diff --git a/docs/credits_acknowledgements.rst b/docs/credits_acknowledgements.rst
index 38c2636d0..9c6602854 100644
--- a/docs/credits_acknowledgements.rst
+++ b/docs/credits_acknowledgements.rst
@@ -116,6 +116,10 @@ The following libraries and components are incorporated into RenderDoc, listed h
 
   Used to intercept nvapi calls on D3D11/D3D12.
 
+* `half.hpp <http://half.sourceforge.net/>`_ - Copyright (c) 2012-2019 Christian Rau. Distributed under the MIT License.
+
+  Used to emulate half-precision operations in shader debugging.
+
 Thanks
 ------
 
diff --git a/renderdoc/3rdparty/half/LICENSE.txt b/renderdoc/3rdparty/half/LICENSE.txt
new file mode 100644
index 000000000..36c20d1e4
--- /dev/null
+++ b/renderdoc/3rdparty/half/LICENSE.txt
@@ -0,0 +1,21 @@
+The MIT License
+
+Copyright (c) 2012-2019 Christian Rau
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
diff --git a/renderdoc/3rdparty/half/README.txt b/renderdoc/3rdparty/half/README.txt
new file mode 100644
index 000000000..b8ca7ead1
--- /dev/null
+++ b/renderdoc/3rdparty/half/README.txt
@@ -0,0 +1,317 @@
+HALF-PRECISION FLOATING-POINT LIBRARY (Version 2.1.0)
+-----------------------------------------------------
+
+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 
+built-in floating-point types at the best performance possible.
+
+
+INSTALLATION AND REQUIREMENTS
+-----------------------------
+
+Conveniently, 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 
+predefining the corresponding preprocessor symbols to either 1 or 0 yourself 
+before including half.hpp. 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 icc 11.1 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, icc 11.1 and newer, overridable with 
+    'HALF_ENABLE_CPP11_STATIC_ASSERT').
+
+  - Generalized constant expressions (enabled for VC++ 2015, gcc 4.6, clang 3.1, 
+    icc 14.0 and newer, overridable with 'HALF_ENABLE_CPP11_CONSTEXPR').
+
+  - noexcept exception specifications (enabled for VC++ 2015, gcc 4.6, 
+    clang 3.0, icc 14.0 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, icc 15.0 and newer, overridable with 
+    'HALF_ENABLE_CPP11_USER_LITERALS').
+
+  - Thread-local storage for per-thread floating-point exception flags (enabled 
+    for VC++ 2015, gcc 4.8, clang 3.3, icc 15.0 and newer, overridable with 
+    'HALF_ENABLE_CPP11_THREAD_LOCAL').
+
+  - 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 
+    floating-point classification during conversions from higher precision types 
+    (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with 
+    'HALF_ENABLE_CPP11_CMATH').
+
+  - Floating-point environment control from <cfenv> for possible exception 
+    propagation to the built-in floating-point platform (enabled for VC++ 2013, 
+    libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CFENV').
+
+  - 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 4-8 
+and clang 3-8 on 32- and 64-bit x86 systems. Please contact me if you have any 
+problems, suggestions or even just success testing it on other platforms.
+
+
+DOCUMENTATION
+-------------
+
+What follows are some general words about the usage of the library and its 
+implementation. For a complete documentation of its interface consult 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.
+
+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, which 
+uses the standard IEEE representation with 1 sign bit, 5 exponent bits and 11 
+mantissa bits (including the hidden bit) and supports all types of special 
+values, like subnormal values, infinity and NaNs. This type behaves like the 
+built-in 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 between half and more precise types 
+as well as for rounding results of arithmetic operations and mathematical 
+functions rounds to the nearest representable value. But by predefining the 
+'HALF_ROUND_STYLE' preprocessor symbol 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 built-in single-precision implementation by defining it to 
+'std::numeric_limits<float>::round_style'):
+
+  - 'std::round_indeterminate' (-1) for the fastest rounding.
+
+  - 'std::round_toward_zero' (0) for rounding toward zero.
+
+  - 'std::round_to_nearest' (1) for rounding to the nearest value (default).
+
+  - 'std::round_toward_infinity' (2) for rounding toward positive infinity.
+
+  - 'std::round_toward_neg_infinity' (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 );
+
+ACCURACY AND PERFORMANCE
+
+From version 2.0 onward the library is implemented without employing the 
+underlying floating-point implementation of the system (except for conversions, 
+of course), providing an entirely self-contained half-precision implementation 
+with results independent from the system's existing single- or double-precision 
+implementation and its rounding behaviour.
+
+As to accuracy, many of the operators and functions provided by this library 
+are exact to rounding for all rounding modes, i.e. the error to the exact 
+result is at most 0.5 ULP (unit in the last place) for rounding to nearest and 
+less than 1 ULP for all other rounding modes. This holds for all the operations 
+required by the IEEE 754 standard and many more. Specifically the following 
+functions might exhibit a deviation from the correctly rounded exact result by 
+1 ULP for a select few input values: 'expm1', 'log1p', 'pow', 'atan2', 'erf', 
+'erfc', 'lgamma', 'tgamma' (for more details see the documentation of the 
+individual functions). All other functions and operators are always exact to 
+rounding or independent of the rounding mode altogether.
+
+The increased IEEE-conformance and cleanliness of this implementation comes 
+with a certain performance cost compared to doing computations and mathematical 
+functions in hardware-accelerated single-precision. On average and depending on 
+the platform, the arithemtic operators are about 75% as fast and the 
+mathematical functions about 33-50% as fast as performing the corresponding 
+operations in single-precision and converting between the inputs and outputs. 
+However, directly computing with half-precision values is a rather rare 
+use-case and usually using actual 'float' values for all computations and 
+temproraries and using 'half's only for storage is the recommended way. But 
+nevertheless the goal of this library was to provide a complete and 
+conceptually clean IEEE-confromant half-precision implementation and in the few 
+cases when you do need to compute directly in half-precision you do so for a 
+reason and want accurate results.
+
+If necessary, this internal implementation can be overridden by predefining the 
+'HALF_ARITHMETIC_TYPE' preprocessor symbol to one of the built-in 
+floating-point types ('float', 'double' or 'long double'), which will cause the 
+library to use this type for computing arithmetic operations and mathematical 
+functions (if available). However, due to using the platform's floating-point 
+implementation (and its rounding behaviour) internally, this might cause 
+results to deviate from the specified half-precision rounding mode. It will of 
+course also inhibit the automatic exception detection described below.
+
+The conversion operations between half-precision and single-precision types can 
+also make use of the F16C extension for x86 processors by using the 
+corresponding compiler intrinsics from <immintrin.h>. Support for this is 
+checked at compile-time by looking for the '__F16C__' macro which at least gcc 
+and clang define based on the target platform. It can also be enabled manually 
+by predefining the 'HALF_ENABLE_F16C_INTRINSICS' preprocessor symbol to 1, or 0 
+for explicitly disabling it. However, this will directly use the corresponding 
+intrinsics for conversion without checking if they are available at runtime 
+(possibly crashing if they are not), so make sure they are supported on the 
+target platform before enabling this.
+
+EXCEPTION HANDLING
+
+The half-precision implementation supports all 5 required floating-point 
+exceptions from the IEEE standard to indicate erroneous inputs or inexact 
+results during operations. These are represented by exception flags which 
+actually use the same values as the corresponding 'FE_...' flags defined in 
+C++11's <cfenv> header if supported, specifically:
+
+  - 'FE_INVALID' for invalid inputs to an operation.
+  - 'FE_DIVBYZERO' for finite inputs producing infinite results.
+  - 'FE_OVERFLOW' if a result is too large to represent finitely.
+  - 'FE_UNDERFLOW' for a subnormal or zero result after rounding.
+  - 'FE_INEXACT' if a result needed rounding to be representable.
+  - 'FE_ALL_EXCEPT' as a convenient OR of all possible exception flags.
+
+The internal exception flag state will start with all flags cleared and is 
+maintained per thread if C++11 thread-local storage is supported, otherwise it 
+will be maintained globally and will theoretically NOT be thread-safe (while 
+practically being as thread-safe as a simple integer variable can be). These 
+flags can be managed explicitly using the library's error handling functions, 
+which again try to mimic the built-in functions for handling floating-point 
+exceptions from <cfenv>. You can clear them with 'feclearexcept' (which is the 
+only way a flag can be cleared), test them with 'fetestexcept', explicitly 
+raise errors with 'feraiseexcept' and save and restore their state using 
+'fegetexceptflag' and 'fesetexceptflag'. You can also throw corresponding C++ 
+exceptions based on the current flag state using 'fethrowexcept'.
+
+However, any automatic exception detection and handling during half-precision 
+operations and functions is DISABLED by default, since it comes with a minor 
+performance overhead due to runtime checks, and reacting to IEEE floating-point 
+exceptions is rarely ever needed in application code. But the library fully 
+supports IEEE-conformant detection of floating-point exceptions and various 
+ways for handling them, which can be enabled by pre-defining the corresponding 
+preprocessor symbols to 1. They can be enabled individually or all at once and 
+they will be processed in the order they are listed here:
+
+  - 'HALF_ERRHANDLING_FLAGS' sets the internal exception flags described above 
+    whenever the corresponding exception occurs.
+  - 'HALF_ERRHANDLING_ERRNO' sets the value of 'errno' from <cerrno> similar to 
+    the behaviour of the built-in floating-point types when 'MATH_ERRNO' is used.
+  - 'HALF_ERRHANDLING_FENV' will propagate exceptions to the built-in 
+    floating-point implementation using 'std::feraiseexcept' if support for 
+    C++11 floating-point control is enabled. However, this does not synchronize 
+    exceptions: neither will clearing  propagate nor will it work in reverse.
+  - 'HALF_ERRHANDLING_THROW_...' can be defined to a string literal which will 
+    be used as description message for a C++ exception that is thrown whenever 
+    a 'FE_...' exception occurs, similar to the behaviour of 'fethrowexcept'.
+
+If any of the above error handling is activated, non-quiet operations on 
+half-precision values will also raise a 'FE_INVALID' exception whenever 
+they encounter a signaling NaN value, in addition to transforming the value 
+into a quiet NaN. If error handling is disabled, signaling NaNs will be 
+treated like quiet NaNs (while still getting explicitly quieted if propagated 
+to the result). There can also be additional treatment of overflow and 
+underflow errors after they have been processed as above, which is ENABLED by 
+default (but of course only takes effect if any other exception handling is 
+activated) unless overridden by pre-defining the corresponding preprocessor 
+symbol to 0:
+
+  - 'HALF_ERRHANDLING_OVERFLOW_TO_INEXACT' will cause overflow errors to also 
+    raise a 'FE_INEXACT' exception.
+  - 'HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT' will cause underflow errors to also 
+    raise a 'FE_INEXACT' exception. This will also slightly change the 
+    behaviour of the underflow exception, which will ONLY be raised if the 
+    result is actually inexact due to underflow. If this is disabled, underflow 
+    exceptions will be raised for ANY (possibly exact) subnormal result.
+
+
+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/renderdoc/3rdparty/half/half.hpp b/renderdoc/3rdparty/half/half.hpp
new file mode 100644
index 000000000..0f60403e9
--- /dev/null
+++ b/renderdoc/3rdparty/half/half.hpp
@@ -0,0 +1,4575 @@
+// half - IEEE 754-based half-precision floating-point library.
+//
+// Copyright (c) 2012-2019 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 2.1.0
+
+/// \file
+/// Main header file for half-precision functionality.
+
+#ifndef HALF_HALF_HPP
+#define HALF_HALF_HPP
+
+#define HALF_GCC_VERSION (__GNUC__*100+__GNUC_MINOR__)
+
+#if defined(__INTEL_COMPILER)
+	#define HALF_ICC_VERSION __INTEL_COMPILER
+#elif defined(__ICC)
+	#define HALF_ICC_VERSION __ICC
+#elif defined(__ICL)
+	#define HALF_ICC_VERSION __ICL
+#else
+	#define HALF_ICC_VERSION 0
+#endif
+
+// check C++11 language features
+#if defined(__clang__)										// clang
+	#if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+	#endif
+	#if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+		#define HALF_ENABLE_CPP11_CONSTEXPR 1
+	#endif
+	#if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+		#define HALF_ENABLE_CPP11_NOEXCEPT 1
+	#endif
+	#if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+		#define HALF_ENABLE_CPP11_USER_LITERALS 1
+	#endif
+	#if __has_feature(cxx_thread_local) && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+	#endif
+	#if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+		#define HALF_ENABLE_CPP11_LONG_LONG 1
+	#endif
+#elif HALF_ICC_VERSION && defined(__INTEL_CXX11_MODE__)		// Intel C++
+	#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+	#endif
+	#if HALF_ICC_VERSION >= 1500 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+		#define HALF_ENABLE_CPP11_USER_LITERALS 1
+	#endif
+	#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+		#define HALF_ENABLE_CPP11_CONSTEXPR 1
+	#endif
+	#if HALF_ICC_VERSION >= 1400 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+		#define HALF_ENABLE_CPP11_NOEXCEPT 1
+	#endif
+	#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+	#endif
+	#if HALF_ICC_VERSION >= 1110 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+		#define HALF_ENABLE_CPP11_LONG_LONG 1
+	#endif
+#elif defined(__GNUC__)										// gcc
+	#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
+		#if HALF_GCC_VERSION >= 408 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+			#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+		#endif
+		#if HALF_GCC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+			#define HALF_ENABLE_CPP11_USER_LITERALS 1
+		#endif
+		#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+			#define HALF_ENABLE_CPP11_CONSTEXPR 1
+		#endif
+		#if HALF_GCC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+			#define HALF_ENABLE_CPP11_NOEXCEPT 1
+		#endif
+		#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+			#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+		#endif
+		#if !defined(HALF_ENABLE_CPP11_LONG_LONG)
+			#define HALF_ENABLE_CPP11_LONG_LONG 1
+		#endif
+	#endif
+	#define HALF_TWOS_COMPLEMENT_INT 1
+#elif defined(_MSC_VER)										// Visual C++
+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_THREAD_LOCAL)
+		#define HALF_ENABLE_CPP11_THREAD_LOCAL 1
+	#endif
+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS)
+		#define HALF_ENABLE_CPP11_USER_LITERALS 1
+	#endif
+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR)
+		#define HALF_ENABLE_CPP11_CONSTEXPR 1
+	#endif
+	#if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT)
+		#define HALF_ENABLE_CPP11_NOEXCEPT 1
+	#endif
+	#if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT)
+		#define HALF_ENABLE_CPP11_STATIC_ASSERT 1
+	#endif
+	#if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG)
+		#define HALF_ENABLE_CPP11_LONG_LONG 1
+	#endif
+	#define HALF_TWOS_COMPLEMENT_INT 1
+	#define HALF_POP_WARNINGS 1
+	#pragma warning(push)
+	#pragma warning(disable : 4099 4127 4146)	//struct vs class, constant in if, negative unsigned
+#endif
+
+// check C++11 library features
+#include <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
+		#ifndef HALF_ENABLE_CPP11_CFENV
+			#define HALF_ENABLE_CPP11_CFENV 1
+		#endif
+	#endif
+#elif defined(__GLIBCXX__)									// libstdc++
+	#if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103
+		#ifdef __clang__
+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+				#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+			#endif
+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+				#define HALF_ENABLE_CPP11_CSTDINT 1
+			#endif
+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH)
+				#define HALF_ENABLE_CPP11_CMATH 1
+			#endif
+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH)
+				#define HALF_ENABLE_CPP11_HASH 1
+			#endif
+			#if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CFENV)
+				#define HALF_ENABLE_CPP11_CFENV 1
+			#endif
+		#else
+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+				#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+			#endif
+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+				#define HALF_ENABLE_CPP11_CSTDINT 1
+			#endif
+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH)
+				#define HALF_ENABLE_CPP11_CMATH 1
+			#endif
+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH)
+				#define HALF_ENABLE_CPP11_HASH 1
+			#endif
+			#if HALF_GCC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CFENV)
+				#define HALF_ENABLE_CPP11_CFENV 1
+			#endif
+		#endif
+	#endif
+#elif defined(_CPPLIB_VER)									// Dinkumware/Visual C++
+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS)
+		#define HALF_ENABLE_CPP11_TYPE_TRAITS 1
+	#endif
+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_CSTDINT)
+			#define HALF_ENABLE_CPP11_CSTDINT 1
+	#endif
+	#if _CPPLIB_VER >= 520 && !defined(HALF_ENABLE_CPP11_HASH)
+		#define HALF_ENABLE_CPP11_HASH 1
+	#endif
+	#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CMATH)
+		#define HALF_ENABLE_CPP11_CMATH 1
+	#endif
+	#if _CPPLIB_VER >= 610 && !defined(HALF_ENABLE_CPP11_CFENV)
+		#define HALF_ENABLE_CPP11_CFENV 1
+	#endif
+#endif
+#undef HALF_GCC_VERSION
+#undef HALF_ICC_VERSION
+
+// any error throwing C++ exceptions?
+#if defined(HALF_ERRHANDLING_THROW_INVALID) || defined(HALF_ERRHANDLING_THROW_DIVBYZERO) || defined(HALF_ERRHANDLING_THROW_OVERFLOW) || defined(HALF_ERRHANDLING_THROW_UNDERFLOW) || defined(HALF_ERRHANDLING_THROW_INEXACT)
+#define HALF_ERRHANDLING_THROWS 1
+#endif
+
+// any error handling enabled?
+#define HALF_ERRHANDLING	(HALF_ERRHANDLING_FLAGS||HALF_ERRHANDLING_ERRNO||HALF_ERRHANDLING_FENV||HALF_ERRHANDLING_THROWS)
+
+#if HALF_ERRHANDLING
+	#define HALF_UNUSED_NOERR(name) name
+#else
+	#define HALF_UNUSED_NOERR(name)
+#endif
+
+// support constexpr
+#if HALF_ENABLE_CPP11_CONSTEXPR
+	#define HALF_CONSTEXPR				constexpr
+	#define HALF_CONSTEXPR_CONST		constexpr
+	#if HALF_ERRHANDLING
+		#define HALF_CONSTEXPR_NOERR
+	#else
+		#define HALF_CONSTEXPR_NOERR	constexpr
+	#endif
+#else
+	#define HALF_CONSTEXPR
+	#define HALF_CONSTEXPR_CONST		const
+	#define HALF_CONSTEXPR_NOERR
+#endif
+
+// support noexcept
+#if HALF_ENABLE_CPP11_NOEXCEPT
+	#define HALF_NOEXCEPT	noexcept
+	#define HALF_NOTHROW	noexcept
+#else
+	#define HALF_NOEXCEPT
+	#define HALF_NOTHROW	throw()
+#endif
+
+// support thread storage
+#if HALF_ENABLE_CPP11_THREAD_LOCAL
+	#define HALF_THREAD_LOCAL	thread_local
+#else
+	#define HALF_THREAD_LOCAL	static
+#endif
+
+#include <utility>
+#include <algorithm>
+#include <istream>
+#include <ostream>
+#include <limits>
+#include <stdexcept>
+#include <climits>
+#include <cmath>
+#include <cstring>
+#include <cstdlib>
+#if HALF_ENABLE_CPP11_TYPE_TRAITS
+	#include <type_traits>
+#endif
+#if HALF_ENABLE_CPP11_CSTDINT
+	#include <cstdint>
+#endif
+#if HALF_ERRHANDLING_ERRNO
+	#include <cerrno>
+#endif
+#if HALF_ENABLE_CPP11_CFENV
+	#include <cfenv>
+#endif
+#if HALF_ENABLE_CPP11_HASH
+	#include <functional>
+#endif
+#if HALF_ENABLE_F16C_INTRINSICS
+	#include <immintrin.h>
+#endif
+
+
+#ifndef HALF_ENABLE_F16C_INTRINSICS
+	/// Enable F16C intruction set intrinsics.
+	/// Defining this to 1 enables the use of [F16C compiler intrinsics](https://en.wikipedia.org/wiki/F16C) for converting between 
+	/// half-precision and single-precision values which may result in improved performance. This will not perform additional checks 
+	/// for support of the F16C instruction set, so an appropriate target platform is required when enabling this feature.
+	///
+	/// Unless predefined it will be enabled automatically when the `__F16C__` symbol is defined, which some compilers do on supporting platforms.
+	#define HALF_ENABLE_F16C_INTRINSICS __F16C__
+#endif
+
+#ifdef HALF_DOXYGEN_ONLY
+/// Type for internal floating-point computations.
+/// This can be predefined to a built-in floating-point type (`float`, `double` or `long double`) to override the internal 
+/// half-precision implementation to use this type for computing arithmetic operations and mathematical function (if available). 
+/// This can result in improved performance for arithmetic operators and mathematical functions but might cause results to 
+/// deviate from the specified half-precision rounding mode and inhibits proper detection of half-precision exceptions.
+#define HALF_ARITHMETIC_TYPE (undefined)
+
+/// Enable internal exception flags.
+/// Defining this to 1 causes operations on half-precision values to raise internal floating-point exception flags according to 
+/// the IEEE 754 standard. These can then be cleared and checked with clearexcept(), testexcept().
+#define HALF_ERRHANDLING_FLAGS	0
+
+/// Enable exception propagation to `errno`.
+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to 
+/// [errno](https://en.cppreference.com/w/cpp/error/errno) from `<cerrno>`. Specifically this will propagate domain errors as 
+/// [EDOM](https://en.cppreference.com/w/cpp/error/errno_macros) and pole, overflow and underflow errors as 
+/// [ERANGE](https://en.cppreference.com/w/cpp/error/errno_macros). Inexact errors won't be propagated.
+#define HALF_ERRHANDLING_ERRNO	0
+
+/// Enable exception propagation to built-in floating-point platform.
+/// Defining this to 1 causes operations on half-precision values to propagate floating-point exceptions to the built-in 
+/// single- and double-precision implementation's exception flags using the 
+/// [C++11 floating-point environment control](https://en.cppreference.com/w/cpp/numeric/fenv) from `<cfenv>`. However, this 
+/// does not work in reverse and single- or double-precision exceptions will not raise the corresponding half-precision 
+/// exception flags, nor will explicitly clearing flags clear the corresponding built-in flags.
+#define HALF_ERRHANDLING_FENV	0
+
+/// Throw C++ exception on domain errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a 
+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on domain errors.
+#define HALF_ERRHANDLING_THROW_INVALID		(undefined)
+
+/// Throw C++ exception on pole errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a 
+/// [std::domain_error](https://en.cppreference.com/w/cpp/error/domain_error) with the specified message on pole errors.
