Implementation details. More...

Classes
struct	conditional
	Conditional type. More...

struct	bool_type
	Helper for tag dispatching. More...

struct	is_float
	Type traits for floating point types. More...

struct	bits
	Type traits for floating point bits. More...

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

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

struct	binary_t
	Tag type for binary construction. More...

struct	expr
	Temporary half-precision expression. More...

struct	enable
	SFINAE helper for generic half-precision functions. More...

struct	result
	Return type for specialized generic 2-argument half-precision functions. More...

struct	unary_specialized
	Wrapper for unary half-precision functions needing specialization for individual argument types. More...

struct	binary_specialized
	Wrapper for binary half-precision functions needing specialization for individual argument types. More...

struct	half_caster
	Helper class for half casts. More...

struct	functions
	Wrapper implementing unspecialized half-precision functions. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

template<typename T >
T	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	round_half_impl (uint16 value)
	Round half-precision number to nearest integer value. More...

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

uint16	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	operator== (T x, U y)
	Comparison for equality. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

expr	abs (expr arg)

half	fabs (half arg)
	Absolute value. More...

expr	fabs (expr arg)

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

expr	fmod (half x, expr y)

expr	fmod (expr x, half y)

expr	fmod (expr x, expr y)

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

expr	remainder (half x, expr y)

expr	remainder (expr x, half y)

expr	remainder (expr x, expr y)

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

expr	remquo (half x, expr y, int *quo)

expr	remquo (expr x, half y, int *quo)

expr	remquo (expr x, expr y, int *quo)

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

expr	fma (half x, half y, expr z)

expr	fma (half x, expr y, half z)

expr	fma (half x, expr y, expr z)

expr	fma (expr x, half y, half z)

expr	fma (expr x, half y, expr z)

expr	fma (expr x, expr y, half z)

expr	fma (expr x, expr y, expr z)

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

expr	fmax (half x, expr y)

expr	fmax (expr x, half y)

expr	fmax (expr x, expr y)

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

expr	fmin (half x, expr y)

expr	fmin (expr x, half y)

expr	fmin (expr x, expr y)

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

expr	fdim (half x, expr y)

expr	fdim (expr x, half y)

expr	fdim (expr x, expr y)

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

Exponential functions
expr	exp (half arg)
	Exponential function. More...

expr	exp (expr arg)

expr	expm1 (half arg)
	Exponential minus one. More...

expr	expm1 (expr arg)

expr	exp2 (half arg)
	Binary exponential. More...

expr	exp2 (expr arg)

expr	log (half arg)
	Natural logorithm. More...

expr	log (expr arg)

expr	log10 (half arg)
	Common logorithm. More...

expr	log10 (expr arg)

expr	log1p (half arg)
	Natural logorithm. More...

expr	log1p (expr arg)

expr	log2 (half arg)
	Binary logorithm. More...

expr	log2 (expr arg)

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

expr	sqrt (expr arg)

expr	cbrt (half arg)
	Cubic root. More...

expr	cbrt (expr arg)

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

expr	hypot (half x, expr y)

expr	hypot (expr x, half y)

expr	hypot (expr x, expr y)

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

expr	pow (half base, expr exp)

expr	pow (expr base, half exp)

expr	pow (expr base, expr exp)

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

expr	sin (expr arg)

expr	cos (half arg)
	Cosine function. More...

expr	cos (expr arg)

expr	tan (half arg)
	Tangent function. More...

expr	tan (expr arg)

expr	asin (half arg)
	Arc sine. More...

expr	asin (expr arg)

expr	acos (half arg)
	Arc cosine function. More...

expr	acos (expr arg)

expr	atan (half arg)
	Arc tangent function. More...

expr	atan (expr arg)

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

expr	atan2 (half x, expr y)

expr	atan2 (expr x, half y)

expr	atan2 (expr x, expr y)

Hyperbolic functions
expr	sinh (half arg)
	Hyperbolic sine. More...

expr	sinh (expr arg)

expr	cosh (half arg)
	Hyperbolic cosine. More...

