diff options
| author | Tor Aamodt <[email protected]> | 2020-07-04 16:26:52 -0700 |
|---|---|---|
| committer | GitHub <[email protected]> | 2020-07-04 16:26:52 -0700 |
| commit | 673f8a9f0056b456871642f4d25be5c598fcba6e (patch) | |
| tree | a9f379ae6ff144e8f3eccd3d510a36c2c0983edd /src/cuda-sim/half.h | |
| parent | c9cc4281bf84ad6cff77d20389b59d14a534ad6b (diff) | |
| parent | 9d3caa1cb2c70a3be186d4704ecab0fe13277516 (diff) | |
Merge pull request #1 from gpgpu-sim/dev
Dev
Diffstat (limited to 'src/cuda-sim/half.h')
| -rw-r--r-- | src/cuda-sim/half.h | 3722 |
1 files changed, 3722 insertions, 0 deletions
diff --git a/src/cuda-sim/half.h b/src/cuda-sim/half.h new file mode 100644 index 0000000..fab1a22 --- /dev/null +++ b/src/cuda-sim/half.h @@ -0,0 +1,3722 @@ +// half - IEEE 754-based half-precision floating point library.
+//
+// Copyright (c) 2012-2017 Christian Rau <[email protected]>
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+// Version 1.12.0
+
+/// \file
+/// Main header file for half precision functionality.
+
+#ifndef HALF_HALF_HPP
+#define HALF_HALF_HPP
+
+/// Combined gcc version number.
+#define HALF_GNUC_VERSION (__GNUC__ * 100 + __GNUC_MINOR__)
+
+// check C++11 language features
+#if defined(__clang__) // clang
+#if __has_feature(cxx_static_assert) && \
+ !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+#endif
+#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+#define HALF_ENABLE_CPP11_CONSTEXPR 1
+#endif
+#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+#define HALF_ENABLE_CPP11_NOEXCEPT 1
+#endif
+#if __has_feature(cxx_user_literals) && \
+ !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+#define HALF_ENABLE_CPP11_USER_LITERALS 1
+#endif
+#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && \
+ !defined(HALF_ENABLE_CPP11_LONG_LONG)
+#define HALF_ENABLE_CPP11_LONG_LONG 1
+#endif
+/*#elif defined(__INTEL_COMPILER)
+ //Intel C++ #if __INTEL_COMPILER >= 1100 &&
+ !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ???????? #define
+ HALF_ENABLE_CPP11_STATIC_ASSERT 1 #endif #if __INTEL_COMPILER >= 1300 &&
+ !defined(HALF_ENABLE_CPP11_CONSTEXPR) ???????? #define
+ HALF_ENABLE_CPP11_CONSTEXPR 1 #endif #if __INTEL_COMPILER >= 1300 &&
+ !defined(HALF_ENABLE_CPP11_NOEXCEPT) ???????? #define
+ HALF_ENABLE_CPP11_NOEXCEPT 1 #endif #if __INTEL_COMPILER >= 1100 &&
+ !defined(HALF_ENABLE_CPP11_LONG_LONG) ???????? #define
+ HALF_ENABLE_CPP11_LONG_LONG 1 #endif*/
+#elif defined(__GNUC__) // gcc
+#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+#endif
+#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+#define HALF_ENABLE_CPP11_CONSTEXPR 1
+#endif
+#if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+#define HALF_ENABLE_CPP11_NOEXCEPT 1
+#endif
+#if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+#define HALF_ENABLE_CPP11_USER_LITERALS 1
+#endif
+#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
+#define HALF_ENABLE_CPP11_LONG_LONG 1
+#endif
+#endif
+#elif defined(_MSC_VER) // Visual C++
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+#define HALF_ENABLE_CPP11_CONSTEXPR 1
+#endif
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+#define HALF_ENABLE_CPP11_NOEXCEPT 1
+#endif
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+#define HALF_ENABLE_CPP11_USER_LITERALS 1
+#endif
+#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+#endif
+#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+#define HALF_ENABLE_CPP11_LONG_LONG 1
+#endif
+#define HALF_POP_WARNINGS 1
+#pragma warning(push)
+#pragma warning(disable : 4099 4127 4146) // struct vs class, constant in if,
+ // negative unsigned
+#endif
+
+// check C++11 library features
+#include <utility>
+#if defined(_LIBCPP_VERSION) // libc++
+#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CSTDINT
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CMATH
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#ifndef HALF_ENABLE_CPP11_HASH
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#elif defined(__GLIBCXX__) // libstdc++
+#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+#ifdef __clang__
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#else
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#endif
+#elif defined(_CPPLIB_VER) // Dinkumware/Visual C++
+#if _CPPLIB_VER >= 520
+#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CSTDINT
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#ifndef HALF_ENABLE_CPP11_HASH
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#if _CPPLIB_VER >= 610
+#ifndef HALF_ENABLE_CPP11_CMATH
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#endif
+#endif
+#undef HALF_GNUC_VERSION
+
+// support constexpr
+#if HALF_ENABLE_CPP11_CONSTEXPR
+#define HALF_CONSTEXPR constexpr
+#define HALF_CONSTEXPR_CONST constexpr
+#else
+#define HALF_CONSTEXPR
+#define HALF_CONSTEXPR_CONST const
+#endif
+
+// support noexcept
+#if HALF_ENABLE_CPP11_NOEXCEPT
+#define HALF_NOEXCEPT noexcept
+#define HALF_NOTHROW noexcept
+#else
+#define HALF_NOEXCEPT
+#define HALF_NOTHROW throw()
+#endif
+
+#include <algorithm>
+#include <climits>
+#include <cmath>
+#include <cstring>
+#include <iostream>
+#include <limits>
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+#include <type_traits>
+#endif
+#if HALF_ENABLE_CPP11_CSTDINT
+#include <cstdint>
+#endif
+#if HALF_ENABLE_CPP11_HASH
+#include <functional>
+#endif
+
+/// Default rounding mode.
