Classes
struct	conditional
	Conditional type. More...

struct	conditional< false, T, F >

struct	bool_type
	Helper for tag dispatching. More...

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

struct	is_float< const T >

struct	is_float< volatile T >

struct	is_float< const volatile T >

struct	is_float< float >

struct	is_float< double >

struct	is_float< long double >

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

struct	bits< const T >

struct	bits< volatile T >

struct	bits< const volatile T >

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	f31
	Class for 1.31 unsigned floating-point computation. More...

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

struct	half_caster< half, U, R >

struct	half_caster< T, half, R >

struct	half_caster< half, half, R >

Typedefs
typedef bool_type< true >	true_type

typedef bool_type< false >	false_type

typedef unsigned short	uint16
	Unsigned integer of (at least) 16 bits width. More...

typedef unsigned long	uint32
	Fastest unsigned integer of (at least) 32 bits width. More...

typedef long	int32
	Fastest unsigned integer of (at least) 32 bits width. More...

Functions
Implementation defined classification and arithmetic
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...

uint32	sign_mask (uint32 arg)
	Platform-independent sign mask. More...

uint32	arithmetic_shift (uint32 arg, int i)
	Platform-independent arithmetic right shift. More...

Error handling
int &	errflags ()
	Internal exception flags. More...

void	raise (int HALF_UNUSED_NOERR(flags), bool HALF_UNUSED_NOERR(cond)=true)
	Raise floating-point exception. More...

HALF_CONSTEXPR_NOERR bool	compsignal (unsigned int x, unsigned int y)
	Check and signal for any NaN. More...

HALF_CONSTEXPR_NOERR unsigned int	signal (unsigned int nan)
	Signal and silence signaling NaN. More...

HALF_CONSTEXPR_NOERR unsigned int	signal (unsigned int x, unsigned int y)
	Signal and silence signaling NaNs. More...

HALF_CONSTEXPR_NOERR unsigned int	signal (unsigned int x, unsigned int y, unsigned int z)
	Signal and silence signaling NaNs. More...

HALF_CONSTEXPR_NOERR unsigned int	select (unsigned int x, unsigned int HALF_UNUSED_NOERR(y))
	Select value or signaling NaN. More...

HALF_CONSTEXPR_NOERR unsigned int	invalid ()
	Raise domain error and return NaN. More...

HALF_CONSTEXPR_NOERR unsigned int	pole (unsigned int sign=0)
	Raise pole error and return infinity. More...

HALF_CONSTEXPR_NOERR unsigned int	check_underflow (unsigned int arg)
	Check value for underflow. More...

Conversion and rounding
template<std::float_round_style R>
HALF_CONSTEXPR_NOERR unsigned int	overflow (unsigned int sign=0)
	Half-precision overflow. More...

template<std::float_round_style R>
HALF_CONSTEXPR_NOERR unsigned int	underflow (unsigned int sign=0)
	Half-precision underflow. More...

template<std::float_round_style R, bool I>
HALF_CONSTEXPR_NOERR unsigned int	rounded (unsigned int value, int g, int s)
	Round half-precision number. More...

template<std::float_round_style R, bool E, bool I>
unsigned int	integral (unsigned int value)
	Round half-precision number to nearest integer value. More...

template<std::float_round_style R, unsigned int F, bool S, bool N, bool I>
unsigned int	fixed2half (uint32 m, int exp=14, unsigned int sign=0, int s=0)
	Convert fixed point to half-precision floating-point. More...

