From 5c99f0fa58caf45f4d457894413aa11c03afdb7d Mon Sep 17 00:00:00 2001 From: Nick Date: Fri, 13 Sep 2019 07:48:07 -0400 Subject: Revert "Add src/cuda-sim formatting" This reverts commit 0c023e41809dba8897c37af6bb03e5c3aa9ebc5e. --- src/cuda-sim/half.h | 6539 ++++++++++++++++++++++----------------------------- 1 file changed, 2877 insertions(+), 3662 deletions(-) (limited to 'src/cuda-sim/half.h') 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 // -// 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__) - -// 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 +#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__) + +//check C++11 language features +#if defined(__clang__) //clang + #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif +/*#elif defined(__INTEL_COMPILER) //Intel C++ + #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ???????? + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) ???????? + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) ???????? + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG) ???????? + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif*/ +#elif defined(__GNUC__) //gcc + #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L + #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif + #endif +#elif defined(_MSC_VER) //Visual C++ + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif + #define HALF_POP_WARNINGS 1 + #pragma warning(push) + #pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned +#endif + +//check C++11 library features #include -#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 +#include +#include #include #include #include -#include -#include #if HALF_ENABLE_CPP11_TYPE_TRAITS -#include + #include #endif #if HALF_ENABLE_CPP11_CSTDINT -#include + #include #endif #if HALF_ENABLE_CPP11_HASH -#include + #include #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::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::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 `` this symbol expands to -/// a positive value signaling the overflow of an +/// In correspondence with `HUGE_VAL[F|L]` from `` 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::infinity() +#define HUGE_VALH std::numeric_limits::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); -} -#endif - -/// \internal -/// \brief Implementation details. -namespace detail { -#if HALF_ENABLE_CPP11_TYPE_TRAITS -/// Conditional type. -template -struct conditional : std::conditional {}; - -/// Helper for tag dispatching. -template -struct bool_type : std::integral_constant {}; -using std::true_type; -using std::false_type; - -/// Type traits for floating point types. -template -struct is_float : std::is_floating_point {}; -#else -/// Conditional type. -template -struct conditional { - typedef T type; -}; -template -struct conditional { - typedef F type; -}; - -/// Helper for tag dispatching. -template -struct bool_type {}; -typedef bool_type true_type; -typedef bool_type false_type; - -/// Type traits for floating point types. -template -struct is_float : false_type {}; -template -struct is_float : is_float {}; -template -struct is_float : is_float {}; -template -struct is_float : is_float {}; -template <> -struct is_float : true_type {}; -template <> -struct is_float : true_type {}; -template <> -struct is_float : true_type {}; -#endif - -/// Type traits for floating point bits. -template -struct bits { - typedef unsigned char type; -}; -template -struct bits : bits {}; -template -struct bits : bits {}; -template -struct bits : bits {}; - -#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 { - typedef std::uint_least32_t type; -}; - -/// Unsigned integer of (at least) 64 bits width. -template <> -struct bits { - 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 - : conditional::digits >= 32, unsigned int, - unsigned long> {}; - -#if HALF_ENABLE_CPP11_LONG_LONG -/// Unsigned integer of (at least) 64 bits width. -template <> -struct bits - : conditional::digits >= 64, - unsigned long, unsigned long long> {}; -#else -/// Unsigned integer of (at least) 64 bits width. -template <> -struct bits { - typedef unsigned long type; -}; -#endif -#endif - -/// Tag type for binary construction. -struct binary_t {}; - -/// Tag for binary construction. -HALF_CONSTEXPR_CONST binary_t binary = binary_t(); - -/// Temporary half-precision expression. -/// This class represents a half-precision expression which just stores a -/// single-precision value internally. -struct expr { - /// Conversion constructor. - /// \param f single-precision value to convert - explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {} - - /// Conversion to single-precision. - /// \return single precision value representing expression value - HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; } - - private: - /// Internal expression value stored in single-precision. - float value_; -}; - -/// SFINAE helper for generic half-precision functions. -/// This class template has to be specialized for each valid combination of -/// argument types to provide a corresponding -/// `type` member equivalent to \a T. -/// \tparam T type to return -template -struct enable {}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - typedef T type; -}; -template -struct enable { - 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 -struct result : enable {}; -template <> -struct result { - typedef half type; -}; - -/// \name Classification helpers -/// \{ - -/// Check for infinity. -/// \tparam T argument type (builtin floating point type) -/// \param arg value to query -/// \retval true if infinity -/// \retval false else -template -bool builtin_isinf(T arg) { -#if HALF_ENABLE_CPP11_CMATH - return std::isinf(arg); -#elif defined(_MSC_VER) - return !::_finite(static_cast(arg)) && - !::_isnan(static_cast(arg)); -#else - return arg == std::numeric_limits::infinity() || - arg == -std::numeric_limits::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 -bool builtin_isnan(T arg) { -#if HALF_ENABLE_CPP11_CMATH - return std::isnan(arg); -#elif defined(_MSC_VER) - return ::_isnan(static_cast(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 -bool builtin_signbit(T arg) { -#if HALF_ENABLE_CPP11_CMATH - return std::signbit(arg); -#else - return arg < T() || (arg == T() && T(1) / arg < T()); -#endif -} - -/// \} -/// \name Conversion -/// \{ - -/// Convert IEEE single-precision to half-precision. -/// Credit for this goes to [Jeroen van der -/// Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). -/// \tparam R rounding mode to use, `std::round_indeterminate` for fastest -/// rounding -/// \param value single-precision value -/// \return binary representation of half-precision value -template -uint16 float2half_impl(float value, true_type) { - typedef bits::type uint32; - uint32 - bits; // = *reinterpret_cast(&value); //violating - // strict aliasing! - std::memcpy(&bits, &value, sizeof(float)); - /* uint16 hbits = (bits>>16) & 0x8000; + /// 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 struct conditional : std::conditional {}; + + /// Helper for tag dispatching. + template struct bool_type : std::integral_constant {}; + using std::true_type; + using std::false_type; + + /// Type traits for floating point types. + template struct is_float : std::is_floating_point {}; + #else + /// Conditional type. + template struct conditional { typedef T type; }; + template struct conditional { typedef F type; }; + + /// Helper for tag dispatching. + template struct bool_type {}; + typedef bool_type true_type; + typedef bool_type false_type; + + /// Type traits for floating point types. + template struct is_float : false_type {}; + template struct is_float : is_float {}; + template struct is_float : is_float {}; + template struct is_float : is_float {}; + template<> struct is_float : true_type {}; + template<> struct is_float : true_type {}; + template<> struct is_float : true_type {}; + #endif + + /// Type traits for floating point bits. + template struct bits { typedef unsigned char type; }; + template struct bits : bits {}; + template struct bits : bits {}; + template struct bits : bits {}; + + #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 { typedef std::uint_least32_t type; }; + + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits { 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 : conditional::digits>=32,unsigned int,unsigned long> {}; + + #if HALF_ENABLE_CPP11_LONG_LONG + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits : conditional::digits>=64,unsigned long,unsigned long long> {}; + #else + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits { typedef unsigned long type; }; + #endif + #endif + + /// Tag type for binary construction. + struct binary_t {}; + + /// Tag for binary construction. + HALF_CONSTEXPR_CONST binary_t binary = binary_t(); + + /// Temporary half-precision expression. + /// This class represents a half-precision expression which just stores a single-precision value internally. + struct expr + { + /// Conversion constructor. + /// \param f single-precision value to convert + explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {} + + /// Conversion to single-precision. + /// \return single precision value representing expression value + HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; } + + private: + /// Internal expression value stored in single-precision. + float value_; + }; + + /// SFINAE helper for generic half-precision functions. + /// This class template has to be specialized for each valid combination of argument types to provide a corresponding + /// `type` member equivalent to \a T. + /// \tparam T type to return + template struct enable {}; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { 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 struct result : enable {}; + template<> struct result { typedef half type; }; + + /// \name Classification helpers + /// \{ + + /// Check for infinity. + /// \tparam T argument type (builtin floating point type) + /// \param arg value to query + /// \retval true if infinity + /// \retval false else + template bool builtin_isinf(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::isinf(arg); + #elif defined(_MSC_VER) + return !::_finite(static_cast(arg)) && !::_isnan(static_cast(arg)); + #else + return arg == std::numeric_limits::infinity() || arg == -std::numeric_limits::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 bool builtin_isnan(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::isnan(arg); + #elif defined(_MSC_VER) + return ::_isnan(static_cast(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 bool builtin_signbit(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::signbit(arg); + #else + return arg < T() || (arg == T() && T(1)/arg < T()); + #endif + } + + /// \} + /// \name Conversion + /// \{ + + /// Convert IEEE single-precision to half-precision. + /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \param value single-precision value + /// \return binary representation of half-precision value + template uint16 float2half_impl(float value, true_type) + { + typedef bits::type uint32; + uint32 bits;// = *reinterpret_cast(&value); //violating strict aliasing! + std::memcpy(&bits, &value, sizeof(float)); +/* uint16 hbits = (bits>>16) & 0x8000; bits &= 0x7FFFFFFF; int exp = bits >> 23; if(exp == 255) @@ -615,3238 +498,2570 @@ 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((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(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(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(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((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(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(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(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 uint16 float2half_impl(double value, true_type) + { + typedef bits::type uint32; + typedef