+#define HALF_ERRHANDLING_THROW_DIVBYZERO	(undefined)
+
+/// Throw C++ exception on overflow errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a 
+/// [std::overflow_error](https://en.cppreference.com/w/cpp/error/overflow_error) with the specified message on overflows.
+#define HALF_ERRHANDLING_THROW_OVERFLOW		(undefined)
+
+/// Throw C++ exception on underflow errors.
+/// Defining this to a string literal causes operations on half-precision values to throw a 
+/// [std::underflow_error](https://en.cppreference.com/w/cpp/error/underflow_error) with the specified message on underflows.
+#define HALF_ERRHANDLING_THROW_UNDERFLOW	(undefined)
+
+/// Throw C++ exception on rounding errors.
+/// Defining this to 1 causes operations on half-precision values to throw a 
+/// [std::range_error](https://en.cppreference.com/w/cpp/error/range_error) with the specified message on general rounding errors.
+#define HALF_ERRHANDLING_THROW_INEXACT		(undefined)
+#endif
+
+#ifndef HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
+/// Raise INEXACT exception on overflow.
+/// Defining this to 1 (default) causes overflow errors to automatically raise inexact exceptions in addition.
+/// These will be raised after any possible handling of the underflow exception.
+#define HALF_ERRHANDLING_OVERFLOW_TO_INEXACT	1
+#endif
+
+#ifndef HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+/// Raise INEXACT exception on underflow.
+/// Defining this to 1 (default) causes underflow errors to automatically raise inexact exceptions in addition.
+/// These will be raised after any possible handling of the underflow exception.
+///
+/// **Note:** This will actually cause underflow (and the accompanying inexact) exceptions to be raised *only* when the result 
+/// is inexact, while if disabled bare underflow errors will be raised for *any* (possibly exact) subnormal result.
+#define HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT	1
+#endif
+
+/// Default rounding mode.
+/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and more precise types 
+/// (unless using half_cast() and specifying the rounding mode directly) as well as in arithmetic operations and mathematical 
+/// functions. It can be redefined (before including half.hpp) to one of the standard rounding modes using their respective 
+/// constants or the equivalent values of 
+/// [std::float_round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/float_round_style):
+///
+/// `std::float_round_style`         | value | rounding
+/// ---------------------------------|-------|-------------------------
+/// `std::round_indeterminate`       | -1    | fastest
+/// `std::round_toward_zero`         | 0     | toward zero
+/// `std::round_to_nearest`          | 1     | to nearest (default)
+/// `std::round_toward_infinity`     | 2     | toward positive infinity
+/// `std::round_toward_neg_infinity` | 3     | toward negative infinity
+///
+/// By default this is set to `1` (`std::round_to_nearest`), which rounds results to the nearest representable value. It can even 
+/// be set to [std::numeric_limits<float>::round_style](https://en.cppreference.com/w/cpp/types/numeric_limits/round_style) to synchronize 
+/// the rounding mode with that of the built-in single-precision implementation (which is likely `std::round_to_nearest`, though).
+#ifndef HALF_ROUND_STYLE
+	#define HALF_ROUND_STYLE	1		// = std::round_to_nearest
+#endif
+
+/// Value signaling overflow.
+/// In correspondence with `HUGE_VAL[F|L]` from `<cmath>` this symbol expands to a positive value signaling the overflow of an 
+/// operation, in particular it just evaluates to positive infinity.
+///
+/// **See also:** Documentation for [HUGE_VAL](https://en.cppreference.com/w/cpp/numeric/math/HUGE_VAL)
+#define HUGE_VALH	std::numeric_limits<half_float::half>::infinity()
+
+/// Fast half-precision fma function.
+/// This symbol is defined if the fma() function generally executes as fast as, or faster than, a separate 
+/// half-precision multiplication followed by an addition, which is always the case.
+///
+/// **See also:** Documentation for [FP_FAST_FMA](https://en.cppreference.com/w/cpp/numeric/math/fma)
+#define FP_FAST_FMAH	1
+
+///	Half rounding mode.
+/// In correspondence with `FLT_ROUNDS` from `<cfloat>` this symbol expands to the rounding mode used for 
+/// half-precision operations. It is an alias for [HALF_ROUND_STYLE](\ref HALF_ROUND_STYLE).
+///
+/// **See also:** Documentation for [FLT_ROUNDS](https://en.cppreference.com/w/cpp/types/climits/FLT_ROUNDS)
+#define HLF_ROUNDS	HALF_ROUND_STYLE
+
+#ifndef FP_ILOGB0
+	#define FP_ILOGB0		INT_MIN
+#endif
+#ifndef FP_ILOGBNAN
+	#define FP_ILOGBNAN		INT_MAX
+#endif
+#ifndef FP_SUBNORMAL
+	#define FP_SUBNORMAL	0
+#endif
+#ifndef FP_ZERO
+	#define FP_ZERO			1
+#endif
+#ifndef FP_NAN
+	#define FP_NAN			2
+#endif
+#ifndef FP_INFINITE
+	#define FP_INFINITE		3
+#endif
+#ifndef FP_NORMAL
+	#define FP_NORMAL		4
+#endif
+
+#if !HALF_ENABLE_CPP11_CFENV && !defined(FE_ALL_EXCEPT)
+	#define FE_INVALID		0x10
+	#define FE_DIVBYZERO	0x08
+	#define FE_OVERFLOW		0x04
+	#define FE_UNDERFLOW	0x02
+	#define FE_INEXACT		0x01
+	#define FE_ALL_EXCEPT	(FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT)
+#endif
+
+
+/// Main namespace for half-precision functionality.
+/// This namespace contains all the functionality provided by the library.
+namespace half_float
+{
+	class half;
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+	/// Library-defined half-precision literals.
+	/// Import this namespace to enable half-precision floating-point literals:
+	/// ~~~~{.cpp}
+	/// using namespace half_float::literal;
+	/// half_float::half = 4.2_h;
+	/// ~~~~
+	namespace literal
+	{
+		half operator "" _h(long double);
+	}
+#endif
+
+	/// \internal
+	/// \brief Implementation details.
+	namespace detail
+	{
+	#if HALF_ENABLE_CPP11_TYPE_TRAITS
+		/// Conditional type.
+		template<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::true_type;
+		using std::false_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;
+
+		/// Fastest unsigned integer of (at least) 32 bits width.
+		typedef std::uint_fast32_t uint32;
+
+		/// Fastest signed integer of (at least) 32 bits width.
+		typedef std::int_fast32_t int32;
+
+		/// Unsigned integer of (at least) 32 bits width.
+		template<> struct bits<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;
+
+		/// Fastest unsigned integer of (at least) 32 bits width.
+		typedef unsigned long uint32;
+
+		/// Fastest unsigned integer of (at least) 32 bits width.
+		typedef long int32;
+
+		/// Unsigned integer of (at least) 32 bits width.
+		template<> struct bits<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
+
+	#ifdef HALF_ARITHMETIC_TYPE
+		/// Type to use for arithmetic computations and mathematic functions internally.
+		typedef HALF_ARITHMETIC_TYPE internal_t;
+	#endif
+
+		/// Tag type for binary construction.
+		struct binary_t {};
+
+		/// Tag for binary construction.
+		HALF_CONSTEXPR_CONST binary_t binary = binary_t();
+
+		/// \name Implementation defined classification and arithmetic
+		/// \{
+
+		/// Check for infinity.
+		/// \tparam T argument type (builtin floating-point type)
+		/// \param arg value to query
+		/// \retval true if infinity
+		/// \retval false else
+		template<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
+		}
+
+		/// Platform-independent sign mask.
+		/// \param arg integer value in two's complement
+		/// \retval -1 if \a arg negative
+		/// \retval 0 if \a arg positive
+		inline uint32 sign_mask(uint32 arg)
+		{
+			static const int N = std::numeric_limits<uint32>::digits - 1;
+		#if HALF_TWOS_COMPLEMENT_INT
+			return static_cast<int32>(arg) >> N;
+		#else
+			return -((arg>>N)&1);
+		#endif
+		}
+
+		/// Platform-independent arithmetic right shift.
+		/// \param arg integer value in two's complement
+		/// \param i shift amount (at most 31)
+		/// \return \a arg right shifted for \a i bits with possible sign extension
+		inline uint32 arithmetic_shift(uint32 arg, int i)
+		{
+		#if HALF_TWOS_COMPLEMENT_INT
+			return static_cast<int32>(arg) >> i;
+		#else
+			return static_cast<int32>(arg)/(static_cast<int32>(1)<<i) - ((arg>>(std::numeric_limits<uint32>::digits-1))&1);
+		#endif
+		}
+
+		/// \}
+		/// \name Error handling
+		/// \{
+
+		/// Internal exception flags.
+		/// \return reference to global exception flags
+		inline int& errflags() { HALF_THREAD_LOCAL int flags = 0; return flags; }
+
+		/// Raise floating-point exception.
+		/// \param flags exceptions to raise
+		/// \param cond condition to raise exceptions for
+		inline void raise(int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond) = true)
+		{
+		#if HALF_ERRHANDLING
+			if(!cond)
+				return;
+		#if HALF_ERRHANDLING_FLAGS
+			errflags() |= flags;
+		#endif
+		#if HALF_ERRHANDLING_ERRNO
+			if(flags & FE_INVALID)
+				errno = EDOM;
+			else if(flags & (FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW))
+				errno = ERANGE;
+		#endif
+		#if HALF_ERRHANDLING_FENV && HALF_ENABLE_CPP11_CFENV
+			std::feraiseexcept(flags);
+		#endif
+		#ifdef HALF_ERRHANDLING_THROW_INVALID
+			if(flags & FE_INVALID)
+				throw std::domain_error(HALF_ERRHANDLING_THROW_INVALID);
+		#endif
+		#ifdef HALF_ERRHANDLING_THROW_DIVBYZERO
+			if(flags & FE_DIVBYZERO)
+				throw std::domain_error(HALF_ERRHANDLING_THROW_DIVBYZERO);
+		#endif
+		#ifdef HALF_ERRHANDLING_THROW_OVERFLOW
+			if(flags & FE_OVERFLOW)
+				throw std::overflow_error(HALF_ERRHANDLING_THROW_OVERFLOW);
+		#endif
+		#ifdef HALF_ERRHANDLING_THROW_UNDERFLOW
+			if(flags & FE_UNDERFLOW)
+				throw std::underflow_error(HALF_ERRHANDLING_THROW_UNDERFLOW);
+		#endif
+		#ifdef HALF_ERRHANDLING_THROW_INEXACT
+			if(flags & FE_INEXACT)
+				throw std::range_error(HALF_ERRHANDLING_THROW_INEXACT);
+		#endif
+		#if HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+			if((flags & FE_UNDERFLOW) && !(flags & FE_INEXACT))
+				raise(FE_INEXACT);
+		#endif
+		#if HALF_ERRHANDLING_OVERFLOW_TO_INEXACT
+			if((flags & FE_OVERFLOW) && !(flags & FE_INEXACT))
+				raise(FE_INEXACT);
+		#endif
+		#endif
+		}
+
+		/// Check and signal for any NaN.
+		/// \param x first half-precision value to check
+		/// \param y second half-precision value to check
+		/// \retval true if either \a x or \a y is NaN
+		/// \retval false else
+		/// \exception FE_INVALID if \a x or \a y is NaN
+		inline HALF_CONSTEXPR_NOERR bool compsignal(unsigned int x, unsigned int y)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_INVALID, (x&0x7FFF)>0x7C00 || (y&0x7FFF)>0x7C00);
+		#endif
+			return (x&0x7FFF) > 0x7C00 || (y&0x7FFF) > 0x7C00;
+		}
+
+		/// Signal and silence signaling NaN.
+		/// \param nan half-precision NaN value
+		/// \return quiet NaN
+		/// \exception FE_INVALID if \a nan is signaling NaN
+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int nan)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_INVALID, !(nan&0x200));
+		#endif
+			return nan | 0x200;
+		}
+
+		/// Signal and silence signaling NaNs.
+		/// \param x first half-precision value to check
+		/// \param y second half-precision value to check
+		/// \return quiet NaN
+		/// \exception FE_INVALID if \a x or \a y is signaling NaN
+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)));
+		#endif
+			return ((x&0x7FFF)>0x7C00) ? (x|0x200) : (y|0x200);
+		}
+
+		/// Signal and silence signaling NaNs.
+		/// \param x first half-precision value to check
+		/// \param y second half-precision value to check
+		/// \param z third half-precision value to check
+		/// \return quiet NaN
+		/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN
+		inline HALF_CONSTEXPR_NOERR unsigned int signal(unsigned int x, unsigned int y, unsigned int z)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_INVALID, ((x&0x7FFF)>0x7C00 && !(x&0x200)) || ((y&0x7FFF)>0x7C00 && !(y&0x200)) || ((z&0x7FFF)>0x7C00 && !(z&0x200)));
+		#endif
+			return ((x&0x7FFF)>0x7C00) ? (x|0x200) : ((y&0x7FFF)>0x7C00) ? (y|0x200) : (z|0x200);
+		}
+
+		/// Select value or signaling NaN.
+		/// \param x preferred half-precision value
+		/// \param y ignored half-precision value except for signaling NaN
+		/// \return \a y if signaling NaN, \a x otherwise
+		/// \exception FE_INVALID if \a y is signaling NaN
+		inline HALF_CONSTEXPR_NOERR unsigned int select(unsigned int x, unsigned int HALF_UNUSED_NOERR(y))
+		{
+		#if HALF_ERRHANDLING
+			return (((y&0x7FFF)>0x7C00) && !(y&0x200)) ? signal(y) : x;
+		#else
+			return x;
+		#endif
+		}
+
+		/// Raise domain error and return NaN.
+		/// return quiet NaN
+		/// \exception FE_INVALID
+		inline HALF_CONSTEXPR_NOERR unsigned int invalid()
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_INVALID);
+		#endif
+			return 0x7FFF;
+		}
+
+		/// Raise pole error and return infinity.
+		/// \param sign half-precision value with sign bit only
+		/// \return half-precision infinity with sign of \a sign
+		/// \exception FE_DIVBYZERO
+		inline HALF_CONSTEXPR_NOERR unsigned int pole(unsigned int sign = 0)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_DIVBYZERO);
+		#endif
+			return sign | 0x7C00;
+		}
+
+		/// Check value for underflow.
+		/// \param arg non-zero half-precision value to check
+		/// \return \a arg
+		/// \exception FE_UNDERFLOW if arg is subnormal
+		inline HALF_CONSTEXPR_NOERR unsigned int check_underflow(unsigned int arg)
+		{
+		#if HALF_ERRHANDLING && !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT
+			raise(FE_UNDERFLOW, !(arg&0x7C00));
+		#endif
+			return arg;
+		}
+
+		/// \}
+		/// \name Conversion and rounding
+		/// \{
+
+		/// Half-precision overflow.
+		/// \tparam R rounding mode to use
+		/// \param sign half-precision value with sign bit only
+		/// \return rounded overflowing half-precision value
+		/// \exception FE_OVERFLOW
+		template<std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int overflow(unsigned int sign = 0)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_OVERFLOW);
+		#endif
+			return	(R==std::round_toward_infinity) ? (sign+0x7C00-(sign>>15)) :
+					(R==std::round_toward_neg_infinity) ? (sign+0x7BFF+(sign>>15)) :
+					(R==std::round_toward_zero) ? (sign|0x7BFF) :
+					(sign|0x7C00);
+		}
+
+		/// Half-precision underflow.
+		/// \tparam R rounding mode to use
+		/// \param sign half-precision value with sign bit only
+		/// \return rounded underflowing half-precision value
+		/// \exception FE_UNDERFLOW
+		template<std::float_round_style R> HALF_CONSTEXPR_NOERR unsigned int underflow(unsigned int sign = 0)
+		{
+		#if HALF_ERRHANDLING
+			raise(FE_UNDERFLOW);
+		#endif
+			return	(R==std::round_toward_infinity) ? (sign+1-(sign>>15)) :
+					(R==std::round_toward_neg_infinity) ? (sign+(sign>>15)) :
+					sign;
+		}
+
+		/// Round half-precision number.
+		/// \tparam R rounding mode to use
+		/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results
+		/// \param value finite half-precision number to round
+		/// \param g guard bit (most significant discarded bit)
+		/// \param s sticky bit (or of all but the most significant discarded bits)
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`
+		template<std::float_round_style R,bool I> HALF_CONSTEXPR_NOERR unsigned int rounded(unsigned int value, int g, int s)
+		{
+		#if HALF_ERRHANDLING
+			value +=	(R==std::round_to_nearest) ? (g&(s|value)) :
+						(R==std::round_toward_infinity) ? (~(value>>15)&(g|s)) :
+						(R==std::round_toward_neg_infinity) ? ((value>>15)&(g|s)) : 0;
+			if((value&0x7C00) == 0x7C00)
+				raise(FE_OVERFLOW);
+			else if(value & 0x7C00)
+				raise(FE_INEXACT, I || (g|s)!=0);
+			else
+				raise(FE_UNDERFLOW, !(HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT) || I || (g|s)!=0);
+			return value;
+		#else
+			return	(R==std::round_to_nearest) ? (value+(g&(s|value))) :
+					(R==std::round_toward_infinity) ? (value+(~(value>>15)&(g|s))) :
+					(R==std::round_toward_neg_infinity) ? (value+((value>>15)&(g|s))) :
+					value;
+		#endif
+		}
+
+		/// Round half-precision number to nearest integer value.
+		/// \tparam R rounding mode to use
+		/// \tparam E `true` for round to even, `false` for round away from zero
+		/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it
+		/// \param value half-precision value to round
+		/// \return half-precision bits for nearest integral value
+		/// \exception FE_INVALID for signaling NaN
+		/// \exception FE_INEXACT if value had to be rounded and \a I is `true`
+		template<std::float_round_style R,bool E,bool I> unsigned int integral(unsigned int value)
+		{
+			unsigned int abs = value & 0x7FFF;
+			if(abs < 0x3C00)
+			{
+				raise(FE_INEXACT, I);
+				return ((R==std::round_to_nearest) ? (0x3C00&-static_cast<unsigned>(abs>=(0x3800+E))) :
+						(R==std::round_toward_infinity) ? (0x3C00&-(~(value>>15)&(abs!=0))) :
+						(R==std::round_toward_neg_infinity) ? (0x3C00&-static_cast<unsigned>(value>0x8000)) :
+						0) | (value&0x8000);
+			}
+			if(abs >= 0x6400)
+				return (abs>0x7C00) ? signal(value) : value;
+			unsigned int exp = 25 - (abs>>10), mask = (1<<exp) - 1;
+			raise(FE_INEXACT, I && (value&mask));
+			return ((	(R==std::round_to_nearest) ? ((1<<(exp-1))-(~(value>>exp)&E)) :
+						(R==std::round_toward_infinity) ? (mask&((value>>15)-1)) :
+						(R==std::round_toward_neg_infinity) ? (mask&-(value>>15)) :
+						0) + value) & ~mask;
+		}
+
+		/// Convert fixed point to half-precision floating-point.
+		/// \tparam R rounding mode to use
+		/// \tparam F number of fractional bits (at least 11)
+		/// \tparam S `true` for signed, `false` for unsigned
+		/// \tparam N `true` for additional normalization step, `false` if already normalized to 1.F
+		/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results
+		/// \param m mantissa in Q1.F fixed point format
+		/// \param exp exponent
+		/// \param sign half-precision value with sign bit only
+		/// \param s sticky bit (or of all but the most significant already discarded bits)
+		/// \return value converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`
+		template<std::float_round_style R,unsigned int F,bool S,bool N,bool I> unsigned int fixed2half(uint32 m, int exp = 14, unsigned int sign = 0, int s = 0)
+		{
+			if(S)
+			{
+				uint32 msign = sign_mask(m);
+				m = (m^msign) - msign;
+				sign = msign & 0x8000;
+			}
+			if(N)
+				for(; m<(static_cast<uint32>(1)<<F) && exp; m<<=1,--exp) ;
+			else if(exp < 0)
+				return rounded<R,I>(sign+(m>>(F-10-exp)), (m>>(F-11-exp))&1, s|((m&((static_cast<uint32>(1)<<(F-11-exp))-1))!=0));
+			return rounded<R,I>(sign+(exp<<10)+(m>>(F-10)), (m>>(F-11))&1, s|((m&((static_cast<uint32>(1)<<(F-11))-1))!=0));
+		}
+
+		/// Convert IEEE single-precision to half-precision.
+		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+		/// \tparam R rounding mode to use
+		/// \param value single-precision value to convert
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R> unsigned int float2half_impl(float value, true_type)
+		{
+		#if HALF_ENABLE_F16C_INTRINSICS
+			return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_set_ss(value),
+				(R==std::round_to_nearest) ? _MM_FROUND_TO_NEAREST_INT :
+				(R==std::round_toward_zero) ? _MM_FROUND_TO_ZERO :
+				(R==std::round_toward_infinity) ? _MM_FROUND_TO_POS_INF :
+				(R==std::round_toward_neg_infinity) ? _MM_FROUND_TO_NEG_INF :
+				_MM_FROUND_CUR_DIRECTION));
+		#else
+			bits<float>::type fbits;
+			std::memcpy(&fbits, &value, sizeof(float));
+		#if 1
+			unsigned int sign = (fbits>>16) & 0x8000;
+			fbits &= 0x7FFFFFFF;
+			if(fbits >= 0x7F800000)
+				return sign | 0x7C00 | ((fbits>0x7F800000) ? (0x200|((fbits>>13)&0x3FF)) : 0);
+			if(fbits >= 0x47800000)
+				return overflow<R>(sign);
+			if(fbits >= 0x38800000)
+				return rounded<R,false>(sign|(((fbits>>23)-112)<<10)|((fbits>>13)&0x3FF), (fbits>>12)&1, (fbits&0xFFF)!=0);
+			if(fbits >= 0x33000000)
+			{
+				int i = 125 - (fbits>>23);
+				fbits = (fbits&0x7FFFFF) | 0x800000;
+				return rounded<R,false>(sign|(fbits>>(i+1)), (fbits>>i)&1, (fbits&((static_cast<uint32>(1)<<i)-1))!=0);
+			}
+			if(fbits != 0)
+				return underflow<R>(sign);
+			return sign;
+		#else
+			static const uint16 base_table[512] = {
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 
+				0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, 
+				0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, 
+				0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 
+				0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7BFF, 0x7C00, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 
+				0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, 
+				0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, 
+				0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 
+				0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFBFF, 0xFC00 };
+			static const unsigned char shift_table[256] = {
+				24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 
+				25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 
+				25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 
+				25, 25, 25, 25, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 
+				13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 
+				24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 };
+			int sexp = fbits >> 23, exp = sexp & 0xFF, i = shift_table[exp];
+			fbits &= 0x7FFFFF;
+			uint32 m = (fbits|((exp!=0)<<23)) & -static_cast<uint32>(exp!=0xFF);
+			return rounded<R,false>(base_table[sexp]+(fbits>>i), (m>>(i-1))&1, (((static_cast<uint32>(1)<<(i-1))-1)&m)!=0);
+		#endif
+		#endif
+		}
+
+		/// Convert IEEE double-precision to half-precision.
