Emulate PACK/UNPACK for non-F16C CPUs

src/xenia/cpu/backend/x64/x64_emitter.cc

@@ -82,6 +82,7 @@ X64Emitter::X64Emitter(X64Backend* backend, XbyakAllocator* allocator)
     feature_flags_ |= cpu_.has(Xbyak::util::Cpu::tFMA) ? kX64EmitFMA : 0;
     feature_flags_ |= cpu_.has(Xbyak::util::Cpu::tLZCNT) ? kX64EmitLZCNT : 0;
     feature_flags_ |= cpu_.has(Xbyak::util::Cpu::tBMI2) ? kX64EmitBMI2 : 0;
+    feature_flags_ |= cpu_.has(Xbyak::util::Cpu::tF16C) ? kX64EmitF16C : 0;
   }
 }
 

src/xenia/cpu/backend/x64/x64_emitter.h

@@ -102,6 +102,7 @@ enum X64EmitterFeatureFlags {
   kX64EmitFMA = 1 << 2,
   kX64EmitLZCNT = 1 << 3,
   kX64EmitBMI2 = 1 << 4,
+  kX64EmitF16C = 1 << 5,
 };
 
 class X64Emitter : public Xbyak::CodeGenerator {

src/xenia/cpu/backend/x64/x64_sequences.cc

@@ -33,6 +33,9 @@
 #include "xenia/cpu/hir/hir_builder.h"
 #include "xenia/cpu/processor.h"
 
+// For OPCODE_PACK/OPCODE_UNPACK
+#include "third_party/half/include/half.hpp"
+
 namespace xe {
 namespace cpu {
 namespace backend {
@@ -5972,22 +5975,60 @@ EMITTER(PACK, MATCH(I<OPCODE_PACK, V128<>, V128<>, V128<>>)) {
     //     ((src1.uy & 0xFF) << 8) | (src1.uz & 0xFF)
     e.vpshufb(i.dest, i.dest, e.GetXmmConstPtr(XMMPackD3DCOLOR));
   }
+  static __m128i EmulateFLOAT16_2(void*, __m128 src1) {
+    alignas(16) float    a[4];
+    alignas(16) uint16_t b[8];
+    _mm_store_ps(a, src1);
+    std::memset(b, 0, sizeof(b));
+
+    for (int i = 0; i < 2; i++) {
+      b[7 - i] = half_float::detail::float2half<std::round_toward_zero>(a[i]);
+    }
+
+    return _mm_load_si128(reinterpret_cast<__m128i*>(b));
+  }
   static void EmitFLOAT16_2(X64Emitter& e, const EmitArgType& i) {
     assert_true(i.src2.value->IsConstantZero());
     // http://blogs.msdn.com/b/chuckw/archive/2012/09/11/directxmath-f16c-and-fma.aspx
     // dest = [(src1.x | src1.y), 0, 0, 0]
+
+    if (e.IsFeatureEnabled(kX64EmitF16C)) {
       // 0|0|0|0|W|Z|Y|X
       e.vcvtps2ph(i.dest, i.dest, B00000011);
       // Shuffle to X|Y|0|0|0|0|0|0
       e.vpshufb(i.dest, i.dest, e.GetXmmConstPtr(XMMPackFLOAT16_2));
