diff --git a/external/half/include/half.hpp b/external/half/include/half.hpp deleted file mode 100644 index 25f543881f..0000000000 --- a/external/half/include/half.hpp +++ /dev/null @@ -1,5670 +0,0 @@ -// half - IEEE 754-based half-precision floating-point library. -// -// Copyright (c) 2012-2019 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 2.1.0 - -/// \file -/// Main header file for half-precision functionality. - -#ifndef HALF_HALF_HPP -#define HALF_HALF_HPP - -#define HALF_GCC_VERSION (__GNUC__ * 100 + __GNUC_MINOR__) - -#if defined(__INTEL_COMPILER) -#define HALF_ICC_VERSION __INTEL_COMPILER -#elif defined(__ICC) -#define HALF_ICC_VERSION __ICC -#elif defined(__ICL) -#define HALF_ICC_VERSION __ICL -#else -#define HALF_ICC_VERSION 0 -#endif - -// 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 __has_feature(cxx_thread_local) && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL) -#define HALF_ENABLE_CPP11_THREAD_LOCAL 1 -#endif -#if(defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && \ - !defined(HALF_ENABLE_CPP11_LONG_LONG) -#define HALF_ENABLE_CPP11_LONG_LONG 1 -#endif -#elif HALF_ICC_VERSION && defined(__INTEL_CXX11_MODE__) // Intel C++ -#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL) -#define HALF_ENABLE_CPP11_THREAD_LOCAL 1 -#endif -#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) -#define HALF_ENABLE_CPP11_USER_LITERALS 1 -#endif -#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) -#define HALF_ENABLE_CPP11_CONSTEXPR 1 -#endif -#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) -#define HALF_ENABLE_CPP11_NOEXCEPT 1 -#endif -#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) -#define HALF_ENABLE_CPP11_STATIC_ASSERT 1 -#endif -#if HALF_ICC_VERSION >= 1110 && !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_GCC_VERSION >= 408 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL) -#define HALF_ENABLE_CPP11_THREAD_LOCAL 1 -#endif -#if HALF_GCC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) -#define HALF_ENABLE_CPP11_USER_LITERALS 1 -#endif -#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) -#define HALF_ENABLE_CPP11_CONSTEXPR 1 -#endif -#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) -#define HALF_ENABLE_CPP11_NOEXCEPT 1 -#endif -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) -#define HALF_ENABLE_CPP11_STATIC_ASSERT 1 -#endif -#if !defined(HALF_ENABLE_CPP11_LONG_LONG) -#define HALF_ENABLE_CPP11_LONG_LONG 1 -#endif -#endif -#define HALF_TWOS_COMPLEMENT_INT 1 -#elif defined(_MSC_VER) // Visual C++ -#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL) -#define HALF_ENABLE_CPP11_THREAD_LOCAL 1 -#endif -#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) -#define HALF_ENABLE_CPP11_USER_LITERALS 1 -#endif -#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 >= 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_TWOS_COMPLEMENT_INT 1 -#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 -#ifndef HALF_ENABLE_CPP11_CFENV -#define HALF_ENABLE_CPP11_CFENV 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 -#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CFENV) -#define HALF_ENABLE_CPP11_CFENV 1 -#endif -#else -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS) -#define HALF_ENABLE_CPP11_TYPE_TRAITS 1 -#endif -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT) -#define HALF_ENABLE_CPP11_CSTDINT 1 -#endif -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH) -#define HALF_ENABLE_CPP11_CMATH 1 -#endif -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH) -#define HALF_ENABLE_CPP11_HASH 1 -#endif -#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CFENV) -#define HALF_ENABLE_CPP11_CFENV 1 -#endif -#endif -#endif -#elif defined(_CPPLIB_VER) // Dinkumware/Visual C++ -#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS) -#define HALF_ENABLE_CPP11_TYPE_TRAITS 1 -#endif -#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_CSTDINT) -#define HALF_ENABLE_CPP11_CSTDINT 1 -#endif -#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_HASH) -#define HALF_ENABLE_CPP11_HASH 1 -#endif -#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CMATH) -#define HALF_ENABLE_CPP11_CMATH 1 -#endif -#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CFENV) -#define HALF_ENABLE_CPP11_CFENV 1 -#endif -#endif -#undef HALF_GCC_VERSION -#undef HALF_ICC_VERSION - -// any error throwing C++ exceptions? -#if defined(HALF_ERRHANDLING_THROW_INVALID) || defined(HALF_ERRHANDLING_THROW_DIVBYZERO) || \ - defined(HALF_ERRHANDLING_THROW_OVERFLOW) || defined(HALF_ERRHANDLING_THROW_UNDERFLOW) || \ - defined(HALF_ERRHANDLING_THROW_INEXACT) -#define HALF_ERRHANDLING_THROWS 1 -#endif - -// any error handling enabled? -#define HALF_ERRHANDLING \ - (HALF_ERRHANDLING_FLAGS || HALF_ERRHANDLING_ERRNO || HALF_ERRHANDLING_FENV || \ - HALF_ERRHANDLING_THROWS) - -#if HALF_ERRHANDLING -#define HALF_UNUSED_NOERR(name) name -#else -#define HALF_UNUSED_NOERR(name) -#endif - -// support constexpr -#if HALF_ENABLE_CPP11_CONSTEXPR -#define HALF_CONSTEXPR constexpr -#define HALF_CONSTEXPR_CONST constexpr -#if HALF_ERRHANDLING -#define HALF_CONSTEXPR_NOERR -#else -#define HALF_CONSTEXPR_NOERR constexpr -#endif -#else -#define HALF_CONSTEXPR -#define HALF_CONSTEXPR_CONST const -#define HALF_CONSTEXPR_NOERR -#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 - -// support thread storage -#if HALF_ENABLE_CPP11_THREAD_LOCAL -#define HALF_THREAD_LOCAL thread_local -#else -#define HALF_THREAD_LOCAL static -#endif - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#if HALF_ENABLE_CPP11_TYPE_TRAITS -#include -#endif -#if HALF_ENABLE_CPP11_CSTDINT -#include -#endif -#if HALF_ERRHANDLING_ERRNO -#include -#endif -#if HALF_ENABLE_CPP11_CFENV -#include -#endif -#if HALF_ENABLE_CPP11_HASH -#include -#endif -#if HALF_ENABLE_F16C_INTRINSICS -#include -#endif - -#ifndef HALF_ENABLE_F16C_INTRINSICS -/// Enable F16C intruction set intrinsics. -/// Defining this to 1 enables the use of [F16C compiler -/// intrinsics](https://en.wikipedia.org/wiki/F16C) for converting between -/// half-precision and single-precision values which may result in improved performance. This will -/// not perform additional checks -/// for support of the F16C instruction set, so an appropriate target platform is required when -/// enabling this feature. -/// -/// Unless predefined it will be enabled automatically when the `__F16C__` symbol is defined, which -/// some compilers do on supporting platforms. -#define HALF_ENABLE_F16C_INTRINSICS __F16C__ -#endif - -#ifdef HALF_DOXYGEN_ONLY -/// Type for internal floating-point computations. -/// This can be predefined to a built-in floating-point type (`float`, `double` or `long double`) to -/// override the internal -/// half-precision implementation to use this type for computing arithmetic operations and -/// mathematical function (if available). -/// This can result in improved performance for arithmetic operators and mathematical functions but -/// might cause results to -/// deviate from the specified half-precision rounding mode and inhibits proper detection of -/// half-precision exceptions. -#define HALF_ARITHMETIC_TYPE (undefined) - -/// Enable internal exception flags. -/// Defining this to 1 causes operations on half-precision values to raise internal floating-point -/// exception flags according to -/// the IEEE 754 standard. These can then be cleared and checked with clearexcept(), testexcept(). -#define HALF_ERRHANDLING_FLAGS 0 - -/// Enable exception propagation to `errno`. -/// Defining this to 1 causes operations on half-precision values to propagate floating-point -/// exceptions to -/// [errno](https://en.cppreference.com/w/cpp/error/errno) from ``. Specifically this will -/// propagate domain errors as -/// [EDOM](https://en.cppreference.com/w/cpp/error/errno_macros) and pole, overflow and underflow -/// errors as -/// [ERANGE](https://en.cppreference.com/w/cpp/error/errno_macros). Inexact errors won't be -/// propagated. -#define HALF_ERRHANDLING_ERRNO 0 - -/// Enable exception propagation to built-in floating-point platform. -/// Defining this to 1 causes operations on half-precision values to propagate floating-point -/// exceptions to the built-in -/// single- and double-precision implementation's exception flags using the -/// [C++11 floating-point environment control](https://en.cppreference.com/w/cpp/numeric/fenv) from -/// ``. However, this -/// does not work in reverse and single- or double-precision exceptions will not raise the -/// corresponding half-precision -/// exception flags, nor will explicitly clearing flags clear the corresponding built-in flags. -#define HALF_ERRHANDLING_FENV 0 - -/// Throw C++ exception on domain errors. -/// Defining this to a string literal causes operations on half-precision values to throw a -/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified -/// message on domain errors. -#define HALF_ERRHANDLING_THROW_INVALID (undefined) - -/// Throw C++ exception on pole errors. -/// Defining this to a string literal causes operations on half-precision values to throw a -/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified -/// message on pole errors. -#define HALF_ERRHANDLING_THROW_DIVBYZERO (undefined) - -/// Throw C++ exception on overflow errors. -/// Defining this to a string literal causes operations on half-precision values to throw a -/// [std::overflow_error](https://en.cppreference.com/w/cpp/error/overflow_error) with the specified -/// message on overflows. -#define HALF_ERRHANDLING_THROW_OVERFLOW (undefined) - -/// Throw C++ exception on underflow errors. -/// Defining this to a string literal causes operations on half-precision values to throw a -/// [std::underflow_error](https://en.cppreference.com/w/cpp/error/underflow_error) with the -/// specified message on underflows. -#define HALF_ERRHANDLING_THROW_UNDERFLOW (undefined) - -/// Throw C++ exception on rounding errors. -/// Defining this to 1 causes operations on half-precision values to throw a -/// [std::range_error](https://en.cppreference.com/w/cpp/error/range_error) with the specified -/// message on general rounding errors. -#define HALF_ERRHANDLING_THROW_INEXACT (undefined) -#endif - -#ifndef HALF_ERRHANDLING_OVERFLOW_TO_INEXACT -/// Raise INEXACT exception on overflow. -/// Defining this to 1 (default) causes overflow errors to automatically raise inexact exceptions in -/// addition. -/// These will be raised after any possible handling of the underflow exception. -#define HALF_ERRHANDLING_OVERFLOW_TO_INEXACT 1 -#endif - -#ifndef HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT -/// Raise INEXACT exception on underflow. -/// Defining this to 1 (default) causes underflow errors to automatically raise inexact exceptions -/// in addition. -/// These will be raised after any possible handling of the underflow exception. -/// -/// **Note:** This will actually cause underflow (and the accompanying inexact) exceptions to be -/// raised *only* when the result -/// is inexact, while if disabled bare underflow errors will be raised for *any* (possibly exact) -/// subnormal result. -#define HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT 1 -#endif - -/// Default rounding mode. -/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s -/// and more precise types -/// (unless using half_cast() and specifying the rounding mode directly) as well as in arithmetic -/// operations and mathematical -/// functions. 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](https://en.cppreference.com/w/cpp/types/numeric_limits/float_round_style): -/// -/// `std::float_round_style` | value | rounding -/// ---------------------------------|-------|------------------------- -/// `std::round_indeterminate` | -1 | fastest -/// `std::round_toward_zero` | 0 | toward zero -/// `std::round_to_nearest` | 1 | to nearest (default) -/// `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_to_nearest`), which rounds results to the nearest -/// representable value. It can even -/// be set to -/// [std::numeric_limits::round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/round_style) -/// to synchronize -/// the rounding mode with that of the built-in single-precision implementation (which is likely -/// `std::round_to_nearest`, though). -#ifndef HALF_ROUND_STYLE -#define HALF_ROUND_STYLE 1 // = std::round_to_nearest -#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. -/// -/// **See also:** Documentation for -/// [HUGE_VAL](https://en.cppreference.com/w/cpp/numeric/math/HUGE_VAL) -#define HUGE_VALH std::numeric_limits::infinity() - -/// Fast half-precision fma function. -/// This symbol is defined if the fma() function generally executes as fast as, or faster than, a -/// separate -/// half-precision multiplication followed by an addition, which is always the case. -/// -/// **See also:** Documentation for -/// [FP_FAST_FMA](https://en.cppreference.com/w/cpp/numeric/math/fma) -#define FP_FAST_FMAH 1 - -/// Half rounding mode. -/// In correspondence with `FLT_ROUNDS` from `` this symbol expands to the rounding mode -/// used for -/// half-precision operations. It is an alias for [HALF_ROUND_STYLE](\ref HALF_ROUND_STYLE). -/// -/// **See also:** Documentation for -/// [FLT_ROUNDS](https://en.cppreference.com/w/cpp/types/climits/FLT_ROUNDS) -#define HLF_ROUNDS HALF_ROUND_STYLE - -#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 - -#if !HALF_ENABLE_CPP11_CFENV && !defined(FE_ALL_EXCEPT) -#define FE_INVALID 0x10 -#define FE_DIVBYZERO 0x08 -#define FE_OVERFLOW 0x04 -#define FE_UNDERFLOW 0x02 -#define FE_INEXACT 0x01 -#define FE_ALL_EXCEPT (FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW | FE_INEXACT) -#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::false_type; -using std::true_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; - -/// Fastest unsigned integer of (at least) 32 bits width. -typedef std::uint_fast32_t uint32; - -/// Fastest signed integer of (at least) 32 bits width. -typedef std::int_fast32_t int32; - -/// 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; - -/// Fastest unsigned integer of (at least) 32 bits width. -typedef unsigned long uint32; - -/// Fastest unsigned integer of (at least) 32 bits width. -typedef long int32; - -/// 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 - -#ifdef HALF_ARITHMETIC_TYPE -/// Type to use for arithmetic computations and mathematic functions internally. -typedef HALF_ARITHMETIC_TYPE internal_t; -#endif - -/// Tag type for binary construction. -struct binary_t -{ -}; - -/// Tag for binary construction. -HALF_CONSTEXPR_CONST binary_t binary = binary_t(); - -/// \name Implementation defined classification and arithmetic -/// \{ - -/// 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 -} - -/// Platform-independent sign mask. -/// \param arg integer value in two's complement -/// \retval -1 if \a arg negative -/// \retval 0 if \a arg positive -inline uint32 sign_mask(uint32 arg) -{ - static const int N = std::numeric_limits::digits - 1; -#if HALF_TWOS_COMPLEMENT_INT - return static_cast(arg) >> N; -#else - return -((arg >> N) & 1); -#endif -} - -/// Platform-independent arithmetic right shift. -/// \param arg integer value in two's complement -/// \param i shift amount (at most 31) -/// \return \a arg right shifted for \a i bits with possible sign extension -inline uint32 arithmetic_shift(uint32 arg, int i) -{ -#if HALF_TWOS_COMPLEMENT_INT - return static_cast(arg) >> i; -#else - return static_cast(arg) / (static_cast(1) << i) - - ((arg >> (std::numeric_limits::digits - 1)) & 1); -#endif -} - -/// \} -/// \name Error handling -/// \{ - -/// Internal exception flags. -/// \return reference to global exception flags -inline int& errflags() -{ - HALF_THREAD_LOCAL int flags = 0; - return flags; -} - -/// Raise floating-point exception. -/// \param flags exceptions to raise -/// \param cond condition to raise exceptions for -inline void raise(int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond) = true) -{ -#if HALF_ERRHANDLING - if(!cond) - return; -#if HALF_ERRHANDLING_FLAGS - errflags() |= flags; -#endif -#if HALF_ERRHANDLING_ERRNO - if(flags & FE_INVALID) - errno = EDOM; - else if(flags & (FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)) - errno = ERANGE; -#endif -#if HALF_ERRHANDLING_FENV && HALF_ENABLE_CPP11_CFENV - std::feraiseexcept(flags); -#endif -#ifdef HALF_ERRHANDLING_THROW_INVALID - if(flags & FE_INVALID) - throw std::domain_error(HALF_ERRHANDLING_THROW_INVALID); -#endif -#ifdef HALF_ERRHANDLING_THROW_DIVBYZERO - if(flags & FE_DIVBYZERO) - throw std::domain_error(HALF_ERRHANDLING_THROW_DIVBYZERO); -#endif -#ifdef HALF_ERRHANDLING_THROW_OVERFLOW - if(flags & FE_OVERFLOW) - throw std::overflow_error(HALF_ERRHANDLING_THROW_OVERFLOW); -#endif -#ifdef HALF_ERRHANDLING_THROW_UNDERFLOW - if(flags & FE_UNDERFLOW) - throw std::underflow_error(HALF_ERRHANDLING_THROW_UNDERFLOW); -#endif -#ifdef HALF_ERRHANDLING_THROW_INEXACT - if(flags & FE_INEXACT) - throw std::range_error(HALF_ERRHANDLING_THROW_INEXACT); -#endif -#if HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT - if((flags & FE_UNDERFLOW) && !(flags & FE_INEXACT)) - raise(FE_INEXACT); -#endif -#if HALF_ERRHANDLING_OVERFLOW_TO_INEXACT - if((flags & FE_OVERFLOW) && !(flags & FE_INEXACT)) - raise(FE_INEXACT); -#endif -#endif -} - -/// Check and signal for any NaN. -/// \param x first half-precision value to check -/// \param y second half-precision value to check -/// \retval true if either \a x or \a y is NaN -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool compsignal(unsigned int x, unsigned int y) -{ -#if HALF_ERRHANDLING - raise(FE_INVALID, (x & 0x7FFF) > 0x7C00 || (y & 0x7FFF) > 0x7C00); -#endif - return (x & 0x7FFF) > 0x7C00 || (y & 0x7FFF) > 0x7C00; -} - -/// Signal and silence signaling NaN. -/// \param nan half-precision NaN value -/// \return quiet NaN -/// \exception FE_INVALID if \a nan is signaling NaN -inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int nan) -{ -#if HALF_ERRHANDLING - raise(FE_INVALID, !(nan & 0x200)); -#endif - return nan | 0x200; -} - -/// Signal and silence signaling NaNs. -/// \param x first half-precision value to check -/// \param y second half-precision value to check -/// \return quiet NaN -/// \exception FE_INVALID if \a x or \a y is signaling NaN -inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y) -{ -#if HALF_ERRHANDLING - raise(FE_INVALID, - ((x & 0x7FFF) > 0x7C00 && !(x & 0x200)) || ((y & 0x7FFF) > 0x7C00 && !(y & 0x200))); -#endif - return ((x & 0x7FFF) > 0x7C00) ? (x | 0x200) : (y | 0x200); -} - -/// Signal and silence signaling NaNs. -/// \param x first half-precision value to check -/// \param y second half-precision value to check -/// \param z third half-precision value to check -/// \return quiet NaN -/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN -inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y, unsigned int z) -{ -#if HALF_ERRHANDLING - raise(FE_INVALID, - ((x & 0x7FFF) > 0x7C00 && !(x & 0x200)) || ((y & 0x7FFF) > 0x7C00 && !(y & 0x200)) || - ((z & 0x7FFF) > 0x7C00 && !(z & 0x200))); -#endif - return ((x & 0x7FFF) > 0x7C00) ? (x | 0x200) - : ((y & 0x7FFF) > 0x7C00) ? (y | 0x200) : (z | 0x200); -} - -/// Select value or signaling NaN. -/// \param x preferred half-precision value -/// \param y ignored half-precision value except for signaling NaN -/// \return \a y if signaling NaN, \a x otherwise -/// \exception FE_INVALID if \a y is signaling NaN -inline HALF_CONSTEXPR_NOERR unsigned int select(unsigned int x, unsigned int HALF_UNUSED_NOERR(y)) -{ -#if HALF_ERRHANDLING - return (((y & 0x7FFF) > 0x7C00) && !(y & 0x200)) ? signal(y) : x; -#else - return x; -#endif -} - -/// Raise domain error and return NaN. -/// return quiet NaN -/// \exception FE_INVALID -inline HALF_CONSTEXPR_NOERR unsigned int invalid() -{ -#if HALF_ERRHANDLING - raise(FE_INVALID); -#endif - return 0x7FFF; -} - -/// Raise pole error and return infinity. -/// \param sign half-precision value with sign bit only -/// \return half-precision infinity with sign of \a sign -/// \exception FE_DIVBYZERO -inline HALF_CONSTEXPR_NOERR unsigned int pole(unsigned int sign = 0) -{ -#if HALF_ERRHANDLING - raise(FE_DIVBYZERO); -#endif - return sign | 0x7C00; -} - -/// Check value for underflow. -/// \param arg non-zero half-precision value to check -/// \return \a arg -/// \exception FE_UNDERFLOW if arg is subnormal -inline HALF_CONSTEXPR_NOERR unsigned int check_underflow(unsigned int arg) -{ -#if HALF_ERRHANDLING && !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT - raise(FE_UNDERFLOW, !