Main header file for half precision functionality. More...

#include <utility>
#include <algorithm>
#include <iostream>
#include <limits>
#include <climits>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <type_traits>
#include <cstdint>
#include <functional>

Classes
struct	half_float::detail::conditional< B, T, F >
	Conditional type. More...

struct	half_float::detail::bool_type< B >
	Helper for tag dispatching. More...

struct	half_float::detail::is_float< T >
	Type traits for floating point types. More...

struct	half_float::detail::bits< T >
	Type traits for floating point bits. More...

struct	half_float::detail::bits< float >
	Unsigned integer of (at least) 32 bits width. More...

struct	half_float::detail::bits< double >
	Unsigned integer of (at least) 64 bits width. More...

struct	half_float::detail::binary_t
	Tag type for binary construction. More...

struct	half_float::detail::expr
	Temporary half-precision expression. More...

struct	half_float::detail::enable< T, typename, typename, typename >
	SFINAE helper for generic half-precision functions. More...

struct	half_float::detail::result< T, U >
	Return type for specialized generic 2-argument half-precision functions. More...

class	half_float::half
	Half-precision floating point type. More...

struct	half_float::detail::functions
	Wrapper implementing unspecialized half-precision functions. More...

struct	half_float::detail::unary_specialized< T >
	Wrapper for unary half-precision functions needing specialization for individual argument types. More...

struct	half_float::detail::binary_specialized< T, U >
	Wrapper for binary half-precision functions needing specialization for individual argument types. More...

struct	half_float::detail::half_caster< T, U, R >
	Helper class for half casts. More...

class	std::numeric_limits< half_float::half >
	Numeric limits for half-precision floats. More...

struct	std::hash< half_float::half >
	Hash function for half-precision floats. More...

Namespaces
	half_float
	Main namespace for half precision functionality.

	half_float::literal
	Library-defined half-precision literals.

	half_float::detail
	Implementation details.

	std
	Extensions to the C++ standard library.

Macros
#define	HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__)
	Combined gcc version number.

#define	HALF_CONSTEXPR constexpr

#define	HALF_CONSTEXPR_CONST constexpr

#define	HALF_NOEXCEPT noexcept

#define	HALF_NOTHROW noexcept

#define	HALF_ROUND_STYLE -1
	Default rounding mode. More...

#define	HALF_ROUND_TIES_TO_EVEN 0
	Tie-breaking behaviour for round to nearest. More...

#define	HUGE_VALH std::numeric_limits<half_float::half>::infinity()
	Value signaling overflow. More...

#define	FP_FAST_FMAH 1
	Fast half-precision fma function. More...

Typedefs
typedef std::uint_least16_t	half_float::detail::uint16
	Unsigned integer of (at least) 16 bits width.

Functions
half	half_float::literal::operator""_h (long double value)
	Half literal. More...

Classification helpers
template<typename T >
bool	half_float::detail::builtin_isinf (T arg)
	Check for infinity. More...

template<typename T >
bool	half_float::detail::builtin_isnan (T arg)
	Check for NaN. More...

template<typename T >
bool	half_float::detail::builtin_signbit (T arg)
	Check sign. More...

Conversion
template<std::float_round_style R>
uint16	half_float::detail::float2half_impl (float value, true_type)
	Convert IEEE single-precision to half-precision. More...

template<std::float_round_style R>
uint16	half_float::detail::float2half_impl (double value, true_type)
	Convert IEEE double-precision to half-precision. More...

template<std::float_round_style R, typename T >
uint16	half_float::detail::float2half_impl (T value,...)
	Convert non-IEEE floating point to half-precision. More...

template<std::float_round_style R, typename T >
uint16	half_float::detail::float2half (T value)
	Convert floating point to half-precision. More...

template<std::float_round_style R, bool S, typename T >
uint16	half_float::detail::int2half_impl (T value)
	Convert integer to half-precision floating point. More...

template<std::float_round_style R, typename T >
uint16	half_float::detail::int2half (T value)
	Convert integer to half-precision floating point. More...

float	half_float::detail::half2float_impl (uint16 value, float, true_type)
	Convert half-precision to IEEE single-precision. More...

double	half_float::detail::half2float_impl (uint16 value, double, true_type)
	Convert half-precision to IEEE double-precision. More...