expr	cosh (expr arg)

expr	tanh (half arg)
	Hyperbolic tangent. More...

expr	tanh (expr arg)

expr	asinh (half arg)
	Hyperbolic area sine. More...

expr	asinh (expr arg)

expr	acosh (half arg)
	Hyperbolic area cosine. More...

expr	acosh (expr arg)

expr	atanh (half arg)
	Hyperbolic area tangent. More...

expr	atanh (expr arg)

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

expr	erf (expr arg)

expr	erfc (half arg)
	Complementary error function. More...

expr	erfc (expr arg)

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

expr	lgamma (expr arg)

expr	tgamma (half arg)
	Gamma function. More...

expr	tgamma (expr arg)

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

half	ceil (expr arg)

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

half	floor (expr arg)

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

half	trunc (expr arg)

half	round (half arg)
	Nearest integer. More...

half	round (expr arg)

long	lround (half arg)
	Nearest integer. More...

long	lround (expr arg)

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

half	nearbyint (expr arg)

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

half	rint (expr arg)

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

long	lrint (expr arg)

long long	llround (half arg)
	Nearest integer. More...

long long	llround (expr arg)

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

long long	llrint (expr arg)

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

half	frexp (expr arg, int *exp)

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

half	ldexp (expr arg, int exp)

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

half	modf (expr arg, half *iptr)

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

half	scalbn (expr arg, int exp)

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

half	scalbln (expr arg, long exp)

int	ilogb (half arg)
	Extract exponent. More...

int	ilogb (expr arg)

half	logb (half arg)
	Extract exponent. More...

half	logb (expr arg)

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

half	nextafter (half from, expr to)

half	nextafter (expr from, half to)

half	nextafter (expr from, expr to)

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

half	nexttoward (expr from, long double to)

half	copysign (half x, half y)
	Take sign. More...

half	copysign (half x, expr y)

half	copysign (expr x, half y)

half	copysign (expr x, expr y)

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

int	fpclassify (expr arg)

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

bool	isfinite (expr arg)

bool	isinf (half arg)
	Check for infinity. More...

bool	isinf (expr arg)

bool	isnan (half arg)
	Check for NaN. More...

bool	isnan (expr arg)

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

bool	isnormal (expr arg)

bool	signbit (half arg)
	Check sign. More...

bool	signbit (expr arg)

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

bool	isgreater (half x, expr y)

bool	isgreater (expr x, half y)

bool	isgreater (expr x, expr y)

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

bool	isgreaterequal (half x, expr y)

bool	isgreaterequal (expr x, half y)

bool	isgreaterequal (expr x, expr y)

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

bool	isless (half x, expr y)

bool	isless (expr x, half y)

bool	isless (expr x, expr y)

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

bool	islessequal (half x, expr y)

bool	islessequal (expr x, half y)

bool	islessequal (expr x, expr y)

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

bool	islessgreater (half x, expr y)

bool	islessgreater (expr x, half y)

bool	islessgreater (expr x, expr y)

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

bool	isunordered (half x, expr y)

bool	isunordered (expr x, half y)

bool	isunordered (expr x, expr y)

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

Variables
constexpr binary_t	binary = binary_t()
	Tag for binary construction.

Detailed Description

Implementation details.

Function Documentation

◆ builtin_isinf()

template<typename T >

bool half_float::detail::builtin_isinf ( T arg )

Check for infinity.

Template Parameters

T	argument type (builtin floating point type)

Parameters

arg	value to query

Return values

true	if infinity
false	else

Definition at line 404 of file half.hpp.

◆ builtin_isnan()

template<typename T >

bool half_float::detail::builtin_isnan ( T arg )

Check for NaN.

Template Parameters

T	argument type (builtin floating point type)

Parameters

arg	value to query

Return values

true	if not a number
false	else

Definition at line 420 of file half.hpp.

◆ builtin_signbit()

template<typename T >

bool half_float::detail::builtin_signbit ( T arg )

Check sign.

Template Parameters

T	argument type (builtin floating point type)

Parameters

arg	value to query

Return values

true	if signbit set
false	else

Definition at line 436 of file half.hpp.

