diff options
Diffstat (limited to 'src/cuda-sim/half.h')
| -rw-r--r-- | src/cuda-sim/half.h | 6061 |
1 files changed, 2638 insertions, 3423 deletions
diff --git a/src/cuda-sim/half.h b/src/cuda-sim/half.h index d33b03c..9f74bb7 100644 --- a/src/cuda-sim/half.h +++ b/src/cuda-sim/half.h @@ -2,25 +2,17 @@ //
// 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
+// 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 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.
+// 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
@@ -31,191 +23,180 @@ #define HALF_HALF_HPP
/// Combined gcc version number.
-#define HALF_GNUC_VERSION (__GNUC__ * 100 + __GNUC_MINOR__)
+#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
+//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
+//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
+#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
+//support constexpr
#if HALF_ENABLE_CPP11_CONSTEXPR
-#define HALF_CONSTEXPR constexpr
-#define HALF_CONSTEXPR_CONST constexpr
+ #define HALF_CONSTEXPR constexpr
+ #define HALF_CONSTEXPR_CONST constexpr
#else
-#define HALF_CONSTEXPR
-#define HALF_CONSTEXPR_CONST const
+ #define HALF_CONSTEXPR
+ #define HALF_CONSTEXPR_CONST const
#endif
-// support noexcept
+//support noexcept
#if HALF_ENABLE_CPP11_NOEXCEPT
-#define HALF_NOEXCEPT noexcept
-#define HALF_NOTHROW noexcept
+ #define HALF_NOEXCEPT noexcept
+ #define HALF_NOTHROW noexcept
#else
-#define HALF_NOEXCEPT
-#define HALF_NOTHROW throw()
+ #define HALF_NOEXCEPT
+ #define HALF_NOTHROW throw()
#endif
#include <algorithm>
+#include <iostream>
+#include <limits>
#include <climits>
#include <cmath>
#include <cstring>
-#include <iostream>
-#include <limits>
#if HALF_ENABLE_CPP11_TYPE_TRAITS
-#include <type_traits>
+ #include <type_traits>
#endif
#if HALF_ENABLE_CPP11_CSTDINT
-#include <cstdint>
+ #include <cstdint>
#endif
#if HALF_ENABLE_CPP11_HASH
-#include <functional>
+ #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`:
+/// 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
/// ---------------------------------|-------|-------------------------
@@ -225,354 +206,256 @@ /// `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.
+/// 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
+ #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
+/// 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
+ #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
+/// 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()
+#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
+/// 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
+#define FP_FAST_FMAH 1
#ifndef FP_ILOGB0
-#define FP_ILOGB0 INT_MIN
+ #define FP_ILOGB0 INT_MIN
#endif
#ifndef FP_ILOGBNAN
-#define FP_ILOGBNAN INT_MAX
+ #define FP_ILOGBNAN INT_MAX
#endif
#ifndef FP_SUBNORMAL
-#define FP_SUBNORMAL 0
+ #define FP_SUBNORMAL 0
#endif
#ifndef FP_ZERO
-#define FP_ZERO 1
+ #define FP_ZERO 1
#endif
#ifndef FP_NAN
-#define FP_NAN 2
+ #define FP_NAN 2
#endif
#ifndef FP_INFINITE
-#define FP_INFINITE 3
+ #define FP_INFINITE 3
#endif
#ifndef FP_NORMAL
-#define FP_NORMAL 4
+ #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;
+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);
-}
+ /// 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> {};
+ /// \internal
+ /// \brief Implementation details.
+ namespace detail
+ {
+ #if HALF_ENABLE_CPP11_TYPE_TRAITS
+ /// Conditional type.
+ template<bool B,typename T,typename F> struct conditional : std::conditional<B,T,F> {};
-/// Helper for tag dispatching.
-template <bool B>
-struct bool_type : std::integral_constant<bool, B> {};
-using std::true_type;
-using std::false_type;
+ /// Helper for tag dispatching.
+ template<bool B> struct bool_type : std::integral_constant<bool,B> {};
+ using std::true_type;
+ using std::false_type;
-/// Type traits for floating point types.
-template <typename T>
-struct is_float : std::is_floating_point<T> {};
-#else
-/// Conditional type.
