Half-precision floating-point type. More...

#include <float16_t.hpp>

Public Member Functions
detail::uint16	get_data () const

Construction and assignment
constexpr	half () noexcept
	Default constructor.

template<detail::arithmetic T>
	half (T rhs)
	Conversion constructor.

	operator float () const
	Conversion to single-precision.

half &	operator= (const float &rhs)
	Assignment operator.

template<detail::arithmetic T>
half &	operator= (const T &rhs)

Arithmetic updates
half &	operator+= (half rhs)
	Arithmetic assignment.

half &	operator-= (half rhs)
	Arithmetic assignment.

half &	operator*= (half rhs)
	Arithmetic assignment.

half &	operator/= (half rhs)
	Arithmetic assignment.

Increment and decrement
half &	operator++ ()
	Prefix increment.

half &	operator-- ()
	Prefix decrement.

half	operator++ (int)
	Postfix increment.

half	operator-- (int)
	Postfix decrement.

Friends
template<class, class, std::float_round_style>
struct	detail::half_caster

class	std::numeric_limits< half >

struct	std::hash< half >

constexpr_NOERR bool	operator== (half x, half y)
	Comparison for equality.

template<detail::arithmetic T>
constexpr_NOERR bool	operator== (half x, T y)

constexpr_NOERR std::partial_ordering	operator<=> (half x, half y)

template<detail::arithmetic T>
constexpr_NOERR std::partial_ordering	operator<=> (half x, T y)

constexpr half	operator+ (half arg)
	Identity.

constexpr half	operator- (half arg)
	Negation.

half	operator+ (half x, half y)
	Addition.

template<class T>
half	operator+ (half x, T y)

template<class T>
half	operator+ (T x, half y)

half	operator- (half x, half y)
	Subtraction.

template<class T>
half	operator- (half x, T y)

template<class T>
half	operator- (T x, half y)

half	operator* (half x, half y)
	Multiplication.

template<class T>
half	operator* (half x, T y)

template<class T>
half	operator* (T x, half y)

half	operator/ (half x, half y)
	Division.

template<class T>
half	operator/ (half x, T y)

template<class T>
half	operator/ (T x, half y)

template<class charT, class traits>
std::basic_ostream< charT, traits > &	operator<< (std::basic_ostream< charT, traits > &out, half arg)
	Output operator.

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

constexpr half	fabs (half arg)
	Absolute value.

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

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

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

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

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

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

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

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

half	exp (half arg)
	Exponential function.

half	exp2 (half arg)
	Binary exponential.

half	expm1 (half arg)
	Exponential minus one.

half	log (half arg)
	Natural logarithm.

half	log10 (half arg)
	Common logarithm.

half	log2 (half arg)
	Binary logarithm.

half	log1p (half arg)
	Natural logarithm plus one.

half	sqrt (half arg)
	Square root.

half	cbrt (half arg)
	Cubic root.

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

half	hypot (half x, half y, half z)
	Hypotenuse function.

half	pow (half x, half y)
	Power function.

void	sincos (half arg, half sin, half cos)
	Compute sine and cosine simultaneously.

half	sin (half arg)
	Sine function.

half	cos (half arg)
	Cosine function.

half	tan (half arg)
	Tangent function.

half	asin (half arg)
	Arc sine.

half	acos (half arg)
	Arc cosine function.

half	atan (half arg)
	Arc tangent function.

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

half	sinh (half arg)
	Hyperbolic sine.

half	cosh (half arg)
	Hyperbolic cosine.

half	tanh (half arg)
	Hyperbolic tangent.

half	asinh (half arg)
	Hyperbolic area sine.

half	acosh (half arg)
	Hyperbolic area cosine.

half	atanh (half arg)
	Hyperbolic area tangent.

half	erf (half arg)
	Error function.

half	erfc (half arg)
	Complementary error function.

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

half	tgamma (half arg)
	Gamma function.

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

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

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

half	round (half arg)
	Nearest integer.

long	lround (half arg)
	Nearest integer.

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

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

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

long long	llround (half arg)
	Nearest integer.

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

half	frexp (half arg, int *exp)
	Decompress floating-point number.

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

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

int	ilogb (half arg)
	Extract exponent.

half	logb (half arg)
	Extract exponent.

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

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

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

constexpr int	fpclassify (half arg)
	Classify floating-point value.

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

constexpr bool	isinf (half arg)
	Check for infinity.

constexpr bool	isnan (half arg)
	Check for NaN.

