diff --git a/WORKSPACE b/WORKSPACE index 6b407184afd5436f7cf4343b3236153fab3bef29..783ddc7acf36eea8ebeeafd8ea063e03958e663d 100644 --- a/WORKSPACE +++ b/WORKSPACE @@ -58,6 +58,13 @@ new_git_repository( remote = "https://github.com/KhronosGroup/OpenCL-CLHPP.git", ) +new_git_repository( + name = "half", + build_file = "mace/third_party/half.BUILD", + commit = "87d7f25f7ba2c7d3b051f6c857031de0ecac5afd", + remote = "http://v9.git.n.xiaomi.com/deep-computing/half.git", +) + git_repository( name = "com_github_gflags_gflags", #tag = "v2.2.0", diff --git a/mace/core/BUILD b/mace/core/BUILD index 8114e6d8b8b47a2936454412626ed679e918d186..f0eae29463eae2744cbb08f2540769650a1ab696 100644 --- a/mace/core/BUILD +++ b/mace/core/BUILD @@ -52,6 +52,7 @@ cc_library( ":opencl_headers", "//mace/utils", "//mace/codegen:generated_version", + "@half//:half", ] + if_production_mode([ "//mace/utils:utils_prod", "//mace/core:opencl_prod", diff --git a/mace/core/half.h b/mace/core/half.h deleted file mode 100644 index 9df24bd43956aa56b5de833800d63cdda5281269..0000000000000000000000000000000000000000 --- a/mace/core/half.h +++ /dev/null @@ -1,3067 +0,0 @@ -// half - IEEE 754-based half-precision floating point library. -// -// 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 -// Software is furnished to do so, subject to the following conditions: -// -// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. -// -// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE -// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR -// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, -// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. - -// Version 1.12.0 - -/// \file -/// Main header file for half precision functionality. - -#ifndef HALF_HALF_HPP -#define HALF_HALF_HPP - -/// Combined gcc version number. -#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__) - -//check C++11 language features -#if defined(__clang__) //clang - #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) - #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 - #endif - #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR) - #define HALF_ENABLE_CPP11_CONSTEXPR 1 - #endif - #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT) - #define HALF_ENABLE_CPP11_NOEXCEPT 1 - #endif - #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS) - #define HALF_ENABLE_CPP11_USER_LITERALS 1 - #endif - #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG) - #define HALF_ENABLE_CPP11_LONG_LONG 1 - #endif -/*#elif defined(__INTEL_COMPILER) //Intel C++ - #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ???????? - #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 - #endif - #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) ???????? - #define HALF_ENABLE_CPP11_CONSTEXPR 1 - #endif - #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) ???????? - #define HALF_ENABLE_CPP11_NOEXCEPT 1 - #endif - #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG) ???????? - #define HALF_ENABLE_CPP11_LONG_LONG 1 - #endif*/ -#elif defined(__GNUC__) //gcc - #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L - #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) - #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 - #endif - #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) - #define HALF_ENABLE_CPP11_CONSTEXPR 1 - #endif - #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) - #define HALF_ENABLE_CPP11_NOEXCEPT 1 - #endif - #if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) - #define HALF_ENABLE_CPP11_USER_LITERALS 1 - #endif - #if !defined(HALF_ENABLE_CPP11_LONG_LONG) - #define HALF_ENABLE_CPP11_LONG_LONG 1 - #endif - #endif -#elif defined(_MSC_VER) //Visual C++ - #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) - #define HALF_ENABLE_CPP11_CONSTEXPR 1 - #endif - #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) - #define HALF_ENABLE_CPP11_NOEXCEPT 1 - #endif - #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) - #define HALF_ENABLE_CPP11_USER_LITERALS 1 - #endif - #if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) - #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 - #endif - #if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG) - #define HALF_ENABLE_CPP11_LONG_LONG 1 - #endif - #define HALF_POP_WARNINGS 1 - #pragma warning(push) - #pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned -#endif - -//check C++11 library features -#include -#if defined(_LIBCPP_VERSION) //libc++ - #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103 - #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS - #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 - #endif - #ifndef HALF_ENABLE_CPP11_CSTDINT - #define HALF_ENABLE_CPP11_CSTDINT 1 - #endif - #ifndef HALF_ENABLE_CPP11_CMATH - #define HALF_ENABLE_CPP11_CMATH 1 - #endif - #ifndef HALF_ENABLE_CPP11_HASH - #define HALF_ENABLE_CPP11_HASH 1 - #endif - #endif -#elif defined(__GLIBCXX__) //libstdc++ - #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103 - #ifdef __clang__ - #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS) - #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 - #endif - #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT) - #define HALF_ENABLE_CPP11_CSTDINT 1 - #endif - #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH) - #define HALF_ENABLE_CPP11_CMATH 1 - #endif - #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH) - #define HALF_ENABLE_CPP11_HASH 1 - #endif - #else - #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT) - #define HALF_ENABLE_CPP11_CSTDINT 1 - #endif - #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH) - #define HALF_ENABLE_CPP11_CMATH 1 - #endif - #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH) - #define HALF_ENABLE_CPP11_HASH 1 - #endif - #endif - #endif -#elif defined(_CPPLIB_VER) //Dinkumware/Visual C++ - #if _CPPLIB_VER >= 520 - #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS - #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 - #endif - #ifndef HALF_ENABLE_CPP11_CSTDINT - #define HALF_ENABLE_CPP11_CSTDINT 1 - #endif - #ifndef HALF_ENABLE_CPP11_HASH - #define HALF_ENABLE_CPP11_HASH 1 - #endif - #endif - #if _CPPLIB_VER >= 610 - #ifndef HALF_ENABLE_CPP11_CMATH - #define HALF_ENABLE_CPP11_CMATH 1 - #endif - #endif -#endif -#undef HALF_GNUC_VERSION - -//support constexpr -#if HALF_ENABLE_CPP11_CONSTEXPR - #define HALF_CONSTEXPR constexpr - #define HALF_CONSTEXPR_CONST constexpr -#else - #define HALF_CONSTEXPR - #define HALF_CONSTEXPR_CONST const -#endif - -//support noexcept -#if HALF_ENABLE_CPP11_NOEXCEPT - #define HALF_NOEXCEPT noexcept - #define HALF_NOTHROW noexcept -#else - #define HALF_NOEXCEPT - #define HALF_NOTHROW throw() -#endif - -#include -#include -#include -#include -#include -#include -#if HALF_ENABLE_CPP11_TYPE_TRAITS - #include -#endif -#if HALF_ENABLE_CPP11_CSTDINT - #include -#endif -#if HALF_ENABLE_CPP11_HASH - #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`: -/// -/// `std::float_round_style` | value | rounding -/// ---------------------------------|-------|------------------------- -/// `std::round_indeterminate` | -1 | fastest (default) -/// `std::round_toward_zero` | 0 | toward zero -/// `std::round_to_nearest` | 1 | to nearest -/// `std::round_toward_infinity` | 2 | toward positive infinity -/// `std::round_toward_neg_infinity` | 3 | toward negative infinity -/// -/// By default this is set