+/// This specifies the rounding mode used for all conversions between
+/// [half](\ref half_float::half)s and `float`s as well as for the half_cast()
+/// if not specifying a rounding mode explicitly. It can be redefined (before
+/// including half.hpp) to one of the standard rounding modes using their
+/// respective constants or the equivalent values of `std::float_round_style`:
+///
+/// `std::float_round_style` | value | rounding
+/// ---------------------------------|-------|-------------------------
+/// `std::round_indeterminate` | -1 | fastest (default)
+/// `std::round_toward_zero` | 0 | toward zero
+/// `std::round_to_nearest` | 1 | to nearest
+/// `std::round_toward_infinity` | 2 | toward positive infinity
+/// `std::round_toward_neg_infinity` | 3 | toward negative infinity
+///
+/// By default this is set to `-1` (`std::round_indeterminate`), which uses
+/// truncation (round toward zero, but with overflows set to infinity) and is
+/// the fastest rounding mode possible. It can even be set to
+/// `std::numeric_limits<float>::round_style` to synchronize the rounding mode
+/// with that of the underlying single-precision implementation.
+#ifndef HALF_ROUND_STYLE
+#define HALF_ROUND_STYLE -1 // = std::round_indeterminate
+#endif
+
+/// Tie-breaking behaviour for round to nearest.
+/// This specifies if ties in round to nearest should be resolved by rounding to
+/// the nearest even value. By default this is defined to `0` resulting in the
+/// faster but slightly more biased behaviour of rounding away from zero in
+/// half-way cases (and thus equal to the round() function), but can be
+/// redefined to `1` (before including half.hpp) if more IEEE-conformant
+/// behaviour is needed.
+#ifndef HALF_ROUND_TIES_TO_EVEN
+#define HALF_ROUND_TIES_TO_EVEN 0 // ties away from zero
+#endif
+
+/// Value signaling overflow.
+/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to
+/// a positive value signaling the overflow of an operation, in particular it
+/// just evaluates to positive infinity.
+#define HUGE_VALH std::numeric_limits<half_float::half>::infinity()
+
+/// Fast half-precision fma function.
+/// This symbol is only defined if the fma() function generally executes as fast
+/// as, or faster than, a separate half-precision multiplication followed by an
+/// addition. Due to the internal single-precision implementation of all
+/// arithmetic operations, this is in fact always the case.
+#define FP_FAST_FMAH 1
+
+#ifndef FP_ILOGB0
+#define FP_ILOGB0 INT_MIN
+#endif
+#ifndef FP_ILOGBNAN
+#define FP_ILOGBNAN INT_MAX
+#endif
+#ifndef FP_SUBNORMAL
+#define FP_SUBNORMAL 0
+#endif
+#ifndef FP_ZERO
+#define FP_ZERO 1
+#endif
+#ifndef FP_NAN
+#define FP_NAN 2
+#endif
+#ifndef FP_INFINITE
+#define FP_INFINITE 3
+#endif
+#ifndef FP_NORMAL
+#define FP_NORMAL 4
+#endif
+
+/// Main namespace for half precision functionality.
+/// This namespace contains all the functionality provided by the library.
+namespace half_float {
+class half;
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+/// Library-defined half-precision literals.
+/// Import this namespace to enable half-precision floating point literals:
+/// ~~~~{.cpp}
+/// using namespace half_float::literal;
+/// half_float::half = 4.2_h;
+/// ~~~~
+namespace literal {
+half operator"" _h(long double);
+}
+#endif
+
+/// \internal
+/// \brief Implementation details.
+namespace detail {
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+/// Conditional type.
+template <bool B, typename T, typename F>
+struct conditional : std::conditional<B, T, F> {};
+
+/// Helper for tag dispatching.
+template <bool B>
+struct bool_type : std::integral_constant<bool, B> {};
+using std::false_type;
+using std::true_type;
+
+/// Type traits for floating point types.
+template <typename T>
+struct is_float : std::is_floating_point<T> {};
+#else
+/// Conditional type.
+template <bool, typename T, typename>
+struct conditional {
+ typedef T type;
+};
+template <typename T, typename F>
+struct conditional<false, T, F> {
+ typedef F type;
+};
+
+/// Helper for tag dispatching.
+template <bool>
+struct bool_type {};
+typedef bool_type<true> true_type;
+typedef bool_type<false> false_type;
+
+/// Type traits for floating point types.
+template <typename>
+struct is_float : false_type {};
+template <typename T>
+struct is_float<const T> : is_float<T> {};
+template <typename T>
+struct is_float<volatile T> : is_float<T> {};
+template <typename T>
+struct is_float<const volatile T> : is_float<T> {};
+template <>
+struct is_float<float> : true_type {};
+template <>
+struct is_float<double> : true_type {};
+template <>
+struct is_float<long double> : true_type {};
+#endif
+
+/// Type traits for floating point bits.
+template <typename T>
+struct bits {
+ typedef unsigned char type;
+};
+template <typename T>
+struct bits<const T> : bits<T> {};
+template <typename T>
+struct bits<volatile T> : bits<T> {};
+template <typename T>
+struct bits<const volatile T> : bits<T> {};
+
+#if HALF_ENABLE_CPP11_CSTDINT
+/// Unsigned integer of (at least) 16 bits width.
+typedef std::uint_least16_t uint16;
+
+/// Unsigned integer of (at least) 32 bits width.
+template <>
+struct bits<float> {
+ typedef std::uint_least32_t type;
+};
+
+/// Unsigned integer of (at least) 64 bits width.
+template <>
+struct bits<double> {
+ typedef std::uint_least64_t type;
+};
+#else
+/// Unsigned integer of (at least) 16 bits width.
+typedef unsigned short uint16;
+
+/// Unsigned integer of (at least) 32 bits width.
+template <>
+struct bits<float>
+ : conditional<std::numeric_limits<unsigned int>::digits >= 32, unsigned int,
+ unsigned long> {};
+
+#if HALF_ENABLE_CPP11_LONG_LONG
+/// Unsigned integer of (at least) 64 bits width.