+    } else {
+      e.lea(e.r8, e.StashXmm(0, i.src1));
+      e.CallNativeSafe(EmulateFLOAT16_2);
+      e.vmovaps(i.dest, e.xmm0);
+    }
+  }
+  static __m128i EmulateFLOAT16_4(void*, __m128 src1) {
+    alignas(16) float    a[4];
+    alignas(16) uint16_t b[8];
+    _mm_store_ps(a, src1);
+    std::memset(b, 0, sizeof(b));
+
+    for (int i = 0; i < 4; i++) {
+      b[7 - i] = half_float::detail::float2half<std::round_toward_zero>(a[i]);
+    }
+
+    return _mm_load_si128(reinterpret_cast<__m128i*>(b));
   }
   static void EmitFLOAT16_4(X64Emitter& e, const EmitArgType& i) {
     assert_true(i.src2.value->IsConstantZero());
     // dest = [(src1.x | src1.y), (src1.z | src1.w), 0, 0]
+
+    if (e.IsFeatureEnabled(kX64EmitF16C)) {
       // 0|0|0|0|W|Z|Y|X
       e.vcvtps2ph(i.dest, i.src1, B00000011);
       // Shuffle to X|Y|Z|W|0|0|0|0
       e.vpshufb(i.dest, i.dest, e.GetXmmConstPtr(XMMPackFLOAT16_4));
+    } else {
+      e.lea(e.r8, e.StashXmm(0, i.src1));
+      e.CallNativeSafe(EmulateFLOAT16_4);
+      e.vmovaps(i.dest, e.xmm0);
+    }
   }
   static void EmitSHORT_2(X64Emitter& e, const EmitArgType& i) {
     assert_true(i.src2.value->IsConstantZero());
@@ -6161,6 +6202,21 @@ EMITTER(UNPACK, MATCH(I<OPCODE_UNPACK, V128<>, V128<>>)) {
     // Add 1.0f to each.
     e.vpor(i.dest, e.GetXmmConstPtr(XMMOne));
   }
+  static __m128 EmulateFLOAT16_2(void*, __m128i src1) {
+    alignas(16) uint16_t a[8];
+    alignas(16) float    b[4];
+    _mm_store_si128(reinterpret_cast<__m128i*>(a), src1);
+
+    for (int i = 0; i < 2; i++) {
+      b[i] = half_float::detail::half2float(a[7 - i]);
+    }
+
+    // Constants, or something
+    b[2] = 0.f;
+    b[3] = 1.f;
+
+    return _mm_load_ps(b);
+  }
   static void EmitFLOAT16_2(X64Emitter& e, const EmitArgType& i) {
     // 1 bit sign, 5 bit exponent, 10 bit mantissa
     // D3D10 half float format
@@ -6172,6 +6228,7 @@ EMITTER(UNPACK, MATCH(I<OPCODE_UNPACK, V128<>, V128<>>)) {
     // Also zero out the high end.
     // TODO(benvanik): special case constant unpacks that just get 0/1/etc.
 
