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3068 lines (2768 loc) · 143 KB
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// half - IEEE 754-based half-precision floating point library.
//
// Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy,
// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
// Version 1.12.0
/// \file
/// Main header file for half precision functionality.
#ifndef HALF_HALF_HPP
#define HALF_HALF_HPP
/// Combined gcc version number.
#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__)
//check C++11 language features
#if defined(__clang__) //clang
#if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
/*#elif defined(__INTEL_COMPILER) //Intel C++
#if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ????????
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) ????????
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) ????????
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG) ????????
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif*/
#elif defined(__GNUC__) //gcc
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#endif
#elif defined(_MSC_VER) //Visual C++
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
#define HALF_ENABLE_CPP11_CONSTEXPR 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
#define HALF_ENABLE_CPP11_NOEXCEPT 1
#endif
#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
#define HALF_ENABLE_CPP11_USER_LITERALS 1
#endif
#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
#endif
#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
#define HALF_ENABLE_CPP11_LONG_LONG 1
#endif
#define HALF_POP_WARNINGS 1
#pragma warning(push)
#pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned
#endif
//check C++11 library features
#include <utility>
#if defined(_LIBCPP_VERSION) //libc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#ifndef HALF_ENABLE_CPP11_CSTDINT
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#ifndef HALF_ENABLE_CPP11_CMATH
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#ifndef HALF_ENABLE_CPP11_HASH
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#elif defined(__GLIBCXX__) //libstdc++
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
#ifdef __clang__
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#else
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#endif
#elif defined(_CPPLIB_VER) //Dinkumware/Visual C++
#if _CPPLIB_VER >= 520
#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
#endif
#ifndef HALF_ENABLE_CPP11_CSTDINT
#define HALF_ENABLE_CPP11_CSTDINT 1
#endif
#ifndef HALF_ENABLE_CPP11_HASH
#define HALF_ENABLE_CPP11_HASH 1
#endif
#endif
#if _CPPLIB_VER >= 610
#ifndef HALF_ENABLE_CPP11_CMATH
#define HALF_ENABLE_CPP11_CMATH 1
#endif
#endif
#endif
#undef HALF_GNUC_VERSION
//support constexpr
#if HALF_ENABLE_CPP11_CONSTEXPR
#define HALF_CONSTEXPR constexpr
#define HALF_CONSTEXPR_CONST constexpr
#else
#define HALF_CONSTEXPR
#define HALF_CONSTEXPR_CONST const
#endif
//support noexcept
#if HALF_ENABLE_CPP11_NOEXCEPT
#define HALF_NOEXCEPT noexcept
#define HALF_NOTHROW noexcept
#else
#define HALF_NOEXCEPT
#define HALF_NOTHROW throw()
#endif
#include <algorithm>
#include <iostream>
#include <limits>
#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_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;
#if HALF_ENABLE_CPP11_USER_LITERALS
/// Library-defined half-precision literals.
/// Import this namespace to enable half-precision floating point literals:
/// ~~~~{.cpp}
/// using namespace half_float::literal;
/// half_float::half = 4.2_h;
/// ~~~~
namespace literal
{
half operator""_h(long double);
}
#endif
/// \internal
/// \brief Implementation details.
namespace detail
{
#if HALF_ENABLE_CPP11_TYPE_TRAITS
/// Conditional type.
template<bool B,typename T,typename F> struct conditional : std::conditional<B,T,F> {};
/// Helper for tag dispatching.
template<bool B> struct bool_type : std::integral_constant<bool,B> {};
using std::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
/// Type traits for floating point bits.
template<typename T> struct bits { typedef unsigned char type; };
template<typename T> struct bits<const T> : bits<T> {};
template<typename T> struct bits<volatile T> : bits<T> {};
template<typename T> struct bits<const volatile T> : bits<T> {};
#if HALF_ENABLE_CPP11_CSTDINT
/// Unsigned integer of (at least) 16 bits width.
typedef std::uint_least16_t uint16;
/// Unsigned integer of (at least) 32 bits width.
template<> struct bits<float> { typedef std::uint_least32_t type; };
/// Unsigned integer of (at least) 64 bits width.
template<> struct bits<double> { typedef std::uint_least64_t type; };
#else
/// Unsigned integer of (at least) 16 bits width.
typedef unsigned short uint16;
/// Unsigned integer of (at least) 32 bits width.
template<> struct bits<float> : conditional<std::numeric_limits<unsigned int>::digits>=32,unsigned int,unsigned long> {};
#if HALF_ENABLE_CPP11_LONG_LONG
/// Unsigned integer of (at least) 64 bits width.
template<> struct bits<double> : conditional<std::numeric_limits<unsigned long>::digits>=64,unsigned long,unsigned long long> {};
#else
/// Unsigned integer of (at least) 64 bits width.
template<> struct bits<double> { typedef unsigned long type; };
#endif
#endif
/// Tag type for binary construction.
struct binary_t {};
/// Tag for binary construction.