template<typename T >
T	half_float::detail::half2float_impl (uint16 value, T,...)
	Convert half-precision to non-IEEE floating point. More...

template<typename T >
T	half_float::detail::half2float (uint16 value)
	Convert half-precision to floating point. More...

template<std::float_round_style R, bool E, typename T >
T	half_float::detail::half2int_impl (uint16 value)
	Convert half-precision floating point to integer. More...

template<std::float_round_style R, typename T >
T	half_float::detail::half2int (uint16 value)
	Convert half-precision floating point to integer. More...

template<typename T >
T	half_float::detail::half2int_up (uint16 value)
	Convert half-precision floating point to integer using round-to-nearest-away-from-zero. More...

template<std::float_round_style R, bool E>
uint16	half_float::detail::round_half_impl (uint16 value)
	Round half-precision number to nearest integer value. More...

template<std::float_round_style R>
uint16	half_float::detail::round_half (uint16 value)
	Round half-precision number to nearest integer value. More...

uint16	half_float::detail::round_half_up (uint16 value)
	Round half-precision number to nearest integer value using round-to-nearest-away-from-zero. More...

Comparison operators
template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator== (T x, U y)
	Comparison for equality. More...

template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator!= (T x, U y)
	Comparison for inequality. More...

template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator< (T x, U y)
	Comparison for less than. More...

template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator> (T x, U y)
	Comparison for greater than. More...

template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator<= (T x, U y)
	Comparison for less equal. More...

template<typename T , typename U >
enable< bool, T, U >::type	half_float::detail::operator>= (T x, U y)
	Comparison for greater equal. More...

Arithmetic operators
template<typename T , typename U >
enable< expr, T, U >::type	half_float::detail::operator+ (T x, U y)
	Add halfs. More...

template<typename T , typename U >
enable< expr, T, U >::type	half_float::detail::operator- (T x, U y)
	Subtract halfs. More...

template<typename T , typename U >
enable< expr, T, U >::type	half_float::detail::operator* (T x, U y)
	Multiply halfs. More...

template<typename T , typename U >
enable< expr, T, U >::type	half_float::detail::operator/ (T x, U y)
	Divide halfs. More...

template<typename T >
constexpr enable< T, T >::type	half_float::detail::operator+ (T arg)
	Identity. More...

template<typename T >
constexpr enable< T, T >::type	half_float::detail::operator- (T arg)
	Negation. More...

Input and output
template<typename T , typename charT , typename traits >
enable< std::basic_ostream< charT, traits > &, T >::type	half_float::detail::operator<< (std::basic_ostream< charT, traits > &out, T arg)
	Output operator. More...

template<typename charT , typename traits >
std::basic_istream< charT, traits > &	half_float::detail::operator>> (std::basic_istream< charT, traits > &in, half &arg)
	Input operator. More...

Basic mathematical operations
half	half_float::detail::abs (half arg)
	Absolute value. More...

expr	half_float::detail::abs (expr arg)

half	half_float::detail::fabs (half arg)
	Absolute value. More...

expr	half_float::detail::fabs (expr arg)

expr	half_float::detail::fmod (half x, half y)
	Remainder of division. More...

expr	half_float::detail::fmod (half x, expr y)

expr	half_float::detail::fmod (expr x, half y)

expr	half_float::detail::fmod (expr x, expr y)

expr	half_float::detail::remainder (half x, half y)
	Remainder of division. More...

expr	half_float::detail::remainder (half x, expr y)

expr	half_float::detail::remainder (expr x, half y)

expr	half_float::detail::remainder (expr x, expr y)

expr	half_float::detail::remquo (half x, half y, int *quo)
	Remainder of division. More...

expr	half_float::detail::remquo (half x, expr y, int *quo)

expr	half_float::detail::remquo (expr x, half y, int *quo)

expr	half_float::detail::remquo (expr x, expr y, int *quo)

expr	half_float::detail::fma (half x, half y, half z)
	Fused multiply add. More...

expr	half_float::detail::fma (half x, half y, expr z)

expr	half_float::detail::fma (half x, expr y, half z)

expr	half_float::detail::fma (half x, expr y, expr z)

expr	half_float::detail::fma (expr x, half y, half z)

expr	half_float::detail::fma (expr x, half y, expr z)

expr	half_float::detail::fma (expr x, expr y, half z)

expr	half_float::detail::fma (expr x, expr y, expr z)

half	half_float::detail::fmax (half x, half y)
	Maximum of half expressions. More...