bits::type uint64; + uint64 bits;// = *reinterpret_cast(&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((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); + } + 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 uint16 float2half_impl(T value, ...) + { + uint16 hbits = static_cast(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(std::abs(static_cast(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 uint16 float2half(T value) + { + return float2half_impl(value, bool_type::is_iec559&&sizeof(typename bits::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 uint16 int2half_impl(T value) + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_integral::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 uint16 int2half(T value) + { + return (value<0) ? int2half_impl(value) : int2half_impl(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::type uint32; +/* uint32 bits = static_cast(value&0x8000) << 16; + int abs = value & 0x7FFF; + if(abs) + { + bits |= 0x38000000 << static_cast(abs>=0x7C00); + for(; abs<0x400; abs<<=1,bits-=0x800000) ; + bits += static_cast(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, 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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(&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::type uint32; + typedef bits::type uint64; + uint32 hi = static_cast(value&0x8000) << 16; + int abs = value & 0x7FFF; + if(abs) + { + hi |= 0x3F000000 << static_cast(abs>=0x7C00); + for(; abs<0x400; abs<<=1,hi-=0x100000) ; + hi += static_cast(abs) << 10; + } + uint64 bits = static_cast(hi) << 32; +// return *reinterpret_cast(&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 T half2float_impl(uint16 value, T, ...) + { + T out; + int abs = value & 0x7FFF; + if(abs > 0x7C00) + out = std::numeric_limits::has_quiet_NaN ? std::numeric_limits::quiet_NaN() : T(); + else if(abs == 0x7C00) + out = std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : std::numeric_limits::max(); + else if(abs > 0x3FF) + out = std::ldexp(static_cast((abs&0x3FF)|0x400), (abs>>10)-25); + else + out = std::ldexp(static_cast(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 T half2float(uint16 value) + { + return half2float_impl(value, T(), bool_type::is_iec559&&sizeof(typename bits::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 T half2int_impl(uint16 value) + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_integral::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::min() : std::numeric_limits::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(m) : static_cast(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 T half2int(uint16 value) { return half2int_impl(value); } + + /// Convert half-precision floating point to integer using round-to-nearest-away-from-zero. + /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits) + /// \param value binary representation of half-precision value + /// \return integral value + template T half2int_up(uint16 value) { return half2int_impl(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 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)&E); + else if(R == std::round_toward_infinity) + result += mask & ((value>>15)-1); + else if(R == std::round_toward_neg_infinity) + result += mask & -(value>>15); + result &= ~mask; + } + return result; + } + + /// Round half-precision number to nearest integer value. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \param value binary representation of half-precision value + /// \return half-precision bits for nearest integral value + template uint16 round_half(uint16 value) { return round_half_impl(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(value); } + /// \} + + struct functions; + template struct unary_specialized; + template struct binary_specialized; + template struct half_caster; + } + + /// Half-precision floating point type. + /// This class implements an IEEE-conformant half-precision floating point type with the usual arithmetic operators and + /// conversions. It is implicitly convertible to single-precision floating point, which makes artihmetic expressions and + /// functions with mixed-type operands to be of the most precise operand type. Additionally all arithmetic operations + /// (and many mathematical functions) are carried out in single-precision internally. All conversions from single- to + /// half-precision are done using 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; + friend struct detail::binary_specialized; + template friend struct detail::half_caster; + friend class std::numeric_limits; + #if HALF_ENABLE_CPP11_HASH + friend struct std::hash; + #endif + #if HALF_ENABLE_CPP11_USER_LITERALS + friend half literal::operator"" _h(long double); + #endif + + public: + /// Default constructor. + /// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics + /// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics. + HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {} + + /// Copy constructor. + /// \tparam T type of concrete half expression + /// \param rhs half expression to copy from + half(detail::expr rhs) : data_(detail::float2half(static_cast(rhs))) {} + + /// Conversion constructor. + /// \param rhs float to convert + explicit half(float rhs) : data_(detail::float2half(rhs)) {} + + /// Conversion to single-precision. + /// \return single precision value representing expression value + operator float() const { return detail::half2float(data_); } + + /// Assignment operator. + /// \tparam T type of concrete half expression + /// \param rhs half expression to copy from + /// \return reference to this half + half& operator=(detail::expr rhs) { return *this = static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to add + /// \return reference to this half + template typename detail::enable::type operator+=(T rhs) { return *this += static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to subtract + /// \return reference to this half + template typename detail::enable::type operator-=(T rhs) { return *this -= static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to multiply with + /// \return reference to this half + template typename detail::enable::type operator*=(T rhs) { return *this *= static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to divide by + /// \return reference to this half + template typename detail::enable::type operator/=(T rhs) { return *this /= static_cast(rhs); } + + /// Assignment operator. + /// \param rhs single-precision value to copy from + /// \return reference to this half + half& operator=(float rhs) { data_ = detail::float2half(rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to add + /// \return reference to this half + half& operator+=(float rhs) { data_ = detail::float2half(detail::half2float(data_)+rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to subtract + /// \return reference to this half + half& operator-=(float rhs) { data_ = detail::float2half(detail::half2float(data_)-rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to multiply with + /// \return reference to this half + half& operator*=(float rhs) { data_ = detail::float2half(detail::half2float(data_)*rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to divide by + /// \return reference to this half + half& operator/=(float rhs) { data_ = detail::float2half(detail::half2float(data_)/rhs); return *this; } + + /// Prefix increment. + /// \return incremented half value + half& operator++() { return *this += 1.0f; } + + /// Prefix decrement. + /// \return decremented half value + half& operator--() { return *this -= 1.0f; } + + /// Postfix increment. + /// \return non-incremented half value + half operator++(int) { half out(*this); ++*this; return out; } + + /// Postfix decrement. + /// \return non-decremented half value + half operator--(int) { half out(*this); --*this; return out; } + + private: + /// Rounding mode to use + static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE); + + /// Constructor. + /// \param bits binary representation to set half to + HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) HALF_NOEXCEPT : data_(bits) {} + + /// Internal binary representation + detail::uint16 data_; + }; -/// 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 -uint16 float2half_impl(double value, true_type) { - typedef bits::type uint32; - typedef bits::type uint64; - uint64 - bits; // = *reinterpret_cast(&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((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; -} +#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(value)); } + } +#endif + + namespace detail + { + /// Wrapper implementing unspecialized half-precision functions. + struct functions + { + /// Addition implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision sum stored in single-precision + static expr plus(float x, float y) { return expr(x+y); } + + /// Subtraction implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision difference stored in single-precision + static expr minus(float x, float y) { return expr(x-y); } + + /// Multiplication implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision product stored in single-precision + static expr multiplies(float x, float y) { return expr(x*y); } + + /// Division implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision quotient stored in single-precision + static expr divides(float x, float y) { return expr(x/y); } + + /// Output implementation. + /// \param out stream to write to + /// \param arg value to write + /// \return reference to stream + template static std::basic_ostream& write(std::basic_ostream &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 static std::basic_istream& read(std::basic_istream &in, half &arg) + { + float f; + if(in >> f) + arg = f; + return in; + } -/// 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 -uint16 float2half_impl(T value, ...) { - uint16 hbits = static_cast(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(std::abs(static_cast(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; -} + /// 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::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::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 + } -/// 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 -uint16 float2half(T value) { - return float2half_impl( - value, bool_type < std::numeric_limits::is_iec559 && - sizeof(typename bits::type) == sizeof(T) > ()); -} + /// 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::quiet_NaN()); + bool sign = builtin_signbit(x), qsign = static_cast(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::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 + } -/// 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 -uint16 int2half_impl(T value) { -#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS - static_assert(std::is_integral::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; -} + /// 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 + } -/// 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 -uint16 int2half(T value) { - return (value < 0) ? int2half_impl(value) - : int2half_impl(value); -} + /// 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 + } -/// 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::type uint32; - /* uint32 bits = static_cast(value&0x8000) << 16; - int abs = value & 0x7FFF; - if(abs) + /// Get NaN. + /// \return Half-precision quiet NaN + static half nanh() { return half(binary, 0x7FFF); } + + /// Exponential implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr exp(float arg) { return expr(std::exp(arg)); } + + /// Exponential implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr expm1(float arg) { - bits |= 0x38000000 << static_cast(abs>=0x7C00); - for(; abs<0x400; abs<<=1,bits-=0x800000) ; - bits += static_cast(abs) << 13; + #if HALF_ENABLE_CPP11_CMATH + return expr(std::expm1(arg)); + #else + return