to `-1` (`std::round_indeterminate`), which uses truncation (round toward zero, but with overflows -/// set to infinity) and is the fastest rounding mode possible. It can even be set to `std::numeric_limits::round_style` -/// to synchronize the rounding mode with that of the underlying single-precision implementation. -#ifndef HALF_ROUND_STYLE - #define HALF_ROUND_STYLE -1 // = std::round_indeterminate -#endif - -/// Tie-breaking behaviour for round to nearest. -/// This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is -/// defined to `0` resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and -/// thus equal to the round() function), but can be redefined to `1` (before including half.hpp) if more IEEE-conformant -/// behaviour is needed. -#ifndef HALF_ROUND_TIES_TO_EVEN - #define HALF_ROUND_TIES_TO_EVEN 0 // ties away from zero -#endif - -/// Value signaling overflow. -/// In correspondence with `HUGE_VAL[F|L]` from `` 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() - -/// Fast half-precision fma function. -/// This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate -/// half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all -/// arithmetic operations, this is in fact always the case. -#define FP_FAST_FMAH 1 - -#ifndef FP_ILOGB0 - #define FP_ILOGB0 INT_MIN -#endif -#ifndef FP_ILOGBNAN - #define FP_ILOGBNAN INT_MAX -#endif -#ifndef FP_SUBNORMAL - #define FP_SUBNORMAL 0 -#endif -#ifndef FP_ZERO - #define FP_ZERO 1 -#endif -#ifndef FP_NAN - #define FP_NAN 2 -#endif -#ifndef FP_INFINITE - #define FP_INFINITE 3 -#endif -#ifndef FP_NORMAL - #define FP_NORMAL 4 -#endif - - -/// Main namespace for half precision functionality. -/// This namespace contains all the functionality provided by the library. -namespace half_float -{ - class half; - -#if HALF_ENABLE_CPP11_USER_LITERALS - /// Library-defined half-precision literals. - /// Import this namespace to enable half-precision floating point literals: - /// ~~~~{.cpp} - /// using namespace half_float::literal; - /// half_float::half = 4.2_h; - /// ~~~~ - namespace literal - { - half operator""_h(long double); - } -#endif - - /// \internal - /// \brief Implementation details. - namespace detail - { - #if HALF_ENABLE_CPP11_TYPE_TRAITS - /// Conditional type. - template 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) - return hbits | 0x7C00 | (0x3FF&-static_cast((bits&0x7FFFFF)!=0)); - if(exp > 142) - { - if(R == std::round_toward_infinity) - return hbits | 0x7C00 - (hbits>>15); - if(R == std::round_toward_neg_infinity) - return hbits | 0x7BFF + (hbits>>15); - return hbits | 0x7BFF + (R!=std::round_toward_zero); - } - int g, s; - if(exp > 112) - { - g = (bits>>12) & 1; - s = (bits&0xFFF) != 0; - hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF); - } - else if(exp > 101) - { - int i = 125 - exp; - bits = (bits&0x7FFFFF) | 0x800000; - g = (bits>>i) & 1; - s = (bits&((1L<> (i+1); - } - else - { - g = 0; - s = bits != 0; - } - if(R == std::round_to_nearest) - #if HALF_ROUND_TIES_TO_EVEN - hbits += g & (s|hbits); - #else - hbits += g; - #endif - else if(R == std::round_toward_infinity) - hbits += ~(hbits>>15) & (s|g); - else if(R == std::round_toward_neg_infinity) - hbits += (hbits>>15) & (g|s); -*/ static const uint16 base_table[512] = { - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, - 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, - 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, - 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, - 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, - 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, - 0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, - 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 }; - static const unsigned char shift_table[512] = { - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, - 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, - 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, - 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 }; - uint16 hbits = base_table[bits>>23] + static_cast((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, - 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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 - 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 - } - - /// 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_); } - - #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)); - } - - /// 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(lfrom0x3FF) ? ((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 - - 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; -} - - -/// 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)); } - }; -#endif -} - - -#undef HALF_CONSTEXPR -#undef HALF_CONSTEXPR_CONST -#undef HALF_NOEXCEPT -#undef HALF_NOTHROW -#ifdef HALF_POP_WARNINGS - #pragma warning(pop) - #undef HALF_POP_WARNINGS -#endif - -#endif diff --git a/mace/core/types.h b/mace/core/types.h index 8ef12da118beb42c3b48f79857466fd254cd8737..5eb7b536a5784df4160bed080f48feaa30efb4cc 100644 --- a/mace/core/types.h +++ b/mace/core/types.h @@ -7,8 +7,8 @@ #include -#include "mace/core/half.h" #include "mace/public/mace.h" +#include "include/half.hpp" namespace mace { diff --git a/mace/kernels/activation.h b/mace/kernels/activation.h index d6689e706f64d705c1bd806e2fd1325de0a1df54..dd750a389b348223392b49fe06a39c8dda9005b9 100644 --- a/mace/kernels/activation.h +++ b/mace/kernels/activation.h @@ -140,7 +140,7 @@ template class ActivationFunctor { public: ActivationFunctor(ActivationType type, T relux_max_limit) - : activation_(type), relux_max_limit_(relux_max_limit) {} + : activation_(type), relux_max_limit_(static_cast(relux_max_limit)) {} void operator()(const Tensor *input, const Tensor *alpha, diff --git a/mace/kernels/pooling.h b/mace/kernels/pooling.h index a2d3bcdb336a94f8ff76e5d0328ab46333124ab2..6bd5d94e1684d5228dcb1a468d05220f904deaae 100644 --- a/mace/kernels/pooling.h +++ b/mace/kernels/pooling.h @@ -138,7 +138,7 @@ struct PoolingFunctor : PoolingFunctorBase { index_t out_offset = (((b * height) + h) * width + w) * channels + c; index_t in_offset = b * in_image_size * input_channels + c; - T sum = 0; + T sum = static_cast(0); int block_size = 0; for (int kh = 0; kh < kernel_h; ++kh) { for (int kw = 0; kw < kernel_w; ++kw) { diff --git a/mace/ops/activation.h b/mace/ops/activation.h index 5f08bc2623b7ff071e7334c38544f1994ff0d4cb..12761927a954c2ffd3e94b1a086bc28911e4aae5 100644 --- a/mace/ops/activation.h +++ b/mace/ops/activation.h @@ -18,7 +18,8 @@ class ActivationOp : public Operator { functor_(kernels::StringToActivationType( OperatorBase::GetSingleArgument("activation", "NOOP")), - OperatorBase::GetSingleArgument("max_limit", 0.0f)) {} + static_cast(OperatorBase::GetSingleArgument( + "max_limit", 0.0f))) {} bool Run(StatsFuture *future) override { const Tensor *input_tensor = this->Input(0); diff --git a/mace/ops/depthwise_conv2d_test.cc b/mace/ops/depthwise_conv2d_test.cc index c5ff2713d73795421e159c2ad9c7f20e9869d8dc..840d13aa0f3f8c34276759e6af99a3363a7ed985 100644 --- a/mace/ops/depthwise_conv2d_test.cc +++ b/mace/ops/depthwise_conv2d_test.cc @@ -64,8 +64,9 @@ void SimpleValidTest() { } // Check - auto expected = CreateTensor({1, 2, 2, 2}, {37.1f, 148.2f, 47.1f, 188.2f, - 67.1f, 268.2f, 77.1f, 308.2f}); + auto expected = CreateTensor( + {1, 2, 2, 2}, VectorStaticCast({37.1f, 148.2f, 47.1f, 188.2f, 67.1f, + 