From 0c023e41809dba8897c37af6bb03e5c3aa9ebc5e Mon Sep 17 00:00:00 2001 From: Nick Date: Fri, 13 Sep 2019 05:32:48 -0400 Subject: Add src/cuda-sim formatting --- src/cuda-sim/half.h | 6539 +++++++++++++++++++++++++++++---------------------- 1 file changed, 3662 insertions(+), 2877 deletions(-) (limited to 'src/cuda-sim/half.h') diff --git a/src/cuda-sim/half.h b/src/cuda-sim/half.h index 9f74bb7..d33b03c 100644 --- a/src/cuda-sim/half.h +++ b/src/cuda-sim/half.h @@ -2,17 +2,25 @@ // // 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 @@ -23,180 +31,191 @@ #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 /// ---------------------------------|-------|------------------------- @@ -206,256 +225,354 @@ /// `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) @@ -498,2570 +615,3238 @@ namespace half_float 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; - } - - /// 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, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, - 0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, - 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, - 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, - 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, - 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, - 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, - 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, - 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, - 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, - 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, - 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, - 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, - 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, - 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, - 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, - 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, - 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, - 0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, - 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, - 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, - 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, - 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, - 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, - 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, - 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, - 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, - 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, - 0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, - 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000, - 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000, - 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, - 0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, - 0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, - 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, - 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, - 0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, - 0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, - 0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, - 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, - 0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, - 0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, - 0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, - 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, - 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000, - 0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, - 0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, - 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, - 0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, - 0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, - 0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, - 0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, - 0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, - 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, - 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, - 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, - 0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, - 0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, - 0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, - 0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, - 0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, - 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000, - 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, - 0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, - 0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, - 0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000, - 0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, - 0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, - 0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, - 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, - 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, - 0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, - 0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, - 0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, - 0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, - 0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, - 0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, - 0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, - 0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, - 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, - 0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, - 0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, - 0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, - 0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, - 0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, - 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, - 0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, - 0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, - 0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, - 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, - 0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, - 0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, - 0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, - 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, - 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, - 0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, - 0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, - 0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, - 0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, - 0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, - 0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, - 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, - 0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, - 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, - 0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, - 0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, - 0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, - 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, - 0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, - 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, - 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, - 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 }; - static const uint32 exponent_table[64] = { - 0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000, - 0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000, - 0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, - 0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 }; - static const unsigned short offset_table[64] = { - 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, - 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 }; - uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10]; -// return *reinterpret_cast(&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_; - }; - -#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; - } - - /// 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 - } +*/ 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; +} - /// 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 - } +/// 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; +} - /// 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 - } +/// 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; +} - /// 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 - } +/// 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) > ()); +} - /// 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 - } +/// 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; +} - /// 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 - } +/// 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); +} - /// Gamma logarithm implementation. - /// \param arg function argument - /// \return function value stored in single-preicision - static expr lgamma(float arg) +/// 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) { - #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 + 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, 0x37838000, 0x37840000, + 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, + 0x37870000, 0x37878000, 0x37880000, 0x37888000, 0x37890000, + 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, + 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, + 