expr(static_cast(std::exp(static_cast(arg))-1.0)); + #endif } -*/ static const uint32 - mantissa_table[2048] = { - 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, - 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, - 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, - 0x35700000, 0x35800000, 0x35880000, 0x35900000, 0x35980000, - 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, - 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, - 0x35F00000, 0x35F80000, 0x36000000, 0x36040000, 0x36080000, - 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, - 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, - 0x36340000, 0x36380000, 0x363C0000, 0x36400000, 0x36440000, - 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, - 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, - 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 0x36800000, - 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, - 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, - 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, - 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, - 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, - 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, - 0x36BE0000, 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, - 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, - 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, - 0x36DC0000, 0x36DE0000, 0x36E00000, 0x36E20000, 0x36E40000, - 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, - 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, - 0x36FA0000, 0x36FC0000, 0x36FE0000, 0x37000000, 0x37010000, - 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, - 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, - 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 0x37100000, - 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, - 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, - 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, - 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, - 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, - 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, - 0x372F0000, 0x37300000, 0x37310000, 0x37320000, 0x37330000, - 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, - 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, - 0x373E0000, 0x373F0000, 0x37400000, 0x37410000, 0x37420000, - 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, - 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, - 0x374D0000, 0x374E0000, 0x374F0000, 0x37500000, 0x37510000, - 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, - 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, - 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, 0x37600000, - 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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(&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::type uint32; - typedef bits::type uint64; - uint32 hi = static_cast(value & 0x8000) << 16; - int abs = value & 0x7FFF; - if (abs) { - hi |= 0x3F000000 << static_cast(abs >= 0x7C00); - for (; abs < 0x400; abs <<= 1, hi -= 0x100000) - ; - hi += static_cast(abs) << 10; - } - uint64 bits = static_cast(hi) << 32; - // return *reinterpret_cast(&bits); //violating - //strict aliasing! - double out; - std::memcpy(&out, &bits, sizeof(double)); - return out; -} + /// 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(std::exp(arg*0.69314718055994530941723212145818))); + #endif + } -/// 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 -T half2float_impl(uint16 value, T, ...) { - T out; - int abs = value & 0x7FFF; - if (abs > 0x7C00) - out = std::numeric_limits::has_quiet_NaN - ? std::numeric_limits::quiet_NaN() - : T(); - else if (abs == 0x7C00) - out = std::numeric_limits::has_infinity - ? std::numeric_limits::infinity() - : std::numeric_limits::max(); - else if (abs > 0x3FF) - out = std::ldexp(static_cast((abs & 0x3FF) | 0x400), (abs >> 10) - 25); - else - out = std::ldexp(static_cast(abs), -24); - return (value & 0x8000) ? -out : out; -} + /// Logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log(float arg) { return expr(std::log(arg)); } -/// 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 -T half2float(uint16 value) { - return half2float_impl(value, T(), - bool_type < std::numeric_limits::is_iec559 && - sizeof(typename bits::type) == sizeof(T) > ()); -} + /// Common logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log10(float arg) { return expr(std::log10(arg)); } -/// 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 -T half2int_impl(uint16 value) { -#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS - static_assert(std::is_integral::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::min() - : std::numeric_limits::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(m) : static_cast(m); -} + /// 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(std::log(1.0+arg))); + #endif + } -/// 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 -T half2int(uint16 value) { - return half2int_impl(value); -} + /// 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(std::log(static_cast(arg))*1.4426950408889634073599246810019)); + #endif + } -/// 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 -T half2int_up(uint16 value) { - return half2int_impl(value); -} + /// Square root implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sqrt(float arg) { return expr(std::sqrt(arg)); } -/// 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 -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; -} + /// 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(std::pow(-static_cast(arg), 1.0/3.0)) : + static_cast(std::pow(static_cast(arg), 1.0/3.0))); + #endif + } -/// 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 -uint16 round_half(uint16 value) { - return round_half_impl(value); -} + /// 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::infinity() : + static_cast(std::sqrt(static_cast(x)*x+static_cast(y)*y))); + #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(value); -} -/// \} - -struct functions; -template -struct unary_specialized; -template -struct binary_specialized; -template -struct half_caster; -} + /// Power implementation. + /// \param base value to exponentiate + /// \param exp power to expontiate to + /// \return function value stored in single-preicision + static expr pow(float base, float exp) { return expr(std::pow(base, exp)); } + + /// Sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sin(float arg) { return expr(std::sin(arg)); } + + /// Cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr cos(float arg) { return expr(std::cos(arg)); } + + /// Tan implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr tan(float arg) { return expr(std::tan(arg)); } + + /// Arc sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr asin(float arg) { return expr(std::asin(arg)); } + + /// Arc cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr acos(float arg) { return expr(std::acos(arg)); } + + /// Arc tangent implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr atan(float arg) { return expr(std::atan(arg)); } + + /// Arc tangent implementation. + /// \param x first argument + /// \param y second argument + /// \return function value stored in single-preicision + static expr atan2(float x, float y) { return expr(std::atan2(x, y)); } + + /// Hyperbolic sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sinh(float arg) { return expr(std::sinh(arg)); } + + /// Hyperbolic cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr cosh(float arg) { return expr(std::cosh(arg)); } + + /// Hyperbolic tangent implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr tanh(float arg) { return expr(std::tanh(arg)); } + + /// Hyperbolic area sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr asinh(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::asinh(arg)); + #else + return expr((arg==-std::numeric_limits::infinity()) ? arg : static_cast(std::log(arg+std::sqrt(arg*arg+1.0)))); + #endif + } -/// 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; - friend struct detail::binary_specialized; - template - friend struct detail::half_caster; - friend class std::numeric_limits; -#if HALF_ENABLE_CPP11_HASH - friend struct std::hash; -#endif -#if HALF_ENABLE_CPP11_USER_LITERALS - friend half literal::operator"" _h(long double); -#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::quiet_NaN() : static_cast(std::log(arg+std::sqrt(arg*arg-1.0)))); + #endif + } - public: - /// Default constructor. - /// This initializes the half to 0. Although this does not match the builtin - /// types' default-initialization semantics - /// and may be less efficient than no initialization, it is needed to provide - /// proper value-initialization semantics. - HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {} - - /// Copy constructor. - /// \tparam T type of concrete half expression - /// \param rhs half expression to copy from - half(detail::expr rhs) - : data_(detail::float2half(static_cast(rhs))) {} - - /// Conversion constructor. - /// \param rhs float to convert - explicit half(float rhs) : data_(detail::float2half(rhs)) {} - - /// Conversion to single-precision. - /// \return single precision value representing expression value - operator float() const { return detail::half2float(data_); } - - /// Assignment operator. - /// \tparam T type of concrete half expression - /// \param rhs half expression to copy from - /// \return reference to this half - half &operator=(detail::expr rhs) { return *this = static_cast(rhs); } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to add - /// \return reference to this half - template - typename detail::enable::type operator+=(T rhs) { - return *this += static_cast(rhs); - } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to subtract - /// \return reference to this half - template - typename detail::enable::type operator-=(T rhs) { - return *this -= static_cast(rhs); - } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to multiply with - /// \return reference to this half - template - typename detail::enable::type operator*=(T rhs) { - return *this *= static_cast(rhs); - } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to divide by - /// \return reference to this half - template - typename detail::enable::type operator/=(T rhs) { - return *this /= static_cast(rhs); - } - - /// Assignment operator. - /// \param rhs single-precision value to copy from - /// \return reference to this half - half &operator=(float rhs) { - data_ = detail::float2half(rhs); - return *this; - } - - /// Arithmetic assignment. - /// \param rhs single-precision value to add - /// \return reference to this half - half &operator+=(float rhs) { - data_ = - detail::float2half(detail::half2float(data_) + rhs); - return *this; - } - - /// Arithmetic assignment. - /// \param rhs single-precision value to subtract - /// \return reference to this half - half &operator-=(float rhs) { - data_ = - detail::float2half(detail::half2float(data_) - rhs); - return *this; - } - - /// Arithmetic assignment. - /// \param rhs single-precision value to multiply with - /// \return reference to this half - half &operator*=(float rhs) { - data_ = - detail::float2half(detail::half2float(data_) * rhs); - return *this; - } - - /// Arithmetic assignment. - /// \param rhs single-precision value to divide by - /// \return reference to this half - half &operator/=(float rhs) { - data_ = - detail::float2half(detail::half2float(data_) / rhs); - return *this; - } - - /// Prefix increment. - /// \return incremented half value - half &operator++() { return *this += 1.0f; } - - /// Prefix decrement. - /// \return decremented half value - half &operator--() { return *this -= 1.0f; } - - /// Postfix increment. - /// \return non-incremented half value - half operator++(int) { - half out(*this); - ++*this; - return out; - } - - /// Postfix decrement. - /// \return