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

constexpr bool	signbit (half arg)
	Check sign.

constexpr bool	isgreater (half x, half y)
	Quiet comparison for greater than.

constexpr bool	isgreaterequal (half x, half y)
	Quiet comparison for greater equal.

constexpr bool	isless (half x, half y)
	Quiet comparison for less than.

constexpr bool	islessequal (half x, half y)
	Quiet comparison for less equal.

constexpr bool	islessgreater (half x, half y)
	Quiet comarison for less or greater.

half	literal::operator""_h (long double)

Detailed Description

Half-precision floating-point type.

This class implements an IEEE-conformant half-precision floating-point type with the usual arithmetic operators and conversions. It is implicitly convertible to single-precision floating-point, which makes artihmetic expressions and functions with mixed-type operands to be of the most precise operand type.

According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on nearly any reasonable platform.

So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation.

Definition at line 1679 of file float16_t.hpp.

Constructor & Destructor Documentation

◆ half() [1/2]

half_float::half::half ( )

inlineconstexprnoexcept

Default constructor.

This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics.

Definition at line 1687 of file float16_t.hpp.

◆ half() [2/2]

template<detail::arithmetic T>

half_float::half::half ( T rhs )

inline

Conversion constructor.

Parameters

rhs	float to convert

Exceptions

FE_OVERFLOW,...UNDERFLOW,...INEXACT according to rounding Conversion constructor.

Parameters

rhs	float to convert

Exceptions

FE_OVERFLOW,...UNDERFLOW,...INEXACT according to rounding

Definition at line 1698 of file float16_t.hpp.

Member Function Documentation

◆ get_data()

detail::uint16 half_float::half::get_data ( ) const

inline

Definition at line 1795 of file float16_t.hpp.

◆ operator float()

half_float::half::operator float ( ) const

inline

Conversion to single-precision.

Returns: single precision value representing expression value

Definition at line 1702 of file float16_t.hpp.

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◆ operator*=()

half & half_float::half::operator*= ( half rhs )

inline

Arithmetic assignment.

Template Parameters

T	type of concrete half expression

Parameters

rhs	half expression to multiply with

Returns: reference to this half

Exceptions

FE_... according to operator*(half,half)

Definition at line 1736 of file float16_t.hpp.

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◆ operator++() [1/2]

half & half_float::half::operator++ ( )

inline

Prefix increment.

Returns: incremented half value

Exceptions

FE_... according to operator+(half,half)

Definition at line 1778 of file float16_t.hpp.

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◆ operator++() [2/2]

half half_float::half::operator++ ( int )

inline

Postfix increment.

Returns: non-incremented half value

Exceptions

FE_... according to operator+(half,half)

Definition at line 1788 of file float16_t.hpp.

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◆ operator+=()

half & half_float::half::operator+= ( half rhs )

inline

Arithmetic assignment.

Template Parameters

T	type of concrete half expression

Parameters

rhs	half expression to add

Returns: reference to this half

Exceptions

FE_... according to operator+(half,half)

Definition at line 1722 of file float16_t.hpp.

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◆ operator--() [1/2]

half & half_float::half::operator-- ( )

inline

Prefix decrement.

Returns: decremented half value

Exceptions

FE_... according to operator-(half,half)

Definition at line 1783 of file float16_t.hpp.

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◆ operator--() [2/2]

half half_float::half::operator-- ( int )

inline

Postfix decrement.

Returns: non-decremented half value

Exceptions

FE_... according to operator-(half,half)

Definition at line 1793 of file float16_t.hpp.

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◆ operator-=()

half & half_float::half::operator-= ( half rhs )

inline

Arithmetic assignment.

Template Parameters

T	type of concrete half expression

Parameters

rhs	half expression to subtract

Returns: reference to this half

Exceptions

FE_... according to operator-(half,half)

Definition at line 1729 of file float16_t.hpp.

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◆ operator/=()

half & half_float::half::operator/= ( half rhs )

inline

Arithmetic assignment.

Template Parameters

T	type of concrete half expression

Parameters

rhs	half expression to divide by

Returns: reference to this half

Exceptions

FE_... according to operator/(half,half)

Definition at line 1743 of file float16_t.hpp.

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◆ operator=() [1/2]

half & half_float::half::operator= ( const float & rhs )

inline

Assignment operator.

Parameters

rhs	single-precision value to copy from

Returns: reference to this half

Exceptions

FE_OVERFLOW,...UNDERFLOW,...INEXACT according to rounding

Definition at line 1708 of file float16_t.hpp.