◆ float2half_impl() [1/3]

template<std::float_round_style R>

uint16 half_float::detail::float2half_impl	(	float	value,
		true_type
	)

Convert IEEE single-precision to half-precision.

Credit for this goes to Jeroen van der Zijp.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding

Parameters

value single-precision value

Returns: binary representation of half-precision value

Definition at line 454 of file half.hpp.

◆ float2half_impl() [2/3]

template<std::float_round_style R>

uint16 half_float::detail::float2half_impl	(	double	value,
		true_type
	)

Convert IEEE double-precision to half-precision.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding

Parameters

value double-precision value

Returns: binary representation of half-precision value

Definition at line 574 of file half.hpp.

◆ float2half_impl() [3/3]

template<std::float_round_style R, typename T >

uint16 half_float::detail::float2half_impl	(	T	value,
			...
	)

Convert non-IEEE floating point to half-precision.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
T	source type (builtin floating point type)

Parameters

value floating point value

Returns: binary representation of half-precision value

Definition at line 632 of file half.hpp.

◆ float2half()

template<std::float_round_style R, typename T >

uint16 half_float::detail::float2half ( T value )

Convert floating point to half-precision.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
T	source type (builtin floating point type)

Parameters

value floating point value

Returns: binary representation of half-precision value

Definition at line 681 of file half.hpp.

◆ int2half_impl()

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.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
S	`true` if value negative, `false` else
T	type to convert (builtin integer type)

Parameters

value non-negative integral value

Returns: binary representation of half-precision value

Definition at line 692 of file half.hpp.

◆ int2half()

template<std::float_round_style R, typename T >

uint16 half_float::detail::int2half ( T value )

Convert integer to half-precision floating point.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
T	type to convert (builtin integer type)

Parameters

value integral value

Returns: binary representation of half-precision value

Definition at line 737 of file half.hpp.

◆ half2float_impl() [1/3]

float half_float::detail::half2float_impl	(	uint16	value,
		float	,
		true_type
	)

inline

Convert half-precision to IEEE single-precision.

Credit for this goes to Jeroen van der Zijp.

Parameters

value binary representation of half-precision value

Returns: single-precision value

Definition at line 746 of file half.hpp.

◆ half2float_impl() [2/3]

double half_float::detail::half2float_impl	(	uint16	value,
		double	,
		true_type
	)

inline

Convert half-precision to IEEE double-precision.

Parameters

value binary representation of half-precision value

Returns: double-precision value

Definition at line 904 of file half.hpp.

◆ half2float_impl() [3/3]

template<typename T >

T half_float::detail::half2float_impl	(	uint16	value,
		T	,
			...
	)

Convert half-precision to non-IEEE floating point.

Template Parameters

T	type to convert to (builtin integer type)

Parameters

value binary representation of half-precision value

Returns: floating point value

Definition at line 927 of file half.hpp.

◆ half2float()

template<typename T >

T half_float::detail::half2float ( uint16 value )

Convert half-precision to floating point.

Template Parameters

T	type to convert to (builtin integer type)

Parameters

value binary representation of half-precision value

Returns: floating point value

Definition at line 946 of file half.hpp.

◆ half2int_impl()

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.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
E	`true` for round to even, `false` for round away from zero
T	type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)

Parameters

value binary representation of half-precision value

Returns: integral value

Definition at line 957 of file half.hpp.

◆ half2int()

template<std::float_round_style R, typename T >

T half_float::detail::half2int ( uint16 value )

Convert half-precision floating point to integer.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
T	type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)

Parameters

value binary representation of half-precision value

Returns: integral value

Definition at line 995 of file half.hpp.

◆ half2int_up()

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.

Template Parameters

T	type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)

Parameters

value binary representation of half-precision value

Returns: integral value

Definition at line 1001 of file half.hpp.

◆ round_half_impl()

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.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding
E	`true` for round to even, `false` for round away from zero

Parameters

value binary representation of half-precision value

Returns: half-precision bits for nearest integral value

Definition at line 1008 of file half.hpp.