HALF_CONSTEXPR_CONST binary_t binary = binary_t();
/// Temporary half-precision expression.
/// This class represents a half-precision expression which just stores a single-precision value internally.
struct expr
{
/// Conversion constructor.
/// \param f single-precision value to convert
explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {}
/// Conversion to single-precision.
/// \return single precision value representing expression value
HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; }
private:
/// Internal expression value stored in single-precision.
float value_;
};
/// SFINAE helper for generic half-precision functions.
/// This class template has to be specialized for each valid combination of argument types to provide a corresponding
/// `type` member equivalent to \a T.
/// \tparam T type to return
template<typename T,typename,typename=void,typename=void> struct enable {};
template<typename T> struct enable<T,half,void,void> { typedef T type; };
template<typename T> struct enable<T,expr,void,void> { typedef T type; };
template<typename T> struct enable<T,half,half,void> { typedef T type; };
template<typename T> struct enable<T,half,expr,void> { typedef T type; };
template<typename T> struct enable<T,expr,half,void> { typedef T type; };
template<typename T> struct enable<T,expr,expr,void> { typedef T type; };
template<typename T> struct enable<T,half,half,half> { typedef T type; };
template<typename T> struct enable<T,half,half,expr> { typedef T type; };
template<typename T> struct enable<T,half,expr,half> { typedef T type; };
template<typename T> struct enable<T,half,expr,expr> { typedef T type; };
template<typename T> struct enable<T,expr,half,half> { typedef T type; };
template<typename T> struct enable<T,expr,half,expr> { typedef T type; };
template<typename T> struct enable<T,expr,expr,half> { typedef T type; };
template<typename T> struct enable<T,expr,expr,expr> { typedef T type; };
/// Return type for specialized generic 2-argument half-precision functions.
/// This class template has to be specialized for each valid combination of argument types to provide a corresponding
/// `type` member denoting the appropriate return type.
/// \tparam T first argument type
/// \tparam U first argument type
template<typename T,typename U> struct result : enable<expr,T,U> {};
template<> struct result<half,half> { typedef half type; };
/// \name Classification helpers
/// \{
/// Check for infinity.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if infinity
/// \retval false else
template<typename T> bool builtin_isinf(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
return std::isinf(arg);
#elif defined(_MSC_VER)
return !::_finite(static_cast<double>(arg)) && !::_isnan(static_cast<double>(arg));
#else
return arg == std::numeric_limits<T>::infinity() || arg == -std::numeric_limits<T>::infinity();
#endif
}
/// Check for NaN.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if not a number
/// \retval false else
template<typename T> bool builtin_isnan(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
return std::isnan(arg);
#elif defined(_MSC_VER)
return ::_isnan(static_cast<double>(arg)) != 0;
#else
return arg != arg;
#endif
}
/// Check sign.
/// \tparam T argument type (builtin floating point type)
/// \param arg value to query
/// \retval true if signbit set
/// \retval false else
template<typename T> bool builtin_signbit(T arg)
{
#if HALF_ENABLE_CPP11_CMATH
return std::signbit(arg);
#else
return arg < T() || (arg == T() && T(1)/arg < T());
#endif
}
/// \}
/// \name Conversion
/// \{
/// Convert IEEE single-precision to half-precision.
/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \param value single-precision value
/// \return binary representation of half-precision value
template<std::float_round_style R> uint16 float2half_impl(float value, true_type)
{
typedef bits<float>::type uint32;
uint32 bits;// = *reinterpret_cast<uint32*>(&value); //violating strict aliasing!
