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xenia/third_party/half/include/half.hpp

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// 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.
/// \return incremented half value
half& operator++() { return *this += 1.0f; }
/// Prefix decrement.
/// \return decremented half value
half& operator--() { return *this -= 1.0f; }
/// Postfix increment.
/// \return non-incremented half value
half operator++(int) { half out(*this); ++*this; return out; }
/// Postfix decrement.
/// \return non-decremented half value
half operator--(int) { half out(*this); --*this; return out; }
private:
/// Rounding mode to use (always `std::round_indeterminate`)
static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
/// Constructor.
/// \param bits binary representation to set half to
HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) : data_(bits) {}
/// Internal binary representation
detail::uint16 data_;
};
#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 literal.
/// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due
/// to rather involved single-to-half conversion.
/// \param value literal value
/// \return half with given value (if representable)
inline half operator "" _h(long double value) { return half(static_cast<float>(value)); }
}
#endif
namespace detail
{
/// Wrapper implementing unspecialized half-precision functions.
struct functions
{
/// Addition implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision sum stored in single-precision
static expr plus(float x, float y) { return expr(x+y); }
/// Subtraction implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision difference stored in single-precision
static expr minus(float x, float y) { return expr(x-y); }
/// Multiplication implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision product stored in single-precision
static expr multiplies(float x, float y) { return expr(x*y); }
/// Division implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision quotient stored in single-precision
static expr divides(float x, float y) { return expr(x/y); }
/// Output implementation.
/// \param out stream to write to
/// \param arg value to write
/// \return reference to stream
template<typename charT,typename traits> static std::basic_ostream<charT,traits>& write(std::basic_ostream<charT,traits> &out, float arg) { return out << arg; }
/// Input implementation.
/// \param in stream to read from
/// \param arg half to read into
/// \return reference to stream
template<typename charT,typename traits> static std::basic_istream<charT,traits>& read(std::basic_istream<charT,traits> &in, half &arg)
{
float f;
if(in >> f)
arg = f;
return in;
}
/// Modulo implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision division remainder stored in single-precision
static expr fmod(float x, float y) { return expr(std::fmod(x, y)); }
/// Remainder implementation.
/// \param x first operand
/// \param y second operand
/// \return Half-precision division remainder stored in single-precision
static expr remainder(float x, float y)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::remainder(x, y));
#else
if(builtin_isnan(x) || builtin_isnan(y))
return expr(std::numeric_limits<float>::quiet_NaN());
float ax = std::fabs(x), ay = std::fabs(y);
if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
return expr(std::numeric_limits<float>::quiet_NaN());
if(ay >= 65536.0f)
return expr(x);
if(ax == ay)
return expr(builtin_signbit(x) ? -0.0f : 0.0f);
ax = std::fmod(ax, ay+ay);
float y2 = 0.5f * ay;
if(ax > y2)
{
ax -= ay;
if(ax >= y2)
ax -= ay;
}
return expr(builtin_signbit(x) ? -ax : ax);
#endif
}
/// Remainder implementation.
/// \param x first operand
/// \param y second operand
/// \param quo address to store quotient bits at
/// \return Half-precision division remainder stored in single-precision
static expr remquo(float x, float y, int *quo)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::remquo(x, y, quo));
#else
if(builtin_isnan(x) || builtin_isnan(y))
return expr(std::numeric_limits<float>::quiet_NaN());
bool sign = builtin_signbit(x), qsign = static_cast<bool>(sign^builtin_signbit(y));
float ax = std::fabs(x), ay = std::fabs(y);
if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
return expr(std::numeric_limits<float>::quiet_NaN());
if(ay >= 65536.0f)
return expr(x);
if(ax == ay)
return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f);
ax = std::fmod(ax, 8.0f*ay);
int cquo = 0;
if(ax >= 4.0f * ay)
{
ax -= 4.0f * ay;
cquo += 4;
}
if(ax >= 2.0f * ay)
{
ax -= 2.0f * ay;
cquo += 2;
}
float y2 = 0.5f * ay;
if(ax > y2)
{
ax -= ay;
++cquo;
if(ax >= y2)
{
ax -= ay;
++cquo;
}
}
return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax);
#endif
}
/// Positive difference implementation.
/// \param x first operand
/// \param y second operand
/// \return Positive difference stored in single-precision
static expr fdim(float x, float y)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::fdim(x, y));
#else
return expr((x<=y) ? 0.0f : (x-y));
#endif
}
/// Fused multiply-add implementation.
/// \param x first operand
/// \param y second operand
/// \param z third operand
/// \return \a x * \a y + \a z stored in single-precision
static expr fma(float x, float y, float z)
{
#if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF)
return expr(std::fma(x, y, z));
#else
return expr(x*y+z);
#endif
}
/// Get NaN.
/// \return Half-precision quiet NaN
static half nanh(const char*) { return half(binary, 0x7FFF); }
/// Exponential implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr exp(float arg) { return expr(std::exp(arg)); }
/// Exponential implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr expm1(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::expm1(arg));
#else
return expr(static_cast<float>(std::exp(static_cast<double>(arg))-1.0));
#endif
}
/// Binary exponential implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr exp2(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::exp2(arg));
#else
return expr(static_cast<float>(std::exp(arg*0.69314718055994530941723212145818)));
#endif
}
/// Logarithm implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr log(float arg) { return expr(std::log(arg)); }
/// Common logarithm implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr log10(float arg) { return expr(std::log10(arg)); }
/// Logarithm implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr log1p(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::log1p(arg));
#else
return expr(static_cast<float>(std::log(1.0+arg)));
#endif
}
/// Binary logarithm implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr log2(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::log2(arg));
#else
return expr(static_cast<float>(std::log(static_cast<double>(arg))*1.4426950408889634073599246810019));
#endif
}
/// Square root implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr sqrt(float arg) { return expr(std::sqrt(arg)); }
/// Cubic root implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr cbrt(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::cbrt(arg));
#else
if(builtin_isnan(arg) || builtin_isinf(arg))
return expr(arg);
return expr(builtin_signbit(arg) ? -static_cast<float>(std::pow(std::fabs(static_cast<double>(arg)), 1.0/3.0)) :
static_cast<float>(std::pow(static_cast<double>(arg), 1.0/3.0)));
#endif
}
/// Hypotenuse implementation.
/// \param x first argument
/// \param y second argument
/// \return function value stored in single-preicision
static expr hypot(float x, float y)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::hypot(x, y));
#else
return expr((builtin_isinf(x) || builtin_isinf(y)) ? std::numeric_limits<float>::infinity() :
static_cast<float>(std::sqrt(static_cast<double>(x)*x+static_cast<double>(y)*y)));
#endif
}
/// Power implementation.
/// \param base value to exponentiate
/// \param exp power to expontiate to
/// \return function value stored in single-preicision
static expr pow(float base, float exp) { return expr(std::pow(base, exp)); }
/// Sine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr sin(float arg) { return expr(std::sin(arg)); }
/// Cosine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr cos(float arg) { return expr(std::cos(arg)); }
/// Tan implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr tan(float arg) { return expr(std::tan(arg)); }
/// Arc sine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr asin(float arg) { return expr(std::asin(arg)); }
/// Arc cosine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr acos(float arg) { return expr(std::acos(arg)); }
/// Arc tangent implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr atan(float arg) { return expr(std::atan(arg)); }
/// Arc tangent implementation.