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◆ operator=() [2/2]

template<detail::arithmetic T>

half & half_float::half::operator= ( const T & rhs )

inline

Definition at line 1711 of file float16_t.hpp.

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Friends And Related Symbol Documentation

◆ acos

half acos ( half arg )

friend

Arc cosine function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::acos.

Parameters

arg	function argument

Returns: arc cosine value of arg

Exceptions

FE_INVALID	for signaling NaN or if abs(arg) > 1
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3181 of file float16_t.hpp.

◆ acosh

half acosh ( half arg )

friend

Hyperbolic area cosine.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::acosh.

Parameters

arg	function argument

Returns: area cosine value of arg

Exceptions

FE_INVALID	for signaling NaN or arguments <1
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3397 of file float16_t.hpp.

◆ asin

half asin ( half arg )

friend

Arc sine.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::asin.

Parameters

arg	function argument

Returns: arc sine value of arg

Exceptions

FE_INVALID	for signaling NaN or if abs(arg) > 1
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3153 of file float16_t.hpp.

◆ asinh

half asinh ( half arg )

friend

Hyperbolic area sine.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::asinh.

Parameters

arg	function argument

Returns: area sine value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3370 of file float16_t.hpp.

◆ atan

half atan ( half arg )

friend

Arc tangent function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::atan.

Parameters

arg	function argument

Returns: arc tangent value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3205 of file float16_t.hpp.

◆ atan2

half atan2	(	half	y,
		half	x )

friend

Arc tangent function.

This function may be 1 ULP off the correctly rounded exact result in ~0.005% of inputs for std::round_to_nearest, in ~0.1% of inputs for std::round_toward_zero and in ~0.02% of inputs for any other rounding mode.

See also: Documentation for std::atan2.

Parameters

y	numerator
x	denominator

Returns: arc tangent value

Exceptions

FE_INVALID	if x or y is signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3234 of file float16_t.hpp.

◆ atanh

half atanh ( half arg )

friend

Hyperbolic area tangent.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::atanh.

Parameters

arg	function argument

Returns: area tangent value of arg

Exceptions

FE_INVALID	for signaling NaN or if abs(arg) > 1
FE_DIVBYZERO	for +/-1
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3421 of file float16_t.hpp.

◆ cbrt

half cbrt ( half arg )

friend

Cubic root.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::cbrt.

Parameters

arg	function argument

Returns: cubic root of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2795 of file float16_t.hpp.

◆ ceil

half ceil ( half arg )

friend

Nearest integer not less than half value.

See also: Documentation for std::ceil.

Parameters

arg	half to round

Returns: nearest integer not less than arg

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded

Definition at line 3554 of file float16_t.hpp.

◆ copysign

half copysign	(	half	x,
		half	y )

friend

Take sign.

See also: Documentation for std::copysign.

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 3818 of file float16_t.hpp.

◆ cos

half cos ( half arg )

friend

Cosine function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::cos.

Parameters

arg	function argument

Returns: cosine value of arg

Exceptions

FE_INVALID	for signaling NaN or infinity
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3090 of file float16_t.hpp.

◆ cosh

half cosh ( half arg )

friend

Hyperbolic cosine.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::cosh.

Parameters

arg	function argument

Returns: hyperbolic cosine value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3313 of file float16_t.hpp.

◆ detail::half_caster

template<class, class, std::float_round_style>

friend struct detail::half_caster

friend

Definition at line 1896 of file float16_t.hpp.

◆ erf

half erf ( half arg )

friend

Error function.

This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.

See also: Documentation for std::erf.

Parameters

arg	function argument

Returns: error function value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3453 of file float16_t.hpp.

◆ erfc

half erfc ( half arg )

friend

Complementary error function.

This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.5% of inputs.

See also: Documentation for std::erfc.

Parameters

arg	function argument

Returns: 1 minus error function value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3474 of file float16_t.hpp.

◆ exp

half exp ( half arg )

friend

Exponential function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::exp.

Parameters

arg	function argument

Returns: e raised to arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2517 of file float16_t.hpp.

◆ exp2

half exp2 ( half arg )

friend

Binary exponential.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::exp2.

Parameters

arg	function argument

Returns: 2 raised to arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2549 of file float16_t.hpp.

◆ expm1

half expm1 ( half arg )

friend

Exponential minus one.

This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for std::round_to_nearest and in <1% of inputs for any other rounding mode.

See also: Documentation for std::expm1.