+    if (e.IsFeatureEnabled(kX64EmitF16C)) {
       // sx = src.iw >> 16;
       // sy = src.iw & 0xFFFF;
       // dest = { XMConvertHalfToFloat(sx),
@@ -6183,12 +6240,45 @@ EMITTER(UNPACK, MATCH(I<OPCODE_UNPACK, V128<>, V128<>>)) {
       e.vcvtph2ps(i.dest, i.dest);
       e.vpshufd(i.dest, i.dest, B10100100);
       e.vpor(i.dest, e.GetXmmConstPtr(XMM0001));
+    } else {
+      e.lea(e.r8, e.StashXmm(0, i.src1));
+      e.CallNativeSafe(EmulateFLOAT16_2);
+      e.vmovaps(i.dest, e.xmm0);
+    }
+  }
+  static __m128 EmulateFLOAT16_4(void*, __m128i src1) {
+    alignas(16) uint16_t a[8];
+    alignas(16) float    b[4];
+    _mm_store_si128(reinterpret_cast<__m128i*>(a), src1);
+
+    // The floats come in swapped for some reason. Swap them back.
+    for (int i = 0; i < 2; i++) {
+      uint16_t &n1 = a[7 - (i * 2)];
+      uint16_t &n2 = a[6 - (i * 2)];
+
+      uint16_t tmp = n1;
+      n1 = n2;
+      n2 = tmp;
+    }
+
+    for (int i = 0; i < 4; i++) {
+      b[3 - i] = half_float::detail::half2float(a[7 - i]);
+    }
+
+    return _mm_load_ps(b);
   }
   static void EmitFLOAT16_4(X64Emitter& e, const EmitArgType& i) {
     // src = [(dest.x | dest.y), (dest.z | dest.w), 0, 0]
+
+    if (e.IsFeatureEnabled(kX64EmitF16C)) {
       // Shuffle to 0|0|0|0|W|Z|Y|X
       e.vpshufb(i.dest, i.src1, e.GetXmmConstPtr(XMMUnpackFLOAT16_4));
       e.vcvtph2ps(i.dest, i.dest);
+    } else {
+      e.lea(e.r8, e.StashXmm(0, i.src1));
+      e.CallNativeSafe(EmulateFLOAT16_4);
+      e.vmovaps(i.dest, e.xmm0);
+    }
   }
   static void EmitSHORT_2(X64Emitter& e, const EmitArgType& i) {
     // (VD.x) = 3.0 + (VB.x>>16)*2^-22