/// \param x first argument
/// \param y second argument
/// \return function value stored in single-preicision
static expr atan2(float x, float y) { return expr(std::atan2(x, y)); }
/// Hyperbolic sine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr sinh(float arg) { return expr(std::sinh(arg)); }
/// Hyperbolic cosine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr cosh(float arg) { return expr(std::cosh(arg)); }
/// Hyperbolic tangent implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr tanh(float arg) { return expr(std::tanh(arg)); }
/// Hyperbolic area sine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr asinh(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::asinh(arg));
#else
return expr((arg==-std::numeric_limits<float>::infinity()) ? arg : static_cast<float>(std::log(arg+std::sqrt(arg*arg+1.0))));
#endif
}
/// Hyperbolic area cosine implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr acosh(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::acosh(arg));
#else
return expr((arg<-1.0f) ? std::numeric_limits<float>::quiet_NaN() : static_cast<float>(std::log(arg+std::sqrt(arg*arg-1.0))));
#endif
}
/// Hyperbolic area tangent implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr atanh(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::atanh(arg));
#else
return expr(static_cast<float>(0.5*std::log((1.0+arg)/(1.0-arg))));
#endif
}
/// Error function implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr erf(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::erf(arg));
#else
return expr(static_cast<float>(erf(static_cast<double>(arg))));
#endif
}
/// Complementary implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr erfc(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::erfc(arg));
#else
return expr(static_cast<float>(1.0-erf(static_cast<double>(arg))));
#endif
}
/// Gamma logarithm implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr lgamma(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::lgamma(arg));
#else
if(builtin_isinf(arg))
return expr(std::numeric_limits<float>::infinity());
double z = static_cast<double>(arg);
if(z < 0)
{
double i, f = std::modf(-z, &i);
if(f == 0.0)
return expr(std::numeric_limits<float>::infinity());
return expr(static_cast<float>(1.1447298858494001741434273513531-std::log(std::abs(std::sin(3.1415926535897932384626433832795*f)))-lgamma(1.0-z)));
}
// if(z < 8.0)
return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
return expr(static_cast<float>(0.5*(1.8378770664093454835606594728112-std::log(z))+z*(std::log(z+1.0/(12.0*z-1.0/(10.0*z)-1.0))-1.0)));
#endif
}
/// Gamma implementation.
/// \param arg function argument
/// \return function value stored in single-preicision
static expr tgamma(float arg)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::tgamma(arg));
#else
double z = static_cast<double>(arg);
if(z == 0.0)
return builtin_signbit(z) ? expr(-std::numeric_limits<float>::infinity()) : expr(std::numeric_limits<float>::infinity());
if(z < 0.0)
{
double i, f = std::modf(-z, &i);
if(f == 0.0)
return expr(std::numeric_limits<float>::quiet_NaN());
double sign = (std::fmod(i, 2.0)==0.0) ? -1.0 : 1.0;
return expr(static_cast<float>(sign*3.1415926535897932384626433832795/(std::sin(3.1415926535897932384626433832795*f)*std::exp(lgamma(1.0-z)))));
}
if(builtin_isinf(arg))
return expr(arg);
// if(arg < 8.0f)
return expr(static_cast<float>(std::exp(lgamma(z))));
return expr(static_cast<float>(std::sqrt(6.283185307179586476925286766559/z)*std::pow(0.36787944117144232159552377016146*(z+1.0/(12.0*z-1.0/(10.0*z))), z)));
#endif
}
/// Floor implementation.
/// \param arg value to round
/// \return rounded value
static half floor(half arg) { return half(binary, round_half<std::round_toward_neg_infinity>(arg.data_)); }
/// Ceiling implementation.
/// \param arg value to round
/// \return rounded value
static half ceil(half arg) { return half(binary, round_half<std::round_toward_infinity>(arg.data_)); }
/// Truncation implementation.
/// \param arg value to round
/// \return rounded value
static half trunc(half arg) { return half(binary, round_half<std::round_toward_zero>(arg.data_)); }
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static half round(half arg) { return half(binary, round_half_up(arg.data_)); }
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static long lround(half arg) { return detail::half2int_up<long>(arg.data_); }
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static half rint(half arg) { return half(binary, round_half<half::round_style>(arg.data_)); }
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static long lrint(half arg) { return detail::half2int<half::round_style,long>(arg.data_); }
#if HALF_ENABLE_CPP11_LONG_LONG
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static long long llround(half arg) { return detail::half2int_up<long long>(arg.data_); }
/// Nearest integer implementation.
/// \param arg value to round
/// \return rounded value
static long long llrint(half arg) { return detail::half2int<half::round_style,long long>(arg.data_); }
#endif
/// Decompression implementation.
/// \param arg number to decompress
/// \param exp address to store exponent at
/// \return normalized significant
static half frexp(half arg, int *exp)
{
unsigned int m = arg.data_ & 0x7FFF;
if(m >= 0x7C00 || !m)
return *exp = 0, arg;
int e = m >> 10;
if(!e)
for(m<<=1; m<0x400; m<<=1,--e) ;
return *exp = e-14, half(binary, static_cast<uint16>((arg.data_&0x8000)|0x3800|(m&0x3FF)));
}
/// Decompression implementation.
/// \param arg number to decompress
/// \param iptr address to store integer part at
/// \return fractional part
static half modf(half arg, half *iptr)
{
unsigned int e = arg.data_ & 0x7C00;
if(e > 0x6000)
return *iptr = arg, (e==0x7C00&&(arg.data_&0x3FF)) ? arg : half(binary, arg.data_&0x8000);
if(e < 0x3C00)
return iptr->data_ = arg.data_ & 0x8000, arg;
e >>= 10;
unsigned int mask = (1<<(25-e)) - 1, m = arg.data_ & mask;
iptr->data_ = arg.data_ & ~mask;
if(!m)
return half(binary, arg.data_&0x8000);
for(; m<0x400; m<<=1,--e) ;
return half(binary, static_cast<uint16>((arg.data_&0x8000)|(e<<10)|(m&0x3FF)));
}
/// Scaling implementation.
/// \param arg number to scale
/// \param exp power of two to scale by
/// \return scaled number
static half scalbln(half arg, long exp)
{
long e = arg.data_ & 0x7C00;
if(e == 0x7C00)
return arg;
unsigned int m = arg.data_ & 0x3FF;
if(e >>= 10)
m |= 0x400;
else
{
if(!m)
return arg;
for(m<<=1; m<0x400; m<<=1,--e) ;
}
e += exp;
uint16 value = arg.data_ & 0x8000;
if(e > 30)
{
if(half::round_style == std::round_toward_zero)
value |= 0x7BFF;
else if(half::round_style == std::round_toward_infinity)
value |= 0x7C00 - (value>>15);
else if(half::round_style == std::round_toward_neg_infinity)
value |= 0x7BFF + (value>>15);
else
value |= 0x7C00;
}
else if(e > 0)
value |= (e<<10) | (m&0x3FF);
else if(e > -11)
{
if(half::round_style == std::round_to_nearest)
{
m += 1 << -e;
#if HALF_ROUND_TIES_TO_EVEN
m -= (m>>(1-e)) & 1;
#endif
}
else if(half::round_style == std::round_toward_infinity)
m += ((value>>15)-1) & ((1<<(1-e))-1U);
else if(half::round_style == std::round_toward_neg_infinity)
m += -(value>>15) & ((1<<(1-e))-1U);
value |= m >> (1-e);
}
else if(half::round_style == std::round_toward_infinity)
value |= ((value>>15)-1) & 1;
else if(half::round_style == std::round_toward_neg_infinity)
value |= value >> 15;
return half(binary, value);
}
/// Exponent implementation.
