Add Half library to third_party (#3897)
Add Half library to be able to use f16 to/from f32 conversion in IREE tools.
diff --git a/third_party/half/LICENSE b/third_party/half/LICENSE
new file mode 100644
index 0000000..9e4618b
--- /dev/null
+++ b/third_party/half/LICENSE
@@ -0,0 +1,21 @@
+The MIT License
+
+Copyright (c) 2012-2017 Christian Rau
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
diff --git a/third_party/half/README.txt b/third_party/half/README.txt
new file mode 100644
index 0000000..3a0960c
--- /dev/null
+++ b/third_party/half/README.txt
@@ -0,0 +1,288 @@
+HALF-PRECISION FLOATING POINT LIBRARY (Version 1.12.0)
+------------------------------------------------------
+
+This is a C++ header-only library to provide an IEEE 754 conformant 16-bit
+half-precision floating point type along with corresponding arithmetic
+operators, type conversions and common mathematical functions. It aims for both
+efficiency and ease of use, trying to accurately mimic the behaviour of the
+builtin floating point types at the best performance possible.
+
+
+INSTALLATION AND REQUIREMENTS
+-----------------------------
+
+Comfortably enough, the library consists of just a single header file
+containing all the functionality, which can be directly included by your
+projects, without the neccessity to build anything or link to anything.
+
+Whereas this library is fully C++98-compatible, it can profit from certain
+C++11 features. Support for those features is checked automatically at compile
+(or rather preprocessing) time, but can be explicitly enabled or disabled by
+defining the corresponding preprocessor symbols to either 1 or 0 yourself. This
+is useful when the automatic detection fails (for more exotic implementations)
+or when a feature should be explicitly disabled:
+
+ - 'long long' integer type for mathematical functions returning 'long long'
+ results (enabled for VC++ 2003 and newer, gcc and clang, overridable with
+ 'HALF_ENABLE_CPP11_LONG_LONG').
+
+ - Static assertions for extended compile-time checks (enabled for VC++ 2010,
+ gcc 4.3, clang 2.9 and newer, overridable with 'HALF_ENABLE_CPP11_STATIC_ASSERT').
+
+ - Generalized constant expressions (enabled for VC++ 2015, gcc 4.6, clang 3.1
+ and newer, overridable with 'HALF_ENABLE_CPP11_CONSTEXPR').
+
+ - noexcept exception specifications (enabled for VC++ 2015, gcc 4.6, clang 3.0
+ and newer, overridable with 'HALF_ENABLE_CPP11_NOEXCEPT').
+
+ - User-defined literals for half-precision literals to work (enabled for
+ VC++ 2015, gcc 4.7, clang 3.1 and newer, overridable with
+ 'HALF_ENABLE_CPP11_USER_LITERALS').
+
+ - Type traits and template meta-programming features from <type_traits>
+ (enabled for VC++ 2010, libstdc++ 4.3, libc++ and newer, overridable with
+ 'HALF_ENABLE_CPP11_TYPE_TRAITS').
+
+ - Special integer types from <cstdint> (enabled for VC++ 2010, libstdc++ 4.3,
+ libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CSTDINT').
+
+ - Certain C++11 single-precision mathematical functions from <cmath> for
+ an improved implementation of their half-precision counterparts to work
+ (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with
+ 'HALF_ENABLE_CPP11_CMATH').
+
+ - Hash functor 'std::hash' from <functional> (enabled for VC++ 2010,
+ libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_HASH').
+
+The library has been tested successfully with Visual C++ 2005-2015, gcc 4.4-4.8
+and clang 3.1. Please contact me if you have any problems, suggestions or even
+just success testing it on other platforms.
+
+
+DOCUMENTATION
+-------------
+
+Here follow some general words about the usage of the library and its
+implementation. For a complete documentation of its iterface look at the
+corresponding website http://half.sourceforge.net. You may also generate the
+complete developer documentation from the library's only include file's doxygen
+comments, but this is more relevant to developers rather than mere users (for
+reasons described below).
+
+BASIC USAGE
+
+To make use of the library just include its only header file half.hpp, which
+defines all half-precision functionality inside the 'half_float' namespace. The
+actual 16-bit half-precision data type is represented by the 'half' type. This
+type behaves like the builtin floating point types as much as possible,
+supporting the usual arithmetic, comparison and streaming operators, which
+makes its use pretty straight-forward:
+
+ using half_float::half;
+ half a(3.4), b(5);
+ half c = a * b;
+ c += 3;
+ if(c > a)
+ std::cout << c << std::endl;
+
+Additionally the 'half_float' namespace also defines half-precision versions
+for all mathematical functions of the C++ standard library, which can be used
+directly through ADL:
+
+ half a(-3.14159);
+ half s = sin(abs(a));
+ long l = lround(s);
+
+You may also specify explicit half-precision literals, since the library
+provides a user-defined literal inside the 'half_float::literal' namespace,
+which you just need to import (assuming support for C++11 user-defined literals):
+
+ using namespace half_float::literal;
+ half x = 1.0_h;
+
+Furthermore the library provides proper specializations for
+'std::numeric_limits', defining various implementation properties, and
+'std::hash' for hashing half-precision numbers (assuming support for C++11
+'std::hash'). Similar to the corresponding preprocessor symbols from <cmath>
+the library also defines the 'HUGE_VALH' constant and maybe the 'FP_FAST_FMAH'
+symbol.
+
+CONVERSIONS AND ROUNDING
+
+The half is explicitly constructible/convertible from a single-precision float
+argument. Thus it is also explicitly constructible/convertible from any type
+implicitly convertible to float, but constructing it from types like double or
+int will involve the usual warnings arising when implicitly converting those to
+float because of the lost precision. On the one hand those warnings are
+intentional, because converting those types to half neccessarily also reduces
+precision. But on the other hand they are raised for explicit conversions from
+those types, when the user knows what he is doing. So if those warnings keep
+bugging you, then you won't get around first explicitly converting to float
+before converting to half, or use the 'half_cast' described below. In addition
+you can also directly assign float values to halfs.
+
+In contrast to the float-to-half conversion, which reduces precision, the
+conversion from half to float (and thus to any other type implicitly
+convertible from float) is implicit, because all values represetable with
+half-precision are also representable with single-precision. This way the
+half-to-float conversion behaves similar to the builtin float-to-double
+conversion and all arithmetic expressions involving both half-precision and
+single-precision arguments will be of single-precision type. This way you can
+also directly use the mathematical functions of the C++ standard library,
+though in this case you will invoke the single-precision versions which will
+also return single-precision values, which is (even if maybe performing the
+exact same computation, see below) not as conceptually clean when working in a
+half-precision environment.
+
+The default rounding mode for conversions from float to half uses truncation
+(round toward zero, but mapping overflows to infinity) for rounding values not
+representable exactly in half-precision. This is the fastest rounding possible
+and is usually sufficient. But by redefining the 'HALF_ROUND_STYLE'
+preprocessor symbol (before including half.hpp) this default can be overridden
+with one of the other standard rounding modes using their respective constants
+or the equivalent values of 'std::float_round_style' (it can even be
+synchronized with the underlying single-precision implementation by defining it
+to 'std::numeric_limits<float>::round_style'):
+
+ - 'std::round_indeterminate' or -1 for the fastest rounding (default).
+
+ - 'std::round_toward_zero' or 0 for rounding toward zero.
+
+ - std::round_to_nearest' or 1 for rounding to the nearest value.
+
+ - std::round_toward_infinity' or 2 for rounding toward positive infinity.
+
+ - std::round_toward_neg_infinity' or 3 for rounding toward negative infinity.
+
+In addition to changing the overall default rounding mode one can also use the
+'half_cast'. This converts between half and any built-in arithmetic type using
+a configurable rounding mode (or the default rounding mode if none is
+specified). In addition to a configurable rounding mode, 'half_cast' has
+another big difference to a mere 'static_cast': Any conversions are performed
+directly using the given rounding mode, without any intermediate conversion
+to/from 'float'. This is especially relevant for conversions to integer types,
+which don't necessarily truncate anymore. But also for conversions from
+'double' or 'long double' this may produce more precise results than a
+pre-conversion to 'float' using the single-precision implementation's current
+rounding mode would.
+
+ half a = half_cast<half>(4.2);
+ half b = half_cast<half,std::numeric_limits<float>::round_style>(4.2f);
+ assert( half_cast<int, std::round_to_nearest>( 0.7_h ) == 1 );
+ assert( half_cast<half,std::round_toward_zero>( 4097 ) == 4096.0_h );
+ assert( half_cast<half,std::round_toward_infinity>( 4097 ) == 4100.0_h );
+ assert( half_cast<half,std::round_toward_infinity>( std::numeric_limits<double>::min() ) > 0.0_h );
+
+When using round to nearest (either as default or through 'half_cast') ties are
+by default resolved by rounding them away from zero (and thus equal to the
+behaviour of the 'round' function). But by redefining the
+'HALF_ROUND_TIES_TO_EVEN' preprocessor symbol to 1 (before including half.hpp)
+this default can be changed to the slightly slower but less biased and more
+IEEE-conformant behaviour of rounding half-way cases to the nearest even value.
+
+ #define HALF_ROUND_TIES_TO_EVEN 1
+ #include <half.hpp>
+ ...
+ assert( half_cast<int,std::round_to_nearest>(3.5_h)
+ == half_cast<int,std::round_to_nearest>(4.5_h) );
+
+IMPLEMENTATION
+
+For performance reasons (and ease of implementation) many of the mathematical
+functions provided by the library as well as all arithmetic operations are
+actually carried out in single-precision under the hood, calling to the C++
+standard library implementations of those functions whenever appropriate,
+meaning the arguments are converted to floats and the result back to half. But
+to reduce the conversion overhead as much as possible any temporary values
+inside of lengthy expressions are kept in single-precision as long as possible,
+while still maintaining a strong half-precision type to the outside world. Only
+when finally assigning the value to a half or calling a function that works
+directly on halfs is the actual conversion done (or never, when further
+converting the result to float.
+
+This approach has two implications. First of all you have to treat the
+library's documentation at http://half.sourceforge.net as a simplified version,
+describing the behaviour of the library as if implemented this way. The actual
+argument and return types of functions and operators may involve other internal
+types (feel free to generate the exact developer documentation from the Doxygen
+comments in the library's header file if you really need to). But nevertheless
+the behaviour is exactly like specified in the documentation. The other
+implication is, that in the presence of rounding errors or over-/underflows
+arithmetic expressions may produce different results when compared to
+converting to half-precision after each individual operation:
+
+ half a = std::numeric_limits<half>::max() * 2.0_h / 2.0_h; // a = MAX
+ half b = half(std::numeric_limits<half>::max() * 2.0_h) / 2.0_h; // b = INF
+ assert( a != b );
+
+But this should only be a problem in very few cases. One last word has to be
+said when talking about performance. Even with its efforts in reducing
+conversion overhead as much as possible, the software half-precision
+implementation can most probably not beat the direct use of single-precision
+computations. Usually using actual float values for all computations and
+temproraries and using halfs only for storage is the recommended way. On the
+one hand this somehow makes the provided mathematical functions obsolete
+(especially in light of the implicit conversion from half to float), but
+nevertheless the goal of this library was to provide a complete and
+conceptually clean half-precision implementation, to which the standard
+mathematical functions belong, even if usually not needed.
+
+IEEE CONFORMANCE
+
+The half type uses the standard IEEE representation with 1 sign bit, 5 exponent
+bits and 10 mantissa bits (11 when counting the hidden bit). It supports all
+types of special values, like subnormal values, infinity and NaNs. But there
+are some limitations to the complete conformance to the IEEE 754 standard:
+
+ - The implementation does not differentiate between signalling and quiet
+ NaNs, this means operations on halfs are not specified to trap on
+ signalling NaNs (though they may, see last point).
+
+ - Though arithmetic operations are internally rounded to single-precision
+ using the underlying single-precision implementation's current rounding
+ mode, those values are then converted to half-precision using the default
+ half-precision rounding mode (changed by defining 'HALF_ROUND_STYLE'
+ accordingly). This mixture of rounding modes is also the reason why
+ 'std::numeric_limits<half>::round_style' may actually return
+ 'std::round_indeterminate' when half- and single-precision rounding modes
+ don't match.
+
+ - Because of internal truncation it may also be that certain single-precision
+ NaNs will be wrongly converted to half-precision infinity, though this is
+ very unlikely to happen, since most single-precision implementations don't
+ tend to only set the lowest bits of a NaN mantissa.
+
+ - The implementation does not provide any floating point exceptions, thus
+ arithmetic operations or mathematical functions are not specified to invoke
+ proper floating point exceptions. But due to many functions implemented in
+ single-precision, those may still invoke floating point exceptions of the
+ underlying single-precision implementation.
+
+Some of those points could have been circumvented by controlling the floating
+point environment using <cfenv> or implementing a similar exception mechanism.
+But this would have required excessive runtime checks giving two high an impact
+on performance for something that is rarely ever needed. If you really need to
+rely on proper floating point exceptions, it is recommended to explicitly
+perform computations using the built-in floating point types to be on the safe
+side. In the same way, if you really need to rely on a particular rounding
+behaviour, it is recommended to either use single-precision computations and
+explicitly convert the result to half-precision using 'half_cast' and
+specifying the desired rounding mode, or synchronize the default half-precision
+rounding mode to the rounding mode of the single-precision implementation (most
+likely 'HALF_ROUND_STYLE=1', 'HALF_ROUND_TIES_TO_EVEN=1'). But this is really
+considered an expert-scenario that should be used only when necessary, since
+actually working with half-precision usually comes with a certain
+tolerance/ignorance of exactness considerations and proper rounding comes with
+a certain performance cost.
+
+
+CREDITS AND CONTACT
+-------------------
+
+This library is developed by CHRISTIAN RAU and released under the MIT License
+(see LICENSE.txt). If you have any questions or problems with it, feel free to
+contact me at rauy@users.sourceforge.net.
+
+Additional credit goes to JEROEN VAN DER ZIJP for his paper on "Fast Half Float
+Conversions", whose algorithms have been used in the library for converting
+between half-precision and single-precision values.
diff --git a/third_party/half/UPDATING.md b/third_party/half/UPDATING.md
new file mode 100644
index 0000000..3a8d2fe
--- /dev/null
+++ b/third_party/half/UPDATING.md
@@ -0,0 +1,8 @@
+This project is from: https://sourceforge.net/p/half/code/HEAD/tree/
+
+This can be updated by running:
+```shell
+curl http://svn.code.sf.net/p/half/code/trunk/include/half.hpp > half.hpp
+curl http://svn.code.sf.net/p/half/code/trunk/README.txt > README.txt
+curl http://svn.code.sf.net/p/half/code/trunk/LICENSE.txt > LICENSE.txt
+```
\ No newline at end of file
diff --git a/third_party/half/half.hpp b/third_party/half/half.hpp
new file mode 100644
index 0000000..e9d1aca
--- /dev/null
+++ b/third_party/half/half.hpp
@@ -0,0 +1,4023 @@
+// half - IEEE 754-based half-precision floating point library.
+//
+// Copyright (c) 2012-2017 Christian Rau <rauy@users.sourceforge.net>
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+// Version 1.12.0
+
+/// \file
+/// Main header file for half precision functionality.
+
+#ifndef HALF_HALF_HPP
+#define HALF_HALF_HPP
+
+/// Combined gcc version number.
+#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__)
+
+//check C++11 language features
+#if defined(__clang__) //clang
+ #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ // Do not use NOEXCEPT. Not approved for google3 yet.
+ // #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #if 0
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ // Do not use user literals. Not approved for google3 yet.
+ // #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #if 0
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+/*#elif defined(__INTEL_COMPILER)
+ //Intel C++ #if __INTEL_COMPILER >= 1100 &&
+ !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ???????? #define
+ HALF_ENABLE_CPP11_STATIC_ASSERT 1 #endif #if __INTEL_COMPILER >= 1300 &&
+ !defined(HALF_ENABLE_CPP11_CONSTEXPR) ???????? #define
+ HALF_ENABLE_CPP11_CONSTEXPR 1 #endif #if __INTEL_COMPILER >= 1300 &&
+ !defined(HALF_ENABLE_CPP11_NOEXCEPT) ???????? #define
+ HALF_ENABLE_CPP11_NOEXCEPT 1 #endif #if __INTEL_COMPILER >= 1100 &&
+ !defined(HALF_ENABLE_CPP11_LONG_LONG) ???????? #define
+ HALF_ENABLE_CPP11_LONG_LONG 1 #endif*/
+#elif defined(__GNUC__) //gcc
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
+ #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+ #define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+ #endif
+ #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+ #define HALF_ENABLE_CPP11_CONSTEXPR 1
+ #endif
+ #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+ #define HALF_ENABLE_CPP11_NOEXCEPT 1
+ #endif
+ #if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+ #define HALF_ENABLE_CPP11_USER_LITERALS 1
+ #endif
+ #if !defined(HALF_ENABLE_CPP11_LONG_LONG)
+ #define HALF_ENABLE_CPP11_LONG_LONG 1
+ #endif
+ #endif
+#elif defined(_MSC_VER) //Visual C++
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+#define HALF_ENABLE_CPP11_CONSTEXPR 1
+#endif
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+#define HALF_ENABLE_CPP11_NOEXCEPT 1
+#endif
+#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+#define HALF_ENABLE_CPP11_USER_LITERALS 1
+#endif
+#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+#endif
+#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+#define HALF_ENABLE_CPP11_LONG_LONG 1
+#endif
+#define HALF_POP_WARNINGS 1
+#pragma warning(push)
+#pragma warning(disable : 4099 4127 4146) // struct vs class, constant in if,
+ // negative unsigned
+#endif
+
+//check C++11 library features
+#include <utility>
+#if defined(_LIBCPP_VERSION) //libc++
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CSTDINT
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CMATH
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#ifndef HALF_ENABLE_CPP11_HASH
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#elif defined(__GLIBCXX__) //libstdc++
+ #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+ #ifdef __clang__
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#else
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#endif
+#elif defined(_CPPLIB_VER) //Dinkumware/Visual C++
+ #if _CPPLIB_VER >= 520
+#ifndef HALF_ENABLE_CPP11_TYPE_TRAITS
+#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+#endif
+#ifndef HALF_ENABLE_CPP11_CSTDINT
+#define HALF_ENABLE_CPP11_CSTDINT 1
+#endif
+#ifndef HALF_ENABLE_CPP11_HASH
+#define HALF_ENABLE_CPP11_HASH 1
+#endif
+#endif
+#if _CPPLIB_VER >= 610
+#ifndef HALF_ENABLE_CPP11_CMATH
+#define HALF_ENABLE_CPP11_CMATH 1
+#endif
+#endif
+#endif
+#undef HALF_GNUC_VERSION
+
+//support constexpr
+#if HALF_ENABLE_CPP11_CONSTEXPR
+ #define HALF_CONSTEXPR constexpr
+ #define HALF_CONSTEXPR_CONST constexpr
+#else
+ #define HALF_CONSTEXPR
+ #define HALF_CONSTEXPR_CONST const
+#endif
+
+//support noexcept
+#if HALF_ENABLE_CPP11_NOEXCEPT
+ #define HALF_NOEXCEPT noexcept
+ #define HALF_NOTHROW noexcept
+#else
+ #define HALF_NOEXCEPT
+ #define HALF_NOTHROW throw()
+#endif
+
+#include <algorithm>
+#include <iostream>
+#include <limits>
+#include <climits>
+#include <cmath>
+#include <cstring>
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+#include <type_traits>
+#endif
+#if HALF_ENABLE_CPP11_CSTDINT
+ #include <cstdint>
+#endif
+#if HALF_ENABLE_CPP11_HASH
+#include <functional>
+#endif
+
+/// Default rounding mode.