+		/// \tparam R rounding mode to use
+		/// \param value double-precision value to convert
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R> unsigned int float2half_impl(double value, true_type)
+		{
+		#if HALF_ENABLE_F16C_INTRINSICS
+			if(R == std::round_indeterminate)
+				return _mm_cvtsi128_si32(_mm_cvtps_ph(_mm_cvtpd_ps(_mm_set_sd(value)), _MM_FROUND_CUR_DIRECTION));
+		#endif
+			bits<double>::type dbits;
+			std::memcpy(&dbits, &value, sizeof(double));
+			uint32 hi = dbits >> 32, lo = dbits & 0xFFFFFFFF;
+			unsigned int sign = (hi>>16) & 0x8000;
+			hi &= 0x7FFFFFFF;
+			if(hi >= 0x7FF00000)
+				return sign | 0x7C00 | ((dbits&0xFFFFFFFFFFFFF) ? (0x200|((hi>>10)&0x3FF)) : 0);
+			if(hi >= 0x40F00000)
+				return overflow<R>(sign);
+			if(hi >= 0x3F100000)
+				return rounded<R,false>(sign|(((hi>>20)-1008)<<10)|((hi>>10)&0x3FF), (hi>>9)&1, ((hi&0x1FF)|lo)!=0);
+			if(hi >= 0x3E600000)
+			{
+				int i = 1018 - (hi>>20);
+				hi = (hi&0xFFFFF) | 0x100000;
+				return rounded<R,false>(sign|(hi>>(i+1)), (hi>>i)&1, ((hi&((static_cast<uint32>(1)<<i)-1))|lo)!=0);
+			}
+			if((hi|lo) != 0)
+				return underflow<R>(sign);
+			return sign;
+		}
+
+		/// Convert non-IEEE floating-point to half-precision.
+		/// \tparam R rounding mode to use
+		/// \tparam T source type (builtin floating-point type)
+		/// \param value floating-point value to convert
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R,typename T> unsigned int float2half_impl(T value, ...)
+		{
+			unsigned int 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)
+				return overflow<R>(hbits);
+			if(exp < -13)
+				value = std::ldexp(value, 25);
+			else
+			{
+				value = std::ldexp(value, 12-exp);
+				hbits |= ((exp+13)<<10);
+			}
+			T ival, frac = std::modf(value, &ival);
+			int m = std::abs(static_cast<int>(ival));
+			return rounded<R,false>(hbits+(m>>1), m&1, frac!=T());
+		}
+
+		/// Convert floating-point to half-precision.
+		/// \tparam R rounding mode to use
+		/// \tparam T source type (builtin floating-point type)
+		/// \param value floating-point value to convert
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R,typename T> unsigned int 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
+		/// \tparam T type to convert (builtin integer type)
+		/// \param value integral value to convert
+		/// \return rounded half-precision value
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R,typename T> unsigned int int2half(T value)
+		{
+			unsigned int bits = static_cast<unsigned>(value<0) << 15;
+			if(!value)
+				return bits;
+			if(bits)
+				value = -value;
+			if(value > 0xFFFF)
+				return overflow<R>(bits);
+			unsigned int m = static_cast<unsigned int>(value), exp = 24;
+			for(; m<0x400; m<<=1,--exp) ;
+			for(; m>0x7FF; m>>=1,++exp) ;
+			bits |= (exp<<10) + m;
+			return (exp>24) ? rounded<R,false>(bits, (value>>(exp-25))&1, (((1<<(exp-25))-1)&value)!=0) : bits;
+		}
+
+		/// Convert half-precision to IEEE single-precision.
+		/// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf).
+		/// \param value half-precision value to convert
+		/// \return single-precision value
+		inline float half2float_impl(unsigned int value, float, true_type)
+		{
+		#if HALF_ENABLE_F16C_INTRINSICS
+			return _mm_cvtss_f32(_mm_cvtph_ps(_mm_cvtsi32_si128(value)));
+		#else
+		#if 0
+			bits<float>::type fbits = static_cast<bits<float>::type>(value&0x8000) << 16;
+			int abs = value & 0x7FFF;
+			if(abs)
+			{
+				fbits |= 0x38000000 << static_cast<unsigned>(abs>=0x7C00);
+				for(; abs<0x400; abs<<=1,fbits-=0x800000) ;
+				fbits += static_cast<bits<float>::type>(abs) << 13;
+			}
+		#else
+			static const bits<float>::type mantissa_table[2048] = {
+				0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000, 
+				0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, 
+				0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, 
+				0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, 
+				0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, 
+				0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, 
+				0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, 
+				0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, 
+				0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, 
+				0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, 
+				0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, 
+				0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, 
+				0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, 
+				0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, 
+				0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000, 
+				0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, 
+				0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, 
+				0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, 
+				0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, 
+				0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, 
+				0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, 
+				0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, 
+				0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, 
+				0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, 
+				0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, 
+				0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, 
+				0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, 
+				0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, 
+				0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, 
+				0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, 
+				0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, 
+				0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, 
+				0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, 
+				0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, 
+				0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, 
+				0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, 
+				0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, 
+				0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, 
+				0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, 
+				0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, 
+				0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, 
+				0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, 
+				0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, 
+				0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, 
+				0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, 
+				0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000, 
+				0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000, 
+				0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, 
+				0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, 
+				0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, 
+				0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, 
+				0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, 
+				0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, 
+				0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, 
+				0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, 
+				0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, 
+				0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, 
+				0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, 
+				0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, 
+				0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, 
+				0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000, 
+				0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, 
+				0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, 
+				0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, 
+				0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, 
+				0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, 
+				0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, 
+				0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, 
+				0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, 
+				0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, 
+				0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, 
+				0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, 
+				0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, 
+				0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, 
+				0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, 
+				0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, 
+				0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, 
+				0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000, 
+				0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, 
+				0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, 
+				0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, 
+				0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000, 
+				0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, 
+				0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, 
+				0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, 
+				0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, 
+				0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, 
+				0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, 
+				0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, 
+				0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, 
+				0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, 
+				0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, 
+				0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, 
+				0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, 
+				0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, 
+				0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, 
+				0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, 
+				0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, 
+				0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, 
+				0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, 
+				0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, 
+				0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, 
+				0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, 
+				0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, 
+				0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, 
+				0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, 
+				0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, 
+				0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, 
+				0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, 
+				0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, 
+				0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, 
+				0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, 
+				0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, 
+				0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, 
+				0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, 
+				0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, 
+				0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, 
+				0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, 
+				0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, 
+				0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, 
+				0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, 
+				0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, 
+				0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, 
+				0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, 
+				0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, 
+				0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, 
+				0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, 
+				0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 };
+			static const bits<float>::type exponent_table[64] = {
+				0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000, 
+				0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000, 
+				0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, 
+				0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 };
+			static const unsigned short offset_table[64] = {
+				0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 
+				0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 };
+			bits<float>::type fbits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10];
+		#endif
+			float out;
+			std::memcpy(&out, &fbits, sizeof(float));
+			return out;
+		#endif
+		}
+
+		/// Convert half-precision to IEEE double-precision.
+		/// \param value half-precision value to convert
+		/// \return double-precision value
+		inline double half2float_impl(unsigned int value, double, true_type)
+		{
+		#if HALF_ENABLE_F16C_INTRINSICS
+			return _mm_cvtsd_f64(_mm_cvtps_pd(_mm_cvtph_ps(_mm_cvtsi32_si128(value))));
+		#else
+			uint32 hi = static_cast<uint32>(value&0x8000) << 16;
+			unsigned 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;
+			}
+			bits<double>::type dbits = static_cast<bits<double>::type>(hi) << 32;
+			double out;
+			std::memcpy(&out, &dbits, sizeof(double));
+			return out;
+		#endif
+		}
+
+		/// Convert half-precision to non-IEEE floating-point.
+		/// \tparam T type to convert to (builtin integer type)
+		/// \param value half-precision value to convert
+		/// \return floating-point value
+		template<typename T> T half2float_impl(unsigned int value, T, ...)
+		{
+			T out;
+			unsigned int abs = value & 0x7FFF;
+			if(abs > 0x7C00)
+				out = (std::numeric_limits<T>::has_signaling_NaN && !(abs&0x200)) ? std::numeric_limits<T>::signaling_NaN() :
+					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 half-precision value to convert
+		/// \return floating-point value
+		template<typename T> T half2float(unsigned int 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
+		/// \tparam E `true` for round to even, `false` for round away from zero
+		/// \tparam I `true` to raise INEXACT exception (if inexact), `false` to never raise it
+		/// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)
+		/// \param value half-precision value to convert
+		/// \return rounded integer value
+		/// \exception FE_INVALID if value is not representable in type \a T
+		/// \exception FE_INEXACT if value had to be rounded and \a I is `true`
+		template<std::float_round_style R,bool E,bool I,typename T> T half2int(unsigned int value)
+		{
+			unsigned int abs = value & 0x7FFF;
+			if(abs >= 0x7C00)
+			{
+				raise(FE_INVALID);
+				return (value&0x8000) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
+			}
+			if(abs < 0x3800)
+			{
+				raise(FE_INEXACT, I);
+				return	(R==std::round_toward_infinity) ? T(~(value>>15)&(abs!=0)) :
+						(R==std::round_toward_neg_infinity) ? -T(value>0x8000) :
+						T();
+			}
+			int exp = 25 - (abs>>10);
+			unsigned int m = (value&0x3FF) | 0x400;
+			int32 i = static_cast<int32>((exp<=0) ? (m<<-exp) : ((m+(
+				(R==std::round_to_nearest) ? ((1<<(exp-1))-(~(m>>exp)&E)) :
+				(R==std::round_toward_infinity) ? (((1<<exp)-1)&((value>>15)-1)) :
+				(R==std::round_toward_neg_infinity) ? (((1<<exp)-1)&-(value>>15)) : 0))>>exp));
+			if((!std::numeric_limits<T>::is_signed && (value&0x8000)) || (std::numeric_limits<T>::digits<16 &&
+				((value&0x8000) ? (-i<std::numeric_limits<T>::min()) : (i>std::numeric_limits<T>::max()))))
+				raise(FE_INVALID);
+			else if(I && exp > 0 && (m&((1<<exp)-1)))
+				raise(FE_INEXACT);
+			return static_cast<T>((value&0x8000) ? -i : i);
+		}
+
+		/// \}
+		/// \name Mathematics
+		/// \{
+
+		/// upper part of 64-bit multiplication.
+		/// \tparam R rounding mode to use
+		/// \param x first factor
+		/// \param y second factor
+		/// \return upper 32 bit of \a x * \a y
+		template<std::float_round_style R> uint32 mulhi(uint32 x, uint32 y)
+		{
+			uint32 xy = (x>>16) * (y&0xFFFF), yx = (x&0xFFFF) * (y>>16), c = (xy&0xFFFF) + (yx&0xFFFF) + (((x&0xFFFF)*(y&0xFFFF))>>16);
+			return (x>>16)*(y>>16) + (xy>>16) + (yx>>16) + (c>>16) +
+				((R==std::round_to_nearest) ? ((c>>15)&1) : (R==std::round_toward_infinity) ? ((c&0xFFFF)!=0) : 0);
+		}
+
+		/// 64-bit multiplication.
+		/// \param x first factor
+		/// \param y second factor
+		/// \return upper 32 bit of \a x * \a y rounded to nearest
+		inline uint32 multiply64(uint32 x, uint32 y)
+		{
+		#if HALF_ENABLE_CPP11_LONG_LONG
+			return static_cast<uint32>((static_cast<unsigned long long>(x)*static_cast<unsigned long long>(y)+0x80000000)>>32);
+		#else
+			return mulhi<std::round_to_nearest>(x, y);
+		#endif
+		}
+
+		/// 64-bit division.
+		/// \param x upper 32 bit of dividend
+		/// \param y divisor
+		/// \param s variable to store sticky bit for rounding
+		/// \return (\a x << 32) / \a y
+		inline uint32 divide64(uint32 x, uint32 y, int &s)
+		{
+		#if HALF_ENABLE_CPP11_LONG_LONG
+			unsigned long long xx = static_cast<unsigned long long>(x) << 32;
+			return s = (xx%y!=0), static_cast<uint32>(xx/y);
+		#else
+			y >>= 1;
+			uint32 rem = x, div = 0;
+			for(unsigned int i=0; i<32; ++i)
+			{
+				div <<= 1;
+				if(rem >= y)
+				{
+					rem -= y;
+					div |= 1;
+				}
+				rem <<= 1;
+			}
+			return s = rem > 1, div;
+		#endif
+		}
+
+		/// Half precision positive modulus.
+		/// \tparam Q `true` to compute full quotient, `false` else
+		/// \tparam R `true` to compute signed remainder, `false` for positive remainder
+		/// \param x first operand as positive finite half-precision value
+		/// \param y second operand as positive finite half-precision value
+		/// \param quo adress to store quotient at, `nullptr` if \a Q `false`
+		/// \return modulus of \a x / \a y
+		template<bool Q,bool R> unsigned int mod(unsigned int x, unsigned int y, int *quo = NULL)
+		{
+			unsigned int q = 0;
+			if(x > y)
+			{
+				int absx = x, absy = y, expx = 0, expy = 0;
+				for(; absx<0x400; absx<<=1,--expx) ;
+				for(; absy<0x400; absy<<=1,--expy) ;
+				expx += absx >> 10;
+				expy += absy >> 10;
+				int mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;
+				for(int d=expx-expy; d; --d)
+				{
+					if(!Q && mx == my)
+						return 0;
+					if(mx >= my)
+					{
+						mx -= my;
+						q += Q;
+					}
+					mx <<= 1;
+					q <<= static_cast<int>(Q);
+				}
+				if(!Q && mx == my)
+					return 0;
+				if(mx >= my)
+				{
+					mx -= my;
+					++q;
+				}
+				if(Q)
+				{
+					q &= (1<<(std::numeric_limits<int>::digits-1)) - 1;
+					if(!mx)
+						return *quo = q, 0;
+				}
+				for(; mx<0x400; mx<<=1,--expy) ;
+				x = (expy>0) ? ((expy<<10)|(mx&0x3FF)) : (mx>>(1-expy));
+			}
+			if(R)
+			{
+				unsigned int a, b;
+				if(y < 0x800)
+				{
+					a = (x<0x400) ? (x<<1) : (x+0x400);
+					b = y;
+				}
+				else
+				{
+					a = x;
+					b = y - 0x400;
+				}
+				if(a > b || (a == b && (q&1)))
+				{
+					int exp = (y>>10) + (y<=0x3FF), d = exp - (x>>10) - (x<=0x3FF);
+					int m = (((y&0x3FF)|((y>0x3FF)<<10))<<1) - (((x&0x3FF)|((x>0x3FF)<<10))<<(1-d));
+					for(; m<0x800 && exp>1; m<<=1,--exp) ;
+					x = 0x8000 + ((exp-1)<<10) + (m>>1);
+					q += Q;
+				}
+			}
+			if(Q)
+				*quo = q;
+			return x;
+		}
+
+		/// Fixed point square root.
+		/// \tparam F number of fractional bits
+		/// \param r radicand in Q1.F fixed point format
+		/// \param exp exponent
+		/// \return square root as Q1.F/2
+		template<unsigned int F> uint32 sqrt(uint32 &r, int &exp)
+		{
+			int i = exp & 1;
+			r <<= i;
+			exp = (exp-i) / 2;
+			uint32 m = 0;
+			for(uint32 bit=static_cast<uint32>(1)<<F; bit; bit>>=2)
+			{
+				if(r < m+bit)
+					m >>= 1;
+				else
+				{
+					r -= m + bit;
+					m = (m>>1) + bit;
+				}
+			}
+			return m;
+		}
+
+		/// Fixed point binary exponential.
+		/// This uses the BKM algorithm in E-mode.
+		/// \param m exponent in [0,1) as Q0.31
+		/// \param n number of iterations (at most 32)
+		/// \return 2 ^ \a m as Q1.31
+		inline uint32 exp2(uint32 m, unsigned int n = 32)
+		{
+			static const uint32 logs[] = {
+				0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,
+				0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,
+				0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
+				0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
+			if(!m)
+				return 0x80000000;
+			uint32 mx = 0x80000000, my = 0;
+			for(unsigned int i=1; i<n; ++i)
+			{
+				uint32 mz = my + logs[i];
+				if(mz <= m)
+				{
+					my = mz;
+					mx += mx >> i;
+				}
+			}
+			return mx;
+		}
+
+		/// Fixed point binary logarithm.
+		/// This uses the BKM algorithm in L-mode.
+		/// \param m mantissa in [1,2) as Q1.30
+		/// \param n number of iterations (at most 32)
+		/// \return log2(\a m) as Q0.31
+		inline uint32 log2(uint32 m, unsigned int n = 32)
+		{
+			static const uint32 logs[] = {
+				0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,
+				0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,
+				0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
+				0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
+			if(m == 0x40000000)
+				return 0;
+			uint32 mx = 0x40000000, my = 0;
+			for(unsigned int i=1; i<n; ++i)
+			{
+				uint32 mz = mx + (mx>>i);
+				if(mz <= m)
+				{
+					mx = mz;
+					my += logs[i];
+				}
+			}
+			return my;
+		}
+
+		/// Fixed point sine and cosine.
+		/// This uses the CORDIC algorithm in rotation mode.
+		/// \param mz angle in [-pi/2,pi/2] as Q1.30
+		/// \param n number of iterations (at most 31)
+		/// \return sine and cosine of \a mz as Q1.30
+		inline std::pair<uint32,uint32> sincos(uint32 mz, unsigned int n = 31)
+		{
+			static const uint32 angles[] = {
+				0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, 0x007FFF55,
+				0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000, 0x00008000,
+				0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,
+				0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };
+			uint32 mx = 0x26DD3B6A, my = 0;
+			for(unsigned int i=0; i<n; ++i)
+			{
+				uint32 sign = sign_mask(mz);
+				uint32 tx = mx - (arithmetic_shift(my, i)^sign) + sign;
+				uint32 ty = my + (arithmetic_shift(mx, i)^sign) - sign;
+				mx = tx; my = ty; mz -= (angles[i]^sign) - sign;
+			}
+			return std::make_pair(my, mx);
+		}
+
+		/// Fixed point arc tangent.
+		/// This uses the CORDIC algorithm in vectoring mode.
+		/// \param my y coordinate as Q0.30
+		/// \param mx x coordinate as Q0.30
+		/// \param n number of iterations (at most 31)
+		/// \return arc tangent of \a my / \a mx as Q1.30
+		inline uint32 atan2(uint32 my, uint32 mx, unsigned int n = 31)
+		{
+			static const uint32 angles[] = {
+				0x3243F6A9, 0x1DAC6705, 0x0FADBAFD, 0x07F56EA7, 0x03FEAB77, 0x01FFD55C, 0x00FFFAAB, 0x007FFF55,
+				0x003FFFEB, 0x001FFFFD, 0x00100000, 0x00080000, 0x00040000, 0x00020000, 0x00010000, 0x00008000,
+				0x00004000, 0x00002000, 0x00001000, 0x00000800, 0x00000400, 0x00000200, 0x00000100, 0x00000080,
+				0x00000040, 0x00000020, 0x00000010, 0x00000008, 0x00000004, 0x00000002, 0x00000001 };
+			uint32 mz = 0;
+			for(unsigned int i=0; i<n; ++i)
+			{
+				uint32 sign = sign_mask(my);
+				uint32 tx = mx + (arithmetic_shift(my, i)^sign) - sign;
+				uint32 ty = my - (arithmetic_shift(mx, i)^sign) + sign;
+				mx = tx; my = ty; mz += (angles[i]^sign) - sign;
+			}
+			return mz;
+		}
+
+		/// Reduce argument for trigonometric functions.
+		/// \param abs half-precision floating-point value
+		/// \param k value to take quarter period
+		/// \return \a abs reduced to [-pi/4,pi/4] as Q0.30
+		inline uint32 angle_arg(unsigned int abs, int &k)
+		{
+			uint32 m = (abs&0x3FF) | ((abs>0x3FF)<<10);
+			int exp = (abs>>10) + (abs<=0x3FF) - 15;
+			if(abs < 0x3A48)
+				return k = 0, m << (exp+20);
+		#if HALF_ENABLE_CPP11_LONG_LONG
+			unsigned long long y = m * 0xA2F9836E4E442, mask = (1ULL<<(62-exp)) - 1, yi = (y+(mask>>1)) & ~mask, f = y - yi;
+			uint32 sign = -static_cast<uint32>(f>>63);
+			k = static_cast<int>(yi>>(62-exp));
+			return (multiply64(static_cast<uint32>((sign ? -f : f)>>(31-exp)), 0xC90FDAA2)^sign) - sign;
+		#else
+			uint32 yh = m*0xA2F98 + mulhi<std::round_toward_zero>(m, 0x36E4E442), yl = (m*0x36E4E442) & 0xFFFFFFFF;
+			uint32 mask = (static_cast<uint32>(1)<<(30-exp)) - 1, yi = (yh+(mask>>1)) & ~mask, sign = -static_cast<uint32>(yi>yh);
+			k = static_cast<int>(yi>>(30-exp));
+			uint32 fh = (yh^sign) + (yi^~sign) - ~sign, fl = (yl^sign) - sign;
+			return (multiply64((exp>-1) ? (((fh<<(1+exp))&0xFFFFFFFF)|((fl&0xFFFFFFFF)>>(31-exp))) : fh, 0xC90FDAA2)^sign) - sign;
+		#endif
+		}
+
+		/// Get arguments for atan2 function.