non-decremented half value - half operator--(int) { - half out(*this); - --*this; - return out; - } - - private: - /// Rounding mode to use - static const std::float_round_style round_style = - (std::float_round_style)(HALF_ROUND_STYLE); - - /// Constructor. - /// \param bits binary representation to set half to - HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) HALF_NOEXCEPT - : data_(bits) {} - - /// Internal binary representation - detail::uint16 data_; -}; + /// 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(0.5*std::log((1.0+arg)/(1.0-arg)))); + #endif + } -#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(value)); -} -} -#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(erf(static_cast(arg)))); + #endif + } -namespace detail { -/// Wrapper implementing unspecialized half-precision functions. -struct functions { - /// Addition implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision sum stored in single-precision - static expr plus(float x, float y) { return expr(x + y); } - - /// Subtraction implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision difference stored in single-precision - static expr minus(float x, float y) { return expr(x - y); } - - /// Multiplication implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision product stored in single-precision - static expr multiplies(float x, float y) { return expr(x * y); } - - /// Division implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision quotient stored in single-precision - static expr divides(float x, float y) { return expr(x / y); } - - /// Output implementation. - /// \param out stream to write to - /// \param arg value to write - /// \return reference to stream - template - static std::basic_ostream &write( - std::basic_ostream &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 - static std::basic_istream &read( - std::basic_istream &in, half &arg) { - float f; - if (in >> f) arg = f; - return in; - } - - /// Modulo implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision division remainder stored in single-precision - static expr fmod(float x, float y) { return expr(std::fmod(x, y)); } - - /// Remainder implementation. - /// \param x first operand - /// \param y second operand - /// \return Half-precision division remainder stored in single-precision - static expr remainder(float x, float y) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::remainder(x, y)); -#else - if (builtin_isnan(x) || builtin_isnan(y)) - return expr(std::numeric_limits::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::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::quiet_NaN()); - bool sign = builtin_signbit(x), - qsign = static_cast(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::quiet_NaN()); - if (ay >= 65536.0f) return expr(x); - if (ax == ay) return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f); - ax = std::fmod(ax, 8.0f * ay); - int cquo = 0; - if (ax >= 4.0f * ay) { - ax -= 4.0f * ay; - cquo += 4; - } - if (ax >= 2.0f * ay) { - ax -= 2.0f * ay; - cquo += 2; - } - float y2 = 0.5f * ay; - if (ax > y2) { - ax -= ay; - ++cquo; - if (ax >= y2) { - ax -= ay; - ++cquo; - } - } - return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax); -#endif - } - - /// Positive difference implementation. - /// \param x first operand - /// \param y second operand - /// \return Positive difference stored in single-precision - static expr fdim(float x, float y) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::fdim(x, y)); -#else - return expr((x <= y) ? 0.0f : (x - y)); -#endif - } - - /// Fused multiply-add implementation. - /// \param x first operand - /// \param y second operand - /// \param z third operand - /// \return \a x * \a y + \a z stored in single-precision - static expr fma(float x, float y, float z) { -#if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF) - return expr(std::fma(x, y, z)); -#else - return expr(x * y + z); -#endif - } - - /// Get NaN. - /// \return Half-precision quiet NaN - static half nanh() { return half(binary, 0x7FFF); } - - /// Exponential implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr exp(float arg) { return expr(std::exp(arg)); } - - /// Exponential implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr expm1(float arg) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::expm1(arg)); -#else - return expr(static_cast(std::exp(static_cast(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(std::exp(arg * 0.69314718055994530941723212145818))); -#endif - } - - /// Logarithm implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr log(float arg) { return expr(std::log(arg)); } - - /// Common logarithm implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr log10(float arg) { return expr(std::log10(arg)); } - - /// Logarithm implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr log1p(float arg) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::log1p(arg)); -#else - return expr(static_cast(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(std::log(static_cast(arg)) * - 1.4426950408889634073599246810019)); -#endif - } - - /// Square root implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr sqrt(float arg) { return expr(std::sqrt(arg)); } - - /// Cubic root implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr cbrt(float arg) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::cbrt(arg)); -#else - if (builtin_isnan(arg) || builtin_isinf(arg)) return expr(arg); - return expr(builtin_signbit(arg) - ? -static_cast( - std::pow(-static_cast(arg), 1.0 / 3.0)) - : static_cast( - std::pow(static_cast(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::infinity() - : static_cast(std::sqrt(static_cast(x) * x + - static_cast(y) * y))); -#endif - } - - /// Power implementation. - /// \param base value to exponentiate - /// \param exp power to expontiate to - /// \return function value stored in single-preicision - static expr pow(float base, float exp) { return expr(std::pow(base, exp)); } - - /// Sine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr sin(float arg) { return expr(std::sin(arg)); } - - /// Cosine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr cos(float arg) { return expr(std::cos(arg)); } - - /// Tan implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr tan(float arg) { return expr(std::tan(arg)); } - - /// Arc sine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr asin(float arg) { return expr(std::asin(arg)); } - - /// Arc cosine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr acos(float arg) { return expr(std::acos(arg)); } - - /// Arc tangent implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr atan(float arg) { return expr(std::atan(arg)); } - - /// Arc tangent implementation. - /// \param x first argument - /// \param y second argument - /// \return function value stored in single-preicision - static expr atan2(float x, float y) { return expr(std::atan2(x, y)); } - - /// Hyperbolic sine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr sinh(float arg) { return expr(std::sinh(arg)); } - - /// Hyperbolic cosine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr cosh(float arg) { return expr(std::cosh(arg)); } - - /// Hyperbolic tangent implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr tanh(float arg) { return expr(std::tanh(arg)); } - - /// Hyperbolic area sine implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr asinh(float arg) { -#if HALF_ENABLE_CPP11_CMATH - return expr(std::asinh(arg)); -#else - return expr( - (arg == -std::numeric_limits::infinity()) - ? arg - : static_cast(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::quiet_NaN() - : static_cast(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(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(erf(static_cast(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(1.0 - erf(static_cast(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::infinity()); - if (arg < 0.0f) { - float i, f = std::modf(-arg, &i); - if (f == 0.0f) return expr(std::numeric_limits::infinity()); - return expr(static_cast( - 1.1447298858494001741434273513531 - - std::log(std::abs(std::sin(3.1415926535897932384626433832795 * f))) - - lgamma(1.0 - arg))); - } - return expr(static_cast(lgamma(static_cast(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::infinity()) - : expr(std::numeric_limits::infinity()); - if (arg < 0.0f) { - float i, f = std::modf(-arg, &i); - if (f == 0.0f) return expr(std::numeric_limits::quiet_NaN()); - double value = 3.1415926535897932384626433832795 / - (std::sin(3.1415926535897932384626433832795 * f) * - std::exp(lgamma(1.0 - arg))); - return expr( - static_cast((std::fmod(i, 2.0f) == 0.0f) ? -value : value)); - } - if (builtin_isinf(arg)) return expr(arg); - return expr(static_cast(std::exp(lgamma(static_cast(arg))))); -#endif - } - - /// Floor implementation. - /// \param arg value to round - /// \return rounded value - static half floor(half arg) { - return half(binary, round_half(arg.data_)); - } - - /// Ceiling implementation. - /// \param arg value to round - /// \return rounded value - static half ceil(half arg) { - return half(binary, round_half(arg.data_)); - } - - /// Truncation implementation. - /// \param arg value to round - /// \return rounded value - static half trunc(half arg) { - return half(binary, round_half(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(arg.data_); } - - /// Nearest integer implementation. - /// \param arg value to round - /// \return rounded value - static half rint(half arg) { - return half(binary, round_half(arg.data_)); - } - - /// Nearest integer implementation. - /// \param arg value to round - /// \return rounded value - static long lrint(half arg) { - return detail::half2int(arg.data_); - } + /// 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(1.0-erf(static_cast(arg)))); + #endif + } -#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(arg.data_); - } - - /// Nearest integer implementation. - /// \param arg value to round - /// \return rounded value - static long long llrint(half arg) { - return detail::half2int(arg.data_); - } -#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::infinity()); + if(arg < 0.0f) + { + float i, f = std::modf(-arg, &i); + if(f == 0.0f) + return expr(std::numeric_limits::infinity()); + return expr(static_cast(1.1447298858494001741434273513531- + std::log(std::abs(std::sin(3.1415926535897932384626433832795*f)))-lgamma(1.0-arg))); + } + return expr(static_cast(lgamma(static_cast(arg)))); + #endif + } - /// Decompression implementation. - /// \param arg number to decompress - /// \param exp address to store exponent at - /// \return normalized significant - static half frexp(half arg, int *exp) { - int m = arg.data_ & 0x7FFF, e = -14; - if (m >= 0x7C00 || !m) return *exp = 0, arg; - for (; m < 0x400; m <<= 1, --e) - ; - return *exp = e + (m >> 10), - half(binary, (arg.data_ & 0x8000) | 0x3800 | (m & 0x3FF)); - } - - /// Decompression implementation. - /// \param arg number to decompress - /// \param iptr address to store integer part at - /// \return fractional part - static half modf(half arg, half *iptr) { - unsigned int e = arg.data_ & 0x7FFF; - if (e >= 0x6400) - return *iptr = arg, half(binary, arg.data_ & (0x8000U | -(e > 0x7C00))); - if (e < 0x3C00) return iptr->data_ = arg.data_ & 0x8000, arg; - e >>= 10; - unsigned int mask = (1 << (25 - e)) - 1, m = arg.data_ & mask; - iptr->data_ = arg.data_ & ~mask; - if (!m) return half(binary, arg.data_ & 0x8000); - for (; m < 0x400; m <<= 1, --e) - ; - return half(binary, static_cast((arg.data_ & 0x8000) | (e << 10) | - (m & 0x3FF))); - } - - /// Scaling implementation. - /// \param arg number to scale - /// \param exp power of two to scale by - /// \return scaled number - static half scalbln(half arg, long exp) { - unsigned int m = arg.data_ & 0x7FFF; - if (m >= 0x7C00 || !m) return arg; - for (; m < 0x400; m <<= 1, --exp) - ; - exp += m >> 10; - uint16 value = arg.data_ & 0x8000; - if (exp > 30) { - if (half::round_style == std::round_toward_zero) - value |= 0x7BFF; - else if (half::round_style == std::round_toward_infinity) - value |= 0x7C00 - (value >> 15); - else if (half::round_style == std::round_toward_neg_infinity) - value |= 0x7BFF + (value >> 15); - else - value |= 0x7C00; - } else if (exp > 0) - value |= (exp << 10) | (m & 0x3FF); - else if (exp > -11) { - m = (m & 0x3FF) | 0x400; - if (half::round_style == std::round_to_nearest) { - m += 1 << -exp; -#if HALF_ROUND_TIES_TO_EVEN - m -= (m >> (1 - exp)) & 1; -#endif - } else if (half::round_style == std::round_toward_infinity) - m += ((value >> 15) - 1) & ((1 << (1 - exp)) - 1U); - else if (half::round_style == std::round_toward_neg_infinity) - m += -(value >> 15) & ((1 << (1 - exp)) - 1U); - value |= m >> (1 - exp); - } else if (half::round_style == std::round_toward_infinity) - value -= (value >> 15) - 1; - else if (half::round_style == std::round_toward_neg_infinity) - value += value >> 15; - return half(binary, value); - } - - /// Exponent implementation. - /// \param arg number to query - /// \return floating point exponent - static int ilogb(half arg) { - int abs = arg.data_ & 0x7FFF; - if (!abs) return FP_ILOGB0; - if (abs < 0x7C00) { - int exp = (abs >> 10) - 15; - if (abs < 0x400) - for (; abs < 0x200; abs <<= 1, --exp) - ; - return exp; - } - if (abs > 0x7C00) return FP_ILOGBNAN; - return INT_MAX; - } - - /// Exponent implementation. - /// \param arg number to query - /// \return floating point exponent - static half logb(half arg) { - int abs = arg.data_ & 0x7FFF; - if (!abs) return half(binary, 0xFC00); - if (abs < 0x7C00) { - int exp = (abs >> 10) - 15; - if (abs < 0x400) - for (; abs < 0x200; abs <<= 1, --exp) - ; - uint16 bits = (exp < 0) << 15; - if (exp) { - unsigned int m = std::abs(exp) << 6, e = 18; - for (; m < 0x400; m <<= 1, --e) - ; - bits |= (e << 10) + m; - } - return half(binary, bits); - } - if (abs > 0x7C00) return arg; - return half(binary, 0x7C00); - } - - /// Enumeration implementation. - /// \param from number to increase/decrease - /// \param to direction to enumerate into - /// \return next representable number - static half nextafter(half from, half to) { - uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF; - if (fabs > 0x7C00) return from; - if (tabs > 0x7C00 || from.data_ == to.data_ || !(fabs | tabs)) return to; - if (!fabs) return half(binary, (to.data_ & 0x8000) + 1); - bool lt = - ((fabs == from.data_) ? static_cast(fabs) - : -static_cast(fabs)) < - ((tabs == to.data_) ? static_cast(tabs) : -static_cast(tabs)); - return half(binary, - from.data_ + - (((from.data_ >> 15) ^ static_cast(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(from); - if (builtin_isnan(to) || lfrom == to) return half(static_cast(to)); - if (!(from.data_ & 0x7FFF)) - return half(binary, - (static_cast(builtin_signbit(to)) << 15) + 1); - return half( - binary, - from.data_ + - (((from.data_ >> 15) ^ static_cast(lfrom < to)) << 1) - - 1); - } - - /// Sign implementation - /// \param x first operand - /// \param y second operand - /// \return composed value - static half copysign(half x, half y) { - return half(binary, x.data_ ^ ((x.data_ ^ y.data_) & 0x8000)); - } - - /// Classification implementation. - /// \param arg value to classify - /// \retval true if infinite number - /// \retval false else - static int fpclassify(half arg) { - unsigned int abs = arg.data_ & 0x7FFF; - return abs ? ((abs > 0x3FF) ? ((abs >= 0x7C00) - ? ((abs > 0x7C00) ? FP_NAN : FP_INFINITE) - : FP_NORMAL) - : FP_SUBNORMAL) - : FP_ZERO; - } - - /// Classification implementation. - /// \param arg value to classify - /// \retval true if finite number - /// \retval false else - static bool isfinite(half arg) { return (arg.data_ & 0x7C00) != 0x7C00; } - - /// Classification implementation. - /// \param arg value to classify - /// \retval true if infinite number - /// \retval false else - static bool isinf(half arg) { return (arg.data_ & 0x7FFF) == 0x7C00; } - - /// Classification implementation. - /// \param arg value to classify - /// \retval true if not a number - /// \retval false else - static bool isnan(half arg) { return (arg.data_ & 0x7FFF) > 0x7C00; } - - /// Classification implementation. - /// \param arg value to classify - /// \retval true if normal number - /// \retval false else - static bool isnormal(half arg) { - return ((arg.data_ & 0x7C00) != 0) & ((arg.data_ & 0x7C00) != 0x7C00); - } - - /// Sign bit implementation. - /// \param arg value to check - /// \retval true if signed - /// \retval false if unsigned - static bool signbit(half arg) { return (arg.data_ & 0x8000) != 0; } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if operands equal - /// \retval false else - static bool isequal(half x, half y) { - return (x.data_ == y.data_ || !((x.data_ | y.data_) & 0x7FFF)) && !isnan(x); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if operands not equal - /// \retval false else - static bool isnotequal(half x, half y) { - return (x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF)) || isnan(x); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if \a x > \a y - /// \retval false else - static bool isgreater(half x, half y) { - int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; - return xabs <= 0x7C00 && yabs <= 0x7C00 && - (((xabs == x.data_) ? xabs : -xabs) > - ((yabs == y.data_) ? yabs : -yabs)); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if \a x >= \a y - /// \retval false else - static bool isgreaterequal(half x, half y) { - int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; - return xabs <= 0x7C00 && yabs <= 0x7C00 && - (((xabs == x.data_) ? xabs : -xabs) >= - ((yabs == y.data_) ? yabs : -yabs)); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if \a x < \a y - /// \retval false else - static bool isless(half x, half y) { - int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; - return xabs <= 0x7C00 && yabs <= 0x7C00 && - (((xabs == x.data_) ? xabs : -xabs) < - ((yabs == y.data_) ? yabs : -yabs)); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if \a x <= \a y - /// \retval false else - static bool islessequal(half x, half y) { - int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; - return xabs <= 0x7C00 && yabs <= 0x7C00 && - (((xabs == x.data_) ? xabs : -xabs) <= - ((yabs == y.data_) ? yabs : -yabs)); - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if either \a x > \a y nor \a x < \a y - /// \retval false else - static bool islessgreater(half x, half y) { - int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; - if (xabs > 0x7C00 || yabs > 0x7C00) return false; - int a = (xabs == x.data_) ? xabs : -xabs, - b = (yabs == y.data_) ? yabs : -yabs; - return a < b || a > b; - } - - /// Comparison implementation. - /// \param x first operand - /// \param y second operand - /// \retval true if operand unordered - /// \retval false else - static bool isunordered(half x, half y) { return isnan(x) || isnan(y); } - - private: - static double erf(double arg) { - if (builtin_isinf(arg)) return (arg < 0.0) ? -1.0 : 1.0; - double x2 = arg * arg, ax2 = 0.147 * x2, - value = std::sqrt( - 1.0 - std::exp(-x2 * (1.2732395447351626861510701069801 + ax2) / - (1.0 + ax2))); - return builtin_signbit(arg) ? -value : value; - } - - static double lgamma(double arg) { - double v = 1.0; - for (; arg < 8.0; ++arg) v *= arg; - double w = 1.0 / (arg * arg); - return (((((((-0.02955065359477124183006535947712 * w + - 0.00641025641025641025641025641026) * - w + - -0.00191752691752691752691752691753) * - w + - 8.4175084175084175084175084175084e-4) * - w + - -5.952380952380952380952380952381e-4) * - w + - 7.9365079365079365079365079365079e-4) * - w + - -0.00277777777777777777777777777778) * - w + - 0.08333333333333333333333333333333) / - arg + - 0.91893853320467274178032973640562 - std::log(v) - arg + - (arg - 0.5) * std::log(arg); - } -}; - -/// Wrapper for unary half-precision functions needing specialization for -/// individual argument types. -/// \tparam T argument type -template -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 { - 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 -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 { - 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 -struct half_caster {}; -template -struct half_caster { -#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS - static_assert(std::is_arithmetic::value, - "half_cast from non-arithmetic type unsupported"); -#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::infinity()) : expr(std::numeric_limits::infinity()); + if(arg < 0.0f) + { + float i, f = std::modf(-arg, &i); + if(f == 0.0f) + return expr(std::numeric_limits::quiet_NaN()); + double value = 3.1415926535897932384626433832795 / (std::sin(3.1415926535897932384626433832795*f)*std::exp(lgamma(1.0-arg))); + return expr(static_cast((std::fmod(i, 2.0f)==0.0f) ? -value : value)); + } + if(builtin_isinf(arg)) + return expr(arg); + return expr(static_cast(std::exp(lgamma(static_cast(arg))))); + #endif + } - static half cast(U arg) { return cast_impl(arg, is_float()); }; - - private: - static half cast_impl(U arg, true_type) { - return half(binary, float2half(arg)); - } - static half cast_impl(U arg, false_type) { - return half(binary, int2half(arg)); - } -}; -template -struct half_caster { -#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS - static_assert(std::is_arithmetic::value, - "half_cast to non-arithmetic type unsupported"); -#endif + /// Floor implementation. + /// \param arg value to round + /// \return rounded value + static half floor(half arg) { return half(binary, round_half(arg.data_)); } + + /// Ceiling implementation. + /// \param arg value to round + /// \return rounded value + static half ceil(half arg) { return half(binary, round_half(arg.data_)); } + + /// Truncation implementation. + /// \param arg value to round + /// \return rounded value + static half trunc(half arg) { return half(binary, round_half(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(arg.data_); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static half rint(half arg) { return half(binary, round_half(arg.data_)); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long lrint(half arg) { return detail::half2int(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(arg.data_); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long long llrint(half arg) { return detail::half2int(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)); + } - static T cast(half arg) { return cast_impl(arg, is_float()); } - - private: - static T cast_impl(half arg, true_type) { return half2float(arg.data_); } - static T cast_impl(half arg, false_type) { return half2int(arg.data_); } -}; -template -struct half_caster { -#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS - static_assert(std::is_arithmetic::value, - "half_cast to non-arithmetic type unsupported"); -#endif + /// 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((arg.data_&0x8000)|(e<<10)|(m&0x3FF))); + } - static T cast(expr arg) { return cast_impl(arg, is_float()); } - - private: - static T cast_impl(float arg, true_type) { return static_cast(arg); } - static T cast_impl(half arg, false_type) { return half2int(arg.data_); } -}; -template -struct half_caster { - static half cast(half arg) { return arg; } -}; -template -struct half_caster : half_caster {}; - -/// \name Comparison operators -/// \{ - -/// Comparison for equality. -/// \param x first operand -/// \param y second operand -/// \retval true if operands equal -/// \retval false else -template -typename enable::type operator==(T x, U y) { - return functions::isequal(x, y); -} + /// 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); + } -/// Comparison for inequality. -/// \param x first operand -/// \param y second operand -/// \retval true if operands not equal -/// \retval false else -template -typename enable::type operator!