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

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

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

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

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

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

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

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

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

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

Mathematics
template<std::float_round_style R>
uint32	mulhi (uint32 x, uint32 y)
	upper part of 64-bit multiplication. More...

uint32	multiply64 (uint32 x, uint32 y)
	64-bit multiplication. More...

uint32	divide64 (uint32 x, uint32 y, int &s)
	64-bit division. More...

template<bool Q, bool R>
unsigned int	mod (unsigned int x, unsigned int y, int *quo=NULL)
	Half precision positive modulus. More...

template<unsigned int F>
uint32	sqrt (uint32 &r, int &exp)
	Fixed point square root. More...

uint32	exp2 (uint32 m, unsigned int n=32)
	Fixed point binary exponential. More...

uint32	log2 (uint32 m, unsigned int n=32)
	Fixed point binary logarithm. More...

std::pair< uint32, uint32 >	sincos (uint32 mz, unsigned int n=31)
	Fixed point sine and cosine. More...

uint32	atan2 (uint32 my, uint32 mx, unsigned int n=31)
	Fixed point arc tangent. More...

uint32	angle_arg (unsigned int abs, int &k)
	Reduce argument for trigonometric functions. More...

std::pair< uint32, uint32 >	atan2_args (unsigned int abs)
	Get arguments for atan2 function. More...

std::pair< uint32, uint32 >	hyperbolic_args (unsigned int abs, int &exp, unsigned int n=32)
	Get exponentials for hyperbolic computation. More...

template<std::float_round_style R>
unsigned int	exp2_post (uint32 m, int exp, bool esign, unsigned int sign=0, unsigned int n=32)
	Postprocessing for binary exponential. More...

template<std::float_round_style R, uint32 L>
unsigned int	log2_post (uint32 m, int ilog, int exp, unsigned int sign=0)
	Postprocessing for binary logarithm. More...

template<std::float_round_style R>
unsigned int	hypot_post (uint32 r, int exp)
	Hypotenuse square root and postprocessing. More...

template<std::float_round_style R>
unsigned int	tangent_post (uint32 my, uint32 mx, int exp, unsigned int sign=0)
	Division and postprocessing for tangents. More...

template<std::float_round_style R, bool S>
unsigned int	area (unsigned int arg)
	Area function and postprocessing. More...

template<std::float_round_style R, bool C>
unsigned int	erf (unsigned int arg)
	Error function and postprocessing. More...

template<std::float_round_style R, bool L>
unsigned int	gamma (unsigned int arg)
	Gamma function and postprocessing. More...

Variables
HALF_CONSTEXPR_CONST binary_t	binary = binary_t()
	Tag for binary construction. More...

Typedef Documentation

◆ false_type

typedef bool_type<false> half_float::detail::false_type

◆ int32

typedef long half_float::detail::int32

Fastest unsigned integer of (at least) 32 bits width.

◆ true_type

typedef bool_type<true> half_float::detail::true_type

◆ uint16

typedef unsigned short half_float::detail::uint16

Unsigned integer of (at least) 16 bits width.

◆ uint32

typedef unsigned long half_float::detail::uint32

Fastest unsigned integer of (at least) 32 bits width.

Function Documentation

◆ angle_arg()

uint32 half_float::detail::angle_arg	(	unsigned int	abs,
		int &	k
	)

inline

Reduce argument for trigonometric functions.

Parameters

abs	half-precision floating-point value
k	value to take quarter period

Returns: abs reduced to [-pi/4,pi/4] as Q0.30

◆ area()

template<std::float_round_style R, bool S>

unsigned int half_float::detail::area ( unsigned int arg )

Area function and postprocessing.

This computes the value directly in Q2.30 using the representation asinh|acosh(x) = log(x+sqrt(x^2+|-1)).

Template Parameters

R	rounding mode to use
S	`true` for asinh, `false` for acosh

Parameters

arg	half-precision argument

Returns: asinh|acosh(arg) converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if no other exception occurred

◆ arithmetic_shift()

uint32 half_float::detail::arithmetic_shift	(	uint32	arg,
		int	i
	)

inline

Platform-independent arithmetic right shift.

Parameters

arg	integer value in two's complement
i	shift amount (at most 31)

Returns: arg right shifted for i bits with possible sign extension

◆ atan2()

uint32 half_float::detail::atan2	(	uint32	my,
		uint32	mx,
		unsigned int	n = `31`
	)

inline

Fixed point arc tangent.