+		/// \param abs half-precision floating-point value
+		/// \return \a abs and sqrt(1 - \a abs^2) as Q0.30
+		inline std::pair<uint32,uint32> atan2_args(unsigned int abs)
+		{
+			int exp = -15;
+			for(; abs<0x400; abs<<=1,--exp) ;
+			exp += abs >> 10;
+			uint32 my = ((abs&0x3FF)|0x400) << 5, r = my * my;
+			int rexp = 2 * exp;
+			r = 0x40000000 - ((rexp>-31) ? ((r>>-rexp)|((r&((static_cast<uint32>(1)<<-rexp)-1))!=0)) : 1);
+			for(rexp=0; r<0x40000000; r<<=1,--rexp) ;
+			uint32 mx = sqrt<30>(r, rexp);
+			int d = exp - rexp;
+			if(d < 0)
+				return std::make_pair((d<-14) ? ((my>>(-d-14))+((my>>(-d-15))&1)) : (my<<(14+d)), (mx<<14)+(r<<13)/mx);
+			if(d > 0)
+				return std::make_pair(my<<14, (d>14) ? ((mx>>(d-14))+((mx>>(d-15))&1)) : ((d==14) ? mx : ((mx<<(14-d))+(r<<(13-d))/mx)));
+			return std::make_pair(my<<13, (mx<<13)+(r<<12)/mx);
+		}
+
+		/// Get exponentials for hyperbolic computation
+		/// \param abs half-precision floating-point value
+		/// \param exp variable to take unbiased exponent of larger result
+		/// \param n number of BKM iterations (at most 32)
+		/// \return exp(abs) and exp(-\a abs) as Q1.31 with same exponent
+		inline std::pair<uint32,uint32> hyperbolic_args(unsigned int abs, int &exp, unsigned int n = 32)
+		{
+			uint32 mx = detail::multiply64(static_cast<uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29), my;
+			int e = (abs>>10) + (abs<=0x3FF);
+			if(e < 14)
+			{
+				exp = 0;
+				mx >>= 14 - e;
+			}
+			else
+			{
+				exp = mx >> (45-e);
+				mx = (mx<<(e-14)) & 0x7FFFFFFF;
+			}
+			mx = exp2(mx, n);
+			int d = exp << 1, s;
+			if(mx > 0x80000000)
+			{
+				my = divide64(0x80000000, mx, s);
+				my |= s;
+				++d;
+			}
+			else
+				my = mx;
+			return std::make_pair(mx, (d<31) ? ((my>>d)|((my&((static_cast<uint32>(1)<<d)-1))!=0)) : 1);
+		}
+
+		/// Postprocessing for binary exponential.
+		/// \tparam R rounding mode to use
+		/// \tparam I `true` to always raise INEXACT exception, `false` to raise only for rounded results
+		/// \param m mantissa as Q1.31
+		/// \param exp absolute value of unbiased exponent
+		/// \param esign sign of actual exponent
+		/// \param sign sign bit of result
+		/// \return value converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded or \a I is `true`
+		template<std::float_round_style R,bool I> unsigned int exp2_post(uint32 m, int exp, bool esign, unsigned int sign = 0)
+		{
+			int s = 0;
+			if(esign)
+			{
+				if(m > 0x80000000)
+				{
+					m = divide64(0x80000000, m, s);
+					++exp;
+				}
+				if(exp > 25)
+					return underflow<R>(sign);
+				else if(exp == 25)
+					return rounded<R,I>(sign, 1, (m&0x7FFFFFFF)!=0);
+				exp = -exp;
+			}
+			else if(exp > 15)
+				return overflow<R>(sign);
+			return fixed2half<R,31,false,false,I>(m, exp+14, sign, s);
+		}
+
+		/// Postprocessing for binary logarithm.
+		/// \tparam R rounding mode to use
+		/// \tparam L logarithm for base transformation as Q1.31
+		/// \param m fractional part of logarithm as Q0.31
+		/// \param ilog signed integer part of logarithm
+		/// \param exp biased exponent of result
+		/// \param sign sign bit of result
+		/// \return value base-transformed and converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if no other exception occurred
+		template<std::float_round_style R,uint32 L> unsigned int log2_post(uint32 m, int ilog, int exp, unsigned int sign = 0)
+		{
+			uint32 msign = sign_mask(ilog);
+			m = (((static_cast<uint32>(ilog)<<27)+(m>>4))^msign) - msign;
+			if(!m)
+				return 0;
+			for(; m<0x80000000; m<<=1,--exp) ;
+			int i = m >= L, s;
+			exp += i;
+			m >>= 1 + i;
+			sign ^= msign & 0x8000;
+			if(exp < -11)
+				return underflow<R>(sign);
+			m = divide64(m, L, s);
+			return fixed2half<R,30,false,false,true>(m, exp, sign, 1);
+		}
+
+		/// Hypotenuse square root and postprocessing.
+		/// \tparam R rounding mode to use
+		/// \param r mantissa as Q2.30
+		/// \param exp unbiased exponent
+		/// \return square root converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if value had to be rounded
+		template<std::float_round_style R> unsigned int hypot_post(uint32 r, int exp)
+		{
+			int i = r >> 31;
+			if((exp+=i) > 46)
+				return overflow<R>();
+			if(exp < -34)
+				return underflow<R>();
+			r = (r>>i) | (r&i);
+			uint32 m = sqrt<30>(r, exp+=15);
+			return fixed2half<R,15,false,false,false>(m, exp-1, 0, r!=0);
+		}
+
+		/// Division and postprocessing for tangents.
+		/// \tparam R rounding mode to use
+		/// \param my dividend as Q1.31
+		/// \param mx divisor as Q1.31
+		/// \param exp biased exponent of result
+		/// \param sign sign bit of result
+		/// \return quotient converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if no other exception occurred
+		template<std::float_round_style R> unsigned int tangent_post(uint32 my, uint32 mx, int exp, unsigned int sign = 0)
+		{
+			int i = my >= mx, s;
+			exp += i;
+			if(exp > 29)
+				return overflow<R>(sign);
+			if(exp < -11)
+				return underflow<R>(sign);
+			uint32 m = divide64(my>>(i+1), mx, s);
+			return fixed2half<R,30,false,false,true>(m, exp, sign, s);
+		}
+
+		/// Area function and postprocessing.
+		/// This computes the value directly in Q2.30 using the representation `asinh|acosh(x) = log(x+sqrt(x^2+|-1))`.
+		/// \tparam R rounding mode to use
+		/// \tparam S `true` for asinh, `false` for acosh
+		/// \param arg half-precision argument
+		/// \return asinh|acosh(\a arg) converted to half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if no other exception occurred
+		template<std::float_round_style R,bool S> unsigned int area(unsigned int arg)
+		{
+			int abs = arg & 0x7FFF, expx = (abs>>10) + (abs<=0x3FF) - 15, expy = -15, ilog, i;
+			uint32 mx = static_cast<uint32>((abs&0x3FF)|((abs>0x3FF)<<10)) << 20, my, r;
+			for(; abs<0x400; abs<<=1,--expy) ;
+			expy += abs >> 10;
+			r = ((abs&0x3FF)|0x400) << 5;
+			r *= r;
+			i = r >> 31;
+			expy = 2*expy + i;
+			r >>= i;
+			if(S)
+			{
+				if(expy < 0)
+				{
+					r = 0x40000000 + ((expy>-30) ? ((r>>-expy)|((r&((static_cast<uint32>(1)<<-expy)-1))!=0)) : 1);
+					expy = 0;
+				}
+				else
+				{
+					r += 0x40000000 >> expy;
+					i = r >> 31;
+					r = (r>>i) | (r&i);
+					expy += i;
+				}
+			}
+			else
+			{
+				r -= 0x40000000 >> expy;
+				for(; r<0x40000000; r<<=1,--expy) ;
+			}
+			my = sqrt<30>(r, expy);
+			my = (my<<15) + (r<<14)/my;
+			if(S)
+			{
+				mx >>= expy - expx;
+				ilog = expy;
+			}
+			else
+			{
+				my >>= expx - expy;
+				ilog = expx;
+			}
+			my += mx;
+			i = my >> 31;
+			static const int G = S && (R==std::round_to_nearest);
+			return log2_post<R,0xB8AA3B2A>(log2(my>>i, 26+S+G)+(G<<3), ilog+i, 17, arg&(static_cast<unsigned>(S)<<15));
+		}
+
+		/// Class for 1.31 unsigned floating-point computation
+		struct f31
+		{
+			/// Constructor.
+			/// \param mant mantissa as 1.31
+			/// \param e exponent
+			HALF_CONSTEXPR f31(uint32 mant, int e) : m(mant), exp(e) {}
+
+			/// Constructor.
+			/// \param abs unsigned half-precision value
+			f31(unsigned int abs) : exp(-15)
+			{
+				for(; abs<0x400; abs<<=1,--exp) ;
+				m = static_cast<uint32>((abs&0x3FF)|0x400) << 21;
+				exp += (abs>>10);
+			}
+
+			/// Addition operator.
+			/// \param a first operand
+			/// \param b second operand
+			/// \return \a a + \a b
+			friend f31 operator+(f31 a, f31 b)
+			{
+				if(b.exp > a.exp)
+					std::swap(a, b);
+				int d = a.exp - b.exp;
+				uint32 m = a.m + ((d<32) ? (b.m>>d) : 0);
+				int i = (m&0xFFFFFFFF) < a.m;
+				return f31(((m+i)>>i)|0x80000000, a.exp+i);
+			}
+
+			/// Subtraction operator.
+			/// \param a first operand
+			/// \param b second operand
+			/// \return \a a - \a b
+			friend f31 operator-(f31 a, f31 b)
+			{
+				int d = a.exp - b.exp, exp = a.exp;
+				uint32 m = a.m - ((d<32) ? (b.m>>d) : 0);
+				if(!m)
+					return f31(0, -32);
+				for(; m<0x80000000; m<<=1,--exp) ;
+				return f31(m, exp);
+			}
+
+			/// Multiplication operator.
+			/// \param a first operand
+			/// \param b second operand
+			/// \return \a a * \a b
+			friend f31 operator*(f31 a, f31 b)
+			{
+				uint32 m = multiply64(a.m, b.m);
+				int i = m >> 31;
+				return f31(m<<(1-i), a.exp + b.exp + i);
+			}
+
+			/// Division operator.
+			/// \param a first operand
+			/// \param b second operand
+			/// \return \a a / \a b
+			friend f31 operator/(f31 a, f31 b)
+			{
+				int i = a.m >= b.m, s;
+				uint32 m = divide64((a.m+i)>>i, b.m, s);
+				return f31(m, a.exp - b.exp + i - 1);
+			}
+
+			uint32 m;			///< mantissa as 1.31.
+			int exp;			///< exponent.
+		};
+
+		/// Error function and postprocessing.
+		/// This computes the value directly in Q1.31 using the approximations given 
+		/// [here](https://en.wikipedia.org/wiki/Error_function#Approximation_with_elementary_functions).
+		/// \tparam R rounding mode to use
+		/// \tparam C `true` for comlementary error function, `false` else
+		/// \param arg half-precision function argument
+		/// \return approximated value of error function in half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if no other exception occurred
+		template<std::float_round_style R,bool C> unsigned int erf(unsigned int arg)
+		{
+			unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
+			f31 x(abs), x2 = x * x * f31(0xB8AA3B29, 0), t = f31(0x80000000, 0) / (f31(0x80000000, 0)+f31(0xA7BA054A, -2)*x), t2 = t * t;
+			f31 e = ((f31(0x87DC2213, 0)*t2+f31(0xB5F0E2AE, 0))*t2+f31(0x82790637, -2)-(f31(0xBA00E2B8, 0)*t2+f31(0x91A98E62, -2))*t) * t /
+					((x2.exp<0) ? f31(exp2((x2.exp>-32) ? (x2.m>>-x2.exp) : 0, 30), 0) : f31(exp2((x2.m<<x2.exp)&0x7FFFFFFF, 22), x2.m>>(31-x2.exp)));
+			return (!C || sign) ? fixed2half<R,31,false,true,true>(0x80000000-(e.m>>(C-e.exp)), 14+C, sign&(C-1U)) :
+					(e.exp<-25) ? underflow<R>() : fixed2half<R,30,false,false,true>(e.m>>1, e.exp+14, 0, e.m&1);
+		}
+
+		/// Gamma function and postprocessing.
+		/// This approximates the value of either the gamma function or its logarithm directly in Q1.31.
+		/// \tparam R rounding mode to use
+		/// \tparam L `true` for lograithm of gamma function, `false` for gamma function
+		/// \param arg half-precision floating-point value
+		/// \return lgamma/tgamma(\a arg) in half-precision
+		/// \exception FE_OVERFLOW on overflows
+		/// \exception FE_UNDERFLOW on underflows
+		/// \exception FE_INEXACT if \a arg is not a positive integer
+		template<std::float_round_style R,bool L> unsigned int gamma(unsigned int arg)
+		{
+/*			static const double p[] ={ 2.50662827563479526904, 225.525584619175212544, -268.295973841304927459, 80.9030806934622512966, -5.00757863970517583837, 0.0114684895434781459556 };
+			double t = arg + 4.65, s = p[0];
+			for(unsigned int i=0; i<5; ++i)
+				s += p[i+1] / (arg+i);
+			return std::log(s) + (arg-0.5)*std::log(t) - t;
+*/			static const f31 pi(0xC90FDAA2, 1), lbe(0xB8AA3B29, 0);
+			unsigned int abs = arg & 0x7FFF, sign = arg & 0x8000;
+			bool bsign = sign != 0;
+			f31 z(abs), x = sign ? (z+f31(0x80000000, 0)) : z, t = x + f31(0x94CCCCCD, 2), s =
+				f31(0xA06C9901, 1) + f31(0xBBE654E2, -7)/(x+f31(0x80000000, 2)) + f31(0xA1CE6098, 6)/(x+f31(0x80000000, 1))
+				+ f31(0xE1868CB7, 7)/x - f31(0x8625E279, 8)/(x+f31(0x80000000, 0)) - f31(0xA03E158F, 2)/(x+f31(0xC0000000, 1));
+			int i = (s.exp>=2) + (s.exp>=4) + (s.exp>=8) + (s.exp>=16);
+			s = f31((static_cast<uint32>(s.exp)<<(31-i))+(log2(s.m>>1, 28)>>i), i) / lbe;
+			if(x.exp != -1 || x.m != 0x80000000)
+			{
+				i = (t.exp>=2) + (t.exp>=4) + (t.exp>=8);
+				f31 l = f31((static_cast<uint32>(t.exp)<<(31-i))+(log2(t.m>>1, 30)>>i), i) / lbe;
+				s = (x.exp<-1) ? (s-(f31(0x80000000, -1)-x)*l) : (s+(x-f31(0x80000000, -1))*l);
+			}
+			s = x.exp ? (s-t) : (t-s);
+			if(bsign)
+			{
+				if(z.exp >= 0)
+				{
+					sign &= (L|((z.m>>(31-z.exp))&1)) - 1;
+					for(z=f31((z.m<<(1+z.exp))&0xFFFFFFFF, -1); z.m<0x80000000; z.m<<=1,--z.exp) ;
+				}
+				if(z.exp == -1)
+					z = f31(0x80000000, 0) - z;
+				if(z.exp < -1)
+				{
+					z = z * pi;
+					z.m = sincos(z.m>>(1-z.exp), 30).first;
+					for(z.exp=1; z.m<0x80000000; z.m<<=1,--z.exp) ;
+				}
+				else
+					z = f31(0x80000000, 0);
+			}
+			if(L)
+			{
+				if(bsign)
+				{
+					f31 l(0x92868247, 0);
+					if(z.exp < 0)
+					{
+						uint32 m = log2((z.m+1)>>1, 27);
+						z = f31(-((static_cast<uint32>(z.exp)<<26)+(m>>5)), 5);
+						for(; z.m<0x80000000; z.m<<=1,--z.exp) ;
+						l = l + z / lbe;
+					}
+					sign = static_cast<unsigned>(x.exp&&(l.exp<s.exp||(l.exp==s.exp&&l.m<s.m))) << 15;
+					s = sign ? (s-l) : x.exp ? (l-s) : (l+s);
+				}
+				else
+				{
+					sign = static_cast<unsigned>(x.exp==0) << 15;
+					if(s.exp < -24)
+						return underflow<R>(sign);
+					if(s.exp > 15)
+						return overflow<R>(sign);
+				}
+			}
+			else
+			{
+				s = s * lbe;
+				uint32 m;
+				if(s.exp < 0)
+				{
+					m = s.m >> -s.exp;
+					s.exp = 0;
+				}
+				else
+				{
+					m = (s.m<<s.exp) & 0x7FFFFFFF;
+					s.exp = (s.m>>(31-s.exp));
+				}
+				s.m = exp2(m, 27);
+				if(!x.exp)
+					s = f31(0x80000000, 0) / s;
+				if(bsign)
+				{
+					if(z.exp < 0)
+						s = s * z;
+					s = pi / s;
+					if(s.exp < -24)
+						return underflow<R>(sign);
+				}
+				else if(z.exp > 0 && !(z.m&((1<<(31-z.exp))-1)))
+					return ((s.exp+14)<<10) + (s.m>>21);
+				if(s.exp > 15)
+					return overflow<R>(sign);
+			}
+			return fixed2half<R,31,false,false,true>(s.m, s.exp+14, sign);
+		}
+		/// \}
+
+		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.
+	///
+	/// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and 
+	/// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which 
+	/// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the 
+	/// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of 
+	/// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most 
+	/// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit 
+	/// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if 
+	/// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on 
+	/// nearly any reasonable platform.
+	///
+	/// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable 
+	/// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.
+	class half
+	{
+	public:
+		/// \name Construction and assignment
+		/// \{
+
+		/// Default constructor.
+		/// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics 
+		/// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.
+		HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {}
+
+		/// Conversion constructor.
+		/// \param rhs float to convert
+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+		explicit half(float rhs) : data_(static_cast<detail::uint16>(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.
+		/// \param rhs single-precision value to copy from
+		/// \return reference to this half
+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+		half& operator=(float rhs) { data_ = static_cast<detail::uint16>(detail::float2half<round_style>(rhs)); return *this; }
+
+		/// \}
+		/// \name Arithmetic updates
+		/// \{
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to add
+		/// \return reference to this half
+		/// \exception FE_... according to operator+(half,half)
+		half& operator+=(half rhs) { return *this = *this + rhs; }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to subtract
+		/// \return reference to this half
+		/// \exception FE_... according to operator-(half,half)
+		half& operator-=(half rhs) { return *this = *this - rhs; }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to multiply with
+		/// \return reference to this half
+		/// \exception FE_... according to operator*(half,half)
+		half& operator*=(half rhs) { return *this = *this * rhs; }
+
+		/// Arithmetic assignment.
+		/// \tparam T type of concrete half expression
+		/// \param rhs half expression to divide by
+		/// \return reference to this half
+		/// \exception FE_... according to operator/(half,half)
+		half& operator/=(half rhs) { return *this = *this / rhs; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to add
+		/// \return reference to this half
+		/// \exception FE_... according to operator=()
+		half& operator+=(float rhs) { return *this = *this + rhs; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to subtract
+		/// \return reference to this half
+		/// \exception FE_... according to operator=()
+		half& operator-=(float rhs) { return *this = *this - rhs; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to multiply with
+		/// \return reference to this half
+		/// \exception FE_... according to operator=()
+		half& operator*=(float rhs) { return *this = *this * rhs; }
+
+		/// Arithmetic assignment.
+		/// \param rhs single-precision value to divide by
+		/// \return reference to this half
+		/// \exception FE_... according to operator=()
+		half& operator/=(float rhs) { return *this = *this / rhs; }
+
+		/// \}
+		/// \name Increment and decrement
+		/// \{
+
+		/// Prefix increment.
+		/// \return incremented half value
+		/// \exception FE_... according to operator+(half,half)
+		half& operator++() { return *this = *this + half(detail::binary, 0x3C00); }
+
+		/// Prefix decrement.
+		/// \return decremented half value
+		/// \exception FE_... according to operator-(half,half)
+		half& operator--() { return *this = *this + half(detail::binary, 0xBC00); }
+
+		/// Postfix increment.
+		/// \return non-incremented half value
+		/// \exception FE_... according to operator+(half,half)
+		half operator++(int) { half out(*this); ++*this; return out; }
+
+		/// Postfix decrement.
+		/// \return non-decremented half value
+		/// \exception FE_... according to operator-(half,half)
+		half operator--(int) { half out(*this); --*this; return out; }
+		/// \}
+	
+	private:
+		/// Rounding mode to use
+		static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE);
+
+		/// Constructor.
+		/// \param bits binary representation to set half to
+		HALF_CONSTEXPR half(detail::binary_t, unsigned int bits) HALF_NOEXCEPT : data_(static_cast<detail::uint16>(bits)) {}
+
+		/// Internal binary representation
+		detail::uint16 data_;
+
+	#ifndef HALF_DOXYGEN_ONLY
+		friend HALF_CONSTEXPR_NOERR bool operator==(half, half);
+		friend HALF_CONSTEXPR_NOERR bool operator!=(half, half);
+		friend HALF_CONSTEXPR_NOERR bool operator<(half, half);
+		friend HALF_CONSTEXPR_NOERR bool operator>(half, half);
+		friend HALF_CONSTEXPR_NOERR bool operator<=(half, half);
+		friend HALF_CONSTEXPR_NOERR bool operator>=(half, half);
+		friend HALF_CONSTEXPR half operator-(half);
+		friend half operator+(half, half);
+		friend half operator-(half, half);
+		friend half operator*(half, half);
+		friend half operator/(half, half);
+		template<typename charT,typename traits> friend std::basic_ostream<charT,traits>& operator<<(std::basic_ostream<charT,traits>&, half);
+		template<typename charT,typename traits> friend std::basic_istream<charT,traits>& operator>>(std::basic_istream<charT,traits>&, half&);
+		friend HALF_CONSTEXPR half fabs(half);
+		friend half fmod(half, half);
+		friend half remainder(half, half);
+		friend half remquo(half, half, int*);
+		friend half fma(half, half, half);
+		friend HALF_CONSTEXPR_NOERR half fmax(half, half);
+		friend HALF_CONSTEXPR_NOERR half fmin(half, half);
+		friend half fdim(half, half);
+		friend half nanh(const char*);
+		friend half exp(half);
+		friend half exp2(half);
+		friend half expm1(half);
+		friend half log(half);
+		friend half log10(half);
+		friend half log2(half);
+		friend half log1p(half);
+		friend half sqrt(half);
+		friend half cbrt(half);
+		friend half hypot(half, half);
+		friend half hypot(half, half, half);
+		friend half pow(half, half);
+		friend void sincos(half, half*, half*);
+		friend half sin(half);
+		friend half cos(half);
+		friend half tan(half);
+		friend half asin(half);
+		friend half acos(half);
+		friend half atan(half);
+		friend half atan2(half, half);
+		friend half sinh(half);
+		friend half cosh(half);
+		friend half tanh(half);
+		friend half asinh(half);
+		friend half acosh(half);
+		friend half atanh(half);
+		friend half erf(half);
+		friend half erfc(half);
+		friend half lgamma(half);
+		friend half tgamma(half);
+		friend half ceil(half);
+		friend half floor(half);
+		friend half trunc(half);
+		friend half round(half);
+		friend long lround(half);
+		friend half rint(half);
+		friend long lrint(half);
+		friend half nearbyint(half);
+	#ifdef HALF_ENABLE_CPP11_LONG_LONG
+		friend long long llround(half);
+		friend long long llrint(half);
+	#endif
+		friend half frexp(half, int*);
+		friend half scalbln(half, long);
+		friend half modf(half, half*);
+		friend int ilogb(half);
+		friend half logb(half);
+		friend half nextafter(half, half);
+		friend half nexttoward(half, long double);
+		friend HALF_CONSTEXPR half copysign(half, half);
+		friend HALF_CONSTEXPR int fpclassify(half);
+		friend HALF_CONSTEXPR bool isfinite(half);
+		friend HALF_CONSTEXPR bool isinf(half);
+		friend HALF_CONSTEXPR bool isnan(half);
+		friend HALF_CONSTEXPR bool isnormal(half);
+		friend HALF_CONSTEXPR bool signbit(half);
+		friend HALF_CONSTEXPR bool isgreater(half, half);
+		friend HALF_CONSTEXPR bool isgreaterequal(half, half);
+		friend HALF_CONSTEXPR bool isless(half, half);
+		friend HALF_CONSTEXPR bool islessequal(half, half);
+		friend HALF_CONSTEXPR bool islessgreater(half, half);
+		template<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
+	#endif
+	};
+
+#if HALF_ENABLE_CPP11_USER_LITERALS
+	namespace literal
+	{
+		/// Half literal.