+template <>
+struct bits<double>
+ : conditional<std::numeric_limits<unsigned long>::digits >= 64,
+ unsigned long, unsigned long long> {};
+#else
+/// Unsigned integer of (at least) 64 bits width.
+template <>
+struct bits<double> {
+ typedef unsigned long type;
+};
+#endif
+#endif
+
+/// Tag type for binary construction.
+struct binary_t {};
+
+/// Tag for binary construction.
+HALF_CONSTEXPR_CONST binary_t binary = binary_t();
+
+/// Temporary half-precision expression.
+/// This class represents a half-precision expression which just stores a
+/// single-precision value internally.
+struct expr {
+ /// Conversion constructor.
+ /// \param f single-precision value to convert
+ explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {}
+
+ /// Conversion to single-precision.
+ /// \return single precision value representing expression value
+ HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; }
+
+ private:
+ /// Internal expression value stored in single-precision.
+ float value_;
+};
+
+/// SFINAE helper for generic half-precision functions.
+/// This class template has to be specialized for each valid combination of
+/// argument types to provide a corresponding `type` member equivalent to \a T.
+/// \tparam T type to return
+template <typename T, typename, typename = void, typename = void>
+struct enable {};
+template <typename T>
+struct enable<T, half, void, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, void, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, half, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, expr, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, half, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, expr, void> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, half, half> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, half, expr> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, expr, half> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, half, expr, expr> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, half, half> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, half, expr> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, expr, half> {
+ typedef T type;
+};
+template <typename T>
+struct enable<T, expr, expr, expr> {
+ typedef T type;
+};
+
+/// Return type for specialized generic 2-argument half-precision functions.
+/// This class template has to be specialized for each valid combination of
+/// argument types to provide a corresponding `type` member denoting the
+/// appropriate return type. \tparam T first argument type \tparam U first
+/// argument type
+template <typename T, typename U>
+struct result : enable<expr, T, U> {};
+template <>
+struct result<half, half> {
+ typedef half type;
+};
+
+/// \name Classification helpers
+/// \{
+
+/// Check for infinity.
+/// \tparam T argument type (builtin floating point type)
+/// \param arg value to query
+/// \retval true if infinity
+/// \retval false else
+template <typename T>
+bool builtin_isinf(T arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return std::isinf(arg);
+#elif defined(_MSC_VER)
+ return !::_finite(static_cast<double>(arg)) &&
+ !::_isnan(static_cast<double>(arg));
+#else
+ return arg == std::numeric_limits<T>::infinity() ||
+ arg == -std::numeric_limits<T>::infinity();
+#endif
+}
+
+/// Check for NaN.
+/// \tparam T argument type (builtin floating point type)
+/// \param arg value to query
+/// \retval true if not a number
+/// \retval false else
+template <typename T>
+bool builtin_isnan(T arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return std::isnan(arg);
+#elif defined(_MSC_VER)
+ return ::_isnan(static_cast<double>(arg)) != 0;
+#else
+ return arg != arg;
+#endif
+}
+
+/// Check sign.
+/// \tparam T argument type (builtin floating point type)
+/// \param arg value to query
+/// \retval true if signbit set
+/// \retval false else
+template <typename T>
+bool builtin_signbit(T arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return std::signbit(arg);
+#else
+ return arg < T() || (arg == T() && T(1) / arg < T());
+#endif
+}
+
+/// \}
+/// \name Conversion
+/// \{
+
+/// Convert IEEE single-precision to half-precision.
+/// Credit for this goes to [Jeroen van der
+/// Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). \tparam R
+/// rounding mode to use, `std::round_indeterminate` for fastest rounding \param
+/// value single-precision value \return binary representation of half-precision
+/// value
+template <std::float_round_style R>
+uint16 float2half_impl(float value, true_type) {
+ typedef bits<float>::type uint32;
+ uint32 bits; // = *reinterpret_cast<uint32*>(&value);
+ // //violating strict aliasing!
+ std::memcpy(&bits, &value, sizeof(float));
+ /* uint16 hbits = (bits>>16) & 0x8000;
+ bits &= 0x7FFFFFFF;
+ int exp = bits >> 23;
+ if(exp == 255)
+ return hbits | 0x7C00 |
+ (0x3FF&-static_cast<unsigned>((bits&0x7FFFFF)!=0)); if(exp > 142)
+ {
+ if(R == std::round_toward_infinity)
+ return hbits | 0x7C00 - (hbits>>15);
+ if(R == std::round_toward_neg_infinity)
+ return hbits | 0x7BFF + (hbits>>15);
+ return hbits | 0x7BFF +
+ (R!=std::round_toward_zero);
+ }
+ int g, s;
+ if(exp > 112)
+ {
+ g = (bits>>12) & 1;
+ s = (bits&0xFFF) != 0;
+ hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF);
+ }
+ else if(exp > 101)
+ {
+ int i = 125 - exp;
+ bits = (bits&0x7FFFFF) | 0x800000;
+ g = (bits>>i) & 1;
+ s = (bits&((1L<<i)-1)) != 0;
+ hbits |= bits >> (i+1);
+ }
+ else
+ {
+ g = 0;
+ s = bits != 0;
+ }
+ if(R == std::round_to_nearest)
+ #if HALF_ROUND_TIES_TO_EVEN
+ hbits += g & (s|hbits);
+ #else
+ hbits += g;
+ #endif
+ else if(R == std::round_toward_infinity)
+ hbits += ~(hbits>>15) & (s|g);
+ else if(R == std::round_toward_neg_infinity)
+ hbits += (hbits>>15) & (g|s);
+ */
+ static const uint16 base_table[512] = {
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010,
+ 0x0020, 0x0040, 0x0080, 0x0100, 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000,
+ 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400,
+ 0x3800, 0x3C00, 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800,
+ 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001,
+ 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 0x8200,
+ 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400,
+ 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 0xC000, 0xC400, 0xC800,
+ 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00,
+ 0xF000, 0xF400, 0xF800, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00};
+ static const unsigned char shift_table[512] = {
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19,
+ 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23,
+ 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 13};
+ uint16 hbits =
+ base_table[bits >> 23] +
+ static_cast<uint16>((bits & 0x7FFFFF) >> shift_table[bits >> 23]);
+ if (R == std::round_to_nearest)
+ hbits +=
+ (((bits & 0x7FFFFF) >> (shift_table[bits >> 23] - 1)) |
+ (((bits >> 23) & 0xFF) == 102)) &
+ ((hbits & 0x7C00) != 0x7C00)
+#if HALF_ROUND_TIES_TO_EVEN
+ & (((((static_cast<uint32>(1) << (shift_table[bits >> 23] - 1)) - 1) &
+ bits) != 0) |
+ hbits)
+#endif
+ ;
+ else if (R == std::round_toward_zero)
+ hbits -= ((hbits & 0x7FFF) == 0x7C00) & ~shift_table[bits >> 23];