Parameters

arg	function argument

Returns: e raised to arg and subtracted by 1

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2583 of file float16_t.hpp.

◆ fabs

half fabs ( half arg )

friend

Absolute value.

See also: Documentation for std::fabs.

Parameters

arg operand

Returns: absolute value of arg

Definition at line 2323 of file float16_t.hpp.

◆ fdim

half fdim	(	half	x,
		half	y )

friend

Positive difference.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::fdim.

Parameters

x	first operand
y	second operand

Returns: x - y or 0 if difference negative

Exceptions

FE_... according to operator-(half,half)

Definition at line 2487 of file float16_t.hpp.

◆ floor

half floor ( half arg )

friend

Nearest integer not greater than half value.

See also: Documentation for std::floor.

Parameters

arg	half to round

Returns: nearest integer not greater than arg

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded

Definition at line 3562 of file float16_t.hpp.

◆ fma

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

friend

Fused multiply add.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::fma.

Parameters

x	first operand
y	second operand
z	third operand

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

Exceptions

FE_INVALID	according to operator*() and operator+() unless any argument is a quiet NaN and no argument is a signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding the final addition

Definition at line 2400 of file float16_t.hpp.

◆ fmax

constexpr_NOERR half fmax	(	half	x,
		half	y )

friend

Maximum of half expressions.

See also: Documentation for std::fmax.

Parameters

x	first operand
y	second operand

Returns: maximum of operands, ignoring quiet NaNs

Exceptions

FE_INVALID if x or y is signaling NaN

Definition at line 2463 of file float16_t.hpp.

◆ fmin

constexpr_NOERR half fmin	(	half	x,
		half	y )

friend

Minimum of half expressions.

See also: Documentation for std::fmin.

Parameters

x	first operand
y	second operand

Returns: minimum of operands, ignoring quiet NaNs

Exceptions

FE_INVALID if x or y is signaling NaN

Definition at line 2474 of file float16_t.hpp.

◆ fmod

half fmod	(	half	x,
		half	y )

friend

Remainder of division.

See also: Documentation for std::fmod.

Parameters

x	first operand
y	second operand

Returns: remainder of floating-point division.

Exceptions

FE_INVALID if x is infinite or y is 0 or if x or y is signaling NaN

Definition at line 2337 of file float16_t.hpp.

◆ fpclassify

int fpclassify ( half arg )

friend

Classify floating-point value.

See also: Documentation for std::fpclassify.

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 3833 of file float16_t.hpp.

◆ frexp

half frexp	(	half	arg,
		int *	exp )

friend

Decompress floating-point number.

See also: Documentation for std::frexp.

Parameters

arg	number to decompress
exp	address to store exponent at

Returns: significant in range [0.5, 1)

Exceptions

FE_INVALID for signaling NaN

Definition at line 3635 of file float16_t.hpp.

◆ hypot [1/2]

half hypot	(	half	x,
		half	y )

friend

Hypotenuse function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::hypot.

Parameters

x	first argument
y	second argument

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

Exceptions

FE_INVALID	if x or y is signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding of the final square root

Definition at line 2840 of file float16_t.hpp.

◆ hypot [2/2]

half hypot	(	half	x,
		half	y,
		half	z )

friend

Hypotenuse function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::hypot.

Parameters

x	first argument
y	second argument
z	third argument

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

Exceptions

FE_INVALID	if x, y or z is signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding of the final square root

Definition at line 2881 of file float16_t.hpp.

◆ ilogb

int ilogb ( half arg )

friend

Extract exponent.

See also: Documentation for std::ilogb.

Parameters

arg	number to query

Returns: floating-point exponent

Return values

FP_ILOGB0	for zero
FP_ILOGBNAN	for NaN
INT_MAX	for infinity

Exceptions

FE_INVALID for 0 or infinite values

Definition at line 3724 of file float16_t.hpp.

◆ isfinite

bool isfinite ( half arg )

friend

Check if finite number.

See also: Documentation for std::isfinite.

Parameters

arg	number to check

Return values

true	if neither infinity nor NaN
false	else

Definition at line 3846 of file float16_t.hpp.

◆ isgreater

bool isgreater	(	half	x,
		half	y )

friend

Quiet comparison for greater than.

See also: Documentation for std::isgreater.

Parameters

x	first operand
y	second operand

Return values

true	if x greater than y
false	else

Definition at line 3887 of file float16_t.hpp.