/// \param arg number to query
/// \return floating point exponent
static int ilogb(half arg)
{
int exp = arg.data_ & 0x7FFF;
if(!exp)
return FP_ILOGB0;
if(exp < 0x7C00)
{
if(!(exp>>=10))
for(unsigned int m=(arg.data_&0x3FF); m<0x200; m<<=1,--exp) ;
return exp - 15;
}
if(exp > 0x7C00)
return FP_ILOGBNAN;
return INT_MAX;
}
/// Exponent implementation.
/// \param arg number to query
/// \return floating point exponent
static half logb(half arg)
{
int exp = arg.data_ & 0x7FFF;
if(!exp)
return half(binary, 0xFC00);
if(exp < 0x7C00)
{
if(!(exp>>=10))
for(unsigned int m=(arg.data_&0x3FF); m<0x200; m<<=1,--exp) ;
return half(static_cast<float>(exp-15));
}
if(exp > 0x7C00)
return arg;
return half(binary, 0x7C00);
}
/// Enumeration implementation.
/// \param from number to increase/decrease
/// \param to direction to enumerate into
/// \return next representable number
static half nextafter(half from, half to)
{
uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
if(fabs > 0x7C00)
return from;
if(tabs > 0x7C00 || from.data_ == to.data_ || !(fabs|tabs))
return to;
if(!fabs)
return half(binary, (to.data_&0x8000)+1);
bool lt = (signbit(from) ? (static_cast<int17>(0x8000)-from.data_) : static_cast<int17>(from.data_)) <
(signbit(to) ? (static_cast<int17>(0x8000)-to.data_) : static_cast<int17>(to.data_));
return half(binary, from.data_+(((from.data_>>15)^static_cast<uint16>(lt))<<1)-1);
}
/// Enumeration implementation.
/// \param from number to increase/decrease
/// \param to direction to enumerate into
/// \return next representable number
static half nexttoward(half from, long double to)
{
if(isnan(from))
return from;
long double lfrom = static_cast<long double>(from);
if(builtin_isnan(to) || lfrom == to)
return half(static_cast<float>(to));
if(!(from.data_&0x7FFF))
return half(binary, (static_cast<detail::uint16>(builtin_signbit(to))<<15)+1);
return half(binary, from.data_+(((from.data_>>15)^static_cast<uint16>(lfrom<to))<<1)-1);
}
/// Sign implementation
/// \param x first operand
/// \param y second operand
/// \return composed value
static half copysign(half x, half y) { return half(binary, x.data_^((x.data_^y.data_)&0x8000)); }
/// Classification implementation.
/// \param arg value to classify
/// \retval true if infinite number
/// \retval false else
static int fpclassify(half arg)
{
unsigned int abs = arg.data_ & 0x7FFF;
if(abs > 0x7C00)
return FP_NAN;
if(abs == 0x7C00)
return FP_INFINITE;
if(abs > 0x3FF)
return FP_NORMAL;
return abs ? FP_SUBNORMAL : FP_ZERO;
}
/// Classification implementation.
/// \param arg value to classify
/// \retval true if finite number
/// \retval false else
static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }
/// Classification implementation.
/// \param arg value to classify
/// \retval true if infinite number
/// \retval false else
static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }
/// Classification implementation.
/// \param arg value to classify
/// \retval true if not a number
/// \retval false else
static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }
/// Classification implementation.
/// \param arg value to classify
/// \retval true if normal number
/// \retval false else
static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }
/// Sign bit implementation.
/// \param arg value to check
/// \retval true if signed
/// \retval false if unsigned
static bool signbit(half arg) { return (arg.data_&0x8000) != 0; }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if operands equal
/// \retval false else
static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if operands not equal
/// \retval false else
static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x > \a y
/// \retval false else
static bool isgreater(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
static_cast<int17>(x.data_)) > (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x >= \a y
/// \retval false else
static bool isgreaterequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
static_cast<int17>(x.data_)) >= (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x < \a y
/// \retval false else
static bool isless(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
static_cast<int17>(x.data_)) < (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x <= \a y
/// \retval false else
static bool islessequal(half x, half y) { return !isnan(x) && !isnan(y) && ((signbit(x) ? (static_cast<int17>(0x8000)-x.data_) :
static_cast<int17>(x.data_)) <= (signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))); }
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true neither \a x > \a y nor \a x < \a y
/// \retval false else
static bool islessgreater(half x, half y)
{
if(isnan(x) || isnan(y))
return false;
int17 a = signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_);
int17 b = signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_);
return a < b || a > b;
}
/// Comparison implementation.
/// \param x first operand
/// \param y second operand
/// \retval true if operand unordered
/// \retval false else
static bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
private:
static double erf(double arg)
{
if(builtin_isinf(arg))
return (arg<0.0) ? -1.0 : 1.0;
double x2 = static_cast<double>(arg) * static_cast<double>(arg), ax2 = 0.147 * x2;
double value = std::sqrt(1.0-std::exp(-x2*(1.2732395447351626861510701069801+ax2)/(1.0+ax2)));
return builtin_signbit(arg) ? -value : value;
}
static double lgamma(double arg)
{
double v = 1.0;
for(; arg<8.0; ++arg) v *= arg;
double w = 1.0 / (arg * arg);
return (((((((-0.02955065359477124183006535947712*w+0.00641025641025641025641025641026)*w+
-0.00191752691752691752691752691753)*w+8.4175084175084175084175084175084e-4)*w+
-5.952380952380952380952380952381e-4)*w+7.9365079365079365079365079365079e-4)*w+
-0.00277777777777777777777777777778)*w+0.08333333333333333333333333333333)/arg +
0.91893853320467274178032973640562 - std::log(v) - arg + (arg-0.5) * std::log(arg);
}
};
/// Wrapper for unary half-precision functions needing specialization for individual argument types.
/// \tparam T argument type
template<typename T> struct unary_specialized
{
/// Negation implementation.
/// \param arg value to negate
/// \return negated value
static HALF_CONSTEXPR half negate(half arg) { return half(binary, arg.data_^0x8000); }
/// Absolute value implementation.
/// \param arg function argument
/// \return absolute value
static half fabs(half arg) { return half(binary, arg.data_&0x7FFF); }
};
template<> struct unary_specialized<expr>
{
static HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); }
static expr fabs(float arg) { return expr(std::fabs(arg)); }
};
/// Wrapper for binary half-precision functions needing specialization for individual argument types.
/// \tparam T first argument type
/// \tparam U first argument type
template<typename T,typename U> struct binary_specialized
{
/// Minimum implementation.
/// \param x first operand
/// \param y second operand
/// \return minimum value
static expr fmin(float x, float y)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::fmin(x, y));
#else
if(builtin_isnan(x))
return expr(y);
if(builtin_isnan(y))
return expr(x);
return expr(std::min(x, y));
#endif
}
/// Maximum implementation.
/// \param x first operand
/// \param y second operand
/// \return maximum value
static expr fmax(float x, float y)
{
#if HALF_ENABLE_CPP11_CMATH
return expr(std::fmax(x, y));
#else
if(builtin_isnan(x))
return expr(y);
if(builtin_isnan(y))
return expr(x);
return expr(std::max(x, y));
#endif
}
};
template<> struct binary_specialized<half,half>
{
static half fmin(half x, half y)
{
if(functions::isnan(x))
return y;
if(functions::isnan(y))
return x;
return ((functions::signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_)) >
(functions::signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))) ? y : x;
}
static half fmax(half x, half y)
{
if(functions::isnan(x))
return y;
if(functions::isnan(y))
return x;
return ((functions::signbit(x) ? (static_cast<int17>(0x8000)-x.data_) : static_cast<int17>(x.data_)) <
(functions::signbit(y) ? (static_cast<int17>(0x8000)-y.data_) : static_cast<int17>(y.data_))) ? y : x;
}
};
/// Helper class for half casts.