+ else if (R == std::round_toward_infinity)
+ hbits +=
+ ((((bits & 0x7FFFFF &
+ ((static_cast<uint32>(1) << (shift_table[bits >> 23])) - 1)) != 0) |
+ (((bits >> 23) <= 102) & ((bits >> 23) != 0))) &
+ (hbits < 0x7C00)) -
+ ((hbits == 0xFC00) & ((bits >> 23) != 511));
+ else if (R == std::round_toward_neg_infinity)
+ hbits +=
+ ((((bits & 0x7FFFFF &
+ ((static_cast<uint32>(1) << (shift_table[bits >> 23])) - 1)) != 0) |
+ (((bits >> 23) <= 358) & ((bits >> 23) != 256))) &
+ (hbits < 0xFC00) & (hbits >> 15)) -
+ ((hbits == 0x7C00) & ((bits >> 23) != 255));
+ return hbits;
+}
+
+/// Convert IEEE double-precision to half-precision.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \param value double-precision value \return binary representation
+/// of half-precision value
+template <std::float_round_style R>
+uint16 float2half_impl(double value, true_type) {
+ typedef bits<float>::type uint32;
+ typedef bits<double>::type uint64;
+ uint64 bits; // = *reinterpret_cast<uint64*>(&value);
+ // //violating strict aliasing!
+ std::memcpy(&bits, &value, sizeof(double));
+ uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF;
+ uint16 hbits = (hi >> 16) & 0x8000;
+ hi &= 0x7FFFFFFF;
+ int exp = hi >> 20;
+ if (exp == 2047)
+ return hbits | 0x7C00 |
+ (0x3FF & -static_cast<unsigned>((bits & 0xFFFFFFFFFFFFF) != 0));
+ if (exp > 1038) {
+ if (R == std::round_toward_infinity) return hbits | 0x7C00 - (hbits >> 15);
+ if (R == std::round_toward_neg_infinity)
+ return hbits | 0x7BFF + (hbits >> 15);
+ return hbits | 0x7BFF + (R != std::round_toward_zero);
+ }
+ int g, s = lo != 0;
+ if (exp > 1008) {
+ g = (hi >> 9) & 1;
+ s |= (hi & 0x1FF) != 0;
+ hbits |= ((exp - 1008) << 10) | ((hi >> 10) & 0x3FF);
+ } else if (exp > 997) {
+ int i = 1018 - exp;
+ hi = (hi & 0xFFFFF) | 0x100000;
+ g = (hi >> i) & 1;
+ s |= (hi & ((1L << i) - 1)) != 0;
+ hbits |= hi >> (i + 1);
+ } else {
+ g = 0;
+ s |= hi != 0;
+ }
+ if (R == std::round_to_nearest)
+#if HALF_ROUND_TIES_TO_EVEN
+ hbits += g & (s | hbits);
+#else
+ hbits += g;
+#endif
+ else if (R == std::round_toward_infinity)
+ hbits += ~(hbits >> 15) & (s | g);
+ else if (R == std::round_toward_neg_infinity)
+ hbits += (hbits >> 15) & (g | s);
+ return hbits;
+}
+
+/// Convert non-IEEE floating point to half-precision.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam T source type (builtin floating point type) \param value
+/// floating point value \return binary representation of half-precision value
+template <std::float_round_style R, typename T>
+uint16 float2half_impl(T value, ...) {
+ uint16 hbits = static_cast<unsigned>(builtin_signbit(value)) << 15;
+ if (value == T()) return hbits;
+ if (builtin_isnan(value)) return hbits | 0x7FFF;
+ if (builtin_isinf(value)) return hbits | 0x7C00;
+ int exp;
+ std::frexp(value, &exp);
+ if (exp > 16) {
+ if (R == std::round_toward_infinity)
+ return hbits | (0x7C00 - (hbits >> 15));
+ else if (R == std::round_toward_neg_infinity)
+ return hbits | (0x7BFF + (hbits >> 15));
+ return hbits | (0x7BFF + (R != std::round_toward_zero));
+ }
+ if (exp < -13)
+ value = std::ldexp(value, 24);
+ else {
+ value = std::ldexp(value, 11 - exp);
+ hbits |= ((exp + 13) << 10);
+ }
+ T ival, frac = std::modf(value, &ival);
+ hbits += static_cast<uint16>(std::abs(static_cast<int>(ival)));
+ if (R == std::round_to_nearest) {
+ frac = std::abs(frac);
+#if HALF_ROUND_TIES_TO_EVEN
+ hbits += (frac > T(0.5)) | ((frac == T(0.5)) & hbits);
+#else
+ hbits += frac >= T(0.5);
+#endif
+ } else if (R == std::round_toward_infinity)
+ hbits += frac > T();
+ else if (R == std::round_toward_neg_infinity)
+ hbits += frac < T();
+ return hbits;
+}
+
+/// Convert floating point to half-precision.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam T source type (builtin floating point type) \param value
+/// floating point value \return binary representation of half-precision value
+template <std::float_round_style R, typename T>
+uint16 float2half(T value) {
+ return float2half_impl<R>(
+ value, bool_type < std::numeric_limits<T>::is_iec559 &&
+ sizeof(typename bits<T>::type) == sizeof(T) > ());
+}
+
+/// Convert integer to half-precision floating point.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam S `true` if value negative, `false` else \tparam T type to
+/// convert (builtin integer type) \param value non-negative integral value
+/// \return binary representation of half-precision value
+template <std::float_round_style R, bool S, typename T>
+uint16 int2half_impl(T value) {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_integral<T>::value,
+ "int to half conversion only supports builtin integer types");
+#endif
+ if (S) value = -value;
+ uint16 bits = S << 15;
+ if (value > 0xFFFF) {
+ if (R == std::round_toward_infinity)
+ bits |= 0x7C00 - S;
+ else if (R == std::round_toward_neg_infinity)
+ bits |= 0x7BFF + S;
+ else
+ bits |= 0x7BFF + (R != std::round_toward_zero);
+ } else if (value) {
+ unsigned int m = value, exp = 24;
+ for (; m < 0x400; m <<= 1, --exp)
+ ;
+ for (; m > 0x7FF; m >>= 1, ++exp)
+ ;
+ bits |= (exp << 10) + m;
+ if (exp > 24) {
+ if (R == std::round_to_nearest)
+ bits += (value >> (exp - 25)) & 1
+#if HALF_ROUND_TIES_TO_EVEN
+ & (((((1 << (exp - 25)) - 1) & value) != 0) | bits)
+#endif
+ ;
+ else if (R == std::round_toward_infinity)
+ bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & !S;
+ else if (R == std::round_toward_neg_infinity)
+ bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & S;
+ }
+ }
+ return bits;
+}
+
+/// Convert integer to half-precision floating point.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam T type to convert (builtin integer type) \param value
+/// integral value \return binary representation of half-precision value
+template <std::float_round_style R, typename T>
+uint16 int2half(T value) {
+ return (value < 0) ? int2half_impl<R, true>(value)
+ : int2half_impl<R, false>(value);
+}
+
+/// Convert half-precision to IEEE single-precision.
+/// Credit for this goes to [Jeroen van der
+/// Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). \param
+/// value binary representation of half-precision value \return single-precision
+/// value
+inline float half2float_impl(uint16 value, float, true_type) {
+ typedef bits<float>::type uint32;
+ /* uint32 bits = static_cast<uint32>(value&0x8000) << 16;
+ int abs = value & 0x7FFF;
+ if(abs)
+ {
+ bits |= 0x38000000 <<
+ static_cast<unsigned>(abs>=0x7C00); for(; abs<0x400;
+ abs<<=1,bits-=0x800000) ; bits += static_cast<uint32>(abs) << 13;
+ }
+ */
+ static const uint32 mantissa_table[2048] = {
+ 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000,
+ 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000,
+ 0x35400000, 0x35500000, 0x35600000, 0x35700000, 0x35800000, 0x35880000,
+ 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000,
+ 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000,
+ 0x35F00000, 0x35F80000, 0x36000000, 0x36040000, 0x36080000, 0x360C0000,
+ 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000,
+ 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
+ 0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000,
+ 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000,