◆ isgreaterequal

bool isgreaterequal	(	half	x,
		half	y )

friend

Quiet comparison for greater equal.

See also: Documentation for std::isgreaterequal.

Parameters

x	first operand
y	second operand

Return values

true	if x greater equal y
false	else

Definition at line 3897 of file float16_t.hpp.

◆ isinf

bool isinf ( half arg )

friend

Check for infinity.

See also: Documentation for std::isinf.

Parameters

arg	number to check

Return values

true	for positive or negative infinity
false	else

Definition at line 3853 of file float16_t.hpp.

◆ isless

bool isless	(	half	x,
		half	y )

friend

Quiet comparison for less than.

See also: Documentation for std::isless.

Parameters

x	first operand
y	second operand

Return values

true	if x less than y
false	else

Definition at line 3907 of file float16_t.hpp.

◆ islessequal

bool islessequal	(	half	x,
		half	y )

friend

Quiet comparison for less equal.

See also: Documentation for std::islessequal.

Parameters

x	first operand
y	second operand

Return values

true	if x less equal y
false	else

Definition at line 3917 of file float16_t.hpp.

◆ islessgreater

bool islessgreater	(	half	x,
		half	y )

friend

Quiet comarison for less or greater.

See also: Documentation for std::islessgreater.

Parameters

x	first operand
y	second operand

Return values

true	if either less or greater
false	else

Definition at line 3927 of file float16_t.hpp.

◆ isnan

bool isnan ( half arg )

friend

Check for NaN.

See also: Documentation for std::isnan.

Parameters

arg	number to check

Return values

true	for NaNs
false	else

Definition at line 3860 of file float16_t.hpp.

◆ isnormal

bool isnormal ( half arg )

friend

Check if normal number.

See also: Documentation for std::isnormal.

Parameters

arg	number to check

Return values

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

Definition at line 3867 of file float16_t.hpp.

◆ lgamma

half lgamma ( half arg )

friend

Natural logarithm of gamma function.

This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.025% of inputs.

See also: Documentation for std::lgamma.

Parameters

arg	function argument

Returns: natural logarith of gamma function for arg

Exceptions

FE_INVALID	for signaling NaN
FE_DIVBYZERO	for 0 or negative integer arguments
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3498 of file float16_t.hpp.

◆ literal::operator""_h

half literal::operator""_h ( long double )

friend

◆ llrint

long long llrint ( half arg )

friend

Nearest integer using half's internal rounding mode.

See also: Documentation for std::llrint.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Exceptions

FE_INVALID	if value is not representable as `long long`
FE_INEXACT	if value had to be rounded

Definition at line 3622 of file float16_t.hpp.

◆ llround

long long llround ( half arg )

friend

Nearest integer.

See also: Documentation for std::llround.

Parameters

arg	half to round

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

Exceptions

FE_INVALID if value is not representable as `long long`

Definition at line 3614 of file float16_t.hpp.

◆ log

half log ( half arg )

friend

Natural logarithm.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::log.

Parameters

arg	function argument

Returns: logarithm of arg to base e

Exceptions

FE_INVALID	for signaling NaN or negative argument
FE_DIVBYZERO	for 0
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2630 of file float16_t.hpp.

◆ log10

half log10 ( half arg )

friend

Common logarithm.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::log10.

Parameters

arg	function argument

Returns: logarithm of arg to base 10

Exceptions

FE_INVALID	for signaling NaN or negative argument
FE_DIVBYZERO	for 0
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2657 of file float16_t.hpp.

◆ log1p

half log1p ( half arg )

friend

Natural logarithm plus one.

This function may be 1 ULP off the correctly rounded exact result in <0.05% of inputs for std::round_to_nearest and in ~1% of inputs for any other rounding mode.

See also: Documentation for std::log1p.

Parameters

arg	function argument

Returns: logarithm of arg plus 1 to base e

Exceptions

FE_INVALID	for signaling NaN or argument <-1
FE_DIVBYZERO	for -1
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2731 of file float16_t.hpp.

◆ log2

half log2 ( half arg )

friend

Binary logarithm.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::log2.

Parameters

arg	function argument

Returns: logarithm of arg to base 2

Exceptions

FE_INVALID	for signaling NaN or negative argument
FE_DIVBYZERO	for 0
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2690 of file float16_t.hpp.

◆ logb

half logb ( half arg )

friend

Extract exponent.

See also: Documentation for std::logb.

Parameters

arg	number to query

Returns: floating-point exponent

Exceptions

FE_INVALID	for signaling NaN
FE_DIVBYZERO	for 0

Definition at line 3747 of file float16_t.hpp.