(arg & 0x7C00)); -#endif - return arg; -} - -/// \} -/// \name Conversion and rounding -/// \{ - -/// Half-precision overflow. -/// \tparam R rounding mode to use -/// \param sign half-precision value with sign bit only -/// \return rounded overflowing half-precision value -/// \exception FE_OVERFLOW -template -HALF_CONSTEXPR_NOERR unsigned int overflow(unsigned int sign = 0) -{ -#if HALF_ERRHANDLING - raise(FE_OVERFLOW); -#endif - return (R == std::round_toward_infinity) - ? (sign + 0x7C00 - (sign >> 15)) - : (R == std::round_toward_neg_infinity) - ? (sign + 0x7BFF + (sign >> 15)) - : (R == std::round_toward_zero) ? (sign | 0x7BFF) : (sign | 0x7C00); -} - -/// Half-precision underflow. -/// \tparam R rounding mode to use -/// \param sign half-precision value with sign bit only -/// \return rounded underflowing half-precision value -/// \exception FE_UNDERFLOW -template -HALF_CONSTEXPR_NOERR unsigned int underflow(unsigned int sign = 0) -{ -#if HALF_ERRHANDLING - raise(FE_UNDERFLOW); -#endif - return (R == std::round_toward_infinity) - ? (sign + 1 - (sign >> 15)) - : (R == std::round_toward_neg_infinity) ? (sign + (sign >> 15)) : sign; -} - -/// Round half-precision number. -/// \tparam R rounding mode to use -/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results -/// \param value finite half-precision number to round -/// \param g guard bit (most significant discarded bit) -/// \param s sticky bit (or of all but the most significant discarded bits) -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded or \a I is `true` -template -HALF_CONSTEXPR_NOERR unsigned int rounded(unsigned int value, int g, int s) -{ -#if HALF_ERRHANDLING - value += (R == std::round_to_nearest) - ? (g & (s | value)) - : (R == std::round_toward_infinity) - ? (~(value >> 15) & (g | s)) - : (R == std::round_toward_neg_infinity) ? ((value >> 15) & (g | s)) : 0; - if((value & 0x7C00) == 0x7C00) - raise(FE_OVERFLOW); - else if(value & 0x7C00) - raise(FE_INEXACT, I || (g | s) != 0); - else - raise(FE_UNDERFLOW, !(HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT) || I || (g | s) != 0); - return value; -#else - return (R == std::round_to_nearest) - ? (value + (g & (s | value))) - : (R == std::round_toward_infinity) - ? (value + (~(value >> 15) & (g | s))) - : (R == std::round_toward_neg_infinity) ? (value + ((value >> 15) & (g | s))) - : value; -#endif -} - -/// Round half-precision number to nearest integer value. -/// \tparam R rounding mode to use -/// \tparam E `true` for round to even, `false` for round away from zero -/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it -/// \param value half-precision value to round -/// \return half-precision bits for nearest integral value -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded and \a I is `true` -template -unsigned int integral(unsigned int value) -{ - unsigned int abs = value & 0x7FFF; - if(abs < 0x3C00) - { - raise(FE_INEXACT, I); - return ((R == std::round_to_nearest) - ? (0x3C00 & -static_cast(abs >= (0x3800 + E))) - : (R == std::round_toward_infinity) - ? (0x3C00 & -(~(value >> 15) & (abs != 0))) - : (R == std::round_toward_neg_infinity) - ? (0x3C00 & -static_cast(value > 0x8000)) - : 0) | - (value & 0x8000); - } - if(abs >= 0x6400) - return (abs > 0x7C00) ? signal(value) : value; - unsigned int exp = 25 - (abs >> 10), mask = (1 << exp) - 1; - raise(FE_INEXACT, I && (value & mask)); - return (((R == std::round_to_nearest) - ? ((1 << (exp - 1)) - (~(value >> exp) & E)) - : (R == std::round_toward_infinity) - ? (mask & ((value >> 15) - 1)) - : (R == std::round_toward_neg_infinity) ? (mask & -(value >> 15)) : 0) + - value) & - ~mask; -} - -/// Convert fixed point to half-precision floating-point. -/// \tparam R rounding mode to use -/// \tparam F number of fractional bits (at least 11) -/// \tparam S `true` for signed, `false` for unsigned -/// \tparam N `true` for additional normalization step, `false` if already normalized to 1.F -/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results -/// \param m mantissa in Q1.F fixed point format -/// \param exp exponent -/// \param sign half-precision value with sign bit only -/// \param s sticky bit (or of all but the most significant already discarded bits) -/// \return value converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded or \a I is `true` -template -unsigned int fixed2half(uint32 m, int exp = 14, unsigned int sign = 0, int s = 0) -{ - if(S) - { - uint32 msign = sign_mask(m); - m = (m ^ msign) - msign; - sign = msign & 0x8000; - } - if(N) - for(; m < (static_cast(1) << F) && exp; m <<= 1, --exp) - ; - else if(exp < 0) - return rounded(sign + (m >> (F - 10 - exp)), - (m >> (F - 11 - exp)) & 1, - s | ((m & ((static_cast(1) << (F - 11 - exp)) - 1)) != 0)); - return rounded(sign + (exp << 10) + (m >> (F - 10)), - (m >> (F - 11)) & 1, - s | ((m & ((static_cast(1) << (F - 11)) - 1)) != 0)); -} - -/// 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 -/// \param value single-precision value to convert -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int float2half_impl(float value, true_type) -{ -#if HALF_ENABLE_F16C_INTRINSICS - return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_set_ss(value), - (R == std::round_to_nearest) - ? _MM_FROUND_TO_NEAREST_INT - : (R == std::round_toward_zero) - ? _MM_FROUND_TO_ZERO - : (R == std::round_toward_infinity) - ? _MM_FROUND_TO_POS_INF - : (R == std::round_toward_neg_infinity) - ? _MM_FROUND_TO_NEG_INF - : _MM_FROUND_CUR_DIRECTION)); -#else - bits::type fbits; - std::memcpy(&fbits, &value, sizeof(float)); -#if 1 - unsigned int sign = (fbits >> 16) & 0x8000; - fbits &= 0x7FFFFFFF; - if(fbits >= 0x7F800000) - return sign | 0x7C00 | ((fbits > 0x7F800000) ? (0x200 | ((fbits >> 13) & 0x3FF)) : 0); - if(fbits >= 0x47800000) - return overflow(sign); - if(fbits >= 0x38800000) - return rounded(sign | (((fbits >> 23) - 112) << 10) | ((fbits >> 13) & 0x3FF), - (fbits >> 12) & 1, - (fbits & 0xFFF) != 0); - if(fbits >= 0x33000000) - { - int i = 125 - (fbits >> 23); - fbits = (fbits & 0x7FFFFF) | 0x800000; - return rounded(sign | (fbits >> (i + 1)), - (fbits >> i) & 1, - (fbits & ((static_cast(1) << i) - 1)) != 0); - } - if(fbits != 0) - return underflow(sign); - return sign; -#else - 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, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, - 0x7BFF, 0x7BFF, 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, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, - 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFC00}; - static const unsigned char shift_table[256] = { - 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, - 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, - 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, - 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, - 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 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}; - int sexp = fbits >> 23, exp = sexp & 0xFF, i = shift_table[exp]; - fbits &= 0x7FFFFF; - uint32 m = (fbits | ((exp != 0) << 23)) & -static_cast(exp != 0xFF); - return rounded(base_table[sexp] + (fbits >> i), - (m >> (i - 1)) & 1, - (((static_cast(1) << (i - 1)) - 1) & m) != 0); -#endif -#endif -} - -/// Convert IEEE double-precision to half-precision. -/// \tparam R rounding mode to use -/// \param value double-precision value to convert -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int float2half_impl(double value, true_type) -{ -#if HALF_ENABLE_F16C_INTRINSICS - if(R == std::round_indeterminate) - return _mm_cvtsi128_si32( - _mm_cvtps_ph(_mm_cvtpd_ps(_mm_set_sd(value)), _MM_FROUND_CUR_DIRECTION)); -#endif - bits::type dbits; - std::memcpy(&dbits, &value, sizeof(double)); - uint32 hi = dbits >> 32, lo = dbits & 0xFFFFFFFF; - unsigned int sign = (hi >> 16) & 0x8000; - hi &= 0x7FFFFFFF; - if(hi >= 0x7FF00000) - return sign | 0x7C00 | ((dbits & 0xFFFFFFFFFFFFF) ? (0x200 | ((hi >> 10) & 0x3FF)) : 0); - if(hi >= 0x40F00000) - return overflow(sign); - if(hi >= 0x3F100000) - return rounded(sign | (((hi >> 20) - 1008) << 10) | ((hi >> 10) & 0x3FF), - (hi >> 9) & 1, - ((hi & 0x1FF) | lo) != 0); - if(hi >= 0x3E600000) - { - int i = 1018 - (hi >> 20); - hi = (hi & 0xFFFFF) | 0x100000; - return rounded(sign | (hi >> (i + 1)), - (hi >> i) & 1, - ((hi & ((static_cast(1) << i) - 1)) | lo) != 0); - } - if((hi | lo) != 0) - return underflow(sign); - return sign; -} - -/// Convert non-IEEE floating-point to half-precision. -/// \tparam R rounding mode to use -/// \tparam T source type (builtin floating-point type) -/// \param value floating-point value to convert -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int float2half_impl(T value, ...) -{ - unsigned int 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) - return overflow(hbits); - if(exp < -13) - value = std::ldexp(value, 25); - else - { - value = std::ldexp(value, 12 - exp); - hbits |= ((exp + 13) << 10); - } - T ival, frac = std::modf(value, &ival); - int m = std::abs(static_cast(ival)); - return rounded(hbits + (m >> 1), m & 1, frac != T()); -} - -/// Convert floating-point to half-precision. -/// \tparam R rounding mode to use -/// \tparam T source type (builtin floating-point type) -/// \param value floating-point value to convert -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int float2half(T value) -{ - return float2half_impl(value, - bool_type < std::numeric_limits::is_iec559 && - sizeof(typename bits::type) == sizeof(T) > ()); -} - -/// Convert integer to half-precision floating-point. -/// \tparam R rounding mode to use -/// \tparam T type to convert (builtin integer type) -/// \param value integral value to convert -/// \return rounded half-precision value -/// \exception FE_OVERFLOW on overflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int int2half(T value) -{ - unsigned int bits = static_cast(value < 0) << 15; - if(!value) - return bits; - if(bits) - value = -value; - if(value > 0xFFFF) - return overflow(bits); - unsigned int m = static_cast(value), exp = 24; - for(; m < 0x400; m <<= 1, --exp) - ; - for(; m > 0x7FF; m >>= 1, ++exp) - ; - bits |= (exp << 10) + m; - return (exp > 24) ? rounded( - bits, (value >> (exp - 25)) & 1, (((1 << (exp - 25)) - 1) & value) != 0) - : bits; -} - -/// 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 half-precision value to convert -/// \return single-precision value -inline float half2float_impl(unsigned int value, float, true_type) -{ -#if HALF_ENABLE_F16C_INTRINSICS - return _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(value))); -#else -#if 0 - bits::type fbits = static_cast::type>(value&0x8000) << 16; - int abs = value & 0x7FFF; - if(abs) - { - fbits |= 0x38000000 << static_cast(abs>=0x7C00); - for(; abs<0x400; abs<<=1,fbits-=0x800000) ; - fbits += static_cast::type>(abs) << 13; - } -#else - static const bits::type mantissa_table[2048] = { - 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, - 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, - 0x35600000, 0x35700000, 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, - 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, - 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, 0x36000000, 0x36040000, 0x36080000, - 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, - 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 0x36400000, - 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, - 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, - 0x367C0000, 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, - 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, - 0x369A0000, 0x369C0000, 0x369E0000, 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, - 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, - 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, 0x36C00000, 0x36C20000, - 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, - 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, - 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, - 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, - 0x36FC0000, 0x36FE0000, 0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, - 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, - 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 0x37100000, 0x37110000, 0x37120000, - 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, - 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, 0x37200000, - 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, - 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, - 0x372F0000, 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, - 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, - 0x373D0000, 0x373E0000, 0x373F0000, 0x37400000, 0x37410000, 0x37420000, 0x37430000, - 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, - 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 0x37500000, 0x37510000, - 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, - 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, - 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, - 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, - 0x376E0000, 0x376F0000, 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, - 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, - 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 0x37800000, 0x37808000, 0x37810000, - 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, - 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 0x37880000, - 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, - 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, - 0x378F8000, 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, - 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, - 0x37968000, 0x37970000, 0x37978000, 0x37980000, 0x37988000, 0x37990000, 0x37998000, - 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, - 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, 0x37A00000, 0x37A08000, - 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, - 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, - 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, - 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, - 0x37AF0000, 0x37AF8000, 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, - 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, - 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, 0x37B80000, 0x37B88000, 0x37B90000, - 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, - 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, 0x37C00000, - 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, - 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, - 0x37C78000, 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, - 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, - 0x37CE8000, 0x37CF0000, 0x37CF8000, 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, - 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, - 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, 0x37D80000, 0x37D88000, - 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, - 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, - 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, - 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, - 0x37E70000, 0x37E78000, 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, - 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, - 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, 0x37F00000, 0x37F08000, 0x37F10000, - 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, - 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 0x37F80000, - 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, - 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, - 0x37FF8000, 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, - 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, - 0x38034000, 0x38038000, 0x3803C000, 0x38040000, 0x38044000, 0x38048000, 0x3804C000, - 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, - 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 0x38080000, 0x38084000, - 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, - 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, - 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, - 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, - 0x380F8000, 0x380FC000, 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, - 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, - 0x38130000, 0x38134000, 0x38138000, 0x3813C000, 0x38140000, 0x38144000, 0x38148000, - 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, - 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, 0x38180000, - 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, - 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, - 0x381BC000, 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, - 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, - 0x381F4000, 0x381F8000, 0x381FC000, 0x38200000, 0x38204000, 0x38208000, 0x3820C000, - 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, - 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, 0x38240000, 0x38244000, - 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, - 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, - 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, - 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, - 0x382B8000, 0x382BC000, 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, - 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, - 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 0x38300000, 0x38304000, 0x38308000, - 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, - 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, 0x38340000, - 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, - 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, - 0x3837C000, 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, - 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, - 0x383B4000, 0x383B8000, 0x383BC000, 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, - 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, - 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, 0x38400000, 0x38404000, - 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, - 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, - 0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, - 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, - 0x38478000, 0x3847C000, 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, - 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, - 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, 0x384C0000, 0x384C4000, 0x384C8000, - 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, - 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, 0x38500000, - 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, - 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, - 0x3853C000, 0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, - 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, - 0x38574000, 0x38578000, 0x3857C000, 0x38580000, 0x38584000, 0x38588000, 0x3858C000, - 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, - 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, 0x385C0000, 0x385C4000, - 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, - 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, - 0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, - 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, - 0x38638000, 0x3863C000, 0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, - 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, - 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 0x38680000, 0x38684000, 0x38688000, - 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, - 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 0x386C0000, - 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, - 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, - 0x386FC000, 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, - 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, - 0x38734000, 0x38738000, 0x3873C000, 0x38740000, 0x38744000, 0x38748000, 0x3874C000, - 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, - 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, 0x38780000, 0x38784000, - 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, - 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, - 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, - 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, - 0x387F8000, 0x387FC000, 0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, - 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, - 