/// This class template has to be specialized for all valid cast argument to define an appropriate static `cast` member
/// function and a corresponding `type` member denoting its return type.
/// \tparam T destination type
/// \tparam U source type
/// \tparam R rounding mode to use
template<typename T,typename U,std::float_round_style R=(std::float_round_style)(HALF_ROUND_STYLE)> struct half_caster {};
template<typename U,std::float_round_style R> struct half_caster<half,U,R>
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
static_assert(std::is_arithmetic<U>::value, "half_cast from non-arithmetic type unsupported");
#endif
typedef half type;
static half cast(U arg) { return cast_impl(arg, is_float<U>()); };
private:
static half cast_impl(U arg, true_type) { return half(binary, float2half<R>(static_cast<float>(arg))); }
static half cast_impl(U arg, false_type) { return half(binary, int2half<R>(arg)); }
};
template<typename T,std::float_round_style R> struct half_caster<T,half,R>
{
#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
static_assert(std::is_arithmetic<T>::value, "half_cast to non-arithmetic type unsupported");
#endif
typedef T type;
template<typename U> static T cast(U arg) { return cast_impl(arg, is_float<T>()); }
private:
static T cast_impl(float arg, true_type) { return static_cast<T>(arg); }
static T cast_impl(half arg, false_type) { return half2int<R,T>(arg.data_); }
};
template<typename T,std::float_round_style R> struct half_caster<T,expr,R> : public half_caster<T,half,R> {};
template<std::float_round_style R> struct half_caster<half,half,R>
{
typedef half type;
static half cast(half arg) { return arg; }
};
template<std::float_round_style R> struct half_caster<half,expr,R> : public half_caster<half,half,R> {};
/// \name Comparison operators
/// \{
/// Comparison for equality.
/// \param x first operand
/// \param y second operand
/// \retval true if operands equal
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator==(T x, U y) { return functions::isequal(x, y); }
/// Comparison for inequality.
/// \param x first operand
/// \param y second operand
/// \retval true if operands not equal
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator!=(T x, U y) { return functions::isnotequal(x, y); }
/// Comparison for less than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less than \a y
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator<(T x, U y) { return functions::isless(x, y); }
/// Comparison for greater than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater than \a y
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator>(T x, U y) { return functions::isgreater(x, y); }
/// Comparison for less equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less equal \a y
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator<=(T x, U y) { return functions::islessequal(x, y); }
/// Comparison for greater equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater equal \a y
/// \retval false else
template<typename T,typename U> typename enable<bool,T,U>::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); }
/// \}
/// \name Arithmetic operators
/// \{
/// Add halfs.
/// \param x left operand
/// \param y right operand
/// \return sum of half expressions
template<typename T,typename U> typename enable<expr,T,U>::type operator+(T x, U y) { return functions::plus(x, y); }
/// Subtract halfs.
/// \param x left operand
/// \param y right operand
/// \return difference of half expressions
template<typename T,typename U> typename enable<expr,T,U>::type operator-(T x, U y) { return functions::minus(x, y); }
/// Multiply halfs.
/// \param x left operand
/// \param y right operand
/// \return product of half expressions
template<typename T,typename U> typename enable<expr,T,U>::type operator*(T x, U y) { return functions::multiplies(x, y); }
/// Divide halfs.
/// \param x left operand
/// \param y right operand
/// \return quotient of half expressions
template<typename T,typename U> typename enable<expr,T,U>::type operator/(T x, U y) { return functions::divides(x, y); }
/// Identity.
/// \param arg operand
/// \return uncahnged operand
template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator+(T arg) { return arg; }
/// Negation.
/// \param arg operand
/// \return negated operand
template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator-(T arg) { return unary_specialized<T>::negate(arg); }
/// \}
/// \name Input and output
/// \{
/// Output operator.
/// \param out output stream to write into
/// \param arg half expression to write
/// \return reference to output stream
template<typename T,typename charT,typename traits> typename enable<std::basic_ostream<charT,traits>&,T>::type
operator<<(std::basic_ostream<charT,traits> &out, T arg) { return functions::write(out, arg); }
/// Input operator.
/// \param in input stream to read from
/// \param arg half to read into
/// \return reference to input stream
template<typename charT,typename traits> std::basic_istream<charT,traits>&
operator>>(std::basic_istream<charT,traits> &in, half &arg) { return functions::read(in, arg); }
/// \}
/// \name Basic mathematical operations
/// \{
/// Absolute value.
/// \param arg operand
/// \return absolute value of \a arg
// template<typename T> typename enable<T,T>::type abs(T arg) { return unary_specialized<T>::fabs(arg); }
inline half abs(half arg) { return unary_specialized<half>::fabs(arg); }
inline expr abs(expr arg) { return unary_specialized<expr>::fabs(arg); }
/// Absolute value.
/// \param arg operand
/// \return absolute value of \a arg
// template<typename T> typename enable<T,T>::type fabs(T arg) { return unary_specialized<T>::fabs(arg); }
inline half fabs(half arg) { return unary_specialized<half>::fabs(arg); }
inline expr fabs(expr arg) { return unary_specialized<expr>::fabs(arg); }
/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \return remainder of floating point division.
// template<typename T,typename U> typename enable<expr,T,U>::type fmod(T x, U y) { return functions::fmod(x, y); }
inline expr fmod(half x, half y) { return functions::fmod(x, y); }
inline expr fmod(half x, expr y) { return functions::fmod(x, y); }
inline expr fmod(expr x, half y) { return functions::fmod(x, y); }
inline expr fmod(expr x, expr y) { return functions::fmod(x, y); }
/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \return remainder of floating point division.
// template<typename T,typename U> typename enable<expr,T,U>::type remainder(T x, U y) { return functions::remainder(x, y); }
inline expr remainder(half x, half y) { return functions::remainder(x, y); }
inline expr remainder(half x, expr y) { return functions::remainder(x, y); }
inline expr remainder(expr x, half y) { return functions::remainder(x, y); }
inline expr remainder(expr x, expr y) { return functions::remainder(x, y); }
/// Remainder of division.
/// \param x first operand
/// \param y second operand
/// \param quo address to store some bits of quotient at
/// \return remainder of floating point division.
// template<typename T,typename U> typename enable<expr,T,U>::type remquo(T x, U y, int *quo) { return functions::remquo(x, y, quo); }
inline expr remquo(half x, half y, int *quo) { return functions::remquo(x, y, quo); }
inline expr remquo(half x, expr y, int *quo) { return functions::remquo(x, y, quo); }
inline expr remquo(expr x, half y, int *quo) { return functions::remquo(x, y, quo); }
inline expr remquo(expr x, expr y, int *quo) { return functions::remquo(x, y, quo); }
/// Fused multiply add.
/// \param x first operand
/// \param y second operand
/// \param z third operand
/// \return ( \a x * \a y ) + \a z rounded as one operation.
// template<typename T,typename U,typename V> typename enable<expr,T,U,V>::type fma(T x, U y, V z) { return functions::fma(x, y, z); }
inline expr fma(half x, half y, half z) { return functions::fma(x, y, z); }
inline expr fma(half x, half y, expr z) { return functions::fma(x, y, z); }
inline expr fma(half x, expr y, half z) { return functions::fma(x, y, z); }
inline expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); }
inline expr fma(expr x, half y, half z) { return functions::fma(x, y, z); }
inline expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); }
inline expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); }
inline expr fma(expr x, expr y, expr z) { return functions::fma(x, y, z); }
/// Maximum of half expressions.