=(T x, U y) { - return functions::isnotequal(x, y); -} + /// 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; + } -/// 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 enable::type operator<(T x, U y) { - return functions::isless(x, y); -} + /// 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); + } -/// 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 enable::type operator>(T x, U y) { - return functions::isgreater(x, y); -} + /// 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(fabs) : -static_cast(fabs)) < + ((tabs==to.data_) ? static_cast(tabs) : -static_cast(tabs)); + return half(binary, from.data_+(((from.data_>>15)^static_cast(lt))<<1)-1); + } -/// 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 enable::type operator<=(T x, U y) { - return functions::islessequal(x, y); -} + /// 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(from); + if(builtin_isnan(to) || lfrom == to) + return half(static_cast(to)); + if(!(from.data_&0x7FFF)) + return half(binary, (static_cast(builtin_signbit(to))<<15)+1); + return half(binary, from.data_+(((from.data_>>15)^static_cast(lfrom -typename enable::type operator>=(T x, U y) { - return functions::isgreaterequal(x, y); -} + /// 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; + } -/// \} -/// \name Arithmetic operators -/// \{ - -/// Add halfs. -/// \param x left operand -/// \param y right operand -/// \return sum of half expressions -template -typename enable::type operator+(T x, U y) { - return functions::plus(x, y); -} + /// Classification implementation. + /// \param arg value to classify + /// \retval true if finite number + /// \retval false else + static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if infinite number + /// \retval false else + static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if not a number + /// \retval false else + static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if normal number + /// \retval false else + static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); } + + /// Sign bit implementation. + /// \param arg value to check + /// \retval true if signed + /// \retval false if unsigned + static bool signbit(half arg) { return (arg.data_&0x8000) != 0; } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if operands equal + /// \retval false else + static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if operands not equal + /// \retval false else + static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x > \a y + /// \retval false else + static bool isgreater(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) > ((yabs==y.data_) ? yabs : -yabs)); + } -/// Subtract halfs. -/// \param x left operand -/// \param y right operand -/// \return difference of half expressions -template -typename enable::type operator-(T x, U y) { - return functions::minus(x, y); -} + /// 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)); + } -/// Multiply halfs. -/// \param x left operand -/// \param y right operand -/// \return product of half expressions -template -typename enable::type operator*(T x, U y) { - return functions::multiplies(x, y); -} + /// 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)); + } -/// Divide halfs. -/// \param x left operand -/// \param y right operand -/// \return quotient of half expressions -template -typename enable::type operator/(T x, U y) { - return functions::divides(x, y); -} + /// 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)); + } -/// Identity. -/// \param arg operand -/// \return uncahnged operand -template -HALF_CONSTEXPR typename enable::type operator+(T arg) { - return arg; -} + /// 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; + } -/// Negation. -/// \param arg operand -/// \return negated operand -template -HALF_CONSTEXPR typename enable::type operator-(T arg) { - return unary_specialized::negate(arg); -} + /// 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); } -/// \} -/// \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 enable &, T>::type operator<<( - std::basic_ostream &out, T arg) { - return functions::write(out, arg); -} + 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; + } -/// Input operator. -/// \param in input stream to read from -/// \param arg half to read into -/// \return reference to input stream -template -std::basic_istream &operator>>( - std::basic_istream &in, half &arg) { - return functions::read(in, 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 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 + { + 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 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 + } -/// \} -/// \name Basic mathematical operations -/// \{ - -/// Absolute value. -/// \param arg operand -/// \return absolute value of \a arg -// template typename enable::type abs(T arg) { -//return unary_specialized::fabs(arg); } -inline half abs(half arg) { return unary_specialized::fabs(arg); } -inline expr abs(expr arg) { return unary_specialized::fabs(arg); } - -/// Absolute value. -/// \param arg operand -/// \return absolute value of \a arg -// template typename enable::type fabs(T arg) { -//return unary_specialized::fabs(arg); } -inline half fabs(half arg) { return unary_specialized::fabs(arg); } -inline expr fabs(expr arg) { return unary_specialized::fabs(arg); } - -/// Remainder of division. -/// \param x first operand -/// \param y second operand -/// \return remainder of floating point division. -// template typename enable::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 enable::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 enable::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); + /// 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 + { + 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 struct half_caster {}; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast from non-arithmetic type unsupported"); + #endif + + static half cast(U arg) { return cast_impl(arg, is_float()); }; + + private: + static half cast_impl(U arg, true_type) { return half(binary, float2half(arg)); } + static half cast_impl(U arg, false_type) { return half(binary, int2half(arg)); } + }; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast to non-arithmetic type unsupported"); + #endif + + static T cast(half arg) { return cast_impl(arg, is_float()); } + + private: + static T cast_impl(half arg, true_type) { return half2float(arg.data_); } + static T cast_impl(half arg, false_type) { return half2int(arg.data_); } + }; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast to non-arithmetic type unsupported"); + #endif + + static T cast(expr arg) { return cast_impl(arg, is_float()); } + + private: + static T cast_impl(float arg, true_type) { return static_cast(arg); } + static T cast_impl(half arg, false_type) { return half2int(arg.data_); } + }; + template struct half_caster + { + static half cast(half arg) { return arg; } + }; + template struct half_caster : half_caster {}; + + /// \name Comparison operators + /// \{ + + /// Comparison for equality. + /// \param x first operand + /// \param y second operand + /// \retval true if operands equal + /// \retval false else + template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); } + + /// \} + /// \name Arithmetic operators + /// \{ + + /// Add halfs. + /// \param x left operand + /// \param y right operand + /// \return sum of half expressions + template typename enable::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 enable::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 enable::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 enable::type operator/(T x, U y) { return functions::divides(x, y); } + + /// Identity. + /// \param arg operand + /// \return uncahnged operand + template HALF_CONSTEXPR typename enable::type operator+(T arg) { return arg; } + + /// Negation. + /// \param arg operand + /// \return negated operand + template HALF_CONSTEXPR typename enable::type operator-(T arg) { return unary_specialized::negate(arg); } + + /// \} + /// \name Input and output + /// \{ + + /// Output operator. + /// \param out output stream to write into + /// \param arg half expression to write + /// \return reference to output stream + template typename enable&,T>::type + operator<<(std::basic_ostream &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 std::basic_istream& + operator>>(std::basic_istream &in, half &arg) { return functions::read(in, arg); } + + /// \} + /// \name Basic mathematical operations + /// \{ + + /// Absolute value. + /// \param arg operand + /// \return absolute value of \a arg +// template typename enable::type abs(T arg) { return unary_specialized::fabs(arg); } + inline half abs(half arg) { return unary_specialized::fabs(arg); } + inline expr abs(expr arg) { return unary_specialized::fabs(arg); } + + /// Absolute value. + /// \param arg operand + /// \return absolute value of \a arg +// template typename enable::type fabs(T arg) { return unary_specialized::fabs(arg); } + inline half fabs(half arg) { return unary_specialized::fabs(arg); } + inline expr fabs(expr arg) { return unary_specialized::fabs(arg); } + + /// Remainder of division. + /// \param x first operand + /// \param y second operand + /// \return remainder of floating point division. +// template typename enable::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 enable::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 enable::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 enable::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 result::type fmax(T x, U y) { return binary_specialized::fmax(x, y); } + inline half fmax(half x, half y) { return binary_specialized::fmax(x, y); } + inline expr fmax(half x, expr y) { return binary_specialized::fmax(x, y); } + inline expr fmax(expr x, half y) { return binary_specialized::fmax(x, y); } + inline expr fmax(expr x, expr y) { return binary_specialized::fmax(x, y); } + + /// Minimum of half expressions. + /// \param x first operand + /// \param y second operand + /// \return minimum of operands +// template typename result::type fmin(T x, U y) { return binary_specialized::fmin(x, y); } + inline half fmin(half x, half y) { return binary_specialized::fmin(x, y); } + inline expr fmin(half x, expr y) { return binary_specialized::fmin(x, y); } + inline expr fmin(expr x, half y) { return binary_specialized::fmin(x, y); } + inline expr fmin(expr x, expr y) { return binary_specialized::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 enable::type fdim(T x, U y) { return functions::fdim(x, y); } + inline expr fdim(half x, half y) { return functions::fdim(x, y); } + inline expr fdim(half x, expr y) { return functions::fdim(x, y); } + inline expr fdim(expr x, half y) { return functions::fdim(x, y); } + inline expr fdim(expr x, expr y) { return functions::fdim(x, y); } + + /// Get NaN value. + /// \return quiet NaN + inline half nanh(const char*) { return functions::nanh(); } + + /// \} + /// \name Exponential functions + /// \{ + + /// Exponential function. + /// \param arg function argument + /// \return e raised to \a arg +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type log2(T arg) { return functions::log2(arg); } + inline expr log2(half arg) { return functions::log2(arg); } + inline expr log2(expr arg) { return functions::log2(arg); } + + /// \} + /// \name Power functions + /// \{ + + /// Square root. + /// \param arg function argument + /// \return square root of \a arg +// template typename enable::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 enable::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 enable::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 enable::type pow(T base, U exp) { return functions::pow(base, exp); } + inline expr pow(half base, half exp) { return functions::pow(base, exp); } + inline expr pow(half base, expr exp) { return functions::pow(base, exp); } + inline expr pow(expr base, half exp) { return functions::pow(base, exp); } + inline