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, 0x38020000, 0x38022000, 0x38024000, - 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, - 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, 0x38040000, - 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, - 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, - 0x3805E000, 0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, - 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, - 0x3807A000, 0x3807C000, 0x3807E000, 0x38080000, 0x38082000, 0x38084000, 0x38086000, - 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, - 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, 0x380A0000, 0x380A2000, - 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, - 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, - 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, - 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, - 0x380DC000, 0x380DE000, 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, - 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, - 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, 0x38100000, 0x38102000, 0x38104000, - 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, - 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, 0x38120000, - 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, - 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, - 0x3813E000, 0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, - 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, - 0x3815A000, 0x3815C000, 0x3815E000, 0x38160000, 0x38162000, 0x38164000, 0x38166000, - 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, - 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 0x38180000, 0x38182000, - 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, - 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, - 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, - 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, - 0x381BC000, 0x381BE000, 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, - 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, - 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, 0x381E0000, 0x381E2000, 0x381E4000, - 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, - 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, 0x38200000, - 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, - 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, - 0x3821E000, 0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, - 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, - 0x3823A000, 0x3823C000, 0x3823E000, 0x38240000, 0x38242000, 0x38244000, 0x38246000, - 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, - 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, 0x38260000, 0x38262000, - 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, - 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, - 0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, - 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, - 0x3829C000, 0x3829E000, 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, - 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, - 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 0x382C0000, 0x382C2000, 0x382C4000, - 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, - 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, 0x382E0000, - 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, - 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, - 0x382FE000, 0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, - 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, - 0x3831A000, 0x3831C000, 0x3831E000, 0x38320000, 0x38322000, 0x38324000, 0x38326000, - 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, - 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 0x38340000, 0x38342000, - 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, - 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, - 0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, - 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, - 0x3837C000, 0x3837E000, 0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, - 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, - 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 0x383A0000, 0x383A2000, 0x383A4000, - 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, - 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 0x383C0000, - 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, - 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, - 0x383DE000, 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, - 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, - 0x383FA000, 0x383FC000, 0x383FE000, 0x38400000, 0x38402000, 0x38404000, 0x38406000, - 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, - 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, 0x38420000, 0x38422000, - 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, - 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, - 0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, - 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, - 0x3845C000, 0x3845E000, 0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, - 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, - 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, 0x38480000, 0x38482000, 0x38484000, - 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, - 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, 0x384A0000, - 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, - 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, - 0x384BE000, 0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, - 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, - 0x384DA000, 0x384DC000, 0x384DE000, 0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, - 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, - 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 0x38500000, 0x38502000, - 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, - 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, - 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, - 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, - 0x3853C000, 0x3853E000, 0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, - 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, - 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 0x38560000, 0x38562000, 0x38564000, - 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, - 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 0x38580000, - 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, - 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, - 0x3859E000, 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, - 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, - 0x385BA000, 0x385BC000, 0x385BE000, 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, - 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, - 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 0x385E0000, 0x385E2000, - 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, - 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, - 0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, - 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, - 0x3861C000, 0x3861E000, 0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, - 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, - 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 0x38640000, 0x38642000, 0x38644000, - 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, - 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, 0x38660000, - 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, - 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, - 0x3867E000, 0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, - 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, - 0x3869A000, 0x3869C000, 0x3869E000, 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, - 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, - 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, 0x386C0000, 0x386C2000, - 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, - 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, - 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, - 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, - 0x386FC000, 0x386FE000, 0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, - 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, - 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 0x38720000, 0x38722000, 0x38724000, - 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, - 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 0x38740000, - 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, - 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, - 0x3875E000, 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, - 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, - 0x3877A000, 0x3877C000, 0x3877E000, 0x38780000, 0x38782000, 0x38784000, 0x38786000, - 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, - 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 0x387A0000, 0x387A2000, - 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, - 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, - 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, - 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, - 0x387DC000, 0x387DE000, 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, - 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, - 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000}; - static const bits::type 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}; - bits::type fbits = - mantissa_table[offset_table[value >> 10] + (value & 0x3FF)] + exponent_table[value >> 10]; -#endif - float out; - std::memcpy(&out, &fbits, sizeof(float)); - return out; -#endif -} - -/// Convert half-precision to IEEE double-precision. -/// \param value half-precision value to convert -/// \return double-precision value -inline double half2float_impl(unsigned int value, double, true_type) -{ -#if HALF_ENABLE_F16C_INTRINSICS - return _mm_cvtsd_f64(_mm_cvtps_pd(_mm_cvtph_ps(_mm_cvtsi32_si128(value)))); -#else - uint32 hi = static_cast(value & 0x8000) << 16; - unsigned int abs = value & 0x7FFF; - if(abs) - { - hi |= 0x3F000000 << static_cast(abs >= 0x7C00); - for(; abs < 0x400; abs <<= 1, hi -= 0x100000) - ; - hi += static_cast(abs) << 10; - } - bits::type dbits = static_cast::type>(hi) << 32; - double out; - std::memcpy(&out, &dbits, sizeof(double)); - return out; -#endif -} - -/// Convert half-precision to non-IEEE floating-point. -/// \tparam T type to convert to (builtin integer type) -/// \param value half-precision value to convert -/// \return floating-point value -template -T half2float_impl(unsigned int value, T, ...) -{ - T out; - unsigned int abs = value & 0x7FFF; - if(abs > 0x7C00) - out = - (std::numeric_limits::has_signaling_NaN && !(abs & 0x200)) - ? std::numeric_limits::signaling_NaN() - : 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 half-precision value to convert -/// \return floating-point value -template -T half2float(unsigned int value) -{ - return half2float_impl(value, - T(), - bool_type < std::numeric_limits::is_iec559 && - sizeof(typename bits::type) == sizeof(T) > ()); -} - -/// Convert half-precision floating-point to integer. -/// \tparam R rounding mode to use -/// \tparam E `true` for round to even, `false` for round away from zero -/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it -/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding -/// any implicit sign bits) -/// \param value half-precision value to convert -/// \return rounded integer value -/// \exception FE_INVALID if value is not representable in type \a T -/// \exception FE_INEXACT if value had to be rounded and \a I is `true` -template -T half2int(unsigned int value) -{ - unsigned int abs = value & 0x7FFF; - if(abs >= 0x7C00) - { - raise(FE_INVALID); - return (value & 0x8000) ? std::numeric_limits::min() : std::numeric_limits::max(); - } - if(abs < 0x3800) - { - raise(FE_INEXACT, I); - return (R == std::round_toward_infinity) - ? T(~(value >> 15) & (abs != 0)) - : (R == std::round_toward_neg_infinity) ? -T(value > 0x8000) : T(); - } - int exp = 25 - (abs >> 10); - unsigned int m = (value & 0x3FF) | 0x400; - int32 i = static_cast( - (exp <= 0) - ? (m << -exp) - : ((m + ((R == std::round_to_nearest) ? ((1 << (exp - 1)) - (~(m >> exp) & E)) - : (R == std::round_toward_infinity) - ? (((1 << exp) - 1) & ((value >> 15) - 1)) - : (R == std::round_toward_neg_infinity) - ? (((1 << exp) - 1) & -(value >> 15)) - : 0)) >> - exp)); - if((!std::numeric_limits::is_signed && (value & 0x8000)) || - (std::numeric_limits::digits < 16 && - ((value & 0x8000) ? (-i < std::numeric_limits::min()) - : (i > std::numeric_limits::max())))) - raise(FE_INVALID); - else if(I && exp > 0 && (m & ((1 << exp) - 1))) - raise(FE_INEXACT); - return static_cast((value & 0x8000) ? -i : i); -} - -/// \} -/// \name Mathematics -/// \{ - -/// upper part of 64-bit multiplication. -/// \tparam R rounding mode to use -/// \param x first factor -/// \param y second factor -/// \return upper 32 bit of \a x * \a y -template -uint32 mulhi(uint32 x, uint32 y) -{ - uint32 xy = (x >> 16) * (y & 0xFFFF), yx = (x & 0xFFFF) * (y >> 16), - c = (xy & 0xFFFF) + (yx & 0xFFFF) + (((x & 0xFFFF) * (y & 0xFFFF)) >> 16); - return (x >> 16) * (y >> 16) + (xy >> 16) + (yx >> 16) + (c >> 16) + - ((R == std::round_to_nearest) - ? ((c >> 15) & 1) - : (R == std::round_toward_infinity) ? ((c & 0xFFFF) != 0) : 0); -} - -/// 64-bit multiplication. -/// \param x first factor -/// \param y second factor -/// \return upper 32 bit of \a x * \a y rounded to nearest -inline uint32 multiply64(uint32 x, uint32 y) -{ -#if HALF_ENABLE_CPP11_LONG_LONG - return static_cast( - (static_cast(x) * static_cast(y) + 0x80000000) >> - 32); -#else - return mulhi(x, y); -#endif -} - -/// 64-bit division. -/// \param x upper 32 bit of dividend -/// \param y divisor -/// \param s variable to store sticky bit for rounding -/// \return (\a x << 32) / \a y -inline uint32 divide64(uint32 x, uint32 y, int& s) -{ -#if HALF_ENABLE_CPP11_LONG_LONG - unsigned long long xx = static_cast(x) << 32; - return s = (xx % y != 0), static_cast(xx / y); -#else - y >>= 1; - uint32 rem = x, div = 0; - for(unsigned int i = 0; i < 32; ++i) - { - div <<= 1; - if(rem >= y) - { - rem -= y; - div |= 1; - } - rem <<= 1; - } - return s = rem > 1, div; -#endif -} - -/// Half precision positive modulus. -/// \tparam Q `true` to compute full quotient, `false` else -/// \tparam R `true` to compute signed remainder, `false` for positive remainder -/// \param x first operand as positive finite half-precision value -/// \param y second operand as positive finite half-precision value -/// \param quo adress to store quotient at, `nullptr` if \a Q `false` -/// \return modulus of \a x / \a y -template -unsigned int mod(unsigned int x, unsigned int y, int* quo = NULL) -{ - unsigned int q = 0; - if(x > y) - { - int absx = x, absy = y, expx = 0, expy = 0; - for(; absx < 0x400; absx <<= 1, --expx) - ; - for(; absy < 0x400; absy <<= 1, --expy) - ; - expx += absx >> 10; - expy += absy >> 10; - int mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400; - for(int d = expx - expy; d; --d) - { - if(!Q && mx == my) - return 0; - if(mx >= my) - { - mx -= my; - q += Q; - } - mx <<= 1; - q <<= static_cast(Q); - } - if(!Q && mx == my) - return 0; - if(mx >= my) - { - mx -= my; - ++q; - } - if(Q) - { - q &= (1 << (std::numeric_limits::digits - 1)) - 1; - if(!mx) - return *quo = q, 0; - } - for(; mx < 0x400; mx <<= 1, --expy) - ; - x = (expy > 0) ? ((expy << 10) | (mx & 0x3FF)) : (mx >> (1 - expy)); - } - if(R) - { - unsigned int a, b; - if(y < 0x800) - { - a = (x < 0x400) ? (x << 1) : (x + 0x400); - b = y; - } - else - { - a = x; - b = y - 0x400; - } - if(a > b || (a == b && (q & 1))) - { - int exp = (y >> 10) + (y <= 0x3FF), d = exp - (x >> 10) - (x <= 0x3FF); - int m = (((y & 0x3FF) | ((y > 0x3FF) << 10)) << 1) - - (((x & 0x3FF) | ((x > 0x3FF) << 10)) << (1 - d)); - for(; m < 0x800 && exp > 1; m <<= 1, --exp) - ; - x = 0x8000 + ((exp - 1) << 10) + (m >> 1); - q += Q; - } - } - if(Q) - *quo = q; - return x; -} - -/// Fixed point square root. -/// \tparam F number of fractional bits -/// \param r radicand in Q1.F fixed point format -/// \param exp exponent -/// \return square root as Q1.F/2 -template -uint32 sqrt(uint32& r, int& exp) -{ - int i = exp & 1; - r <<= i; - exp = (exp - i) / 2; - uint32 m = 0; - for(uint32 bit = static_cast(1) << F; bit; bit >>= 2) - { - if(r < m + bit) - m >>= 1; - else - { - r -= m + bit; - m = (m >> 1) + bit; - } - } - return m; -} - -/// Fixed point binary exponential. -/// This uses the BKM algorithm in E-mode. -/// \param m exponent in [0,1) as Q0.31 -/// \param n number of iterations (at most 32) -/// \return 2 ^ \a m as Q1.31 -inline uint32 exp2(uint32 m, unsigned int n = 32) -{ - static const uint32 logs[] = { - 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, - 0x016FE50B, 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, - 0x0002E2A3, 0x00017153, 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, - 0x000005C5, 0x000002E3, 0x00000171, 0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, - 0x0000000C, 0x00000006, 0x00000003, 0x00000001}; - if(!m) - return 0x80000000; - uint32 mx = 0x80000000, my = 0; - for(unsigned int i = 1; i < n; ++i) - { - uint32 mz = my + logs[i]; - if(mz <= m) - { - my = mz; - mx += mx >> i; - } - } - return mx; -} - -/// Fixed point binary logarithm. -/// This uses the BKM algorithm in L-mode. -/// \param m mantissa in [1,2) as Q1.30 -/// \param n number of iterations (at most 32) -/// \return log2(\a m) as Q0.31 -inline uint32 log2(uint32 m, unsigned int n = 32) -{ - static const uint32 logs[] = { - 0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, - 0x016FE50B, 0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, - 0x0002E2A3, 0x00017153, 0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, - 0x000005C5, 0x000002E3, 0x00000171, 0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, - 0x0000000C, 0x00000006, 0x00000003, 0x00000001}; - if(m == 0x40000000) - return 0; - uint32 mx = 0x40000000, my = 0; - for(unsigned int i = 1; i < n; ++i) - { - uint32 mz = mx + (mx >> i); - if(mz <= m) - { - mx = mz; - my += logs[i]; - } - } - return my; -} - -/// Fixed point sine and cosine. -/// This uses the CORDIC algorithm in rotation mode. -/// \param mz angle in [-pi/2,pi/2] as Q1.30 -/// \param n number of iterations (at most 31) -/// \return sine and cosine of \a mz as Q1.30 -inline std::pair sincos(uint32 mz, unsigned int n = 31) -{ - static const uint32 angles[] = { - 0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, - 0x007FFF55, 0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, - 0x00010000, 0x00008000, 0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, - 0x00000200, 0x00000100, 0x00000080, 0x00000040, 0x00000020, 0x00000010, 0x00000008, - 0x00000004, 0x00000002, 0x00000001}; - uint32 mx = 0x26DD3B6A, my = 0; - for(unsigned int i = 0; i < n; ++i) - { - uint32 sign = sign_mask(mz); - uint32 tx = mx - (arithmetic_shift(my, i) ^ sign) + sign; - uint32 ty = my + (arithmetic_shift(mx, i) ^ sign) - sign; - mx = tx; - my = ty; - mz -= (angles[i] ^ sign) - sign; - } - return std::make_pair(my, mx); -} - -/// Fixed point arc tangent. -/// This uses the CORDIC algorithm in vectoring mode. -/// \param my y coordinate as Q0.30 -/// \param mx x coordinate as Q0.30 -/// \param n number of iterations (at most 31) -/// \return arc tangent of \a my / \a mx as Q1.30 -inline uint32 atan2(uint32 my, uint32 mx, unsigned int n = 31) -{ - static const uint32 angles[] = { - 0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, - 0x007FFF55, 0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, - 0x00010000, 0x00008000, 0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, - 0x00000200, 0x00000100, 0x00000080, 0x00000040, 0x00000020, 0x00000010, 0x00000008, - 0x00000004, 0x00000002, 0x00000001}; - uint32 mz = 0; - for(unsigned int i = 0; i < n; ++i) - { - uint32 sign = sign_mask(my); - uint32 tx = mx + (arithmetic_shift(my, i) ^ sign) - sign; - uint32 ty = my - (arithmetic_shift(mx, i) ^ sign) + sign; - mx = tx; - my = ty; - mz += (angles[i] ^ sign) - sign; - } - return mz; -} - -/// Reduce argument for trigonometric functions. -/// \param abs half-precision floating-point value -/// \param k value to take quarter period -/// \return \a abs reduced to [-pi/4,pi/4] as Q0.30 -inline uint32 angle_arg(unsigned int abs, int& k) -{ - uint32 m = (abs & 0x3FF) | ((abs > 0x3FF) << 10); - int exp = (abs >> 10) + (abs <= 0x3FF) - 15; - if(abs < 0x3A48) - return k = 0, m << (exp + 20); -#if HALF_ENABLE_CPP11_LONG_LONG - unsigned long long y = m * 0xA2F9836E4E442, mask = (1ULL << (62 - exp)) - 1, - yi = (y + (mask >> 1)) & ~mask, f = y - yi; - uint32 sign = -static_cast(f >> 63); - k = static_cast(yi >> (62 - exp)); - return (multiply64(static_cast((sign ? -f : f) >> (31 - exp)), 0xC90FDAA2) ^ sign) - - sign; -#else - uint32 yh = m * 0xA2F98 + mulhi(m, 0x36E4E442), - yl = (m * 0x36E4E442) & 0xFFFFFFFF; - uint32 mask = (static_cast(1) << (30 - exp)) - 1, yi = (yh + (mask >> 1)) & ~mask, - sign = -static_cast(yi > yh); - k = static_cast(yi >> (30 - exp)); - uint32 fh = (yh ^ sign) + (yi ^ ~sign) - ~sign, fl = (yl ^ sign) - sign; - return (multiply64((exp > -1) - ? (((fh << (1 + exp)) & 0xFFFFFFFF) | ((fl & 0xFFFFFFFF) >> (31 - exp))) - : fh, - 0xC90FDAA2) ^ - sign) - - sign; -#endif -} - -/// Get arguments for atan2 function. -/// \param abs half-precision floating-point value -/// \return \a abs and sqrt(1 - \a abs^2) as Q0.30 -inline std::pair atan2_args(unsigned int abs) -{ - int exp = -15; - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += abs >> 10; - uint32 my = ((abs & 0x3FF) | 0x400) << 5, r = my * my; - int rexp = 2 * exp; - r = 0x40000000 - - ((rexp > -31) ? ((r >> -rexp) | ((r & ((static_cast(1) << -rexp) - 1)) != 0)) : 1); - for(rexp = 0; r < 0x40000000; r <<= 1, --rexp) - ; - uint32 mx = sqrt<30>(r, rexp); - int d = exp - rexp; - if(d < 0) - return std::make_pair((d < -14) ? ((my >> (-d - 14)) + ((my >> (-d - 15)) & 1)) - : (my << (14 + d)), - (mx << 14) + (r << 13) / mx); - if(d > 0) - return std::make_pair(my << 14, - (d > 14) - ? ((mx >> (d - 14)) + ((mx >> (d - 15)) & 1)) - : ((d == 14) ? mx : ((mx << (14 - d)) + (r << (13 - d)) / mx))); - return std::make_pair(my << 13, (mx << 13) + (r << 12) / mx); -} - -/// Get exponentials for hyperbolic computation -/// \param abs half-precision floating-point value -/// \param exp variable to take unbiased exponent of larger result -/// \param n number of BKM iterations (at most 32) -/// \return exp(abs) and exp(-\a abs) as Q1.31 with same exponent -inline std::pair hyperbolic_args(unsigned int abs, int& exp, unsigned int n = 32) -{ - uint32 mx = detail::multiply64(static_cast((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, - 0xB8AA3B29), - my; - int e = (abs >> 10) + (abs <= 0x3FF); - if(e < 14) - { - exp = 0; - mx >>= 14 - e; - } - else - { - exp = mx >> (45 - e); - mx = (mx << (e - 14)) & 0x7FFFFFFF; - } - mx = exp2(mx, n); - int d = exp << 1, s; - if(mx > 0x80000000) - { - my = divide64(0x80000000, mx, s); - my |= s; - ++d; - } - else - my = mx; - return std::make_pair( - mx, (d < 31) ? ((my >> d) | ((my & ((static_cast(1) << d) - 1)) != 0)) : 1); -} - -/// Postprocessing for binary exponential. -/// \tparam R rounding mode to use -/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results -/// \param m mantissa as Q1.31 -/// \param exp absolute value of unbiased exponent -/// \param esign sign of actual exponent -/// \param sign sign bit of result -/// \return value converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded or \a I is `true` -template -unsigned int exp2_post(uint32 m, int exp, bool esign, unsigned int sign = 0) -{ - int s = 0; - if(esign) - { - if(m > 0x80000000) - { - m = divide64(0x80000000, m, s); - ++exp; - } - if(exp > 25) - return underflow(sign); - else if(exp == 25) - return rounded(sign, 1, (m & 0x7FFFFFFF) != 0); - exp = -exp; - } - else if(exp > 15) - return overflow(sign); - return fixed2half(m, exp + 14, sign, s); -} - -/// Postprocessing for binary logarithm. -/// \tparam R rounding mode to use -/// \tparam L logarithm for base transformation as Q1.31 -/// \param m fractional part of logarithm as Q0.31 -/// \param ilog signed integer part of logarithm -/// \param exp biased exponent of result -/// \param sign sign bit of result -/// \return value base-transformed and converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if no other exception occurred -template -unsigned int log2_post(uint32 m, int ilog, int exp, unsigned int sign = 0) -{ - uint32 msign = sign_mask(ilog); - m = (((static_cast(ilog) << 27) + (m >> 4)) ^ msign) - msign; - if(!m) - return 0; - for(; m < 0x80000000; m <<= 1, --exp) - ; - int i = m >= L, s; - exp += i; - m >>= 1 + i; - sign ^= msign & 0x8000; - if(exp < -11) - return underflow(sign); - m = divide64(m, L, s); - return fixed2half(m, exp, sign, 1); -} - -/// Hypotenuse square root and postprocessing. -/// \tparam R rounding mode to use -/// \param r mantissa as Q2.30 -/// \param exp unbiased exponent -/// \return square root converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if value had to be rounded -template -unsigned int hypot_post(uint32 r, int exp) -{ - int i = r >> 31; - if((exp += i) > 46) - return overflow(); - if(exp < -34) - return underflow(); - r = (r >> i) | (r & i); - uint32 m = sqrt<30>(r, exp += 15); - return fixed2half(m, exp - 1, 0, r != 0); -} - -/// Division and postprocessing for tangents. -/// \tparam R rounding mode to use -/// \param my dividend as Q1.31 -/// \param mx divisor as Q1.31 -/// \param exp biased exponent of result -/// \param sign sign bit of result -/// \return quotient converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if no other exception occurred -template -unsigned int tangent_post(uint32 my, uint32 mx, int exp, unsigned int sign = 0) -{ - int i = my >= mx, s; - exp += i; - if(exp > 29) - return overflow(sign); - if(exp < -11) - return underflow(sign); - uint32 m = divide64(my >> (i + 1), mx, s); - return fixed2half(m, exp, sign, s); -} - -/// Area function and postprocessing. -/// This computes the value directly in Q2.30 using the representation `asinh|acosh(x) = -/// log(x+sqrt(x^2+|-1))`. -/// \tparam R rounding mode to use -/// \tparam S `true` for asinh, `false` for acosh -/// \param arg half-precision argument -/// \return asinh|acosh(\a arg) converted to half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if no other exception occurred -template -unsigned int area(unsigned int arg) -{ - int abs = arg & 0x7FFF, expx = (abs >> 10) + (abs <= 0x3FF) - 15, expy = -15, ilog, i; - uint32 mx = static_cast((abs & 0x3FF) | ((abs > 0x3FF) << 10)) << 20, my, r; - for(; abs < 0x400; abs <<= 1, --expy) - ; - expy += abs >> 10; - r = ((abs & 0x3FF) | 0x400) << 5; - r *= r; - i = r >> 31; - expy = 2 * expy + i; - r >>= i; - if(S) - { - if(expy < 0) - { - r = 0x40000000 + ((expy > -30) ? ((r >> -expy) | - ((r & ((static_cast(1) << -expy) - 1)) != 0)) - : 1); - expy = 0; - } - else - { - r += 0x40000000 >> expy; - i = r >> 31; - r = (r >> i) | (r & i); - expy += i; - } - } - else - { - r -= 0x40000000 >> expy; - for(; r < 0x40000000; r <<= 1, --expy) - ; - } - my = sqrt<30>(r, expy); - my = (my << 15) + (r << 14) / my; - if(S) - { - mx >>= expy - expx; - ilog = expy; - } - else - { - my >>= expx - expy; - ilog = expx; - } - my += mx; - i = my >> 31; - static const int G = S && (R == std::round_to_nearest); - return log2_post( - log2(my >> i, 26 + S + G) + (G << 3), ilog + i, 17, arg & (static_cast(S) << 15)); -} - -/// Class for 1.31 unsigned floating-point computation -struct f31 -{ - /// Constructor. - /// \param mant mantissa as 1.31 - /// \param e exponent - HALF_CONSTEXPR f31(uint32 mant, int e) : m(mant), exp(e) {} - - /// Constructor. - /// \param abs unsigned half-precision value - f31(unsigned int abs) : exp(-15) - { - for(; abs < 0x400; abs <<= 1, --exp) - ; - m = static_cast((abs & 0x3FF) | 0x400) << 21; - exp += (abs >> 10); - } - - /// Addition operator. - /// \param a first operand - /// \param b second operand - /// \return \a a + \a b - friend f31 operator+(f31 a, f31 b) - { - if(b.exp > a.exp) - std::swap(a, b); - int d = a.exp - b.exp; - uint32 m = a.m + ((d < 32) ? (b.m >> d) : 0); - int i = (m & 0xFFFFFFFF) < a.m; - return f31(((m + i) >> i) | 0x80000000, a.exp + i); - } - - /// Subtraction operator. - /// \param a first operand - /// \param b second operand - /// \return \a a - \a b - friend f31 operator-(f31 a, f31 b) - { - int d = a.exp - b.exp, exp = a.exp; - uint32 m = a.m - ((d < 32) ? (b.m >> d) : 0); - if(!m) - return f31(0, -32); - for(; m < 0x80000000; m <<= 1, --exp) - ; - return f31(m, exp); - } - - /// Multiplication operator. - /// \param a first operand - /// \param b second operand - /// \return \a a * \a b - friend f31 operator*(f31 a, f31 b) - { - uint32 m = multiply64(a.m, b.m); - int i = m >> 31; - return f31(m << (1 - i), a.exp + b.exp + i); - } - - /// Division operator. - /// \param a first operand - /// \param b second operand - /// \return \a a / \a b - friend f31 operator/(f31 a, f31 b) - { - int i = a.m >= b.m, s; - uint32 m = divide64((a.m + i) >> i, b.m, s); - return f31(m, a.exp - b.exp + i - 1); - } - - uint32 m; ///< mantissa as 1.31. - int exp; ///< exponent. -}; - -/// Error function and postprocessing. -/// This computes the value directly in Q1.31 using the approximations given -/// [here](https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions). -/// \tparam R rounding mode to use -/// \tparam C `true` for comlementary error function, `false` else -/// \param arg half-precision function argument -/// \return approximated value of error function in half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if no other exception occurred -template -unsigned int erf(unsigned int arg) -{ - unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000; - f31 x(abs), x2 = x * x * f31(0xB8AA3B29, 0), - t = f31(0x80000000, 0) / (f31(0x80000000, 0) + f31(0xA7BA054A, -2) * x), t2 = t * t; - f31 e = ((f31(0x87DC2213, 0) * t2 + f31(0xB5F0E2AE, 0)) * t2 + f31(0x82790637, -2) - - (f31(0xBA00E2B8, 0) * t2 + f31(0x91A98E62, -2)) * t) * - t / - ((x2.exp < 0) ? f31(exp2((x2.exp > -32) ? (x2.m >> -x2.exp) : 0, 30), 0) - : f31(exp2((x2.m << x2.exp) & 0x7FFFFFFF, 22), x2.m >> (31 - x2.exp))); - return (!C || sign) - ? fixed2half( - 0x80000000 - (e.m >> (C - e.exp)), 14 + C, sign & (C - 1U)) - : (e.exp < -25) - ? underflow() - : fixed2half(e.m >> 1, e.exp + 14, 0, e.m & 1); -} - -/// Gamma function and postprocessing. -/// This approximates the value of either the gamma function or its logarithm directly in Q1.31. -/// \tparam R rounding mode to use -/// \tparam L `true` for lograithm of gamma function, `false` for gamma function -/// \param arg half-precision floating-point value -/// \return lgamma/tgamma(\a arg) in half-precision -/// \exception FE_OVERFLOW on overflows -/// \exception FE_UNDERFLOW on underflows -/// \exception FE_INEXACT if \a arg is not a positive integer -template -unsigned int gamma(unsigned int arg) -{ - /* static const double p[] ={ 2.50662827563479526904, 225.525584619175212544, - -268.295973841304927459, 80.9030806934622512966, -5.00757863970517583837, - 0.0114684895434781459556 }; double t = arg + 4.65, s = p[0]; for(unsigned int i=0; i<5; ++i) - s += p[i+1] / (arg+i); - return std::log(s) + (arg-0.5)*std::log(t) - t; -*/ static const f31 pi(0xC90FDAA2, 1), lbe(0xB8AA3B29, 0); - unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000; - bool bsign = sign != 0; - f31 z(abs), x = sign ? (z + f31(0x80000000, 0)) : z, t = x + f31(0x94CCCCCD, 2), - s = f31(0xA06C9901, 1) + f31(0xBBE654E2, -7) / (x + f31(0x80000000, 2)) + - f31(0xA1CE6098, 6) / (x + f31(0x80000000, 1)) + f31(0xE1868CB7, 7) / x - - f31(0x8625E279, 8) / (x + f31(0x80000000, 0)) - - f31(0xA03E158F, 2) / (x + f31(0xC0000000, 1)); - int i = (s.exp >= 2) + (s.exp >= 4) + (s.exp >= 8) + (s.exp >= 16); - s = f31((static_cast(s.exp) << (31 - i)) + (log2(s.m >> 1, 28) >> i), i) / lbe; - if(x.exp != -1 || x.m != 0x80000000) - { - i = (t.exp >= 2) + (t.exp >= 4) + (t.exp >= 8); - f31 l = f31((static_cast(t.exp) << (31 - i)) + (log2(t.m >> 1, 30) >> i), i) / lbe; - s = (x.exp < -1) ? (s - (f31(0x80000000, -1) - x) * l) - : (s + (x - f31(0x80000000, -1)) * l); - } - s = x.exp ? (s - t) : (t - s); - if(bsign) - { - if(z.exp >= 0) - { - sign &= (L | ((z.m >> (31 - z.exp)) & 1)) - 1; - for(z = f31((z.m << (1 + z.exp)) & 0xFFFFFFFF, -1); z.m < 0x80000000; - z.m <<= 1, --z.exp) - ; - } - if(z.exp == -1) - z = f31(0x80000000, 0) - z; - if(z.exp < -1) - { - z = z * pi; - z.m = sincos(z.m >> (1 - z.exp), 30).first; - for(z.exp = 1; z.m < 0x80000000; z.m <<= 1, --z.exp) - ; - } - else - z = f31(0x80000000, 0); - } - if(L) - { - if(bsign) - { - f31 l(0x92868247, 0); - if(z.exp < 0) - { - uint32 m = log2((z.m + 1) >> 1, 27); - z = f31(-((static_cast(z.exp) << 26) + (m >> 5)), 5); - for(; z.m < 0x80000000; z.m <<= 1, --z.exp) - ; - l = l + z / lbe; - } - sign = static_cast(x.exp && (l.exp < s.exp || (l.exp == s.exp && l.m < s.m))) - << 15; - s = sign ? (s - l) : x.exp ? (l - s) : (l + s); - } - else - { - sign = static_cast(x.exp == 0) << 15; - if(s.exp < -24) - return underflow(sign); - if(s.exp > 15) - return overflow(sign); - } - } - else - { - s = s * lbe; - uint32 m; - if(s.exp < 0) - { - m = s.m >> -s.exp; - s.exp = 0; - } - else - { - m = (s.m << s.exp) & 0x7FFFFFFF; - s.exp = (s.m >> (31 - s.exp)); - } - s.m = exp2(m, 27); - if(!x.exp) - s = f31(0x80000000, 0) / s; - if(bsign) - { - if(z.exp < 0) - s = s * z; - s = pi / s; - if(s.exp < -24) - return underflow(sign); - } - else if(z.exp > 0 && !(z.m & ((1 << (31 - z.exp)) - 1))) - return ((s.exp + 14) << 10) + (s.m >> 21); - if(s.exp > 15) - return overflow(sign); - } - return fixed2half(s.m, s.exp + 14, sign); -} -/// \} - -template -struct half_caster; -} // namespace detail - -/// Half-precision floating-point type. -/// This class implements an IEEE-conformant half-precision floating-point type with the usual -/// arithmetic -/// operators and conversions. It is implicitly convertible to single-precision floating-point, -/// which makes artihmetic -/// expressions and functions with mixed-type operands to be of the most precise operand type. -/// -/// 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 -{ - public: - /// \name Construction and assignment - /// \{ - - /// Default constructor. - /// This initializes the half to 0. Although this does not match the builtin types' - /// default-initialization semantics - /// and may be less efficient than no initialization, it is needed to provide proper - /// value-initialization semantics. - HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {} - - /// Conversion constructor. - /// \param rhs float to convert - /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding - explicit half(float rhs) - : data_(static_cast(detail::float2half(rhs))) - { - } - - /// Conversion to single-precision. - /// \return single precision value representing expression value - operator float() const { return detail::half2float(data_); } - - /// Assignment operator. - /// \param rhs single-precision value to copy from - /// \return reference to this half - /// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding - half& operator=(float rhs) - { - data_ = static_cast(detail::float2half(rhs)); - return *this; - } - - /// \} - /// \name Arithmetic updates - /// \{ - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to add - /// \return reference to this half - /// \exception FE_... according to operator+(half,half) - half& operator+=(half rhs) { return *this = *this + rhs; } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to subtract - /// \return reference to this half - /// \exception FE_... according to operator-(half,half) - half& operator-=(half rhs) { return *this = *this - rhs; } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to multiply with - /// \return reference to this half - /// \exception FE_... according to operator*(half,half) - half& operator*=(half rhs) { return *this = *this * rhs; } - - /// Arithmetic assignment. - /// \tparam T type of concrete half expression - /// \param rhs half expression to divide by - /// \return reference to this half - /// \exception FE_... according to operator/(half,half) - half& operator/=(half rhs) { return *this = *this / rhs; } - - /// Arithmetic assignment. - /// \param rhs single-precision value to add - /// \return reference to this half - /// \exception FE_... according to operator=() - half& operator+=(float rhs) { return *this = *this + rhs; } - - /// Arithmetic assignment. - /// \param rhs single-precision value to subtract - /// \return reference to this half - /// \exception FE_... according to operator=() - half& operator-=(float rhs) { return *this = *this - rhs; } - - /// Arithmetic assignment. - /// \param rhs single-precision value to multiply with - /// \return reference to this half - /// \exception FE_... according to operator=() - half& operator*=(float rhs) { return *this = *this * rhs; } - - /// Arithmetic assignment. - /// \param rhs single-precision value to divide by - /// \return reference to this half - /// \exception FE_... according to operator=() - half& operator/=(float rhs) { return *this = *this / rhs; } - - /// \} - /// \name Increment and decrement - /// \{ - - /// Prefix increment. - /// \return incremented half value - /// \exception FE_... according to operator+(half,half) - half& operator++() { return *this = *this + half(detail::binary, 0x3C00); } - - /// Prefix decrement. - /// \return decremented half value - /// \exception FE_... according to operator-(half,half) - half& operator--() { return *this = *this + half(detail::binary, 0xBC00); } - - /// Postfix increment. - /// \return non-incremented half value - /// \exception FE_... according to operator+(half,half) - half operator++(int) - { - half out(*this); - ++*this; - return out; - } - - /// Postfix decrement. - /// \return non-decremented half value - /// \exception FE_... according to operator-(half,half) - 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, unsigned int bits) HALF_NOEXCEPT - : data_(static_cast(bits)) - { - } - - /// Internal binary representation - detail::uint16 data_; - -#ifndef HALF_DOXYGEN_ONLY - friend HALF_CONSTEXPR_NOERR bool operator==(half, half); - friend HALF_CONSTEXPR_NOERR bool operator!