+		/// While this returns a properly rounded half-precision value, half literals can unfortunately not be constant 
+		/// expressions due to rather involved conversions. So don't expect this to be a literal literal without involving 
+		/// conversion operations at runtime. It is a convenience feature, not a performance optimization.
+		/// \param value literal value
+		/// \return half with of given value (possibly rounded)
+		/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+		inline half operator "" _h(long double value) { return half(detail::binary, detail::float2half<half::round_style>(value)); }
+	}
+#endif
+
+	namespace detail
+	{
+		/// Helper class for half casts.
+		/// This class template has to be specialized for all valid cast arguments to define an appropriate static 
+		/// `cast` member function and a corresponding `type` member denoting its return type.
+		/// \tparam T destination type
+		/// \tparam U source type
+		/// \tparam R rounding mode to use
+		template<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,true,true,T>(arg.data_); }
+		};
+		template<std::float_round_style R> struct half_caster<half,half,R>
+		{
+			static half cast(half arg) { return arg; }
+		};
+	}
+}
+
+/// Extensions to the C++ standard library.
+namespace std
+{
+	/// Numeric limits for half-precision floats.
+	/// **See also:** Documentation for [std::numeric_limits](https://en.cppreference.com/w/cpp/types/numeric_limits)
+	template<> class numeric_limits<half_float::half>
+	{
+	public:
+		/// Is template specialization.
+		static HALF_CONSTEXPR_CONST bool is_specialized = true;
+
+		/// Supports signed values.
+		static HALF_CONSTEXPR_CONST bool is_signed = true;
+
+		/// Is not an integer type.
+		static HALF_CONSTEXPR_CONST bool is_integer = false;
+
+		/// Is not exact.
+		static HALF_CONSTEXPR_CONST bool is_exact = false;
+
+		/// Doesn't provide modulo arithmetic.
+		static HALF_CONSTEXPR_CONST bool is_modulo = false;
+
+		/// Has a finite set of values.
+		static HALF_CONSTEXPR_CONST bool is_bounded = true;
+
+		/// IEEE conformant.
+		static HALF_CONSTEXPR_CONST bool is_iec559 = true;
+
+		/// Supports infinity.
+		static HALF_CONSTEXPR_CONST bool has_infinity = true;
+
+		/// Supports quiet NaNs.
+		static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true;
+
+		/// Supports signaling NaNs.
+		static HALF_CONSTEXPR_CONST bool has_signaling_NaN = true;
+
+		/// Supports subnormal values.
+		static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present;
+
+		/// Supports no denormalization detection.
+		static HALF_CONSTEXPR_CONST bool has_denorm_loss = false;
+
+	#if HALF_ERRHANDLING_THROWS
+		static HALF_CONSTEXPR_CONST bool traps = true;
+	#else
+		/// Traps only if [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID) is acitvated.
+		static HALF_CONSTEXPR_CONST bool traps = false;
+	#endif
+
+		/// Does not support no pre-rounding underflow detection.
+		static HALF_CONSTEXPR_CONST bool tinyness_before = false;
+
+		/// Rounding mode.
+		static HALF_CONSTEXPR_CONST float_round_style round_style = half_float::half::round_style;
+
+		/// Significant digits.
+		static HALF_CONSTEXPR_CONST int digits = 11;
+
+		/// Significant decimal digits.
+		static HALF_CONSTEXPR_CONST int digits10 = 3;
+
+		/// Required decimal digits to represent all possible values.
+		static HALF_CONSTEXPR_CONST int max_digits10 = 5;
+
+		/// Number base.
+		static HALF_CONSTEXPR_CONST int radix = 2;
+
+		/// One more than smallest exponent.
+		static HALF_CONSTEXPR_CONST int min_exponent = -13;
+
+		/// Smallest normalized representable power of 10.
+		static HALF_CONSTEXPR_CONST int min_exponent10 = -4;
+
+		/// One more than largest exponent
+		static HALF_CONSTEXPR_CONST int max_exponent = 16;
+
+		/// Largest finitely representable power of 10.
+		static HALF_CONSTEXPR_CONST int max_exponent10 = 4;
+
+		/// Smallest positive normal value.
+		static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); }
+
+		/// Smallest finite value.
+		static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); }
+
+		/// Largest finite value.
+		static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); }
+
+		/// Difference between 1 and next representable value.
+		static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); }
+
+		/// Maximum rounding error in ULP (units in the last place).
+		static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW
+			{ return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); }
+
+		/// Positive infinity.
+		static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); }
+
+		/// Quiet NaN.
+		static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); }
+
+		/// Signaling NaN.
+		static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); }
+
+		/// Smallest positive subnormal value.
+		static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); }
+	};
+
+#if HALF_ENABLE_CPP11_HASH
+	/// Hash function for half-precision floats.
+	/// This is only defined if C++11 `std::hash` is supported and enabled.
+	///
+	/// **See also:** Documentation for [std::hash](https://en.cppreference.com/w/cpp/utility/hash)
+	template<> struct hash<half_float::half>
+	{
+		/// 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>()(arg.data_&-static_cast<unsigned>(arg.data_!=0x8000)); }
+	};
+#endif
+}
+
+namespace half_float
+{
+	/// \anchor compop
+	/// \name Comparison operators
+	/// \{
+
+	/// Comparison for equality.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if operands equal
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator==(half x, half y)
+	{
+		return !detail::compsignal(x.data_, y.data_) && (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF));
+	}
+
+	/// Comparison for inequality.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if operands not equal
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator!=(half x, half y)
+	{
+		return detail::compsignal(x.data_, y.data_) || (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF));
+	}
+
+	/// Comparison for less than.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x less than \a y
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator<(half x, half y)
+	{
+		return !detail::compsignal(x.data_, y.data_) &&
+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));
+	}
+
+	/// Comparison for greater than.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x greater than \a y
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator>(half x, half y)
+	{
+		return !detail::compsignal(x.data_, y.data_) &&
+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));
+	}
+
+	/// Comparison for less equal.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x less equal \a y
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator<=(half x, half y)
+	{
+		return !detail::compsignal(x.data_, y.data_) &&
+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));
+	}
+
+	/// Comparison for greater equal.
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x greater equal \a y
+	/// \retval false else
+	/// \exception FE_INVALID if \a x or \a y is NaN
+	inline HALF_CONSTEXPR_NOERR bool operator>=(half x, half y)
+	{
+		return !detail::compsignal(x.data_, y.data_) &&
+			((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15));
+	}
+
+	/// \}
+	/// \anchor arithmetics
+	/// \name Arithmetic operators
+	/// \{
+
+	/// Identity.
+	/// \param arg operand
+	/// \return unchanged operand
+	inline HALF_CONSTEXPR half operator+(half arg) { return arg; }
+
+	/// Negation.
+	/// \param arg operand
+	/// \return negated operand
+	inline HALF_CONSTEXPR half operator-(half arg) { return half(detail::binary, arg.data_^0x8000); }
+
+	/// Addition.
+	/// This operation is exact to rounding for all rounding modes.
+	/// \param x left operand
+	/// \param y right operand
+	/// \return sum of half expressions
+	/// \exception FE_INVALID if \a x and \a y are infinities with different signs or signaling NaNs
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half operator+(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)+detail::half2float<detail::internal_t>(y.data_)));
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF;
+		bool sub = ((x.data_^y.data_)&0x8000) != 0;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) : (absy!=0x7C00) ? x.data_ :
+										(sub && absx==0x7C00) ? detail::invalid() : y.data_);
+		if(!absx)
+			return absy ? y : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (x.data_|y.data_) : (x.data_&y.data_));
+		if(!absy)
+			return x;
+		unsigned int sign = ((sub && absy>absx) ? y.data_ : x.data_) & 0x8000;
+		if(absy > absx)
+			std::swap(absx, absy);
+		int exp = (absx>>10) + (absx<=0x3FF), d = exp - (absy>>10) - (absy<=0x3FF), mx = ((absx&0x3FF)|((absx>0x3FF)<<10)) << 3, my;
+		if(d < 13)
+		{
+			my = ((absy&0x3FF)|((absy>0x3FF)<<10)) << 3;
+			my = (my>>d) | ((my&((1<<d)-1))!=0);
+		}
+		else
+			my = 1;
+		if(sub)
+		{
+			if(!(mx-=my))
+				return half(detail::binary, static_cast<unsigned>(half::round_style==std::round_toward_neg_infinity)<<15);
+			for(; mx<0x2000 && exp>1; mx<<=1,--exp) ;
+		}
+		else
+		{
+			mx += my;
+			int i = mx >> 14;
+			if((exp+=i) > 30)
+				return half(detail::binary, detail::overflow<half::round_style>(sign));
+			mx = (mx>>i) | (mx&i);
+		}
+		return half(detail::binary, detail::rounded<half::round_style,false>(sign+((exp-1)<<10)+(mx>>3), (mx>>2)&1, (mx&0x3)!=0));
+	#endif
+	}
+
+	/// Subtraction.
+	/// This operation is exact to rounding for all rounding modes.
+	/// \param x left operand
+	/// \param y right operand
+	/// \return difference of half expressions
+	/// \exception FE_INVALID if \a x and \a y are infinities with equal signs or signaling NaNs
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half operator-(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)-detail::half2float<detail::internal_t>(y.data_)));
+	#else
+		return x + -y;
+	#endif
+	}
+
+	/// Multiplication.
+	/// This operation is exact to rounding for all rounding modes.
+	/// \param x left operand
+	/// \param y right operand
+	/// \return product of half expressions
+	/// \exception FE_INVALID if multiplying 0 with infinity or if \a x or \a y is signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half operator*(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)*detail::half2float<detail::internal_t>(y.data_)));
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -16;
+		unsigned int sign = (x.data_^y.data_) & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										((absx==0x7C00 && !absy)||(absy==0x7C00 && !absx)) ? detail::invalid() : (sign|0x7C00));
+		if(!absx || !absy)
+			return half(detail::binary, sign);
+		for(; absx<0x400; absx<<=1,--exp) ;
+		for(; absy<0x400; absy<<=1,--exp) ;
+		detail::uint32 m = static_cast<detail::uint32>((absx&0x3FF)|0x400) * static_cast<detail::uint32>((absy&0x3FF)|0x400);
+		int i = m >> 21, s = m & i;
+		exp += (absx>>10) + (absy>>10) + i;
+		if(exp > 29)
+			return half(detail::binary, detail::overflow<half::round_style>(sign));
+		else if(exp < -11)
+			return half(detail::binary, detail::underflow<half::round_style>(sign));
+		return half(detail::binary, detail::fixed2half<half::round_style,20,false,false,false>(m>>i, exp, sign, s));
+	#endif
+	}
+
+	/// Division.
+	/// This operation is exact to rounding for all rounding modes.
+	/// \param x left operand
+	/// \param y right operand
+	/// \return quotient of half expressions
+	/// \exception FE_INVALID if dividing 0s or infinities with each other or if \a x or \a y is signaling NaN
+	/// \exception FE_DIVBYZERO if dividing finite value by 0
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half operator/(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(detail::half2float<detail::internal_t>(x.data_)/detail::half2float<detail::internal_t>(y.data_)));
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = 14;
+		unsigned int sign = (x.data_^y.data_) & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										(absx==absy) ? detail::invalid() : (sign|((absx==0x7C00) ? 0x7C00 : 0)));
+		if(!absx)
+			return half(detail::binary, absy ? sign : detail::invalid());
+		if(!absy)
+			return half(detail::binary, detail::pole(sign));
+		for(; absx<0x400; absx<<=1,--exp) ;
+		for(; absy<0x400; absy<<=1,++exp) ;
+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;
+		int i = mx < my;
+		exp += (absx>>10) - (absy>>10) - i;
+		if(exp > 29)
+			return half(detail::binary, detail::overflow<half::round_style>(sign));
+		else if(exp < -11)
+			return half(detail::binary, detail::underflow<half::round_style>(sign));
+		mx <<= 12 + i;
+		my <<= 1;
+		return half(detail::binary, detail::fixed2half<half::round_style,11,false,false,false>(mx/my, exp, sign, mx%my!=0));
+	#endif
+	}
+
+	/// \}
+	/// \anchor streaming
+	/// \name Input and output
+	/// \{
+
+	/// Output operator.
+	///	This uses the built-in functionality for streaming out floating-point numbers.
+	/// \param out output stream to write into
+	/// \param arg half expression to write
+	/// \return reference to output stream
+	template<typename charT,typename traits> std::basic_ostream<charT,traits>& operator<<(std::basic_ostream<charT,traits> &out, half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return out << detail::half2float<detail::internal_t>(arg.data_);
+	#else
+		return out << detail::half2float<float>(arg.data_);
+	#endif
+	}
+
+	/// Input operator.
+	///	This uses the built-in functionality for streaming in floating-point numbers, specifically double precision floating 
+	/// point numbers (unless overridden with [HALF_ARITHMETIC_TYPE](\ref HALF_ARITHMETIC_TYPE)). So the input string is first 
+	/// rounded to double precision using the underlying platform's current floating-point rounding mode before being rounded 
+	/// to half-precision using the library's half-precision rounding mode.
+	/// \param in input stream to read from
+	/// \param arg half to read into
+	/// \return reference to input stream
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	template<typename charT,typename traits> std::basic_istream<charT,traits>& operator>>(std::basic_istream<charT,traits> &in, half &arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		detail::internal_t f;
+	#else
+		double f;
+	#endif
+		if(in >> f)
+			arg.data_ = detail::float2half<half::round_style>(f);
+		return in;
+	}
+
+	/// \}
+	/// \anchor basic
+	/// \name Basic mathematical operations
+	/// \{
+
+	/// Absolute value.
+	/// **See also:** Documentation for [std::fabs](https://en.cppreference.com/w/cpp/numeric/math/fabs).
+	/// \param arg operand
+	/// \return absolute value of \a arg
+	inline HALF_CONSTEXPR half fabs(half arg) { return half(detail::binary, arg.data_&0x7FFF); }
+
+	/// Absolute value.
+	/// **See also:** Documentation for [std::abs](https://en.cppreference.com/w/cpp/numeric/math/fabs).
+	/// \param arg operand
+	/// \return absolute value of \a arg
+	inline HALF_CONSTEXPR half abs(half arg) { return fabs(arg); }
+
+	/// Remainder of division.
+	/// **See also:** Documentation for [std::fmod](https://en.cppreference.com/w/cpp/numeric/math/fmod).
+	/// \param x first operand
+	/// \param y second operand
+	/// \return remainder of floating-point division.
+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN
+	inline half fmod(half x, half y)
+	{
+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										(absx==0x7C00) ? detail::invalid() : x.data_);
+		if(!absy)
+			return half(detail::binary, detail::invalid());
+		if(!absx)
+			return x;
+		if(absx == absy)
+			return half(detail::binary, sign);
+		return half(detail::binary, sign|detail::mod<false,false>(absx, absy));
+	}
+
+	/// Remainder of division.
+	/// **See also:** Documentation for [std::remainder](https://en.cppreference.com/w/cpp/numeric/math/remainder).
+	/// \param x first operand
+	/// \param y second operand
+	/// \return remainder of floating-point division.
+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN
+	inline half remainder(half x, half y)
+	{
+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, sign = x.data_ & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										(absx==0x7C00) ? detail::invalid() : x.data_);
+		if(!absy)
+			return half(detail::binary, detail::invalid());
+		if(absx == absy)
+			return half(detail::binary, sign);
+		return half(detail::binary, sign^detail::mod<false,true>(absx, absy));
+	}
+
+	/// Remainder of division.
+	/// **See also:** Documentation for [std::remquo](https://en.cppreference.com/w/cpp/numeric/math/remquo).
+	/// \param x first operand
+	/// \param y second operand
+	/// \param quo address to store some bits of quotient at
+	/// \return remainder of floating-point division.
+	/// \exception FE_INVALID if \a x is infinite or \a y is 0 or if \a x or \a y is signaling NaN
+	inline half remquo(half x, half y, int *quo)
+	{
+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, value = x.data_ & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										(absx==0x7C00) ? detail::invalid() : (*quo = 0, x.data_));
+		if(!absy)
+			return half(detail::binary, detail::invalid());
+		bool qsign = ((value^y.data_)&0x8000) != 0;
+		int q = 1;
+		if(absx != absy)
+			value ^= detail::mod<true, true>(absx, absy, &q);
+		return *quo = qsign ? -q : q, half(detail::binary, value);
+	}
+
+	/// Fused multiply add.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::fma](https://en.cppreference.com/w/cpp/numeric/math/fma).
+	/// \param x first operand
+	/// \param y second operand
+	/// \param z third operand
+	/// \return ( \a x * \a y ) + \a z rounded as one operation.
+	/// \exception FE_INVALID according to operator*() and operator+() unless any argument is a quiet NaN and no argument is a signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding the final addition
+	inline half fma(half x, half y, half z)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_), fz = detail::half2float<detail::internal_t>(z.data_);
+		#if HALF_ENABLE_CPP11_CMATH && FP_FAST_FMA
+			return half(detail::binary, detail::float2half<half::round_style>(std::fma(fx, fy, fz)));
+		#else
+			return half(detail::binary, detail::float2half<half::round_style>(fx*fy+fz));
+		#endif
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, exp = -15;
+		unsigned int sign = (x.data_^y.data_) & 0x8000;
+		bool sub = ((sign^z.data_)&0x8000) != 0;
+		if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)
+			return	(absx>0x7C00 || absy>0x7C00 || absz>0x7C00) ? half(detail::binary, detail::signal(x.data_, y.data_, z.data_)) :
+					(absx==0x7C00) ? half(detail::binary, (!absy || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) :
+					(absy==0x7C00) ? half(detail::binary, (!absx || (sub && absz==0x7C00)) ? detail::invalid() : (sign|0x7C00)) : z;
+		if(!absx || !absy)
+			return absz ? z : half(detail::binary, (half::round_style==std::round_toward_neg_infinity) ? (z.data_|sign) : (z.data_&sign));
+		for(; absx<0x400; absx<<=1,--exp) ;
+		for(; absy<0x400; absy<<=1,--exp) ;
+		detail::uint32 m = static_cast<detail::uint32>((absx&0x3FF)|0x400) * static_cast<detail::uint32>((absy&0x3FF)|0x400);
+		int i = m >> 21;
+		exp += (absx>>10) + (absy>>10) + i;
+		m <<= 3 - i;
+		if(absz)
+		{
+			int expz = 0;
+			for(; absz<0x400; absz<<=1,--expz) ;
+			expz += absz >> 10;
+			detail::uint32 mz = static_cast<detail::uint32>((absz&0x3FF)|0x400) << 13;
+			if(expz > exp || (expz == exp && mz > m))
+			{
+				std::swap(m, mz);
+				std::swap(exp, expz);
+				if(sub)
+					sign = z.data_ & 0x8000;
+			}
+			int d = exp - expz;
+			mz = (d<23) ? ((mz>>d)|((mz&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;
+			if(sub)
+			{
+				m = m - mz;
+				if(!m)
+					return half(detail::binary, static_cast<unsigned>(half::round_style==std::round_toward_neg_infinity)<<15);
+				for(; m<0x800000; m<<=1,--exp) ;
+			}
+			else
+			{
+				m += mz;
+				i = m >> 24;
+				m = (m>>i) | (m&i);
+				exp += i;
+			}
+		}
+		if(exp > 30)
+			return half(detail::binary, detail::overflow<half::round_style>(sign));
+		else if(exp < -10)
+			return half(detail::binary, detail::underflow<half::round_style>(sign));
+		return half(detail::binary, detail::fixed2half<half::round_style,23,false,false,false>(m, exp-1, sign));
+	#endif
+	}
+
+	/// Maximum of half expressions.
+	/// **See also:** Documentation for [std::fmax](https://en.cppreference.com/w/cpp/numeric/math/fmax).
+	/// \param x first operand
+	/// \param y second operand
+	/// \return maximum of operands, ignoring quiet NaNs
+	/// \exception FE_INVALID if \a x or \a y is signaling NaN
+	inline HALF_CONSTEXPR_NOERR half fmax(half x, half y)
+	{
+		return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) < 
+			(y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_));
+	}
+
+	/// Minimum of half expressions.
+	/// **See also:** Documentation for [std::fmin](https://en.cppreference.com/w/cpp/numeric/math/fmin).