268.2f, 77.1f, 308.2f})); ExpectTensorNear(*expected, *net.GetOutput("Output"), 1e-5); } @@ -169,21 +170,22 @@ void ComplexValidTest() { // Check auto expected = CreateTensor( {1, 5, 5, 3}, - {4.48200035, 4.63479996, 4.79079962, 5.85899973, 6.05599976, - 6.25699997, 6.38100004, 6.59000015, 6.80300045, 6.90299988, - 7.1239996, 7.34899998, 4.03559971, 4.16820002, 4.30319977, - 8.90999985, 9.1760006, 9.44599915, 11.20499992, 11.54500103, - 11.89000034, 11.74499989, 12.09999943, 12.46000004, 12.28499985, - 12.65500069, 13.03000069, 7.00200033, 7.22399998, 7.44900036, - 13.4100008, 13.79599953, 14.18599987, 16.60500145, 17.09499741, - 17.59000015, 17.14500046, 17.65000153, 18.15999794, 17.68499947, - 18.20499992, 18.72999954, 9.97200012, 10.28399944, 10.59899998, - 17.90999985, 18.41600037, 18.92599869, 22.00500107, 22.64500046, - 23.28999901, 22.54500008, 23.19999886, 23.8599987, 23.0850029, - 23.75500107, 24.43000031, 12.94200039, 13.34400082, 13.7489996, - 6.97500038, 7.29659986, 7.62060022, 8.32049942, 8.72700024, - 9.13650036, 8.5095005, 8.92500019, 9.34349918, 8.69849968, - 9.12300014, 9.55049992, 4.55220032, 4.80690002, 5.06340027}); + VectorStaticCast( + {4.48200035, 4.63479996, 4.79079962, 5.85899973, 6.05599976, + 6.25699997, 6.38100004, 6.59000015, 6.80300045, 6.90299988, + 7.1239996, 7.34899998, 4.03559971, 4.16820002, 4.30319977, + 8.90999985, 9.1760006, 9.44599915, 11.20499992, 11.54500103, + 11.89000034, 11.74499989, 12.09999943, 12.46000004, 12.28499985, + 12.65500069, 13.03000069, 7.00200033, 7.22399998, 7.44900036, + 13.4100008, 13.79599953, 14.18599987, 16.60500145, 17.09499741, + 17.59000015, 17.14500046, 17.65000153, 18.15999794, 17.68499947, + 18.20499992, 18.72999954, 9.97200012, 10.28399944, 10.59899998, + 17.90999985, 18.41600037, 18.92599869, 22.00500107, 22.64500046, + 23.28999901, 22.54500008, 23.19999886, 23.8599987, 23.0850029, + 23.75500107, 24.43000031, 12.94200039, 13.34400082, 13.7489996, + 6.97500038, 7.29659986, 7.62060022, 8.32049942, 8.72700024, + 9.13650036, 8.5095005, 8.92500019, 9.34349918, 8.69849968, + 9.12300014, 9.55049992, 4.55220032, 4.80690002, 5.06340027})); ExpectTensorNear(*expected, *net.GetOutput("Output"), 0.2); } diff --git a/mace/ops/ops_test_util.h b/mace/ops/ops_test_util.h index 50c2f2ca758cfef7b9943d3dfab270089ee2a03f..3003fffe4c185b7200c331d064f85f88da5bc004 100644 --- a/mace/ops/ops_test_util.h +++ b/mace/ops/ops_test_util.h @@ -237,6 +237,16 @@ void GenerateRandomIntTypeData(const std::vector &shape, std::generate(res.begin(), res.end(), [&gen, &nd] { return nd(gen); }); } +template +std::vector VectorStaticCast(const std::vector &&src) { + std::vector dest; + dest.reserve(src.size()); + for (float f : src) { + dest.push_back(static_cast(f)); + } + return std::move(dest); +} + template std::unique_ptr CreateTensor(const std::vector &shape, const std::vector &data) { diff --git a/mace/third_party/half.BUILD b/mace/third_party/half.BUILD new file mode 100644 index 0000000000000000000000000000000000000000..6048911b720ef8ef17d977ae0ebe2db778818687 --- /dev/null +++ b/mace/third_party/half.BUILD @@ -0,0 +1,7 @@ +cc_library( + name = "half", + hdrs = glob([ + "include/half.hpp", + ]), + visibility = ["//visibility:public"], +) diff --git a/mace/third_party/opencl-clhpp.BUILD b/mace/third_party/opencl-clhpp.BUILD index b14abc5dcc848bbabe0b6c005d7ea43b053487b8..83737b3c3b93d0dc3320d4597e86a4c5606d664e 100644 --- a/mace/third_party/opencl-clhpp.BUILD +++ b/mace/third_party/opencl-clhpp.BUILD @@ -10,6 +10,6 @@ genrule( cc_library( name = "opencl_clhpp", - srcs = ["include/CL/cl.hpp", "include/CL/cl2.hpp"], + hdrs = ["include/CL/cl.hpp", "include/CL/cl2.hpp"], visibility = ["//visibility:public"], )