0x378E8000, 0x378F0000, 0x378F8000, 0x37900000, 0x37908000, + 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, + 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, + 0x37960000, 0x37968000, 0x37970000, 0x37978000, 0x37980000, + 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, + 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, + 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, + 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, + 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, + 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, + 0x37A78000, 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, + 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, + 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, + 0x37AF0000, 0x37AF8000, 0x37B00000, 0x37B08000, 0x37B10000, + 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, + 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, + 0x37B68000, 0x37B70000, 0x37B78000, 0x37B80000, 0x37B88000, + 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, + 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, + 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, 0x37C00000, + 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, + 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, + 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, + 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, + 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, + 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, + 0x37CF8000, 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, + 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, + 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, + 0x37D70000, 0x37D78000, 0x37D80000, 0x37D88000, 0x37D90000, + 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, + 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, + 0x37DE8000, 0x37DF0000, 0x37DF8000, 0x37E00000, 0x37E08000, + 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, + 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, + 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, 0x37E80000, + 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, + 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, + 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, + 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, + 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, + 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, + 0x37F78000, 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, + 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, + 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, + 0x37FF0000, 0x37FF8000, 0x38000000, 0x38004000, 0x38008000, + 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, + 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, + 0x38034000, 0x38038000, 0x3803C000, 0x38040000, 0x38044000, + 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, + 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, + 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 0x38080000, + 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, + 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, + 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, + 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, + 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, + 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, + 0x380FC000, 0x38100000, 0x38104000, 0x38108000, 0x3810C000, + 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, + 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, + 0x38138000, 0x3813C000, 0x38140000, 0x38144000, 0x38148000, + 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, + 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, + 0x38174000, 0x38178000, 0x3817C000, 0x38180000, 0x38184000, + 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, + 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, + 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, 0x381C0000, + 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, + 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, + 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, + 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, + 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, + 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, + 0x3823C000, 0x38240000, 0x38244000, 0x38248000, 0x3824C000, + 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, + 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, + 0x38278000, 0x3827C000, 0x38280000, 0x38284000, 0x38288000, + 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, + 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, + 0x382B4000, 0x382B8000, 0x382BC000, 0x382C0000, 0x382C4000, + 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, + 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, + 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 0x38300000, + 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, + 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, + 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, + 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, + 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, + 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, + 0x3837C000, 0x38380000, 0x38384000, 0x38388000, 0x3838C000, + 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, + 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, + 0x383B8000, 0x383BC000, 0x383C0000, 0x383C4000, 0x383C8000, + 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, + 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, + 0x383F4000, 0x383F8000, 0x383FC000, 0x38400000, 0x38404000, + 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, + 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, + 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 0x38440000, + 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, + 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, + 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, + 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, + 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, + 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, + 0x384BC000, 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, + 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, + 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, + 0x384F8000, 0x384FC000, 0x38500000, 0x38504000, 0x38508000, + 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, + 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, + 0x38534000, 0x38538000, 0x3853C000, 0x38540000, 0x38544000, + 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, + 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, + 0x38570000, 0x38574000, 0x38578000, 0x3857C000, 0x38580000, + 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, + 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, + 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, + 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, + 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, + 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, + 0x385FC000, 0x38600000, 0x38604000, 0x38608000, 0x3860C000, + 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, + 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, + 0x38638000, 0x3863C000, 0x38640000, 0x38644000, 0x38648000, + 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, + 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, + 0x38674000, 0x38678000, 0x3867C000, 0x38680000, 0x38684000, + 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, + 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, + 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 0x386C0000, + 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, + 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, + 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, + 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, + 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, + 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, + 0x3873C000, 0x38740000, 0x38744000, 0x38748000, 0x3874C000, + 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, + 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, + 0x38778000, 0x3877C000, 0x38780000, 0x38784000, 0x38788000, + 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, + 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, + 0x387B4000, 0x387B8000, 0x387BC000, 0x387C0000, 0x387C4000, + 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, + 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, + 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, 0x38000000, + 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, + 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, + 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, + 0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, + 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, + 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, + 0x3803E000, 0x38040000, 0x38042000, 0x38044000, 0x38046000, + 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, + 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, + 0x3805C000, 0x3805E000, 0x38060000, 0x38062000, 0x38064000, + 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, + 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, + 0x3807A000, 0x3807C000, 0x3807E000, 