+	/// \param x first operand
+	/// \param y second operand
+	/// \return minimum of operands, ignoring quiet NaNs
+	/// \exception FE_INVALID if \a x or \a y is signaling NaN
+	inline HALF_CONSTEXPR_NOERR half fmin(half x, half y)
+	{
+		return half(detail::binary, (!isnan(y) && (isnan(x) || (x.data_^(0x8000|(0x8000-(x.data_>>15)))) >
+			(y.data_^(0x8000|(0x8000-(y.data_>>15)))))) ? detail::select(y.data_, x.data_) : detail::select(x.data_, y.data_));
+	}
+
+	/// Positive difference.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::fdim](https://en.cppreference.com/w/cpp/numeric/math/fdim).
+	/// \param x first operand
+	/// \param y second operand
+	/// \return \a x - \a y or 0 if difference negative
+	/// \exception FE_... according to operator-(half,half)
+	inline half fdim(half x, half y)
+	{
+		if(isnan(x) || isnan(y))
+			return half(detail::binary, detail::signal(x.data_, y.data_));
+		return (x.data_^(0x8000|(0x8000-(x.data_>>15)))) <= (y.data_^(0x8000|(0x8000-(y.data_>>15)))) ? half(detail::binary, 0) : (x-y);
+	}
+
+	/// Get NaN value.
+	/// **See also:** Documentation for [std::nan](https://en.cppreference.com/w/cpp/numeric/math/nan).
+	/// \param arg string code
+	/// \return quiet NaN
+	inline half nanh(const char *arg)
+	{
+		unsigned int value = 0x7FFF;
+		while(*arg)
+			value ^= static_cast<unsigned>(*arg++) & 0xFF;
+		return half(detail::binary, value);
+	}
+
+	/// \}
+	/// \anchor exponential
+	/// \name Exponential functions
+	/// \{
+
+	/// Exponential function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::exp](https://en.cppreference.com/w/cpp/numeric/math/exp).
+	/// \param arg function argument
+	/// \return e raised to \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half exp(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::exp(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF;
+		if(!abs)
+			return half(detail::binary, 0x3C00);
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_));
+		if(abs >= 0x4C80)
+			return half(detail::binary, (arg.data_&0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());
+		detail::uint32 m = detail::multiply64(static_cast<detail::uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29);
+		int e = (abs>>10) + (abs<=0x3FF), exp;
+		if(e < 14)
+		{
+			exp = 0;
+			m >>= 14 - e;
+		}
+		else
+		{
+			exp = m >> (45-e);
+			m = (m<<(e-14)) & 0x7FFFFFFF;
+		}
+		return half(detail::binary, detail::exp2_post<half::round_style,true>(detail::exp2(m, 26), exp, (arg.data_&0x8000)!=0));
+	#endif
+	}
+
+	/// Binary exponential.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::exp2](https://en.cppreference.com/w/cpp/numeric/math/exp2).
+	/// \param arg function argument
+	/// \return 2 raised to \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half exp2(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::exp2(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF;
+		if(!abs)
+			return half(detail::binary, 0x3C00);
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? (0x7C00&((arg.data_>>15)-1U)) : detail::signal(arg.data_));
+		if(abs >= 0x4E40)
+			return half(detail::binary, (arg.data_&0x8000) ? detail::underflow<half::round_style>() : detail::overflow<half::round_style>());
+		int e = (abs>>10) + (abs<=0x3FF), exp = (abs&0x3FF) + ((abs>0x3FF)<<10);
+		detail::uint32 m = detail::exp2((static_cast<detail::uint32>(exp)<<(6+e))&0x7FFFFFFF, 28);
+		exp >>= 25 - e;
+		if(m == 0x80000000)
+		{
+			if(arg.data_&0x8000)
+				exp = -exp;
+			else if(exp > 15)
+				return half(detail::binary, detail::overflow<half::round_style>());
+			return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,false>(m, exp+14));
+		}
+		return half(detail::binary, detail::exp2_post<half::round_style,true>(m, exp, (arg.data_&0x8000)!=0));
+	#endif
+	}
+
+	/// Exponential minus one.
+	/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` 
+	/// and in <1% of inputs for any other rounding mode.
+	///
+	/// **See also:** Documentation for [std::expm1](https://en.cppreference.com/w/cpp/numeric/math/expm1).
+	/// \param arg function argument
+	/// \return e raised to \a arg and subtracted by 1
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half expm1(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::expm1(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
+		if(!abs)
+			return arg;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? (0x7C00+(sign>>1)) : detail::signal(arg.data_));
+		if(abs >= 0x4A00)
+			return half(detail::binary, (arg.data_&0x8000) ? detail::rounded<half::round_style,true>(0xBBFF, 1, 1) : detail::overflow<half::round_style>());
+		detail::uint32 m = detail::multiply64(static_cast<detail::uint32>((abs&0x3FF)+((abs>0x3FF)<<10))<<21, 0xB8AA3B29);
+		int e = (abs>>10) + (abs<=0x3FF), exp;
+		if(e < 14)
+		{
+			exp = 0;
+			m >>= 14 - e;
+		}
+		else
+		{
+			exp = m >> (45-e);
+			m = (m<<(e-14)) & 0x7FFFFFFF;
+		}
+		m = detail::exp2(m);
+		if(sign)
+		{
+			int s = 0;
+			if(m > 0x80000000)
+			{
+				++exp;
+				m = detail::divide64(0x80000000, m, s);
+			}
+			m = 0x80000000 - ((m>>exp)|((m&((static_cast<detail::uint32>(1)<<exp)-1))!=0)|s);
+			exp = 0;
+		}
+		else
+			m -= (exp<31) ? (0x80000000>>exp) : 1;
+		for(exp+=14; m<0x80000000 && exp; m<<=1,--exp) ;
+		if(exp > 29)
+			return half(detail::binary, detail::overflow<half::round_style>());
+		return half(detail::binary, detail::rounded<half::round_style,true>(sign+(exp<<10)+(m>>21), (m>>20)&1, (m&0xFFFFF)!=0));
+	#endif
+	}
+
+	/// Natural logarithm.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::log](https://en.cppreference.com/w/cpp/numeric/math/log).
+	/// \param arg function argument
+	/// \return logarithm of \a arg to base e
+	/// \exception FE_INVALID for signaling NaN or negative argument
+	/// \exception FE_DIVBYZERO for 0
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half log(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::log(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = -15;
+		if(!abs)
+			return half(detail::binary, detail::pole(0x8000));
+		if(arg.data_ & 0x8000)
+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs >= 0x7C00)
+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
+		for(; abs<0x400; abs<<=1,--exp) ;
+		exp += abs >> 10;
+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(
+			detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 27)+8, exp, 17));
+	#endif
+	}
+
+	/// Common logarithm.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::log10](https://en.cppreference.com/w/cpp/numeric/math/log10).
+	/// \param arg function argument
+	/// \return logarithm of \a arg to base 10
+	/// \exception FE_INVALID for signaling NaN or negative argument
+	/// \exception FE_DIVBYZERO for 0
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half log10(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::log10(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = -15;
+		if(!abs)
+			return half(detail::binary, detail::pole(0x8000));
+		if(arg.data_ & 0x8000)
+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs >= 0x7C00)
+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
+		switch(abs)
+		{
+			case 0x4900: return half(detail::binary, 0x3C00);
+			case 0x5640: return half(detail::binary, 0x4000);
+			case 0x63D0: return half(detail::binary, 0x4200);
+			case 0x70E2: return half(detail::binary, 0x4400);
+		}
+		for(; abs<0x400; abs<<=1,--exp) ;
+		exp += abs >> 10;
+		return half(detail::binary, detail::log2_post<half::round_style,0xD49A784C>(
+			detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 27)+8, exp, 16));
+	#endif
+	}
+
+	/// Binary logarithm.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::log2](https://en.cppreference.com/w/cpp/numeric/math/log2).
+	/// \param arg function argument
+	/// \return logarithm of \a arg to base 2
+	/// \exception FE_INVALID for signaling NaN or negative argument
+	/// \exception FE_DIVBYZERO for 0
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half log2(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::log2(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = -15, s = 0;
+		if(!abs)
+			return half(detail::binary, detail::pole(0x8000));
+		if(arg.data_ & 0x8000)
+			return half(detail::binary, (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs >= 0x7C00)
+			return (abs==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
+		if(abs == 0x3C00)
+			return half(detail::binary, 0);
+		for(; abs<0x400; abs<<=1,--exp) ;
+		exp += (abs>>10);
+		if(!(abs&0x3FF))
+		{
+			unsigned int value = static_cast<unsigned>(exp<0) << 15, m = std::abs(exp) << 6;
+			for(exp=18; m<0x400; m<<=1,--exp) ;
+			return half(detail::binary, value+(exp<<10)+m);
+		}
+		detail::uint32 ilog = exp, sign = detail::sign_mask(ilog), m = 
+			(((ilog<<27)+(detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 28)>>4))^sign) - sign;
+		if(!m)
+			return half(detail::binary, 0);
+		for(exp=14; m<0x8000000 && exp; m<<=1,--exp) ;
+		for(; m>0xFFFFFFF; m>>=1,++exp)
+			s |= m & 1;
+		return half(detail::binary, detail::fixed2half<half::round_style,27,false,false,true>(m, exp, sign&0x8000, s));
+	#endif
+	}
+
+	/// Natural logarithm plus one.
+	/// This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for `std::round_to_nearest` 
+	/// and in ~1% of inputs for any other rounding mode.
+	///
+	/// **See also:** Documentation for [std::log1p](https://en.cppreference.com/w/cpp/numeric/math/log1p).
+	/// \param arg function argument
+	/// \return logarithm of \a arg plus 1 to base e
+	/// \exception FE_INVALID for signaling NaN or argument <-1
+	/// \exception FE_DIVBYZERO for -1
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half log1p(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::log1p(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		if(arg.data_ >= 0xBC00)
+			return half(detail::binary, (arg.data_==0xBC00) ? detail::pole(0x8000) : (arg.data_<=0xFC00) ? detail::invalid() : detail::signal(arg.data_));
+		int abs = arg.data_ & 0x7FFF, exp = -15;
+		if(!abs || abs >= 0x7C00)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		for(; abs<0x400; abs<<=1,--exp) ;
+		exp += abs >> 10;
+		detail::uint32 m = static_cast<detail::uint32>((abs&0x3FF)|0x400) << 20;
+		if(arg.data_ & 0x8000)
+		{
+			m = 0x40000000 - (m>>-exp);
+			for(exp=0; m<0x40000000; m<<=1,--exp) ;
+		}
+		else
+		{
+			if(exp < 0)
+			{
+				m = 0x40000000 + (m>>-exp);
+				exp = 0;
+			}
+			else
+			{
+				m += 0x40000000 >> exp;
+				int i = m >> 31;
+				m >>= i;
+				exp += i;
+			}
+		}
+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(detail::log2(m), exp, 17));
+	#endif
+	}
+
+	/// \}
+	/// \anchor power
+	/// \name Power functions
+	/// \{
+
+	/// Square root.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::sqrt](https://en.cppreference.com/w/cpp/numeric/math/sqrt).
+	/// \param arg function argument
+	/// \return square root of \a arg
+	/// \exception FE_INVALID for signaling NaN and negative arguments
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half sqrt(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = 15;
+		if(!abs || arg.data_ >= 0x7C00)
+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_>0x8000) ? detail::invalid() : arg.data_);
+		for(; abs<0x400; abs<<=1,--exp) ;
+		detail::uint32 r = static_cast<detail::uint32>((abs&0x3FF)|0x400) << 10, m = detail::sqrt<20>(r, exp+=abs>>10);
+		return half(detail::binary, detail::rounded<half::round_style,false>((exp<<10)+(m&0x3FF), r>m, r!=0));
+	#endif
+	}
+
+	/// Cubic root.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::cbrt](https://en.cppreference.com/w/cpp/numeric/math/cbrt).
+	/// \param arg function argument
+	/// \return cubic root of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half cbrt(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::cbrt(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = -15;
+		if(!abs || abs == 0x3C00 || abs >= 0x7C00)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		for(; abs<0x400; abs<<=1, --exp);
+		detail::uint32 ilog = exp + (abs>>10), sign = detail::sign_mask(ilog), f, m = 
+			(((ilog<<27)+(detail::log2(static_cast<detail::uint32>((abs&0x3FF)|0x400)<<20, 24)>>4))^sign) - sign;
+		for(exp=2; m<0x80000000; m<<=1,--exp) ;
+		m = detail::multiply64(m, 0xAAAAAAAB);
+		int i = m >> 31, s;
+		exp += i;
+		m <<= 1 - i;
+		if(exp < 0)
+		{
+			f = m >> -exp;
+			exp = 0;
+		}
+		else
+		{
+			f = (m<<exp) & 0x7FFFFFFF;
+			exp = m >> (31-exp);
+		}
+		m = detail::exp2(f, (half::round_style==std::round_to_nearest) ? 29 : 26);
+		if(sign)
+		{
+			if(m > 0x80000000)
+			{
+				m = detail::divide64(0x80000000, m, s);
+				++exp;
+			}
+			exp = -exp;
+		}
+		return half(detail::binary, (half::round_style==std::round_to_nearest) ?
+			detail::fixed2half<half::round_style,31,false,false,false>(m, exp+14, arg.data_&0x8000) :
+			detail::fixed2half<half::round_style,23,false,false,false>((m+0x80)>>8, exp+14, arg.data_&0x8000));
+	#endif
+	}
+
+	/// Hypotenuse function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot).
+	/// \param x first argument
+	/// \param y second argument
+	/// \return square root of sum of squares without internal over- or underflows
+	/// \exception FE_INVALID if \a x or \a y is signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root
+	inline half hypot(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_);
+		#if HALF_ENABLE_CPP11_CMATH
+			return half(detail::binary, detail::float2half<half::round_style>(std::hypot(fx, fy)));
+		#else
+			return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx*fx+fy*fy)));
+		#endif
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx==0x7C00) ? detail::select(0x7C00, y.data_) :
+				(absy==0x7C00) ? detail::select(0x7C00, x.data_) : detail::signal(x.data_, y.data_));
+		if(!absx)
+			return half(detail::binary, absy ? detail::check_underflow(absy) : 0);
+		if(!absy)
+			return half(detail::binary, detail::check_underflow(absx));
+		if(absy > absx)
+			std::swap(absx, absy);
+		for(; absx<0x400; absx<<=1,--expx) ;
+		for(; absy<0x400; absy<<=1,--expy) ;
+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;
+		mx *= mx;
+		my *= my;
+		int ix = mx >> 21, iy = my >> 21;
+		expx = 2*(expx+(absx>>10)) - 15 + ix;
+		expy = 2*(expy+(absy>>10)) - 15 + iy;
+		mx <<= 10 - ix;
+		my <<= 10 - iy;
+		int d = expx - expy;
+		my = (d<30) ? ((my>>d)|((my&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;
+		return half(detail::binary, detail::hypot_post<half::round_style>(mx+my, expx));
+	#endif
+	}
+
+	/// Hypotenuse function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot).
+	/// \param x first argument
+	/// \param y second argument
+	/// \param z third argument
+	/// \return square root of sum of squares without internal over- or underflows
+	/// \exception FE_INVALID if \a x, \a y or \a z is signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root
+	inline half hypot(half x, half y, half z)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_), fz = detail::half2float<detail::internal_t>(z.data_);
+		return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx*fx+fy*fy+fz*fz)));
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, absz = z.data_ & 0x7FFF, expx = 0, expy = 0, expz = 0;
+		if(!absx)
+			return hypot(y, z);
+		if(!absy)
+			return hypot(x, z);
+		if(!absz)
+			return hypot(x, y);
+		if(absx >= 0x7C00 || absy >= 0x7C00 || absz >= 0x7C00)
+			return half(detail::binary,	(absx==0x7C00) ? detail::select(0x7C00, detail::select(y.data_, z.data_)) :
+										(absy==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, z.data_)) :
+										(absz==0x7C00) ? detail::select(0x7C00, detail::select(x.data_, y.data_)) :
+										detail::signal(x.data_, y.data_, z.data_));
+		if(absz > absy)
+			std::swap(absy, absz);
+		if(absy > absx)
+			std::swap(absx, absy);
+		if(absz > absy)
+			std::swap(absy, absz);
+		for(; absx<0x400; absx<<=1,--expx) ;
+		for(; absy<0x400; absy<<=1,--expy) ;
+		for(; absz<0x400; absz<<=1,--expz) ;
+		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400, mz = (absz&0x3FF) | 0x400;
+		mx *= mx;
+		my *= my;
+		mz *= mz;
+		int ix = mx >> 21, iy = my >> 21, iz = mz >> 21;
+		expx = 2*(expx+(absx>>10)) - 15 + ix;
+		expy = 2*(expy+(absy>>10)) - 15 + iy;
+		expz = 2*(expz+(absz>>10)) - 15 + iz;
+		mx <<= 10 - ix;
+		my <<= 10 - iy;
+		mz <<= 10 - iz;
+		int d = expy - expz;
+		mz = (d<30) ? ((mz>>d)|((mz&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;
+		my += mz;
+		if(my & 0x80000000)
+		{
+			my = (my>>1) | (my&1);
+			if(++expy > expx)
+			{
+				std::swap(mx, my);
+				std::swap(expx, expy);
+			}
+		}
+		d = expx - expy;
+		my = (d<30) ? ((my>>d)|((my&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;
+		return half(detail::binary, detail::hypot_post<half::round_style>(mx+my, expx));
+	#endif
+	}
+
+	/// Power function.
+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.00025% of inputs.
+	///
+	/// **See also:** Documentation for [std::pow](https://en.cppreference.com/w/cpp/numeric/math/pow).
+	/// \param x base
+	/// \param y exponent
+	/// \return \a x raised to \a y
+	/// \exception FE_INVALID if \a x or \a y is signaling NaN or if \a x is finite an negative and \a y is finite and not integral
+	/// \exception FE_DIVBYZERO if \a x is 0 and \a y is negative
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half pow(half x, half y)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::pow(detail::half2float<detail::internal_t>(x.data_), detail::half2float<detail::internal_t>(y.data_))));
+	#else
+		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, exp = -15;
+		if(!absy || x.data_ == 0x3C00)
+			return half(detail::binary, detail::select(0x3C00, (x.data_==0x3C00) ? y.data_ : x.data_));
+		bool is_int = absy >= 0x6400 || (absy>=0x3C00 && !(absy&((1<<(25-(absy>>10)))-1)));
+		unsigned int sign = x.data_ & (static_cast<unsigned>((absy<0x6800)&&is_int&&((absy>>(25-(absy>>10)))&1))<<15);
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+			return half(detail::binary,	(absx>0x7C00 || absy>0x7C00) ? detail::signal(x.data_, y.data_) :
+										(absy==0x7C00) ? ((absx==0x3C00) ? 0x3C00 : (!absx && y.data_==0xFC00) ? detail::pole() :
+										(0x7C00&-((y.data_>>15)^(absx>0x3C00)))) : (sign|(0x7C00&((y.data_>>15)-1U))));
+		if(!absx)
+			return half(detail::binary, (y.data_&0x8000) ? detail::pole(sign) : sign);
+		if((x.data_&0x8000) && !is_int)
+			return half(detail::binary, detail::invalid());
+		if(x.data_ == 0xBC00)
+			return half(detail::binary, sign|0x3C00);
+		if(y.data_ == 0x3800)
+			return sqrt(x);
+		if(y.data_ == 0x3C00)
+			return half(detail::binary, detail::check_underflow(x.data_));
+		if(y.data_ == 0x4000)
+			return x * x;
+		for(; absx<0x400; absx<<=1,--exp) ;
+		detail::uint32 ilog = exp + (absx>>10), msign = detail::sign_mask(ilog), f, m = 
+			(((ilog<<27)+((detail::log2(static_cast<detail::uint32>((absx&0x3FF)|0x400)<<20)+8)>>4))^msign) - msign;
+		for(exp=-11; m<0x80000000; m<<=1,--exp) ;
+		for(; absy<0x400; absy<<=1,--exp) ;
+		m = detail::multiply64(m, static_cast<detail::uint32>((absy&0x3FF)|0x400)<<21);
+		int i = m >> 31;
+		exp += (absy>>10) + i;
+		m <<= 1 - i;
+		if(exp < 0)
+		{
+			f = m >> -exp;
+			exp = 0;
+		}
+		else
+		{
+			f = (m<<exp) & 0x7FFFFFFF;
+			exp = m >> (31-exp);
+		}
+		return half(detail::binary, detail::exp2_post<half::round_style,false>(detail::exp2(f), exp, ((msign&1)^(y.data_>>15))!=0, sign));
+	#endif
+	}
+
+	/// \}
+	/// \anchor trigonometric
+	/// \name Trigonometric functions
+	/// \{
+
+	/// Compute sine and cosine simultaneously.
+	///	This returns the same results as sin() and cos() but is faster than calling each function individually.
+	///
+	/// This function is exact to rounding for all rounding modes.
+	/// \param arg function argument
+	/// \param sin variable to take sine of \a arg
+	/// \param cos variable to take cosine of \a arg
+	/// \exception FE_INVALID for signaling NaN or infinity
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline void sincos(half arg, half *sin, half *cos)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		detail::internal_t f = detail::half2float<detail::internal_t>(arg.data_);
+		*sin = half(detail::binary, detail::float2half<half::round_style>(std::sin(f)));
+		*cos = half(detail::binary, detail::float2half<half::round_style>(std::cos(f)));
+	#else
+		int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15, k;
+		if(abs >= 0x7C00)
+			*sin = *cos = half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		else if(!abs)
+		{
+			*sin = arg;
+			*cos = half(detail::binary, 0x3C00);
+		}
+		else if(abs < 0x2500)
+		{
+			*sin = half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));
+			*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));
+		}
+		else
+		{
+			if(half::round_style != std::round_to_nearest)
+			{
+				switch(abs)
+				{
+				case 0x48B7:
+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x1D07, 1, 1));
+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0xBBFF, 1, 1));
+					return;
+				case 0x598C:
+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));
+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x80FC, 1, 1));
+					return;
+				case 0x6A64:
+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x3BFE, 1, 1));
+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x27FF, 1, 1));
+					return;
+				case 0x6D8C:
+					*sin = half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x0FE6, 1, 1));
+					*cos = half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));
+					return;
+				}
+			}
+			std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
+			switch(k & 3)
+			{
+				case 1: sc = std::make_pair(sc.second, -sc.first); break;
+				case 2: sc = std::make_pair(-sc.first, -sc.second); break;
+				case 3: sc = std::make_pair(-sc.second, sc.first); break;
+			}
+			*sin = half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((sc.first^-static_cast<detail::uint32>(sign))+sign));
+			*cos = half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>(sc.second));
+		}
+	#endif
+	}
+
+	/// Sine function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::sin](https://en.cppreference.com/w/cpp/numeric/math/sin).