/// \param x first operand
/// \param y second operand
/// \return maximum of operands
// template<typename T,typename U> typename result<T,U>::type fmax(T x, U y) { return binary_specialized<T,U>::fmax(x, y); }
inline half fmax(half x, half y) { return binary_specialized<half,half>::fmax(x, y); }
inline expr fmax(half x, expr y) { return binary_specialized<half,expr>::fmax(x, y); }
inline expr fmax(expr x, half y) { return binary_specialized<expr,half>::fmax(x, y); }
inline expr fmax(expr x, expr y) { return binary_specialized<expr,expr>::fmax(x, y); }
/// Minimum of half expressions.
/// \param x first operand
/// \param y second operand
/// \return minimum of operands
// template<typename T,typename U> typename result<T,U>::type fmin(T x, U y) { return binary_specialized<T,U>::fmin(x, y); }
inline half fmin(half x, half y) { return binary_specialized<half,half>::fmin(x, y); }
inline expr fmin(half x, expr y) { return binary_specialized<half,expr>::fmin(x, y); }
inline expr fmin(expr x, half y) { return binary_specialized<expr,half>::fmin(x, y); }
inline expr fmin(expr x, expr y) { return binary_specialized<expr,expr>::fmin(x, y); }
/// Positive difference.
/// \param x first operand
/// \param y second operand
/// \return \a x - \a y or 0 if difference negative
// template<typename T,typename U> typename enable<expr,T,U>::type fdim(T x, U y) { return functions::fdim(x, y); }
inline expr fdim(half x, half y) { return functions::fdim(x, y); }
inline expr fdim(half x, expr y) { return functions::fdim(x, y); }
inline expr fdim(expr x, half y) { return functions::fdim(x, y); }
inline expr fdim(expr x, expr y) { return functions::fdim(x, y); }
/// Get NaN value.
/// \param arg descriptive string (ignored)
/// \return quiet NaN
inline half nanh(const char *arg) { return functions::nanh(arg); }
/// \}
/// \name Exponential functions
/// \{
/// Exponential function.
/// \param arg function argument
/// \return e raised to \a arg
// template<typename T> typename enable<expr,T>::type exp(T arg) { return functions::exp(arg); }
inline expr exp(half arg) { return functions::exp(arg); }
inline expr exp(expr arg) { return functions::exp(arg); }
/// Exponential minus one.
/// \param arg function argument
/// \return e raised to \a arg subtracted by 1
// template<typename T> typename enable<expr,T>::type expm1(T arg) { return functions::expm1(arg); }
inline expr expm1(half arg) { return functions::expm1(arg); }
inline expr expm1(expr arg) { return functions::expm1(arg); }
/// Binary exponential.
/// \param arg function argument
/// \return 2 raised to \a arg
// template<typename T> typename enable<expr,T>::type exp2(T arg) { return functions::exp2(arg); }
inline expr exp2(half arg) { return functions::exp2(arg); }
inline expr exp2(expr arg) { return functions::exp2(arg); }
/// Natural logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base e
// template<typename T> typename enable<expr,T>::type log(T arg) { return functions::log(arg); }
inline expr log(half arg) { return functions::log(arg); }
inline expr log(expr arg) { return functions::log(arg); }
/// Common logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base 10
// template<typename T> typename enable<expr,T>::type log10(T arg) { return functions::log10(arg); }
inline expr log10(half arg) { return functions::log10(arg); }
inline expr log10(expr arg) { return functions::log10(arg); }
/// Natural logorithm.
/// \param arg function argument
/// \return logarithm of \a arg plus 1 to base e
// template<typename T> typename enable<expr,T>::type log1p(T arg) { return functions::log1p(arg); }
inline expr log1p(half arg) { return functions::log1p(arg); }
inline expr log1p(expr arg) { return functions::log1p(arg); }
/// Binary logorithm.
/// \param arg function argument
/// \return logarithm of \a arg to base 2
// template<typename T> typename enable<expr,T>::type log2(T arg) { return functions::log2(arg); }
inline expr log2(half arg) { return functions::log2(arg); }
inline expr log2(expr arg) { return functions::log2(arg); }
/// \}
/// \name Power functions
/// \{
/// Square root.
/// \param arg function argument
/// \return square root of \a arg
// template<typename T> typename enable<expr,T>::type sqrt(T arg) { return functions::sqrt(arg); }
inline expr sqrt(half arg) { return functions::sqrt(arg); }
inline expr sqrt(expr arg) { return functions::sqrt(arg); }
/// Cubic root.
/// \param arg function argument
/// \return cubic root of \a arg
// template<typename T> typename enable<expr,T>::type cbrt(T arg) { return functions::cbrt(arg); }
inline expr cbrt(half arg) { return functions::cbrt(arg); }
inline expr cbrt(expr arg) { return functions::cbrt(arg); }
/// Hypotenuse function.
/// \param x first argument
/// \param y second argument
/// \return square root of sum of squares without internal over- or underflows
// template<typename T,typename U> typename enable<expr,T,U>::type hypot(T x, U y) { return functions::hypot(x, y); }
inline expr hypot(half x, half y) { return functions::hypot(x, y); }
inline expr hypot(half x, expr y) { return functions::hypot(x, y); }
inline expr hypot(expr x, half y) { return functions::hypot(x, y); }
inline expr hypot(expr x, expr y) { return functions::hypot(x, y); }
/// Power function.
/// \param base first argument
/// \param exp second argument
/// \return \a base raised to \a exp
// template<typename T,typename U> typename enable<expr,T,U>::type pow(T base, U exp) { return functions::pow(base, exp); }
inline expr pow(half base, half exp) { return functions::pow(base, exp); }
inline expr pow(half base, expr exp) { return functions::pow(base, exp); }
inline expr pow(expr base, half exp) { return functions::pow(base, exp); }
inline expr pow(expr base, expr exp) { return functions::pow(base, exp); }
/// \}
/// \name Trigonometric functions
/// \{
/// Sine function.
/// \param arg function argument
/// \return sine value of \a arg
// template<typename T> typename enable<expr,T>::type sin(T arg) { return functions::sin(arg); }
inline expr sin(half arg) { return functions::sin(arg); }
inline expr sin(expr arg) { return functions::sin(arg); }
/// Cosine function.
/// \param arg function argument
/// \return cosine value of \a arg
// template<typename T> typename enable<expr,T>::type cos(T arg) { return functions::cos(arg); }
inline expr cos(half arg) { return functions::cos(arg); }
inline expr cos(expr arg) { return functions::cos(arg); }
/// Tangent function.
/// \param arg function argument
/// \return tangent value of \a arg
// template<typename T> typename enable<expr,T>::type tan(T arg) { return functions::tan(arg); }
inline expr tan(half arg) { return functions::tan(arg); }
inline expr tan(expr arg) { return functions::tan(arg); }
/// Arc sine.
/// \param arg function argument
/// \return arc sine value of \a arg
// template<typename T> typename enable<expr,T>::type asin(T arg) { return functions::asin(arg); }
inline expr asin(half arg) { return functions::asin(arg); }
inline expr asin(expr arg) { return functions::asin(arg); }
/// Arc cosine function.
/// \param arg function argument
/// \return arc cosine value of \a arg
// template<typename T> typename enable<expr,T>::type acos(T arg) { return functions::acos(arg); }
inline expr acos(half arg) { return functions::acos(arg); }
inline expr acos(expr arg) { return functions::acos(arg); }
/// Arc tangent function.
/// \param arg function argument
/// \return arc tangent value of \a arg
// template<typename T> typename enable<expr,T>::type atan(T arg) { return functions::atan(arg); }
inline expr atan(half arg) { return functions::atan(arg); }
inline expr atan(expr arg) { return functions::atan(arg); }
/// Arc tangent function.