This uses the CORDIC algorithm in vectoring mode.

Parameters

my	y coordinate as Q0.30
mx	x coordinate as Q0.30
n	number of iterations (at most 31)

Returns: arc tangent of my / mx as Q1.30

◆ atan2_args()

std::pair<uint32, uint32> half_float::detail::atan2_args ( unsigned int abs )

inline

Get arguments for atan2 function.

Parameters

abs	half-precision floating-point value

Returns: abs and sqrt(1 - abs^2) as Q0.30

◆ 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

◆ 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

◆ 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

◆ check_underflow()

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::check_underflow ( unsigned int arg )

inline

Check value for underflow.

Parameters

arg	non-zero half-precision value to check

Returns: arg

Exceptions

FE_UNDERFLOW if arg is subnormal

◆ compsignal()

HALF_CONSTEXPR_NOERR bool half_float::detail::compsignal	(	unsigned int	x,
		unsigned int	y
	)

inline

Check and signal for any NaN.

Parameters

x	first half-precision value to check
y	second half-precision value to check

Return values

true	if either x or y is NaN
false	else

Exceptions

FE_INVALID if x or y is NaN

◆ divide64()

uint32 half_float::detail::divide64	(	uint32	x,
		uint32	y,
		int &	s
	)

inline

64-bit division.

Parameters

x	upper 32 bit of dividend
y	divisor
s	variable to store sticky bit for rounding

Returns: (x << 32) / y

◆ erf()

template<std::float_round_style R, bool C>

unsigned int half_float::detail::erf ( unsigned int arg )

Error function and postprocessing.

This computes the value directly in Q1.31 using the approximations given here.

Template Parameters

R	rounding mode to use
C	`true` for comlementary error function, `false` else

Parameters

arg	half-precision function argument

Returns: approximated value of error function in half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if no other exception occurred

◆ errflags()

int& half_float::detail::errflags ( )

inline

Internal exception flags.

Returns: reference to global exception flags

◆ exp2()

uint32 half_float::detail::exp2	(	uint32	m,
		unsigned int	n = `32`
	)

inline

Fixed point binary exponential.

This uses the BKM algorithm in E-mode.

Parameters

m	exponent in [0,1) as Q0.31
n	number of iterations (at most 32)

Returns: 2 ^ m as Q1.31

◆ exp2_post()

template<std::float_round_style R>

unsigned int half_float::detail::exp2_post	(	uint32	m,
		int	exp,
		bool	esign,
		unsigned int	sign = `0`,
		unsigned int	n = `32`
	)

Postprocessing for binary exponential.

Template Parameters

R	rounding mode to use

Parameters

m	fractional part of as Q0.31
exp	absolute value of unbiased exponent
esign	sign of actual exponent
sign	sign bit of result
n	number of BKM iterations (at most 32)

Returns: value converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded or I is `true`

◆ fixed2half()

template<std::float_round_style R, unsigned int F, bool S, bool N, bool I>

unsigned int half_float::detail::fixed2half	(	uint32	m,
		int	exp = `14`,
		unsigned int	sign = `0`,
		int	s = `0`
	)

Convert fixed point to half-precision floating-point.

Template Parameters

R	rounding mode to use
F	number of fractional bits in [11,31]
S	`true` for signed, `false` for unsigned
N	`true` for additional normalization step, `false` if already normalized to 1.F
I	`true` to always raise INEXACT exception, `false` to raise only for rounded results

Parameters

m	mantissa in Q1.F fixed point format
exp	biased exponent - 1
sign	half-precision value with sign bit only
s	sticky bit (or of all but the most significant already discarded bits)

Returns: value converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded or I is `true`

◆ float2half()

template<std::float_round_style R, typename T >

unsigned int half_float::detail::float2half ( T value )

Convert floating-point to half-precision.