std::memcpy(&bits, &value, sizeof(float));
/* uint16 hbits = (bits>>16) & 0x8000;
bits &= 0x7FFFFFFF;
int exp = bits >> 23;
if(exp == 255)
return hbits | 0x7C00 | (0x3FF&-static_cast<unsigned>((bits&0x7FFFFF)!=0));
if(exp > 142)
{
if(R == std::round_toward_infinity)
return hbits | 0x7C00 - (hbits>>15);
if(R == std::round_toward_neg_infinity)
return hbits | 0x7BFF + (hbits>>15);
return hbits | 0x7BFF + (R!=std::round_toward_zero);
}
int g, s;
if(exp > 112)
{
g = (bits>>12) & 1;
s = (bits&0xFFF) != 0;
hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF);
}
else if(exp > 101)
{
int i = 125 - exp;
bits = (bits&0x7FFFFF) | 0x800000;
g = (bits>>i) & 1;
s = (bits&((1L<<i)-1)) != 0;
hbits |= bits >> (i+1);
}
else
{
g = 0;
s = bits != 0;
}
if(R == std::round_to_nearest)
#if HALF_ROUND_TIES_TO_EVEN
hbits += g & (s|hbits);
#else
hbits += g;
#endif
else if(R == std::round_toward_infinity)
hbits += ~(hbits>>15) & (s|g);
else if(R == std::round_toward_neg_infinity)
hbits += (hbits>>15) & (g|s);
*/ static const uint16 base_table[512] = {
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100,
0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00,
0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100,
0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00,
0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 };
static const unsigned char shift_table[512] = {
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
uint16 hbits = base_table[bits>>23] + static_cast<uint16>((bits&0x7FFFFF)>>shift_table[bits>>23]);
if(R == std::round_to_nearest)
hbits += (((bits&0x7FFFFF)>>(shift_table[bits>>23]-1))|(((bits>>23)&0xFF)==102)) & ((hbits&0x7C00)!=0x7C00)
#if HALF_ROUND_TIES_TO_EVEN
& (((((static_cast<uint32>(1)<<(shift_table[bits>>23]-1))-1)&bits)!=0)|hbits)
#endif
;
else if(R == std::round_toward_zero)
hbits -= ((hbits&0x7FFF)==0x7C00) & ~shift_table[bits>>23];
else if(R == std::round_toward_infinity)
hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=102)&
((bits>>23)!=0)))&(hbits<0x7C00)) - ((hbits==0xFC00)&((bits>>23)!=511));
else if(R == std::round_toward_neg_infinity)
hbits += ((((bits&0x7FFFFF&((static_cast<uint32>(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=358)&
((bits>>23)!=256)))&(hbits<0xFC00)&(hbits>>15)) - ((hbits==0x7C00)&((bits>>23)!=255));
return hbits;
}
/// Convert IEEE double-precision to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \param value double-precision value
/// \return binary representation of half-precision value
template<std::float_round_style R> uint16 float2half_impl(double value, true_type)
{
typedef bits<float>::type uint32;
typedef bits<double>::type uint64;
uint64 bits;// = *reinterpret_cast<uint64*>(&value); //violating strict aliasing!
std::memcpy(&bits, &value, sizeof(double));
uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF;
uint16 hbits = (hi>>16) & 0x8000;
hi &= 0x7FFFFFFF;
int exp = hi >> 20;
if(exp == 2047)
return hbits | 0x7C00 | (0x3FF&-static_cast<unsigned>((bits&0xFFFFFFFFFFFFF)!=0));
if(exp > 1038)
{
if(R == std::round_toward_infinity)
return hbits | 0x7C00 - (hbits>>15);
if(R == std::round_toward_neg_infinity)
return hbits | 0x7BFF + (hbits>>15);
return hbits | 0x7BFF + (R!=std::round_toward_zero);
}
int g, s = lo != 0;
if(exp > 1008)
{
g = (hi>>9) & 1;
s |= (hi&0x1FF) != 0;
hbits |= ((exp-1008)<<10) | ((hi>>10)&0x3FF);
}
else if(exp > 997)
{
int i = 1018 - exp;
hi = (hi&0xFFFFF) | 0x100000;
g = (hi>>i) & 1;
s |= (hi&((1L<<i)-1)) != 0;
hbits |= hi >> (i+1);
}
else
{
g = 0;
s |= hi != 0;
}
if(R == std::round_to_nearest)
#if HALF_ROUND_TIES_TO_EVEN
hbits += g & (s|hbits);
#else
hbits += g;
#endif
else if(R == std::round_toward_infinity)
hbits += ~(hbits>>15) & (s|g);
else if(R == std::round_toward_neg_infinity)
hbits += (hbits>>15) & (g|s);
return hbits;
}
/// Convert non-IEEE floating point to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T source type (builtin floating point type)
/// \param value floating point value
/// \return binary representation of half-precision value
template<std::float_round_style R,typename T> uint16 float2half_impl(T value, ...)
