diff options
Diffstat (limited to 'third_party/half/README.txt')
| -rw-r--r-- | third_party/half/README.txt | 317 |
1 files changed, 317 insertions, 0 deletions
diff --git a/third_party/half/README.txt b/third_party/half/README.txt new file mode 100644 index 0000000..3dd0d1c --- /dev/null +++ b/third_party/half/README.txt @@ -0,0 +1,317 @@ +HALF-PRECISION FLOATING-POINT LIBRARY (Version 2.2.0)
+-----------------------------------------------------
+
+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.
|