+ 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 0x36800000, 0x36820000,
+ 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000,
+ 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000,
+ 0x369C0000, 0x369E0000, 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000,
+ 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000,
+ 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
+ 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000,
+ 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000,
+ 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, 0x36E00000, 0x36E20000,
+ 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000,
+ 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000,
+ 0x36FC0000, 0x36FE0000, 0x37000000, 0x37010000, 0x37020000, 0x37030000,
+ 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000,
+ 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
+ 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000,
+ 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000,
+ 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, 0x37200000, 0x37210000,
+ 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000,
+ 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000,
+ 0x372E0000, 0x372F0000, 0x37300000, 0x37310000, 0x37320000, 0x37330000,
+ 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000,
+ 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
+ 0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000,
+ 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000,
+ 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 0x37500000, 0x37510000,
+ 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000,
+ 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000,
+ 0x375E0000, 0x375F0000, 0x37600000, 0x37610000, 0x37620000, 0x37630000,
+ 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000,
+ 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
+ 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000,
+ 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000,
+ 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 0x37800000, 0x37808000,
+ 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000,
+ 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000,
+ 0x37870000, 0x37878000, 0x37880000, 0x37888000, 0x37890000, 0x37898000,
+ 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000,
+ 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
+ 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000,
+ 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000,
+ 0x37960000, 0x37968000, 0x37970000, 0x37978000, 0x37980000, 0x37988000,
+ 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000,
+ 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000,
+ 0x379F0000, 0x379F8000, 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000,
+ 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000,
+ 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
+ 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000,
+ 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000,
+ 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 0x37B00000, 0x37B08000,
+ 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000,
+ 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000,
+ 0x37B70000, 0x37B78000, 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000,
+ 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000,
+ 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
+ 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000,
+ 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000,
+ 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, 0x37C80000, 0x37C88000,
+ 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000,
+ 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000,
+ 0x37CF0000, 0x37CF8000, 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000,
+ 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000,
+ 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
+ 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000,
+ 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000,
+ 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, 0x37E00000, 0x37E08000,
+ 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000,
+ 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000,
+ 0x37E70000, 0x37E78000, 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000,
+ 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000,
+ 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
+ 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000,
+ 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000,
+ 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 0x37F80000, 0x37F88000,
+ 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000,
+ 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000,
+ 0x37FF0000, 0x37FF8000, 0x38000000, 0x38004000, 0x38008000, 0x3800C000,
+ 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000,
+ 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
+ 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000,
+ 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000,
+ 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 0x38080000, 0x38084000,
+ 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000,
+ 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000,
+ 0x380B8000, 0x380BC000, 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000,
+ 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000,
+ 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
+ 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000,
+ 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000,
+ 0x38130000, 0x38134000, 0x38138000, 0x3813C000, 0x38140000, 0x38144000,
+ 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000,
+ 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000,
+ 0x38178000, 0x3817C000, 0x38180000, 0x38184000, 0x38188000, 0x3818C000,
+ 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000,
+ 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
+ 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000,
+ 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000,
+ 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, 0x38200000, 0x38204000,
+ 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000,
+ 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000,
+ 0x38238000, 0x3823C000, 0x38240000, 0x38244000, 0x38248000, 0x3824C000,
+ 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000,
+ 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
+ 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000,
+ 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000,
+ 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, 0x382C0000, 0x382C4000,
+ 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000,
+ 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000,
+ 0x382F8000, 0x382FC000, 0x38300000, 0x38304000, 0x38308000, 0x3830C000,
+ 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000,
+ 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
+ 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000,
+ 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000,
+ 0x38370000, 0x38374000, 0x38378000, 0x3837C000, 0x38380000, 0x38384000,