+	/// \param arg function argument
+	/// \return sine value of \a arg
+	/// \exception FE_INVALID for signaling NaN or infinity
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half sin(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::sin(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, k;
+		if(!abs)
+			return arg;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs < 0x2900)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));
+		if(half::round_style != std::round_to_nearest)
+			switch(abs)
+			{
+				case 0x48B7: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x1D07, 1, 1));
+				case 0x6A64: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x3BFE, 1, 1));
+				case 0x6D8C: return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x0FE6, 1, 1));
+			}
+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
+		detail::uint32 sign = -static_cast<detail::uint32>(((k>>1)&1)^(arg.data_>>15));
+		return half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((((k&1) ? sc.second : sc.first)^sign) - sign));
+	#endif
+	}
+
+	/// Cosine function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::cos](https://en.cppreference.com/w/cpp/numeric/math/cos).
+	/// \param arg function argument
+	/// \return cosine value of \a arg
+	/// \exception FE_INVALID for signaling NaN or infinity
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half cos(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::cos(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, k;
+		if(!abs)
+			return half(detail::binary, 0x3C00);
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs < 0x2500)
+			return half(detail::binary, detail::rounded<half::round_style,true>(0x3BFF, 1, 1));
+		if(half::round_style != std::round_to_nearest && abs == 0x598C)
+			return half(detail::binary, detail::rounded<half::round_style,true>(0x80FC, 1, 1));
+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 28);
+		detail::uint32 sign = -static_cast<detail::uint32>(((k>>1)^k)&1);
+		return half(detail::binary, detail::fixed2half<half::round_style,30,true,true,true>((((k&1) ? sc.first : sc.second)^sign) - sign));
+	#endif
+	}
+
+	/// Tangent function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::tan](https://en.cppreference.com/w/cpp/numeric/math/tan).
+	/// \param arg function argument
+	/// \return tangent value of \a arg
+	/// \exception FE_INVALID for signaling NaN or infinity
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half tan(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::tan(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = 13, k;
+		if(!abs)
+			return arg;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs < 0x2700)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
+		if(half::round_style != std::round_to_nearest)
+			switch(abs)
+			{
+				case 0x658C: return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x07E6, 1, 1));
+				case 0x7330: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x4B62, 1, 1));
+			}
+		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 30);
+		if(k & 1)
+			sc = std::make_pair(-sc.second, sc.first);
+		detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second);
+		detail::uint32 my = (sc.first^signy) - signy, mx = (sc.second^signx) - signx;
+		for(; my<0x80000000; my<<=1,--exp) ;
+		for(; mx<0x80000000; mx<<=1,++exp) ;
+		return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp, (signy^signx^arg.data_)&0x8000));
+	#endif
+	}
+
+	/// Arc sine.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::asin](https://en.cppreference.com/w/cpp/numeric/math/asin).
+	/// \param arg function argument
+	/// \return arc sine value of \a arg
+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half asin(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::asin(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
+		if(!abs)
+			return arg;
+		if(abs >= 0x3C00)
+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() :
+										detail::rounded<half::round_style,true>(sign|0x3E48, 0, 1));
+		if(abs < 0x2900)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
+		if(half::round_style != std::round_to_nearest && (abs == 0x2B44 || abs == 0x2DC3))
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_+1, 1, 1));
+		std::pair<detail::uint32,detail::uint32> sc = detail::atan2_args(abs);
+		detail::uint32 m = detail::atan2(sc.first, sc.second, (half::round_style==std::round_to_nearest) ? 27 : 26);
+		return half(detail::binary, detail::fixed2half<half::round_style,30,false,true,true>(m, 14, sign));
+	#endif
+	}
+
+	/// Arc cosine function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::acos](https://en.cppreference.com/w/cpp/numeric/math/acos).
+	/// \param arg function argument
+	/// \return arc cosine value of \a arg
+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half acos(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::acos(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ >> 15;
+		if(!abs)
+			return half(detail::binary, detail::rounded<half::round_style,true>(0x3E48, 0, 1));
+		if(abs >= 0x3C00)
+			return half(detail::binary,	(abs>0x7C00) ? detail::signal(arg.data_) : (abs>0x3C00) ? detail::invalid() :
+										sign ? detail::rounded<half::round_style,true>(0x4248, 0, 1) : 0);
+		std::pair<detail::uint32,detail::uint32> cs = detail::atan2_args(abs);
+		detail::uint32 m = detail::atan2(cs.second, cs.first, 28);
+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,true,true>(sign ? (0xC90FDAA2-m) : m, 15, 0, sign));
+	#endif
+	}
+
+	/// Arc tangent function.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::atan](https://en.cppreference.com/w/cpp/numeric/math/atan).
+	/// \param arg function argument
+	/// \return arc tangent value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half atan(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::atan(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
+		if(!abs)
+			return arg;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? detail::rounded<half::round_style,true>(sign|0x3E48, 0, 1) : detail::signal(arg.data_));
+		if(abs <= 0x2700)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));
+		int exp = (abs>>10) + (abs<=0x3FF);
+		detail::uint32 my = (abs&0x3FF) | ((abs>0x3FF)<<10);
+		detail::uint32 m = (exp>15) ?	detail::atan2(my<<19, 0x20000000>>(exp-15), (half::round_style==std::round_to_nearest) ? 26 : 24) :
+										detail::atan2(my<<(exp+4), 0x20000000, (half::round_style==std::round_to_nearest) ? 30 : 28);
+		return half(detail::binary, detail::fixed2half<half::round_style,30,false,true,true>(m, 14, sign));
+	#endif
+	}
+
+	/// Arc tangent function.
+	/// This function may be 1 ULP off the correctly rounded exact result in ~0.005% of inputs for `std::round_to_nearest`, 
+	/// in ~0.1% of inputs for `std::round_toward_zero` and in ~0.02% of inputs for any other rounding mode.
+	///
+	/// **See also:** Documentation for [std::atan2](https://en.cppreference.com/w/cpp/numeric/math/atan2).
+	/// \param y numerator
+	/// \param x denominator
+	/// \return arc tangent value
+	/// \exception FE_INVALID if \a x or \a y is signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half atan2(half y, half x)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::atan2(detail::half2float<detail::internal_t>(y.data_), detail::half2float<detail::internal_t>(x.data_))));
+	#else
+		unsigned int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, signx = x.data_ >> 15, signy = y.data_ & 0x8000;
+		if(absx >= 0x7C00 || absy >= 0x7C00)
+		{
+			if(absx > 0x7C00 || absy > 0x7C00)
+				return half(detail::binary, detail::signal(x.data_, y.data_));
+			if(absy == 0x7C00)
+				return half(detail::binary, (absx<0x7C00) ?	detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1) :
+													signx ?	detail::rounded<half::round_style,true>(signy|0x40B6, 0, 1) :
+															detail::rounded<half::round_style,true>(signy|0x3A48, 0, 1));
+			return (x.data_==0x7C00) ? half(detail::binary, signy) : half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1));
+		}
+		if(!absy)
+			return signx ? half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1)) : y;
+		if(!absx)
+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1));
+		int d = (absy>>10) + (absy<=0x3FF) - (absx>>10) - (absx<=0x3FF);
+		if(d > (signx ? 18 : 12))
+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x3E48, 0, 1));
+		if(signx && d < -11)
+			return half(detail::binary, detail::rounded<half::round_style,true>(signy|0x4248, 0, 1));
+		if(!signx && d < ((half::round_style==std::round_toward_zero) ? -15 : -9))
+		{
+			for(; absy<0x400; absy<<=1,--d) ;
+			detail::uint32 mx = ((absx<<1)&0x7FF) | 0x800, my = ((absy<<1)&0x7FF) | 0x800;
+			int i = my < mx;
+			d -= i;
+			if(d < -25)
+				return half(detail::binary, detail::underflow<half::round_style>(signy));
+			my <<= 11 + i;
+			return half(detail::binary, detail::fixed2half<half::round_style,11,false,false,true>(my/mx, d+14, signy, my%mx!=0));
+		}
+		detail::uint32 m = detail::atan2(	((absy&0x3FF)|((absy>0x3FF)<<10))<<(19+((d<0) ? d : (d>0) ? 0 : -1)),
+											((absx&0x3FF)|((absx>0x3FF)<<10))<<(19-((d>0) ? d : (d<0) ? 0 : 1)));
+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,true,true>(signx ? (0xC90FDAA2-m) : m, 15, signy, signx));
+	#endif
+	}
+
+	/// \}
+	/// \anchor hyperbolic
+	/// \name Hyperbolic functions
+	/// \{
+
+	/// Hyperbolic sine.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::sinh](https://en.cppreference.com/w/cpp/numeric/math/sinh).
+	/// \param arg function argument
+	/// \return hyperbolic sine value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half sinh(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::sinh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp;
+		if(!abs || abs >= 0x7C00)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		if(abs <= 0x2900)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 29 : 27);
+		detail::uint32 m = mm.first - mm.second;
+		for(exp+=13; m<0x80000000 && exp; m<<=1,--exp) ;
+		unsigned int sign = arg.data_ & 0x8000;
+		if(exp > 29)
+			return half(detail::binary, detail::overflow<half::round_style>(sign));
+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,true>(m, exp, sign));
+	#endif
+	}
+
+	/// Hyperbolic cosine.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::cosh](https://en.cppreference.com/w/cpp/numeric/math/cosh).
+	/// \param arg function argument
+	/// \return hyperbolic cosine value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half cosh(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::cosh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp;
+		if(!abs)
+			return half(detail::binary, 0x3C00);
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : 0x7C00);
+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 23 : 26);
+		detail::uint32 m = mm.first + mm.second, i = (~m&0xFFFFFFFF) >> 31;
+		m = (m>>i) | (m&i) | 0x80000000;
+		if((exp+=13+i) > 29)
+			return half(detail::binary, detail::overflow<half::round_style>());
+		return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,true>(m, exp));
+	#endif
+	}
+
+	/// Hyperbolic tangent.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::tanh](https://en.cppreference.com/w/cpp/numeric/math/tanh).
+	/// \param arg function argument
+	/// \return hyperbolic tangent value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half tanh(half arg)
+	{
+	#ifdef HALF_ARITHMETIC_TYPE
+		return half(detail::binary, detail::float2half<half::round_style>(std::tanh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp;
+		if(!abs)
+			return arg;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs>0x7C00) ? detail::signal(arg.data_) : (arg.data_-0x4000));
+		if(abs >= 0x4500)
+			return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));
+		if(abs < 0x2700)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));
+		if(half::round_style != std::round_to_nearest && abs == 0x2D3F)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-3, 0, 1));
+		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, 27);
+		detail::uint32 my = mm.first - mm.second - (half::round_style!=std::round_to_nearest), mx = mm.first + mm.second, i = (~mx&0xFFFFFFFF) >> 31;
+		for(exp=13; my<0x80000000; my<<=1,--exp) ;
+		mx = (mx>>i) | 0x80000000;
+		return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp-i, arg.data_&0x8000));
+	#endif
+	}
+
+	/// Hyperbolic area sine.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::asinh](https://en.cppreference.com/w/cpp/numeric/math/asinh).
+	/// \param arg function argument
+	/// \return area sine value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half asinh(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::asinh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF;
+		if(!abs || abs >= 0x7C00)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		if(abs <= 0x2900)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-1, 1, 1));
+		if(half::round_style != std::round_to_nearest)
+			switch(abs)
+			{
+				case 0x32D4: return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-13, 1, 1));
+				case 0x3B5B: return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_-197, 1, 1));
+			}
+		return half(detail::binary, detail::area<half::round_style,true>(arg.data_));
+	#endif
+	}
+
+	/// Hyperbolic area cosine.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::acosh](https://en.cppreference.com/w/cpp/numeric/math/acosh).
+	/// \param arg function argument
+	/// \return area cosine value of \a arg
+	/// \exception FE_INVALID for signaling NaN or arguments <1
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half acosh(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::acosh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF;
+		if((arg.data_&0x8000) || abs < 0x3C00)
+			return half(detail::binary, (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs == 0x3C00)
+			return half(detail::binary, 0);
+		if(arg.data_ >= 0x7C00)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		return half(detail::binary, detail::area<half::round_style,false>(arg.data_));
+	#endif
+	}
+
+	/// Hyperbolic area tangent.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::atanh](https://en.cppreference.com/w/cpp/numeric/math/atanh).
+	/// \param arg function argument
+	/// \return area tangent value of \a arg
+	/// \exception FE_INVALID for signaling NaN or if abs(\a arg) > 1
+	/// \exception FE_DIVBYZERO for +/-1
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half atanh(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::atanh(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF, exp = 0;
+		if(!abs)
+			return arg;
+		if(abs >= 0x3C00)
+			return half(detail::binary, (abs==0x3C00) ? detail::pole(arg.data_&0x8000) : (abs<=0x7C00) ? detail::invalid() : detail::signal(arg.data_));
+		if(abs < 0x2700)
+			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
+		detail::uint32 m = static_cast<detail::uint32>((abs&0x3FF)|((abs>0x3FF)<<10)) << ((abs>>10)+(abs<=0x3FF)+6), my = 0x80000000 + m, mx = 0x80000000 - m;
+		for(; mx<0x80000000; mx<<=1,++exp) ;
+		int i = my >= mx, s;
+		return half(detail::binary, detail::log2_post<half::round_style,0xB8AA3B2A>(detail::log2(
+			(detail::divide64(my>>i, mx, s)+1)>>1, 27)+0x10, exp+i-1, 16, arg.data_&0x8000));
+	#endif
+	}
+
+	/// \}
+	/// \anchor special
+	/// \name Error and gamma functions
+	/// \{
+
+	/// Error function.
+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.
+	///
+	/// **See also:** Documentation for [std::erf](https://en.cppreference.com/w/cpp/numeric/math/erf).
+	/// \param arg function argument
+	/// \return error function value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half erf(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::erf(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF;
+		if(!abs || abs >= 0x7C00)
+			return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (arg.data_-0x4000) : detail::signal(arg.data_)) : arg;
+		if(abs >= 0x4200)
+			return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x3BFF, 1, 1));
+		return half(detail::binary, detail::erf<half::round_style,false>(arg.data_));
+	#endif
+	}
+
+	/// Complementary error function.
+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.
+	///
+	/// **See also:** Documentation for [std::erfc](https://en.cppreference.com/w/cpp/numeric/math/erfc).
+	/// \param arg function argument
+	/// \return 1 minus error function value of \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half erfc(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::erfc(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
+		if(abs >= 0x7C00)
+			return (abs>=0x7C00) ? half(detail::binary, (abs==0x7C00) ? (sign>>1) : detail::signal(arg.data_)) : arg;
+		if(!abs)
+			return half(detail::binary, 0x3C00);
+		if(abs >= 0x4400)
+			return half(detail::binary, detail::rounded<half::round_style,true>((sign>>1)-(sign>>15), sign>>15, 1));
+		return half(detail::binary, detail::erf<half::round_style,true>(arg.data_));
+	#endif
+	}
+
+	/// Natural logarithm of gamma function.
+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.025% of inputs.
+	///
+	/// **See also:** Documentation for [std::lgamma](https://en.cppreference.com/w/cpp/numeric/math/lgamma).
+	/// \param arg function argument
+	/// \return natural logarith of gamma function for \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_DIVBYZERO for 0 or negative integer arguments
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half lgamma(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::lgamma(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		int abs = arg.data_ & 0x7FFF;
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_));
+		if(!abs || arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1))))
+			return half(detail::binary, detail::pole());
+		if(arg.data_ == 0x3C00 || arg.data_ == 0x4000)
+			return half(detail::binary, 0);
+		return half(detail::binary, detail::gamma<half::round_style,true>(arg.data_));
+	#endif
+	}
+
+	/// Gamma function.
+	/// This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.25% of inputs.
+	///
+	/// **See also:** Documentation for [std::tgamma](https://en.cppreference.com/w/cpp/numeric/math/tgamma).
+	/// \param arg function argument
+	/// \return gamma function value of \a arg
+	/// \exception FE_INVALID for signaling NaN, negative infinity or negative integer arguments
+	/// \exception FE_DIVBYZERO for 0
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half tgamma(half arg)
+	{
+	#if defined(HALF_ARITHMETIC_TYPE) && HALF_ENABLE_CPP11_CMATH
+		return half(detail::binary, detail::float2half<half::round_style>(std::tgamma(detail::half2float<detail::internal_t>(arg.data_))));
+	#else
+		unsigned int abs = arg.data_ & 0x7FFF;
+		if(!abs)
+			return half(detail::binary, detail::pole(arg.data_));
+		if(abs >= 0x7C00)
+			return (arg.data_==0x7C00) ? arg : half(detail::binary, detail::signal(arg.data_));
+		if(arg.data_ >= 0xE400 || (arg.data_ >= 0xBC00 && !(abs&((1<<(25-(abs>>10)))-1))))
+			return half(detail::binary, detail::invalid());
+		if(arg.data_ >= 0xCA80)
+			return half(detail::binary, detail::underflow<half::round_style>((1-((abs>>(25-(abs>>10)))&1))<<15));
+		if(arg.data_ <= 0x100 || (arg.data_ >= 0x4900 && arg.data_ < 0x8000))
+			return half(detail::binary, detail::overflow<half::round_style>());
+		if(arg.data_ == 0x3C00)
+			return arg;
+		return half(detail::binary, detail::gamma<half::round_style,false>(arg.data_));
+	#endif
+	}
+
+	/// \}
+	/// \anchor rounding
+	/// \name Rounding
+	/// \{
+
+	/// Nearest integer not less than half value.
+	/// **See also:** Documentation for [std::ceil](https://en.cppreference.com/w/cpp/numeric/math/ceil).
+	/// \param arg half to round
+	/// \return nearest integer not less than \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_INEXACT if value had to be rounded
+	inline half ceil(half arg) { return half(detail::binary, detail::integral<std::round_toward_infinity,true,true>(arg.data_)); }
+
+	/// Nearest integer not greater than half value.
+	/// **See also:** Documentation for [std::floor](https://en.cppreference.com/w/cpp/numeric/math/floor).
+	/// \param arg half to round
+	/// \return nearest integer not greater than \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_INEXACT if value had to be rounded
+	inline half floor(half arg) { return half(detail::binary, detail::integral<std::round_toward_neg_infinity,true,true>(arg.data_)); }
+
+	/// Nearest integer not greater in magnitude than half value.
+	/// **See also:** Documentation for [std::trunc](https://en.cppreference.com/w/cpp/numeric/math/trunc).
+	/// \param arg half to round
+	/// \return nearest integer not greater in magnitude than \a arg
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_INEXACT if value had to be rounded
+	inline half trunc(half arg) { return half(detail::binary, detail::integral<std::round_toward_zero,true,true>(arg.data_)); }
+
+	/// Nearest integer.
+	/// **See also:** Documentation for [std::round](https://en.cppreference.com/w/cpp/numeric/math/round).
+	/// \param arg half to round
+	/// \return nearest integer, rounded away from zero in half-way cases
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_INEXACT if value had to be rounded
+	inline half round(half arg) { return half(detail::binary, detail::integral<std::round_to_nearest,false,true>(arg.data_)); }
+
+	/// Nearest integer.
+	/// **See also:** Documentation for [std::lround](https://en.cppreference.com/w/cpp/numeric/math/round).
+	/// \param arg half to round
+	/// \return nearest integer, rounded away from zero in half-way cases
+	/// \exception FE_INVALID if value is not representable as `long`
+	inline long lround(half arg) { return detail::half2int<std::round_to_nearest,false,false,long>(arg.data_); }
+
+	/// Nearest integer using half's internal rounding mode.
+	/// **See also:** Documentation for [std::rint](https://en.cppreference.com/w/cpp/numeric/math/rint).
+	/// \param arg half expression to round
+	/// \return nearest integer using default rounding mode
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_INEXACT if value had to be rounded
+	inline half rint(half arg) { return half(detail::binary, detail::integral<half::round_style,true,true>(arg.data_)); }
+
+	/// Nearest integer using half's internal rounding mode.
+	/// **See also:** Documentation for [std::lrint](https://en.cppreference.com/w/cpp/numeric/math/rint).
+	/// \param arg half expression to round
+	/// \return nearest integer using default rounding mode
+	/// \exception FE_INVALID if value is not representable as `long`
+	/// \exception FE_INEXACT if value had to be rounded
+	inline long lrint(half arg) { return detail::half2int<half::round_style,true,true,long>(arg.data_); }
+
+	/// Nearest integer using half's internal rounding mode.
+	/// **See also:** Documentation for [std::nearbyint](https://en.cppreference.com/w/cpp/numeric/math/nearbyint).
+	/// \param arg half expression to round
+	/// \return nearest integer using default rounding mode
+	/// \exception FE_INVALID for signaling NaN
+	inline half nearbyint(half arg) { return half(detail::binary, detail::integral<half::round_style,true,false>(arg.data_)); }
+#if HALF_ENABLE_CPP11_LONG_LONG
+	/// Nearest integer.
+	/// **See also:** Documentation for [std::llround](https://en.cppreference.com/w/cpp/numeric/math/round).
+	/// \param arg half to round
+	/// \return nearest integer, rounded away from zero in half-way cases
+	/// \exception FE_INVALID if value is not representable as `long long`
+	inline long long llround(half arg) { return detail::half2int<std::round_to_nearest,false,false,long long>(arg.data_); }
+
+	/// Nearest integer using half's internal rounding mode.
+	/// **See also:** Documentation for [std::llrint](https://en.cppreference.com/w/cpp/numeric/math/rint).
+	/// \param arg half expression to round
+	/// \return nearest integer using default rounding mode
+	/// \exception FE_INVALID if value is not representable as `long long`
+	/// \exception FE_INEXACT if value had to be rounded
+	inline long long llrint(half arg) { return detail::half2int<half::round_style,true,true,long long>(arg.data_); }
+#endif
+
+	/// \}
+	/// \anchor float
+	/// \name Floating point manipulation
+	/// \{
+
+	/// Decompress floating-point number.
+	/// **See also:** Documentation for [std::frexp](https://en.cppreference.com/w/cpp/numeric/math/frexp).