◆ lrint

long lrint ( half arg )

friend

Nearest integer using half's internal rounding mode.

See also: Documentation for std::lrint.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Exceptions

FE_INVALID	if value is not representable as `long`
FE_INEXACT	if value had to be rounded

Definition at line 3601 of file float16_t.hpp.

◆ lround

long lround ( half arg )

friend

Nearest integer.

See also: Documentation for std::lround.

Parameters

arg	half to round

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

Exceptions

FE_INVALID if value is not representable as `long`

Definition at line 3585 of file float16_t.hpp.

◆ modf

half modf	(	half	arg,
		half *	iptr )

friend

Extract integer and fractional parts.

See also: Documentation for std::modf.

Parameters

arg	number to decompress
iptr	address to store integer part at

Returns: fractional part

Exceptions

FE_INVALID for signaling NaN

Definition at line 3698 of file float16_t.hpp.

◆ nanh

half nanh ( const char * arg )

friend

Get NaN value.

See also: Documentation for std::nan.

Parameters

arg	string code

Returns: quiet NaN

Definition at line 2497 of file float16_t.hpp.

◆ nearbyint

half nearbyint ( half arg )

friend

Nearest integer using half's internal rounding mode.

See also: Documentation for std::nearbyint.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Exceptions

FE_INVALID for signaling NaN

Definition at line 3608 of file float16_t.hpp.

◆ nextafter

half nextafter	(	half	from,
		half	to )

friend

Next representable value.

See also: Documentation for std::nextafter.

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

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW	for infinite result from finite argument
FE_UNDERFLOW	for subnormal result

Definition at line 3771 of file float16_t.hpp.

◆ nexttoward

half nexttoward	(	half	from,
		long double	to )

friend

Next representable value.

See also: Documentation for std::nexttoward.

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

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW	for infinite result from finite argument
FE_UNDERFLOW	for subnormal result

Definition at line 3796 of file float16_t.hpp.

◆ operator* [1/3]

half operator*	(	half	x,
		half	y )

friend

Multiplication.

This operation is exact to rounding for all rounding modes.

Parameters

x	left operand
y	right operand

Returns: product of half expressions

Exceptions

FE_INVALID	if multiplying 0 with infinity or if x or y is signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2208 of file float16_t.hpp.

◆ operator* [2/3]

template<class T>

half operator*	(	half	x,
		T	y )

friend

Definition at line 2232 of file float16_t.hpp.

◆ operator* [3/3]

template<class T>

half operator*	(	T	x,
		half	y )

friend

Definition at line 2234 of file float16_t.hpp.

◆ operator+ [1/4]

half operator+ ( half arg )

friend

Identity.

Parameters

arg operand

Returns: unchanged operand

Definition at line 2127 of file float16_t.hpp.

◆ operator+ [2/4]

half operator+	(	half	x,
		half	y )

friend

Addition.

This operation is exact to rounding for all rounding modes.

Parameters

x	left operand
y	right operand

Returns: sum of half expressions

Exceptions

FE_INVALID	if x and y are infinities with different signs or signaling NaNs
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2141 of file float16_t.hpp.

◆ operator+ [3/4]

template<class T>

half operator+	(	half	x,
		T	y )

friend

Definition at line 2178 of file float16_t.hpp.

◆ operator+ [4/4]

template<class T>

half operator+	(	T	x,
		half	y )

friend

Definition at line 2180 of file float16_t.hpp.

◆ operator- [1/4]

half operator- ( half arg )

friend

Negation.

Parameters

arg operand

Returns: negated operand

Definition at line 2132 of file float16_t.hpp.

◆ operator- [2/4]

half operator-	(	half	x,
		half	y )

friend

Subtraction.

This operation is exact to rounding for all rounding modes.

Parameters

x	left operand
y	right operand

Returns: difference of half expressions

Exceptions

FE_INVALID	if x and y are infinities with equal signs or signaling NaNs
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2189 of file float16_t.hpp.

◆ operator- [3/4]

template<class T>

half operator-	(	half	x,
		T	y )

friend

Definition at line 2197 of file float16_t.hpp.

◆ operator- [4/4]

template<class T>

half operator-	(	T	x,
		half	y )

friend

Definition at line 2199 of file float16_t.hpp.

◆ operator/ [1/3]

half operator/	(	half	x,
		half	y )

friend

Division.

This operation is exact to rounding for all rounding modes.