Template Parameters

R	rounding mode to use
T	source type (builtin floating-point type)

Parameters

value floating-point value to convert

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded

◆ float2half_impl() [1/3]

template<std::float_round_style R>

unsigned int half_float::detail::float2half_impl	(	double	value,
		true_type
	)

Convert IEEE double-precision to half-precision.

Template Parameters

R	rounding mode to use

Parameters

value double-precision value to convert

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded

◆ float2half_impl() [2/3]

template<std::float_round_style R>

unsigned int 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

Parameters

value single-precision value to convert

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded

◆ float2half_impl() [3/3]

template<std::float_round_style R, typename T >

unsigned int half_float::detail::float2half_impl	(	T	value,
			...
	)

Convert non-IEEE floating-point to half-precision.

Template Parameters

R	rounding mode to use
T	source type (builtin floating-point type)

Parameters

value floating-point value to convert

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded

◆ gamma()

template<std::float_round_style R, bool L>

unsigned int half_float::detail::gamma ( unsigned int arg )

Gamma function and postprocessing.

This approximates the value of either the gamma function or its logarithm directly in Q1.31.

Template Parameters

R	rounding mode to use
L	`true` for lograithm of gamma function, `false` for gamma function

Parameters

arg	half-precision floating-point value

Returns: lgamma/tgamma(arg) in half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if arg is not a positive integer

◆ half2float()

template<typename T >

T half_float::detail::half2float ( unsigned int value )

Convert half-precision to floating-point.

Template Parameters

T	type to convert to (builtin integer type)

Parameters

value half-precision value to convert

Returns: floating-point value

◆ half2float_impl() [1/3]

double half_float::detail::half2float_impl	(	unsigned int	value,
		double	,
		true_type
	)

inline

Convert half-precision to IEEE double-precision.

Parameters

value half-precision value to convert

Returns: double-precision value

◆ half2float_impl() [2/3]

float half_float::detail::half2float_impl	(	unsigned int	value,
		float	,
		true_type
	)

inline

Convert half-precision to IEEE single-precision.

Credit for this goes to Jeroen van der Zijp.

Parameters

value half-precision value to convert

Returns: single-precision value

◆ half2float_impl() [3/3]

template<typename T >

T half_float::detail::half2float_impl	(	unsigned int	value,
		T	,
			...
	)

Convert half-precision to non-IEEE floating-point.

Template Parameters

T	type to convert to (builtin integer type)

Parameters

value half-precision value to convert

Returns: floating-point value

◆ half2int()

template<std::float_round_style R, bool E, bool I, typename T >

T half_float::detail::half2int ( unsigned int value )

Convert half-precision floating-point to integer.

Template Parameters

R	rounding mode to use
E	`true` for round to even, `false` for round away from zero
I	`true` to raise INEXACT exception (if inexact), `false` to never raise it
T	type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits)

Parameters

value half-precision value to convert

Returns: rounded integer value

Exceptions

FE_INVALID	if value is not representable in type T
FE_INEXACT	if value had to be rounded and I is `true`

◆ hyperbolic_args()

std::pair<uint32, uint32> half_float::detail::hyperbolic_args	(	unsigned int	abs,
		int &	exp,
		unsigned int	n = `32`
	)

inline

Get exponentials for hyperbolic computation.

Parameters

abs	half-precision floating-point value
exp	variable to take unbiased exponent of larger result
n	number of BKM iterations (at most 32)

Returns: exp(abs) and exp(-abs) as Q1.31 with same exponent

◆ hypot_post()

template<std::float_round_style R>

unsigned int half_float::detail::hypot_post	(	uint32	r,
		int	exp
	)

Hypotenuse square root and postprocessing.

Template Parameters

R	rounding mode to use

Parameters

r	mantissa as Q2.30
exp	biased exponent

Returns: square root converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded

◆ int2half()

template<std::float_round_style R, typename T >

unsigned int half_float::detail::int2half ( T value )

Convert integer to half-precision floating-point.