expr	half_float::detail::fmax (half x, expr y)

expr	half_float::detail::fmax (expr x, half y)

expr	half_float::detail::fmax (expr x, expr y)

half	half_float::detail::fmin (half x, half y)
	Minimum of half expressions. More...

expr	half_float::detail::fmin (half x, expr y)

expr	half_float::detail::fmin (expr x, half y)

expr	half_float::detail::fmin (expr x, expr y)

expr	half_float::detail::fdim (half x, half y)
	Positive difference. More...

expr	half_float::detail::fdim (half x, expr y)

expr	half_float::detail::fdim (expr x, half y)

expr	half_float::detail::fdim (expr x, expr y)

half	half_float::detail::nanh (const char *)
	Get NaN value. More...

Exponential functions
expr	half_float::detail::exp (half arg)
	Exponential function. More...

expr	half_float::detail::exp (expr arg)

expr	half_float::detail::expm1 (half arg)
	Exponential minus one. More...

expr	half_float::detail::expm1 (expr arg)

expr	half_float::detail::exp2 (half arg)
	Binary exponential. More...

expr	half_float::detail::exp2 (expr arg)

expr	half_float::detail::log (half arg)
	Natural logorithm. More...

expr	half_float::detail::log (expr arg)

expr	half_float::detail::log10 (half arg)
	Common logorithm. More...

expr	half_float::detail::log10 (expr arg)

expr	half_float::detail::log1p (half arg)
	Natural logorithm. More...

expr	half_float::detail::log1p (expr arg)

expr	half_float::detail::log2 (half arg)
	Binary logorithm. More...

expr	half_float::detail::log2 (expr arg)

Power functions
expr	half_float::detail::sqrt (half arg)
	Square root. More...

expr	half_float::detail::sqrt (expr arg)

expr	half_float::detail::cbrt (half arg)
	Cubic root. More...

expr	half_float::detail::cbrt (expr arg)

expr	half_float::detail::hypot (half x, half y)
	Hypotenuse function. More...

expr	half_float::detail::hypot (half x, expr y)

expr	half_float::detail::hypot (expr x, half y)

expr	half_float::detail::hypot (expr x, expr y)

expr	half_float::detail::pow (half base, half exp)
	Power function. More...

expr	half_float::detail::pow (half base, expr exp)

expr	half_float::detail::pow (expr base, half exp)

expr	half_float::detail::pow (expr base, expr exp)

Trigonometric functions
expr	half_float::detail::sin (half arg)
	Sine function. More...

expr	half_float::detail::sin (expr arg)

expr	half_float::detail::cos (half arg)
	Cosine function. More...

expr	half_float::detail::cos (expr arg)

expr	half_float::detail::tan (half arg)
	Tangent function. More...

expr	half_float::detail::tan (expr arg)

expr	half_float::detail::asin (half arg)
	Arc sine. More...

expr	half_float::detail::asin (expr arg)

expr	half_float::detail::acos (half arg)
	Arc cosine function. More...

expr	half_float::detail::acos (expr arg)

expr	half_float::detail::atan (half arg)
	Arc tangent function. More...

expr	half_float::detail::atan (expr arg)

expr	half_float::detail::atan2 (half x, half y)
	Arc tangent function. More...

expr	half_float::detail::atan2 (half x, expr y)

expr	half_float::detail::atan2 (expr x, half y)

expr	half_float::detail::atan2 (expr x, expr y)

Hyperbolic functions
expr	half_float::detail::sinh (half arg)
	Hyperbolic sine. More...

expr	half_float::detail::sinh (expr arg)

expr	half_float::detail::cosh (half arg)
	Hyperbolic cosine. More...

expr	half_float::detail::cosh (expr arg)

expr	half_float::detail::tanh (half arg)
	Hyperbolic tangent. More...

expr	half_float::detail::tanh (expr arg)

expr	half_float::detail::asinh (half arg)
	Hyperbolic area sine. More...

expr	half_float::detail::asinh (expr arg)

expr	half_float::detail::acosh (half arg)
	Hyperbolic area cosine. More...