third_party/half/ChangeLog.txt

@@ -0,0 +1,173 @@
+Release Notes
+=============
+
+1.11.0 release (2013-11-16):
+----------------------------
+
+- Made tie-breaking behaviour in round to nearest configurable by 
+  `HALF_ROUND_TIES_TO_EVEN` macro.
+- Completed support for all C++11 mathematical functions even if single-
+  precision versions from `<cmath>` are unsupported.
+- Fixed inability to disable support for C++11 mathematical functions on 
+  *VC++ 2013*.
+
+
+1.10.0 release (2013-11-09):
+----------------------------
+
+- Made default rounding mode configurable by `HALF_ROUND_STYLE` macro.
+- Added support for non-IEEE single-precision implementations.
+- Added `HALF_ENABLE_CPP11_TYPE_TRAITS` preprocessor flag for checking 
+  support for C++11 type traits and TMP features.
+- Restricted `half_cast` to support built-in arithmetic types only.
+- Changed behaviour of `half_cast` to respect rounding mode when casting 
+  to/from integer types.
+
+
+1.9.2 release (2013-11-01):
+---------------------------
+
+- Tested for *gcc 4.8*.
+- Tested and fixed for *VC++ 2013*.
+- Removed unnecessary warnings in *MSVC*.
+
+
+1.9.1 release (2013-08-08):
+---------------------------
+
+- Fixed problems with older gcc and MSVC versions.
+- Small fix to non-C++11 implementations of `remainder` and `remquo`.
+
+
+1.9.0 release (2013-08-07):
+---------------------------
+
+- Changed behaviour of `nearbyint`, `rint`, `lrint` and `llrint` to use 
+  rounding mode of half-precision implementation (which is 
+  truncating/indeterminate) instead of single-precision rounding mode.
+- Added support for more C++11 mathematical functions even if single-
+  precision versions from `<cmath>` are unsupported, in particular 
+  `remainder`, `remquo` and `cbrt`.
+- Minor implementation changes.
+
+
+1.8.1 release (2013-01-22):
+---------------------------
+
+- Fixed bug resulting in multiple definitions of the `nanh` function due to 
+  a missing `inline` specification.
+
+
+1.8.0 release (2013-01-19):
+---------------------------
+
+- Added support for more C++11 mathematical functions even if single-
+  precision versions from `<cmath>` are unsupported, in particular 
+  exponential and logarithm functions, hyperbolic area functions and the 
+  hypotenuse function.
+- Made `fma` function use default implementation if single-precision version
+  from `<cmath>` is not faster and thus `FP_FAST_FMAH` to be defined always.
+- Fixed overload resolution issues when invoking certain mathematical 
+  functions by unqualified calls.
+
+
+1.7.0 release (2012-10-26):
+---------------------------
+
+- Added support for C++11 `noexcept` specifiers.
+- Changed C++11 `long long` to be supported on *VC++ 2003* and up.
+
+
+1.6.1 release (2012-09-13):
+---------------------------
+
+- Made `fma` and `fdim` functions available even if corresponding 
+  single-precision functions are not.
+
+
+1.6.0 release (2012-09-12):
+---------------------------
+
+- Added `HALF_ENABLE_CPP11_LONG_LONG` to control support for `long long` 
+  integers and corresponding mathematical functions.
+- Fixed C++98 compatibility on non-VC compilers.
+
+
+1.5.1 release (2012-08-17):
+---------------------------
+
+- Recorrected `std::numeric_limits::round_style` to always return 
+  `std::round_indeterminate`, due to overflow-handling deviating from 
+  correct round-toward-zero behaviour.
+
+
+1.5.0 release (2012-08-16):
+---------------------------
+
+- Added `half_cast` for explicitly casting between half and any type 
+  convertible to/from `float` and allowing the explicit specification of 
+  the rounding mode to use.
+
+
+1.4.0 release (2012-08-12):
+---------------------------
+
+- Added support for C++11 generalized constant expressions (`constexpr`).
+
+
+1.3.1 release (2012-08-11):
+---------------------------
+
+- Fixed requirement for `std::signbit` and `std::isnan` (even if C++11 
+  `<cmath>` functions disabled) on non-VC compilers.
+
+
+1.3.0 release (2012-08-10):
+---------------------------
+
+- Made requirement for `<cstdint>` and `static_assert` optional and thus 
+  made the library C++98-compatible.
+- Made support for C++11 features user-overridable through explicit 
+  definition of corresponding preprocessor symbols to either 0 or 1.
+- Renamed `HALF_ENABLE_HASH` to `HALF_ENABLE_CPP11_HASH` in correspondence 
+  with other C++11 preprocessor symbols.
+
+
+1.2.0 release (2012-08-07):
+---------------------------
+
+- Added proper preprocessor definitions for `HUGE_VALH` and `FP_FAST_FMAH` 
+  in correspondence with their single-precision counterparts from `<cmath>`.
+- Fixed internal preprocessor macros to be properly undefined after use.
+
+
+1.1.2 release (2012-08-07):
+---------------------------
+
+- Revised `std::numeric_limits::round_style` to return 
+  `std::round_toward_zero` if the `float` version also does and 
+  `std::round_indeterminate` otherwise.
+- Fixed `std::numeric_limits::round_error` to reflect worst-case round 
+  toward zero behaviour.
+
+
+1.1.1 release (2012-08-06):
+---------------------------
+
+- Fixed `std::numeric_limits::min` to return smallest positive normal 
+  number, instead of subnormal number.
+- Fixed `std::numeric_limits::round_style` to return 
+  `std::round_indeterminate` due to mixture of separately rounded 
+  single-precision arithmetics with truncating single-to-half conversions.
+
+
+1.1.0 release (2012-08-06):
+---------------------------
+
+- Added half-precision literals.
+
+
+1.0.0 release (2012-08-05):
+---------------------------
+
+- First release.