+/// This specifies the rounding mode used for all conversions between
+/// [half](\ref half_float::half)s and `float`s as well as for the half_cast()
+/// if not specifying a rounding mode explicitly. It can be redefined (before
+/// including half.hpp) to one of the standard rounding modes using their
+/// respective constants or the equivalent values of `std::float_round_style`:
+///
+/// `std::float_round_style` | value | rounding
+/// ---------------------------------|-------|-------------------------
+/// `std::round_indeterminate` | -1 | fastest (default)
+/// `std::round_toward_zero` | 0 | toward zero
+/// `std::round_to_nearest` | 1 | to nearest
+/// `std::round_toward_infinity` | 2 | toward positive infinity
+/// `std::round_toward_neg_infinity` | 3 | toward negative infinity
+///
+/// By default this is set to `-1` (`std::round_indeterminate`), which uses
+/// truncation (round toward zero, but with overflows set to infinity) and is
+/// the fastest rounding mode possible. It can even be set to
+/// `std::numeric_limits<float>::round_style` to synchronize the rounding mode
+/// with that of the underlying single-precision implementation.
+#ifndef HALF_ROUND_STYLE
+#define HALF_ROUND_STYLE -1 // = std::round_indeterminate
+#endif
+
+/// Tie-breaking behaviour for round to nearest.
+/// This specifies if ties in round to nearest should be resolved by rounding to
+/// the nearest even value. By default this is defined to `0` resulting in the
+/// faster but slightly more biased behaviour of rounding away from zero in
+/// half-way cases (and thus equal to the round() function), but can be
+/// redefined to `1` (before including half.hpp) if more IEEE-conformant
+/// behaviour is needed.
+#ifndef HALF_ROUND_TIES_TO_EVEN
+#define HALF_ROUND_TIES_TO_EVEN 0 // ties away from zero
+#endif
+
+/// Value signaling overflow.
+/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to
+/// a positive value signaling the overflow of an operation, in particular it
+/// just evaluates to positive infinity.
+#define HUGE_VALH std::numeric_limits<half_float::half>::infinity()
+
+/// Fast half-precision fma function.
+/// This symbol is only defined if the fma() function generally executes as fast
+/// as, or faster than, a separate half-precision multiplication followed by an
+/// addition. Due to the internal single-precision implementation of all
+/// arithmetic operations, this is in fact always the case.
+#define FP_FAST_FMAH 1
+
+#ifndef FP_ILOGB0
+ #define FP_ILOGB0 INT_MIN
+#endif
+#ifndef FP_ILOGBNAN
+ #define FP_ILOGBNAN INT_MAX
+#endif
+#ifndef FP_SUBNORMAL
+ #define FP_SUBNORMAL 0
+#endif
+#ifndef FP_ZERO
+ #define FP_ZERO 1
+#endif
+#ifndef FP_NAN
+ #define FP_NAN 2
+#endif
+#ifndef FP_INFINITE
+ #define FP_INFINITE 3
+#endif
+#ifndef FP_NORMAL
+ #define FP_NORMAL 4
+#endif
+
+
+/// Main namespace for half precision functionality.
+/// This namespace contains all the functionality provided by the library.
+namespace half_float
+{
+ class half;
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+ /// Library-defined half-precision literals.
+ /// Import this namespace to enable half-precision floating point
+ /// literals:
+ /// ~~~~{.cpp}
+ /// using namespace half_float::literal;
+ /// half_float::half = 4.2_h;
+ /// ~~~~
+ namespace literal {
+ half operator""_h(long double);
+ }
+#endif
+
+ /// \internal
+ /// \brief Implementation details.
+ namespace detail
+ {
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+ /// Conditional type.
+ template <bool B, typename T, typename F>
+ struct conditional : std::conditional<B, T, F> {};
+
+ /// Helper for tag dispatching.
+ template <bool B>
+ struct bool_type : std::integral_constant<bool, B> {};
+ using std::false_type;
+ using std::true_type;
+
+ /// Type traits for floating point types.
+ template <typename T>
+ struct is_float : std::is_floating_point<T> {};
+#else
+ /// Conditional type.
+ template <bool, typename T, typename>
+ struct conditional {
+ typedef T type;
+ };
+ template <typename T, typename F>
+ struct conditional<false, T, F> {
+ typedef F type;
+ };
+
+ /// Helper for tag dispatching.
+ template <bool>
+ struct bool_type {};
+ typedef bool_type<true> true_type;
+ typedef bool_type<false> false_type;
+
+ /// Type traits for floating point types.
+ template <typename>
+ struct is_float : false_type {};
+ template <typename T>
+ struct is_float<const T> : is_float<T> {};
+ template <typename T>
+ struct is_float<volatile T> : is_float<T> {};
+ template <typename T>
+ struct is_float<const volatile T> : is_float<T> {};
+ template <>
+ struct is_float<float> : true_type {};
+ template <>
+ struct is_float<double> : true_type {};
+ template <>
+ struct is_float<long double> : true_type {};
+#endif
+
+ /// Type traits for floating point bits.
+ template <typename T>
+ struct bits {
+ typedef unsigned char type;
+ };
+ template <typename T>
+ struct bits<const T> : bits<T> {};
+ template <typename T>
+ struct bits<volatile T> : bits<T> {};
+ template <typename T>
+ struct bits<const volatile T> : bits<T> {};
+
+#if HALF_ENABLE_CPP11_CSTDINT
+ /// Unsigned integer of (at least) 16 bits width.
+ typedef std::uint_least16_t uint16;
+
+ /// Unsigned integer of (at least) 32 bits width.
+ template <>
+ struct bits<float> {
+ typedef std::uint_least32_t type;
+ };
+
+ /// Unsigned integer of (at least) 64 bits width.
+ template <>
+ struct bits<double> {
+ typedef std::uint_least64_t type;
+ };
+#else
+ /// Unsigned integer of (at least) 16 bits width.
+ typedef unsigned short uint16;
+
+ /// Unsigned integer of (at least) 32 bits width.
+ template <>
+ struct bits<float>
+ : conditional<std::numeric_limits<unsigned int>::digits >= 32,
+ unsigned int, unsigned long> {};
+
+#if HALF_ENABLE_CPP11_LONG_LONG
+ /// Unsigned integer of (at least) 64 bits width.
+ template <>
+ struct bits<double>
+ : conditional<std::numeric_limits<unsigned long>::digits >= 64,
+ unsigned long, unsigned long long> {};
+#else
+ /// Unsigned integer of (at least) 64 bits width.
+ template <>
+ struct bits<double> {
+ typedef unsigned long type;
+ };
+#endif
+#endif
+
+ /// Tag type for binary construction.
+ struct binary_t {};
+
+ /// Tag for binary construction.
+ HALF_CONSTEXPR_CONST binary_t binary = binary_t();
+
+ /// Temporary half-precision expression.
+ /// This class represents a half-precision expression which just stores
+ /// a single-precision value internally.
+ struct expr {
+ /// Conversion constructor.
+ /// \param f single-precision value to convert
+ explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {}
+
+ /// Conversion to single-precision.
+ /// \return single precision value representing expression value
+ HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; }
+
+ private:
+ /// Internal expression value stored in single-precision.
+ float value_;
+ };
+
+ /// SFINAE helper for generic half-precision functions.
+ /// This class template has to be specialized for each valid
+ /// combination of argument types to provide a corresponding
+ /// `type` member equivalent to \a T.
+ /// \tparam T type to return
+ template <typename T, typename, typename = void, typename = void>
+ struct enable {};
+ template <typename T>
+ struct enable<T, half, void, void> {
+ typedef T type; };
+ template<typename T> struct enable<T,expr,void,void> { typedef T type; };
+ template<typename T> struct enable<T,half,half,void> { typedef T type; };
+ template<typename T> struct enable<T,half,expr,void> { typedef T type; };
+ template<typename T> struct enable<T,expr,half,void> { typedef T type; };
+ template<typename T> struct enable<T,expr,expr,void> { typedef T type; };
+ template<typename T> struct enable<T,half,half,half> { typedef T type; };
+ template<typename T> struct enable<T,half,half,expr> { typedef T type; };
+ template<typename T> struct enable<T,half,expr,half> { typedef T type; };
+ template<typename T> struct enable<T,half,expr,expr> { typedef T type; };
+ template<typename T> struct enable<T,expr,half,half> { typedef T type; };
+ template<typename T> struct enable<T,expr,half,expr> { typedef T type; };
+ template<typename T> struct enable<T,expr,expr,half> { typedef T type; };
+ template<typename T> struct enable<T,expr,expr,expr> { typedef T type; };
+
+ /// Return type for specialized generic 2-argument
+ /// half-precision functions. This class template has to be
+ /// specialized for each valid combination of argument types to
+ /// provide a corresponding `type` member denoting the
+ /// appropriate return type. \tparam T first argument type
+ /// \tparam U first argument type
+ template <typename T, typename U>
+ struct result : enable<expr, T, U> {};
+ template<> struct result<half,half> { typedef half type; };
+
+ /// \name Classification helpers
+ /// \{
+
+ /// Check for infinity.
+ /// \tparam T argument type (builtin floating point type)
+ /// \param arg value to query
+ /// \retval true if infinity
+ /// \retval false else
+ template<typename T> bool builtin_isinf(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::isinf(arg);
+ #elif defined(_MSC_VER)
+ return !::_finite(static_cast<double>(arg)) &&
+ !::_isnan(static_cast<double>(arg));
+#else
+ return arg == std::numeric_limits<T>::infinity() ||
+ arg == -std::numeric_limits<T>::infinity();
+#endif
+ }
+
+ /// Check for NaN.
+ /// \tparam T argument type (builtin floating point type)
+ /// \param arg value to query
+ /// \retval true if not a number
+ /// \retval false else
+ template<typename T> bool builtin_isnan(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::isnan(arg);
+ #elif defined(_MSC_VER)
+ return ::_isnan(static_cast<double>(arg)) != 0;
+#else
+ return arg != arg;
+#endif
+ }
+
+ /// Check sign.
+ /// \tparam T argument type (builtin floating point type)
+ /// \param arg value to query
+ /// \retval true if signbit set
+ /// \retval false else
+ template<typename T> bool builtin_signbit(T arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return std::signbit(arg);
+ #else
+ return arg < T() || (arg == T() && T(1) / arg < T());
+#endif
+ }
+
+ /// \}
+ /// \name Conversion
+ /// \{
+
+ /// Convert IEEE single-precision to half-precision.
+ /// Credit for this goes to [Jeroen van der
+ /// Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \param value single-precision value
+ /// \return binary representation of half-precision value
+ template <std::float_round_style R>
+ uint16 float2half_impl(float value, true_type) {
+ typedef bits<float>::type uint32;
+ uint32 bits; // = *reinterpret_cast<uint32*>(&value);
+ // //violating strict aliasing!
+ std::memcpy(&bits, &value, sizeof(float));
+ /* uint16 hbits = (bits>>16) & 0x8000;
+ bits &= 0x7FFFFFFF;
+ int exp = bits >> 23;
+ if(exp == 255)
+ return hbits | 0x7C00 |
+ (0x3FF&-static_cast<unsigned>((bits&0x7FFFFF)!=0)); if(exp
+ > 142)
+ {
+ if(R ==
+ std::round_toward_infinity) return hbits | 0x7C00 -
+ (hbits>>15); if(R == std::round_toward_neg_infinity) return
+ hbits | 0x7BFF + (hbits>>15); return hbits | 0x7BFF +
+ (R!=std::round_toward_zero);
+ }
+ int g, s;
+ if(exp > 112)
+ {
+ g = (bits>>12) & 1;
+ s = (bits&0xFFF) != 0;
+ hbits |= ((exp-112)<<10) |
+ ((bits>>13)&0x3FF);
+ }
+ else if(exp > 101)
+ {
+ int i = 125 - exp;
+ bits = (bits&0x7FFFFF) |
+ 0x800000; g = (bits>>i) & 1; s = (bits&((1L<<i)-1)) != 0;
+ hbits |= bits >> (i+1);
+ }
+ else
+ {
+ g = 0;
+ s = bits != 0;
+ }
+ if(R == std::round_to_nearest)
+ #if HALF_ROUND_TIES_TO_EVEN
+ hbits += g &
+ (s|hbits); #else hbits += g; #endif else if(R ==
+ std::round_toward_infinity) hbits += ~(hbits>>15) & (s|g);
+ else if(R ==
+ std::round_toward_neg_infinity) hbits += (hbits>>15) &
+ (g|s);
+ */
+ static const uint16 base_table[512] = {
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002,
+ 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100,
+ 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800,
+ 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400,
+ 0x3800, 0x3C00, 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000,
+ 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00,
+ 0x7000, 0x7400, 0x7800, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00,
+ 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000,
+ 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010,
+ 0x8020, 0x8040, 0x8080, 0x8100, 0x8200, 0x8400, 0x8800,
+ 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400,
+ 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 0xC000,
+ 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00,
+ 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00,
+ 0xFC00};
+ static const unsigned char shift_table[512] = {
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15,
+ 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19,
+ 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
+ 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
+ 24, 24, 24, 24, 24, 24, 24, 13};
+ uint16 hbits = base_table[bits >> 23] +
+ static_cast<uint16>((bits & 0x7FFFFF) >>
+ shift_table[bits >> 23]);
+ if (R == std::round_to_nearest)
+ hbits +=
+ (((bits & 0x7FFFFF) >> (shift_table[bits >> 23] - 1)) |
+ (((bits >> 23) & 0xFF) == 102)) &
+ ((hbits & 0x7C00) != 0x7C00)
+#if HALF_ROUND_TIES_TO_EVEN
+ & (((((static_cast<uint32>(1)
+ << (shift_table[bits >> 23] - 1)) -
+ 1) &
+ bits) != 0) |
+ hbits)
+#endif
+ ;
+ else if (R == std::round_toward_zero)
+ hbits -=
+ ((hbits & 0x7FFF) == 0x7C00) & ~shift_table[bits >> 23];
+ else if (R == std::round_toward_infinity)
+ hbits += ((((bits & 0x7FFFFF &
+ ((static_cast<uint32>(1)
+ << (shift_table[bits >> 23])) -
+ 1)) != 0) |
+ (((bits >> 23) <= 102) & ((bits >> 23) != 0))) &
+ (hbits < 0x7C00)) -
+ ((hbits == 0xFC00) & ((bits >> 23) != 511));
+ else if (R == std::round_toward_neg_infinity)
+ hbits +=
+ ((((bits & 0x7FFFFF &
+ ((static_cast<uint32>(1)
+ << (shift_table[bits >> 23])) -
+ 1)) != 0) |
+ (((bits >> 23) <= 358) & ((bits >> 23) != 256))) &
+ (hbits < 0xFC00) & (hbits >> 15)) -
+ ((hbits == 0x7C00) & ((bits >> 23) != 255));
+ return hbits;
+ }
+
+ /// Convert IEEE double-precision to half-precision.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \param value double-precision value
+ /// \return binary representation of half-precision value
+ template <std::float_round_style R>
+ uint16 float2half_impl(double value, true_type) {
+ typedef bits<float>::type uint32;
+ typedef bits<double>::type uint64;
+ uint64 bits; // = *reinterpret_cast<uint64*>(&value);
+ // //violating strict aliasing!