+ 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000,
+ 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000,
+ 0x383B8000, 0x383BC000, 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000,
+ 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000,
+ 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
+ 0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000,
+ 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000,
+ 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 0x38440000, 0x38444000,
+ 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000,
+ 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000,
+ 0x38478000, 0x3847C000, 0x38480000, 0x38484000, 0x38488000, 0x3848C000,
+ 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000,
+ 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000,
+ 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000,
+ 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000,
+ 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, 0x38500000, 0x38504000,
+ 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000,
+ 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000,
+ 0x38538000, 0x3853C000, 0x38540000, 0x38544000, 0x38548000, 0x3854C000,
+ 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000,
+ 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000,
+ 0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000,
+ 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000,
+ 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, 0x385C0000, 0x385C4000,
+ 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000,
+ 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000,
+ 0x385F8000, 0x385FC000, 0x38600000, 0x38604000, 0x38608000, 0x3860C000,
+ 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000,
+ 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000,
+ 0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000,
+ 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000,
+ 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 0x38680000, 0x38684000,
+ 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000,
+ 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000,
+ 0x386B8000, 0x386BC000, 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000,
+ 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000,
+ 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000,
+ 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000,
+ 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000,
+ 0x38730000, 0x38734000, 0x38738000, 0x3873C000, 0x38740000, 0x38744000,
+ 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000,
+ 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000,
+ 0x38778000, 0x3877C000, 0x38780000, 0x38784000, 0x38788000, 0x3878C000,
+ 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000,
+ 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000,
+ 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000,
+ 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000,
+ 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, 0x38000000, 0x38002000,
+ 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000,
+ 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000,
+ 0x3801C000, 0x3801E000, 0x38020000, 0x38022000, 0x38024000, 0x38026000,
+ 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000,
+ 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000,
+ 0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000,
+ 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000,
+ 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, 0x38060000, 0x38062000,
+ 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000,
+ 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000,
+ 0x3807C000, 0x3807E000, 0x38080000, 0x38082000, 0x38084000, 0x38086000,
+ 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000,
+ 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000,
+ 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000,
+ 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000,
+ 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, 0x380C0000, 0x380C2000,
+ 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000,
+ 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000,
+ 0x380DC000, 0x380DE000, 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000,
+ 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000,
+ 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000,
+ 0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000,
+ 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000,
+ 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, 0x38120000, 0x38122000,
+ 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000,
+ 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000,
+ 0x3813C000, 0x3813E000, 0x38140000, 0x38142000, 0x38144000, 0x38146000,
+ 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000,
+ 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000,
+ 0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000,
+ 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000,
+ 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 0x38180000, 0x38182000,
+ 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000,
+ 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000,
+ 0x3819C000, 0x3819E000, 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000,
+ 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000,
+ 0x381B4000, 0x381B6000, 0x381B8000, 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];
+ // return *reinterpret_cast<float*>(&bits);
+ ////violating strict aliasing!
+ float out;
+ std::memcpy(&out, &bits, sizeof(float));
+ return out;
+}
+
+/// Convert half-precision to IEEE double-precision.
+/// \param value binary representation of half-precision value
+/// \return double-precision value
+inline double half2float_impl(uint16 value, double, true_type) {
+ typedef bits<float>::type uint32;
+ typedef bits<double>::type uint64;
+ uint32 hi = static_cast<uint32>(value & 0x8000) << 16;
+ int abs = value & 0x7FFF;
+ if (abs) {
+ hi |= 0x3F000000 << static_cast<unsigned>(abs >= 0x7C00);
+ for (; abs < 0x400; abs <<= 1, hi -= 0x100000)
+ ;
+ hi += static_cast<uint32>(abs) << 10;
+ }
+ uint64 bits = static_cast<uint64>(hi) << 32;
+ // return *reinterpret_cast<double*>(&bits);
+ ////violating strict aliasing!
+ double out;
+ std::memcpy(&out, &bits, sizeof(double));
+ return out;
+}
+
+/// Convert half-precision to non-IEEE floating point.
+/// \tparam T type to convert to (builtin integer type)
+/// \param value binary representation of half-precision value
+/// \return floating point value
+template <typename T>
+T half2float_impl(uint16 value, T, ...) {
+ T out;
+ int abs = value & 0x7FFF;
+ if (abs > 0x7C00)
+ out = std::numeric_limits<T>::has_quiet_NaN
+ ? std::numeric_limits<T>::quiet_NaN()
+ : T();
+ else if (abs == 0x7C00)
+ out = std::numeric_limits<T>::has_infinity
+ ? std::numeric_limits<T>::infinity()
+ : std::numeric_limits<T>::max();
+ else if (abs > 0x3FF)
+ out = std::ldexp(static_cast<T>((abs & 0x3FF) | 0x400), (abs >> 10) - 25);
+ else
+ out = std::ldexp(static_cast<T>(abs), -24);
+ return (value & 0x8000) ? -out : out;
+}
+
+/// Convert half-precision to floating point.
