof(uint32)==sizeof(float)>());
		}

		/// Convert half-precision floating point to integer.
		/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
		/// \tparam E `true` for round to even, `false` for round away from zero
		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
		/// \param value binary representation of half-precision value
		/// \return integral value
		template<std::float_round_style R,bool E,typename T> T half2int_impl(uint16 value)
		{
			unsigned int e = value & 0x7FFF;
			if(e >= 0x7C00)
				return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
			if(e < 0x3800)
			{
				if(R == std::round_toward_infinity)
					return T(~(value>>15)&(e!=0));
				else if(R == std::round_toward_neg_infinity)
					return -T(value>0x8000);
				return T();
			}
			int17 m = (value&0x3FF) | 0x400;
			e >>= 10;
			if(e < 25)
			{
				if(R == std::round_indeterminate || R == std::round_toward_zero)
					m >>= 25 - e;
				else
				{
					if(R == std::round_to_nearest)
						m += (1<<(24-e)) - (~(m>>(25-e))&E);
					else if(R == std::round_toward_infinity)
						m += ((value>>15)-1) & ((1<<(25-e))-1U);
					else if(R == std::round_toward_neg_infinity)
						m += -(value>>15) & ((1<<(25-e))-1U);
					m >>= 25 - e;
				}
			}
			else
				m <<= e - 25;
//			if(std::numeric_limits<T>::digits < 16)
//				return std::min(std::max(m, static_cast<int17>(std::numeric_limits<T>::min())), static_cast<int17>(std::numeric_limits<T>::max()));
			return static_cast<T>((value&0x8000) ? -m : m);
		}

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

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

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

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

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

		struct functions;
		template<typename> struct unary_specialized;
		template<typename,typename> struct binary_specialized;
		template<typename,typename,std::float_round_style> struct half_caster;
	}

	/// Half-precision floating point type.
	/// This class implements an IEEE-conformant half-precision floating point type with the usual arithmetic operators and 
	/// conversions. It is implicitly convertible to single-precision floating point, which makes artihmetic expressions and 
	/// functions with mixed-type operands to be of the most precise operand type. Additionally all arithmetic operations 
	/// (and many mathematical functions) are carried out in single-precision internally. All conversions from single- to 
	/// half-precision are done using truncation (round towards zero), but temporary results inside chained arithmetic 
	/// expressions are kept in single-precision as long as possible (while of course still maintaining a strong half-precision type).
	///
	/// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and 
	/// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which 
	/// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the 
	/// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of 
	/// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most 
	/// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit 
	/// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if 
	/// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on 
	/// nearly any reasonable platform.
	///
	/// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable 
	/// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.
	class half
	{
		friend struct detail::functions;
		friend struct detail::unary_specialized<half>;
		friend struct detail::binary_specialized<half,half>;
		template<typename,typename,std::float_round_style> friend struct detail::half_caster;
		friend class std::numeric_limits<half>;
	#if HALF_ENABLE_CPP11_HASH
		friend struct std::hash<half>;
	#endif

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

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

		/// Conversion constructor.
		/// \param rhs float to convert
		explicit half(float rhs) : data_(detail::float2half<round_style>(rhs)) {}
	
		/// Conversion to single-precision.
		/// \return single precision value representing expression value
		operator float() const { return detail::half2float(data_); }

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

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

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

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

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

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

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

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

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

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

		/// Prefix increment.