+ std::memcpy(&bits, &value, sizeof(double));
+ uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF;
+ uint16 hbits = (hi >> 16) & 0x8000;
+ hi &= 0x7FFFFFFF;
+ int exp = hi >> 20;
+ if (exp == 2047)
+ return hbits | 0x7C00 |
+ (0x3FF & -static_cast<unsigned>(
+ (bits & 0xFFFFFFFFFFFFF) != 0));
+ if (exp > 1038) {
+ if (R == std::round_toward_infinity)
+ return hbits | 0x7C00 - (hbits >> 15);
+ if (R == std::round_toward_neg_infinity)
+ return hbits | 0x7BFF + (hbits >> 15);
+ return hbits | 0x7BFF + (R != std::round_toward_zero);
+ }
+ int g, s = lo != 0;
+ if (exp > 1008) {
+ g = (hi >> 9) & 1;
+ s |= (hi & 0x1FF) != 0;
+ hbits |= ((exp - 1008) << 10) | ((hi >> 10) & 0x3FF);
+ } else if (exp > 997) {
+ int i = 1018 - exp;
+ hi = (hi & 0xFFFFF) | 0x100000;
+ g = (hi >> i) & 1;
+ s |= (hi & ((1L << i) - 1)) != 0;
+ hbits |= hi >> (i + 1);
+ } else {
+ g = 0;
+ s |= hi != 0;
+ }
+ if (R == std::round_to_nearest)
+#if HALF_ROUND_TIES_TO_EVEN
+ hbits += g & (s | hbits);
+#else
+ hbits += g;
+#endif
+ else if (R == std::round_toward_infinity)
+ hbits += ~(hbits >> 15) & (s | g);
+ else if (R == std::round_toward_neg_infinity)
+ hbits += (hbits >> 15) & (g | s);
+ return hbits;
+ }
+
+ /// Convert non-IEEE floating point to half-precision.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam T source type (builtin floating
+ /// point type) \param value floating point value \return binary
+ /// representation of half-precision value
+ template <std::float_round_style R, typename T>
+ uint16 float2half_impl(T value, ...) {
+ uint16 hbits = static_cast<unsigned>(builtin_signbit(value))
+ << 15;
+ if (value == T()) return hbits;
+ if (builtin_isnan(value)) return hbits | 0x7FFF;
+ if (builtin_isinf(value)) return hbits | 0x7C00;
+ int exp;
+ std::frexp(value, &exp);
+ if (exp > 16) {
+ if (R == std::round_toward_infinity)
+ return hbits | 0x7C00 - (hbits >> 15);
+ else if (R == std::round_toward_neg_infinity)
+ return hbits | 0x7BFF + (hbits >> 15);
+ return hbits | 0x7BFF + (R != std::round_toward_zero);
+ }
+ if (exp < -13)
+ value = std::ldexp(value, 24);
+ else {
+ value = std::ldexp(value, 11 - exp);
+ hbits |= ((exp + 13) << 10);
+ }
+ T ival, frac = std::modf(value, &ival);
+ hbits +=
+ static_cast<uint16>(std::abs(static_cast<int>(ival)));
+ if (R == std::round_to_nearest) {
+ frac = std::abs(frac);
+#if HALF_ROUND_TIES_TO_EVEN
+ hbits += (frac > T(0.5)) | ((frac == T(0.5)) & hbits);
+#else
+ hbits += frac >= T(0.5);
+#endif
+ } else if (R == std::round_toward_infinity)
+ hbits += frac > T();
+ else if (R == std::round_toward_neg_infinity)
+ hbits += frac < T();
+ return hbits;
+ }
+
+ /// Convert floating point to half-precision.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam T source type (builtin floating
+ /// point type) \param value floating point value \return binary
+ /// representation of half-precision value
+ template <std::float_round_style R, typename T>
+ uint16 float2half(T value) {
+ return float2half_impl<R>(
+ value,
+ bool_type < std::numeric_limits<T>::is_iec559 &&
+ sizeof(typename bits<T>::type) == sizeof(T) > ());
+ }
+
+ /// Convert integer to half-precision floating point.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam S `true` if value negative,
+ /// `false` else \tparam T type to convert (builtin integer
+ /// type) \param value non-negative integral value \return
+ /// binary representation of half-precision value
+ template <std::float_round_style R, bool S, typename T>
+ uint16 int2half_impl(T value) {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_integral<T>::value,
+ "int to half conversion only supports builtin "
+ "integer types");
+#endif
+ if (S) value = -value;
+ uint16 bits = S << 15;
+ if (value > 0xFFFF) {
+ if (R == std::round_toward_infinity)
+ bits |= 0x7C00 - S;
+ else if (R == std::round_toward_neg_infinity)
+ bits |= 0x7BFF + S;
+ else
+ bits |= 0x7BFF + (R != std::round_toward_zero);
+ } else if (value) {
+ unsigned int m = value, exp = 24;
+ for (; m < 0x400; m <<= 1, --exp)
+ ;
+ for (; m > 0x7FF; m >>= 1, ++exp)
+ ;
+ bits |= (exp << 10) + m;
+ if (exp > 24) {
+ if (R == std::round_to_nearest)
+ bits +=
+ (value >> (exp - 25)) & 1
+#if HALF_ROUND_TIES_TO_EVEN
+ & (((((1 << (exp - 25)) - 1) & value) != 0) | bits)
+#endif
+ ;
+ else if (R == std::round_toward_infinity)
+ bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & !S;
+ else if (R == std::round_toward_neg_infinity)
+ bits += ((value & ((1 << (exp - 24)) - 1)) != 0) & S;
+ }
+ }
+ return bits;
+ }
+
+ /// Convert integer to half-precision floating point.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam T type to convert (builtin
+ /// integer type) \param value integral value \return binary
+ /// representation of half-precision value
+ template<std::float_round_style R,typename T> uint16 int2half(T value)
+ {
+ return (value < 0) ? int2half_impl<R, true>(value)
+ : int2half_impl<R, false>(value);
+ }
+
+ /// Convert half-precision to IEEE single-precision.
+ /// Credit for this goes to [Jeroen van der
+ /// Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+ /// \param value binary representation of half-precision value
+ /// \return single-precision value
+ inline float half2float_impl(uint16 value, float, true_type) {
+ typedef bits<float>::type uint32;
+ /* uint32 bits =
+ static_cast<uint32>(value&0x8000)
+ << 16; int abs = value & 0x7FFF; if(abs)
+ {
+ bits |= 0x38000000 <<
+ static_cast<unsigned>(abs>=0x7C00); for(; abs<0x400;
+ abs<<=1,bits-=0x800000) ; bits += static_cast<uint32>(abs)
+ << 13;
+ }
+ */
+ static const uint32 mantissa_table[2048] = {
+ 0x00000000, 0x33800000, 0x34000000, 0x34400000,
+ 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000,
+ 0x35000000, 0x35100000, 0x35200000, 0x35300000,
+ 0x35400000, 0x35500000, 0x35600000, 0x35700000,
+ 0x35800000, 0x35880000, 0x35900000, 0x35980000,
+ 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000,
+ 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000,
+ 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000,
+ 0x36000000, 0x36040000, 0x36080000, 0x360C0000,
+ 0x36100000, 0x36140000, 0x36180000, 0x361C0000,
+ 0x36200000, 0x36240000, 0x36280000, 0x362C0000,
+ 0x36300000, 0x36340000, 0x36380000, 0x363C0000,
+ 0x36400000, 0x36440000, 0x36480000, 0x364C0000,
+ 0x36500000, 0x36540000, 0x36580000, 0x365C0000,
+ 0x36600000, 0x36640000, 0x36680000, 0x366C0000,
+ 0x36700000, 0x36740000, 0x36780000, 0x367C0000,
+ 0x36800000, 0x36820000, 0x36840000, 0x36860000,
+ 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000,
+ 0x36900000, 0x36920000, 0x36940000, 0x36960000,
+ 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000,
+ 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000,
+ 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000,
+ 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000,
+ 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000,
+ 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000,
+ 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000,
+ 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000,
+ 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000,
+ 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000,
+ 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000,
+ 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000,
+ 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000,
+ 0x37000000, 0x37010000, 0x37020000, 0x37030000,
+ 0x37040000, 0x37050000, 0x37060000, 0x37070000,
+ 0x37080000, 0x37090000, 0x370A0000, 0x370B0000,
+ 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000,
+ 0x37100000, 0x37110000, 0x37120000, 0x37130000,
+ 0x37140000, 0x37150000, 0x37160000, 0x37170000,
+ 0x37180000, 0x37190000, 0x371A0000, 0x371B0000,
+ 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000,
+ 0x37200000, 0x37210000, 0x37220000, 0x37230000,
+ 0x37240000, 0x37250000, 0x37260000, 0x37270000,
+ 0x37280000, 0x37290000, 0x372A0000, 0x372B0000,
+ 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000,
+ 0x37300000, 0x37310000, 0x37320000, 0x37330000,
+ 0x37340000, 0x37350000, 0x37360000, 0x37370000,
+ 0x37380000, 0x37390000, 0x373A0000, 0x373B0000,
+ 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000,
+ 0x37400000, 0x37410000, 0x37420000, 0x37430000,
+ 0x37440000, 0x37450000, 0x37460000, 0x37470000,
+ 0x37480000, 0x37490000, 0x374A0000, 0x374B0000,
+ 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000,
+ 0x37500000, 0x37510000, 0x37520000, 0x37530000,
+ 0x37540000, 0x37550000, 0x37560000, 0x37570000,
+ 0x37580000, 0x37590000, 0x375A0000, 0x375B0000,
+ 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000,
+ 0x37600000, 0x37610000, 0x37620000, 0x37630000,
+ 0x37640000, 0x37650000, 0x37660000, 0x37670000,
+ 0x37680000, 0x37690000, 0x376A0000, 0x376B0000,
+ 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000,
+ 0x37700000, 0x37710000, 0x37720000, 0x37730000,
+ 0x37740000, 0x37750000, 0x37760000, 0x37770000,
+ 0x37780000, 0x37790000, 0x377A0000, 0x377B0000,
+ 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000,
+ 0x37800000, 0x37808000, 0x37810000, 0x37818000,
+ 0x37820000, 0x37828000, 0x37830000, 0x37838000,
+ 0x37840000, 0x37848000, 0x37850000, 0x37858000,
+ 0x37860000, 0x37868000, 0x37870000, 0x37878000,
+ 0x37880000, 0x37888000, 0x37890000, 0x37898000,
+ 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000,
+ 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000,
+ 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000,
+ 0x37900000, 0x37908000, 0x37910000, 0x37918000,
+ 0x37920000, 0x37928000, 0x37930000, 0x37938000,
+ 0x37940000, 0x37948000, 0x37950000, 0x37958000,
+ 0x37960000, 0x37968000, 0x37970000, 0x37978000,
+ 0x37980000, 0x37988000, 0x37990000, 0x37998000,
+ 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000,
+ 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000,
+ 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000,
+ 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000,
+ 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000,
+ 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000,
+ 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000,
+ 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000,
+ 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000,
+ 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000,
+ 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000,
+ 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000,
+ 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000,
+ 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000,
+ 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000,
+ 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000,
+ 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000,
+ 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000,
+ 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000,
+ 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000,
+ 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000,
+ 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000,
+ 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000,
+ 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000,
+ 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000,
+ 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000,
+ 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000,
+ 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000,
+ 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000,
+ 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000,
+ 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000,
+ 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000,
+ 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000,
+ 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000,
+ 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000,
+ 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000,
+ 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000,
+ 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000,
+ 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000,
+ 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000,
+ 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000,
+ 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000,
+ 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000,
+ 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000,
+ 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000,
+ 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000,
+ 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000,
+ 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000,
+ 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000,
+ 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000,
+ 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000,
+ 0x38000000, 0x38004000, 0x38008000, 0x3800C000,
+ 0x38010000, 0x38014000, 0x38018000, 0x3801C000,
+ 0x38020000, 0x38024000, 0x38028000, 0x3802C000,
+ 0x38030000, 0x38034000, 0x38038000, 0x3803C000,
+ 0x38040000, 0x38044000, 0x38048000, 0x3804C000,
+ 0x38050000, 0x38054000, 0x38058000, 0x3805C000,
+ 0x38060000, 0x38064000, 0x38068000, 0x3806C000,
+ 0x38070000, 0x38074000, 0x38078000, 0x3807C000,
+ 0x38080000, 0x38084000, 0x38088000, 0x3808C000,
+ 0x38090000, 0x38094000, 0x38098000, 0x3809C000,
+ 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000,
+ 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000,
+ 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000,
+ 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000,
+ 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000,
+ 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000,
+ 0x38100000, 0x38104000, 0x38108000, 0x3810C000,
+ 0x38110000, 0x38114000, 0x38118000, 0x3811C000,
+ 0x38120000, 0x38124000, 0x38128000, 0x3812C000,
+ 0x38130000, 0x38134000, 0x38138000, 0x3813C000,
+ 0x38140000, 0x38144000, 0x38148000, 0x3814C000,
+ 0x38150000, 0x38154000, 0x38158000, 0x3815C000,
+ 0x38160000, 0x38164000, 0x38168000, 0x3816C000,
+ 0x38170000, 0x38174000, 0x38178000, 0x3817C000,
+ 0x38180000, 0x38184000, 0x38188000, 0x3818C000,
+ 0x38190000, 0x38194000, 0x38198000, 0x3819C000,
+ 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000,
+ 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000,
+ 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000,
+ 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000,
+ 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000,
+ 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000,
+ 0x38200000, 0x38204000, 0x38208000, 0x3820C000,
+ 0x38210000, 0x38214000, 0x38218000, 0x3821C000,
+ 0x38220000, 0x38224000, 0x38228000, 0x3822C000,
+ 0x38230000, 0x38234000, 0x38238000, 0x3823C000,
+ 0x38240000, 0x38244000, 0x38248000, 0x3824C000,
+ 0x38250000, 0x38254000, 0x38258000, 0x3825C000,
+ 0x38260000, 0x38264000, 0x38268000, 0x3826C000,
+ 0x38270000, 0x38274000, 0x38278000, 0x3827C000,
+ 0x38280000, 0x38284000, 0x38288000, 0x3828C000,
+ 0x38290000, 0x38294000, 0x38298000, 0x3829C000,
+ 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000,
+ 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000,
+ 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000,
+ 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000,
+ 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000,
+ 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000,
+ 0x38300000, 0x38304000, 0x38308000, 0x3830C000,
+ 0x38310000, 0x38314000, 0x38318000, 0x3831C000,
+ 0x38320000, 0x38324000, 0x38328000, 0x3832C000,
+ 0x38330000, 0x38334000, 0x38338000, 0x3833C000,
+ 0x38340000, 0x38344000, 0x38348000, 0x3834C000,
+ 0x38350000, 0x38354000, 0x38358000, 0x3835C000,
+ 0x38360000, 0x38364000, 0x38368000, 0x3836C000,
+ 0x38370000, 0x38374000, 0x38378000, 0x3837C000,
+ 0x38380000, 0x38384000, 0x38388000, 0x3838C000,
+ 0x38390000, 0x38394000, 0x38398000, 0x3839C000,
+ 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000,
+ 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000,
+ 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000,
+ 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000,
+ 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000,
+ 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000,
+ 0x38400000, 0x38404000, 0x38408000, 0x3840C000,
+ 0x38410000, 0x38414000, 0x38418000, 0x3841C000,
+ 0x38420000, 0x38424000, 0x38428000, 0x3842C000,
+ 0x38430000, 0x38434000, 0x38438000, 0x3843C000,
+ 0x38440000, 0x38444000, 0x38448000, 0x3844C000,
+ 0x38450000, 0x38454000, 0x38458000, 0x3845C000,
+ 0x38460000, 0x38464000, 0x38468000, 0x3846C000,
+ 0x38470000, 0x38474000, 0x38478000, 0x3847C000,
+ 0x38480000, 0x38484000, 0x38488000, 0x3848C000,
+ 0x38490000, 0x38494000, 0x38498000, 0x3849C000,
+ 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000,
+ 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000,
+ 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000,
+ 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000,
+ 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000,
+ 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000,
+ 0x38500000, 0x38504000, 0x38508000, 0x3850C000,
+ 0x38510000, 0x38514000, 0x38518000, 0x3851C000,
+ 0x38520000, 0x38524000, 0x38528000, 0x3852C000,
+ 0x38530000, 0x38534000, 0x38538000, 0x3853C000,
+ 0x38540000, 0x38544000, 0x38548000, 0x3854C000,
+ 0x38550000, 0x38554000, 0x38558000, 0x3855C000,
+ 0x38560000, 0x38564000, 0x38568000, 0x3856C000,
+ 0x38570000, 0x38574000, 0x38578000, 0x3857C000,
+ 0x38580000, 0x38584000, 0x38588000, 0x3858C000,
+ 0x38590000, 0x38594000, 0x38598000, 0x3859C000,
+ 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000,
+ 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000,
+ 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000,
+ 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000,
+ 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000,
+ 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000,
+ 0x38600000, 0x38604000, 0x38608000, 0x3860C000,
+ 0x38610000, 0x38614000, 0x38618000, 0x3861C000,
+ 0x38620000, 0x38624000, 0x38628000, 0x3862C000,
+ 0x38630000, 0x38634000, 0x38638000, 0x3863C000,
+ 0x38640000, 0x38644000, 0x38648000, 0x3864C000,
+ 0x38650000, 0x38654000, 0x38658000, 0x3865C000,
+ 0x38660000, 0x38664000, 0x38668000, 0x3866C000,
+ 0x38670000, 0x38674000, 0x38678000, 0x3867C000,
+ 0x38680000, 0x38684000, 0x38688000, 0x3868C000,
+ 0x38690000, 0x38694000, 0x38698000, 0x3869C000,
+ 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000,
+ 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000,
+ 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000,
+ 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000,
+ 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000,
+ 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000,
+ 0x38700000, 0x38704000, 0x38708000, 0x3870C000,
+ 0x38710000, 0x38714000, 0x38718000, 0x3871C000,
+ 0x38720000, 0x38724000, 0x38728000, 0x3872C000,
+ 0x38730000, 0x38734000, 0x38738000, 0x3873C000,
+ 0x38740000, 0x38744000, 0x38748000, 0x3874C000,
+ 0x38750000, 0x38754000, 0x38758000, 0x3875C000,
+ 0x38760000, 0x38764000, 0x38768000, 0x3876C000,
+ 0x38770000, 0x38774000, 0x38778000, 0x3877C000,
+ 0x38780000, 0x38784000, 0x38788000, 0x3878C000,
+ 0x38790000, 0x38794000, 0x38798000, 0x3879C000,
+ 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000,
+ 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000,
+ 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000,
+ 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000,
+ 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000,
+ 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000,
+ 0x38000000, 0x38002000, 0x38004000, 0x38006000,
+ 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000,
+ 0x38010000, 0x38012000, 0x38014000, 0x38016000,
+ 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000,
+ 0x38020000, 0x38022000, 0x38024000, 0x38026000,
+ 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000,
+ 0x38030000, 0x38032000, 0x38034000, 0x38036000,
+ 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000,
+ 0x38040000, 0x38042000, 0x38044000, 0x38046000,
+ 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000,
+ 0x38050000, 0x38052000, 0x38054000, 0x38056000,
+ 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000,
+ 0x38060000, 0x38062000, 0x38064000, 0x38066000,
+ 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000,
+ 0x38070000, 0x38072000, 0x38074000, 0x38076000,
+ 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000,
+ 0x38080000, 0x38082000, 0x38084000, 0x38086000,
+ 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000,
+ 0x38090000, 0x38092000, 0x38094000, 0x38096000,
+ 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000,
+ 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000,
+ 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000,
+ 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000,
+ 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000,
+ 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000,
+ 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000,
+ 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000,
+ 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000,
+ 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000,
+ 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000,
+ 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000,
+ 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000,
+ 0x38100000, 0x38102000, 0x38104000, 0x38106000,
+ 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000,
+ 0x38110000, 0x38112000, 0x38114000, 0x38116000,
+ 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000,
+ 0x38120000, 0x38122000, 0x38124000, 0x38126000,
+ 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000,
+ 0x38130000, 0x38132000, 0x38134000, 0x38136000,
+ 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000,
+ 0x38140000, 0x38142000, 0x38144000, 0x38146000,
+ 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000,
+ 0x38150000, 0x38152000, 0x38154000, 0x38156000,
+ 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000,
+ 0x38160000, 0x38162000, 0x38164000, 0x38166000,
+ 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000,
+ 0x38170000, 0x38172000, 0x38174000, 0x38176000,
+ 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000,
+ 0x38180000, 0x38182000, 0x38184000, 0x38186000,
+ 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000,
+ 0x38190000, 0x38192000, 0x38194000, 0x38196000,
+ 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000,