expr pow(expr base, expr exp) { return functions::pow(base, exp); } + + /// \} + /// \name Trigonometric functions + /// \{ + + /// Sine function. + /// \param arg function argument + /// \return sine value of \a arg +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type atan2(T x, U y) { return functions::atan2(x, y); } + inline expr atan2(half x, half y) { return functions::atan2(x, y); } + inline expr atan2(half x, expr y) { return functions::atan2(x, y); } + inline expr atan2(expr x, half y) { return functions::atan2(x, y); } + inline expr atan2(expr x, expr y) { return functions::atan2(x, y); } + + /// \} + /// \name Hyperbolic functions + /// \{ + + /// Hyperbolic sine. + /// \param arg function argument + /// \return hyperbolic sine value of \a arg +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type atanh(T arg) { return functions::atanh(arg); } + inline expr atanh(half arg) { return functions::atanh(arg); } + inline expr atanh(expr arg) { return functions::atanh(arg); } + + /// \} + /// \name Error and gamma functions + /// \{ + + /// Error function. + /// \param arg function argument + /// \return error function value of \a arg +// template typename enable::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 enable::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 enable::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 enable::type tgamma(T arg) { return functions::tgamma(arg); } + inline expr tgamma(half arg) { return functions::tgamma(arg); } + inline expr tgamma(expr arg) { return functions::tgamma(arg); } + + /// \} + /// \name Rounding + /// \{ + + /// Nearest integer not less than half value. + /// \param arg half to round + /// \return nearest integer not less than \a arg +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type llrint(T arg) { return functions::llrint(arg); } + inline long long llrint(half arg) { return functions::llrint(arg); } + inline long long llrint(expr arg) { return functions::llrint(arg); } + #endif + + /// \} + /// \name Floating point manipulation + /// \{ + + /// Decompress floating point number. + /// \param arg number to decompress + /// \param exp address to store exponent at + /// \return significant in range [0.5, 1) +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type copysign(T x, U y) { return functions::copysign(x, y); } + inline half copysign(half x, half y) { return functions::copysign(x, y); } + inline half copysign(half x, expr y) { return functions::copysign(x, y); } + inline half copysign(expr x, half y) { return functions::copysign(x, y); } + inline half copysign(expr x, expr y) { return functions::copysign(x, y); } + + /// \} + /// \name Floating point classification + /// \{ + + + /// Classify floating point value. + /// \param arg number to classify + /// \retval FP_ZERO for positive and negative zero + /// \retval FP_SUBNORMAL for subnormal numbers + /// \retval FP_INFINITY for positive and negative infinity + /// \retval FP_NAN for NaNs + /// \retval FP_NORMAL for all other (normal) values +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type signbit(T arg) { return functions::signbit(arg); } + inline bool signbit(half arg) { return functions::signbit(arg); } + inline bool signbit(expr arg) { return functions::signbit(arg); } + + /// \} + /// \name Comparison + /// \{ + + /// Comparison for greater than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater than \a y + /// \retval false else +// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type isunordered(T x, U y) { return functions::isunordered(x, y); } + inline bool isunordered(half x, half y) { return functions::isunordered(x, y); } + inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); } + inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); } + inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); } + + /// \name Casting + /// \{ + + /// Cast to or from half-precision floating point number. + /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted + /// directly using the given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. + /// It uses the default rounding mode. + /// + /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types + /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler + /// error and casting between [half](\ref half_float::half)s is just a no-op. + /// \tparam T destination type (half or built-in arithmetic type) + /// \tparam U source type (half or built-in arithmetic type) + /// \param arg value to cast + /// \return \a arg converted to destination type + template T half_cast(U arg) { return half_caster::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 T half_cast(U arg) { return half_caster::cast(arg); } + /// \} + } + + using detail::operator==; + using detail::operator!=; + using detail::operator<; + using detail::operator>; + using detail::operator<=; + using detail::operator>=; + using detail::operator+; + using detail::operator-; + using detail::operator*; + using detail::operator/; + using detail::operator<<; + using detail::operator>>; + + using detail::abs; + using detail::fabs; + using detail::fmod; + using detail::remainder; + using detail::remquo; + using detail::fma; + using detail::fmax; + using detail::fmin; + using detail::fdim; + using detail::nanh; + using detail::exp; + using detail::expm1; + using detail::exp2; + using detail::log; + using detail::log10; + using detail::log1p; + using detail::log2; + using detail::sqrt; + using detail::cbrt; + using detail::hypot; + using detail::pow; + using detail::sin; + using detail::cos; + using detail::tan; + using detail::asin; + using detail::acos; + using detail::atan; + using detail::atan2; + using detail::sinh; + using detail::cosh; + using detail::tanh; + using detail::asinh; + using detail::acosh; + using detail::atanh; + using detail::erf; + using detail::erfc; + using detail::lgamma; + using detail::tgamma; + using detail::ceil; + using detail::floor; + using detail::trunc; + using detail::round; + using detail::lround; + using detail::nearbyint; + using detail::rint; + using detail::lrint; +#if HALF_ENABLE_CPP11_LONG_LONG + using detail::llround; + using detail::llrint; +#endif + using detail::frexp; + using detail::ldexp; + using detail::modf; + using detail::scalbn; + using detail::scalbln; + using detail::ilogb; + using detail::logb; + using detail::nextafter; + using detail::nexttoward; + using detail::copysign; + using detail::fpclassify; + using detail::isfinite; + using detail::isinf; + using detail::isnan; + using detail::isnormal; + using detail::signbit; + using detail::isgreater; + using detail::isgreaterequal; + using detail::isless; + using detail::islessequal; + using detail::islessgreater; + using detail::isunordered; + + using detail::half_cast; } -/// 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 -//enable::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 result::type fmax(T -//x, U y) { return binary_specialized::fmax(x, y); } -inline half fmax(half x, half y) { - return binary_specialized::fmax(x, y); -} -inline expr fmax(half x, expr y) { - return binary_specialized::fmax(x, y); -} -inline expr fmax(expr x, half y) { - return binary_specialized::fmax(x, y); -} -inline expr fmax(expr x, expr y) { - return binary_specialized::fmax(x, y); -} -/// Minimum of half expressions. -/// \param x first operand -/// \param y second operand -/// \return minimum of operands -// template typename result::type fmin(T -//x, U y) { return binary_specialized::fmin(x, y); } -inline half fmin(half x, half y) { - return binary_specialized::fmin(x, y); -} -inline expr fmin(half x, expr y) { - return binary_specialized::fmin(x, y); -} -inline expr fmin(expr x, half y) { - return binary_specialized::fmin(x, y); -} -inline expr fmin(expr x, expr y) { - return binary_specialized::fmin(x, y); -} +/// 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`. + template<> class numeric_limits : public numeric_limits + { + public: + /// Supports signed values. + static HALF_CONSTEXPR_CONST bool is_signed = true; -/// Positive difference. -/// \param x first operand -/// \param y second operand -/// \return \a x - \a y or 0 if difference negative -// template typename enable::type -//fdim(T x, U y) { return functions::fdim(x, y); } -inline expr fdim(half x, half y) { return functions::fdim(x, y); } -inline expr fdim(half x, expr y) { return functions::fdim(x, y); } -inline expr fdim(expr x, half y) { return functions::fdim(x, y); } -inline expr fdim(expr x, expr y) { return functions::fdim(x, y); } - -/// Get NaN value. -/// \return quiet NaN -inline half nanh(const char *) { return functions::nanh(); } - -/// \} -/// \name Exponential functions -/// \{ - -/// Exponential function. -/// \param arg function argument -/// \return e raised to \a arg -// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type log2(T arg) { -//return functions::log2(arg); } -inline expr log2(half arg) { return functions::log2(arg); } -inline expr log2(expr arg) { return functions::log2(arg); } - -/// \} -/// \name Power functions -/// \{ - -/// Square root. -/// \param arg function argument -/// \return square root of \a arg -// template typename enable::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 enable::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 enable::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 enable::type -//pow(T base, U exp) { return functions::pow(base, exp); } -inline expr pow(half base, half exp) { return functions::pow(base, exp); } -inline expr pow(half base, expr exp) { return functions::pow(base, exp); } -inline expr pow(expr base, half exp) { return functions::pow(base, exp); } -inline expr pow(expr base, expr exp) { return functions::pow(base, exp); } - -/// \} -/// \name Trigonometric functions -/// \{ - -/// Sine function. -/// \param arg function argument -/// \return sine value of \a arg -// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::type -//atan2(T x, U y) { return functions::atan2(x, y); } -inline expr atan2(half x, half y) { return functions::atan2(x, y); } -inline expr atan2(half x, expr y) { return functions::atan2(x, y); } -inline expr atan2(expr x, half y) { return functions::atan2(x, y); } -inline expr atan2(expr x, expr y) { return functions::atan2(x, y); } - -/// \} -/// \name Hyperbolic functions -/// \{ - -/// Hyperbolic sine. -/// \param arg function argument -/// \return hyperbolic sine value of \a arg -// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type atanh(T arg) { -//return functions::atanh(arg); } -inline expr atanh(half arg) { return functions::atanh(arg); } -inline expr atanh(expr arg) { return functions::atanh(arg); } - -/// \} -/// \name Error and gamma functions -/// \{ - -/// Error function. -/// \param arg function argument -/// \return error function value of \a arg -// template typename enable::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 enable::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 enable::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 enable::type tgamma(T arg) { -//return functions::tgamma(arg); } -inline expr tgamma(half arg) { return functions::tgamma(arg); } -inline expr tgamma(expr arg) { return functions::tgamma(arg); } - -/// \} -/// \name Rounding -/// \{ - -/// Nearest integer not less than half value. -/// \param arg half to round -/// \return nearest integer not less than \a arg -// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 + /// Is not exact. + static HALF_CONSTEXPR_CONST bool is_exact = false; -/// \} -/// \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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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 enable::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); -} + /// Doesn't provide modulo arithmetic. + static HALF_CONSTEXPR_CONST bool is_modulo = false; -/// 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 enable::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); -} + /// IEEE