Template Parameters

R	rounding mode to use
T	type to convert (builtin integer type)

Parameters

value integral value to convert

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_INEXACT	if value had to be rounded

◆ integral()

template<std::float_round_style R, bool E, bool I>

unsigned int half_float::detail::integral ( unsigned int value )

Round half-precision number to nearest integer value.

Template Parameters

R	rounding mode to use
E	`true` for round to even, `false` for round away from zero
I	`true` to raise INEXACT exception (if inexact), `false` to never raise it

Parameters

value half-precision value to round

Returns: half-precision bits for nearest integral value

Exceptions

FE_INVALID	for signaling NaN
FE_INEXACT	if value had to be rounded and I is `true`

◆ invalid()

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::invalid ( )

inline

Raise domain error and return NaN.

return quiet NaN

Exceptions

FE_INVALID

◆ log2()

uint32 half_float::detail::log2	(	uint32	m,
		unsigned int	n = `32`
	)

inline

Fixed point binary logarithm.

This uses the BKM algorithm in L-mode.

Parameters

m	mantissa in [1,2) as Q1.30
n	number of iterations (at most 32)

Returns: log2(m) as Q0.31

◆ log2_post()

template<std::float_round_style R, uint32 L>

unsigned int half_float::detail::log2_post	(	uint32	m,
		int	ilog,
		int	exp,
		unsigned int	sign = `0`
	)

Postprocessing for binary logarithm.

Template Parameters

R	rounding mode to use
L	logarithm for base transformation as Q1.31

Parameters

m	fractional part of logarithm as Q0.31
ilog	signed integer part of logarithm
exp	biased exponent of result
sign	sign bit of result

Returns: value base-transformed and converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if no other exception occurred

◆ mod()

template<bool Q, bool R>

unsigned int half_float::detail::mod	(	unsigned int	x,
		unsigned int	y,
		int *	quo = `NULL`
	)

Half precision positive modulus.

Template Parameters

Q	`true` to compute full quotient, `false` else
R	`true` to compute signed remainder, `false` for positive remainder

Parameters

x	first operand as positive finite half-precision value
y	second operand as positive finite half-precision value
quo	adress to store quotient at, `nullptr` if Q `false`

Returns: modulus of x / y

◆ mulhi()

template<std::float_round_style R>

uint32 half_float::detail::mulhi	(	uint32	x,
		uint32	y
	)

upper part of 64-bit multiplication.

Template Parameters

R	rounding mode to use

Parameters

x	first factor
y	second factor

Returns: upper 32 bit of x * y

◆ multiply64()

uint32 half_float::detail::multiply64	(	uint32	x,
		uint32	y
	)

inline

64-bit multiplication.

Parameters

x	first factor
y	second factor

Returns: upper 32 bit of x * y rounded to nearest

◆ overflow()

template<std::float_round_style R>

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::overflow ( unsigned int sign = 0 )

Half-precision overflow.

Template Parameters

R	rounding mode to use

Parameters

sign	half-precision value with sign bit only

Returns: rounded overflowing half-precision value

Exceptions

FE_OVERFLOW

◆ pole()

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::pole ( unsigned int sign = 0 )

inline

Raise pole error and return infinity.

Parameters

sign	half-precision value with sign bit only

Returns: half-precision infinity with sign of sign

Exceptions

FE_DIVBYZERO

◆ raise()

void half_float::detail::raise	(	int	HALF_UNUSED_NOERRflags,
		bool	HALF_UNUSED_NOERRcond = `true`
	)

inline

Raise floating-point exception.

Parameters

flags	exceptions to raise
cond	condition to raise exceptions for

◆ rounded()

template<std::float_round_style R, bool I>

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::rounded	(	unsigned int	value,
		int	g,
		int	s
	)

Round half-precision number.