-template <bool, typename T, typename>
-struct conditional {
- typedef T type;
-};
-template <typename T, typename F>
-struct conditional<false, T, F> {
- typedef F type;
-};
+ /// 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;
+ /// 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 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> {};
+ /// 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;
+ #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) 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) 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> {};
+ /// 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
+ #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 type for binary construction.
+ struct binary_t {};
-/// Tag for binary construction.
-HALF_CONSTEXPR_CONST binary_t binary = 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) {}
+ /// 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_; }
+ /// 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_;
-};
+ 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;
-};
+ /// 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;
-};
+ /// 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
-/// \{
+ /// \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 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 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
-}
+ /// 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
-/// \{
+ /// \}
+ /// \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;
+ /// 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)
@@ -615,310 +498,254 @@ uint16 float2half_impl(float value, true_type) { 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;
-}
+*/ 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 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 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 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 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 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;
+ /// 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)
{
@@ -926,2927 +753,2315 @@ inline float half2float_impl(uint16 value, float, true_type) { 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;
-}
+*/ 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 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 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 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.
+ /// \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 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);
-}
+ /// 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); }
-/// 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;
-}
+ /// 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
-/// \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);
-}
-/// \}
+ /// 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;
+ }
-struct functions;
-template <typename>
-struct unary_specialized;
-template <typename, typename>
-struct binary_specialized;
-template <typename, typename, std::float_round_style>
-struct half_caster;
-}
+ /// 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); }
-/// 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
+ /// 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); }
+ /// \}
- 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_() {}
+ struct functions;
+ template<typename> struct unary_specialized;
+ template<typename,typename> struct binary_specialized;
+ template<typename,typename,std::float_round_style> struct half_caster;
+ }
- /// 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))) {}
+ /// 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
- /// Conversion constructor.
- /// \param rhs float to convert
- explicit half(float rhs) : data_(detail::float2half<round_style>(rhs)) {}
+ 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_() {}
- /// Conversion to single-precision.
- /// \return single precision value representing expression value
- operator float() const { return detail::half2float<float>(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))) {}
- /// 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); }
+ /// 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_); }
- /// 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);
- }
+ /// 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 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 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 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 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 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);
- }
+ /// 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); }
- /// 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.
+ /// \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); }
- /// 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;
- }
+ /// 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 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 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 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 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 divide by
- /// \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; }
- /// Prefix increment.
- /// \return incremented half value
- half &operator++() { return *this += 1.0f; }
+ /// 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 decrement.
- /// \return decremented half value
- half &operator--() { return *this -= 1.0f; }
+ /// Prefix increment.
+ /// \return incremented half value
+ half& operator++() { return *this += 1.0f; }
- /// Postfix increment.
- /// \return non-incremented half value
- half operator++(int) {
- half out(*this);
- ++*this;
- return out;
- }
+ /// Prefix decrement.
+ /// \return decremented half value
+ half& operator--() { return *this -= 1.0f; }
- /// Postfix decrement.
- /// \return non-decremented half value
- half operator--(int) {
- half out(*this);
- --*this;
- return out;
- }
+ /// Postfix increment.
+ /// \return non-incremented 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);
+ /// 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) {}
+ /// 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_;
-};
+ /// 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
+ {
+ /// 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)); }
+ }
#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); }
+ 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); }
+ /// 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); }
+ /// 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); }
+ /// 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;
- }
+ /// 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;
- }
+ /// 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)); }
+ /// 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
+ /// \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
- }
+ /// 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
- }
+ /// 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
- }
+ /// 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); }
+ /// 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 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
- }
+ /// 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
- }
+ /// 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)); }
+ /// 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)); }
+ /// 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
- }
+ /// 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
- }
+ /// 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)); }
+ /// 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
- }
+ /// 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
- }
+ /// 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)); }
+ /// 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)); }
+ /// 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)); }
+ /// 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)); }
+ /// 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 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 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 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)); }
+ /// 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 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 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 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 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 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
- }
+ /// 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
- }
+ /// 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
- }
+ /// 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 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
- }
+ /// 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_));
- }
+ /// 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_));
- }
+ /// 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_));
- }
+ /// 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 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 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 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_);
- }
+ /// 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_);
- }
+ #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
+ /// 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 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)));
- }
+ /// 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);
- }
+ /// 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 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);
+ }
- /// 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 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);
+ }
- /// 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)); }
- /// 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 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 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 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 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); }
- /// 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; }
- /// 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 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 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 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 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 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 \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 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); }
- /// 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;
+ }
- 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);
+ }
+ };
- 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); }
-/// 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)); }
+ };
- /// 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
+ }
-/// 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;
+ }
+ };
- /// 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
-/// 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>()); };
- 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
- 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>()); }
- 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
- 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>()); }
- 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> {};
- 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
+ /// \{
-/// \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 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 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 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 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 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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; }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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 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); }
-/// 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
-//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
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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(); }
-/// Get NaN value.