◆ round_half()

template<std::float_round_style R>

uint16 half_float::detail::round_half ( uint16 value )

Round half-precision number to nearest integer value.

Template Parameters

R	rounding mode to use, `std::round_indeterminate` for fastest rounding

Parameters

value binary representation of half-precision value

Returns: half-precision bits for nearest integral value

Definition at line 1041 of file half.hpp.

◆ round_half_up()

uint16 half_float::detail::round_half_up ( uint16 value )

inline

Round half-precision number to nearest integer value using round-to-nearest-away-from-zero.

Parameters

value binary representation of half-precision value

Returns: half-precision bits for nearest integral value

Definition at line 1046 of file half.hpp.

◆ operator==()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator==	(	T	x,
		U	y
	)

Comparison for equality.

Parameters

x	first operand
y	second operand

Return values

true	if operands equal
false	else

Definition at line 2118 of file half.hpp.

◆ operator!=()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator!=	(	T	x,
		U	y
	)

Comparison for inequality.

Parameters

x	first operand
y	second operand

Return values

true	if operands not equal
false	else

Definition at line 2125 of file half.hpp.

◆ operator<()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator<	(	T	x,
		U	y
	)

Comparison for less than.

Parameters

x	first operand
y	second operand

Return values

true	if x less than y
false	else

Definition at line 2132 of file half.hpp.

◆ operator>()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator>	(	T	x,
		U	y
	)

Comparison for greater than.

Parameters

x	first operand
y	second operand

Return values

true	if x greater than y
false	else

Definition at line 2139 of file half.hpp.

◆ operator<=()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator<=	(	T	x,
		U	y
	)

Comparison for less equal.

Parameters

x	first operand
y	second operand

Return values

true	if x less equal y
false	else

Definition at line 2146 of file half.hpp.

◆ operator>=()

template<typename T , typename U >

enable<bool,T,U>::type half_float::detail::operator>=	(	T	x,
		U	y
	)

Comparison for greater equal.

Parameters

x	first operand
y	second operand

Return values

true	if x greater equal y
false	else

Definition at line 2153 of file half.hpp.

◆ operator+() [1/2]

template<typename T , typename U >

enable<expr,T,U>::type half_float::detail::operator+	(	T	x,
		U	y
	)

Add halfs.

Parameters

x	left operand
y	right operand

Returns: sum of half expressions

Definition at line 2163 of file half.hpp.

◆ operator-() [1/2]

template<typename T , typename U >

enable<expr,T,U>::type half_float::detail::operator-	(	T	x,
		U	y
	)

Subtract halfs.

Parameters

x	left operand
y	right operand

Returns: difference of half expressions

Definition at line 2169 of file half.hpp.

◆ operator*()

template<typename T , typename U >

enable<expr,T,U>::type half_float::detail::operator*	(	T	x,
		U	y
	)

Multiply halfs.

Parameters

x	left operand
y	right operand

Returns: product of half expressions

Definition at line 2175 of file half.hpp.

◆ operator/()

template<typename T , typename U >

enable<expr,T,U>::type half_float::detail::operator/	(	T	x,
		U	y
	)

Divide halfs.

Parameters

x	left operand
y	right operand

Returns: quotient of half expressions

Definition at line 2181 of file half.hpp.

◆ operator+() [2/2]

template<typename T >

constexpr enable<T,T>::type half_float::detail::operator+ ( T arg )

constexpr

Identity.

Parameters

arg operand

Returns: uncahnged operand

Definition at line 2186 of file half.hpp.

◆ operator-() [2/2]

template<typename T >

constexpr enable<T,T>::type half_float::detail::operator- ( T arg )

constexpr

Negation.

Parameters

arg operand

Returns: negated operand

Definition at line 2191 of file half.hpp.

◆ operator<<()

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.

Parameters

out	output stream to write into
arg	half expression to write

Returns: reference to output stream

Definition at line 2201 of file half.hpp.