+	/// \param arg number to decompress
+	/// \param exp address to store exponent at
+	/// \return significant in range [0.5, 1)
+	/// \exception FE_INVALID for signaling NaN
+	inline half frexp(half arg, int *exp)
+	{
+		*exp = 0;
+		unsigned int abs = arg.data_ & 0x7FFF;
+		if(abs >= 0x7C00 || !abs)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		for(; abs<0x400; abs<<=1,--*exp) ;
+		*exp += (abs>>10) - 14;
+		return half(detail::binary, (arg.data_&0x8000)|0x3800|(abs&0x3FF));
+	}
+
+	/// Multiply by power of two.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::scalbln](https://en.cppreference.com/w/cpp/numeric/math/scalbn).
+	/// \param arg number to modify
+	/// \param exp power of two to multiply with
+	/// \return \a arg multplied by 2 raised to \a exp
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half scalbln(half arg, long exp)
+	{
+		unsigned int abs = arg.data_ & 0x7FFF, sign = arg.data_ & 0x8000;
+		if(abs >= 0x7C00 || !abs)
+			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
+		for(; abs<0x400; abs<<=1,--exp) ;
+		exp += abs >> 10;
+		if(exp > 30)
+			return half(detail::binary, detail::overflow<half::round_style>(sign));
+		else if(exp < -10)
+			return half(detail::binary, detail::underflow<half::round_style>(sign));
+		else if(exp > 0)
+			return half(detail::binary, sign|(exp<<10)|(abs&0x3FF));
+		unsigned int m = (abs&0x3FF) | 0x400;
+		return half(detail::binary, detail::rounded<half::round_style,false>(sign|(m>>(1-exp)), (m>>-exp)&1, (m&((1<<-exp)-1))!=0));
+	}
+
+	/// Multiply by power of two.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::scalbn](https://en.cppreference.com/w/cpp/numeric/math/scalbn).
+	/// \param arg number to modify
+	/// \param exp power of two to multiply with
+	/// \return \a arg multplied by 2 raised to \a exp
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half scalbn(half arg, int exp) { return scalbln(arg, exp); }
+
+	/// Multiply by power of two.
+	/// This function is exact to rounding for all rounding modes.
+	///
+	/// **See also:** Documentation for [std::ldexp](https://en.cppreference.com/w/cpp/numeric/math/ldexp).
+	/// \param arg number to modify
+	/// \param exp power of two to multiply with
+	/// \return \a arg multplied by 2 raised to \a exp
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	inline half ldexp(half arg, int exp) { return scalbln(arg, exp); }
+
+	/// Extract integer and fractional parts.
+	/// **See also:** Documentation for [std::modf](https://en.cppreference.com/w/cpp/numeric/math/modf).
+	/// \param arg number to decompress
+	/// \param iptr address to store integer part at
+	/// \return fractional part
+	/// \exception FE_INVALID for signaling NaN
+	inline half modf(half arg, half *iptr)
+	{
+		unsigned int abs = arg.data_ & 0x7FFF;
+		if(abs > 0x7C00)
+		{
+			arg = half(detail::binary, detail::signal(arg.data_));
+			return *iptr = arg, arg;
+		}
+		if(abs >= 0x6400)
+			return *iptr = arg, half(detail::binary, arg.data_&0x8000);
+		if(abs < 0x3C00)
+			return iptr->data_ = arg.data_ & 0x8000, arg;
+		unsigned int exp = abs >> 10, mask = (1<<(25-exp)) - 1, m = arg.data_ & mask;
+		iptr->data_ = arg.data_ & ~mask;
+		if(!m)
+			return half(detail::binary, arg.data_&0x8000);
+		for(; m<0x400; m<<=1,--exp) ;
+		return half(detail::binary, (arg.data_&0x8000)|(exp<<10)|(m&0x3FF));
+	}
+
+	/// Extract exponent.
+	/// **See also:** Documentation for [std::ilogb](https://en.cppreference.com/w/cpp/numeric/math/ilogb).
+	/// \param arg number to query
+	/// \return floating-point exponent
+	/// \retval FP_ILOGB0 for zero
+	/// \retval FP_ILOGBNAN for NaN
+	/// \retval INT_MAX for infinity
+	/// \exception FE_INVALID for 0 or infinite values
+	inline int ilogb(half arg)
+	{
+		int abs = arg.data_ & 0x7FFF, exp;
+		if(!abs || abs >= 0x7C00)
+		{
+			detail::raise(FE_INVALID);
+			return !abs ? FP_ILOGB0 : (abs==0x7C00) ? INT_MAX : FP_ILOGBNAN;
+		}
+		for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ;
+		return exp;
+	}
+
+	/// Extract exponent.
+	/// **See also:** Documentation for [std::logb](https://en.cppreference.com/w/cpp/numeric/math/logb).
+	/// \param arg number to query
+	/// \return floating-point exponent
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_DIVBYZERO for 0
+	inline half logb(half arg)
+	{
+		int abs = arg.data_ & 0x7FFF, exp;
+		if(!abs)
+			return half(detail::binary, detail::pole(0x8000));
+		if(abs >= 0x7C00)
+			return half(detail::binary, (abs==0x7C00) ? 0x7C00 : detail::signal(arg.data_));
+		for(exp=(abs>>10)-15; abs<0x200; abs<<=1,--exp) ;
+		unsigned int value = static_cast<unsigned>(exp<0) << 15;
+		if(exp)
+		{
+			unsigned int m = std::abs(exp) << 6;
+			for(exp=18; m<0x400; m<<=1,--exp) ;
+			value |= (exp<<10) + m;
+		}
+		return half(detail::binary, value);
+	}
+
+	/// Next representable value.
+	/// **See also:** Documentation for [std::nextafter](https://en.cppreference.com/w/cpp/numeric/math/nextafter).
+	/// \param from value to compute next representable value for
+	/// \param to direction towards which to compute next value
+	/// \return next representable value after \a from in direction towards \a to
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW for infinite result from finite argument
+	/// \exception FE_UNDERFLOW for subnormal result
+	inline half nextafter(half from, half to)
+	{
+		int fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF;
+		if(fabs > 0x7C00 || tabs > 0x7C00)
+			return half(detail::binary, detail::signal(from.data_, to.data_));
+		if(from.data_ == to.data_ || !(fabs|tabs))
+			return to;
+		if(!fabs)
+		{
+			detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);
+			return half(detail::binary, (to.data_&0x8000)+1);
+		}
+		unsigned int out = from.data_ + (((from.data_>>15)^static_cast<unsigned>(
+			(from.data_^(0x8000|(0x8000-(from.data_>>15))))<(to.data_^(0x8000|(0x8000-(to.data_>>15))))))<<1) - 1;
+		detail::raise(FE_OVERFLOW, fabs<0x7C00 && (out&0x7C00)==0x7C00);
+		detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out&0x7C00)<0x400);
+		return half(detail::binary, out);
+	}
+
+	/// Next representable value.
+	/// **See also:** Documentation for [std::nexttoward](https://en.cppreference.com/w/cpp/numeric/math/nexttoward).
+	/// \param from value to compute next representable value for
+	/// \param to direction towards which to compute next value
+	/// \return next representable value after \a from in direction towards \a to
+	/// \exception FE_INVALID for signaling NaN
+	/// \exception FE_OVERFLOW for infinite result from finite argument
+	/// \exception FE_UNDERFLOW for subnormal result
+	inline half nexttoward(half from, long double to)
+	{
+		int fabs = from.data_ & 0x7FFF;
+		if(fabs > 0x7C00)
+			return half(detail::binary, detail::signal(from.data_));
+		long double lfrom = static_cast<long double>(from);
+		if(detail::builtin_isnan(to) || lfrom == to)
+			return half(static_cast<float>(to));
+		if(!fabs)
+		{
+			detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT);
+			return half(detail::binary, (static_cast<unsigned>(detail::builtin_signbit(to))<<15)+1);
+		}
+		unsigned int out = from.data_ + (((from.data_>>15)^static_cast<unsigned>(lfrom<to))<<1) - 1;
+		detail::raise(FE_OVERFLOW, (out&0x7FFF)==0x7C00);
+		detail::raise(FE_UNDERFLOW, !HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT && (out&0x7FFF)<0x400);
+		return half(detail::binary, out);
+	}
+
+	/// Take sign.
+	/// **See also:** Documentation for [std::copysign](https://en.cppreference.com/w/cpp/numeric/math/copysign).
+	/// \param x value to change sign for
+	/// \param y value to take sign from
+	/// \return value equal to \a x in magnitude and to \a y in sign
+	inline HALF_CONSTEXPR half copysign(half x, half y) { return half(detail::binary, x.data_^((x.data_^y.data_)&0x8000)); }
+
+	/// \}
+	/// \anchor classification
+	/// \name Floating point classification
+	/// \{
+
+	/// Classify floating-point value.
+	/// **See also:** Documentation for [std::fpclassify](https://en.cppreference.com/w/cpp/numeric/math/fpclassify).
+	/// \param arg number to classify
+	/// \retval FP_ZERO for positive and negative zero
+	/// \retval FP_SUBNORMAL for subnormal numbers
+	/// \retval FP_INFINITY for positive and negative infinity
+	/// \retval FP_NAN for NaNs
+	/// \retval FP_NORMAL for all other (normal) values
+	inline HALF_CONSTEXPR int fpclassify(half arg)
+	{
+		return	!(arg.data_&0x7FFF) ? FP_ZERO :
+				((arg.data_&0x7FFF)<0x400) ? FP_SUBNORMAL :
+				((arg.data_&0x7FFF)<0x7C00) ? FP_NORMAL :
+				((arg.data_&0x7FFF)==0x7C00) ? FP_INFINITE :
+				FP_NAN;
+	}
+
+	/// Check if finite number.
+	/// **See also:** Documentation for [std::isfinite](https://en.cppreference.com/w/cpp/numeric/math/isfinite).
+	/// \param arg number to check
+	/// \retval true if neither infinity nor NaN
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; }
+
+	/// Check for infinity.
+	/// **See also:** Documentation for [std::isinf](https://en.cppreference.com/w/cpp/numeric/math/isinf).
+	/// \param arg number to check
+	/// \retval true for positive or negative infinity
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; }
+
+	/// Check for NaN.
+	/// **See also:** Documentation for [std::isnan](https://en.cppreference.com/w/cpp/numeric/math/isnan).
+	/// \param arg number to check
+	/// \retval true for NaNs
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; }
+
+	/// Check if normal number.
+	/// **See also:** Documentation for [std::isnormal](https://en.cppreference.com/w/cpp/numeric/math/isnormal).
+	/// \param arg number to check
+	/// \retval true if normal number
+	/// \retval false if either subnormal, zero, infinity or NaN
+	inline HALF_CONSTEXPR bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); }
+
+	/// Check sign.
+	/// **See also:** Documentation for [std::signbit](https://en.cppreference.com/w/cpp/numeric/math/signbit).
+	/// \param arg number to check
+	/// \retval true for negative number
+	/// \retval false for positive number
+	inline HALF_CONSTEXPR bool signbit(half arg) { return (arg.data_&0x8000) != 0; }
+
+	/// \}
+	/// \anchor compfunc
+	/// \name Comparison
+	/// \{
+
+	/// Quiet comparison for greater than.
+	/// **See also:** Documentation for [std::isgreater](https://en.cppreference.com/w/cpp/numeric/math/isgreater).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x greater than \a y
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isgreater(half x, half y)
+	{
+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) > ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);
+	}
+
+	/// Quiet comparison for greater equal.
+	/// **See also:** Documentation for [std::isgreaterequal](https://en.cppreference.com/w/cpp/numeric/math/isgreaterequal).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x greater equal \a y
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isgreaterequal(half x, half y)
+	{
+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) >= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);
+	}
+
+	/// Quiet comparison for less than.
+	/// **See also:** Documentation for [std::isless](https://en.cppreference.com/w/cpp/numeric/math/isless).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x less than \a y
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isless(half x, half y)
+	{
+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) < ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);
+	}
+
+	/// Quiet comparison for less equal.
+	/// **See also:** Documentation for [std::islessequal](https://en.cppreference.com/w/cpp/numeric/math/islessequal).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if \a x less equal \a y
+	/// \retval false else
+	inline HALF_CONSTEXPR bool islessequal(half x, half y)
+	{
+		return ((x.data_^(0x8000|(0x8000-(x.data_>>15))))+(x.data_>>15)) <= ((y.data_^(0x8000|(0x8000-(y.data_>>15))))+(y.data_>>15)) && !isnan(x) && !isnan(y);
+	}
+
+	/// Quiet comarison for less or greater.
+	/// **See also:** Documentation for [std::islessgreater](https://en.cppreference.com/w/cpp/numeric/math/islessgreater).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if either less or greater
+	/// \retval false else
+	inline HALF_CONSTEXPR bool islessgreater(half x, half y)
+	{
+		return x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF) && !isnan(x) && !isnan(y);
+	}
+
+	/// Quiet check if unordered.
+	/// **See also:** Documentation for [std::isunordered](https://en.cppreference.com/w/cpp/numeric/math/isunordered).
+	/// \param x first operand
+	/// \param y second operand
+	/// \retval true if unordered (one or two NaN operands)
+	/// \retval false else
+	inline HALF_CONSTEXPR bool isunordered(half x, half y) { return isnan(x) || isnan(y); }
+
+	/// \}
+	/// \anchor casting
+	/// \name Casting
+	/// \{
+
+	/// Cast to or from half-precision floating-point number.
+	/// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted 
+	/// directly using the default rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.
+	///
+	/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types 
+	/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler 
+	/// error and casting between [half](\ref half_float::half)s returns the argument unmodified.
+	/// \tparam T destination type (half or built-in arithmetic type)
+	/// \tparam U source type (half or built-in arithmetic type)
+	/// \param arg value to cast
+	/// \return \a arg converted to destination type
+	/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	template<typename T,typename U> T half_cast(U arg) { return detail::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 specified rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do.
+	///
+	/// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types 
+	/// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler 
+	/// error and casting between [half](\ref half_float::half)s returns the argument unmodified.
+	/// \tparam T destination type (half or built-in arithmetic type)
+	/// \tparam R rounding mode to use.
+	/// \tparam U source type (half or built-in arithmetic type)
+	/// \param arg value to cast
+	/// \return \a arg converted to destination type
+	/// \exception FE_INVALID if \a T is integer type and result is not representable as \a T
+	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
+	template<typename T,std::float_round_style R,typename U> T half_cast(U arg) { return detail::half_caster<T,U,R>::cast(arg); }
+	/// \}
+
+	/// \}
+	/// \anchor errors
+	/// \name Error handling
+	/// \{
+
+	/// Clear exception flags.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	///
+	/// **See also:** Documentation for [std::feclearexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feclearexcept).
+	/// \param excepts OR of exceptions to clear
+	/// \retval 0 all selected flags cleared successfully
+	inline int feclearexcept(int excepts) { detail::errflags() &= ~excepts; return 0; }
+
+	/// Test exception flags.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	///
+	/// **See also:** Documentation for [std::fetestexcept](https://en.cppreference.com/w/cpp/numeric/fenv/fetestexcept).
+	/// \param excepts OR of exceptions to test
+	/// \return OR of selected exceptions if raised
+	inline int fetestexcept(int excepts) { return detail::errflags() & excepts; }
+
+	/// Raise exception flags.
+	/// This raises the specified floating point exceptions and also invokes any additional automatic exception handling as 
+	/// configured with the [HALF_ERRHANDLIG_...](\ref HALF_ERRHANDLING_ERRNO) preprocessor symbols.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	///
+	/// **See also:** Documentation for [std::feraiseexcept](https://en.cppreference.com/w/cpp/numeric/fenv/feraiseexcept).
+	/// \param excepts OR of exceptions to raise
+	/// \retval 0 all selected exceptions raised successfully
+	inline int feraiseexcept(int excepts) { detail::errflags() |= excepts; detail::raise(excepts); return 0; }
+
+	/// Save exception flags.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	///
+	/// **See also:** Documentation for [std::fegetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag).
+	/// \param flagp adress to store flag state at
+	/// \param excepts OR of flags to save
+	/// \retval 0 for success
+	inline int fegetexceptflag(int *flagp, int excepts) { *flagp = detail::errflags() & excepts; return 0; }
+
+	/// Restore exception flags.
+	/// This only copies the specified exception state (including unset flags) without incurring any additional exception handling.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	///
+	/// **See also:** Documentation for [std::fesetexceptflag](https://en.cppreference.com/w/cpp/numeric/fenv/feexceptflag).
+	/// \param flagp adress to take flag state from
+	/// \param excepts OR of flags to restore
+	/// \retval 0 for success
+	inline int fesetexceptflag(const int *flagp, int excepts) { detail::errflags() = (detail::errflags()|(*flagp&excepts)) & (*flagp|~excepts); return 0; }
+
+	/// Throw C++ exceptions based on set exception flags.
+	/// This function manually throws a corresponding C++ exception if one of the specified flags is set, 
+	/// no matter if automatic throwing (via [HALF_ERRHANDLING_THROW_...](\ref HALF_ERRHANDLING_THROW_INVALID)) is enabled or not.
+	/// This function works even if [automatic exception flag handling](\ref HALF_ERRHANDLING_FLAGS) is disabled, 
+	/// but in that case manual flag management is the only way to raise flags.
+	/// \param excepts OR of exceptions to test
+	/// \param msg error message to use for exception description
+	/// \throw std::domain_error if `FE_INVALID` or `FE_DIVBYZERO` is selected and set
+	/// \throw std::overflow_error if `FE_OVERFLOW` is selected and set
+	/// \throw std::underflow_error if `FE_UNDERFLOW` is selected and set
+	/// \throw std::range_error if `FE_INEXACT` is selected and set
+	inline void fethrowexcept(int excepts, const char *msg = "")
+	{
+		excepts &= detail::errflags();
+		if(excepts & (FE_INVALID|FE_DIVBYZERO))
+			throw std::domain_error(msg);
+		if(excepts & FE_OVERFLOW)
+			throw std::overflow_error(msg);
+		if(excepts & FE_UNDERFLOW)
+			throw std::underflow_error(msg);
+		if(excepts & FE_INEXACT)
+			throw std::range_error(msg);
+	}
+	/// \}
+}
+
+
+#undef HALF_UNUSED_NOERR
+#undef HALF_CONSTEXPR
+#undef HALF_CONSTEXPR_CONST
+#undef HALF_CONSTEXPR_NOERR
+#undef HALF_NOEXCEPT
+#undef HALF_NOTHROW
+#undef HALF_THREAD_LOCAL
+#undef HALF_TWOS_COMPLEMENT_INT
+#ifdef HALF_POP_WARNINGS
+	#pragma warning(pop)
+	#undef HALF_POP_WARNINGS
+#endif
+
+#endif
diff --git a/renderdoc/renderdoc.vcxproj b/renderdoc/renderdoc.vcxproj
index 9d05f290d..c52671c72 100644
--- a/renderdoc/renderdoc.vcxproj
+++ b/renderdoc/renderdoc.vcxproj
@@ -122,6 +122,7 @@
     <ClInclude Include="3rdparty\compressonator\CMP_Core.h" />
     <ClInclude Include="3rdparty\compressonator\cmp_math_vec4.h" />
     <ClInclude Include="3rdparty\compressonator\Common_Def.h" />
+    <ClInclude Include="3rdparty\half\half.hpp" />
     <ClInclude Include="3rdparty\interceptor-lib\lib\AArch64\target_aarch64.h" />
     <ClInclude Include="3rdparty\interceptor-lib\lib\ARM\target_arm.h" />
     <ClInclude Include="3rdparty\interceptor-lib\lib\code_generator.h" />
diff --git a/renderdoc/renderdoc.vcxproj.filters b/renderdoc/renderdoc.vcxproj.filters
index 304aa6d8a..82568b6b0 100644
--- a/renderdoc/renderdoc.vcxproj.filters
+++ b/renderdoc/renderdoc.vcxproj.filters
@@ -142,6 +142,9 @@
     <Filter Include="3rdparty\compressonator">
       <UniqueIdentifier>{3d212b9b-bf42-40db-84a3-b94e064fd281}</UniqueIdentifier>
     </Filter>
+    <Filter Include="3rdparty\half">
+      <UniqueIdentifier>{1b49d2aa-1cfb-4f0a-8fcf-1065af55ea2b}</UniqueIdentifier>
+    </Filter>
   </ItemGroup>
   <ItemGroup>
     <ClInclude Include="maths\camera.h">
@@ -543,6 +546,9 @@
     <ClInclude Include="3rdparty\compressonator\Common_Def.h">
       <Filter>3rdparty\compressonator</Filter>
     </ClInclude>
+    <ClInclude Include="3rdparty\half\half.hpp">
+      <Filter>3rdparty\half</Filter>
+    </ClInclude>
     <ClInclude Include="api\replay\rdcflatmap.h">
       <Filter>API\Replay</Filter>
     </ClInclude>
diff --git a/util/installer/LICENSE.rtf b/util/installer/LICENSE.rtf
index a357fc653..20afad73f 100644
--- a/util/installer/LICENSE.rtf
+++ b/util/installer/LICENSE.rtf
@@ -38,5 +38,6 @@ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLI
 {\field{\*\fldinst{HYPERLINK "{\pntext\f1\'B7\tab}https://github.com/Microsoft/microsoft-pdb/"}}{\fldrslt{\ul\cf1 https://github.com/Microsoft/microsoft-pdb}}}\f0\fs22\line Microsoft PDB Information distributed under the MIT License. Copyright (c) 2015 Microsoft Corporation.\par
 {\field{\*\fldinst{HYPERLINK "{\pntext\f1\'B7\tab}https://github.com/GPUOpen-Tools/compressonator/"}}{\fldrslt{\ul\cf1 https://github.com/GPUOpen-Tools/compressonator}}}\f0\fs22\line Compressonator distributed under the MIT License. Copyright (c) 2018 Advanced Micro Devices, Inc. Copyright (c) 2004-2006 ATI Technologies Inc. Distributed under the MIT License.\par
 {\field{\*\fldinst{HYPERLINK "{\pntext\f1\'B7\tab}http://download.nvidia.com/XFree86/nvapi-open-source-sdk/"}}{\fldrslt{\ul\cf1 http://download.nvidia.com/XFree86/nvapi-open-source-sdk}}}\f0\fs22\line nvapi open source SDK distributed under the MIT License. Copyright (c) 2019, NVIDIA CORPORATION.\par
+{\field{\*\fldinst{HYPERLINK "{\pntext\f1\'B7\tab}http://half.sourceforge.net/"}}{\fldrslt{\ul\cf1 http://half.sourceforge.net/}}}\f0\fs22\line half.hpp distributed under the MIT License. Copyright (c) 2012-2019 Christian Rau.\par
 }