/// \param x first argument
/// \param y second argument
/// \return arc tangent value
// template<typename T,typename U> typename enable<expr,T,U>::type atan2(T x, U y) { return functions::atan2(x, y); }
inline expr atan2(half x, half y) { return functions::atan2(x, y); }
inline expr atan2(half x, expr y) { return functions::atan2(x, y); }
inline expr atan2(expr x, half y) { return functions::atan2(x, y); }
inline expr atan2(expr x, expr y) { return functions::atan2(x, y); }
/// \}
/// \name Hyperbolic functions
/// \{
/// Hyperbolic sine.
/// \param arg function argument
/// \return hyperbolic sine value of \a arg
// template<typename T> typename enable<expr,T>::type sinh(T arg) { return functions::sinh(arg); }
inline expr sinh(half arg) { return functions::sinh(arg); }
inline expr sinh(expr arg) { return functions::sinh(arg); }
/// Hyperbolic cosine.
/// \param arg function argument
/// \return hyperbolic cosine value of \a arg
// template<typename T> typename enable<expr,T>::type cosh(T arg) { return functions::cosh(arg); }
inline expr cosh(half arg) { return functions::cosh(arg); }
inline expr cosh(expr arg) { return functions::cosh(arg); }
/// Hyperbolic tangent.
/// \param arg function argument
/// \return hyperbolic tangent value of \a arg
// template<typename T> typename enable<expr,T>::type tanh(T arg) { return functions::tanh(arg); }
inline expr tanh(half arg) { return functions::tanh(arg); }
inline expr tanh(expr arg) { return functions::tanh(arg); }
/// Hyperbolic area sine.
/// \param arg function argument
/// \return area sine value of \a arg
// template<typename T> typename enable<expr,T>::type asinh(T arg) { return functions::asinh(arg); }
inline expr asinh(half arg) { return functions::asinh(arg); }
inline expr asinh(expr arg) { return functions::asinh(arg); }
/// Hyperbolic area cosine.
/// \param arg function argument
/// \return area cosine value of \a arg
// template<typename T> typename enable<expr,T>::type acosh(T arg) { return functions::acosh(arg); }
inline expr acosh(half arg) { return functions::acosh(arg); }
inline expr acosh(expr arg) { return functions::acosh(arg); }
/// Hyperbolic area tangent.
/// \param arg function argument
/// \return area tangent value of \a arg
// template<typename T> typename enable<expr,T>::type atanh(T arg) { return functions::atanh(arg); }
inline expr atanh(half arg) { return functions::atanh(arg); }
inline expr atanh(expr arg) { return functions::atanh(arg); }
/// \}
/// \name Error and gamma functions
/// \{
/// Error function.
/// \param arg function argument
/// \return error function value of \a arg
// template<typename T> typename enable<expr,T>::type erf(T arg) { return functions::erf(arg); }
inline expr erf(half arg) { return functions::erf(arg); }
inline expr erf(expr arg) { return functions::erf(arg); }
/// Complementary error function.
/// \param arg function argument
/// \return 1 minus error function value of \a arg
// template<typename T> typename enable<expr,T>::type erfc(T arg) { return functions::erfc(arg); }
inline expr erfc(half arg) { return functions::erfc(arg); }
inline expr erfc(expr arg) { return functions::erfc(arg); }
/// Natural logarithm of gamma function.
/// \param arg function argument
/// \return natural logarith of gamma function for \a arg
// template<typename T> typename enable<expr,T>::type lgamma(T arg) { return functions::lgamma(arg); }
inline expr lgamma(half arg) { return functions::lgamma(arg); }
inline expr lgamma(expr arg) { return functions::lgamma(arg); }
/// Gamma function.
/// \param arg function argument
/// \return gamma function value of \a arg
// template<typename T> typename enable<expr,T>::type tgamma(T arg) { return functions::tgamma(arg); }
inline expr tgamma(half arg) { return functions::tgamma(arg); }
inline expr tgamma(expr arg) { return functions::tgamma(arg); }
/// \}
/// \name Rounding
/// \{
/// Nearest integer not less than half value.
/// \param arg half to round
/// \return nearest integer not less than \a arg
// template<typename T> typename enable<half,T>::type ceil(T arg) { return functions::ceil(arg); }
inline half ceil(half arg) { return functions::ceil(arg); }
inline half ceil(expr arg) { return functions::ceil(arg); }
/// Nearest integer not greater than half value.
/// \param arg half to round
/// \return nearest integer not greater than \a arg
// template<typename T> typename enable<half,T>::type floor(T arg) { return functions::floor(arg); }
inline half floor(half arg) { return functions::floor(arg); }
inline half floor(expr arg) { return functions::floor(arg); }
/// Nearest integer not greater in magnitude than half value.
/// \param arg half to round
/// \return nearest integer not greater in magnitude than \a arg
// template<typename T> typename enable<half,T>::type trunc(T arg) { return functions::trunc(arg); }
inline half trunc(half arg) { return functions::trunc(arg); }
inline half trunc(expr arg) { return functions::trunc(arg); }
/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
// template<typename T> typename enable<half,T>::type round(T arg) { return functions::round(arg); }
inline half round(half arg) { return functions::round(arg); }
inline half round(expr arg) { return functions::round(arg); }
/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
// template<typename T> typename enable<long,T>::type lround(T arg) { return functions::lround(arg); }
inline long lround(half arg) { return functions::lround(arg); }
inline long lround(expr arg) { return functions::lround(arg); }
/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
// template<typename T> typename enable<half,T>::type nearbyint(T arg) { return functions::nearbyint(arg); }
inline half nearbyint(half arg) { return functions::rint(arg); }
inline half nearbyint(expr arg) { return functions::rint(arg); }
/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
// template<typename T> typename enable<half,T>::type rint(T arg) { return functions::rint(arg); }
inline half rint(half arg) { return functions::rint(arg); }
inline half rint(expr arg) { return functions::rint(arg); }
/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
// template<typename T> typename enable<long,T>::type lrint(T arg) { return functions::lrint(arg); }
inline long lrint(half arg) { return functions::lrint(arg); }
inline long lrint(expr arg) { return functions::lrint(arg); }
#if HALF_ENABLE_CPP11_LONG_LONG
/// Nearest integer.
/// \param arg half to round
/// \return nearest integer, rounded away from zero in half-way cases
// template<typename T> typename enable<long long,T>::type llround(T arg) { return functions::llround(arg); }
inline long long llround(half arg) { return functions::llround(arg); }
inline long long llround(expr arg) { return functions::llround(arg); }
/// Nearest integer using half's internal rounding mode.
/// \param arg half expression to round
/// \return nearest integer using default rounding mode
// template<typename T> typename enable<long long,T>::type llrint(T arg) { return functions::llrint(arg); }
inline long long llrint(half arg) { return functions::llrint(arg); }
inline long long llrint(expr arg) { return functions::llrint(arg); }
#endif
/// \}
/// \name Floating point manipulation
/// \{
/// Decompress floating point number.
/// \param arg number to decompress
/// \param exp address to store exponent at
/// \return significant in range [0.5, 1)
// template<typename T> typename enable<half,T>::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); }
inline half frexp(half arg, int *exp) { return functions::frexp(arg, exp); }
inline half frexp(expr arg, int *exp) { return functions::frexp(arg, exp); }
/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
// template<typename T> typename enable<half,T>::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp); }
inline half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); }
inline half ldexp(expr arg, int exp) { return functions::scalbln(arg, exp); }
/// Extract integer and fractional parts.