0x38080000, 0x38082000, + 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, + 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, + 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, 0x380A0000, + 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, + 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, + 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, + 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, + 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, + 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, + 0x380DE000, 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, + 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, + 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, + 0x380FC000, 0x380FE000, 0x38100000, 0x38102000, 0x38104000, + 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, + 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, + 0x3811A000, 0x3811C000, 0x3811E000, 0x38120000, 0x38122000, + 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, + 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, + 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, 0x38140000, + 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, + 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, + 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, + 0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, + 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, + 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, + 0x3817E000, 0x38180000, 0x38182000, 0x38184000, 0x38186000, + 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, + 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, + 0x3819C000, 0x3819E000, 0x381A0000, 0x381A2000, 0x381A4000, + 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, + 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, + 0x381BA000, 0x381BC000, 0x381BE000, 0x381C0000, 0x381C2000, + 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, + 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, + 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, 0x381E0000, + 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, + 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, + 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, + 0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, + 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, + 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, + 0x3821E000, 0x38220000, 0x38222000, 0x38224000, 0x38226000, + 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, + 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, + 0x3823C000, 0x3823E000, 0x38240000, 0x38242000, 0x38244000, + 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, + 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, + 0x3825A000, 0x3825C000, 0x3825E000, 0x38260000, 0x38262000, + 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, + 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, + 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 0x38280000, + 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, + 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, + 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, + 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, + 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, + 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, + 0x382BE000, 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, + 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, + 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, + 0x382DC000, 0x382DE000, 0x382E0000, 0x382E2000, 0x382E4000, + 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, + 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, + 0x382FA000, 0x382FC000, 0x382FE000, 0x38300000, 0x38302000, + 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, + 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, + 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 0x38320000, + 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, + 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, + 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, + 0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, + 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, + 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, + 0x3835E000, 0x38360000, 0x38362000, 0x38364000, 0x38366000, + 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, + 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, + 0x3837C000, 0x3837E000, 0x38380000, 0x38382000, 0x38384000, + 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, + 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, + 0x3839A000, 0x3839C000, 0x3839E000, 0x383A0000, 0x383A2000, + 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, + 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, + 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 0x383C0000, + 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, + 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, + 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, + 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, + 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, + 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, + 0x383FE000, 0x38400000, 0x38402000, 0x38404000, 0x38406000, + 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, + 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, + 0x3841C000, 0x3841E000, 0x38420000, 0x38422000, 0x38424000, + 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, + 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, + 0x3843A000, 0x3843C000, 0x3843E000, 0x38440000, 0x38442000, + 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, + 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, + 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 0x38460000, + 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, + 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, + 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, + 0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, + 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, + 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, + 0x3849E000, 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, + 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, + 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, + 0x384BC000, 0x384BE000, 0x384C0000, 0x384C2000, 0x384C4000, + 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, + 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, + 0x384DA000, 0x384DC000, 0x384DE000, 0x384E0000, 0x384E2000, + 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, + 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, + 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 0x38500000, + 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, + 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, + 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, + 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, + 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, + 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, + 0x3853E000, 0x38540000, 0x38542000, 0x38544000, 0x38546000, + 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, + 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, + 0x3855C000, 0x3855E000, 0x38560000, 0x38562000, 0x38564000, + 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, + 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, + 0x3857A000, 0x3857C000, 0x3857E000, 0x38580000, 0x38582000, + 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, + 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, + 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, 0x385A0000, + 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, + 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, + 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, + 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, + 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, + 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, + 0x385DE000, 0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, + 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, + 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, + 0x385FC000, 0x385FE000, 0x38600000, 0x38602000, 0x38604000, + 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, + 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, + 0x3861A000, 0x3861C000, 0x3861E000, 0x38620000, 0x38622000, + 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, + 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, + 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 0x38640000, + 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, + 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, + 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, + 0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, + 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, + 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, + 0x3867E000, 0x38680000, 0x38682000, 0x38684000, 0x38686000, + 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, + 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, + 0x3869C000, 0x3869E000, 0x386A0000, 0x386A2000, 0x386A4000, + 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, + 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, + 0x386BA000, 0x386BC000, 0x386BE000, 0x386C0000, 