+/// \tparam T type to convert to (builtin integer type)
+/// \param value binary representation of half-precision value
+/// \return floating point value
+template <typename T>
+T half2float(uint16 value) {
+ return half2float_impl(value, T(),
+ bool_type < std::numeric_limits<T>::is_iec559 &&
+ sizeof(typename bits<T>::type) == sizeof(T) > ());
+}
+
+/// Convert half-precision floating point to integer.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam E `true` for round to even, `false` for round away from
+/// zero \tparam T type to convert to (buitlin integer type with at least 16
+/// bits precision, excluding any implicit sign bits) \param value binary
+/// representation of half-precision value \return integral value
+template <std::float_round_style R, bool E, typename T>
+T half2int_impl(uint16 value) {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_integral<T>::value,
+ "half to int conversion only supports builtin integer types");
+#endif
+ unsigned int e = value & 0x7FFF;
+ if (e >= 0x7C00)
+ return (value & 0x8000) ? std::numeric_limits<T>::min()
+ : std::numeric_limits<T>::max();
+ if (e < 0x3800) {
+ if (R == std::round_toward_infinity)
+ return T(~(value >> 15) & (e != 0));
+ else if (R == std::round_toward_neg_infinity)
+ return -T(value > 0x8000);
+ return T();
+ }
+ unsigned int m = (value & 0x3FF) | 0x400;
+ e >>= 10;
+ if (e < 25) {
+ if (R == std::round_to_nearest)
+ m += (1 << (24 - e)) - (~(m >> (25 - e)) & E);
+ else if (R == std::round_toward_infinity)
+ m += ((value >> 15) - 1) & ((1 << (25 - e)) - 1U);
+ else if (R == std::round_toward_neg_infinity)
+ m += -(value >> 15) & ((1 << (25 - e)) - 1U);
+ m >>= 25 - e;
+ } else
+ m <<= e - 25;
+ return (value & 0x8000) ? -static_cast<T>(m) : static_cast<T>(m);
+}
+
+/// Convert half-precision floating point to integer.
+/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest
+/// rounding \tparam T type to convert to (buitlin integer type with at least 16
+/// bits precision, excluding any implicit sign bits) \param value binary
+/// representation of half-precision value \return integral value
+template <std::float_round_style R, typename T>
+T half2int(uint16 value) {
+ return half2int_impl<R, HALF_ROUND_TIES_TO_EVEN, T>(value);
+}
+
+/// Convert half-precision floating point to integer using
+/// round-to-nearest-away-from-zero. \tparam T type to convert to (buitlin
+/// integer type with at least 16 bits precision, excluding any implicit sign
+/// bits) \param value binary representation of half-precision value \return
+/// integral value
+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;
+} // namespace detail
+
+/// 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 the library's default rounding
+/// mode, 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
+#if HALF_ENABLE_CPP11_USER_LITERALS
+ friend half literal::operator"" _h(long double);
+#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() HALF_NOEXCEPT : 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>(static_cast<float>(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<float>(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<float>(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<float>(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<float>(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<float>(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
+ 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) HALF_NOEXCEPT
+ : data_(bits) {}
+
+ /// Internal binary representation
+ detail::uint16 data_;
+};
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+namespace literal {
+/// Half literal.
+/// While this returns an actual half-precision value, half literals can
+/// unfortunately not be constant expressions due to rather involved
+/// conversions. \param value literal value \return half with given value (if
+/// representable)
+inline half operator"" _h(long double value) {
+ return half(detail::binary, detail::float2half<half::round_style>(value));
+}
+} // namespace literal
+#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() { 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(-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());
+ if (arg < 0.0f) {
+ float i, f = std::modf(-arg, &i);
+ if (f == 0.0f) 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 - arg)));
+ }
+ return expr(static_cast<float>(lgamma(static_cast<double>(arg))));
+#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
+ if (arg == 0.0f)
+ return builtin_signbit(arg)
+ ? expr(-std::numeric_limits<float>::infinity())
+ : expr(std::numeric_limits<float>::infinity());
+ if (arg < 0.0f) {
+ float i, f = std::modf(-arg, &i);
+ if (f == 0.0f) return expr(std::numeric_limits<float>::quiet_NaN());
+ double value = 3.1415926535897932384626433832795 /
+ (std::sin(3.1415926535897932384626433832795 * f) *
+ std::exp(lgamma(1.0 - arg)));
+ return expr(
+ static_cast<float>((std::fmod(i, 2.0f) == 0.0f) ? -value : value));
+ }
+ if (builtin_isinf(arg)) return expr(arg);
+ return expr(static_cast<float>(std::exp(lgamma(static_cast<double>(arg)))));
+#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) {
+ int m = arg.data_ & 0x7FFF, e = -14;
+ if (m >= 0x7C00 || !m) return *exp = 0, arg;
+ for (; m < 0x400; m <<= 1, --e)
+ ;
+ return *exp = e + (m >> 10),
+ half(binary, (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_ & 0x7FFF;
+ if (e >= 0x6400)
+ return *iptr = arg, half(binary, arg.data_ & (0x8000U | -(e > 0x7C00)));
+ 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) {
+ unsigned int m = arg.data_ & 0x7FFF;
+ if (m >= 0x7C00 || !m) return arg;
+ for (; m < 0x400; m <<= 1, --exp)
+ ;
+ exp += m >> 10;
+ uint16 value = arg.data_ & 0x8000;
+ if (exp > 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 (exp > 0)
+ value |= (exp << 10) | (m & 0x3FF);
+ else if (exp > -11) {
+ m = (m & 0x3FF) | 0x400;
+ if (half::round_style == std::round_to_nearest) {
+ m += 1 << -exp;
+#if HALF_ROUND_TIES_TO_EVEN
+ m -= (m >> (1 - exp)) & 1;
+#endif
+ } else if (half::round_style == std::round_toward_infinity)
+ m += ((value >> 15) - 1) & ((1 << (1 - exp)) - 1U);
+ else if (half::round_style == std::round_toward_neg_infinity)
+ m += -(value >> 15) & ((1 << (1 - exp)) - 1U);
+ value |= m >> (1 - exp);
+ } else if (half::round_style == std::round_toward_infinity)
+ value -= (value >> 15) - 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 abs = arg.data_ & 0x7FFF;
+ if (!abs) return FP_ILOGB0;
+ if (abs < 0x7C00) {
+ int exp = (abs >> 10) - 15;
+ if (abs < 0x400)
+ for (; abs < 0x200; abs <<= 1, --exp)
+ ;
+ return exp;
+ }
+ if (abs > 0x7C00) return FP_ILOGBNAN;
+ return INT_MAX;
+ }
+
+ /// Exponent implementation.