=(half, half); - friend HALF_CONSTEXPR_NOERR bool operator<(half, half); - friend HALF_CONSTEXPR_NOERR bool operator>(half, half); - friend HALF_CONSTEXPR_NOERR bool operator<=(half, half); - friend HALF_CONSTEXPR_NOERR bool operator>=(half, half); - friend HALF_CONSTEXPR half operator-(half); - friend half operator+(half, half); - friend half operator-(half, half); - friend half operator*(half, half); - friend half operator/(half, half); - template - friend std::basic_ostream& operator<<(std::basic_ostream&, half); - template - friend std::basic_istream& operator>>(std::basic_istream&, half&); - friend HALF_CONSTEXPR half fabs(half); - friend half fmod(half, half); - friend half remainder(half, half); - friend half remquo(half, half, int*); - friend half fma(half, half, half); - friend HALF_CONSTEXPR_NOERR half fmax(half, half); - friend HALF_CONSTEXPR_NOERR half fmin(half, half); - friend half fdim(half, half); - friend half nanh(const char*); - friend half exp(half); - friend half exp2(half); - friend half expm1(half); - friend half log(half); - friend half log10(half); - friend half log2(half); - friend half log1p(half); - friend half sqrt(half); - friend half cbrt(half); - friend half hypot(half, half); - friend half hypot(half, half, half); - friend half pow(half, half); - friend void sincos(half, half*, half*); - friend half sin(half); - friend half cos(half); - friend half tan(half); - friend half asin(half); - friend half acos(half); - friend half atan(half); - friend half atan2(half, half); - friend half sinh(half); - friend half cosh(half); - friend half tanh(half); - friend half asinh(half); - friend half acosh(half); - friend half atanh(half); - friend half erf(half); - friend half erfc(half); - friend half lgamma(half); - friend half tgamma(half); - friend half ceil(half); - friend half floor(half); - friend half trunc(half); - friend half round(half); - friend long lround(half); - friend half rint(half); - friend long lrint(half); - friend half nearbyint(half); -#ifdef HALF_ENABLE_CPP11_LONG_LONG - friend long long llround(half); - friend long long llrint(half); -#endif - friend half frexp(half, int*); - friend half scalbln(half, long); - friend half modf(half, half*); - friend int ilogb(half); - friend half logb(half); - friend half nextafter(half, half); - friend half nexttoward(half, long double); - friend HALF_CONSTEXPR half copysign(half, half); - friend HALF_CONSTEXPR int fpclassify(half); - friend HALF_CONSTEXPR bool isfinite(half); - friend HALF_CONSTEXPR bool isinf(half); - friend HALF_CONSTEXPR bool isnan(half); - friend HALF_CONSTEXPR bool isnormal(half); - friend HALF_CONSTEXPR bool signbit(half); - friend HALF_CONSTEXPR bool isgreater(half, half); - friend HALF_CONSTEXPR bool isgreaterequal(half, half); - friend HALF_CONSTEXPR bool isless(half, half); - friend HALF_CONSTEXPR bool islessequal(half, half); - friend HALF_CONSTEXPR bool islessgreater(half, half); - 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 -#endif -}; - -#if HALF_ENABLE_CPP11_USER_LITERALS -namespace literal { -/// Half literal. -/// While this returns a properly rounded half-precision value, half literals can unfortunately not -/// be constant -/// expressions due to rather involved conversions. So don't expect this to be a literal literal -/// without involving -/// conversion operations at runtime. It is a convenience feature, not a performance optimization. -/// \param value literal value -/// \return half with of given value (possibly rounded) -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half operator"" _h(long double value) -{ - return half(detail::binary, detail::float2half(value)); -} -} // namespace literal -#endif - -namespace detail { -/// Helper class for half casts. -/// This class template has to be specialized for all valid cast arguments 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 -{ - static half cast(half arg) { return arg; } -}; -} // namespace detail -} // namespace half_float - -/// Extensions to the C++ standard library. -namespace std { -/// Numeric limits for half-precision floats. -/// **See also:** Documentation for -/// [std::numeric_limits](https://en.cppreference.com/w/cpp/types/numeric_limits) -template <> -class numeric_limits -{ - public: - /// Is template specialization. - static HALF_CONSTEXPR_CONST bool is_specialized = true; - - /// Supports signed values. - static HALF_CONSTEXPR_CONST bool is_signed = true; - - /// Is not an integer type. - static HALF_CONSTEXPR_CONST bool is_integer = false; - - /// Is not exact. - static HALF_CONSTEXPR_CONST bool is_exact = false; - - /// Doesn't provide modulo arithmetic. - static HALF_CONSTEXPR_CONST bool is_modulo = false; - - /// Has a finite set of values. - static HALF_CONSTEXPR_CONST bool is_bounded = true; - - /// 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 signaling NaNs. - static HALF_CONSTEXPR_CONST bool has_signaling_NaN = true; - - /// Supports subnormal values. - static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; - - /// Supports no denormalization detection. - static HALF_CONSTEXPR_CONST bool has_denorm_loss = false; - -#if HALF_ERRHANDLING_THROWS - static HALF_CONSTEXPR_CONST bool traps = true; -#else - /// Traps only if [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID) is - /// acitvated. - static HALF_CONSTEXPR_CONST bool traps = false; -#endif - - /// Does not support no pre-rounding underflow detection. - static HALF_CONSTEXPR_CONST bool tinyness_before = false; - - /// Rounding mode. - static HALF_CONSTEXPR_CONST float_round_style round_style = half_float::half::round_style; - - /// 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 1 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 in ULP (units in the last place). - 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); - } - - /// Signaling 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. -/// -/// **See also:** Documentation for [std::hash](https://en.cppreference.com/w/cpp/utility/hash) -template <> -struct hash -{ - /// 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()(arg.data_ & - -static_cast(arg.data_ != 0x8000)); - } -}; -#endif -} // namespace std - -namespace half_float { -/// \anchor compop -/// \name Comparison operators -/// \{ - -/// Comparison for equality. -/// \param x first operand -/// \param y second operand -/// \retval true if operands equal -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator==(half x, half y) -{ - return !detail::compsignal(x.data_, y.data_) && - (x.data_ == y.data_ || !((x.data_ | y.data_) & 0x7FFF)); -} - -/// Comparison for inequality. -/// \param x first operand -/// \param y second operand -/// \retval true if operands not equal -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator!=(half x, half y) -{ - return detail::compsignal(x.data_, y.data_) || - (x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF)); -} - -/// Comparison for less than. -/// \param x first operand -/// \param y second operand -/// \retval true if \a x less than \a y -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator<(half x, half y) -{ - return !detail::compsignal(x.data_, y.data_) && - ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) < - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)); -} - -/// Comparison for greater than. -/// \param x first operand -/// \param y second operand -/// \retval true if \a x greater than \a y -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator>(half x, half y) -{ - return !detail::compsignal(x.data_, y.data_) && - ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) > - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)); -} - -/// Comparison for less equal. -/// \param x first operand -/// \param y second operand -/// \retval true if \a x less equal \a y -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator<=(half x, half y) -{ - return !detail::compsignal(x.data_, y.data_) && - ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <= - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)); -} - -/// Comparison for greater equal. -/// \param x first operand -/// \param y second operand -/// \retval true if \a x greater equal \a y -/// \retval false else -/// \exception FE_INVALID if \a x or \a y is NaN -inline HALF_CONSTEXPR_NOERR bool operator>=(half x, half y) -{ - return !detail::compsignal(x.data_, y.data_) && - ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >= - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)); -} - -/// \} -/// \anchor arithmetics -/// \name Arithmetic operators -/// \{ - -/// Identity. -/// \param arg operand -/// \return unchanged operand -inline HALF_CONSTEXPR half operator+(half arg) { return arg; } - -/// Negation. -/// \param arg operand -/// \return negated operand -inline HALF_CONSTEXPR half operator-(half arg) { return half(detail::binary, arg.data_ ^ 0x8000); } - -/// Addition. -/// This operation is exact to rounding for all rounding modes. -/// \param x left operand -/// \param y right operand -/// \return sum of half expressions -/// \exception FE_INVALID if \a x and \a y are infinities with different signs or signaling NaNs -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half operator+(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half( - detail::binary, - detail::float2half(detail::half2float(x.data_) + - detail::half2float(y.data_))); -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF; - bool sub = ((x.data_ ^ y.data_) & 0x8000) != 0; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absy != 0x7C00) ? x.data_ - : (sub && absx == 0x7C00) ? detail::invalid() : y.data_); - if(!absx) - return absy ? y - : half(detail::binary, - (half::round_style == std::round_toward_neg_infinity) - ? (x.data_ | y.data_) - : (x.data_ & y.data_)); - if(!absy) - return x; - unsigned int sign = ((sub && absy > absx) ? y.data_ : x.data_) & 0x8000; - if(absy > absx) - std::swap(absx, absy); - int exp = (absx >> 10) + (absx <= 0x3FF), d = exp - (absy >> 10) - (absy <= 0x3FF), - mx = ((absx & 0x3FF) | ((absx > 0x3FF) << 10)) << 3, my; - if(d < 13) - { - my = ((absy & 0x3FF) | ((absy > 0x3FF) << 10)) << 3; - my = (my >> d) | ((my & ((1 << d) - 1)) != 0); - } - else - my = 1; - if(sub) - { - if(!(mx -= my)) - return half(detail::binary, - static_cast(half::round_style == std::round_toward_neg_infinity) - << 15); - for(; mx < 0x2000 && exp > 1; mx <<= 1, --exp) - ; - } - else - { - mx += my; - int i = mx >> 14; - if((exp += i) > 30) - return half(detail::binary, detail::overflow(sign)); - mx = (mx >> i) | (mx & i); - } - return half(detail::binary, - detail::rounded( - sign + ((exp - 1) << 10) + (mx >> 3), (mx >> 2) & 1, (mx & 0x3) != 0)); -#endif -} - -/// Subtraction. -/// This operation is exact to rounding for all rounding modes. -/// \param x left operand -/// \param y right operand -/// \return difference of half expressions -/// \exception FE_INVALID if \a x and \a y are infinities with equal signs or signaling NaNs -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half operator-(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half( - detail::binary, - detail::float2half(detail::half2float(x.data_) - - detail::half2float(y.data_))); -#else - return x + -y; -#endif -} - -/// Multiplication. -/// This operation is exact to rounding for all rounding modes. -/// \param x left operand -/// \param y right operand -/// \return product of half expressions -/// \exception FE_INVALID if multiplying 0 with infinity or if \a x or \a y is signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half operator*(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half( - detail::binary, - detail::float2half(detail::half2float(x.data_) * - detail::half2float(y.data_))); -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -16; - unsigned int sign = (x.data_ ^ y.data_) & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : ((absx == 0x7C00 && !absy) || (absy == 0x7C00 && !absx)) - ? detail::invalid() - : (sign | 0x7C00)); - if(!absx || !absy) - return half(detail::binary, sign); - for(; absx < 0x400; absx <<= 1, --exp) - ; - for(; absy < 0x400; absy <<= 1, --exp) - ; - detail::uint32 m = static_cast((absx & 0x3FF) | 0x400) * - static_cast((absy & 0x3FF) | 0x400); - int i = m >> 21, s = m & i; - exp += (absx >> 10) + (absy >> 10) + i; - if(exp > 29) - return half(detail::binary, detail::overflow(sign)); - else if(exp < -11) - return half(detail::binary, detail::underflow(sign)); - return half( - detail::binary, - detail::fixed2half(m >> i, exp, sign, s)); -#endif -} - -/// Division. -/// This operation is exact to rounding for all rounding modes. -/// \param x left operand -/// \param y right operand -/// \return quotient of half expressions -/// \exception FE_INVALID if dividing 0s or infinities with each other or if \a x or \a y is -/// signaling NaN -/// \exception FE_DIVBYZERO if dividing finite value by 0 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half operator/(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half( - detail::binary, - detail::float2half(detail::half2float(x.data_) / - detail::half2float(y.data_))); -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = 14; - unsigned int sign = (x.data_ ^ y.data_) & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absx == absy) ? detail::invalid() - : (sign | ((absx == 0x7C00) ? 0x7C00 : 0))); - if(!absx) - return half(detail::binary, absy ? sign : detail::invalid()); - if(!absy) - return half(detail::binary, detail::pole(sign)); - for(; absx < 0x400; absx <<= 1, --exp) - ; - for(; absy < 0x400; absy <<= 1, ++exp) - ; - detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400; - int i = mx < my; - exp += (absx >> 10) - (absy >> 10) - i; - if(exp > 29) - return half(detail::binary, detail::overflow(sign)); - else if(exp < -11) - return half(detail::binary, detail::underflow(sign)); - mx <<= 12 + i; - my <<= 1; - return half(detail::binary, - detail::fixed2half( - mx / my, exp, sign, mx % my != 0)); -#endif -} - -/// \} -/// \anchor streaming -/// \name Input and output -/// \{ - -/// Output operator. -/// This uses the built-in functionality for streaming out floating-point numbers. -/// \param out output stream to write into -/// \param arg half expression to write -/// \return reference to output stream -template -std::basic_ostream& operator<<(std::basic_ostream& out, half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return out << detail::half2float(arg.data_); -#else - return out << detail::half2float(arg.data_); -#endif -} - -/// Input operator. -/// This uses the built-in functionality for streaming in floating-point numbers, specifically -/// double precision floating -/// point numbers (unless overridden with [HALF_ARITHMETIC_TYPE](\ref HALF_ARITHMETIC_TYPE)). So the -/// input string is first -/// rounded to double precision using the underlying platform's current floating-point rounding mode -/// before being rounded -/// to half-precision using the library's half-precision rounding mode. -/// \param in input stream to read from -/// \param arg half to read into -/// \return reference to input stream -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -template -std::basic_istream& operator>>(std::basic_istream& in, half& arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - detail::internal_t f; -#else - double f; -#endif - if(in >> f) - arg.data_ = detail::float2half(f); - return in; -} - -/// \} -/// \anchor basic -/// \name Basic mathematical operations -/// \{ - -/// Absolute value. -/// **See also:** Documentation for -/// [std::fabs](https://en.cppreference.com/w/cpp/numeric/math/fabs). -/// \param arg operand -/// \return absolute value of \a arg -inline HALF_CONSTEXPR half fabs(half arg) { return half(detail::binary, arg.data_ & 0x7FFF); } - -/// Absolute value. -/// **See also:** Documentation for [std::abs](https://en.cppreference.com/w/cpp/numeric/math/fabs). -/// \param arg operand -/// \return absolute value of \a arg -inline HALF_CONSTEXPR half abs(half arg) { return fabs(arg); } - -/// Remainder of division. -/// **See also:** Documentation for -/// [std::fmod](https://en.cppreference.com/w/cpp/numeric/math/fmod). -/// \param x first operand -/// \param y second operand -/// \return remainder of floating-point division. -/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN -inline half fmod(half x, half y) -{ - unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absx == 0x7C00) ? detail::invalid() : x.data_); - if(!absy) - return half(detail::binary, detail::invalid()); - if(!absx) - return x; - if(absx == absy) - return half(detail::binary, sign); - return half(detail::binary, sign | detail::mod(absx, absy)); -} - -/// Remainder of division. -/// **See also:** Documentation for -/// [std::remainder](https://en.cppreference.com/w/cpp/numeric/math/remainder). -/// \param x first operand -/// \param y second operand -/// \return remainder of floating-point division. -/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN -inline half remainder(half x, half y) -{ - unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absx == 0x7C00) ? detail::invalid() : x.data_); - if(!absy) - return half(detail::binary, detail::invalid()); - if(absx == absy) - return half(detail::binary, sign); - return half(detail::binary, sign ^ detail::mod(absx, absy)); -} - -/// Remainder of division. -/// **See also:** Documentation for -/// [std::remquo](https://en.cppreference.com/w/cpp/numeric/math/remquo). -/// \param x first operand -/// \param y second operand -/// \param quo address to store some bits of quotient at -/// \return remainder of floating-point division. -/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN -inline half remquo(half x, half y, int* quo) -{ - unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, value = x.data_ & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absx == 0x7C00) ? detail::invalid() : (*quo = 0, x.data_)); - if(!absy) - return half(detail::binary, detail::invalid()); - bool qsign = ((value ^ y.data_) & 0x8000) != 0; - int q = 1; - if(absx != absy) - value ^= detail::mod(absx, absy, &q); - return *quo = qsign ? -q : q, half(detail::binary, value); -} - -/// Fused multiply add. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::fma](https://en.cppreference.com/w/cpp/numeric/math/fma). -/// \param x first operand -/// \param y second operand -/// \param z third operand -/// \return ( \a x * \a y ) + \a z rounded as one operation. -/// \exception FE_INVALID according to operator*() and operator+() unless any argument is a quiet -/// NaN and no argument is a signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding the final addition -inline half fma(half x, half y, half z) -{ -#ifdef HALF_ARITHMETIC_TYPE - detail::internal_t fx = detail::half2float(x.data_), - fy = detail::half2float(y.data_), - fz = detail::half2float(z.data_); -#if HALF_ENABLE_CPP11_CMATH && FP_FAST_FMA - return half(detail::binary, detail::float2half(std::fma(fx, fy, fz))); -#else - return half(detail::binary, detail::float2half(fx * fy + fz)); -#endif -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, exp = -15; - unsigned int sign = (x.data_ ^ y.data_) & 0x8000; - bool sub = ((sign ^ z.data_) & 0x8000) != 0; - if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00) - return (absx > 0x7C00 || absy > 0x7C00 || absz > 0x7C00) - ? half(detail::binary, detail::signal(x.data_, y.data_, z.data_)) - : (absx == 0x7C00) ? half(detail::binary, - (!absy || (sub && absz == 0x7C00)) ? detail::invalid() - : (sign | 0x7C00)) - : (absy == 0x7C00) ? half(detail::binary, - (!absx || (sub && absz == 0x7C00)) - ? detail::invalid() - : (sign | 0x7C00)) - : z; - if(!absx || !absy) - return absz - ? z - : half(detail::binary, - (half::round_style == std::round_toward_neg_infinity) ? (z.data_ | sign) - : (z.data_ & sign)); - for(; absx < 0x400; absx <<= 1, --exp) - ; - for(; absy < 0x400; absy <<= 1, --exp) - ; - detail::uint32 m = static_cast((absx & 0x3FF) | 0x400) * - static_cast((absy & 0x3FF) | 0x400); - int i = m >> 21; - exp += (absx >> 10) + (absy >> 10) + i; - m <<= 3 - i; - if(absz) - { - int expz = 0; - for(; absz < 0x400; absz <<= 1, --expz) - ; - expz += absz >> 10; - detail::uint32 mz = static_cast((absz & 0x3FF) | 0x400) << 13; - if(expz > exp || (expz == exp && mz > m)) - { - std::swap(m, mz); - std::swap(exp, expz); - if(sub) - sign = z.data_ & 0x8000; - } - int d = exp - expz; - mz = (d < 23) ? ((mz >> d) | ((mz & ((static_cast(1) << d) - 1)) != 0)) : 1; - if(sub) - { - m = m - mz; - if(!m) - return half( - detail::binary, - static_cast(half::round_style == std::round_toward_neg_infinity) - << 15); - for(; m < 0x800000; m <<= 1, --exp) - ; - } - else - { - m += mz; - i = m >> 24; - m = (m >> i) | (m & i); - exp += i; - } - } - if(exp > 30) - return half(detail::binary, detail::overflow(sign)); - else if(exp < -10) - return half(detail::binary, detail::underflow(sign)); - return half(detail::binary, - detail::fixed2half(m, exp - 1, sign)); -#endif -} - -/// Maximum of half expressions. -/// **See also:** Documentation for -/// [std::fmax](https://en.cppreference.com/w/cpp/numeric/math/fmax). -/// \param x first operand -/// \param y second operand -/// \return maximum of operands, ignoring quiet NaNs -/// \exception FE_INVALID if \a x or \a y is signaling NaN -inline HALF_CONSTEXPR_NOERR half fmax(half x, half y) -{ - return half(detail::binary, - (!isnan(y) && (isnan(x) || (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) < - (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))))) - ? detail::select(y.data_, x.data_) - : detail::select(x.data_, y.data_)); -} - -/// Minimum of half expressions. -/// **See also:** Documentation for -/// [std::fmin](https://en.cppreference.com/w/cpp/numeric/math/fmin). -/// \param x first operand -/// \param y second operand -/// \return minimum of operands, ignoring quiet NaNs -/// \exception FE_INVALID if \a x or \a y is signaling NaN -inline HALF_CONSTEXPR_NOERR half fmin(half x, half y) -{ - return half(detail::binary, - (!isnan(y) && (isnan(x) || (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) > - (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))))) - ? detail::select(y.data_, x.data_) - : detail::select(x.data_, y.data_)); -} - -/// Positive difference. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::fdim](https://en.cppreference.com/w/cpp/numeric/math/fdim). -/// \param x first operand -/// \param y second operand -/// \return \a x - \a y or 0 if difference negative -/// \exception FE_... according to operator-(half,half) -inline half fdim(half x, half y) -{ - if(isnan(x) || isnan(y)) - return half(detail::binary, detail::signal(x.data_, y.data_)); - return (x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) <= - (y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) - ? half(detail::binary, 0) - : (x - y); -} - -/// Get NaN value. -/// **See also:** Documentation for [std::nan](https://en.cppreference.com/w/cpp/numeric/math/nan). -/// \param arg string code -/// \return quiet NaN -inline half nanh(const char* arg) -{ - unsigned int value = 0x7FFF; - while(*arg) - value ^= static_cast(*arg++) & 0xFF; - return half(detail::binary, value); -} - -/// \} -/// \anchor exponential -/// \name Exponential functions -/// \{ - -/// Exponential function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::exp](https://en.cppreference.com/w/cpp/numeric/math/exp). -/// \param arg function argument -/// \return e raised to \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half exp(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::exp(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF; - if(!abs) - return half(detail::binary, 0x3C00); - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? (0x7C00 & ((arg.data_ >> 15) - 1U)) - : detail::signal(arg.data_)); - if(abs >= 0x4C80) - return half(detail::binary, - (arg.data_ & 0x8000) ? detail::underflow() - : detail::overflow()); - detail::uint32 m = detail::multiply64( - static_cast((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, 0xB8AA3B29); - int e = (abs >> 10) + (abs <= 0x3FF), exp; - if(e < 14) - { - exp = 0; - m >>= 14 - e; - } - else - { - exp = m >> (45 - e); - m = (m << (e - 14)) & 0x7FFFFFFF; - } - return half(detail::binary, - detail::exp2_post( - detail::exp2(m, 26), exp, (arg.data_ & 0x8000) != 0)); -#endif -} - -/// Binary exponential. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::exp2](https://en.cppreference.com/w/cpp/numeric/math/exp2). -/// \param arg function argument -/// \return 2 raised to \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half exp2(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::exp2(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF; - if(!abs) - return half(detail::binary, 0x3C00); - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? (0x7C00 & ((arg.data_ >> 15) - 1U)) - : detail::signal(arg.data_)); - if(abs >= 0x4E40) - return half(detail::binary, - (arg.data_ & 0x8000) ? detail::underflow() - : detail::overflow()); - int e = (abs >> 10) + (abs <= 0x3FF), exp = (abs & 0x3FF) + ((abs > 0x3FF) << 10); - detail::uint32 m = detail::exp2((static_cast(exp) << (6 + e)) & 0x7FFFFFFF, 28); - exp >>= 25 - e; - if(m == 0x80000000) - { - if(arg.data_ & 0x8000) - exp = -exp; - else if(exp > 15) - return half(detail::binary, detail::overflow()); - return half(detail::binary, - detail::fixed2half(m, exp + 14)); - } - return half(detail::binary, - detail::exp2_post(m, exp, (arg.data_ & 0x8000) != 0)); -#endif -} - -/// Exponential minus one. -/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for -/// `std::round_to_nearest` -/// and in <1% of inputs for any other rounding mode. -/// -/// **See also:** Documentation for -/// [std::expm1](https://en.cppreference.com/w/cpp/numeric/math/expm1). -/// \param arg function argument -/// \return e raised to \a arg and subtracted by 1 -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half expm1(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::expm1(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; - if(!abs) - return arg; - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? (0x7C00 + (sign >> 1)) : detail::signal(arg.data_)); - if(abs >= 0x4A00) - return half(detail::binary, - (arg.data_ & 0x8000) ? detail::rounded(0xBBFF, 1, 1) - : detail::overflow()); - detail::uint32 m = detail::multiply64( - static_cast((abs & 0x3FF) + ((abs > 0x3FF) << 10)) << 21, 0xB8AA3B29); - int e = (abs >> 10) + (abs <= 0x3FF), exp; - if(e < 14) - { - exp = 0; - m >>= 14 - e; - } - else - { - exp = m >> (45 - e); - m = (m << (e - 14)) & 0x7FFFFFFF; - } - m = detail::exp2(m); - if(sign) - { - int s = 0; - if(m > 0x80000000) - { - ++exp; - m = detail::divide64(0x80000000, m, s); - } - m = 0x80000000 - - ((m >> exp) | ((m & ((static_cast(1) << exp) - 1)) != 0) | s); - exp = 0; - } - else - m -= (exp < 31) ? (0x80000000 >> exp) : 1; - for(exp += 14; m < 0x80000000 && exp; m <<= 1, --exp) - ; - if(exp > 29) - return half(detail::binary, detail::overflow()); - return half(detail::binary, - detail::rounded( - sign + (exp << 10) + (m >> 21), (m >> 20) & 1, (m & 0xFFFFF) != 0)); -#endif -} - -/// Natural logarithm. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::log](https://en.cppreference.com/w/cpp/numeric/math/log). -/// \param arg function argument -/// \return logarithm of \a arg to base e -/// \exception FE_INVALID for signaling NaN or negative argument -/// \exception FE_DIVBYZERO for 0 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half log(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::log(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = -15; - if(!abs) - return half(detail::binary, detail::pole(0x8000)); - if(arg.data_ & 0x8000) - return half(detail::binary, - (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs >= 0x7C00) - return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += abs >> 10; - return half(detail::binary, - detail::log2_post( - detail::log2(static_cast((abs & 0x3FF) | 0x400) << 20, 27) + 8, - exp, - 17)); -#endif -} - -/// Common logarithm. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::log10](https://en.cppreference.com/w/cpp/numeric/math/log10). -/// \param arg function argument -/// \return logarithm of \a arg to base 10 -/// \exception FE_INVALID for signaling NaN or negative argument -/// \exception FE_DIVBYZERO for 0 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half log10(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::log10(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = -15; - if(!abs) - return half(detail::binary, detail::pole(0x8000)); - if(arg.data_ & 0x8000) - return half(detail::binary, - (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs >= 0x7C00) - return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); - switch(abs) - { - case 0x4900: return half(detail::binary, 0x3C00); - case 0x5640: return half(detail::binary, 0x4000); - case 0x63D0: return half(detail::binary, 0x4200); - case 0x70E2: return half(detail::binary, 0x4400); - } - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += abs >> 10; - return half(detail::binary, - detail::log2_post( - detail::log2(static_cast((abs & 0x3FF) | 0x400) << 20, 27) + 8, - exp, - 16)); -#endif -} - -/// Binary logarithm. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::log2](https://en.cppreference.com/w/cpp/numeric/math/log2). -/// \param arg function argument -/// \return logarithm of \a arg to base 2 -/// \exception FE_INVALID for signaling NaN or negative argument -/// \exception FE_DIVBYZERO for 0 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half log2(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::log2(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = -15, s = 0; - if(!abs) - return half(detail::binary, detail::pole(0x8000)); - if(arg.data_ & 0x8000) - return half(detail::binary, - (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs >= 0x7C00) - return (abs == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); - if(abs == 0x3C00) - return half(detail::binary, 0); - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += (abs >> 10); - if(!(abs & 0x3FF)) - { - unsigned int value = static_cast(exp < 0) << 15, m = std::abs(exp) << 6; - for(exp = 18; m < 0x400; m <<= 1, --exp) - ; - return half(detail::binary, value + (exp << 10) + m); - } - detail::uint32 ilog = exp, sign = detail::sign_mask(ilog), - m = (((ilog << 27) + - (detail::log2(static_cast((abs & 0x3FF) | 0x400) << 20, - 28) >> - 4)) ^ - sign) - - sign; - if(!m) - return half(detail::binary, 0); - for(exp = 14; m < 0x8000000 && exp; m <<= 1, --exp) - ; - for(; m > 0xFFFFFFF; m >>= 1, ++exp) - s |= m & 1; - return half( - detail::binary, - detail::fixed2half(m, exp, sign & 0x8000, s)); -#endif -} - -/// Natural logarithm plus one. -/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for -/// `std::round_to_nearest` -/// and in ~1% of inputs for any other rounding mode. -/// -/// **See also:** Documentation for -/// [std::log1p](https://en.cppreference.com/w/cpp/numeric/math/log1p). -/// \param arg function argument -/// \return logarithm of \a arg plus 1 to base e -/// \exception FE_INVALID for signaling NaN or argument <-1 -/// \exception FE_DIVBYZERO for -1 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half log1p(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::log1p(detail::half2float(arg.data_)))); -#else - if(arg.data_ >= 0xBC00) - return half(detail::binary, - (arg.data_ == 0xBC00) - ? detail::pole(0x8000) - : (arg.data_ <= 0xFC00) ? detail::invalid() : detail::signal(arg.data_)); - int abs = arg.data_ & 0x7FFF, exp = -15; - if(!abs || abs >= 0x7C00) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += abs >> 10; - detail::uint32 m = static_cast((abs & 0x3FF) | 0x400) << 20; - if(arg.data_ & 0x8000) - { - m = 0x40000000 - (m >> -exp); - for(exp = 0; m < 0x40000000; m <<= 1, --exp) - ; - } - else - { - if(exp < 0) - { - m = 0x40000000 + (m >> -exp); - exp = 0; - } - else - { - m += 0x40000000 >> exp; - int i = m >> 31; - m >>= i; - exp += i; - } - } - return half(detail::binary, - detail::log2_post(detail::log2(m), exp, 17)); -#endif -} - -/// \} -/// \anchor power -/// \name Power functions -/// \{ - -/// Square root. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::sqrt](https://en.cppreference.com/w/cpp/numeric/math/sqrt). -/// \param arg function argument -/// \return square root of \a arg -/// \exception FE_INVALID for signaling NaN and negative arguments -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half sqrt(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::sqrt(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = 15; - if(!abs || arg.data_ >= 0x7C00) - return half(detail::binary, - (abs > 0x7C00) ? detail::signal(arg.data_) - : (arg.data_ > 0x8000) ? detail::invalid() : arg.data_); - for(; abs < 0x400; abs <<= 1, --exp) - ; - detail::uint32 r = static_cast((abs & 0x3FF) | 0x400) << 10, - m = detail::sqrt<20>(r, exp += abs >> 10); - return half( - detail::binary, - detail::rounded((exp << 10) + (m & 0x3FF), r > m, r != 0)); -#endif -} - -/// Cubic root. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::cbrt](https://en.cppreference.com/w/cpp/numeric/math/cbrt). -/// \param arg function argument -/// \return cubic root of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half cbrt(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::cbrt(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = -15; - if(!abs || abs == 0x3C00 || abs >= 0x7C00) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - for(; abs < 0x400; abs <<= 1, --exp) - ; - detail::uint32 ilog = exp + (abs >> 10), sign = detail::sign_mask(ilog), f, - m = (((ilog << 27) + - (detail::log2(static_cast((abs & 0x3FF) | 0x400) << 20, - 24) >> - 4)) ^ - sign) - - sign; - for(exp = 2; m < 0x80000000; m <<= 1, --exp) - ; - m = detail::multiply64(m, 0xAAAAAAAB); - int i = m >> 31, s; - exp += i; - m <<= 1 - i; - if(exp < 0) - { - f = m >> -exp; - exp = 0; - } - else - { - f = (m << exp) & 0x7FFFFFFF; - exp = m >> (31 - exp); - } - m = detail::exp2(f, (half::round_style == std::round_to_nearest) ? 29 : 26); - if(sign) - { - if(m > 0x80000000) - { - m = detail::divide64(0x80000000, m, s); - ++exp; - } - exp = -exp; - } - return half(detail::binary, - (half::round_style == std::round_to_nearest) - ? detail::fixed2half( - m, exp + 14, arg.data_ & 0x8000) - : detail::fixed2half( - (m + 0x80) >> 8, exp + 14, arg.data_ & 0x8000)); -#endif -} - -/// Hypotenuse function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot). -/// \param x first argument -/// \param y second argument -/// \return square root of sum of squares without internal over- or underflows -/// \exception FE_INVALID if \a x or \a y is signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root -inline half hypot(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - detail::internal_t fx = detail::half2float(x.data_), - fy = detail::half2float(y.data_); -#if HALF_ENABLE_CPP11_CMATH - return half(detail::binary, detail::float2half(std::hypot(fx, fy))); -#else - return half(detail::binary, - detail::float2half(std::sqrt(fx * fx + fy * fy))); -#endif -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0; - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx == 0x7C00) ? detail::select(0x7C00, y.data_) - : (absy == 0x7C00) ? detail::select(0x7C00, x.data_) - : detail::signal(x.data_, y.data_)); - if(!absx) - return half(detail::binary, absy ? detail::check_underflow(absy) : 0); - if(!absy) - return half(detail::binary, detail::check_underflow(absx)); - if(absy > absx) - std::swap(absx, absy); - for(; absx < 0x400; absx <<= 1, --expx) - ; - for(; absy < 0x400; absy <<= 1, --expy) - ; - detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400; - mx *= mx; - my *= my; - int ix = mx >> 21, iy = my >> 21; - expx = 2 * (expx + (absx >> 10)) - 15 + ix; - expy = 2 * (expy + (absy >> 10)) - 15 + iy; - mx <<= 10 - ix; - my <<= 10 - iy; - int d = expx - expy; - my = (d < 30) ? ((my >> d) | ((my & ((static_cast(1) << d) - 1)) != 0)) : 1; - return half(detail::binary, detail::hypot_post(mx + my, expx)); -#endif -} - -/// Hypotenuse function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot). -/// \param x first argument -/// \param y second argument -/// \param z third argument -/// \return square root of sum of squares without internal over- or underflows -/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root -inline half hypot(half x, half y, half z) -{ -#ifdef HALF_ARITHMETIC_TYPE - detail::internal_t fx = detail::half2float(x.data_), - fy = detail::half2float(y.data_), - fz = detail::half2float(z.data_); - return half(detail::binary, - detail::float2half(std::sqrt(fx * fx + fy * fy + fz * fz))); -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, expx = 0, - expy = 0, expz = 0; - if(!absx) - return hypot(y, z); - if(!absy) - return hypot(x, z); - if(!absz) - return hypot(x, y); - if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00) - return half(detail::binary, - (absx == 0x7C00) - ? detail::select(0x7C00, detail::select(y.data_, z.data_)) - : (absy == 0x7C00) - ? detail::select(0x7C00, detail::select(x.data_, z.data_)) - : (absz == 0x7C00) - ? detail::select(0x7C00, detail::select(x.data_, y.data_)) - : detail::signal(x.data_, y.data_, z.data_)); - if(absz > absy) - std::swap(absy, absz); - if(absy > absx) - std::swap(absx, absy); - if(absz > absy) - std::swap(absy, absz); - for(; absx < 0x400; absx <<= 1, --expx) - ; - for(; absy < 0x400; absy <<= 1, --expy) - ; - for(; absz < 0x400; absz <<= 1, --expz) - ; - detail::uint32 mx = (absx & 0x3FF) | 0x400, my = (absy & 0x3FF) | 0x400, - mz = (absz & 0x3FF) | 0x400; - mx *= mx; - my *= my; - mz *= mz; - int ix = mx >> 21, iy = my >> 21, iz = mz >> 21; - expx = 2 * (expx + (absx >> 10)) - 15 + ix; - expy = 2 * (expy + (absy >> 10)) - 15 + iy; - expz = 2 * (expz + (absz >> 10)) - 15 + iz; - mx <<= 10 - ix; - my <<= 10 - iy; - mz <<= 10 - iz; - int d = expy - expz; - mz = (d < 30) ? ((mz >> d) | ((mz & ((static_cast(1) << d) - 1)) != 0)) : 1; - my += mz; - if(my & 0x80000000) - { - my = (my >> 1) | (my & 1); - if(++expy > expx) - { - std::swap(mx, my); - std::swap(expx, expy); - } - } - d = expx - expy; - my = (d < 30) ? ((my >> d) | ((my & ((static_cast(1) << d) - 1)) != 0)) : 1; - return half(detail::binary, detail::hypot_post(mx + my, expx)); -#endif -} - -/// Power function. -/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in -/// ~0.00025% of inputs. -/// -/// **See also:** Documentation for [std::pow](https://en.cppreference.com/w/cpp/numeric/math/pow). -/// \param x base -/// \param y exponent -/// \return \a x raised to \a y -/// \exception FE_INVALID if \a x or \a y is signaling NaN or if \a x is finite an negative and \a y -/// is finite and not integral -/// \exception FE_DIVBYZERO if \a x is 0 and \a y is negative -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half pow(half x, half y) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::pow(detail::half2float(x.data_), - detail::half2float(y.data_)))); -#else - int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -15; - if(!absy || x.data_ == 0x3C00) - return half(detail::binary, - detail::select(0x3C00, (x.data_ == 0x3C00) ? y.data_ : x.data_)); - bool is_int = absy >= 0x6400 || (absy >= 0x3C00 && !(absy & ((1 << (25 - (absy >> 10))) - 1))); - unsigned int sign = - x.data_ & - (static_cast((absy < 0x6800) && is_int && ((absy >> (25 - (absy >> 10))) & 1)) - << 15); - if(absx >= 0x7C00 || absy >= 0x7C00) - return half(detail::binary, - (absx > 0x7C00 || absy > 0x7C00) - ? detail::signal(x.data_, y.data_) - : (absy == 0x7C00) - ? ((absx == 0x3C00) - ? 0x3C00 - : (!absx && y.data_ == 0xFC00) - ? detail::pole() - : (0x7C00 & -((y.data_ >> 15) ^ (absx > 0x3C00)))) - : (sign | (0x7C00 & ((y.data_ >> 15) - 1U)))); - if(!absx) - return half(detail::binary, (y.data_ & 0x8000) ? detail::pole(sign) : sign); - if((x.data_ & 0x8000) && !is_int) - return half(detail::binary, detail::invalid()); - if(x.data_ == 0xBC00) - return half(detail::binary, sign | 0x3C00); - if(y.data_ == 0x3800) - return sqrt(x); - if(y.data_ == 0x3C00) - return half(detail::binary, detail::check_underflow(x.data_)); - if(y.data_ == 0x4000) - return x * x; - for(; absx < 0x400; absx <<= 1, --exp) - ; - detail::uint32 ilog = exp + (absx >> 10), msign = detail::sign_mask(ilog), f, - m = (((ilog << 27) + - ((detail::log2(static_cast((absx & 0x3FF) | 0x400) << 20) + - 8) >> - 4)) ^ - msign) - - msign; - for(exp = -11; m < 0x80000000; m <<= 1, --exp) - ; - for(; absy < 0x400; absy <<= 1, --exp) - ; - m = detail::multiply64(m, static_cast((absy & 0x3FF) | 0x400) << 21); - int i = m >> 31; - exp += (absy >> 10) + i; - m <<= 1 - i; - if(exp < 0) - { - f = m >> -exp; - exp = 0; - } - else - { - f = (m << exp) & 0x7FFFFFFF; - exp = m >> (31 - exp); - } - return half(detail::binary, - detail::exp2_post( - detail::exp2(f), exp, ((msign & 1) ^ (y.data_ >> 15)) != 0, sign)); -#endif -} - -/// \} -/// \anchor trigonometric -/// \name Trigonometric functions -/// \{ - -/// Compute sine and cosine simultaneously. -/// This returns the same results as sin() and cos() but is faster than calling each function -/// individually. -/// -/// This function is exact to rounding for all rounding modes. -/// \param arg function argument -/// \param sin variable to take sine of \a arg -/// \param cos variable to take cosine of \a arg -/// \exception FE_INVALID for signaling NaN or infinity -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline void sincos(half arg, half* sin, half* cos) -{ -#ifdef HALF_ARITHMETIC_TYPE - detail::internal_t f = detail::half2float(arg.data_); - *sin = half(detail::binary, detail::float2half(std::sin(f))); - *cos = half(detail::binary, detail::float2half(std::cos(f))); -#else - int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15, k; - if(abs >= 0x7C00) - *sin = *cos = - half(detail::binary, (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - else if(!abs) - { - *sin = arg; - *cos = half(detail::binary, 0x3C00); - } - else if(abs < 0x2500) - { - *sin = half(detail::binary, detail::rounded(arg.data_ - 1, 1, 1)); - *cos = half(detail::binary, detail::rounded(0x3BFF, 1, 1)); - } - else - { - if(half::round_style != std::round_to_nearest) - { - switch(abs) - { - case 0x48B7: - *sin = half( - detail::binary, - detail::rounded((~arg.data_ & 0x8000) | 0x1D07, 1, 1)); - *cos = half(detail::binary, detail::rounded(0xBBFF, 1, 1)); - return; - case 0x598C: - *sin = half( - detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x3BFF, 1, 1)); - *cos = half(detail::binary, detail::rounded(0x80FC, 1, 1)); - return; - case 0x6A64: - *sin = half( - detail::binary, - detail::rounded((~arg.data_ & 0x8000) | 0x3BFE, 1, 1)); - *cos = half(detail::binary, detail::rounded(0x27FF, 1, 1)); - return; - case 0x6D8C: - *sin = half( - detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x0FE6, 1, 1)); - *cos = half(detail::binary, detail::rounded(0x3BFF, 1, 1)); - return; - } - } - std::pair sc = - detail::sincos(detail::angle_arg(abs, k), 28); - switch(k & 3) - { - case 1: sc = std::make_pair(sc.second, -sc.first); break; - case 2: sc = std::make_pair(-sc.first, -sc.second); break; - case 3: sc = std::make_pair(-sc.second, sc.first); break; - } - *sin = half(detail::binary, - detail::fixed2half( - (sc.first ^ -static_cast(sign)) + sign)); - *cos = half(detail::binary, - detail::fixed2half(sc.second)); - } -#endif -} - -/// Sine function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::sin](https://en.cppreference.com/w/cpp/numeric/math/sin). -/// \param arg function argument -/// \return sine value of \a arg -/// \exception FE_INVALID for signaling NaN or infinity -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half sin(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::sin(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, k; - if(!abs) - return arg; - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs < 0x2900) - return half(detail::binary, detail::rounded(arg.data_ - 1, 1, 1)); - if(half::round_style != std::round_to_nearest) - switch(abs) - { - case 0x48B7: - return half( - detail::binary, - detail::rounded((~arg.data_ & 0x8000) | 0x1D07, 1, 1)); - case 0x6A64: - return half( - detail::binary, - detail::rounded((~arg.data_ & 0x8000) | 0x3BFE, 1, 1)); - case 0x6D8C: - return half( - detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x0FE6, 1, 1)); - } - std::pair sc = detail::sincos(detail::angle_arg(abs, k), 28); - detail::uint32 sign = -static_cast(((k >> 1) & 1) ^ (arg.data_ >> 15)); - return half(detail::binary, - detail::fixed2half( - (((k & 1) ? sc.second : sc.first) ^ sign) - sign)); -#endif -} - -/// Cosine function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::cos](https://en.cppreference.com/w/cpp/numeric/math/cos). -/// \param arg function argument -/// \return cosine value of \a arg -/// \exception FE_INVALID for signaling NaN or infinity -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half cos(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::cos(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, k; - if(!abs) - return half(detail::binary, 0x3C00); - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs < 0x2500) - return half(detail::binary, detail::rounded(0x3BFF, 1, 1)); - if(half::round_style != std::round_to_nearest && abs == 0x598C) - return half(detail::binary, detail::rounded(0x80FC, 1, 1)); - std::pair sc = detail::sincos(detail::angle_arg(abs, k), 28); - detail::uint32 sign = -static_cast(((k >> 1) ^ k) & 1); - return half(detail::binary, - detail::fixed2half( - (((k & 1) ? sc.first : sc.second) ^ sign) - sign)); -#endif -} - -/// Tangent function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for [std::tan](https://en.cppreference.com/w/cpp/numeric/math/tan). -/// \param arg function argument -/// \return tangent value of \a arg -/// \exception FE_INVALID for signaling NaN or infinity -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half tan(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::tan(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = 13, k; - if(!abs) - return arg; - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs < 0x2700) - return half(detail::binary, detail::rounded(arg.data_, 0, 1)); - if(half::round_style != std::round_to_nearest) - switch(abs) - { - case 0x658C: - return half( - detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x07E6, 1, 1)); - case 0x7330: - return half( - detail::binary, - detail::rounded((~arg.data_ & 0x8000) | 0x4B62, 1, 1)); - } - std::pair sc = detail::sincos(detail::angle_arg(abs, k), 30); - if(k & 1) - sc = std::make_pair(-sc.second, sc.first); - detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second); - detail::uint32 my = (sc.first ^ signy) - signy, mx = (sc.second ^ signx) - signx; - for(; my < 0x80000000; my <<= 1, --exp) - ; - for(; mx < 0x80000000; mx <<= 1, ++exp) - ; - return half( - detail::binary, - detail::tangent_post(my, mx, exp, (signy ^ signx ^ arg.data_) & 0x8000)); -#endif -} - -/// Arc sine. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::asin](https://en.cppreference.com/w/cpp/numeric/math/asin). -/// \param arg function argument -/// \return arc sine value of \a arg -/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half asin(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::asin(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; - if(!abs) - return arg; - if(abs >= 0x3C00) - return half(detail::binary, - (abs > 0x7C00) - ? detail::signal(arg.data_) - : (abs > 0x3C00) - ? detail::invalid() - : detail::rounded(sign | 0x3E48, 0, 1)); - if(abs < 0x2900) - return half(detail::binary, detail::rounded(arg.data_, 0, 1)); - if(half::round_style != std::round_to_nearest && (abs == 0x2B44 || abs == 0x2DC3)) - return half(detail::binary, detail::rounded(arg.data_ + 1, 1, 1)); - std::pair sc = detail::atan2_args(abs); - detail::uint32 m = - detail::atan2(sc.first, sc.second, (half::round_style == std::round_to_nearest) ? 27 : 26); - return half(detail::binary, - detail::fixed2half(m, 14, sign)); -#endif -} - -/// Arc cosine function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::acos](https://en.cppreference.com/w/cpp/numeric/math/acos). -/// \param arg function argument -/// \return arc cosine value of \a arg -/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half acos(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::acos(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15; - if(!abs) - return half(detail::binary, detail::rounded(0x3E48, 0, 1)); - if(abs >= 0x3C00) - return half(detail::binary, - (abs > 0x7C00) - ? detail::signal(arg.data_) - : (abs > 0x3C00) - ? detail::invalid() - : sign ? detail::rounded(0x4248, 0, 1) : 0); - std::pair cs = detail::atan2_args(abs); - detail::uint32 m = detail::atan2(cs.second, cs.first, 28); - return half(detail::binary, - detail::fixed2half( - sign ? (0xC90FDAA2 - m) : m, 15, 0, sign)); -#endif -} - -/// Arc tangent function. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::atan](https://en.cppreference.com/w/cpp/numeric/math/atan). -/// \param arg function argument -/// \return arc tangent value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half atan(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::atan(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; - if(!abs) - return arg; - if(abs >= 0x7C00) - return half(detail::binary, - (abs == 0x7C00) ? detail::rounded(sign | 0x3E48, 0, 1) - : detail::signal(arg.data_)); - if(abs <= 0x2700) - return half(detail::binary, detail::rounded(arg.data_ - 1, 1, 1)); - int exp = (abs >> 10) + (abs <= 0x3FF); - detail::uint32 my = (abs & 0x3FF) | ((abs > 0x3FF) << 10); - detail::uint32 m = (exp > 15) - ? detail::atan2(my << 19, - 0x20000000 >> (exp - 15), - (half::round_style == std::round_to_nearest) ? 26 : 24) - : detail::atan2(my << (exp + 4), - 0x20000000, - (half::round_style == std::round_to_nearest) ? 30 : 28); - return half(detail::binary, - detail::fixed2half(m, 14, sign)); -#endif -} - -/// Arc tangent function. -/// This function may be 1 ULP off the correctly rounded exact result in ~0.005% of inputs for -/// `std::round_to_nearest`, -/// in ~0.1% of inputs for `std::round_toward_zero` and in ~0.02% of inputs for any other rounding -/// mode. -/// -/// **See also:** Documentation for -/// [std::atan2](https://en.cppreference.com/w/cpp/numeric/math/atan2). -/// \param y numerator -/// \param x denominator -/// \return arc tangent value -/// \exception FE_INVALID if \a x or \a y is signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half atan2(half y, half x) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::atan2(detail::half2float(y.data_), - detail::half2float(x.data_)))); -#else - unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, signx = x.data_ >> 15, - signy = y.data_ & 0x8000; - if(absx >= 0x7C00 || absy >= 0x7C00) - { - if(absx > 0x7C00 || absy > 0x7C00) - return half(detail::binary, detail::signal(x.data_, y.data_)); - if(absy == 0x7C00) - return half(detail::binary, - (absx < 0x7C00) - ? detail::rounded(signy | 0x3E48, 0, 1) - : signx - ? detail::rounded(signy | 0x40B6, 0, 1) - : detail::rounded(signy | 0x3A48, 0, 1)); - return (x.data_ == 0x7C00) - ? half(detail::binary, signy) - : half(detail::binary, - detail::rounded(signy | 0x4248, 0, 1)); - } - if(!absy) - return signx ? half(detail::binary, - detail::rounded(signy | 0x4248, 0, 1)) - : y; - if(!absx) - return half(detail::binary, detail::rounded(signy | 0x3E48, 0, 1)); - int d = (absy >> 10) + (absy <= 0x3FF) - (absx >> 10) - (absx <= 0x3FF); - if(d > (signx ? 18 : 12)) - return half(detail::binary, detail::rounded(signy | 0x3E48, 0, 1)); - if(signx && d < -11) - return half(detail::binary, detail::rounded(signy | 0x4248, 0, 1)); - if(!signx && d < ((half::round_style == std::round_toward_zero) ? -15 : -9)) - { - for(; absy < 0x400; absy <<= 1, --d) - ; - detail::uint32 mx = ((absx << 1) & 0x7FF) | 0x800, my = ((absy << 1) & 0x7FF) | 0x800; - int i = my < mx; - d -= i; - if(d < -25) - return half(detail::binary, detail::underflow(signy)); - my <<= 11 + i; - return half(detail::binary, - detail::fixed2half( - my / mx, d + 14, signy, my % mx != 0)); - } - detail::uint32 m = detail::atan2( - ((absy & 0x3FF) | ((absy > 0x3FF) << 10)) << (19 + ((d < 0) ? d : (d > 0) ? 0 : -1)), - ((absx & 0x3FF) | ((absx > 0x3FF) << 10)) << (19 - ((d > 0) ? d : (d < 0) ? 0 : 1))); - return half(detail::binary, - detail::fixed2half( - signx ? (0xC90FDAA2 - m) : m, 15, signy, signx)); -#endif -} - -/// \} -/// \anchor hyperbolic -/// \name Hyperbolic functions -/// \{ - -/// Hyperbolic sine. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::sinh](https://en.cppreference.com/w/cpp/numeric/math/sinh). -/// \param arg function argument -/// \return hyperbolic sine value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half sinh(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::sinh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp; - if(!abs || abs >= 0x7C00) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - if(abs <= 0x2900) - return half(detail::binary, detail::rounded(arg.data_, 0, 1)); - std::pair mm = - detail::hyperbolic_args(abs, exp, (half::round_style == std::round_to_nearest) ? 29 : 27); - detail::uint32 m = mm.first - mm.second; - for(exp += 13; m < 0x80000000 && exp; m <<= 1, --exp) - ; - unsigned int sign = arg.data_ & 0x8000; - if(exp > 29) - return half(detail::binary, detail::overflow(sign)); - return half(detail::binary, - detail::fixed2half(m, exp, sign)); -#endif -} - -/// Hyperbolic cosine. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::cosh](https://en.cppreference.com/w/cpp/numeric/math/cosh). -/// \param arg function argument -/// \return hyperbolic cosine value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half cosh(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::cosh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp; - if(!abs) - return half(detail::binary, 0x3C00); - if(abs >= 0x7C00) - return half(detail::binary, (abs > 0x7C00) ? detail::signal(arg.data_) : 0x7C00); - std::pair mm = - detail::hyperbolic_args(abs, exp, (half::round_style == std::round_to_nearest) ? 23 : 26); - detail::uint32 m = mm.first + mm.second, i = (~m & 0xFFFFFFFF) >> 31; - m = (m >> i) | (m & i) | 0x80000000; - if((exp += 13 + i) > 29) - return half(detail::binary, detail::overflow()); - return half(detail::binary, - detail::fixed2half(m, exp)); -#endif -} - -/// Hyperbolic tangent. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::tanh](https://en.cppreference.com/w/cpp/numeric/math/tanh). -/// \param arg function argument -/// \return hyperbolic tangent value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half tanh(half arg) -{ -#ifdef HALF_ARITHMETIC_TYPE - return half(detail::binary, - detail::float2half( - std::tanh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp; - if(!abs) - return arg; - if(abs >= 0x7C00) - return half(detail::binary, - (abs > 0x7C00) ? detail::signal(arg.data_) : (arg.data_ - 0x4000)); - if(abs >= 0x4500) - return half(detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x3BFF, 1, 1)); - if(abs < 0x2700) - return half(detail::binary, detail::rounded(arg.data_ - 1, 1, 1)); - if(half::round_style != std::round_to_nearest && abs == 0x2D3F) - return half(detail::binary, detail::rounded(arg.data_ - 3, 0, 1)); - std::pair mm = detail::hyperbolic_args(abs, exp, 27); - detail::uint32 my = mm.first - mm.second - (half::round_style != std::round_to_nearest), - mx = mm.first + mm.second, i = (~mx & 0xFFFFFFFF) >> 31; - for(exp = 13; my < 0x80000000; my <<= 1, --exp) - ; - mx = (mx >> i) | 0x80000000; - return half(detail::binary, - detail::tangent_post(my, mx, exp - i, arg.data_ & 0x8000)); -#endif -} - -/// Hyperbolic area sine. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::asinh](https://en.cppreference.com/w/cpp/numeric/math/asinh). -/// \param arg function argument -/// \return area sine value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half asinh(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::asinh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF; - if(!abs || abs >= 0x7C00) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - if(abs <= 0x2900) - return half(detail::binary, detail::rounded(arg.data_ - 1, 1, 1)); - if(half::round_style != std::round_to_nearest) - switch(abs) - { - case 0x32D4: - return half(detail::binary, - detail::rounded(arg.data_ - 13, 1, 1)); - case 0x3B5B: - return half(detail::binary, - detail::rounded(arg.data_ - 197, 1, 1)); - } - return half(detail::binary, detail::area(arg.data_)); -#endif -} - -/// Hyperbolic area cosine. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::acosh](https://en.cppreference.com/w/cpp/numeric/math/acosh). -/// \param arg function argument -/// \return area cosine value of \a arg -/// \exception FE_INVALID for signaling NaN or arguments <1 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half acosh(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::acosh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF; - if((arg.data_ & 0x8000) || abs < 0x3C00) - return half(detail::binary, - (abs <= 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs == 0x3C00) - return half(detail::binary, 0); - if(arg.data_ >= 0x7C00) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - return half(detail::binary, detail::area(arg.data_)); -#endif -} - -/// Hyperbolic area tangent. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::atanh](https://en.cppreference.com/w/cpp/numeric/math/atanh). -/// \param arg function argument -/// \return area tangent value of \a arg -/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1 -/// \exception FE_DIVBYZERO for +/-1 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half atanh(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::atanh(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF, exp = 0; - if(!abs) - return arg; - if(abs >= 0x3C00) - return half(detail::binary, - (abs == 0x3C00) - ? detail::pole(arg.data_ & 0x8000) - : (abs <= 0x7C00) ? detail::invalid() : detail::signal(arg.data_)); - if(abs < 0x2700) - return half(detail::binary, detail::rounded(arg.data_, 0, 1)); - detail::uint32 m = static_cast((abs & 0x3FF) | ((abs > 0x3FF) << 10)) - << ((abs >> 10) + (abs <= 0x3FF) + 6), - my = 0x80000000 + m, mx = 0x80000000 - m; - for(; mx < 0x80000000; mx <<= 1, ++exp) - ; - int i = my >= mx, s; - return half(detail::binary, - detail::log2_post( - detail::log2((detail::divide64(my >> i, mx, s) + 1) >> 1, 27) + 0x10, - exp + i - 1, - 16, - arg.data_ & 0x8000)); -#endif -} - -/// \} -/// \anchor special -/// \name Error and gamma functions -/// \{ - -/// Error function. -/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% -/// of inputs. -/// -/// **See also:** Documentation for [std::erf](https://en.cppreference.com/w/cpp/numeric/math/erf). -/// \param arg function argument -/// \return error function value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half erf(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::erf(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF; - if(!abs || abs >= 0x7C00) - return (abs >= 0x7C00) - ? half(detail::binary, - (abs == 0x7C00) ? (arg.data_ - 0x4000) : detail::signal(arg.data_)) - : arg; - if(abs >= 0x4200) - return half(detail::binary, - detail::rounded((arg.data_ & 0x8000) | 0x3BFF, 1, 1)); - return half(detail::binary, detail::erf(arg.data_)); -#endif -} - -/// Complementary error function. -/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% -/// of inputs. -/// -/// **See also:** Documentation for -/// [std::erfc](https://en.cppreference.com/w/cpp/numeric/math/erfc). -/// \param arg function argument -/// \return 1 minus error function value of \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half erfc(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::erfc(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; - if(abs >= 0x7C00) - return (abs >= 0x7C00) - ? half(detail::binary, (abs == 0x7C00) ? (sign >> 1) : detail::signal(arg.data_)) - : arg; - if(!abs) - return half(detail::binary, 0x3C00); - if(abs >= 0x4400) - return half( - detail::binary, - detail::rounded((sign >> 1) - (sign >> 15), sign >> 15, 1)); - return half(detail::binary, detail::erf(arg.data_)); -#endif -} - -/// Natural logarithm of gamma function. -/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in -/// ~0.025% of inputs. -/// -/// **See also:** Documentation for -/// [std::lgamma](https://en.cppreference.com/w/cpp/numeric/math/lgamma). -/// \param arg function argument -/// \return natural logarith of gamma function for \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_DIVBYZERO for 0 or negative integer arguments -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half lgamma(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::lgamma(detail::half2float(arg.data_)))); -#else - int abs = arg.data_ & 0x7FFF; - if(abs >= 0x7C00) - return half(detail::binary, (abs == 0x7C00) ? 0x7C00 : detail::signal(arg.data_)); - if(!abs || arg.data_ >= 0xE400 || - (arg.data_ >= 0xBC00 && !