third_party/half/LICENSE.txt

@@ -0,0 +1,21 @@
+The MIT License
+
+Copyright (c) 2012-2013 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.

third_party/half/README.txt

@@ -0,0 +1,284 @@
+HALF-PRECISION FLOATING POINT LIBRARY (Version 1.11.0)
+------------------------------------------------------
+
+This is a C++ header-only library to provide an IEEE 754 conformant 16-bit 
+half-precision floating point type along with corresponding arithmetic 
+operators, type conversions and common mathematical functions. It aims for both 
+efficiency and ease of use, trying to accurately mimic the behaviour of the 
+builtin floating point types at the best performance possible.
+
+
+INSTALLATION AND REQUIREMENTS
+-----------------------------
+
+Comfortably enough, the library consists of just a single header file 
+containing all the functionality, which can be directly included by your 
+projects, without the neccessity to build anything or link to anything.
+
+Whereas this library is fully C++98-compatible, it can profit from certain 
+C++11 features. Support for those features is checked automatically at compile 
+(or rather preprocessing) time, but can be explicitly enabled or disabled by 
+defining the corresponding preprocessor symbols to either 1 or 0 yourself. This 
+is useful when the automatic detection fails (for more exotic implementations) 
+or when a feature should be explicitly disabled:
+
+  - 'long long' integer type for mathematical functions returning 'long long' 
+    results (enabled for VC++ 2003 and newer, gcc and clang, overridable with 
+    'HALF_ENABLE_CPP11_LONG_LONG').
+
+  - Static assertions for extended compile-time checks (enabled for VC++ 2010, 
+    gcc 4.3, clang 2.9 and newer, overridable with 'HALF_ENABLE_CPP11_STATIC_ASSERT').
+
+  - Generalized constant expressions (enabled for gcc 4.6, clang 3.1 and newer, 
+    overridable with 'HALF_ENABLE_CPP11_CONSTEXPR').
+
+  - noexcept exception specifications (enabled for gcc 4.6, clang 3.0 and newer, 
+    overridable with 'HALF_ENABLE_CPP11_NOEXCEPT').
+
+  - User-defined literals for half-precision literals to work (enabled for 
+    gcc 4.7, clang 3.1 and newer, overridable with 'HALF_ENABLE_CPP11_USER_LITERALS').
+
+  - Type traits and template meta-programming features from <type_traits> 
+    (enabled for VC++ 2010, libstdc++ 4.3, libc++ and newer, overridable with 
+    'HALF_ENABLE_CPP11_TYPE_TRAITS').
+
+  - Special integer types from <cstdint> (enabled for VC++ 2010, libstdc++ 4.3, 
+    libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CSTDINT').
+
+  - Certain C++11 single-precision mathematical functions from <cmath> for 
+    an improved implementation of their half-precision counterparts to work 
+    (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with 
+    'HALF_ENABLE_CPP11_CMATH').
+
+  - Hash functor 'std::hash' from <functional> (enabled for VC++ 2010, 
+    libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_HASH').
+
+The library has been tested successfully with Visual C++ 2005-2013, gcc 4.4-4.8 
+and clang 3.1. Please contact me if you have any problems, suggestions or even 
+just success testing it on other platforms.
+
+
+DOCUMENTATION
+-------------
+
+Here follow some general words about the usage of the library and its 
+implementation. For a complete documentation of its iterface look at the 
+corresponding website http://half.sourceforge.net. You may also generate the 
+complete developer documentation from the library's only include file's doxygen 
+comments, but this is more relevant to developers rather than mere users (for 
+reasons described below).
+
+BASIC USAGE
+
+To make use of the library just include its only header file half.hpp, which 
+defines all half-precision functionality inside the 'half_float' namespace. The 
+actual 16-bit half-precision data type is represented by the 'half' type. This 
+type behaves like the builtin floating point types as much as possible, 
+supporting the usual arithmetic, comparison and streaming operators, which 
+makes its use pretty straight-forward:
+
+    using half_float::half;
+    half a(3.4), b(5);
+    half c = a * b;
+    c += 3;
+    if(c > a)
+	    std::cout << c << std::endl;
+
+Additionally the 'half_float' namespace also defines half-precision versions 
+for all mathematical functions of the C++ standard library, which can be used 
+directly through ADL:
+
+    half a(-3.14159);
+    half s = sin(abs(a));
+    long l = lround(s);
+
+You may also specify explicit half-precision literals, since the library 
+provides a user-defined literal inside the 'half_float::literal' namespace, 
+which you just need to import (assuming support for C++11 user-defined literals):
+
+    using namespace half_float::literal;
+    half x = 1.0_h;
+
+Furthermore the library provides proper specializations for 