/// \param arg number to decompress
/// \param iptr address to store integer part at
/// \return fractional part
// template<typename T> typename enable<half,T>::type modf(T arg, half *iptr) { return functions::modf(arg, iptr); }
inline half modf(half arg, half *iptr) { return functions::modf(arg, iptr); }
inline half modf(expr arg, half *iptr) { return functions::modf(arg, iptr); }
/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
// template<typename T> typename enable<half,T>::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp); }
inline half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); }
inline half scalbn(expr arg, int exp) { return functions::scalbln(arg, exp); }
/// Multiply by power of two.
/// \param arg number to modify
/// \param exp power of two to multiply with
/// \return \a arg multplied by 2 raised to \a exp
// template<typename T> typename enable<half,T>::type scalbln(T arg, long exp) { return functions::scalbln(arg, exp); }
inline half scalbln(half arg, long exp) { return functions::scalbln(arg, exp); }
inline half scalbln(expr arg, long exp) { return functions::scalbln(arg, exp); }
/// Extract exponent.
/// \param arg number to query
/// \return floating point exponent
/// \retval FP_ILOGB0 for zero
/// \retval FP_ILOGBNAN for NaN
/// \retval MAX_INT for infinity
// template<typename T> typename enable<int,T>::type ilogb(T arg) { return functions::ilogb(arg); }
inline int ilogb(half arg) { return functions::ilogb(arg); }
inline int ilogb(expr arg) { return functions::ilogb(arg); }
/// Extract exponent.
/// \param arg number to query
/// \return floating point exponent
// template<typename T> typename enable<half,T>::type logb(T arg) { return functions::logb(arg); }
inline half logb(half arg) { return functions::logb(arg); }
inline half logb(expr arg) { return functions::logb(arg); }
/// Next representable value.
/// \param from value to compute next representable value for
/// \param to direction towards which to compute next value
/// \return next representable value after \a from in direction towards \a to
// template<typename T,typename U> typename enable<half,T,U>::type nextafter(T from, U to) { return functions::nextafter(from, to); }
inline half nextafter(half from, half to) { return functions::nextafter(from, to); }
inline half nextafter(half from, expr to) { return functions::nextafter(from, to); }
inline half nextafter(expr from, half to) { return functions::nextafter(from, to); }
inline half nextafter(expr from, expr to) { return functions::nextafter(from, to); }
/// Next representable value.
/// \param from value to compute next representable value for
/// \param to direction towards which to compute next value
/// \return next representable value after \a from in direction towards \a to
// template<typename T> typename enable<half,T>::type nexttoward(T from, long double to) { return functions::nexttoward(from, to); }
inline half nexttoward(half from, long double to) { return functions::nexttoward(from, to); }
inline half nexttoward(expr from, long double to) { return functions::nexttoward(from, to); }
/// Take sign.
/// \param x value to change sign for
/// \param y value to take sign from
/// \return value equal to \a x in magnitude and to \a y in sign
// template<typename T,typename U> typename enable<half,T,U>::type copysign(T x, U y) { return functions::copysign(x, y); }
inline half copysign(half x, half y) { return functions::copysign(x, y); }
inline half copysign(half x, expr y) { return functions::copysign(x, y); }
inline half copysign(expr x, half y) { return functions::copysign(x, y); }
inline half copysign(expr x, expr y) { return functions::copysign(x, y); }
/// \}
/// \name Floating point classification
/// \{
/// Classify floating point value.
/// \param arg number to classify
/// \retval FP_ZERO for positive and negative zero
/// \retval FP_SUBNORMAL for subnormal numbers
/// \retval FP_INFINITY for positive and negative infinity
/// \retval FP_NAN for NaNs
/// \retval FP_NORMAL for all other (normal) values
// template<typename T> typename enable<int,T>::type fpclassify(T arg) { return functions::fpclassify(arg); }
inline int fpclassify(half arg) { return functions::fpclassify(arg); }
inline int fpclassify(expr arg) { return functions::fpclassify(arg); }
/// Check if finite number.
/// \param arg number to check
/// \retval true if neither infinity nor NaN
/// \retval false else
// template<typename T> typename enable<bool,T>::type isfinite(T arg) { return functions::isfinite(arg); }
inline bool isfinite(half arg) { return functions::isfinite(arg); }
inline bool isfinite(expr arg) { return functions::isfinite(arg); }
/// Check for infinity.
/// \param arg number to check
/// \retval true for positive or negative infinity
/// \retval false else
// template<typename T> typename enable<bool,T>::type isinf(T arg) { return functions::isinf(arg); }
inline bool isinf(half arg) { return functions::isinf(arg); }
inline bool isinf(expr arg) { return functions::isinf(arg); }
/// Check for NaN.
/// \param arg number to check
/// \retval true for NaNs
/// \retval false else
// template<typename T> typename enable<bool,T>::type isnan(T arg) { return functions::isnan(arg); }
inline bool isnan(half arg) { return functions::isnan(arg); }
inline bool isnan(expr arg) { return functions::isnan(arg); }
/// Check if normal number.
/// \param arg number to check
/// \retval true if normal number
/// \retval false if either subnormal, zero, infinity or NaN
// template<typename T> typename enable<bool,T>::type isnormal(T arg) { return functions::isnormal(arg); }
inline bool isnormal(half arg) { return functions::isnormal(arg); }
inline bool isnormal(expr arg) { return functions::isnormal(arg); }
/// Check sign.
/// \param arg number to check
/// \retval true for negative number
/// \retval false for positive number
// template<typename T> typename enable<bool,T>::type signbit(T arg) { return functions::signbit(arg); }
inline bool signbit(half arg) { return functions::signbit(arg); }
inline bool signbit(expr arg) { return functions::signbit(arg); }
/// \}
/// \name Comparison
/// \{
/// Comparison for greater than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater than \a y
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type isgreater(T x, U y) { return functions::isgreater(x, y); }
inline bool isgreater(half x, half y) { return functions::isgreater(x, y); }
inline bool isgreater(half x, expr y) { return functions::isgreater(x, y); }
inline bool isgreater(expr x, half y) { return functions::isgreater(x, y); }
inline bool isgreater(expr x, expr y) { return functions::isgreater(x, y); }
/// Comparison for greater equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x greater equal \a y
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type isgreaterequal(T x, U y) { return functions::isgreaterequal(x, y); }
inline bool isgreaterequal(half x, half y) { return functions::isgreaterequal(x, y); }
inline bool isgreaterequal(half x, expr y) { return functions::isgreaterequal(x, y); }
inline bool isgreaterequal(expr x, half y) { return functions::isgreaterequal(x, y); }
inline bool isgreaterequal(expr x, expr y) { return functions::isgreaterequal(x, y); }
/// Comparison for less than.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less than \a y
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type isless(T x, U y) { return functions::isless(x, y); }
inline bool isless(half x, half y) { return functions::isless(x, y); }
inline bool isless(half x, expr y) { return functions::isless(x, y); }
inline bool isless(expr x, half y) { return functions::isless(x, y); }
inline bool isless(expr x, expr y) { return functions::isless(x, y); }
/// Comparison for less equal.
/// \param x first operand
/// \param y second operand
/// \retval true if \a x less equal \a y
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type islessequal(T x, U y) { return functions::islessequal(x, y); }
inline bool islessequal(half x, half y) { return functions::islessequal(x, y); }
inline bool islessequal(half x, expr y) { return functions::islessequal(x, y); }
inline bool islessequal(expr x, half y) { return functions::islessequal(x, y); }
inline bool islessequal(expr x, expr y) { return functions::islessequal(x, y); }
/// Comarison for less or greater.