(abs & ((1 << (25 - (abs >> 10))) - 1)))) - return half(detail::binary, detail::pole()); - if(arg.data_ == 0x3C00 || arg.data_ == 0x4000) - return half(detail::binary, 0); - return half(detail::binary, detail::gamma(arg.data_)); -#endif -} - -/// Gamma function. -/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in -/// <0.25% of inputs. -/// -/// **See also:** Documentation for -/// [std::tgamma](https://en.cppreference.com/w/cpp/numeric/math/tgamma). -/// \param arg function argument -/// \return gamma function value of \a arg -/// \exception FE_INVALID for signaling NaN, negative infinity or negative integer arguments -/// \exception FE_DIVBYZERO for 0 -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half tgamma(half arg) -{ -#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH - return half(detail::binary, - detail::float2half( - std::tgamma(detail::half2float(arg.data_)))); -#else - unsigned int abs = arg.data_ & 0x7FFF; - if(!abs) - return half(detail::binary, detail::pole(arg.data_)); - if(abs >= 0x7C00) - return (arg.data_ == 0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_)); - if(arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs & ((1 << (25 - (abs >> 10))) - 1)))) - return half(detail::binary, detail::invalid()); - if(arg.data_ >= 0xCA80) - return half( - detail::binary, - detail::underflow((1 - ((abs >> (25 - (abs >> 10))) & 1)) << 15)); - if(arg.data_ <= 0x100 || (arg.data_ >= 0x4900 && arg.data_ < 0x8000)) - return half(detail::binary, detail::overflow()); - if(arg.data_ == 0x3C00) - return arg; - return half(detail::binary, detail::gamma(arg.data_)); -#endif -} - -/// \} -/// \anchor rounding -/// \name Rounding -/// \{ - -/// Nearest integer not less than half value. -/// **See also:** Documentation for -/// [std::ceil](https://en.cppreference.com/w/cpp/numeric/math/ceil). -/// \param arg half to round -/// \return nearest integer not less than \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded -inline half ceil(half arg) -{ - return half(detail::binary, - detail::integral(arg.data_)); -} - -/// Nearest integer not greater than half value. -/// **See also:** Documentation for -/// [std::floor](https://en.cppreference.com/w/cpp/numeric/math/floor). -/// \param arg half to round -/// \return nearest integer not greater than \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded -inline half floor(half arg) -{ - return half(detail::binary, - detail::integral(arg.data_)); -} - -/// Nearest integer not greater in magnitude than half value. -/// **See also:** Documentation for -/// [std::trunc](https://en.cppreference.com/w/cpp/numeric/math/trunc). -/// \param arg half to round -/// \return nearest integer not greater in magnitude than \a arg -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded -inline half trunc(half arg) -{ - return half(detail::binary, detail::integral(arg.data_)); -} - -/// Nearest integer. -/// **See also:** Documentation for -/// [std::round](https://en.cppreference.com/w/cpp/numeric/math/round). -/// \param arg half to round -/// \return nearest integer, rounded away from zero in half-way cases -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded -inline half round(half arg) -{ - return half(detail::binary, detail::integral(arg.data_)); -} - -/// Nearest integer. -/// **See also:** Documentation for -/// [std::lround](https://en.cppreference.com/w/cpp/numeric/math/round). -/// \param arg half to round -/// \return nearest integer, rounded away from zero in half-way cases -/// \exception FE_INVALID if value is not representable as `long` -inline long lround(half arg) -{ - return detail::half2int(arg.data_); -} - -/// Nearest integer using half's internal rounding mode. -/// **See also:** Documentation for -/// [std::rint](https://en.cppreference.com/w/cpp/numeric/math/rint). -/// \param arg half expression to round -/// \return nearest integer using default rounding mode -/// \exception FE_INVALID for signaling NaN -/// \exception FE_INEXACT if value had to be rounded -inline half rint(half arg) -{ - return half(detail::binary, detail::integral(arg.data_)); -} - -/// Nearest integer using half's internal rounding mode. -/// **See also:** Documentation for -/// [std::lrint](https://en.cppreference.com/w/cpp/numeric/math/rint). -/// \param arg half expression to round -/// \return nearest integer using default rounding mode -/// \exception FE_INVALID if value is not representable as `long` -/// \exception FE_INEXACT if value had to be rounded -inline long lrint(half arg) -{ - return detail::half2int(arg.data_); -} - -/// Nearest integer using half's internal rounding mode. -/// **See also:** Documentation for -/// [std::nearbyint](https://en.cppreference.com/w/cpp/numeric/math/nearbyint). -/// \param arg half expression to round -/// \return nearest integer using default rounding mode -/// \exception FE_INVALID for signaling NaN -inline half nearbyint(half arg) -{ - return half(detail::binary, detail::integral(arg.data_)); -} -#if HALF_ENABLE_CPP11_LONG_LONG -/// Nearest integer. -/// **See also:** Documentation for -/// [std::llround](https://en.cppreference.com/w/cpp/numeric/math/round). -/// \param arg half to round -/// \return nearest integer, rounded away from zero in half-way cases -/// \exception FE_INVALID if value is not representable as `long long` -inline long long llround(half arg) -{ - return detail::half2int(arg.data_); -} - -/// Nearest integer using half's internal rounding mode. -/// **See also:** Documentation for -/// [std::llrint](https://en.cppreference.com/w/cpp/numeric/math/rint). -/// \param arg half expression to round -/// \return nearest integer using default rounding mode -/// \exception FE_INVALID if value is not representable as `long long` -/// \exception FE_INEXACT if value had to be rounded -inline long long llrint(half arg) -{ - return detail::half2int(arg.data_); -} -#endif - -/// \} -/// \anchor float -/// \name Floating point manipulation -/// \{ - -/// Decompress floating-point number. -/// **See also:** Documentation for -/// [std::frexp](https://en.cppreference.com/w/cpp/numeric/math/frexp). -/// \param arg number to decompress -/// \param exp address to store exponent at -/// \return significant in range [0.5, 1) -/// \exception FE_INVALID for signaling NaN -inline half frexp(half arg, int* exp) -{ - *exp = 0; - unsigned int abs = arg.data_ & 0x7FFF; - if(abs >= 0x7C00 || !abs) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - for(; abs < 0x400; abs <<= 1, --*exp) - ; - *exp += (abs >> 10) - 14; - return half(detail::binary, (arg.data_ & 0x8000) | 0x3800 | (abs & 0x3FF)); -} - -/// Multiply by power of two. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::scalbln](https://en.cppreference.com/w/cpp/numeric/math/scalbn). -/// \param arg number to modify -/// \param exp power of two to multiply with -/// \return \a arg multplied by 2 raised to \a exp -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half scalbln(half arg, long exp) -{ - unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000; - if(abs >= 0x7C00 || !abs) - return (abs > 0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg; - for(; abs < 0x400; abs <<= 1, --exp) - ; - exp += abs >> 10; - if(exp > 30) - return half(detail::binary, detail::overflow(sign)); - else if(exp < -10) - return half(detail::binary, detail::underflow(sign)); - else if(exp > 0) - return half(detail::binary, sign | (exp << 10) | (abs & 0x3FF)); - unsigned int m = (abs & 0x3FF) | 0x400; - return half(detail::binary, - detail::rounded( - sign | (m >> (1 - exp)), (m >> -exp) & 1, (m & ((1 << -exp) - 1)) != 0)); -} - -/// Multiply by power of two. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::scalbn](https://en.cppreference.com/w/cpp/numeric/math/scalbn). -/// \param arg number to modify -/// \param exp power of two to multiply with -/// \return \a arg multplied by 2 raised to \a exp -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half scalbn(half arg, int exp) { return scalbln(arg, exp); } - -/// Multiply by power of two. -/// This function is exact to rounding for all rounding modes. -/// -/// **See also:** Documentation for -/// [std::ldexp](https://en.cppreference.com/w/cpp/numeric/math/ldexp). -/// \param arg number to modify -/// \param exp power of two to multiply with -/// \return \a arg multplied by 2 raised to \a exp -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -inline half ldexp(half arg, int exp) { return scalbln(arg, exp); } - -/// Extract integer and fractional parts. -/// **See also:** Documentation for -/// [std::modf](https://en.cppreference.com/w/cpp/numeric/math/modf). -/// \param arg number to decompress -/// \param iptr address to store integer part at -/// \return fractional part -/// \exception FE_INVALID for signaling NaN -inline half modf(half arg, half* iptr) -{ - unsigned int abs = arg.data_ & 0x7FFF; - if(abs > 0x7C00) - { - arg = half(detail::binary, detail::signal(arg.data_)); - return *iptr = arg, arg; - } - if(abs >= 0x6400) - return *iptr = arg, half(detail::binary, arg.data_ & 0x8000); - if(abs < 0x3C00) - return iptr->data_ = arg.data_ & 0x8000, arg; - unsigned int exp = abs >> 10, mask = (1 << (25 - exp)) - 1, m = arg.data_ & mask; - iptr->data_ = arg.data_ & ~mask; - if(!m) - return half(detail::binary, arg.data_ & 0x8000); - for(; m < 0x400; m <<= 1, --exp) - ; - return half(detail::binary, (arg.data_ & 0x8000) | (exp << 10) | (m & 0x3FF)); -} - -/// Extract exponent. -/// **See also:** Documentation for -/// [std::ilogb](https://en.cppreference.com/w/cpp/numeric/math/ilogb). -/// \param arg number to query -/// \return floating-point exponent -/// \retval FP_ILOGB0 for zero -/// \retval FP_ILOGBNAN for NaN -/// \retval INT_MAX for infinity -/// \exception FE_INVALID for 0 or infinite values -inline int ilogb(half arg) -{ - int abs = arg.data_ & 0x7FFF, exp; - if(!abs || abs >= 0x7C00) - { - detail::raise(FE_INVALID); - return !abs ? FP_ILOGB0 : (abs == 0x7C00) ? INT_MAX : FP_ILOGBNAN; - } - for(exp = (abs >> 10) - 15; abs < 0x200; abs <<= 1, --exp) - ; - return exp; -} - -/// Extract exponent. -/// **See also:** Documentation for -/// [std::logb](https://en.cppreference.com/w/cpp/numeric/math/logb). -/// \param arg number to query -/// \return floating-point exponent -/// \exception FE_INVALID for signaling NaN -/// \exception FE_DIVBYZERO for 0 -inline half logb(half arg) -{ - int abs = arg.data_ & 0x7FFF, exp; - if(!abs) - return half(detail::binary, detail::pole(0x8000)); - if(abs >= 0x7C00) - return half(detail::binary, (abs == 0x7C00) ? 0x7C00 : detail::signal(arg.data_)); - for(exp = (abs >> 10) - 15; abs < 0x200; abs <<= 1, --exp) - ; - unsigned int value = static_cast(exp < 0) << 15; - if(exp) - { - unsigned int m = std::abs(exp) << 6; - for(exp = 18; m < 0x400; m <<= 1, --exp) - ; - value |= (exp << 10) + m; - } - return half(detail::binary, value); -} - -/// Next representable value. -/// **See also:** Documentation for -/// [std::nextafter](https://en.cppreference.com/w/cpp/numeric/math/nextafter). -/// \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 -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW for infinite result from finite argument -/// \exception FE_UNDERFLOW for subnormal result -inline half nextafter(half from, half to) -{ - int fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF; - if(fabs > 0x7C00 || tabs > 0x7C00) - return half(detail::binary, detail::signal(from.data_, to.data_)); - if(from.data_ == to.data_ || !(fabs | tabs)) - return to; - if(!fabs) - { - detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT); - return half(detail::binary, (to.data_ & 0x8000) + 1); - } - unsigned int out = - from.data_ + - (((from.data_ >> 15) ^ - static_cast((from.data_ ^ (0x8000 | (0x8000 - (from.data_ >> 15)))) < - (to.data_ ^ (0x8000 | (0x8000 - (to.data_ >> 15)))))) - << 1) - - 1; - detail::raise(FE_OVERFLOW, fabs < 0x7C00 && (out & 0x7C00) == 0x7C00); - detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out & 0x7C00) < 0x400); - return half(detail::binary, out); -} - -/// Next representable value. -/// **See also:** Documentation for -/// [std::nexttoward](https://en.cppreference.com/w/cpp/numeric/math/nexttoward). -/// \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 -/// \exception FE_INVALID for signaling NaN -/// \exception FE_OVERFLOW for infinite result from finite argument -/// \exception FE_UNDERFLOW for subnormal result -inline half nexttoward(half from, long double to) -{ - int fabs = from.data_ & 0x7FFF; - if(fabs > 0x7C00) - return half(detail::binary, detail::signal(from.data_)); - long double lfrom = static_cast(from); - if(detail::builtin_isnan(to) || lfrom == to) - return half(static_cast(to)); - if(!fabs) - { - detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT); - return half(detail::binary, (static_cast(detail::builtin_signbit(to)) << 15) + 1); - } - unsigned int out = - from.data_ + (((from.data_ >> 15) ^ static_cast(lfrom < to)) << 1) - 1; - detail::raise(FE_OVERFLOW, (out & 0x7FFF) == 0x7C00); - detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out & 0x7FFF) < 0x400); - return half(detail::binary, out); -} - -/// Take sign. -/// **See also:** Documentation for -/// [std::copysign](https://en.cppreference.com/w/cpp/numeric/math/copysign). -/// \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 -inline HALF_CONSTEXPR half copysign(half x, half y) -{ - return half(detail::binary, x.data_ ^ ((x.data_ ^ y.data_) & 0x8000)); -} - -/// \} -/// \anchor classification -/// \name Floating point classification -/// \{ - -/// Classify floating-point value. -/// **See also:** Documentation for -/// [std::fpclassify](https://en.cppreference.com/w/cpp/numeric/math/fpclassify). -/// \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 -inline HALF_CONSTEXPR int fpclassify(half arg) -{ - return !(arg.data_ & 0x7FFF) - ? FP_ZERO - : ((arg.data_ & 0x7FFF) < 0x400) - ? FP_SUBNORMAL - : ((arg.data_ & 0x7FFF) < 0x7C00) - ? FP_NORMAL - : ((arg.data_ & 0x7FFF) == 0x7C00) ? FP_INFINITE : FP_NAN; -} - -/// Check if finite number. -/// **See also:** Documentation for -/// [std::isfinite](https://en.cppreference.com/w/cpp/numeric/math/isfinite). -/// \param arg number to check -/// \retval true if neither infinity nor NaN -/// \retval false else -inline HALF_CONSTEXPR bool isfinite(half arg) { return (arg.data_ & 0x7C00) != 0x7C00; } - -/// Check for infinity. -/// **See also:** Documentation for -/// [std::isinf](https://en.cppreference.com/w/cpp/numeric/math/isinf). -/// \param arg number to check -/// \retval true for positive or negative infinity -/// \retval false else -inline HALF_CONSTEXPR bool isinf(half arg) { return (arg.data_ & 0x7FFF) == 0x7C00; } - -/// Check for NaN. -/// **See also:** Documentation for -/// [std::isnan](https://en.cppreference.com/w/cpp/numeric/math/isnan). -/// \param arg number to check -/// \retval true for NaNs -/// \retval false else -inline HALF_CONSTEXPR bool isnan(half arg) { return (arg.data_ & 0x7FFF) > 0x7C00; } - -/// Check if normal number. -/// **See also:** Documentation for -/// [std::isnormal](https://en.cppreference.com/w/cpp/numeric/math/isnormal). -/// \param arg number to check -/// \retval true if normal number -/// \retval false if either subnormal, zero, infinity or NaN -inline HALF_CONSTEXPR bool isnormal(half arg) -{ - return ((arg.data_ & 0x7C00) != 0) & ((arg.data_ & 0x7C00) != 0x7C00); -} - -/// Check sign. -/// **See also:** Documentation for -/// [std::signbit](https://en.cppreference.com/w/cpp/numeric/math/signbit). -/// \param arg number to check -/// \retval true for negative number -/// \retval false for positive number -inline HALF_CONSTEXPR bool signbit(half arg) { return (arg.data_ & 0x8000) != 0; } - -/// \} -/// \anchor compfunc -/// \name Comparison -/// \{ - -/// Quiet comparison for greater than. -/// **See also:** Documentation for -/// [std::isgreater](https://en.cppreference.com/w/cpp/numeric/math/isgreater). -/// \param x first operand -/// \param y second operand -/// \retval true if \a x greater than \a y -/// \retval false else -inline HALF_CONSTEXPR bool isgreater(half x, half y) -{ - return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) > - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) && - !isnan(x) && !isnan(y); -} - -/// Quiet comparison for greater equal. -/// **See also:** Documentation for -/// [std::isgreaterequal](https://en.cppreference.com/w/cpp/numeric/math/isgreaterequal). -/// \param x first operand -/// \param y second operand -/// \retval true if \a x greater equal \a y -/// \retval false else -inline HALF_CONSTEXPR bool isgreaterequal(half x, half y) -{ - return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) >= - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) && - !isnan(x) && !isnan(y); -} - -/// Quiet comparison for less than. -/// **See also:** Documentation for -/// [std::isless](https://en.cppreference.com/w/cpp/numeric/math/isless). -/// \param x first operand -/// \param y second operand -/// \retval true if \a x less than \a y -/// \retval false else -inline HALF_CONSTEXPR bool isless(half x, half y) -{ - return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) < - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) && - !isnan(x) && !isnan(y); -} - -/// Quiet comparison for less equal. -/// **See also:** Documentation for -/// [std::islessequal](https://en.cppreference.com/w/cpp/numeric/math/islessequal). -/// \param x first operand -/// \param y second operand -/// \retval true if \a x less equal \a y -/// \retval false else -inline HALF_CONSTEXPR bool islessequal(half x, half y) -{ - return ((x.data_ ^ (0x8000 | (0x8000 - (x.data_ >> 15)))) + (x.data_ >> 15)) <= - ((y.data_ ^ (0x8000 | (0x8000 - (y.data_ >> 15)))) + (y.data_ >> 15)) && - !isnan(x) && !isnan(y); -} - -/// Quiet comarison for less or greater. -/// **See also:** Documentation for -/// [std::islessgreater](https://en.cppreference.com/w/cpp/numeric/math/islessgreater). -/// \param x first operand -/// \param y second operand -/// \retval true if either less or greater -/// \retval false else -inline HALF_CONSTEXPR bool islessgreater(half x, half y) -{ - return x.data_ != y.data_ && ((x.data_ | y.data_) & 0x7FFF) && !isnan(x) && !isnan(y); -} - -/// Quiet check if unordered. -/// **See also:** Documentation for -/// [std::isunordered](https://en.cppreference.com/w/cpp/numeric/math/isunordered). -/// \param x first operand -/// \param y second operand -/// \retval true if unordered (one or two NaN operands) -/// \retval false else -inline HALF_CONSTEXPR bool isunordered(half x, half y) { return isnan(x) || isnan(y); } - -/// \} -/// \anchor casting -/// \name Casting -/// \{ - -/// Cast to or from half-precision floating-point number. -/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values -/// are converted -/// directly using the default 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 returns the argument unmodified. -/// \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 -/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -template -T half_cast(U arg) -{ - return detail::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 specified 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 returns the argument unmodified. -/// \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 -/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T -/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding -template -T half_cast(U arg) -{ - return detail::half_caster::cast(arg); -} -/// \} - -/// \} -/// \anchor errors -/// \name Error handling -/// \{ - -/// Clear exception flags. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// -/// **See also:** Documentation for -/// [std::feclearexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feclearexcept). -/// \param excepts OR of exceptions to clear -/// \retval 0 all selected flags cleared successfully -inline int feclearexcept(int excepts) -{ - detail::errflags() &= ~excepts; - return 0; -} - -/// Test exception flags. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// -/// **See also:** Documentation for -/// [std::fetestexcept](https://en.cppreference.com/w/cpp/numeric/fenv/fetestexcept). -/// \param excepts OR of exceptions to test -/// \return OR of selected exceptions if raised -inline int fetestexcept(int excepts) { return detail::errflags() & excepts; } - -/// Raise exception flags. -/// This raises the specified floating point exceptions and also invokes any additional automatic -/// exception handling as -/// configured with the [HALF_ERRHANDLIG_...](\ref HALF_ERRHANDLING_ERRNO) preprocessor symbols. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// -/// **See also:** Documentation for -/// [std::feraiseexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feraiseexcept). -/// \param excepts OR of exceptions to raise -/// \retval 0 all selected exceptions raised successfully -inline int feraiseexcept(int excepts) -{ - detail::errflags() |= excepts; - detail::raise(excepts); - return 0; -} - -/// Save exception flags. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// -/// **See also:** Documentation for -/// [std::fegetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag). -/// \param flagp adress to store flag state at -/// \param excepts OR of flags to save -/// \retval 0 for success -inline int fegetexceptflag(int* flagp, int excepts) -{ - *flagp = detail::errflags() & excepts; - return 0; -} - -/// Restore exception flags. -/// This only copies the specified exception state (including unset flags) without incurring any -/// additional exception handling. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// -/// **See also:** Documentation for -/// [std::fesetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag). -/// \param flagp adress to take flag state from -/// \param excepts OR of flags to restore -/// \retval 0 for success -inline int fesetexceptflag(const int* flagp, int excepts) -{ - detail::errflags() = (detail::errflags() | (*flagp & excepts)) & (*flagp | ~excepts); - return 0; -} - -/// Throw C++ exceptions based on set exception flags. -/// This function manually throws a corresponding C++ exception if one of the specified flags is -/// set, -/// no matter if automatic throwing (via [HALF_ERRHANDLING_THROW_...](\ref -/// HALF_ERRHANDLING_THROW_INVALID)) is enabled or not. -/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is -/// disabled, -/// but in that case manual flag management is the only way to raise flags. -/// \param excepts OR of exceptions to test -/// \param msg error message to use for exception description -/// \throw std::domain_error if `FE_INVALID` or `FE_DIVBYZERO` is selected and set -/// \throw std::overflow_error if `FE_OVERFLOW` is selected and set -/// \throw std::underflow_error if `FE_UNDERFLOW` is selected and set -/// \throw std::range_error if `FE_INEXACT` is selected and set -inline void fethrowexcept(int excepts, const char* msg = "") -{ - excepts &= detail::errflags(); - if(excepts & (FE_INVALID | FE_DIVBYZERO)) - throw std::domain_error(msg); - if(excepts & FE_OVERFLOW) - throw std::overflow_error(msg); - if(excepts & FE_UNDERFLOW) - throw std::underflow_error(msg); - if(excepts & FE_INEXACT) - throw std::range_error(msg); -} -/// \} -} // namespace half_float - -#undef HALF_UNUSED_NOERR -#undef HALF_CONSTEXPR -#undef HALF_CONSTEXPR_CONST -#undef HALF_CONSTEXPR_NOERR -#undef HALF_NOEXCEPT -#undef HALF_NOTHROW -#undef HALF_THREAD_LOCAL -#undef HALF_TWOS_COMPLEMENT_INT -#ifdef HALF_POP_WARNINGS -#pragma warning(pop) -#undef HALF_POP_WARNINGS -#endif - -#endif