+'std::numeric_limits', defining various implementation properties, and 
+'std::hash' for hashing half-precision numbers (assuming support for C++11 
+'std::hash'). Similar to the corresponding preprocessor symbols from <cmath> 
+the library also defines the 'HUGE_VALH' constant and maybe the 'FP_FAST_FMAH' 
+symbol.
+
+CONVERSIONS
+
+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 to float) is implicit, because all values represetable with 
+half-precision are also representable with single-precision. This way the 
+half-to-float conversion behaves similar to the builtin float-to-double 
+conversion and all arithmetic expressions involving both half-precision and 
+single-precision arguments will be of single-precision type. This way you can 
+also directly use the mathematical functions of the C++ standard library, 
+though in this case you will invoke the single-precision versions which will 
+also return single-precision values, which is (even if maybe performing the 
+exact same computation, see below) not as conceptually clean when working in a 
+half-precision environment.
+
+The default rounding mode for conversions from float to half uses truncation 
+(round toward zero, but mapping overflows to infinity) for rounding values not 
+representable exactly in half-precision. This is the fastest rounding possible 
+and is usually sufficient. But by redefining the 'HALF_ROUND_STYLE' 
+preprocessor symbol (before including half.hpp) this default can be overridden 
+with one of the other standard rounding modes using their respective constants 
+or the equivalent values of 'std::float_round_style' (it can even be 
+synchronized with the underlying single-precision implementation by defining it 
+to 'std::numeric_limits<float>::round_style'):
+
+  - 'std::round_indeterminate' or -1 for the fastest rounding (default).
+
+  - 'std::round_toward_zero' or 0 for rounding toward zero.
+
+  - std::round_to_nearest' or 1 for rounding to the nearest value.
+
+  - std::round_toward_infinity' or 2 for rounding toward positive infinity.
+
+  - std::round_toward_neg_infinity' or 3 for rounding toward negative infinity.
+
+In addition to changing the overall default rounding mode one can also use the 
+'half_cast'. This converts between half and any built-in arithmetic type using 
+a configurable rounding mode (or the default rounding mode if none is 
+specified). In addition to a configurable rounding mode, 'half_cast' has two 
+other differences to a mere 'static_cast': (1) Floating point types are 
+explicitly cast to float before being converted to half-precision and thus any 
+warnings for narrowing conversions are suppressed. (2) Conversions to/from 
+integer types are performed directly using the given rounding mode, without any 
+intermediate conversion to/from float.
+
+    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 );
+
+When using round to nearest (either as default or thorugh 'half_cast') ties are 
+by default resolved by rounding them away from zero (and thus equal to the 
+behaviour of the 'round' function). But by redefining the 
+'HALF_ROUND_TIES_TO_EVEN' preprocessor symbol to 1 (before including half.hpp) 
+this default can be changed to the slightly slower but less biased and more 
+IEEE-conformant behaviour of rounding half-way cases to the nearest even value.
+
+    #define HALF_ROUND_TIES_TO_EVEN 1
+    #include <half.hpp>
+    ...
+    assert( half_cast<int,std::round_to_nearest>(3.5_h) 
+         == half_cast<int,std::round_to_nearest>(4.5_h) );
+
+IMPLEMENTATION
+
+For performance reasons (and ease of implementation) many of the mathematical 
+functions provided by the library as well as all arithmetic operations are 
+actually carried out in single-precision under the hood, calling to the C++ 
+standard library implementations of those functions whenever appropriate, 
+meaning the arguments are converted to floats and the result back to half. But 
+to reduce the conversion overhead as much as possible any temporary values 
+inside of lengthy expressions are kept in single-precision as long as possible, 
+while still maintaining a strong half-precision type to the outside world. Only 
+when finally assigning the value to a half or calling a function that works 
+directly on halfs is the actual conversion done (or never, when further 
+converting the result to float.
+
+This approach has two implications. First of all you have to treat the 
+library's documentation at http://half.sourceforge.net as a simplified version, 
+describing the behaviour of the library as if implemented this way. The actual 
+argument and return types of functions and operators may involve other internal 
+types (feel free to generate the exact developer documentation from the Doxygen 