expr	half_float::detail::acosh (expr arg)

expr	half_float::detail::atanh (half arg)
	Hyperbolic area tangent. More...

expr	half_float::detail::atanh (expr arg)

Error and gamma functions
expr	half_float::detail::erf (half arg)
	Error function. More...

expr	half_float::detail::erf (expr arg)

expr	half_float::detail::erfc (half arg)
	Complementary error function. More...

expr	half_float::detail::erfc (expr arg)

expr	half_float::detail::lgamma (half arg)
	Natural logarithm of gamma function. More...

expr	half_float::detail::lgamma (expr arg)

expr	half_float::detail::tgamma (half arg)
	Gamma function. More...

expr	half_float::detail::tgamma (expr arg)

Rounding
half	half_float::detail::ceil (half arg)
	Nearest integer not less than half value. More...

half	half_float::detail::ceil (expr arg)

half	half_float::detail::floor (half arg)
	Nearest integer not greater than half value. More...

half	half_float::detail::floor (expr arg)

half	half_float::detail::trunc (half arg)
	Nearest integer not greater in magnitude than half value. More...

half	half_float::detail::trunc (expr arg)

half	half_float::detail::round (half arg)
	Nearest integer. More...

half	half_float::detail::round (expr arg)

long	half_float::detail::lround (half arg)
	Nearest integer. More...

long	half_float::detail::lround (expr arg)

half	half_float::detail::nearbyint (half arg)
	Nearest integer using half's internal rounding mode. More...

half	half_float::detail::nearbyint (expr arg)

half	half_float::detail::rint (half arg)
	Nearest integer using half's internal rounding mode. More...

half	half_float::detail::rint (expr arg)

long	half_float::detail::lrint (half arg)
	Nearest integer using half's internal rounding mode. More...

long	half_float::detail::lrint (expr arg)

long long	half_float::detail::llround (half arg)
	Nearest integer. More...

long long	half_float::detail::llround (expr arg)

long long	half_float::detail::llrint (half arg)
	Nearest integer using half's internal rounding mode. More...

long long	half_float::detail::llrint (expr arg)

Floating point manipulation
half	half_float::detail::frexp (half arg, int *exp)
	Decompress floating point number. More...

half	half_float::detail::frexp (expr arg, int *exp)

half	half_float::detail::ldexp (half arg, int exp)
	Multiply by power of two. More...

half	half_float::detail::ldexp (expr arg, int exp)

half	half_float::detail::modf (half arg, half *iptr)
	Extract integer and fractional parts. More...

half	half_float::detail::modf (expr arg, half *iptr)

half	half_float::detail::scalbn (half arg, int exp)
	Multiply by power of two. More...

half	half_float::detail::scalbn (expr arg, int exp)

half	half_float::detail::scalbln (half arg, long exp)
	Multiply by power of two. More...

half	half_float::detail::scalbln (expr arg, long exp)

int	half_float::detail::ilogb (half arg)
	Extract exponent. More...

int	half_float::detail::ilogb (expr arg)

half	half_float::detail::logb (half arg)
	Extract exponent. More...

half	half_float::detail::logb (expr arg)

half	half_float::detail::nextafter (half from, half to)
	Next representable value. More...

half	half_float::detail::nextafter (half from, expr to)

half	half_float::detail::nextafter (expr from, half to)

half	half_float::detail::nextafter (expr from, expr to)

half	half_float::detail::nexttoward (half from, long double to)
	Next representable value. More...

half	half_float::detail::nexttoward (expr from, long double to)

half	half_float::detail::copysign (half x, half y)
	Take sign. More...

half	half_float::detail::copysign (half x, expr y)

half	half_float::detail::copysign (expr x, half y)

half	half_float::detail::copysign (expr x, expr y)

Floating point classification
int	half_float::detail::fpclassify (half arg)
	Classify floating point value. More...

int	half_float::detail::fpclassify (expr arg)

bool	half_float::detail::isfinite (half arg)
	Check if finite number. More...

bool	half_float::detail::isfinite (expr arg)

bool	half_float::detail::isinf (half arg)
	Check for infinity. More...

bool	half_float::detail::isinf (expr arg)

bool	half_float::detail::isnan (half arg)
	Check for NaN. More...