+ 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000,
+ 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000,
+ 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000,
+ 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000,
+ 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000,
+ 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000,
+ 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000,
+ 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000,
+ 0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000,
+ 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000,
+ 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000,
+ 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000,
+ 0x38200000, 0x38202000, 0x38204000, 0x38206000,
+ 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000,
+ 0x38210000, 0x38212000, 0x38214000, 0x38216000,
+ 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000,
+ 0x38220000, 0x38222000, 0x38224000, 0x38226000,
+ 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000,
+ 0x38230000, 0x38232000, 0x38234000, 0x38236000,
+ 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000,
+ 0x38240000, 0x38242000, 0x38244000, 0x38246000,
+ 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000,
+ 0x38250000, 0x38252000, 0x38254000, 0x38256000,
+ 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000,
+ 0x38260000, 0x38262000, 0x38264000, 0x38266000,
+ 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000,
+ 0x38270000, 0x38272000, 0x38274000, 0x38276000,
+ 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000,
+ 0x38280000, 0x38282000, 0x38284000, 0x38286000,
+ 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000,
+ 0x38290000, 0x38292000, 0x38294000, 0x38296000,
+ 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000,
+ 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000,
+ 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000,
+ 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000,
+ 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000,
+ 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000,
+ 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000,
+ 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000,
+ 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000,
+ 0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000,
+ 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000,
+ 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000,
+ 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000,
+ 0x38300000, 0x38302000, 0x38304000, 0x38306000,
+ 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000,
+ 0x38310000, 0x38312000, 0x38314000, 0x38316000,
+ 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000,
+ 0x38320000, 0x38322000, 0x38324000, 0x38326000,
+ 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000,
+ 0x38330000, 0x38332000, 0x38334000, 0x38336000,
+ 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000,
+ 0x38340000, 0x38342000, 0x38344000, 0x38346000,
+ 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000,
+ 0x38350000, 0x38352000, 0x38354000, 0x38356000,
+ 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000,
+ 0x38360000, 0x38362000, 0x38364000, 0x38366000,
+ 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000,
+ 0x38370000, 0x38372000, 0x38374000, 0x38376000,
+ 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000,
+ 0x38380000, 0x38382000, 0x38384000, 0x38386000,
+ 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000,
+ 0x38390000, 0x38392000, 0x38394000, 0x38396000,
+ 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000,
+ 0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000,
+ 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000,
+ 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000,
+ 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000,
+ 0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000,
+ 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000,
+ 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000,
+ 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000,
+ 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000,
+ 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000,
+ 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000,
+ 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000,
+ 0x38400000, 0x38402000, 0x38404000, 0x38406000,
+ 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000,
+ 0x38410000, 0x38412000, 0x38414000, 0x38416000,
+ 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000,
+ 0x38420000, 0x38422000, 0x38424000, 0x38426000,
+ 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000,
+ 0x38430000, 0x38432000, 0x38434000, 0x38436000,
+ 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000,
+ 0x38440000, 0x38442000, 0x38444000, 0x38446000,
+ 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000,
+ 0x38450000, 0x38452000, 0x38454000, 0x38456000,
+ 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000,
+ 0x38460000, 0x38462000, 0x38464000, 0x38466000,
+ 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000,
+ 0x38470000, 0x38472000, 0x38474000, 0x38476000,
+ 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000,
+ 0x38480000, 0x38482000, 0x38484000, 0x38486000,
+ 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000,
+ 0x38490000, 0x38492000, 0x38494000, 0x38496000,
+ 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000,
+ 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000,
+ 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000,
+ 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000,
+ 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000,
+ 0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000,
+ 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000,
+ 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000,
+ 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000,
+ 0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000,
+ 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000,
+ 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000,
+ 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000,
+ 0x38500000, 0x38502000, 0x38504000, 0x38506000,
+ 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000,
+ 0x38510000, 0x38512000, 0x38514000, 0x38516000,
+ 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000,
+ 0x38520000, 0x38522000, 0x38524000, 0x38526000,
+ 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000,
+ 0x38530000, 0x38532000, 0x38534000, 0x38536000,
+ 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000,
+ 0x38540000, 0x38542000, 0x38544000, 0x38546000,
+ 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000,
+ 0x38550000, 0x38552000, 0x38554000, 0x38556000,
+ 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000,
+ 0x38560000, 0x38562000, 0x38564000, 0x38566000,
+ 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000,
+ 0x38570000, 0x38572000, 0x38574000, 0x38576000,
+ 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000,
+ 0x38580000, 0x38582000, 0x38584000, 0x38586000,
+ 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000,
+ 0x38590000, 0x38592000, 0x38594000, 0x38596000,
+ 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000,
+ 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000,
+ 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000,
+ 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000,
+ 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000,
+ 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000,
+ 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000,
+ 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000,
+ 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000,
+ 0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000,
+ 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000,
+ 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000,
+ 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000,
+ 0x38600000, 0x38602000, 0x38604000, 0x38606000,
+ 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000,
+ 0x38610000, 0x38612000, 0x38614000, 0x38616000,
+ 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000,
+ 0x38620000, 0x38622000, 0x38624000, 0x38626000,
+ 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000,
+ 0x38630000, 0x38632000, 0x38634000, 0x38636000,
+ 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000,
+ 0x38640000, 0x38642000, 0x38644000, 0x38646000,
+ 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000,
+ 0x38650000, 0x38652000, 0x38654000, 0x38656000,
+ 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000,
+ 0x38660000, 0x38662000, 0x38664000, 0x38666000,
+ 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000,
+ 0x38670000, 0x38672000, 0x38674000, 0x38676000,
+ 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000,
+ 0x38680000, 0x38682000, 0x38684000, 0x38686000,
+ 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000,
+ 0x38690000, 0x38692000, 0x38694000, 0x38696000,
+ 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000,
+ 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000,
+ 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000,
+ 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000,
+ 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000,
+ 0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000,
+ 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000,
+ 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000,
+ 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000,
+ 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000,
+ 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000,
+ 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000,
+ 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000,
+ 0x38700000, 0x38702000, 0x38704000, 0x38706000,
+ 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000,
+ 0x38710000, 0x38712000, 0x38714000, 0x38716000,
+ 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000,
+ 0x38720000, 0x38722000, 0x38724000, 0x38726000,
+ 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000,
+ 0x38730000, 0x38732000, 0x38734000, 0x38736000,
+ 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000,
+ 0x38740000, 0x38742000, 0x38744000, 0x38746000,
+ 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000,
+ 0x38750000, 0x38752000, 0x38754000, 0x38756000,
+ 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000,
+ 0x38760000, 0x38762000, 0x38764000, 0x38766000,
+ 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000,
+ 0x38770000, 0x38772000, 0x38774000, 0x38776000,
+ 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000,
+ 0x38780000, 0x38782000, 0x38784000, 0x38786000,
+ 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000,
+ 0x38790000, 0x38792000, 0x38794000, 0x38796000,
+ 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000,
+ 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000,
+ 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000,
+ 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000,
+ 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000,
+ 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000,
+ 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000,
+ 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000,
+ 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000,
+ 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000,
+ 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000,
+ 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000,
+ 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000};
+ static const uint32 exponent_table[64] = {
+ 0x00000000, 0x00800000, 0x01000000, 0x01800000,
+ 0x02000000, 0x02800000, 0x03000000, 0x03800000,
+ 0x04000000, 0x04800000, 0x05000000, 0x05800000,
+ 0x06000000, 0x06800000, 0x07000000, 0x07800000,
+ 0x08000000, 0x08800000, 0x09000000, 0x09800000,
+ 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000,
+ 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000,
+ 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000,
+ 0x80000000, 0x80800000, 0x81000000, 0x81800000,
+ 0x82000000, 0x82800000, 0x83000000, 0x83800000,
+ 0x84000000, 0x84800000, 0x85000000, 0x85800000,
+ 0x86000000, 0x86800000, 0x87000000, 0x87800000,
+ 0x88000000, 0x88800000, 0x89000000, 0x89800000,
+ 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000,
+ 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000,
+ 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000};
+ static const unsigned short offset_table[64] = {
+ 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024,
+ 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024};
+ uint32 bits = mantissa_table[offset_table[value >> 10] +
+ (value & 0x3FF)] +
+ exponent_table[value >> 10];
+ // return *reinterpret_cast<float*>(&bits);
+ ////violating strict aliasing!
+ float out;
+ std::memcpy(&out, &bits, sizeof(float));
+ return out;
+ }
+
+ /// Convert half-precision to IEEE double-precision.
+ /// \param value binary representation of half-precision value
+ /// \return double-precision value
+ inline double half2float_impl(uint16 value, double, true_type) {
+ typedef bits<float>::type uint32;
+ typedef bits<double>::type uint64;
+ uint32 hi = static_cast<uint32>(value & 0x8000) << 16;
+ int abs = value & 0x7FFF;
+ if (abs) {
+ hi |= 0x3F000000 << static_cast<unsigned>(abs >= 0x7C00);
+ for (; abs < 0x400; abs <<= 1, hi -= 0x100000)
+ ;
+ hi += static_cast<uint32>(abs) << 10;
+ }
+ uint64 bits = static_cast<uint64>(hi) << 32;
+ // return
+ //*reinterpret_cast<double*>(&bits);
+ ////violating strict aliasing!
+ double out;
+ std::memcpy(&out, &bits, sizeof(double));
+ return out;
+ }
+
+ /// Convert half-precision to non-IEEE floating point.
+ /// \tparam T type to convert to (builtin integer type)
+ /// \param value binary representation of half-precision value
+ /// \return floating point value
+ template <typename T>
+ T half2float_impl(uint16 value, T, ...) {
+ T out;
+ int abs = value & 0x7FFF;
+ if (abs > 0x7C00)
+ out = std::numeric_limits<T>::has_quiet_NaN
+ ? std::numeric_limits<T>::quiet_NaN()
+ : T();
+ else if (abs == 0x7C00)
+ out = std::numeric_limits<T>::has_infinity
+ ? std::numeric_limits<T>::infinity()
+ : std::numeric_limits<T>::max();
+ else if (abs > 0x3FF)
+ out = std::ldexp(static_cast<T>((abs & 0x3FF) | 0x400),
+ (abs >> 10) - 25);
+ else
+ out = std::ldexp(static_cast<T>(abs), -24);
+ return (value & 0x8000) ? -out : out;
+ }
+
+ /// Convert half-precision to floating point.
+ /// \tparam T type to convert to (builtin integer type)
+ /// \param value binary representation of half-precision value
+ /// \return floating point value
+ template <typename T>
+ T half2float(uint16 value) {
+ return half2float_impl(
+ value, T(),
+ bool_type < std::numeric_limits<T>::is_iec559 &&
+ sizeof(typename bits<T>::type) == sizeof(T) > ());
+ }
+
+ /// Convert half-precision floating point to integer.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam E `true` for round to even,
+ /// `false` for round away from zero \tparam T type to convert
+ /// to (buitlin integer type with at least 16 bits precision,
+ /// excluding any implicit sign bits) \param value binary
+ /// representation of half-precision value \return integral
+ /// value
+ template <std::float_round_style R, bool E, typename T>
+ T half2int_impl(uint16 value) {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_integral<T>::value,
+ "half to int conversion only supports builtin "
+ "integer types");
+#endif
+ unsigned int e = value & 0x7FFF;
+ if (e >= 0x7C00)
+ return (value & 0x8000) ? std::numeric_limits<T>::min()
+ : std::numeric_limits<T>::max();
+ if (e < 0x3800) {
+ if (R == std::round_toward_infinity)
+ return T(~(value >> 15) & (e != 0));
+ else if (R == std::round_toward_neg_infinity)
+ return -T(value > 0x8000);
+ return T();
+ }
+ unsigned int m = (value & 0x3FF) | 0x400;
+ e >>= 10;
+ if (e < 25) {
+ if (R == std::round_to_nearest)
+ m += (1 << (24 - e)) - (~(m >> (25 - e)) & E);
+ else if (R == std::round_toward_infinity)
+ m += ((value >> 15) - 1) & ((1 << (25 - e)) - 1U);
+ else if (R == std::round_toward_neg_infinity)
+ m += -(value >> 15) & ((1 << (25 - e)) - 1U);
+ m >>= 25 - e;
+ } else
+ m <<= e - 25;
+ return (value & 0x8000) ? -static_cast<T>(m)
+ : static_cast<T>(m);
+ }
+
+ /// Convert half-precision floating point to integer.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam T type to convert to (buitlin
+ /// integer type with at least 16 bits precision, excluding any
+ /// implicit sign bits) \param value binary representation of
+ /// half-precision value \return integral value
+ template <std::float_round_style R, typename T>
+ T half2int(uint16 value) {
+ return half2int_impl<R, HALF_ROUND_TIES_TO_EVEN, T>(value);
+ }
+
+ /// Convert half-precision floating point to integer using
+ /// round-to-nearest-away-from-zero. \tparam T type to convert
+ /// to (buitlin integer type with at least 16 bits precision,
+ /// excluding any implicit sign bits) \param value binary
+ /// representation of half-precision value \return integral
+ /// value
+ template <typename T>
+ T half2int_up(uint16 value) {
+ return half2int_impl<std::round_to_nearest, 0, T>(value);
+ }
+
+ /// Round half-precision number to nearest integer value.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \tparam E `true` for round to even,
+ /// `false` for round away from zero \param value binary
+ /// representation of half-precision value \return
+ /// half-precision bits for nearest integral value
+ template <std::float_round_style R, bool E>
+ uint16 round_half_impl(uint16 value) {
+ unsigned int e = value & 0x7FFF;
+ uint16 result = value;
+ if (e < 0x3C00) {
+ result &= 0x8000;
+ if (R == std::round_to_nearest)
+ result |= 0x3C00U & -(e >= (0x3800 + E));
+ else if (R == std::round_toward_infinity)
+ result |= 0x3C00U & -(~(value >> 15) & (e != 0));
+ else if (R == std::round_toward_neg_infinity)
+ result |= 0x3C00U & -(value > 0x8000);
+ } else if (e < 0x6400) {
+ e = 25 - (e >> 10);
+ unsigned int mask = (1 << e) - 1;
+ if (R == std::round_to_nearest)
+ result += (1 << (e - 1)) - (~(result >> e) & E);
+ else if (R == std::round_toward_infinity)
+ result += mask & ((value >> 15) - 1);
+ else if (R == std::round_toward_neg_infinity)
+ result += mask & -(value >> 15);
+ result &= ~mask;
+ }
+ return result;
+ }
+
+ /// Round half-precision number to nearest integer value.
+ /// \tparam R rounding mode to use, `std::round_indeterminate`
+ /// for fastest rounding \param value binary representation of
+ /// half-precision value \return half-precision bits for nearest
+ /// integral value
+ template <std::float_round_style R>
+ uint16 round_half(uint16 value) {
+ return round_half_impl<R, HALF_ROUND_TIES_TO_EVEN>(value);
+ }
+
+ /// Round half-precision number to nearest integer value using
+ /// round-to-nearest-away-from-zero. \param value binary
+ /// representation of half-precision value \return
+ /// half-precision bits for nearest integral value
+ inline uint16 round_half_up(uint16 value) {
+ return round_half_impl<std::round_to_nearest, 0>(value);
+ }
+ /// \}
+
+ struct functions;
+ template<typename> struct unary_specialized;
+ template<typename,typename> struct binary_specialized;
+ template<typename,typename,std::float_round_style> struct half_caster;
+ }
+
+ /// Half-precision floating point type.
+ /// This class implements an IEEE-conformant half-precision floating
+ /// point type with the usual arithmetic operators and conversions. It
+ /// is implicitly convertible to single-precision floating point, which
+ /// makes artihmetic expressions and functions with mixed-type operands
+ /// to be of the most precise operand type. Additionally all arithmetic
+ /// operations (and many mathematical functions) are carried out in
+ /// single-precision internally. All conversions from single- to
+ /// half-precision are done using the library's default rounding mode,
+ /// but temporary results inside chained arithmetic expressions are kept
+ /// in single-precision as long as possible (while of course still
+ /// maintaining a strong half-precision type).
+ ///
+ /// According to the C++98/03 definition, the half type is not a POD
+ /// type. But according to C++11's less strict and extended definitions
+ /// it is both a standard layout type and a trivially copyable type
+ /// (even if not a POD type), which means it can be
+ /// standard-conformantly copied using raw binary copies. But in this
+ /// context some more words about the actual size of the type. Although
+ /// the half is representing an IEEE 16-bit type, it does not
+ /// neccessarily have to be of exactly 16-bits size. But on any
+ /// reasonable implementation the actual binary representation of this
+ /// type will most probably not ivolve any additional "magic" or padding
+ /// beyond the simple binary representation of the underlying 16-bit
+ /// IEEE number, even if not strictly guaranteed by the standard. But
+ /// even then it only has an actual size of 16 bits if your C++
+ /// implementation supports an unsigned integer type of exactly 16 bits
+ /// width. But this should be the case on nearly any reasonable
+ /// platform.
+ ///
+ /// So if your C++ implementation is not totally exotic or imposes
+ /// special alignment requirements, it is a reasonable assumption that
+ /// the data of a half is just comprised of the 2 bytes of the
+ /// underlying IEEE representation.
+ class half {
+ friend struct detail::functions;
+ friend struct detail::unary_specialized<half>;
+ friend struct detail::binary_specialized<half, half>;
+ template <typename, typename, std::float_round_style>
+ friend struct detail::half_caster;
+ friend class std::numeric_limits<half>;
+#if HALF_ENABLE_CPP11_HASH
+ friend struct std::hash<half>;
+#endif
+#if HALF_ENABLE_CPP11_USER_LITERALS
+ friend half literal::operator""_h(long double);
+#endif
+
+ public:
+ /// Default constructor.
+ /// This initializes the half to 0. Although this does not match
+ /// the builtin types' default-initialization semantics and may
+ /// be less efficient than no initialization, it is needed to
+ /// provide proper value-initialization semantics.
+ HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}
+
+ /// Copy constructor.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to copy from
+ half(detail::expr rhs)
+ : data_(
+ detail::float2half<round_style>(static_cast<float>(rhs))) {}
+
+ /// Conversion constructor.