Parameters

x	left operand
y	right operand

Returns: quotient of half expressions

Exceptions

FE_INVALID	if dividing 0s or infinities with each other or if x or y is signaling NaN
FE_DIVBYZERO	if dividing finite value by 0
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2244 of file float16_t.hpp.

◆ operator/ [2/3]

template<class T>

half operator/	(	half	x,
		T	y )

friend

Definition at line 2272 of file float16_t.hpp.

◆ operator/ [3/3]

template<class T>

half operator/	(	T	x,
		half	y )

friend

Definition at line 2274 of file float16_t.hpp.

◆ operator<<

template<class charT, class traits>

std::basic_ostream< charT, traits > & operator<<	(	std::basic_ostream< charT, traits > &	out,
		half	arg )

friend

Output operator.

This uses the built-in functionality for streaming out floating-point numbers.

Parameters

out	output stream to write into
arg	half expression to write

Returns: reference to output stream

Definition at line 2274 of file float16_t.hpp.

◆ operator<=> [1/2]

constexpr_NOERR std::partial_ordering operator<=>	(	half	x,
		half	y )

friend

Definition at line 2103 of file float16_t.hpp.

◆ operator<=> [2/2]

template<detail::arithmetic T>

constexpr_NOERR std::partial_ordering operator<=>	(	half	x,
		T	y )

friend

Definition at line 2114 of file float16_t.hpp.

◆ operator== [1/2]

constexpr_NOERR bool operator==	(	half	x,
		half	y )

friend

Comparison for equality.

Parameters

x	first operand
y	second operand

Return values

true	if operands equal
false	else

Exceptions

FE_INVALID if x or y is NaN

Definition at line 2097 of file float16_t.hpp.

◆ operator== [2/2]

template<detail::arithmetic T>

constexpr_NOERR bool operator==	(	half	x,
		T	y )

friend

Definition at line 2101 of file float16_t.hpp.

◆ operator>>

template<class charT, class traits>

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

friend

Input operator.

This uses the built-in functionality for streaming in floating-point numbers, specifically double precision floating point numbers (unless overridden with HALF_ARITHMETIC_TYPE). So the input string is first rounded to double precision using the underlying platform's current floating-point rounding mode before being rounded to half-precision using the library's half-precision rounding mode.

Parameters

in	input stream to read from
arg	half to read into

Returns: reference to input stream

Exceptions

FE_OVERFLOW,...UNDERFLOW,...INEXACT according to rounding

Definition at line 2303 of file float16_t.hpp.

◆ pow

half pow	(	half	x,
		half	y )

friend

Power function.

This function may be 1 ULP off the correctly rounded exact result for any rounding mode in ~0.00025% of inputs.

See also: Documentation for std::pow.

Parameters

x	base
y	exponent

Returns: x raised to y

Exceptions

FE_INVALID	if x or y is signaling NaN or if x is finite an negative and y is finite and not integral
FE_DIVBYZERO	if x is 0 and y is negative
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2944 of file float16_t.hpp.

◆ remainder

half remainder	(	half	x,
		half	y )

friend

Remainder of division.

See also: Documentation for std::remainder.

Parameters

x	first operand
y	second operand

Returns: remainder of floating-point division.

Exceptions

FE_INVALID if x is infinite or y is 0 or if x or y is signaling NaN

Definition at line 2357 of file float16_t.hpp.

◆ remquo

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

friend

Remainder of division.

See also: Documentation for std::remquo.

Parameters

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

Returns: remainder of floating-point division.

Exceptions

FE_INVALID if x is infinite or y is 0 or if x or y is signaling NaN

Definition at line 2376 of file float16_t.hpp.

◆ rint

half rint ( half arg )

friend

Nearest integer using half's internal rounding mode.

See also: Documentation for std::rint.

Parameters

arg	half expression to round

Returns: nearest integer using default rounding mode

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded

Definition at line 3593 of file float16_t.hpp.

◆ round

half round ( half arg )

friend

Nearest integer.

See also: Documentation for std::round.

Parameters

arg	half to round

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

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded

Definition at line 3578 of file float16_t.hpp.

◆ scalbln

half scalbln	(	half	arg,
		long	exp )

friend

Multiply by power of two.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::scalbln.

Parameters

arg	number to modify
exp	power of two to multiply with

Returns: arg multplied by 2 raised to exp

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3654 of file float16_t.hpp.

◆ signbit

bool signbit ( half arg )

friend

Check sign.