◆ operator>>()

template<typename charT , typename traits >

std::basic_istream<charT,traits>& half_float::detail::operator>>	(	std::basic_istream< charT, traits > &	in,
		half &	arg
	)

Input operator.

Parameters

in	input stream to read from
arg	half to read into

Returns: reference to input stream

Definition at line 2209 of file half.hpp.

◆ abs()

half half_float::detail::abs ( half arg )

inline

Absolute value.

Parameters

arg operand

Returns: absolute value of arg

Definition at line 2219 of file half.hpp.

◆ fabs()

half half_float::detail::fabs ( half arg )

inline

Absolute value.

Parameters

arg operand

Returns: absolute value of arg

Definition at line 2226 of file half.hpp.

◆ fmod()

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

inline

Remainder of division.

Parameters

x	first operand
y	second operand

Returns: remainder of floating point division.

Definition at line 2234 of file half.hpp.

◆ remainder()

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

inline

Remainder of division.

Parameters

x	first operand
y	second operand

Returns: remainder of floating point division.

Definition at line 2244 of file half.hpp.

◆ remquo()

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

inline

Remainder of division.

Parameters

x	first operand
y	second operand
quo	address to store some bits of quotient at

Returns: remainder of floating point division.

Definition at line 2255 of file half.hpp.

◆ fma()

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

inline

Fused multiply add.

Parameters

x	first operand
y	second operand
z	third operand

Returns: ( x * y ) + z rounded as one operation.

Definition at line 2266 of file half.hpp.

◆ fmax()

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

inline

Maximum of half expressions.

Parameters

x	first operand
y	second operand

Returns: maximum of operands

Definition at line 2280 of file half.hpp.

◆ fmin()

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

inline

Minimum of half expressions.

Parameters

x	first operand
y	second operand

Returns: minimum of operands

Definition at line 2290 of file half.hpp.

◆ fdim()

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

inline

Positive difference.

Parameters

x	first operand
y	second operand

Returns: x - y or 0 if difference negative

Definition at line 2300 of file half.hpp.

◆ nanh()

half half_float::detail::nanh ( const char * )

inline

Get NaN value.

Returns: quiet NaN

Definition at line 2307 of file half.hpp.

◆ exp()

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

inline

Exponential function.

Parameters

arg	function argument

Returns: e raised to arg

Definition at line 2317 of file half.hpp.

◆ expm1()

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

inline

Exponential minus one.

Parameters

arg	function argument

Returns: e raised to arg subtracted by 1

Definition at line 2324 of file half.hpp.

◆ exp2()

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

inline

Binary exponential.

Parameters

arg	function argument

Returns: 2 raised to arg

Definition at line 2331 of file half.hpp.

◆ log()

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

inline

Natural logorithm.

Parameters

arg	function argument

Returns: logarithm of arg to base e

Definition at line 2338 of file half.hpp.

◆ log10()

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

inline

Common logorithm.

Parameters

arg	function argument

Returns: logarithm of arg to base 10

Definition at line 2345 of file half.hpp.

◆ log1p()

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

inline

Natural logorithm.

Parameters

arg	function argument

Returns: logarithm of arg plus 1 to base e

Definition at line 2352 of file half.hpp.

◆ log2()

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

inline

Binary logorithm.

Parameters

arg	function argument

Returns: logarithm of arg to base 2

Definition at line 2359 of file half.hpp.

◆ sqrt()

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

inline

Square root.

Parameters

arg	function argument

Returns: square root of arg

Definition at line 2370 of file half.hpp.

◆ cbrt()

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

inline

Cubic root.

Parameters

arg	function argument

Returns: cubic root of arg

Definition at line 2377 of file half.hpp.

◆ hypot()

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

inline

Hypotenuse function.

Parameters

x	first argument
y	second argument

Returns: square root of sum of squares without internal over- or underflows

Definition at line 2385 of file half.hpp.

◆ pow()

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

inline

Power function.

Parameters

base	first argument
exp	second argument

Returns: base raised to exp

Definition at line 2395 of file half.hpp.

◆ sin()

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

inline

Sine function.