+ /// \param arg number to query
+ /// \return floating point exponent
+ static half logb(half arg) {
+ int abs = arg.data_ & 0x7FFF;
+ if (!abs) return half(binary, 0xFC00);
+ if (abs < 0x7C00) {
+ int exp = (abs >> 10) - 15;
+ if (abs < 0x400)
+ for (; abs < 0x200; abs <<= 1, --exp)
+ ;
+ uint16 bits = (exp < 0) << 15;
+ if (exp) {
+ unsigned int m = std::abs(exp) << 6, e = 18;
+ for (; m < 0x400; m <<= 1, --e)
+ ;
+ bits |= (e << 10) + m;
+ }
+ return half(binary, bits);
+ }
+ if (abs > 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 =
+ ((fabs == from.data_) ? static_cast<int>(fabs)
+ : -static_cast<int>(fabs)) <
+ ((tabs == to.data_) ? static_cast<int>(tabs) : -static_cast<int>(tabs));
+ return half(binary,
+ from.data_ +
+ (((from.data_ >> 15) ^ static_cast<unsigned>(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<unsigned>(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;
+ return abs ? ((abs > 0x3FF) ? ((abs >= 0x7C00)
+ ? ((abs > 0x7C00) ? FP_NAN : FP_INFINITE)
+ : FP_NORMAL)
+ : 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) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) >
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// 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) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) >=
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// 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) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) <
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// 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) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) <=
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if either \a x > \a y nor \a x < \a y
+ /// \retval false else
+ static bool islessgreater(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00 || yabs > 0x7C00) return false;
+ int a = (xabs == x.data_) ? xabs : -xabs,
+ b = (yabs == y.data_) ? yabs : -yabs;
+ 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 = arg * arg, ax2 = 0.147 * x2,
+ 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) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00) return y;
+ if (yabs > 0x7C00) return x;
+ return (((xabs == x.data_) ? xabs : -xabs) >
+ ((yabs == y.data_) ? yabs : -yabs))
+ ? y
+ : x;
+ }
+ static half fmax(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00) return y;
+ if (yabs > 0x7C00) return x;
+ return (((xabs == x.data_) ? xabs : -xabs) <
+ ((yabs == y.data_) ? yabs : -yabs))
+ ? 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
+
+ static half cast(U arg) { return cast_impl(arg, is_float<U>()); };
+
+ private:
+ static half cast_impl(U arg, true_type) {
+ return half(binary, float2half<R>(arg));
+ }
+ static half cast_impl(U arg, false_type) {
+ return half(binary, int2half<R>(arg));
+ }
+};
+template <typename T, std::float_round_style R>
+struct half_caster<T, half, R> {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_arithmetic<T>::value,
+ "half_cast to non-arithmetic type unsupported");
+#endif
+
+ static T cast(half arg) { return cast_impl(arg, is_float<T>()); }
+
+ private:
+ static T cast_impl(half arg, true_type) { return half2float<T>(arg.data_); }
+ static T cast_impl(half arg, false_type) { return half2int<R, T>(arg.data_); }
+};
+template <typename T, std::float_round_style R>
+struct half_caster<T, expr, R> {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_arithmetic<T>::value,
+ "half_cast to non-arithmetic type unsupported");
+#endif
+
+ static T cast(expr 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 <std::float_round_style R>
+struct half_caster<half, half, R> {
+ static half cast(half arg) { return arg; }
+};
+template <std::float_round_style R>
+struct half_caster<half, expr, R> : 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.
+/// \return quiet NaN
+inline half nanh(const char *) { return functions::nanh(); }
+
+/// \}
+/// \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. The values 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>
+T 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. The values 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>
+T half_cast(U arg) {
+ return half_caster<T, U, R>::cast(arg);
+}
+/// \}
+} // namespace detail
+
+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::acos;
+using detail::acosh;
+using detail::asin;
+using detail::asinh;
+using detail::atan;
+using detail::atan2;
+using detail::atanh;
+using detail::cbrt;
+using detail::ceil;
+using detail::cos;
+using detail::cosh;
+using detail::erf;
+using detail::erfc;
+using detail::exp;
+using detail::exp2;
+using detail::expm1;
+using detail::fabs;
+using detail::fdim;
+using detail::floor;
+using detail::fma;
+using detail::fmax;
+using detail::fmin;
+using detail::fmod;
+using detail::hypot;
+using detail::lgamma;
+using detail::log;
+using detail::log10;
+using detail::log1p;
+using detail::log2;
+using detail::lrint;
+using detail::lround;
+using detail::nanh;
+using detail::nearbyint;
+using detail::pow;
+using detail::remainder;
+using detail::remquo;
+using detail::rint;
+using detail::round;
+using detail::sin;
+using detail::sinh;
+using detail::sqrt;
+using detail::tan;
+using detail::tanh;
+using detail::tgamma;
+using detail::trunc;
+#if HALF_ENABLE_CPP11_LONG_LONG
+using detail::llrint;
+using detail::llround;
+#endif
+using detail::copysign;
+using detail::fpclassify;
+using detail::frexp;
+using detail::ilogb;
+using detail::isfinite;
+using detail::isgreater;
+using detail::isgreaterequal;
+using detail::isinf;
+using detail::isless;
+using detail::islessequal;
+using detail::islessgreater;
+using detail::isnan;
+using detail::isnormal;
+using detail::isunordered;
+using detail::ldexp;
+using detail::logb;
+using detail::modf;
+using detail::nextafter;
+using detail::nexttoward;
+using detail::scalbln;
+using detail::scalbn;
+using detail::signbit;
+
+using detail::half_cast;
+} // namespace half_float
+
+/// 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 the
+ /// rounding mode of the single-to-half conversions, the actual rounding mode
+ /// might be `std::round_indeterminate` if the default half-precision rounding
+ /// mode doesn't match the single-precision rounding mode.
+ 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>(arg.data_) &
+ -(arg.data_ != 0x8000));
+ }
+};
+#endif
+} // namespace std
+
+#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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