{
uint16 hbits = static_cast<unsigned>(builtin_signbit(value)) << 15;
if(value == T())
return hbits;
if(builtin_isnan(value))
return hbits | 0x7FFF;
if(builtin_isinf(value))
return hbits | 0x7C00;
int exp;
std::frexp(value, &exp);
if(exp > 16)
{
if(R == std::round_toward_infinity)
return hbits | (0x7C00-(hbits>>15));
else if(R == std::round_toward_neg_infinity)
return hbits | (0x7BFF+(hbits>>15));
return hbits | (0x7BFF+(R!=std::round_toward_zero));
}
if(exp < -13)
value = std::ldexp(value, 24);
else
{
value = std::ldexp(value, 11-exp);
hbits |= ((exp+13)<<10);
}
T ival, frac = std::modf(value, &ival);
hbits += static_cast<uint16>(std::abs(static_cast<int>(ival)));
if(R == std::round_to_nearest)
{
frac = std::abs(frac);
#if HALF_ROUND_TIES_TO_EVEN
hbits += (frac>T(0.5)) | ((frac==T(0.5))&hbits);
#else
hbits += frac >= T(0.5);
#endif
}
else if(R == std::round_toward_infinity)
hbits += frac > T();
else if(R == std::round_toward_neg_infinity)
hbits += frac < T();
return hbits;
}
/// Convert floating point to half-precision.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T source type (builtin floating point type)
/// \param value floating point value
/// \return binary representation of half-precision value
template<std::float_round_style R,typename T> uint16 float2half(T value)
{
return float2half_impl<R>(value, bool_type<std::numeric_limits<T>::is_iec559&&sizeof(typename bits<T>::type)==sizeof(T)>());
}
/// Convert integer to half-precision floating point.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam S `true` if value negative, `false` else
/// \tparam T type to convert (builtin integer type)
/// \param value non-negative integral value
/// \return binary representation of half-precision value
template<std::float_round_style R,bool S,typename T> uint16 int2half_impl(T value)
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
static_assert(std::is_integral<T>::value, "int to half conversion only supports builtin integer types");
#endif
if(S)
value = -value;
uint16 bits = S << 15;
if(value > 0xFFFF)
{
if(R == std::round_toward_infinity)
bits |= 0x7C00 - S;
else if(R == std::round_toward_neg_infinity)
bits |= 0x7BFF + S;
else
bits |= 0x7BFF + (R!=std::round_toward_zero);
}
else if(value)
{
unsigned int m = value, exp = 24;
for(; m<0x400; m<<=1,--exp) ;
for(; m>0x7FF; m>>=1,++exp) ;
bits |= (exp<<10) + m;
if(exp > 24)
{
if(R == std::round_to_nearest)
bits += (value>>(exp-25)) & 1
#if HALF_ROUND_TIES_TO_EVEN
& (((((1<<(exp-25))-1)&value)!=0)|bits)
#endif
;
else if(R == std::round_toward_infinity)
bits += ((value&((1<<(exp-24))-1))!=0) & !S;
else if(R == std::round_toward_neg_infinity)
bits += ((value&((1<<(exp-24))-1))!=0) & S;
}
}
return bits;
}
/// Convert integer to half-precision floating point.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T type to convert (builtin integer type)
/// \param value integral value
/// \return binary representation of half-precision value
template<std::float_round_style R,typename T> uint16 int2half(T value)
{
return (value<0) ? int2half_impl<R,true>(value) : int2half_impl<R,false>(value);
}
/// Convert half-precision to IEEE single-precision.
/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
/// \param value binary representation of half-precision value
/// \return single-precision value
inline float half2float_impl(uint16 value, float, true_type)
{
typedef bits<float>::type uint32;
/* uint32 bits = static_cast<uint32>(value&0x8000) << 16;
int abs = value & 0x7FFF;
if(abs)
{
bits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);
for(; abs<0x400; abs<<=1,bits-=0x800000) ;
bits += static_cast<uint32>(abs) << 13;
}
*/ static const uint32 mantissa_table[2048] = {
0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000,
0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000,
0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000,
0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000,
0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000,
0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000,
0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000,
0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000,
0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000,
0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000,
0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000,
0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000,
0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000,
0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000,
0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000,
0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000,
0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000,
0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000,
0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000,
0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000,
0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000,
0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000,
0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000,
0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000,
0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000,
0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000,
0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000,
0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000,
0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000,
0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000,
0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000,
0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000,
0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000,
0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000,
0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000,
0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000,
0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000,
0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000,
0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000,
0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000,
0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000,
0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000,
0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000,
0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000,
0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000,
0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000,
0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000,
0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000,
0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000,
0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000,
0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000,
0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000,
0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000,
0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000,
0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000,
0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000,
0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA
FC98
000, 0x381BC000, 0x381BE000,
0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000,
0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000,
0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000,
0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000,
0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000,
0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000,
0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000,
0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000,
0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000,
0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000,
0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000,
0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000,
0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000,
0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000,
0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000,
0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000,
0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000,
0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000,
0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000,
0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000,
0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000,
0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000,
0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000,
0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000,
0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000,
0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000,
0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000,
0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000,
0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000,
0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000,
0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000,
0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000,
0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000,
0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000,
0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000,
0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000,
0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000,
0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000,
0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000,
0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000,
0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000,
0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000,
0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000,
0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000,
0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000,
0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000,
0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000,
0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
static const uint32 exponent_table[64] = {
0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000,
0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000,
0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000,
0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
static const unsigned short offset_table[64] = {
0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
// return *reinterpret_cast<float*>(&bits); //violating strict aliasing!