Parameters

arg	function argument

Returns: sine value of arg

Definition at line 2408 of file half.hpp.

◆ cos()

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

inline

Cosine function.

Parameters

arg	function argument

Returns: cosine value of arg

Definition at line 2415 of file half.hpp.

◆ tan()

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

inline

Tangent function.

Parameters

arg	function argument

Returns: tangent value of arg

Definition at line 2422 of file half.hpp.

◆ asin()

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

inline

Arc sine.

Parameters

arg	function argument

Returns: arc sine value of arg

Definition at line 2429 of file half.hpp.

◆ acos()

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

inline

Arc cosine function.

Parameters

arg	function argument

Returns: arc cosine value of arg

Definition at line 2436 of file half.hpp.

◆ atan()

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

inline

Arc tangent function.

Parameters

arg	function argument

Returns: arc tangent value of arg

Definition at line 2443 of file half.hpp.

◆ atan2()

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

inline

Arc tangent function.

Parameters

x	first argument
y	second argument

Returns: arc tangent value

Definition at line 2451 of file half.hpp.

◆ sinh()

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

inline

Hyperbolic sine.

Parameters

arg	function argument

Returns: hyperbolic sine value of arg

Definition at line 2464 of file half.hpp.

◆ cosh()

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

inline

Hyperbolic cosine.

Parameters

arg	function argument

Returns: hyperbolic cosine value of arg

Definition at line 2471 of file half.hpp.

◆ tanh()

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

inline

Hyperbolic tangent.

Parameters

arg	function argument

Returns: hyperbolic tangent value of arg

Definition at line 2478 of file half.hpp.

◆ asinh()

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

inline

Hyperbolic area sine.

Parameters

arg	function argument

Returns: area sine value of arg

Definition at line 2485 of file half.hpp.

◆ acosh()

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

inline

Hyperbolic area cosine.

Parameters

arg	function argument

Returns: area cosine value of arg

Definition at line 2492 of file half.hpp.

◆ atanh()

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

inline

Hyperbolic area tangent.

Parameters

arg	function argument

Returns: area tangent value of arg

Definition at line 2499 of file half.hpp.

◆ erf()

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

inline

Error function.

Parameters

arg	function argument

Returns: error function value of arg

Definition at line 2510 of file half.hpp.

◆ erfc()

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

inline

Complementary error function.

Parameters

arg	function argument

Returns: 1 minus error function value of arg

Definition at line 2517 of file half.hpp.

◆ lgamma()

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

inline

Natural logarithm of gamma function.

Parameters

arg	function argument

Returns: natural logarith of gamma function for arg

Definition at line 2524 of file half.hpp.

◆ tgamma()

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

inline

Gamma function.

Parameters

arg	function argument

Returns: gamma function value of arg

Definition at line 2531 of file half.hpp.

◆ ceil()

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

inline

Nearest integer not less than half value.

Parameters

arg	half to round

Returns: nearest integer not less than arg

Definition at line 2542 of file half.hpp.

◆ floor()

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

inline

Nearest integer not greater than half value.

Parameters

arg	half to round

Returns: nearest integer not greater than arg

Definition at line 2549 of file half.hpp.

◆ trunc()

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

inline

Nearest integer not greater in magnitude than half value.

Parameters

arg	half to round

Returns: nearest integer not greater in magnitude than arg

Definition at line 2556 of file half.hpp.

◆ round()

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

inline

Nearest integer.

Parameters

arg	half to round

Returns: nearest integer, rounded away from zero in half-way cases

Definition at line 2563 of file half.hpp.

◆ lround()

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

inline

Nearest integer.

Parameters

arg	half to round

Returns: nearest integer, rounded away from zero in half-way cases

Definition at line 2570 of file half.hpp.

◆ nearbyint()

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

inline

Nearest integer using half's internal rounding mode.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Definition at line 2577 of file half.hpp.

◆ rint()

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

inline

Nearest integer using half's internal rounding mode.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Definition at line 2584 of file half.hpp.