+ /// \param rhs float to convert
+ explicit half(float rhs)
+ : data_(detail::float2half<round_style>(rhs)) {}
+
+ /// Conversion to single-precision.
+ /// \return single precision value representing expression value
+ operator float() const { return detail::half2float<float>(data_); }
+
+ /// Assignment operator.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to copy from
+ /// \return reference to this half
+ half &operator=(detail::expr rhs) {
+ return *this = static_cast<float>(rhs);
+ }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to add
+ /// \return reference to this half
+ template <typename T>
+ typename detail::enable<half &, T>::type operator+=(T rhs) {
+ return *this += static_cast<float>(rhs);
+ }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to subtract
+ /// \return reference to this half
+ template <typename T>
+ typename detail::enable<half &, T>::type operator-=(T rhs) {
+ return *this -= static_cast<float>(rhs);
+ }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to multiply with
+ /// \return reference to this half
+ template <typename T>
+ typename detail::enable<half &, T>::type operator*=(T rhs) {
+ return *this *= static_cast<float>(rhs);
+ }
+
+ /// Arithmetic assignment.
+ /// \tparam T type of concrete half expression
+ /// \param rhs half expression to divide by
+ /// \return reference to this half
+ template <typename T>
+ typename detail::enable<half &, T>::type operator/=(T rhs) {
+ return *this /= static_cast<float>(rhs);
+ }
+
+ /// Assignment operator.
+ /// \param rhs single-precision value to copy from
+ /// \return reference to this half
+ half &operator=(float rhs) {
+ data_ = detail::float2half<round_style>(rhs);
+ return *this;
+ }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to add
+ /// \return reference to this half
+ half &operator+=(float rhs) {
+ data_ = detail::float2half<round_style>(
+ detail::half2float<float>(data_) + rhs);
+ return *this;
+ }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to subtract
+ /// \return reference to this half
+ half &operator-=(float rhs) {
+ data_ = detail::float2half<round_style>(
+ detail::half2float<float>(data_) - rhs);
+ return *this;
+ }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to multiply with
+ /// \return reference to this half
+ half &operator*=(float rhs) {
+ data_ = detail::float2half<round_style>(
+ detail::half2float<float>(data_) * rhs);
+ return *this;
+ }
+
+ /// Arithmetic assignment.
+ /// \param rhs single-precision value to divide by
+ /// \return reference to this half
+ half &operator/=(float rhs) {
+ data_ = detail::float2half<round_style>(
+ detail::half2float<float>(data_) / rhs);
+ return *this;
+ }
+
+ /// Prefix increment.
+ /// \return incremented half value
+ half &operator++() { return *this += 1.0f; }
+
+ /// Prefix decrement.
+ /// \return decremented half value
+ half &operator--() { return *this -= 1.0f; }
+
+ /// Postfix increment.
+ /// \return non-incremented half value
+ half operator++(int) {
+ half out(*this);
+ ++*this;
+ return out;
+ }
+
+ /// Postfix decrement.
+ /// \return non-decremented half value
+ half operator--(int) {
+ half out(*this);
+ --*this;
+ return out;
+ }
+
+ private:
+ /// Rounding mode to use
+ static const std::float_round_style round_style =
+ (std::float_round_style)(HALF_ROUND_STYLE);
+
+ /// Constructor.
+ /// \param bits binary representation to set half to
+ HALF_CONSTEXPR half(detail::binary_t,
+ detail::uint16 bits) HALF_NOEXCEPT : data_(bits) {
+ }
+
+ /// Internal binary representation
+ detail::uint16 data_;
+ };
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+ namespace literal
+ {
+ /// Half literal.
+ /// While this returns an actual half-precision value, half literals can
+ /// unfortunately not be constant expressions due to rather involved
+ /// conversions. \param value literal value \return half with given
+ /// value (if representable)
+ inline half operator""_h(long double value) {
+ return half(detail::binary,
+ detail::float2half<half::round_style>(value));
+ }
+ } // namespace literal
+#endif
+
+ namespace detail
+ {
+ /// Wrapper implementing unspecialized half-precision functions.
+ struct functions
+ {
+ /// Addition implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision sum stored in single-precision
+ static expr plus(float x, float y) { return expr(x+y); }
+
+ /// Subtraction implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision difference stored in single-precision
+ static expr minus(float x, float y) { return expr(x-y); }
+
+ /// Multiplication implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision product stored in single-precision
+ static expr multiplies(float x, float y) { return expr(x*y); }
+
+ /// Division implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision quotient stored in single-precision
+ static expr divides(float x, float y) { return expr(x/y); }
+
+ /// Output implementation.
+ /// \param out stream to write to
+ /// \param arg value to write
+ /// \return reference to stream
+ template<typename charT,typename traits> static std::basic_ostream<charT,traits>& write(std::basic_ostream<charT,traits> &out, float arg) { return out << arg; }
+
+ /// Input implementation.
+ /// \param in stream to read from
+ /// \param arg half to read into
+ /// \return reference to stream
+ template<typename charT,typename traits> static std::basic_istream<charT,traits>& read(std::basic_istream<charT,traits> &in, half &arg)
+ {
+ float f;
+ if(in >> f)
+ arg = f;
+ return in;
+ }
+
+ /// Modulo implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision division remainder stored in
+ /// single-precision
+ static expr fmod(float x, float y) {
+ return expr(std::fmod(x, y));
+ }
+
+ /// Remainder implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Half-precision division remainder stored in
+ /// single-precision
+ static expr remainder(float x, float y) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::remainder(x, y));
+#else
+ if (builtin_isnan(x) || builtin_isnan(y))
+ return expr(
+ std::numeric_limits<float>::quiet_NaN());
+ float ax = std::fabs(x), ay = std::fabs(y);
+ if (ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
+ return expr(
+ std::numeric_limits<float>::quiet_NaN());
+ if (ay >= 65536.0f) return expr(x);
+ if (ax == ay)
+ return expr(builtin_signbit(x) ? -0.0f : 0.0f);
+ ax = std::fmod(ax, ay + ay);
+ float y2 = 0.5f * ay;
+ if (ax > y2) {
+ ax -= ay;
+ if (ax >= y2) ax -= ay;
+ }
+ return expr(builtin_signbit(x) ? -ax : ax);
+#endif
+ }
+
+ /// Remainder implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \param quo address to store quotient bits at
+ /// \return Half-precision division remainder stored in
+ /// single-precision
+ static expr remquo(float x, float y, int *quo) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::remquo(x, y, quo));
+#else
+ if (builtin_isnan(x) || builtin_isnan(y))
+ return expr(
+ std::numeric_limits<float>::quiet_NaN());
+ bool sign = builtin_signbit(x),
+ qsign =
+ static_cast<bool>(sign ^ builtin_signbit(y));
+ float ax = std::fabs(x), ay = std::fabs(y);
+ if (ax >= 65536.0f || ay < std::ldexp(1.0f, -24))
+ return expr(
+ std::numeric_limits<float>::quiet_NaN());
+ if (ay >= 65536.0f) return expr(x);
+ if (ax == ay)
+ return *quo = qsign ? -1 : 1,
+ expr(sign ? -0.0f : 0.0f);
+ ax = std::fmod(ax, 8.0f * ay);
+ int cquo = 0;
+ if (ax >= 4.0f * ay) {
+ ax -= 4.0f * ay;
+ cquo += 4;
+ }
+ if (ax >= 2.0f * ay) {
+ ax -= 2.0f * ay;
+ cquo += 2;
+ }
+ float y2 = 0.5f * ay;
+ if (ax > y2) {
+ ax -= ay;
+ ++cquo;
+ if (ax >= y2) {
+ ax -= ay;
+ ++cquo;
+ }
+ }
+ return *quo = qsign ? -cquo : cquo,
+ expr(sign ? -ax : ax);
+#endif
+ }
+
+ /// Positive difference implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return Positive difference stored in
+ /// single-precision
+ static expr fdim(float x, float y)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::fdim(x, y));
+ #else
+ return expr((x <= y) ? 0.0f : (x - y));
+#endif
+ }
+
+ /// Fused multiply-add implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \param z third operand
+ /// \return \a x * \a y + \a z stored in single-precision
+ static expr fma(float x, float y, float z)
+ {
+ #if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF)
+ return expr(std::fma(x, y, z));
+ #else
+ return expr(x*y+z);
+ #endif
+ }
+
+ /// Get NaN.
+ /// \return Half-precision quiet NaN
+ static half nanh() { return half(binary, 0x7FFF); }
+
+ /// Exponential implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr exp(float arg) { return expr(std::exp(arg)); }
+
+ /// Exponential implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr expm1(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::expm1(arg));
+ #else
+ return expr(static_cast<float>(
+ std::exp(static_cast<double>(arg)) - 1.0));
+#endif
+ }
+
+ /// Binary exponential implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr exp2(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::exp2(arg));
+ #else
+ return expr(static_cast<float>(std::exp(
+ arg * 0.69314718055994530941723212145818)));
+#endif
+ }
+
+ /// Logarithm implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr log(float arg) { return expr(std::log(arg)); }
+
+ /// Common logarithm implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr log10(float arg) { return expr(std::log10(arg)); }
+
+ /// Logarithm implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr log1p(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::log1p(arg));
+ #else
+ return expr(static_cast<float>(std::log(1.0 + arg)));
+#endif
+ }
+
+ /// Binary logarithm implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr log2(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::log2(arg));
+ #else
+ return expr(static_cast<float>(
+ std::log(static_cast<double>(arg)) *
+ 1.4426950408889634073599246810019));
+#endif
+ }
+
+ /// Square root implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr sqrt(float arg) { return expr(std::sqrt(arg)); }
+
+ /// Cubic root implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr cbrt(float arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::cbrt(arg));
+#else
+ if (builtin_isnan(arg) || builtin_isinf(arg))
+ return expr(arg);
+ return expr(
+ builtin_signbit(arg)
+ ? -static_cast<float>(std::pow(
+ -static_cast<double>(arg), 1.0 / 3.0))
+ : static_cast<float>(std::pow(
+ static_cast<double>(arg), 1.0 / 3.0)));
+#endif
+ }
+
+ /// Hypotenuse implementation.
+ /// \param x first argument
+ /// \param y second argument
+ /// \return function value stored in single-preicision
+ static expr hypot(float x, float y)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::hypot(x, y));
+ #else
+ return expr(
+ (builtin_isinf(x) || builtin_isinf(y))
+ ? std::numeric_limits<float>::infinity()
+ : static_cast<float>(
+ std::sqrt(static_cast<double>(x) * x +
+ static_cast<double>(y) * y)));
+#endif
+ }
+
+ /// Power implementation.
+ /// \param base value to exponentiate
+ /// \param exp power to expontiate to
+ /// \return function value stored in single-preicision
+ static expr pow(float base, float exp) { return expr(std::pow(base, exp)); }
+
+ /// Sine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr sin(float arg) { return expr(std::sin(arg)); }
+
+ /// Cosine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr cos(float arg) { return expr(std::cos(arg)); }
+
+ /// Tan implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr tan(float arg) { return expr(std::tan(arg)); }
+
+ /// Arc sine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr asin(float arg) { return expr(std::asin(arg)); }
+
+ /// Arc cosine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr acos(float arg) { return expr(std::acos(arg)); }
+
+ /// Arc tangent implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr atan(float arg) { return expr(std::atan(arg)); }
+
+ /// Arc tangent implementation.
+ /// \param x first argument
+ /// \param y second argument
+ /// \return function value stored in single-preicision
+ static expr atan2(float x, float y) { return expr(std::atan2(x, y)); }
+
+ /// Hyperbolic sine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr sinh(float arg) { return expr(std::sinh(arg)); }
+
+ /// Hyperbolic cosine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr cosh(float arg) { return expr(std::cosh(arg)); }
+
+ /// Hyperbolic tangent implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr tanh(float arg) { return expr(std::tanh(arg)); }
+
+ /// Hyperbolic area sine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr asinh(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::asinh(arg));
+ #else
+ return expr(
+ (arg == -std::numeric_limits<float>::infinity())
+ ? arg
+ : static_cast<float>(std::log(
+ arg + std::sqrt(arg * arg + 1.0))));
+#endif
+ }
+
+ /// Hyperbolic area cosine implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr acosh(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::acosh(arg));
+ #else
+ return expr(
+ (arg < -1.0f)
+ ? std::numeric_limits<float>::quiet_NaN()
+ : static_cast<float>(std::log(
+ arg + std::sqrt(arg * arg - 1.0))));
+#endif
+ }
+
+ /// Hyperbolic area tangent implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr atanh(float arg)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::atanh(arg));
+ #else
+ return expr(static_cast<float>(
+ 0.5 * std::log((1.0 + arg) / (1.0 - arg))));
+#endif
+ }
+
+ /// Error function implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr erf(float arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::erf(arg));
+#else
+ return expr(static_cast<float>(
+ erf(static_cast<double>(arg))));
+#endif
+ }
+
+ /// Complementary implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr erfc(float arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::erfc(arg));
+#else
+ return expr(static_cast<float>(
+ 1.0 - erf(static_cast<double>(arg))));
+#endif
+ }
+
+ /// Gamma logarithm implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr lgamma(float arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::lgamma(arg));
+#else
+ if (builtin_isinf(arg))
+ return expr(std::numeric_limits<float>::infinity());
+ if (arg < 0.0f) {
+ float i, f = std::modf(-arg, &i);
+ if (f == 0.0f)
+ return expr(
+ std::numeric_limits<float>::infinity());
+ return expr(static_cast<float>(
+ 1.1447298858494001741434273513531 -
+ std::log(std::abs(std::sin(
+ 3.1415926535897932384626433832795 * f))) -
+ lgamma(1.0 - arg)));
+ }
+ return expr(static_cast<float>(
+ lgamma(static_cast<double>(arg))));
+#endif
+ }
+
+ /// Gamma implementation.
+ /// \param arg function argument
+ /// \return function value stored in single-preicision
+ static expr tgamma(float arg) {
+#if HALF_ENABLE_CPP11_CMATH
+ return expr(std::tgamma(arg));
+#else
+ if (arg == 0.0f)
+ return builtin_signbit(arg)
+ ? expr(-std::numeric_limits<
+ float>::infinity())
+ : expr(std::numeric_limits<
+ float>::infinity());
+ if (arg < 0.0f) {
+ float i, f = std::modf(-arg, &i);
+ if (f == 0.0f)
+ return expr(
+ std::numeric_limits<float>::quiet_NaN());
+ double value =
+ 3.1415926535897932384626433832795 /
+ (std::sin(3.1415926535897932384626433832795 *
+ f) *
+ std::exp(lgamma(1.0 - arg)));
+ return expr(static_cast<float>(
+ (std::fmod(i, 2.0f) == 0.0f) ? -value : value));
+ }
+ if (builtin_isinf(arg)) return expr(arg);
+ return expr(static_cast<float>(
+ std::exp(lgamma(static_cast<double>(arg)))));
+#endif
+ }
+
+ /// Floor implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static half floor(half arg) {
+ return half(
+ binary,
+ round_half<std::round_toward_neg_infinity>(
+ arg.data_));
+ }
+
+ /// Ceiling implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static half ceil(half arg) {
+ return half(binary,
+ round_half<std::round_toward_infinity>(
+ arg.data_));
+ }
+
+ /// Truncation implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static half trunc(half arg) {
+ return half(
+ binary,
+ round_half<std::round_toward_zero>(arg.data_));
+ }
+
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static half round(half arg) {
+ return half(binary, round_half_up(arg.data_));
+ }
+
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static long lround(half arg) {
+ return detail::half2int_up<long>(arg.data_);
+ }
+
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static half rint(half arg) {
+ return half(binary,
+ round_half<half::round_style>(arg.data_));
+ }
+
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static long lrint(half arg) {
+ return detail::half2int<half::round_style, long>(
+ arg.data_);
+ }
+
+#if HALF_ENABLE_CPP11_LONG_LONG
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static long long llround(half arg) {
+ return detail::half2int_up<long long>(arg.data_);
+ }
+
+ /// Nearest integer implementation.
+ /// \param arg value to round
+ /// \return rounded value
+ static long long llrint(half arg) {
+ return detail::half2int<half::round_style, long long>(
+ arg.data_);
+ }
+#endif
+
+ /// Decompression implementation.
+ /// \param arg number to decompress
+ /// \param exp address to store exponent at
+ /// \return normalized significant
+ static half frexp(half arg, int *exp)
+ {
+ int m = arg.data_ & 0x7FFF, e = -14;
+ if (m >= 0x7C00 || !m) return *exp = 0, arg;
+ for (; m < 0x400; m <<= 1, --e)
+ ;
+ return *exp = e + (m >> 10),
+ half(binary, (arg.data_ & 0x8000) | 0x3800 |
+ (m & 0x3FF));
+ }
+
+ /// Decompression implementation.
+ /// \param arg number to decompress
+ /// \param iptr address to store integer part at
+ /// \return fractional part
+ static half modf(half arg, half *iptr)
+ {
+ unsigned int e = arg.data_ & 0x7FFF;
+ if (e >= 0x6400)
+ return *iptr = arg,
+ half(binary,
+ arg.data_ & (0x8000U | -(e > 0x7C00)));
+ if (e < 0x3C00)
+ return iptr->data_ = arg.data_ & 0x8000, arg;
+ e >>= 10;
+ unsigned int mask = (1 << (25 - e)) - 1,
+ m = arg.data_ & mask;
+ iptr->data_ = arg.data_ & ~mask;
+ if (!m) return half(binary, arg.data_ & 0x8000);
+ for (; m < 0x400; m <<= 1, --e)
+ ;
+ return half(binary, static_cast<uint16>(
+ (arg.data_ & 0x8000) |
+ (e << 10) | (m & 0x3FF)));
+ }
+
+ /// Scaling implementation.