float out;
std::memcpy(&out, &bits, sizeof(float));
return out;
}
/// Convert half-precision to IEEE double-precision.
/// \param value binary representation of half-precision value
/// \return double-precision value
inline double half2float_impl(uint16 value, double, true_type)
{
typedef bits<float>::type uint32;
typedef bits<double>::type uint64;
uint32 hi = static_cast<uint32>(value&0x8000) << 16;
int abs = value & 0x7FFF;
if(abs)
{
hi |= 0x3F000000 << static_cast<unsigned>(abs>=0x7C00);
for(; abs<0x400; abs<<=1,hi-=0x100000) ;
hi += static_cast<uint32>(abs) << 10;
}
uint64 bits = static_cast<uint64>(hi) << 32;
// return *reinterpret_cast<double*>(&bits); //violating strict aliasing!
double out;
std::memcpy(&out, &bits, sizeof(double));
return out;
}
/// Convert half-precision to non-IEEE floating point.
/// \tparam T type to convert to (builtin integer type)
/// \param value binary representation of half-precision value
/// \return floating point value
template<typename T> T half2float_impl(uint16 value, T, ...)
{
T out;
int abs = value & 0x7FFF;
if(abs > 0x7C00)
out = std::numeric_limits<T>::has_quiet_NaN ? std::numeric_limits<T>::quiet_NaN() : T();
else if(abs == 0x7C00)
out = std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : std::numeric_limits<T>::max();
else if(abs > 0x3FF)
out = std::ldexp(static_cast<T>((abs&0x3FF)|0x400), (abs>>10)-25);
else
out = std::ldexp(static_cast<T>(abs), -24);
return (value&0x8000) ? -out : out;
}
/// Convert half-precision to floating point.
/// \tparam T type to convert to (builtin integer type)
/// \param value binary representation of half-precision value
/// \return floating point value
template<typename T> T half2float(uint16 value)
{
return half2float_impl(value, T(), bool_type<std::numeric_limits<T>::is_iec559&&sizeof(typename bits<T>::type)==sizeof(T)>());
}
/// Convert half-precision floating point to integer.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam E `true` for round to even, `false` for round away from zero
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
/// \param value binary representation of half-precision value
/// \return integral value
template<std::float_round_style R,bool E,typename T> T half2int_impl(uint16 value)
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
static_assert(std::is_integral<T>::value, "half to int conversion only supports builtin integer types");
#endif
unsigned int e = value & 0x7FFF;
if(e >= 0x7C00)
return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
if(e < 0x3800)
{
if(R == std::round_toward_infinity)
return T(~(value>>15)&(e!=0));
else if(R == std::round_toward_neg_infinity)
return -T(value>0x8000);
return T();
}
unsigned int m = (value&0x3FF) | 0x400;
e >>= 10;
if(e < 25)
{
if(R == std::round_to_nearest)
m += (1<<(24-e)) - (~(m>>(25-e))&E);
else if(R == std::round_toward_infinity)
m += ((value>>15)-1) & ((1<<(25-e))-1U);
else if(R == std::round_toward_neg_infinity)
m += -(value>>15) & ((1<<(25-e))-1U);
m >>= 25 - e;
}
else
m <<= e - 25;
return (value&0x8000) ? -static_cast<T>(m) : static_cast<T>(m);
}
/// Convert half-precision floating point to integer.
/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
/// \param value binary representation of half-precision value
/// \return integral value
template<std::float_round_style R,typename T> T half2int(uint16 value) { return half2int_impl<R,HALF_ROUND_TIES_TO_EVEN,T>(value); }
/// Convert half-precision floating point to integer using round-to-nearest-away-from-zero.
/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
/// \param value binary representation of half-precision value
/// \return integral value