0x386C2000, + 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, + 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, + 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, 0x386E0000, + 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, + 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, + 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, + 0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, + 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, + 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, + 0x3871E000, 0x38720000, 0x38722000, 0x38724000, 0x38726000, + 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, + 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, + 0x3873C000, 0x3873E000, 0x38740000, 0x38742000, 0x38744000, + 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, + 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, + 0x3875A000, 0x3875C000, 0x3875E000, 0x38760000, 0x38762000, + 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, + 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, + 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, 0x38780000, + 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, + 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, + 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, + 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, + 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, + 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, + 0x387BE000, 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, + 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, + 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, + 0x387DC000, 0x387DE000, 0x387E0000, 0x387E2000, 0x387E4000, + 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, + 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, + 0x387FA000, 0x387FC000, 0x387FE000}; + static const uint32 exponent_table[64] = { + 0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, + 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, + 0x06000000, 0x06800000, 0x07000000, 0x07800000, 0x08000000, 0x08800000, + 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, + 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, + 0x0F000000, 0x47800000, 0x80000000, 0x80800000, 0x81000000, 0x81800000, + 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, + 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, + 0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, + 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, + 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000}; + static const unsigned short offset_table[64] = { + 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, + 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, + 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 0, + 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, + 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, + 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024}; + uint32 bits = mantissa_table[offset_table[value >> 10] + (value & 0x3FF)] + + exponent_table[value >> 10]; + // return *reinterpret_cast(&bits); //violating + //strict aliasing! + float out; + std::memcpy(&out, &bits, sizeof(float)); + return out; +} - /// 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 - } +/// 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; +} - /// 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)); - } +/// 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; +} - /// 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))); - } +/// 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) > ()); +} - /// 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); - } +/// 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); +} - /// 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; - } +/// 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); +} - /// 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); - } +/// 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); +} - /// 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); - } +/// 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; +} - /// 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 +uint16 round_half(uint16 value) { + return round_half_impl(value); +} - /// 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; - } +/// 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; +} - /// 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)); - } +/// 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 - /// 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)); - } + 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_; +}; - /// 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)); - } +#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 - /// 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)); - } +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_); + } - /// 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; - } +#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 - /// 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); } + /// 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 - 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 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 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 - } + 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 - /// 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; + 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); +} -/// 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; +/// 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); +} - /// Doesn't provide modulo arithmetic. - static HALF_CONSTEXPR_CONST bool is_modulo = false; +/// 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); +} - /// IEEE conformant. - static HALF_CONSTEXPR_CONST bool is_iec559 = true; +/// 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); +} - /// Supports infinity. - static HALF_CONSTEXPR_CONST bool has_infinity = true; +/// 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); +} - /// Supports quiet NaNs. - static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true; +/// \} +/// \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); +} - /// Supports subnormal values. - static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; +/// 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); +} - /// 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; +/// 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); +} - /// Significant digits. - static HALF_CONSTEXPR_CONST int digits = 11; +/// 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); +} - /// Significant decimal digits. - static HALF_CONSTEXPR_CONST int digits10 = 3; +/// Identity. +/// \param arg operand +/// \return uncahnged operand +template +HALF_CONSTEXPR typename enable::type operator+(T arg) { + return arg; +} - /// Required decimal digits to represent all possible values. - static HALF_CONSTEXPR_CONST int max_digits10 = 5; +/// Negation. +/// \param arg operand +/// \return negated operand +template +HALF_CONSTEXPR typename enable::type operator-(T arg) { + return unary_specialized::negate(arg); +} - /// Number base. - static HALF_CONSTEXPR_CONST int radix = 2; +/// \} +/// \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); +} - /// One more than smallest exponent. - static HALF_CONSTEXPR_CONST int min_exponent = -13; +/// 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); +} - /// Smallest normalized representable power of 10. - static HALF_CONSTEXPR_CONST int min_exponent10 = -4; +/// \} +/// \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); +} - /// One more than largest exponent - static HALF_CONSTEXPR_CONST int max_exponent = 16; +/// 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); +} - /// Largest finitely representable power of 10. - static HALF_CONSTEXPR_CONST int max_exponent10 = 4; +/// 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); +} - /// Smallest positive normal value. - static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); } +/// 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 - /// Smallest finite value. - static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); } +/// \} +/// \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); +} - /// Largest finite value. - static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); } +/// 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); +} - /// 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); } +/// 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); +} - /// 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); } +/// 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); +} - /// Positive infinity. - static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); } +/// 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); +} - /// Quiet NaN. - static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); } +/// 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); +} +/// \} +} - /// Signalling NaN. - static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); } +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; +} - /// Smallest positive subnormal value. - static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); } - }; +/// 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); + } +}; #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