conformant. + static HALF_CONSTEXPR_CONST bool is_iec559 = true; -/// 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 enable::type -//copysign(T x, U y) { return functions::copysign(x, y); } -inline half copysign(half x, half y) { return functions::copysign(x, y); } -inline half copysign(half x, expr y) { return functions::copysign(x, y); } -inline half copysign(expr x, half y) { return functions::copysign(x, y); } -inline half copysign(expr x, expr y) { return functions::copysign(x, y); } - -/// \} -/// \name Floating point classification -/// \{ - -/// Classify floating point value. -/// \param arg number to classify -/// \retval FP_ZERO for positive and negative zero -/// \retval FP_SUBNORMAL for subnormal numbers -/// \retval FP_INFINITY for positive and negative infinity -/// \retval FP_NAN for NaNs -/// \retval FP_NORMAL for all other (normal) values -// template typename enable::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 enable::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 enable::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 enable::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 enable::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 enable::type signbit(T arg) -//{ return functions::signbit(arg); } -inline bool signbit(half arg) { return functions::signbit(arg); } -inline bool signbit(expr arg) { return functions::signbit(arg); } - -/// \} -/// \name Comparison -/// \{ - -/// Comparison for greater than. -/// \param x first operand -/// \param y second operand -/// \retval true if \a x greater than \a y -/// \retval false else -// template typename enable::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 enable::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); -} + /// Supports infinity. + static HALF_CONSTEXPR_CONST bool has_infinity = true; -/// 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 enable::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 enable::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 enable::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); -} + /// Supports quiet NaNs. + static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true; -/// 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 enable::type -//isunordered(T x, U y) { return functions::isunordered(x, y); } -inline bool isunordered(half x, half y) { return functions::isunordered(x, y); } -inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); } -inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); } -inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); } - -/// \name Casting -/// \{ - -/// Cast to or from half-precision floating point number. -/// This casts between [half](\ref half_float::half) and any built-in arithmetic -/// type. The values are converted -/// directly using the given rounding mode, without any roundtrip over `float` -/// that a `static_cast` would otherwise do. -/// It uses the default rounding mode. -/// -/// Using this cast with neither of the two types being a [half](\ref -/// half_float::half) or with any of the two types -/// not being a built-in arithmetic type (apart from [half](\ref -/// half_float::half), of course) results in a compiler -/// error and casting between [half](\ref half_float::half)s is just a no-op. -/// \tparam T destination type (half or built-in arithmetic type) -/// \tparam U source type (half or built-in arithmetic type) -/// \param arg value to cast -/// \return \a arg converted to destination type -template -T half_cast(U arg) { - return half_caster::cast(arg); -} + /// Supports subnormal values. + static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; -/// 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 -T half_cast(U arg) { - return half_caster::cast(arg); -} -/// \} -} + /// 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::round_style== + half_float::half::round_style) ? half_float::half::round_style : round_indeterminate; -using detail::operator==; -using detail::operator!=; -using detail::operator<; -using detail::operator>; -using detail::operator<=; -using detail::operator>=; -using detail::operator+; -using detail::operator-; -using detail::operator*; -using detail::operator/; -using detail::operator<<; -using detail::operator>>; - -using detail::abs; -using detail::fabs; -using detail::fmod; -using detail::remainder; -using detail::remquo; -using detail::fma; -using detail::fmax; -using detail::fmin; -using detail::fdim; -using detail::nanh; -using detail::exp; -using detail::expm1; -using detail::exp2; -using detail::log; -using detail::log10; -using detail::log1p; -using detail::log2; -using detail::sqrt; -using detail::cbrt; -using detail::hypot; -using detail::pow; -using detail::sin; -using detail::cos; -using detail::tan; -using detail::asin; -using detail::acos; -using detail::atan; -using detail::atan2; -using detail::sinh; -using detail::cosh; -using detail::tanh; -using detail::asinh; -using detail::acosh; -using detail::atanh; -using detail::erf; -using detail::erfc; -using detail::lgamma; -using detail::tgamma; -using detail::ceil; -using detail::floor; -using detail::trunc; -using detail::round; -using detail::lround; -using detail::nearbyint; -using detail::rint; -using detail::lrint; -#if HALF_ENABLE_CPP11_LONG_LONG -using detail::llround; -using detail::llrint; -#endif -using detail::frexp; -using detail::ldexp; -using detail::modf; -using detail::scalbn; -using detail::scalbln; -using detail::ilogb; -using detail::logb; -using detail::nextafter; -using detail::nexttoward; -using detail::copysign; -using detail::fpclassify; -using detail::isfinite; -using detail::isinf; -using detail::isnan; -using detail::isnormal; -using detail::signbit; -using detail::isgreater; -using detail::isgreaterequal; -using detail::isless; -using detail::islessequal; -using detail::islessgreater; -using detail::isunordered; - -using detail::half_cast; -} + /// Significant digits. + static HALF_CONSTEXPR_CONST int digits = 11; -/// 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`. -template <> -class numeric_limits : public numeric_limits { - public: - /// Supports signed values. - static HALF_CONSTEXPR_CONST bool is_signed = true; - - /// Is not exact. - static HALF_CONSTEXPR_CONST bool is_exact = false; - - /// Doesn't provide modulo arithmetic. - static HALF_CONSTEXPR_CONST bool is_modulo = false; - - /// IEEE conformant. - static HALF_CONSTEXPR_CONST bool is_iec559 = true; - - /// Supports infinity. - static HALF_CONSTEXPR_CONST bool has_infinity = true; - - /// Supports quiet NaNs. - static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true; - - /// Supports subnormal values. - static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; - - /// Rounding mode. - /// Due to the mix of internal single-precision computations (using the - /// rounding mode of the underlying - /// single-precision implementation) with the rounding mode of the - /// single-to-half conversions, the actual rounding - /// mode might be `std::round_indeterminate` if the default half-precision - /// rounding mode doesn't match the - /// single-precision rounding mode. - static HALF_CONSTEXPR_CONST float_round_style round_style = - (std::numeric_limits::round_style == half_float::half::round_style) - ? half_float::half::round_style - : round_indeterminate; - - /// Significant digits. - static HALF_CONSTEXPR_CONST int digits = 11; - - /// Significant decimal digits. - static HALF_CONSTEXPR_CONST int digits10 = 3; - - /// Required decimal digits to represent all possible values. - static HALF_CONSTEXPR_CONST int max_digits10 = 5; - - /// Number base. - static HALF_CONSTEXPR_CONST int radix = 2; - - /// One more than smallest exponent. - static HALF_CONSTEXPR_CONST int min_exponent = -13; - - /// Smallest normalized representable power of 10. - static HALF_CONSTEXPR_CONST int min_exponent10 = -4; - - /// One more than largest exponent - static HALF_CONSTEXPR_CONST int max_exponent = 16; - - /// Largest finitely representable power of 10. - static HALF_CONSTEXPR_CONST int max_exponent10 = 4; - - /// Smallest positive normal value. - static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x0400); - } - - /// Smallest finite value. - static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0xFBFF); - } - - /// Largest finite value. - static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x7BFF); - } - - /// Difference between one and next representable value. - static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x1400); - } - - /// Maximum rounding error. - static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW { - return half_float::half( - half_float::detail::binary, - (round_style == std::round_to_nearest) ? 0x3800 : 0x3C00); - } - - /// Positive infinity. - static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x7C00); - } - - /// Quiet NaN. - static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x7FFF); - } - - /// Signalling NaN. - static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x7DFF); - } - - /// Smallest positive subnormal value. - static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { - return half_float::half(half_float::detail::binary, 0x0001); - } -}; + /// Significant decimal digits. + static HALF_CONSTEXPR_CONST int digits10 = 3; + + /// Required decimal digits to represent all possible values. + static HALF_CONSTEXPR_CONST int max_digits10 = 5; + + /// Number base. + static HALF_CONSTEXPR_CONST int radix = 2; + + /// One more than smallest exponent. + static HALF_CONSTEXPR_CONST int min_exponent = -13; + + /// Smallest normalized representable power of 10. + static HALF_CONSTEXPR_CONST int min_exponent10 = -4; + + /// One more than largest exponent + static HALF_CONSTEXPR_CONST int max_exponent = 16; + + /// Largest finitely representable power of 10. + static HALF_CONSTEXPR_CONST int max_exponent10 = 4; + + /// Smallest positive normal value. + static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); } + + /// Smallest finite value. + static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); } + + /// Largest finite value. + static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); } + + /// Difference between one and next representable value. + static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); } + + /// Maximum rounding error. + static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW + { return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); } + + /// Positive infinity. + static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); } + + /// Quiet NaN. + static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); } + + /// Signalling NaN. + static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); } + + /// Smallest positive subnormal value. + static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); } + }; #if HALF_ENABLE_CPP11_HASH -/// Hash function for half-precision floats. -/// This is only defined if C++11 `std::hash` is supported and enabled. -template <> -struct hash //: unary_function -{ - /// Type of function argument. - typedef half_float::half argument_type; - - /// Function return type. - typedef size_t result_type; - - /// Compute hash function. - /// \param arg half to hash - /// \return hash value - result_type operator()(argument_type arg) const { - return hash()(static_cast(arg.data_) & - -(arg.data_ != 0x8000)); - } -}; + /// Hash function for half-precision floats. + /// This is only defined if C++11 `std::hash` is supported and enabled. + template<> struct hash //: unary_function + { + /// Type of function argument. + typedef half_float::half argument_type; + + /// Function return type. + typedef size_t result_type; + + /// Compute hash function. + /// \param arg half to hash + /// \return hash value + result_type operator()(argument_type arg) const + { return hash()(static_cast(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 -- cgit v1.3