+ /// \param arg number to scale
+ /// \param exp power of two to scale by
+ /// \return scaled number
+ static half scalbln(half arg, long exp)
+ {
+ unsigned int m = arg.data_ & 0x7FFF;
+ if (m >= 0x7C00 || !m) return arg;
+ for (; m < 0x400; m <<= 1, --exp)
+ ;
+ exp += m >> 10;
+ uint16 value = arg.data_ & 0x8000;
+ if (exp > 30) {
+ if (half::round_style == std::round_toward_zero)
+ value |= 0x7BFF;
+ else if (half::round_style ==
+ std::round_toward_infinity)
+ value |= 0x7C00 - (value >> 15);
+ else if (half::round_style ==
+ std::round_toward_neg_infinity)
+ value |= 0x7BFF + (value >> 15);
+ else
+ value |= 0x7C00;
+ } else if (exp > 0)
+ value |= (exp << 10) | (m & 0x3FF);
+ else if (exp > -11) {
+ m = (m & 0x3FF) | 0x400;
+ if (half::round_style == std::round_to_nearest) {
+ m += 1 << -exp;
+#if HALF_ROUND_TIES_TO_EVEN
+ m -= (m >> (1 - exp)) & 1;
+#endif
+ } else if (half::round_style ==
+ std::round_toward_infinity)
+ m +=
+ ((value >> 15) - 1) & ((1 << (1 - exp)) - 1U);
+ else if (half::round_style ==
+ std::round_toward_neg_infinity)
+ m += -(value >> 15) & ((1 << (1 - exp)) - 1U);
+ value |= m >> (1 - exp);
+ } else if (half::round_style ==
+ std::round_toward_infinity)
+ value -= (value >> 15) - 1;
+ else if (half::round_style ==
+ std::round_toward_neg_infinity)
+ value += value >> 15;
+ return half(binary, value);
+ }
+
+ /// Exponent implementation.
+ /// \param arg number to query
+ /// \return floating point exponent
+ static int ilogb(half arg)
+ {
+ int abs = arg.data_ & 0x7FFF;
+ if (!abs) return FP_ILOGB0;
+ if (abs < 0x7C00) {
+ int exp = (abs >> 10) - 15;
+ if (abs < 0x400)
+ for (; abs < 0x200; abs <<= 1, --exp)
+ ;
+ return exp;
+ }
+ if (abs > 0x7C00) return FP_ILOGBNAN;
+ return INT_MAX;
+ }
+
+ /// Exponent implementation.
+ /// \param arg number to query
+ /// \return floating point exponent
+ static half logb(half arg)
+ {
+ int abs = arg.data_ & 0x7FFF;
+ if (!abs) return half(binary, 0xFC00);
+ if (abs < 0x7C00) {
+ int exp = (abs >> 10) - 15;
+ if (abs < 0x400)
+ for (; abs < 0x200; abs <<= 1, --exp)
+ ;
+ uint16 bits = (exp < 0) << 15;
+ if (exp) {
+ unsigned int m = std::abs(exp) << 6, e = 18;
+ for (; m < 0x400; m <<= 1, --e)
+ ;
+ bits |= (e << 10) + m;
+ }
+ return half(binary, bits);
+ }
+ if (abs > 0x7C00) return arg;
+ return half(binary, 0x7C00);
+ }
+
+ /// Enumeration implementation.
+ /// \param from number to increase/decrease
+ /// \param to direction to enumerate into
+ /// \return next representable number
+ static half nextafter(half from, half to)
+ {
+ uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
+ if(fabs > 0x7C00)
+ return from;
+ if (tabs > 0x7C00 || from.data_ == to.data_ ||
+ !(fabs | tabs))
+ return to;
+ if(!fabs)
+ return half(binary, (to.data_ & 0x8000) + 1);
+ bool lt = ((fabs == from.data_)
+ ? static_cast<int>(fabs)
+ : -static_cast<int>(fabs)) <
+ ((tabs == to.data_)
+ ? static_cast<int>(tabs)
+ : -static_cast<int>(tabs));
+ return half(binary,
+ from.data_ +
+ (((from.data_ >> 15) ^
+ static_cast<unsigned>(lt))
+ << 1) -
+ 1);
+ }
+
+ /// Enumeration implementation.
+ /// \param from number to increase/decrease
+ /// \param to direction to enumerate into
+ /// \return next representable number
+ static half nexttoward(half from, long double to)
+ {
+ if(isnan(from))
+ return from;
+ long double lfrom = static_cast<long double>(from);
+ if(builtin_isnan(to) || lfrom == to)
+ return half(static_cast<float>(to));
+ if(!(from.data_&0x7FFF))
+ return half(binary,
+ (static_cast<detail::uint16>(
+ builtin_signbit(to))
+ << 15) +
+ 1);
+ return half(
+ binary,
+ from.data_ +
+ (((from.data_ >> 15) ^
+ static_cast<unsigned>(lfrom < to))
+ << 1) -
+ 1);
+ }
+
+ /// Sign implementation
+ /// \param x first operand
+ /// \param y second operand
+ /// \return composed value
+ static half copysign(half x, half y) {
+ return half(binary,
+ x.data_ ^ ((x.data_ ^ y.data_) & 0x8000));
+ }
+
+ /// Classification implementation.
+ /// \param arg value to classify
+ /// \retval true if infinite number
+ /// \retval false else
+ static int fpclassify(half arg)
+ {
+ unsigned int abs = arg.data_ & 0x7FFF;
+ return abs ? ((abs > 0x3FF)
+ ? ((abs >= 0x7C00)
+ ? ((abs > 0x7C00)
+ ? FP_NAN
+ : FP_INFINITE)
+ : FP_NORMAL)
+ : FP_SUBNORMAL)
+ : FP_ZERO;
+ }
+
+ /// Classification implementation.
+ /// \param arg value to classify
+ /// \retval true if finite number
+ /// \retval false else
+ static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }
+
+ /// Classification implementation.
+ /// \param arg value to classify
+ /// \retval true if infinite number
+ /// \retval false else
+ static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }
+
+ /// Classification implementation.
+ /// \param arg value to classify
+ /// \retval true if not a number
+ /// \retval false else
+ static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }
+
+ /// Classification implementation.
+ /// \param arg value to classify
+ /// \retval true if normal number
+ /// \retval false else
+ static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }
+
+ /// Sign bit implementation.
+ /// \param arg value to check
+ /// \retval true if signed
+ /// \retval false if unsigned
+ static bool signbit(half arg) { return (arg.data_&0x8000) != 0; }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if operands equal
+ /// \retval false else
+ static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if operands not equal
+ /// \retval false else
+ static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x > \a y
+ /// \retval false else
+ static bool isgreater(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) >
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x >= \a y
+ /// \retval false else
+ static bool isgreaterequal(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) >=
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x < \a y
+ /// \retval false else
+ static bool isless(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) <
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x <= \a y
+ /// \retval false else
+ static bool islessequal(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ return xabs <= 0x7C00 && yabs <= 0x7C00 &&
+ (((xabs == x.data_) ? xabs : -xabs) <=
+ ((yabs == y.data_) ? yabs : -yabs));
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if either \a x > \a y nor \a x < \a y
+ /// \retval false else
+ static bool islessgreater(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00 || yabs > 0x7C00) return false;
+ int a = (xabs == x.data_) ? xabs : -xabs,
+ b = (yabs == y.data_) ? yabs : -yabs;
+ return a < b || a > b;
+ }
+
+ /// Comparison implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if operand unordered
+ /// \retval false else
+ static bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
+
+ private:
+ static double erf(double arg) {
+ if (builtin_isinf(arg))
+ return (arg < 0.0) ? -1.0 : 1.0;
+ double x2 = arg * arg, ax2 = 0.147 * x2,
+ value = std::sqrt(
+ 1.0 -
+ std::exp(
+ -x2 *
+ (1.2732395447351626861510701069801 +
+ ax2) /
+ (1.0 + ax2)));
+ return builtin_signbit(arg) ? -value : value;
+ }
+
+ static double lgamma(double arg) {
+ double v = 1.0;
+ for (; arg < 8.0; ++arg) v *= arg;
+ double w = 1.0 / (arg * arg);
+ return (((((((-0.02955065359477124183006535947712 *
+ w +
+ 0.00641025641025641025641025641026) *
+ w +
+ -0.00191752691752691752691752691753) *
+ w +
+ 8.4175084175084175084175084175084e-4) *
+ w +
+ -5.952380952380952380952380952381e-4) *
+ w +
+ 7.9365079365079365079365079365079e-4) *
+ w +
+ -0.00277777777777777777777777777778) *
+ w +
+ 0.08333333333333333333333333333333) /
+ arg +
+ 0.91893853320467274178032973640562 -
+ std::log(v) - arg +
+ (arg - 0.5) * std::log(arg);
+ }
+ };
+
+ /// Wrapper for unary half-precision functions needing specialization for individual argument types.
+ /// \tparam T argument type
+ template<typename T> struct unary_specialized
+ {
+ /// Negation implementation.
+ /// \param arg value to negate
+ /// \return negated value
+ static HALF_CONSTEXPR half negate(half arg) {
+ return half(binary, arg.data_ ^ 0x8000);
+ }
+
+ /// Absolute value implementation.
+ /// \param arg function argument
+ /// \return absolute value
+ static half fabs(half arg) {
+ return half(binary, arg.data_ & 0x7FFF);
+ }
+ };
+ template<> struct unary_specialized<expr>
+ {
+ static HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); }
+ static expr fabs(float arg) { return expr(std::fabs(arg)); }
+ };
+
+ /// Wrapper for binary half-precision functions needing specialization for individual argument types.
+ /// \tparam T first argument type
+ /// \tparam U first argument type
+ template<typename T,typename U> struct binary_specialized
+ {
+ /// Minimum implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return minimum value
+ static expr fmin(float x, float y)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::fmin(x, y));
+ #else
+ if (builtin_isnan(x)) return expr(y);
+ if (builtin_isnan(y)) return expr(x);
+ return expr(std::min(x, y));
+#endif
+ }
+
+ /// Maximum implementation.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return maximum value
+ static expr fmax(float x, float y)
+ {
+ #if HALF_ENABLE_CPP11_CMATH
+ return expr(std::fmax(x, y));
+ #else
+ if (builtin_isnan(x)) return expr(y);
+ if (builtin_isnan(y)) return expr(x);
+ return expr(std::max(x, y));
+#endif
+ }
+ };
+ template<> struct binary_specialized<half,half>
+ {
+ static half fmin(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00) return y;
+ if (yabs > 0x7C00) return x;
+ return (((xabs == x.data_) ? xabs : -xabs) >
+ ((yabs == y.data_) ? yabs : -yabs))
+ ? y
+ : x;
+ }
+ static half fmax(half x, half y) {
+ int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF;
+ if (xabs > 0x7C00) return y;
+ if (yabs > 0x7C00) return x;
+ return (((xabs == x.data_) ? xabs : -xabs) <
+ ((yabs == y.data_) ? yabs : -yabs))
+ ? y
+ : x;
+ }
+ };
+
+ /// Helper class for half casts.
+ /// This class template has to be specialized for all valid cast
+ /// argument to define an appropriate static `cast` member
+ /// function and a corresponding `type` member denoting its
+ /// return type. \tparam T destination type \tparam U source
+ /// type \tparam R rounding mode to use
+ template <typename T, typename U,
+ std::float_round_style R =
+ (std::float_round_style)(HALF_ROUND_STYLE)>
+ struct half_caster {};
+ template <typename U, std::float_round_style R>
+ struct half_caster<half, U, R> {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(
+ std::is_arithmetic<U>::value,
+ "half_cast from non-arithmetic type unsupported");
+#endif
+
+ static half cast(U arg) {
+ return cast_impl(arg, is_float<U>());
+ };
+
+ private:
+ static half cast_impl(U arg, true_type) {
+ return half(binary, float2half<R>(arg));
+ }
+ static half cast_impl(U arg, false_type) {
+ return half(binary, int2half<R>(arg));
+ }
+ };
+ template<typename T,std::float_round_style R> struct half_caster<T,half,R>
+ {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_arithmetic<T>::value,
+ "half_cast to non-arithmetic type unsupported");
+#endif
+
+ static T cast(half arg) {
+ return cast_impl(arg, is_float<T>());
+ }
+
+ private:
+ static T cast_impl(half arg, true_type) {
+ return half2float<T>(arg.data_);
+ }
+ static T cast_impl(half arg, false_type) {
+ return half2int<R, T>(arg.data_);
+ }
+ };
+ template <typename T, std::float_round_style R>
+ struct half_caster<T, expr, R> {
+#if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS
+ static_assert(std::is_arithmetic<T>::value,
+ "half_cast to non-arithmetic type unsupported");
+#endif
+
+ static T cast(expr arg) {
+ return cast_impl(arg, is_float<T>());
+ }
+
+ private:
+ static T cast_impl(float arg, true_type) {
+ return static_cast<T>(arg);
+ }
+ static T cast_impl(half arg, false_type) {
+ return half2int<R, T>(arg.data_);
+ }
+ };
+ template <std::float_round_style R>
+ struct half_caster<half, half, R> {
+ static half cast(half arg) { return arg; }
+ };
+ template <std::float_round_style R>
+ struct half_caster<half, expr, R> : half_caster<half, half, R> {
+ };
+
+ /// \name Comparison operators
+ /// \{
+
+ /// Comparison for equality.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if operands equal
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator==(T x, U y) { return functions::isequal(x, y); }
+
+ /// Comparison for inequality.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if operands not equal
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator!=(T x, U y) { return functions::isnotequal(x, y); }
+
+ /// Comparison for less than.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x less than \a y
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator<(T x, U y) { return functions::isless(x, y); }
+
+ /// Comparison for greater than.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x greater than \a y
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator>(T x, U y) { return functions::isgreater(x, y); }
+
+ /// Comparison for less equal.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x less equal \a y
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator<=(T x, U y) { return functions::islessequal(x, y); }
+
+ /// Comparison for greater equal.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x greater equal \a y
+ /// \retval false else
+ template<typename T,typename U> typename enable<bool,T,U>::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); }
+
+ /// \}
+ /// \name Arithmetic operators
+ /// \{
+
+ /// Add halfs.
+ /// \param x left operand
+ /// \param y right operand
+ /// \return sum of half expressions
+ template<typename T,typename U> typename enable<expr,T,U>::type operator+(T x, U y) { return functions::plus(x, y); }
+
+ /// Subtract halfs.
+ /// \param x left operand
+ /// \param y right operand
+ /// \return difference of half expressions
+ template<typename T,typename U> typename enable<expr,T,U>::type operator-(T x, U y) { return functions::minus(x, y); }
+
+ /// Multiply halfs.
+ /// \param x left operand
+ /// \param y right operand
+ /// \return product of half expressions
+ template<typename T,typename U> typename enable<expr,T,U>::type operator*(T x, U y) { return functions::multiplies(x, y); }
+
+ /// Divide halfs.
+ /// \param x left operand
+ /// \param y right operand
+ /// \return quotient of half expressions
+ template<typename T,typename U> typename enable<expr,T,U>::type operator/(T x, U y) { return functions::divides(x, y); }
+
+ /// Identity.
+ /// \param arg operand
+ /// \return uncahnged operand
+ template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator+(T arg) { return arg; }
+
+ /// Negation.
+ /// \param arg operand
+ /// \return negated operand
+ template<typename T> HALF_CONSTEXPR typename enable<T,T>::type operator-(T arg) { return unary_specialized<T>::negate(arg); }
+
+ /// \}
+ /// \name Input and output
+ /// \{
+
+ /// Output operator.
+ /// \param out output stream to write into
+ /// \param arg half expression to write
+ /// \return reference to output stream
+ template<typename T,typename charT,typename traits> typename enable<std::basic_ostream<charT,traits>&,T>::type
+ operator<<(std::basic_ostream<charT,traits> &out, T arg) { return functions::write(out, arg); }
+
+ /// Input operator.
+ /// \param in input stream to read from
+ /// \param arg half to read into
+ /// \return reference to input stream
+ template<typename charT,typename traits> std::basic_istream<charT,traits>&
+ operator>>(std::basic_istream<charT,traits> &in, half &arg) { return functions::read(in, arg); }
+
+ /// \}
+ /// \name Basic mathematical operations
+ /// \{
+
+ /// Absolute value.
+ /// \param arg operand
+ /// \return absolute value of \a arg
+// template<typename T> typename enable<T,T>::type abs(T arg) { return unary_specialized<T>::fabs(arg); }
+ inline half abs(half arg) { return unary_specialized<half>::fabs(arg); }
+ inline expr abs(expr arg) { return unary_specialized<expr>::fabs(arg); }
+
+ /// Absolute value.
+ /// \param arg operand
+ /// \return absolute value of \a arg
+// template<typename T> typename enable<T,T>::type fabs(T arg) { return unary_specialized<T>::fabs(arg); }
+ inline half fabs(half arg) { return unary_specialized<half>::fabs(arg); }
+ inline expr fabs(expr arg) { return unary_specialized<expr>::fabs(arg); }
+
+ /// Remainder of division.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return remainder of floating point division.
+// template<typename T,typename U> typename enable<expr,T,U>::type fmod(T x, U y) { return functions::fmod(x, y); }
+ inline expr fmod(half x, half y) { return functions::fmod(x, y); }
+ inline expr fmod(half x, expr y) { return functions::fmod(x, y); }
+ inline expr fmod(expr x, half y) { return functions::fmod(x, y); }
+ inline expr fmod(expr x, expr y) { return functions::fmod(x, y); }
+
+ /// Remainder of division.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return remainder of floating point division.
+ // template<typename T,typename U> typename
+ // enable<expr,T,U>::type remainder(T x, U y) { return
+ // functions::remainder(x, y); }
+ inline expr remainder(half x, half y) {
+ return functions::remainder(x, y);
+ }
+ inline expr remainder(half x, expr y) {
+ return functions::remainder(x, y);
+ }
+ inline expr remainder(expr x, half y) {
+ return functions::remainder(x, y);
+ }
+ inline expr remainder(expr x, expr y) {
+ return functions::remainder(x, y);
+ }
+
+ /// Remainder of division.
+ /// \param x first operand
+ /// \param y second operand
+ /// \param quo address to store some bits of quotient at
+ /// \return remainder of floating point division.
+ // template<typename T,typename U> typename
+ // enable<expr,T,U>::type remquo(T x, U y, int *quo) { return
+ // functions::remquo(x, y, quo); }
+ inline expr remquo(half x, half y, int *quo) {
+ return functions::remquo(x, y, quo);
+ }
+ inline expr remquo(half x, expr y, int *quo) {
+ return functions::remquo(x, y, quo);
+ }
+ inline expr remquo(expr x, half y, int *quo) {
+ return functions::remquo(x, y, quo);
+ }
+ inline expr remquo(expr x, expr y, int *quo) {
+ return functions::remquo(x, y, quo);
+ }
+
+ /// Fused multiply add.
+ /// \param x first operand
+ /// \param y second operand
+ /// \param z third operand
+ /// \return ( \a x * \a y ) + \a z rounded as one operation.