/// \param x first operand
/// \param y second operand
/// \retval true if either less or greater
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type islessgreater(T x, U y) { return functions::islessgreater(x, y); }
inline bool islessgreater(half x, half y) { return functions::islessgreater(x, y); }
inline bool islessgreater(half x, expr y) { return functions::islessgreater(x, y); }
inline bool islessgreater(expr x, half y) { return functions::islessgreater(x, y); }
inline bool islessgreater(expr x, expr y) { return functions::islessgreater(x, y); }
/// Check if unordered.
/// \param x first operand
/// \param y second operand
/// \retval true if unordered (one or two NaN operands)
/// \retval false else
// template<typename T,typename U> typename enable<bool,T,U>::type isunordered(T x, U y) { return functions::isunordered(x, y); }
inline bool isunordered(half x, half y) { return functions::isunordered(x, y); }
inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); }
inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); }
inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); }
/// \name Casting
/// \{
/// Cast to or from half-precision floating point number.
/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. Floating point types are
/// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
/// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
/// suppressed. Integer types are converted directly using the given rounding mode, without any roundtrip over `float`
/// that a `static_cast` would otherwise do. It uses the default rounding mode.
///
/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
/// error and casting between [half](\ref half_float::half)s is just a no-op.
/// \tparam T destination type (half or built-in arithmetic type)
/// \tparam U source type (half or built-in arithmetic type)
/// \param arg value to cast
/// \return \a arg converted to destination type
template<typename T,typename U> typename half_caster<T,U>::type half_cast(U arg) { return half_caster<T,U>::cast(arg); }
/// Cast to or from half-precision floating point number.
/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. Floating point types are
/// converted via an explicit cast to/from `float` (using the rounding mode of the built-in single precision
/// implementation) and thus any possible warnings due to an otherwise implicit conversion to/from `float` will be
/// suppressed. Integer types are converted directly using the given rounding mode, without any roundtrip over `float`
/// that a `static_cast` would otherwise do.
///
/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types
/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler
/// error and casting between [half](\ref half_float::half)s is just a no-op.
/// \tparam T destination type (half or built-in arithmetic type)
/// \tparam R rounding mode to use.
/// \tparam U source type (half or built-in arithmetic type)
/// \param arg value to cast
/// \return \a arg converted to destination type
template<typename T,std::float_round_style R,typename U> typename half_caster<T,U,R>::type half_cast(U arg)
{ return half_caster<T,U,R>::cast(arg); }
/// \}
}
using detail::operator==;
using detail::operator!=;
using detail::operator<;
using detail::operator>;
using detail::operator<=;
using detail::operator>=;
using detail::operator+;
using detail::operator-;
using detail::operator*;
using detail::operator/;
using detail::operator<<;
using detail::operator>>;
using detail::abs;
using detail::fabs;
using detail::fmod;
using detail::remainder;
using detail::remquo;
using detail::fma;
using detail::fmax;
using detail::fmin;
using detail::fdim;
using detail::nanh;
using detail::exp;
using detail::expm1;
using detail::exp2;
using detail::log;
using detail::log10;
using detail::log1p;
using detail::log2;
using detail::sqrt;
using detail::cbrt;
using detail::hypot;
using detail::pow;
using detail::sin;
using detail::cos;
using detail::tan;
using detail::asin;
using detail::acos;
using detail::atan;
using detail::atan2;
using detail::sinh;
using detail::cosh;
using detail::tanh;
using detail::asinh;
using detail::acosh;
using detail::atanh;
using detail::erf;
using detail::erfc;
using detail::lgamma;
using detail::tgamma;
using detail::ceil;
using detail::floor;
using detail::trunc;
using detail::round;
using detail::lround;
using detail::nearbyint;
using detail::rint;
using detail::lrint;
#if HALF_ENABLE_CPP11_LONG_LONG
using detail::llround;
using detail::llrint;
#endif
using detail::frexp;
using detail::ldexp;
using detail::modf;
using detail::scalbn;
using detail::scalbln;
using detail::ilogb;
using detail::logb;
using detail::nextafter;
using detail::nexttoward;
using detail::copysign;
using detail::fpclassify;
using detail::isfinite;
using detail::isinf;
using detail::isnan;
using detail::isnormal;
using detail::signbit;
using detail::isgreater;
using detail::isgreaterequal;
using detail::isless;
using detail::islessequal;
using detail::islessgreater;
using detail::isunordered;
using detail::half_cast;
}
/// Extensions to the C++ standard library.
namespace std
{
/// Numeric limits for half-precision floats.
/// Because of the underlying single-precision implementation of many operations, it inherits some properties from
/// `std::numeric_limits<float>`.
template<> class numeric_limits<half_float::half> : public numeric_limits<float>
{
public:
/// Supports signed values.
static HALF_CONSTEXPR_CONST bool is_signed = true;
/// Is not exact.
static HALF_CONSTEXPR_CONST bool is_exact = false;
/// Doesn't provide modulo arithmetic.
static HALF_CONSTEXPR_CONST bool is_modulo = false;
/// IEEE conformant.
static HALF_CONSTEXPR_CONST bool is_iec559 = true;
/// Supports infinity.
static HALF_CONSTEXPR_CONST bool has_infinity = true;
/// Supports quiet NaNs.
static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;
/// Supports subnormal values.
static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
/// Rounding mode.
/// Due to the mix of internal single-precision computations (using the rounding mode of the underlying
/// single-precision implementation) with explicit truncation of the single-to-half conversions, the actual rounding
/// mode is indeterminate.
static HALF_CONSTEXPR_CONST float_round_style round_style = (std::numeric_limits<float>::round_style==
half_float::half::round_style) ? half_float::half::round_style : round_indeterminate;
/// Significant digits.
static HALF_CONSTEXPR_CONST int digits = 11;
/// Significant decimal digits.
static HALF_CONSTEXPR_CONST int digits10 = 3;
/// Required decimal digits to represent all possible values.
static HALF_CONSTEXPR_CONST int max_digits10 = 5;
/// Number base.
static HALF_CONSTEXPR_CONST int radix = 2;
/// One more than smallest exponent.
static HALF_CONSTEXPR_CONST int min_exponent = -13;
/// Smallest normalized representable power of 10.
static HALF_CONSTEXPR_CONST int min_exponent10 = -4;
/// One more than largest exponent
static HALF_CONSTEXPR_CONST int max_exponent = 16;
/// Largest finitely representable power of 10.
static HALF_CONSTEXPR_CONST int max_exponent10 = 4;
/// Smallest positive normal value.
static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); }
/// Smallest finite value.
static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); }
/// Largest finite value.
static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); }
/// Difference between one and next representable value.
static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); }
/// Maximum rounding error.
static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW
{ return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); }
/// Positive infinity.
static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); }
/// Quiet NaN.
static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); }
/// Signalling NaN.
static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); }
/// Smallest positive subnormal value.
static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); }
};
#if HALF_ENABLE_CPP11_HASH
/// Hash function for half-precision floats.
/// This is only defined if C++11 `std::hash` is supported and enabled.
template<> struct hash<half_float::half> //: unary_function<half_float::half,size_t>
{
/// Type of function argument.
typedef half_float::half argument_type;
/// Function return type.
typedef size_t result_type;
/// Compute hash function.
/// \param arg half to hash
/// \return hash value
result_type operator()(argument_type arg) const
{ return hash<half_float::detail::uint16>()(static_cast<unsigned int>(arg.data_)&-(arg.data_!=0x8000)); }
};
#endif
}
#undef HALF_CONSTEXPR
#undef HALF_CONSTEXPR_CONST
#undef HALF_NOEXCEPT
#undef HALF_NOTHROW
#ifdef HALF_POP_WARNINGS
#pragma warning(pop)
#undef HALF_POP_WARNINGS
#endif
#endif
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