See also: Documentation for std::signbit.

Parameters

arg	number to check

Return values

true	for negative number
false	for positive number

Definition at line 3874 of file float16_t.hpp.

◆ sin

half sin ( half arg )

friend

Sine function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::sin.

Parameters

arg	function argument

Returns: sine value of arg

Exceptions

FE_INVALID	for signaling NaN or infinity
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3059 of file float16_t.hpp.

◆ sincos

void sincos	(	half	arg,
		half *	sin,
		half *	cos )

friend

Compute sine and cosine simultaneously.

This returns the same results as sin() and cos() but is faster than calling each function individually.

This function is exact to rounding for all rounding modes.

Parameters

arg	function argument
sin	variable to take sine of arg
cos	variable to take cosine of arg

Exceptions

FE_INVALID	for signaling NaN or infinity
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3003 of file float16_t.hpp.

◆ sinh

half sinh ( half arg )

friend

Hyperbolic sine.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::sinh.

Parameters

arg	function argument

Returns: hyperbolic sine value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3286 of file float16_t.hpp.

◆ sqrt

half sqrt ( half arg )

friend

Square root.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::sqrt.

Parameters

arg	function argument

Returns: square root of arg

Exceptions

FE_INVALID	for signaling NaN and negative arguments
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 2774 of file float16_t.hpp.

◆ std::hash< half >

friend struct std::hash< half >

friend

Definition at line 1896 of file float16_t.hpp.

◆ std::numeric_limits< half >

friend class std::numeric_limits< half >

friend

Definition at line 1896 of file float16_t.hpp.

◆ tan

half tan ( half arg )

friend

Tangent function.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::tan.

Parameters

arg	function argument

Returns: tangent value of arg

Exceptions

FE_INVALID	for signaling NaN or infinity
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3118 of file float16_t.hpp.

◆ tanh

half tanh ( half arg )

friend

Hyperbolic tangent.

This function is exact to rounding for all rounding modes.

See also: Documentation for std::tanh.

Parameters

arg	function argument

Returns: hyperbolic tangent value of arg

Exceptions

FE_INVALID	for signaling NaN
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3339 of file float16_t.hpp.

◆ tgamma

half tgamma ( half arg )

friend

Gamma function.

This function may be 1 ULP off the correctly rounded exact result for any rounding mode in <0.25% of inputs.

See also: Documentation for std::tgamma.

Parameters

arg	function argument

Returns: gamma function value of arg

Exceptions

FE_INVALID	for signaling NaN, negative infinity or negative integer arguments
FE_DIVBYZERO	for 0
FE_OVERFLOW,...UNDERFLOW,...INEXACT	according to rounding

Definition at line 3522 of file float16_t.hpp.

◆ trunc

half trunc ( half arg )

friend

Nearest integer not greater in magnitude than half value.

See also: Documentation for std::trunc.

Parameters

arg	half to round

Returns: nearest integer not greater in magnitude than arg

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded

Definition at line 3570 of file float16_t.hpp.

The documentation for this class was generated from the following file:

sparrow/details/3rdparty/float16_t.hpp

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ half() [1/2]

◆ half() [2/2]

Member Function Documentation

◆ get_data()

◆ operator float()

◆ operator*=()

◆ operator++() [1/2]

◆ operator++() [2/2]

◆ operator+=()

◆ operator--() [1/2]

◆ operator--() [2/2]

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

Friends And Related Symbol Documentation

◆ acos

◆ acosh

◆ asin

◆ asinh

◆ atan

◆ atan2

◆ atanh

◆ cbrt

◆ ceil

◆ copysign

◆ cos

◆ cosh

◆ detail::half_caster

◆ erf

◆ erfc

◆ exp

◆ exp2

◆ expm1

◆ fabs

◆ fdim

◆ floor

◆ fma

◆ fmax

◆ fmin

◆ fmod

◆ fpclassify

◆ frexp

◆ hypot [1/2]

◆ hypot [2/2]

◆ ilogb

◆ isfinite

◆ isgreater

◆ isgreaterequal

◆ isinf

◆ isless

◆ islessequal

◆ islessgreater

◆ isnan

◆ isnormal

◆ lgamma

◆ literal::operator""_h

◆ llrint

◆ llround

◆ log

◆ log10

◆ log1p

◆ log2

◆ logb

◆ lrint

◆ lround

◆ modf

◆ nanh

◆ nearbyint

◆ nextafter

◆ nexttoward

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+ [1/4]

◆ operator+ [2/4]