+ // template<typename T,typename U,typename V>
+ //typename enable<expr,T,U,V>::type fma(T x, U y, V z) { return
+ //functions::fma(x, y, z); }
+ inline expr fma(half x, half y, half z) { return functions::fma(x, y, z); }
+ inline expr fma(half x, half y, expr z) { return functions::fma(x, y, z); }
+ inline expr fma(half x, expr y, half z) { return functions::fma(x, y, z); }
+ inline expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); }
+ inline expr fma(expr x, half y, half z) { return functions::fma(x, y, z); }
+ inline expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); }
+ inline expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); }
+ inline expr fma(expr x, expr y, expr z) { return functions::fma(x, y, z); }
+
+ /// Maximum of half expressions.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return maximum of operands
+// template<typename T,typename U> typename result<T,U>::type fmax(T x, U y) { return binary_specialized<T,U>::fmax(x, y); }
+ inline half fmax(half x, half y) { return binary_specialized<half,half>::fmax(x, y); }
+ inline expr fmax(half x, expr y) { return binary_specialized<half,expr>::fmax(x, y); }
+ inline expr fmax(expr x, half y) { return binary_specialized<expr,half>::fmax(x, y); }
+ inline expr fmax(expr x, expr y) { return binary_specialized<expr,expr>::fmax(x, y); }
+
+ /// Minimum of half expressions.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return minimum of operands
+// template<typename T,typename U> typename result<T,U>::type fmin(T x, U y) { return binary_specialized<T,U>::fmin(x, y); }
+ inline half fmin(half x, half y) { return binary_specialized<half,half>::fmin(x, y); }
+ inline expr fmin(half x, expr y) { return binary_specialized<half,expr>::fmin(x, y); }
+ inline expr fmin(expr x, half y) { return binary_specialized<expr,half>::fmin(x, y); }
+ inline expr fmin(expr x, expr y) { return binary_specialized<expr,expr>::fmin(x, y); }
+
+ /// Positive difference.
+ /// \param x first operand
+ /// \param y second operand
+ /// \return \a x - \a y or 0 if difference negative
+// template<typename T,typename U> typename enable<expr,T,U>::type fdim(T x, U y) { return functions::fdim(x, y); }
+ inline expr fdim(half x, half y) { return functions::fdim(x, y); }
+ inline expr fdim(half x, expr y) { return functions::fdim(x, y); }
+ inline expr fdim(expr x, half y) { return functions::fdim(x, y); }
+ inline expr fdim(expr x, expr y) { return functions::fdim(x, y); }
+
+ /// Get NaN value.
+ /// \return quiet NaN
+ inline half nanh(const char *) { return functions::nanh(); }
+
+ /// \}
+ /// \name Exponential functions
+ /// \{
+
+ /// Exponential function.
+ /// \param arg function argument
+ /// \return e raised to \a arg
+// template<typename T> typename enable<expr,T>::type exp(T arg) { return functions::exp(arg); }
+ inline expr exp(half arg) { return functions::exp(arg); }
+ inline expr exp(expr arg) { return functions::exp(arg); }
+
+ /// Exponential minus one.
+ /// \param arg function argument
+ /// \return e raised to \a arg subtracted by 1
+// template<typename T> typename enable<expr,T>::type expm1(T arg) { return functions::expm1(arg); }
+ inline expr expm1(half arg) { return functions::expm1(arg); }
+ inline expr expm1(expr arg) { return functions::expm1(arg); }
+
+ /// Binary exponential.
+ /// \param arg function argument
+ /// \return 2 raised to \a arg
+// template<typename T> typename enable<expr,T>::type exp2(T arg) { return functions::exp2(arg); }
+ inline expr exp2(half arg) { return functions::exp2(arg); }
+ inline expr exp2(expr arg) { return functions::exp2(arg); }
+
+ /// Natural logorithm.
+ /// \param arg function argument
+ /// \return logarithm of \a arg to base e
+// template<typename T> typename enable<expr,T>::type log(T arg) { return functions::log(arg); }
+ inline expr log(half arg) { return functions::log(arg); }
+ inline expr log(expr arg) { return functions::log(arg); }
+
+ /// Common logorithm.
+ /// \param arg function argument
+ /// \return logarithm of \a arg to base 10
+// template<typename T> typename enable<expr,T>::type log10(T arg) { return functions::log10(arg); }
+ inline expr log10(half arg) { return functions::log10(arg); }
+ inline expr log10(expr arg) { return functions::log10(arg); }
+
+ /// Natural logorithm.
+ /// \param arg function argument
+ /// \return logarithm of \a arg plus 1 to base e
+// template<typename T> typename enable<expr,T>::type log1p(T arg) { return functions::log1p(arg); }
+ inline expr log1p(half arg) { return functions::log1p(arg); }
+ inline expr log1p(expr arg) { return functions::log1p(arg); }
+
+ /// Binary logorithm.
+ /// \param arg function argument
+ /// \return logarithm of \a arg to base 2
+// template<typename T> typename enable<expr,T>::type log2(T arg) { return functions::log2(arg); }
+ inline expr log2(half arg) { return functions::log2(arg); }
+ inline expr log2(expr arg) { return functions::log2(arg); }
+
+ /// \}
+ /// \name Power functions
+ /// \{
+
+ /// Square root.
+ /// \param arg function argument
+ /// \return square root of \a arg
+// template<typename T> typename enable<expr,T>::type sqrt(T arg) { return functions::sqrt(arg); }
+ inline expr sqrt(half arg) { return functions::sqrt(arg); }
+ inline expr sqrt(expr arg) { return functions::sqrt(arg); }
+
+ /// Cubic root.
+ /// \param arg function argument
+ /// \return cubic root of \a arg
+ // template<typename T> typename
+ //enable<expr,T>::type cbrt(T arg) { return
+ // functions::cbrt(arg); }
+ inline expr cbrt(half arg) { return functions::cbrt(arg); }
+ inline expr cbrt(expr arg) { return functions::cbrt(arg); }
+
+ /// Hypotenuse function.
+ /// \param x first argument
+ /// \param y second argument
+ /// \return square root of sum of squares without internal over-
+ /// or underflows
+ // template<typename T,typename U> typename
+ //enable<expr,T,U>::type hypot(T x, U y) { return
+ //functions::hypot(x, y); }
+ inline expr hypot(half x, half y) { return functions::hypot(x, y); }
+ inline expr hypot(half x, expr y) { return functions::hypot(x, y); }
+ inline expr hypot(expr x, half y) { return functions::hypot(x, y); }
+ inline expr hypot(expr x, expr y) { return functions::hypot(x, y); }
+
+ /// Power function.
+ /// \param base first argument
+ /// \param exp second argument
+ /// \return \a base raised to \a exp
+// template<typename T,typename U> typename enable<expr,T,U>::type pow(T base, U exp) { return functions::pow(base, exp); }
+ inline expr pow(half base, half exp) { return functions::pow(base, exp); }
+ inline expr pow(half base, expr exp) { return functions::pow(base, exp); }
+ inline expr pow(expr base, half exp) { return functions::pow(base, exp); }
+ inline expr pow(expr base, expr exp) { return functions::pow(base, exp); }
+
+ /// \}
+ /// \name Trigonometric functions
+ /// \{
+
+ /// Sine function.
+ /// \param arg function argument
+ /// \return sine value of \a arg
+// template<typename T> typename enable<expr,T>::type sin(T arg) { return functions::sin(arg); }
+ inline expr sin(half arg) { return functions::sin(arg); }
+ inline expr sin(expr arg) { return functions::sin(arg); }
+
+ /// Cosine function.
+ /// \param arg function argument
+ /// \return cosine value of \a arg
+// template<typename T> typename enable<expr,T>::type cos(T arg) { return functions::cos(arg); }
+ inline expr cos(half arg) { return functions::cos(arg); }
+ inline expr cos(expr arg) { return functions::cos(arg); }
+
+ /// Tangent function.
+ /// \param arg function argument
+ /// \return tangent value of \a arg
+// template<typename T> typename enable<expr,T>::type tan(T arg) { return functions::tan(arg); }
+ inline expr tan(half arg) { return functions::tan(arg); }
+ inline expr tan(expr arg) { return functions::tan(arg); }
+
+ /// Arc sine.
+ /// \param arg function argument
+ /// \return arc sine value of \a arg
+// template<typename T> typename enable<expr,T>::type asin(T arg) { return functions::asin(arg); }
+ inline expr asin(half arg) { return functions::asin(arg); }
+ inline expr asin(expr arg) { return functions::asin(arg); }
+
+ /// Arc cosine function.
+ /// \param arg function argument
+ /// \return arc cosine value of \a arg
+// template<typename T> typename enable<expr,T>::type acos(T arg) { return functions::acos(arg); }
+ inline expr acos(half arg) { return functions::acos(arg); }
+ inline expr acos(expr arg) { return functions::acos(arg); }
+
+ /// Arc tangent function.
+ /// \param arg function argument
+ /// \return arc tangent value of \a arg
+// template<typename T> typename enable<expr,T>::type atan(T arg) { return functions::atan(arg); }
+ inline expr atan(half arg) { return functions::atan(arg); }
+ inline expr atan(expr arg) { return functions::atan(arg); }
+
+ /// Arc tangent function.
+ /// \param x first argument
+ /// \param y second argument
+ /// \return arc tangent value
+// template<typename T,typename U> typename enable<expr,T,U>::type atan2(T x, U y) { return functions::atan2(x, y); }
+ inline expr atan2(half x, half y) { return functions::atan2(x, y); }
+ inline expr atan2(half x, expr y) { return functions::atan2(x, y); }
+ inline expr atan2(expr x, half y) { return functions::atan2(x, y); }
+ inline expr atan2(expr x, expr y) { return functions::atan2(x, y); }
+
+ /// \}
+ /// \name Hyperbolic functions
+ /// \{
+
+ /// Hyperbolic sine.
+ /// \param arg function argument
+ /// \return hyperbolic sine value of \a arg
+// template<typename T> typename enable<expr,T>::type sinh(T arg) { return functions::sinh(arg); }
+ inline expr sinh(half arg) { return functions::sinh(arg); }
+ inline expr sinh(expr arg) { return functions::sinh(arg); }
+
+ /// Hyperbolic cosine.
+ /// \param arg function argument
+ /// \return hyperbolic cosine value of \a arg
+// template<typename T> typename enable<expr,T>::type cosh(T arg) { return functions::cosh(arg); }
+ inline expr cosh(half arg) { return functions::cosh(arg); }
+ inline expr cosh(expr arg) { return functions::cosh(arg); }
+
+ /// Hyperbolic tangent.
+ /// \param arg function argument
+ /// \return hyperbolic tangent value of \a arg
+// template<typename T> typename enable<expr,T>::type tanh(T arg) { return functions::tanh(arg); }
+ inline expr tanh(half arg) { return functions::tanh(arg); }
+ inline expr tanh(expr arg) { return functions::tanh(arg); }
+
+ /// Hyperbolic area sine.
+ /// \param arg function argument
+ /// \return area sine value of \a arg
+// template<typename T> typename enable<expr,T>::type asinh(T arg) { return functions::asinh(arg); }
+ inline expr asinh(half arg) { return functions::asinh(arg); }
+ inline expr asinh(expr arg) { return functions::asinh(arg); }
+
+ /// Hyperbolic area cosine.
+ /// \param arg function argument
+ /// \return area cosine value of \a arg
+// template<typename T> typename enable<expr,T>::type acosh(T arg) { return functions::acosh(arg); }
+ inline expr acosh(half arg) { return functions::acosh(arg); }
+ inline expr acosh(expr arg) { return functions::acosh(arg); }
+
+ /// Hyperbolic area tangent.
+ /// \param arg function argument
+ /// \return area tangent value of \a arg
+// template<typename T> typename enable<expr,T>::type atanh(T arg) { return functions::atanh(arg); }
+ inline expr atanh(half arg) { return functions::atanh(arg); }
+ inline expr atanh(expr arg) { return functions::atanh(arg); }
+
+ /// \}
+ /// \name Error and gamma functions
+ /// \{
+
+ /// Error function.
+ /// \param arg function argument
+ /// \return error function value of \a arg
+// template<typename T> typename enable<expr,T>::type erf(T arg) { return functions::erf(arg); }
+ inline expr erf(half arg) { return functions::erf(arg); }
+ inline expr erf(expr arg) { return functions::erf(arg); }
+
+ /// Complementary error function.
+ /// \param arg function argument
+ /// \return 1 minus error function value of \a arg
+// template<typename T> typename enable<expr,T>::type erfc(T arg) { return functions::erfc(arg); }
+ inline expr erfc(half arg) { return functions::erfc(arg); }
+ inline expr erfc(expr arg) { return functions::erfc(arg); }
+
+ /// Natural logarithm of gamma function.
+ /// \param arg function argument
+ /// \return natural logarith of gamma function for \a arg
+// template<typename T> typename enable<expr,T>::type lgamma(T arg) { return functions::lgamma(arg); }
+ inline expr lgamma(half arg) { return functions::lgamma(arg); }
+ inline expr lgamma(expr arg) { return functions::lgamma(arg); }
+
+ /// Gamma function.
+ /// \param arg function argument
+ /// \return gamma function value of \a arg
+// template<typename T> typename enable<expr,T>::type tgamma(T arg) { return functions::tgamma(arg); }
+ inline expr tgamma(half arg) { return functions::tgamma(arg); }
+ inline expr tgamma(expr arg) { return functions::tgamma(arg); }
+
+ /// \}
+ /// \name Rounding
+ /// \{
+
+ /// Nearest integer not less than half value.
+ /// \param arg half to round
+ /// \return nearest integer not less than \a arg
+// template<typename T> typename enable<half,T>::type ceil(T arg) { return functions::ceil(arg); }
+ inline half ceil(half arg) { return functions::ceil(arg); }
+ inline half ceil(expr arg) { return functions::ceil(arg); }
+
+ /// Nearest integer not greater than half value.
+ /// \param arg half to round
+ /// \return nearest integer not greater than \a arg
+// template<typename T> typename enable<half,T>::type floor(T arg) { return functions::floor(arg); }
+ inline half floor(half arg) { return functions::floor(arg); }
+ inline half floor(expr arg) { return functions::floor(arg); }
+
+ /// Nearest integer not greater in magnitude than half value.
+ /// \param arg half to round
+ /// \return nearest integer not greater in magnitude than \a arg
+// template<typename T> typename enable<half,T>::type trunc(T arg) { return functions::trunc(arg); }
+ inline half trunc(half arg) { return functions::trunc(arg); }
+ inline half trunc(expr arg) { return functions::trunc(arg); }
+
+ /// Nearest integer.
+ /// \param arg half to round
+ /// \return nearest integer, rounded away from zero in half-way cases
+// template<typename T> typename enable<half,T>::type round(T arg) { return functions::round(arg); }
+ inline half round(half arg) { return functions::round(arg); }
+ inline half round(expr arg) { return functions::round(arg); }
+
+ /// Nearest integer.
+ /// \param arg half to round
+ /// \return nearest integer, rounded away from zero in half-way cases
+// template<typename T> typename enable<long,T>::type lround(T arg) { return functions::lround(arg); }
+ inline long lround(half arg) { return functions::lround(arg); }
+ inline long lround(expr arg) { return functions::lround(arg); }
+
+ /// Nearest integer using half's internal rounding mode.
+ /// \param arg half expression to round
+ /// \return nearest integer using default rounding mode
+ // template<typename T> typename
+ //enable<half,T>::type nearbyint(T arg) { return
+ // functions::nearbyint(arg); }
+ inline half nearbyint(half arg) { return functions::rint(arg); }
+ inline half nearbyint(expr arg) { return functions::rint(arg); }
+
+ /// Nearest integer using half's internal rounding mode.
+ /// \param arg half expression to round
+ /// \return nearest integer using default rounding mode
+ // template<typename T> typename
+ //enable<half,T>::type rint(T arg) { return
+ // functions::rint(arg); }
+ inline half rint(half arg) { return functions::rint(arg); }
+ inline half rint(expr arg) { return functions::rint(arg); }
+
+ /// Nearest integer using half's internal rounding mode.
+ /// \param arg half expression to round
+ /// \return nearest integer using default rounding mode
+ // template<typename T> typename
+ //enable<long,T>::type lrint(T arg) { return
+ // functions::lrint(arg); }
+ inline long lrint(half arg) { return functions::lrint(arg); }
+ inline long lrint(expr arg) { return functions::lrint(arg); }
+ #if HALF_ENABLE_CPP11_LONG_LONG
+ /// Nearest integer.
+ /// \param arg half to round
+ /// \return nearest integer, rounded away from zero in half-way cases
+// template<typename T> typename enable<long long,T>::type llround(T arg) { return functions::llround(arg); }
+ inline long long llround(half arg) { return functions::llround(arg); }
+ inline long long llround(expr arg) { return functions::llround(arg); }
+
+ /// Nearest integer using half's internal rounding mode.
+ /// \param arg half expression to round
+ /// \return nearest integer using default rounding mode
+ // template<typename T> typename enable<long
+ // long,T>::type llrint(T arg) { return functions::llrint(arg);
+ // }
+ inline long long llrint(half arg) {
+ return functions::llrint(arg);
+ }
+ inline long long llrint(expr arg) {
+ return functions::llrint(arg);
+ }
+#endif
+
+ /// \}
+ /// \name Floating point manipulation
+ /// \{
+
+ /// Decompress floating point number.
+ /// \param arg number to decompress
+ /// \param exp address to store exponent at
+ /// \return significant in range [0.5, 1)
+// template<typename T> typename enable<half,T>::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); }
+ inline half frexp(half arg, int *exp) { return functions::frexp(arg, exp); }
+ inline half frexp(expr arg, int *exp) { return functions::frexp(arg, exp); }
+
+ /// Multiply by power of two.
+ /// \param arg number to modify
+ /// \param exp power of two to multiply with
+ /// \return \a arg multplied by 2 raised to \a exp
+// template<typename T> typename enable<half,T>::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp); }
+ inline half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); }
+ inline half ldexp(expr arg, int exp) { return functions::scalbln(arg, exp); }
+
+ /// Extract integer and fractional parts.
+ /// \param arg number to decompress
+ /// \param iptr address to store integer part at
+ /// \return fractional part
+// template<typename T> typename enable<half,T>::type modf(T arg, half *iptr) { return functions::modf(arg, iptr); }
+ inline half modf(half arg, half *iptr) { return functions::modf(arg, iptr); }
+ inline half modf(expr arg, half *iptr) { return functions::modf(arg, iptr); }
+
+ /// Multiply by power of two.