◆ lrint()

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

inline

Nearest integer using half's internal rounding mode.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Definition at line 2591 of file half.hpp.

◆ llround()

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

inline

Nearest integer.

Parameters

arg	half to round

Returns: nearest integer, rounded away from zero in half-way cases

Definition at line 2598 of file half.hpp.

◆ llrint()

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

inline

Nearest integer using half's internal rounding mode.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Definition at line 2605 of file half.hpp.

◆ frexp()

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

inline

Decompress floating point number.

Parameters

arg	number to decompress
exp	address to store exponent at

Returns: significant in range [0.5, 1)

Definition at line 2618 of file half.hpp.

◆ ldexp()

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

inline

Multiply by power of two.

Parameters

arg	number to modify
exp	power of two to multiply with

Returns: arg multplied by 2 raised to exp

Definition at line 2626 of file half.hpp.

◆ modf()

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

inline

Extract integer and fractional parts.

Parameters

arg	number to decompress
iptr	address to store integer part at

Returns: fractional part

Definition at line 2634 of file half.hpp.

◆ scalbn()

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

inline

Multiply by power of two.

Parameters

arg	number to modify
exp	power of two to multiply with

Returns: arg multplied by 2 raised to exp

Definition at line 2642 of file half.hpp.

◆ scalbln()

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

inline

Multiply by power of two.

Parameters

arg	number to modify
exp	power of two to multiply with

Returns: arg multplied by 2 raised to exp

Definition at line 2650 of file half.hpp.

◆ ilogb()

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

inline

Extract exponent.

Parameters

arg	number to query

Returns: floating point exponent

Return values

FP_ILOGB0	for zero
FP_ILOGBNAN	for NaN
MAX_INT	for infinity

Definition at line 2660 of file half.hpp.

◆ logb()

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

inline

Extract exponent.

Parameters

arg	number to query

Returns: floating point exponent

Definition at line 2667 of file half.hpp.

◆ nextafter()

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

inline

Next representable value.

Parameters

from	value to compute next representable value for
to	direction towards which to compute next value

Returns: next representable value after from in direction towards to

Definition at line 2675 of file half.hpp.

◆ nexttoward()

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

inline

Next representable value.

Parameters

from	value to compute next representable value for
to	direction towards which to compute next value

Returns: next representable value after from in direction towards to

Definition at line 2685 of file half.hpp.

◆ copysign()

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

inline

Take sign.

Parameters

x	value to change sign for
y	value to take sign from

Returns: value equal to x in magnitude and to y in sign

Definition at line 2693 of file half.hpp.

◆ fpclassify()

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

inline

Classify floating point value.

Parameters

arg	number to classify

Return values

FP_ZERO	for positive and negative zero
FP_SUBNORMAL	for subnormal numbers
FP_INFINITY	for positive and negative infinity
FP_NAN	for NaNs
FP_NORMAL	for all other (normal) values

Definition at line 2711 of file half.hpp.

◆ isfinite()

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

inline

Check if finite number.

Parameters

arg	number to check

Return values

true	if neither infinity nor NaN
false	else

Definition at line 2719 of file half.hpp.

◆ isinf()

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

inline

Check for infinity.

Parameters

arg	number to check

Return values

true	for positive or negative infinity
false	else

Definition at line 2727 of file half.hpp.

◆ isnan()

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

inline

Check for NaN.

Parameters

arg	number to check

Return values

true	for NaNs
false	else

Definition at line 2735 of file half.hpp.

◆ isnormal()

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

inline

Check if normal number.

Parameters

arg	number to check

Return values

true	if normal number
false	if either subnormal, zero, infinity or NaN

Definition at line 2743 of file half.hpp.

◆ signbit()

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

inline

Check sign.

Parameters

arg	number to check

Return values

true	for negative number
false	for positive number

Definition at line 2751 of file half.hpp.

◆ isgreater()

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

inline

Comparison for greater than.

Parameters

x	first operand
y	second operand

Return values

true	if x greater than y
false	else

Definition at line 2764 of file half.hpp.

◆ isgreaterequal()

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

inline

Comparison for greater equal.