-/// \return quiet NaN
-inline half nanh(const char *) { return functions::nanh(); }
+ /// \}
+ /// \name Exponential functions
+ /// \{
-/// \}
-/// \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 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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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 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 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 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); }
-/// 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
+ /// \{
-/// \}
-/// \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 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 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 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 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 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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 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 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 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<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.
-/// \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 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<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,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
-/// 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
+ /// \{
-/// \}
-/// \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); }
-/// 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); }
-/// 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); }
-/// 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 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); }
-/// 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
-/// \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); }
-/// 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 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); }
-/// 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); }
-/// 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
+ /// \{
-/// \}
-/// \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); }
+ /// 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 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 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 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 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); }
+ /// 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
-/// \{
+ /// \}
+ /// \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 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 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 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); }
+ /// 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);
-}
+ /// 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); }
+ /// 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
-/// \{
+ /// \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.
+ /// 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);
-}
-/// \}
-}
+ /// 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); }
+ /// \}
+ }
-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::operator==;
+ using detail::operator!=;
+ using detail::operator<;
+ using detail::operator>;
+ using detail::operator<=;
+ using detail::operator>=;
+ using detail::operator+;
+ using detail::operator-;
+ using detail::operator*;
+ using detail::operator/;
+ using detail::operator<<;
+ using detail::operator>>;
-using detail::abs;
-using detail::fabs;
-using detail::fmod;
-using detail::remainder;
-using detail::remquo;
-using detail::fma;
-using detail::fmax;
-using detail::fmin;
-using detail::fdim;
-using detail::nanh;
-using detail::exp;
-using detail::expm1;
-using detail::exp2;
-using detail::log;
-using detail::log10;
-using detail::log1p;
-using detail::log2;
-using detail::sqrt;
-using detail::cbrt;
-using detail::hypot;
-using detail::pow;
-using detail::sin;
-using detail::cos;
-using detail::tan;
-using detail::asin;
-using detail::acos;
-using detail::atan;
-using detail::atan2;
-using detail::sinh;
-using detail::cosh;
-using detail::tanh;
-using detail::asinh;
-using detail::acosh;
-using detail::atanh;
-using detail::erf;
-using detail::erfc;
-using detail::lgamma;
-using detail::tgamma;
-using detail::ceil;
-using detail::floor;
-using detail::trunc;
-using detail::round;
-using detail::lround;
-using detail::nearbyint;
-using detail::rint;
-using detail::lrint;
+ using detail::abs;
+ using detail::fabs;
+ using detail::fmod;
+ using detail::remainder;
+ using detail::remquo;
+ using detail::fma;
+ using detail::fmax;
+ using detail::fmin;
+ using detail::fdim;
+ using detail::nanh;
+ using detail::exp;
+ using detail::expm1;
+ using detail::exp2;
+ using detail::log;
+ using detail::log10;
+ using detail::log1p;
+ using detail::log2;