+ /// \param arg number to modify
+ /// \param exp power of two to multiply with
+ /// \return \a arg multplied by 2 raised to \a exp
+// template<typename T> typename enable<half,T>::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp); }
+ inline half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); }
+ inline half scalbn(expr arg, int exp) { return functions::scalbln(arg, exp); }
+
+ /// Multiply by power of two.
+ /// \param arg number to modify
+ /// \param exp power of two to multiply with
+ /// \return \a arg multplied by 2 raised to \a exp
+ // template<typename T> typename
+ //enable<half,T>::type scalbln(T arg, long exp) { return
+ // functions::scalbln(arg, exp); }
+ inline half scalbln(half arg, long exp) {
+ return functions::scalbln(arg, exp);
+ }
+ inline half scalbln(expr arg, long exp) { return functions::scalbln(arg, exp); }
+
+ /// Extract exponent.
+ /// \param arg number to query
+ /// \return floating point exponent
+ /// \retval FP_ILOGB0 for zero
+ /// \retval FP_ILOGBNAN for NaN
+ /// \retval MAX_INT for infinity
+// template<typename T> typename enable<int,T>::type ilogb(T arg) { return functions::ilogb(arg); }
+ inline int ilogb(half arg) { return functions::ilogb(arg); }
+ inline int ilogb(expr arg) { return functions::ilogb(arg); }
+
+ /// Extract exponent.
+ /// \param arg number to query
+ /// \return floating point exponent
+// template<typename T> typename enable<half,T>::type logb(T arg) { return functions::logb(arg); }
+ inline half logb(half arg) { return functions::logb(arg); }
+ inline half logb(expr arg) { return functions::logb(arg); }
+
+ /// Next representable value.
+ /// \param from value to compute next representable value for
+ /// \param to direction towards which to compute next value
+ /// \return next representable value after \a from in direction towards \a to
+// template<typename T,typename U> typename enable<half,T,U>::type nextafter(T from, U to) { return functions::nextafter(from, to); }
+ inline half nextafter(half from, half to) { return functions::nextafter(from, to); }
+ inline half nextafter(half from, expr to) { return functions::nextafter(from, to); }
+ inline half nextafter(expr from, half to) { return functions::nextafter(from, to); }
+ inline half nextafter(expr from, expr to) { return functions::nextafter(from, to); }
+
+ /// Next representable value.
+ /// \param from value to compute next representable value for
+ /// \param to direction towards which to compute next value
+ /// \return next representable value after \a from in direction towards \a to
+// template<typename T> typename enable<half,T>::type nexttoward(T from, long double to) { return functions::nexttoward(from, to); }
+ inline half nexttoward(half from, long double to) { return functions::nexttoward(from, to); }
+ inline half nexttoward(expr from, long double to) { return functions::nexttoward(from, to); }
+
+ /// Take sign.
+ /// \param x value to change sign for
+ /// \param y value to take sign from
+ /// \return value equal to \a x in magnitude and to \a y in sign
+// template<typename T,typename U> typename enable<half,T,U>::type copysign(T x, U y) { return functions::copysign(x, y); }
+ inline half copysign(half x, half y) { return functions::copysign(x, y); }
+ inline half copysign(half x, expr y) { return functions::copysign(x, y); }
+ inline half copysign(expr x, half y) { return functions::copysign(x, y); }
+ inline half copysign(expr x, expr y) { return functions::copysign(x, y); }
+
+ /// \}
+ /// \name Floating point classification
+ /// \{
+
+ /// Classify floating point value.
+ /// \param arg number to classify
+ /// \retval FP_ZERO for positive and negative zero
+ /// \retval FP_SUBNORMAL for subnormal numbers
+ /// \retval FP_INFINITY for positive and negative infinity
+ /// \retval FP_NAN for NaNs
+ /// \retval FP_NORMAL for all other (normal) values
+ // template<typename T> typename
+ //enable<int,T>::type fpclassify(T arg) { return
+ // functions::fpclassify(arg); }
+ inline int fpclassify(half arg) {
+ return functions::fpclassify(arg);
+ }
+ inline int fpclassify(expr arg) {
+ return functions::fpclassify(arg);
+ }
+
+ /// Check if finite number.
+ /// \param arg number to check
+ /// \retval true if neither infinity nor NaN
+ /// \retval false else
+ // template<typename T> typename
+ //enable<bool,T>::type isfinite(T arg) { return
+ // functions::isfinite(arg); }
+ inline bool isfinite(half arg) {
+ return functions::isfinite(arg);
+ }
+ inline bool isfinite(expr arg) {
+ return functions::isfinite(arg);
+ }
+
+ /// Check for infinity.
+ /// \param arg number to check
+ /// \retval true for positive or negative infinity
+ /// \retval false else
+ // template<typename T> typename
+ //enable<bool,T>::type isinf(T arg) { return
+ // functions::isinf(arg); }
+ inline bool isinf(half arg) { return functions::isinf(arg); }
+ inline bool isinf(expr arg) { return functions::isinf(arg); }
+
+ /// Check for NaN.
+ /// \param arg number to check
+ /// \retval true for NaNs
+ /// \retval false else
+ // template<typename T> typename
+ //enable<bool,T>::type isnan(T arg) { return
+ // functions::isnan(arg); }
+ inline bool isnan(half arg) { return functions::isnan(arg); }
+ inline bool isnan(expr arg) { return functions::isnan(arg); }
+
+ /// Check if normal number.
+ /// \param arg number to check
+ /// \retval true if normal number
+ /// \retval false if either subnormal, zero, infinity or NaN
+ // template<typename T> typename
+ //enable<bool,T>::type isnormal(T arg) { return
+ // functions::isnormal(arg); }
+ inline bool isnormal(half arg) {
+ return functions::isnormal(arg);
+ }
+ inline bool isnormal(expr arg) {
+ return functions::isnormal(arg);
+ }
+
+ /// Check sign.
+ /// \param arg number to check
+ /// \retval true for negative number
+ /// \retval false for positive number
+ // template<typename T> typename
+ //enable<bool,T>::type signbit(T arg) { return
+ // functions::signbit(arg); }
+ inline bool signbit(half arg) {
+ return functions::signbit(arg);
+ }
+ inline bool signbit(expr arg) {
+ return functions::signbit(arg);
+ }
+
+ /// \}
+ /// \name Comparison
+ /// \{
+
+ /// Comparison for greater than.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x greater than \a y
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type isgreater(T x, U y) { return
+ // functions::isgreater(x, y); }
+ inline bool isgreater(half x, half y) {
+ return functions::isgreater(x, y);
+ }
+ inline bool isgreater(half x, expr y) {
+ return functions::isgreater(x, y);
+ }
+ inline bool isgreater(expr x, half y) {
+ return functions::isgreater(x, y);
+ }
+ inline bool isgreater(expr x, expr y) {
+ return functions::isgreater(x, y);
+ }
+
+ /// Comparison for greater equal.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x greater equal \a y
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type isgreaterequal(T x, U y) { return
+ // functions::isgreaterequal(x, y); }
+ inline bool isgreaterequal(half x, half y) {
+ return functions::isgreaterequal(x, y);
+ }
+ inline bool isgreaterequal(half x, expr y) {
+ return functions::isgreaterequal(x, y);
+ }
+ inline bool isgreaterequal(expr x, half y) {
+ return functions::isgreaterequal(x, y);
+ }
+ inline bool isgreaterequal(expr x, expr y) {
+ return functions::isgreaterequal(x, y);
+ }
+
+ /// Comparison for less than.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x less than \a y
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type isless(T x, U y) { return
+ // functions::isless(x, y); }
+ inline bool isless(half x, half y) {
+ return functions::isless(x, y);
+ }
+ inline bool isless(half x, expr y) {
+ return functions::isless(x, y);
+ }
+ inline bool isless(expr x, half y) {
+ return functions::isless(x, y);
+ }
+ inline bool isless(expr x, expr y) {
+ return functions::isless(x, y);
+ }
+
+ /// Comparison for less equal.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if \a x less equal \a y
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type islessequal(T x, U y) { return
+ // functions::islessequal(x, y); }
+ inline bool islessequal(half x, half y) {
+ return functions::islessequal(x, y);
+ }
+ inline bool islessequal(half x, expr y) {
+ return functions::islessequal(x, y);
+ }
+ inline bool islessequal(expr x, half y) {
+ return functions::islessequal(x, y);
+ }
+ inline bool islessequal(expr x, expr y) {
+ return functions::islessequal(x, y);
+ }
+
+ /// Comarison for less or greater.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if either less or greater
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type islessgreater(T x, U y) { return
+ // functions::islessgreater(x, y); }
+ inline bool islessgreater(half x, half y) {
+ return functions::islessgreater(x, y);
+ }
+ inline bool islessgreater(half x, expr y) {
+ return functions::islessgreater(x, y);
+ }
+ inline bool islessgreater(expr x, half y) {
+ return functions::islessgreater(x, y);
+ }
+ inline bool islessgreater(expr x, expr y) {
+ return functions::islessgreater(x, y);
+ }
+
+ /// Check if unordered.
+ /// \param x first operand
+ /// \param y second operand
+ /// \retval true if unordered (one or two NaN operands)
+ /// \retval false else
+ // template<typename T,typename U> typename
+ // enable<bool,T,U>::type isunordered(T x, U y) { return
+ // functions::isunordered(x, y); }
+ inline bool isunordered(half x, half y) {
+ return functions::isunordered(x, y);
+ }
+ inline bool isunordered(half x, expr y) {
+ return functions::isunordered(x, y);
+ }
+ inline bool isunordered(expr x, half y) {
+ return functions::isunordered(x, y);
+ }
+ inline bool isunordered(expr x, expr y) {
+ return functions::isunordered(x, y);
+ }
+
+ /// \name Casting
+ /// \{
+
+ /// Cast to or from half-precision floating point number.
+ /// This casts between [half](\ref half_float::half) and any
+ /// built-in arithmetic type. The values are converted directly
+ /// using the given rounding mode, without any roundtrip over
+ /// `float` that a `static_cast` would otherwise do. It uses the
+ /// default rounding mode.
+ ///
+ /// Using this cast with neither of the two types being a
+ /// [half](\ref half_float::half) or with any of the two types
+ /// not being a built-in arithmetic type (apart from [half](\ref
+ /// half_float::half), of course) results in a compiler error
+ /// and casting between [half](\ref half_float::half)s is just a
+ /// no-op. \tparam T destination type (half or built-in
+ /// arithmetic type) \tparam U source type (half or built-in
+ /// arithmetic type) \param arg value to cast \return \a arg
+ /// converted to destination type
+ template <typename T, typename U>
+ T half_cast(U arg) {
+ return half_caster<T, U>::cast(arg);
+ }
+
+ /// Cast to or from half-precision floating point number.
+ /// This casts between [half](\ref half_float::half) and any
+ /// built-in arithmetic type. The values are converted directly
+ /// using the given rounding mode, without any roundtrip over
+ /// `float` that a `static_cast` would otherwise do.
+ ///
+ /// Using this cast with neither of the two types being a
+ /// [half](\ref half_float::half) or with any of the two types
+ /// not being a built-in arithmetic type (apart from [half](\ref
+ /// half_float::half), of course) results in a compiler error
+ /// and casting between [half](\ref half_float::half)s is just a
+ /// no-op. \tparam T destination type (half or built-in
+ /// arithmetic type) \tparam R rounding mode to use. \tparam U
+ /// source type (half or built-in arithmetic type) \param arg
+ /// value to cast \return \a arg converted to destination type
+ template <typename T, std::float_round_style R, typename U>
+ T half_cast(U arg) {
+ return half_caster<T, U, R>::cast(arg);
+ }
+ /// \}
+ }
+
+ using detail::operator==;
+ using detail::operator!=;
+ using detail::operator<;
+ using detail::operator>;
+ using detail::operator<=;
+ using detail::operator>=;
+ using detail::operator+;
+ using detail::operator-;
+ using detail::operator*;
+ using detail::operator/;
+ using detail::operator<<;
+ using detail::operator>>;
+
+ using detail::abs;
+ using detail::acos;
+ using detail::acosh;
+ using detail::asin;
+ using detail::asinh;
+ using detail::atan;
+ using detail::atan2;
+ using detail::atanh;
+ using detail::cbrt;
+ using detail::ceil;
+ using detail::cos;
+ using detail::cosh;
+ using detail::erf;
+ using detail::erfc;
+ using detail::exp;
+ using detail::exp2;
+ using detail::expm1;
+ using detail::fabs;
+ using detail::fdim;
+ using detail::floor;
+ using detail::fma;
+ using detail::fmax;
+ using detail::fmin;
+ using detail::fmod;
+ using detail::hypot;
+ using detail::lgamma;
+ using detail::log;
+ using detail::log10;
+ using detail::log1p;
+ using detail::log2;
+ using detail::lrint;
+ using detail::lround;
+ using detail::nanh;
+ using detail::nearbyint;
+ using detail::pow;
+ using detail::remainder;
+ using detail::remquo;
+ using detail::rint;
+ using detail::round;
+ using detail::sin;
+ using detail::sinh;
+ using detail::sqrt;
+ using detail::tan;
+ using detail::tanh;
+ using detail::tgamma;
+ using detail::trunc;
+#if HALF_ENABLE_CPP11_LONG_LONG
+ using detail::llrint;
+ using detail::llround;
+#endif
+ using detail::frexp;
+ using detail::ldexp;
+ using detail::modf;
+ using detail::scalbn;
+ using detail::scalbln;
+ using detail::ilogb;
+ using detail::logb;
+ using detail::nextafter;
+ using detail::nexttoward;
+ using detail::copysign;
+ using detail::fpclassify;
+ using detail::isfinite;
+ using detail::isinf;
+ using detail::isnan;
+ using detail::isnormal;
+ using detail::signbit;
+ using detail::isgreater;
+ using detail::isgreaterequal;
+ using detail::isless;
+ using detail::islessequal;
+ using detail::islessgreater;
+ using detail::isunordered;
+
+ using detail::half_cast;
+}
+
+
+/// Extensions to the C++ standard library.
+namespace std
+{
+/// Numeric limits for half-precision floats.
+/// Because of the underlying single-precision implementation of many
+/// operations, it inherits some properties from `std::numeric_limits<float>`.
+template <>
+class numeric_limits<half_float::half> : public numeric_limits<float> {
+ public:
+ /// Supports signed values.
+ static HALF_CONSTEXPR_CONST bool is_signed = true;
+
+ /// Is not exact.
+ static HALF_CONSTEXPR_CONST bool is_exact = false;
+
+ /// Doesn't provide modulo arithmetic.
+ static HALF_CONSTEXPR_CONST bool is_modulo = false;
+
+ /// IEEE conformant.
+ static HALF_CONSTEXPR_CONST bool is_iec559 = true;
+
+ /// Supports infinity.
+ static HALF_CONSTEXPR_CONST bool has_infinity = true;
+
+ /// Supports quiet NaNs.
+ static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;
+
+ /// Supports subnormal values.
+ static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
+
+ /// Rounding mode.
+ /// Due to the mix of internal single-precision computations (using the
+ /// rounding mode of the underlying single-precision implementation) with the
+ /// rounding mode of the single-to-half conversions, the actual rounding mode
+ /// might be `std::round_indeterminate` if the default half-precision rounding
+ /// mode doesn't match the single-precision rounding mode.
+ static HALF_CONSTEXPR_CONST float_round_style round_style =
+ (std::numeric_limits<float>::round_style == half_float::half::round_style)
+ ? half_float::half::round_style
+ : round_indeterminate;
+
+ /// Significant digits.
+ static HALF_CONSTEXPR_CONST int digits = 11;
+
+ /// Significant decimal digits.
+ static HALF_CONSTEXPR_CONST int digits10 = 3;
+
+ /// Required decimal digits to represent all possible values.
+ static HALF_CONSTEXPR_CONST int max_digits10 = 5;
+
+ /// Number base.
+ static HALF_CONSTEXPR_CONST int radix = 2;
+
+ /// One more than smallest exponent.
+ static HALF_CONSTEXPR_CONST int min_exponent = -13;
+
+ /// Smallest normalized representable power of 10.
+ static HALF_CONSTEXPR_CONST int min_exponent10 = -4;
+
+ /// One more than largest exponent
+ static HALF_CONSTEXPR_CONST int max_exponent = 16;
+
+ /// Largest finitely representable power of 10.
+ static HALF_CONSTEXPR_CONST int max_exponent10 = 4;
+
+ /// Smallest positive normal value.
+ static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x0400);
+ }
+
+ /// Smallest finite value.
+ static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0xFBFF);
+ }
+
+ /// Largest finite value.
+ static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x7BFF);
+ }
+
+ /// Difference between one and next representable value.
+ static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x1400);
+ }
+
+ /// Maximum rounding error.
+ static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW {
+ return half_float::half(
+ half_float::detail::binary,
+ (round_style == std::round_to_nearest) ? 0x3800 : 0x3C00);
+ }
+
+ /// Positive infinity.
+ static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x7C00);
+ }
+
+ /// Quiet NaN.
+ static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x7FFF);
+ }
+
+ /// Signalling NaN.
+ static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x7DFF);
+ }
+
+ /// Smallest positive subnormal value.
+ static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW {
+ return half_float::half(half_float::detail::binary, 0x0001);
+ }
+};
+
+#if HALF_ENABLE_CPP11_HASH
+ /// Hash function for half-precision floats.
+ /// This is only defined if C++11 `std::hash` is supported and enabled.
+ template<> struct hash<half_float::half> //: unary_function<half_float::half,size_t>
+ {
+ /// Type of function argument.
+ typedef half_float::half argument_type;
+
+ /// Function return type.
+ typedef size_t result_type;
+
+ /// Compute hash function.
+ /// \param arg half to hash
+ /// \return hash value
+ result_type operator()(argument_type arg) const {
+ return hash<half_float::detail::uint16>()(
+ static_cast<unsigned>(arg.data_) &
+ -(arg.data_ != 0x8000));
+ }
+ };
+#endif
+}
+
+
+#undef HALF_CONSTEXPR
+#undef HALF_CONSTEXPR_CONST
+#undef HALF_NOEXCEPT
+#undef HALF_NOTHROW
+#ifdef HALF_POP_WARNINGS
+#pragma warning(pop)
+#undef HALF_POP_WARNINGS
+#endif
+
+#endif