Parameters

x	first operand
y	second operand

Return values

true	if x greater equal y
false	else

Definition at line 2775 of file half.hpp.

◆ isless()

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

inline

Comparison for less than.

Parameters

x	first operand
y	second operand

Return values

true	if x less than y
false	else

Definition at line 2786 of file half.hpp.

◆ islessequal()

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

inline

Comparison for less equal.

Parameters

x	first operand
y	second operand

Return values

true	if x less equal y
false	else

Definition at line 2797 of file half.hpp.

◆ islessgreater()

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

inline

Comarison for less or greater.

Parameters

x	first operand
y	second operand

Return values

true	if either less or greater
false	else

Definition at line 2808 of file half.hpp.

◆ isunordered()

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

inline

Check if unordered.

Parameters

x	first operand
y	second operand

Return values

true	if unordered (one or two NaN operands)
false	else

Definition at line 2819 of file half.hpp.

◆ half_cast() [1/2]

template<typename T , typename U >

T half_float::detail::half_cast ( U arg )

Cast to or from half-precision floating point number.

This casts between half and any built-in arithmetic type. The values are converted directly using the given rounding mode, without any roundtrip over float that a static_cast would otherwise do. It uses the default rounding mode.

Using this cast with neither of the two types being a half or with any of the two types not being a built-in arithmetic type (apart from half, of course) results in a compiler error and casting between halfs is just a no-op.

Template Parameters

T	destination type (half or built-in arithmetic type)
U	source type (half or built-in arithmetic type)

Parameters

arg	value to cast

Returns: arg converted to destination type

Definition at line 2839 of file half.hpp.

◆ half_cast() [2/2]

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.

This casts between half and any built-in arithmetic type. The values are converted directly using the given rounding mode, without any roundtrip over float that a static_cast would otherwise do.

Using this cast with neither of the two types being a half or with any of the two types not being a built-in arithmetic type (apart from half, of course) results in a compiler error and casting between halfs is just a no-op.

Template Parameters

T	destination type (half or built-in arithmetic type)
R	rounding mode to use.
U	source type (half or built-in arithmetic type)

Parameters

arg	value to cast

Returns: arg converted to destination type

Definition at line 2853 of file half.hpp.

detail Namespace Reference

detail Namespace Reference#

Classes

Typedefs

Functions

Variables

Detailed Description

Function Documentation

◆ builtin_isinf()

◆ builtin_isnan()

◆ builtin_signbit()

◆ float2half_impl() [1/3]

◆ float2half_impl() [2/3]

◆ float2half_impl() [3/3]

◆ float2half()

◆ int2half_impl()

◆ int2half()

◆ half2float_impl() [1/3]

◆ half2float_impl() [2/3]

◆ half2float_impl() [3/3]

◆ half2float()

◆ half2int_impl()

◆ half2int()

◆ half2int_up()

◆ round_half_impl()

◆ round_half()

◆ round_half_up()

◆ operator==()

◆ operator!=()

◆ operator<()

◆ operator>()

◆ operator<=()

◆ operator>=()

◆ operator+() [1/2]

◆ operator-() [1/2]

◆ operator*()

◆ operator/()

◆ operator+() [2/2]

◆ operator-() [2/2]

◆ operator<<()

◆ operator>>()

◆ abs()

◆ fabs()

◆ fmod()

◆ remainder()

◆ remquo()

◆ fma()

◆ fmax()

◆ fmin()

◆ fdim()

◆ nanh()

◆ exp()

◆ expm1()

◆ exp2()

◆ log()

◆ log10()

◆ log1p()

◆ log2()

◆ sqrt()

◆ cbrt()

◆ hypot()

◆ pow()

◆ sin()

◆ cos()

◆ tan()

◆ asin()

◆ acos()

◆ atan()

◆ atan2()

◆ sinh()

◆ cosh()

◆ tanh()

◆ asinh()

◆ acosh()

◆ atanh()

◆ erf()

◆ erfc()

◆ lgamma()

◆ tgamma()

◆ ceil()