bool	half_float::detail::isnan (expr arg)

bool	half_float::detail::isnormal (half arg)
	Check if normal number. More...

bool	half_float::detail::isnormal (expr arg)

bool	half_float::detail::signbit (half arg)
	Check sign. More...

bool	half_float::detail::signbit (expr arg)

Comparison
bool	half_float::detail::isgreater (half x, half y)
	Comparison for greater than. More...

bool	half_float::detail::isgreater (half x, expr y)

bool	half_float::detail::isgreater (expr x, half y)

bool	half_float::detail::isgreater (expr x, expr y)

bool	half_float::detail::isgreaterequal (half x, half y)
	Comparison for greater equal. More...

bool	half_float::detail::isgreaterequal (half x, expr y)

bool	half_float::detail::isgreaterequal (expr x, half y)

bool	half_float::detail::isgreaterequal (expr x, expr y)

bool	half_float::detail::isless (half x, half y)
	Comparison for less than. More...

bool	half_float::detail::isless (half x, expr y)

bool	half_float::detail::isless (expr x, half y)

bool	half_float::detail::isless (expr x, expr y)

bool	half_float::detail::islessequal (half x, half y)
	Comparison for less equal. More...

bool	half_float::detail::islessequal (half x, expr y)

bool	half_float::detail::islessequal (expr x, half y)

bool	half_float::detail::islessequal (expr x, expr y)

bool	half_float::detail::islessgreater (half x, half y)
	Comarison for less or greater. More...

bool	half_float::detail::islessgreater (half x, expr y)

bool	half_float::detail::islessgreater (expr x, half y)

bool	half_float::detail::islessgreater (expr x, expr y)

bool	half_float::detail::isunordered (half x, half y)
	Check if unordered. More...

bool	half_float::detail::isunordered (half x, expr y)

bool	half_float::detail::isunordered (expr x, half y)

bool	half_float::detail::isunordered (expr x, expr y)

Casting
template<typename T , typename U >
T	half_float::detail::half_cast (U arg)
	Cast to or from half-precision floating point number. More...

template<typename T , std::float_round_style R, typename U >
T	half_float::detail::half_cast (U arg)
	Cast to or from half-precision floating point number. More...

Variables
constexpr binary_t	half_float::detail::binary = binary_t()
	Tag for binary construction.

Detailed Description

Main header file for half precision functionality.

Definition in file half.hpp.

Macro Definition Documentation

◆ HALF_ROUND_STYLE

#define HALF_ROUND_STYLE -1

Default rounding mode.

This specifies the rounding mode used for all conversions between halfs and floats as well as for the half_cast() if not specifying a rounding mode explicitly. It can be redefined (before including half.hpp) to one of the standard rounding modes using their respective constants or the equivalent values of std::float_round_style:

`std::float_round_style`	value	rounding
`std::round_indeterminate`	-1	fastest (default)
`std::round_toward_zero`	0	toward zero
`std::round_to_nearest`	1	to nearest
`std::round_toward_infinity`	2	toward positive infinity
`std::round_toward_neg_infinity`	3	toward negative infinity

By default this is set to -1 (std::round_indeterminate), which uses truncation (round toward zero, but with overflows set to infinity) and is the fastest rounding mode possible. It can even be set to std::numeric_limits<float>::round_style to synchronize the rounding mode with that of the underlying single-precision implementation.

Definition at line 214 of file half.hpp.

◆ HALF_ROUND_TIES_TO_EVEN

#define HALF_ROUND_TIES_TO_EVEN 0

Tie-breaking behaviour for round to nearest.

This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is defined to 0 resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and thus equal to the round() function), but can be redefined to 1 (before including half.hpp) if more IEEE-conformant behaviour is needed.

Definition at line 223 of file half.hpp.

◆ HUGE_VALH

#define HUGE_VALH std::numeric_limits<half_float::half>::infinity()

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.

Definition at line 229 of file half.hpp.

◆ FP_FAST_FMAH

#define FP_FAST_FMAH 1

Fast half-precision fma function.

This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all arithmetic operations, this is in fact always the case.

Definition at line 235 of file half.hpp.

/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-half/checkouts/latest/include/half.hpp File Reference

/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-half/checkouts/latest/include/half.hpp File Reference#

Classes

Namespaces

Macros

Typedefs

Functions

Variables