+ using detail::sqrt;
+ using detail::cbrt;
+ using detail::hypot;
+ using detail::pow;
+ using detail::sin;
+ using detail::cos;
+ using detail::tan;
+ using detail::asin;
+ using detail::acos;
+ using detail::atan;
+ using detail::atan2;
+ using detail::sinh;
+ using detail::cosh;
+ using detail::tanh;
+ using detail::asinh;
+ using detail::acosh;
+ using detail::atanh;
+ using detail::erf;
+ using detail::erfc;
+ using detail::lgamma;
+ using detail::tgamma;
+ using detail::ceil;
+ using detail::floor;
+ using detail::trunc;
+ using detail::round;
+ using detail::lround;
+ using detail::nearbyint;
+ using detail::rint;
+ using detail::lrint;
#if HALF_ENABLE_CPP11_LONG_LONG
-using detail::llround;
-using detail::llrint;
+ using detail::llround;
+ using detail::llrint;
#endif
-using detail::frexp;
-using detail::ldexp;
-using detail::modf;
-using detail::scalbn;
-using detail::scalbln;
-using detail::ilogb;
-using detail::logb;
-using detail::nextafter;
-using detail::nexttoward;
-using detail::copysign;
-using detail::fpclassify;
-using detail::isfinite;
-using detail::isinf;
-using detail::isnan;
-using detail::isnormal;
-using detail::signbit;
-using detail::isgreater;
-using detail::isgreaterequal;
-using detail::isless;
-using detail::islessequal;
-using detail::islessgreater;
-using detail::isunordered;
+ using detail::frexp;
+ using detail::ldexp;
+ using detail::modf;
+ using detail::scalbn;
+ using detail::scalbln;
+ using detail::ilogb;
+ using detail::logb;
+ using detail::nextafter;
+ using detail::nexttoward;
+ using detail::copysign;
+ using detail::fpclassify;
+ using detail::isfinite;
+ using detail::isinf;
+ using detail::isnan;
+ using detail::isnormal;
+ using detail::signbit;
+ using detail::isgreater;
+ using detail::isgreaterequal;
+ using detail::isless;
+ using detail::islessequal;
+ using detail::islessgreater;
+ using detail::isunordered;
-using detail::half_cast;
+ using detail::half_cast;
}
+
/// Extensions to the C++ standard library.
-namespace std {
-/// Numeric limits for half-precision floats.
-/// Because of the underlying single-precision implementation of many
-/// operations, it inherits some properties from
-/// `std::numeric_limits<float>`.
-template <>
-class numeric_limits<half_float::half> : public numeric_limits<float> {
- public:
- /// Supports signed values.
- static HALF_CONSTEXPR_CONST bool is_signed = true;
+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;
+ /// Is not exact.
+ static HALF_CONSTEXPR_CONST bool is_exact = false;
- /// Doesn't provide modulo arithmetic.
- static HALF_CONSTEXPR_CONST bool is_modulo = false;
+ /// Doesn't provide modulo arithmetic.
+ static HALF_CONSTEXPR_CONST bool is_modulo = false;
- /// IEEE conformant.
- static HALF_CONSTEXPR_CONST bool is_iec559 = true;
+ /// IEEE conformant.
+ static HALF_CONSTEXPR_CONST bool is_iec559 = true;
- /// Supports infinity.
- static HALF_CONSTEXPR_CONST bool has_infinity = true;
+ /// Supports infinity.
+ static HALF_CONSTEXPR_CONST bool has_infinity = true;
- /// Supports quiet NaNs.
- static HALF_CONSTEXPR_CONST bool has_quiet_NaN = 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;
+ /// 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;
+ /// 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 digits.
+ static HALF_CONSTEXPR_CONST int digits = 11;
- /// Significant decimal digits.
- static HALF_CONSTEXPR_CONST int digits10 = 3;
+ /// 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;
+ /// 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;
+ /// Number base.
+ static HALF_CONSTEXPR_CONST int radix = 2;
- /// One more than smallest exponent.
- static HALF_CONSTEXPR_CONST int min_exponent = -13;
+ /// 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;
+ /// 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;
+ /// 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;
+ /// 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 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);
- }
+ /// 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);
- }
+ /// 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);
- }
+ /// 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);
- }
+ /// 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);
- }
+ /// 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);
- }
+ /// 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);
- }
+ /// 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);
- }
-};
+ /// 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;
+ /// 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;
+ /// 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));
- }
-};
+ /// 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
}
+
#undef HALF_CONSTEXPR
#undef HALF_CONSTEXPR_CONST
#undef HALF_NOEXCEPT
#undef HALF_NOTHROW
#ifdef HALF_POP_WARNINGS
-#pragma warning(pop)
-#undef HALF_POP_WARNINGS
+ #pragma warning(pop)
+ #undef HALF_POP_WARNINGS
#endif
#endif
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