+comments in the library's header file if you really need to). But nevertheless 
+the behaviour is exactly like specified in the documentation. The other 
+implication is, that in the presence of rounding errors or over-/underflows 
+arithmetic expressions may produce different results when compared to 
+converting to half-precision after each individual operation:
+
+    half a = (std::numeric_limits<half>::max() * 2.0_h) / 2.0_h; // a = MAX
+    half b = std::numeric_limits<half>::max() * 2.0_h;           // b = INF
+    b /= 2.0_h;                                                  // b stays INF
+
+But this should only be a problem in very few cases. One last word has to be 
+said when talking about performance. Even with its efforts in reducing 
+conversion overhead as much as possible, the software half-precision 
+implementation can most probably not beat the direct use of single-precision 
+computations. Usually using actual float values for all computations and 
+temproraries and using halfs only for storage is the recommended way. On the 
+one hand this somehow makes the provided mathematical functions obsolete 
+(especially in light of the implicit conversion from half to float), but 
+nevertheless the goal of this library was to provide a complete and 
+conceptually clean half-precision implementation, to which the standard 
+mathematical functions belong, even if usually not needed.
+
+IEEE CONFORMANCE
+
+The half type uses the standard IEEE representation with 1 sign bit, 5 exponent 
+bits and 10 mantissa bits (11 when counting the hidden bit). It supports all 
+types of special values, like subnormal values, infinity and NaNs. But there 
+are some limitations to the complete conformance to the IEEE 754 standard:
+
+  - The implementation does not differentiate between signalling and quiet 
+    NaNs, this means operations on halfs are not specified to trap on 
+    signalling NaNs (though they may, see last point).
+
+  - Though arithmetic operations are internally rounded to single-precision 
+    using the underlying single-precision implementation's current rounding 
+    mode, those values are then converted to half-precision using the default 
+    half-precision rounding mode (changed by defining 'HALF_ROUND_STYLE' 
+    accordingly). This mixture of rounding modes is also the reason why 
+    'std::numeric_limits<half>::round_style' may actually return 
+    'std::round_indeterminate' when half- and single-precision rounding modes 
+    don't match.
+
+  - Because of internal truncation it may also be that certain single-precision 
+    NaNs will be wrongly converted to half-precision infinity, though this is 
+    very unlikely to happen, since most single-precision implementations don't 
+    tend to only set the lowest bits of a NaN mantissa.
+
+  - The implementation does not provide any floating point exceptions, thus 
+    arithmetic operations or mathematical functions are not specified to invoke 
+    proper floating point exceptions. But due to many functions implemented in 
+    single-precision, those may still invoke floating point exceptions of the 
+    underlying single-precision implementation.
+
+Some of those points could have been circumvented by controlling the floating 
+point environment using <cfenv> or implementing a similar exception mechanism. 
+But this would have required excessive runtime checks giving two high an impact 
+on performance for something that is rarely ever needed. If you really need to 
+rely on proper floating point exceptions, it is recommended to explicitly 
+perform computations using the built-in floating point types to be on the safe 
+side. In the same way, if you really need to rely on a particular rounding 
+behaviour, it is recommended to either use single-precision computations and 
+explicitly convert the result to half-precision using 'half_cast' and 
+specifying the desired rounding mode, or synchronize the default half-precision 
+rounding mode to the rounding mode of the single-precision implementation (most 
+likely 'HALF_ROUND_STYLE=1', 'HALF_ROUND_TIES_TO_EVEN=1'). But this is really 
+considered an expert-scenario that should be used only when necessary, since 
+actually working with half-precision usually comes with a certain 
+tolerance/ignorance of exactness considerations and proper rounding comes with 
+a certain performance cost.
+
+
+CREDITS AND CONTACT
+-------------------
+
+This library is developed by CHRISTIAN RAU and released under the MIT License 
+(see LICENSE.txt). If you have any questions or problems with it, feel free to 
+contact me at rauy@users.sourceforge.net.
+
+Additional credit goes to JEROEN VAN DER ZIJP for his paper on "Fast Half Float 
+Conversions", whose algorithms have been used in the library for converting 
+between half-precision and single-precision values.