Template Parameters

R	rounding mode to use
I	`true` to always raise INEXACT exception, `false` to raise only for rounded results

Parameters

value	finite half-precision number to round
g	guard bit (most significant discarded bit)
s	sticky bit (or of all but the most significant discarded bits)

Returns: rounded half-precision value

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if value had to be rounded or I is `true`

◆ select()

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::select	(	unsigned int	x,
		unsigned int	HALF_UNUSED_NOERRy
	)

inline

Select value or signaling NaN.

Parameters

x	preferred half-precision value
y	ignored half-precision value except for signaling NaN

Returns: y if signaling NaN, x otherwise

Exceptions

FE_INVALID if y is signaling NaN

◆ sign_mask()

uint32 half_float::detail::sign_mask ( uint32 arg )

inline

Platform-independent sign mask.

Parameters

arg	integer value in two's complement

Return values

-1	if arg negative
0	if arg positive

◆ signal() [1/3]

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::signal ( unsigned int nan )

inline

Signal and silence signaling NaN.

Parameters

nan	half-precision NaN value

Returns: quiet NaN

Exceptions

FE_INVALID if nan is signaling NaN

◆ signal() [2/3]

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::signal	(	unsigned int	x,
		unsigned int	y
	)

inline

Signal and silence signaling NaNs.

Parameters

x	first half-precision value to check
y	second half-precision value to check

Returns: quiet NaN

Exceptions

FE_INVALID if x or y is signaling NaN

◆ signal() [3/3]

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::signal	(	unsigned int	x,
		unsigned int	y,
		unsigned int	z
	)

inline

Signal and silence signaling NaNs.

Parameters

x	first half-precision value to check
y	second half-precision value to check
z	third half-precision value to check

Returns: quiet NaN

Exceptions

FE_INVALID if x, y or z is signaling NaN

◆ sincos()

std::pair<uint32, uint32> half_float::detail::sincos	(	uint32	mz,
		unsigned int	n = `31`
	)

inline

Fixed point sine and cosine.

This uses the CORDIC algorithm in rotation mode.

Parameters

mz	angle in [-pi/2,pi/2] as Q1.30
n	number of iterations (at most 31)

Returns: sine and cosine of mz as Q1.30

◆ sqrt()

template<unsigned int F>

uint32 half_float::detail::sqrt	(	uint32 &	r,
		int &	exp
	)

Fixed point square root.

Template Parameters

F	number of fractional bits

Parameters

r	radicand in Q1.F fixed point format
exp	exponent

Returns: square root as Q1.F/2

◆ tangent_post()

template<std::float_round_style R>

unsigned int half_float::detail::tangent_post	(	uint32	my,
		uint32	mx,
		int	exp,
		unsigned int	sign = `0`
	)

Division and postprocessing for tangents.

Template Parameters

R	rounding mode to use

Parameters

my	dividend as Q1.31
mx	divisor as Q1.31
exp	biased exponent of result
sign	sign bit of result

Returns: quotient converted to half-precision

Exceptions

FE_OVERFLOW	on overflows
FE_UNDERFLOW	on underflows
FE_INEXACT	if no other exception occurred

◆ underflow()

template<std::float_round_style R>

HALF_CONSTEXPR_NOERR unsigned int half_float::detail::underflow ( unsigned int sign = 0 )

Half-precision underflow.

Template Parameters

R	rounding mode to use

Parameters

sign	half-precision value with sign bit only

Returns: rounded underflowing half-precision value

Exceptions

FE_UNDERFLOW

Variable Documentation

◆ binary

HALF_CONSTEXPR_CONST binary_t half_float::detail::binary = binary_t()

Tag for binary construction.

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ false_type

◆ int32

◆ true_type

◆ uint16

◆ uint32

Function Documentation

◆ angle_arg()

◆ area()

◆ arithmetic_shift()

◆ atan2()

◆ atan2_args()

◆ builtin_isinf()

◆ builtin_isnan()

◆ builtin_signbit()

◆ check_underflow()

◆ compsignal()

◆ divide64()

◆ erf()

◆ errflags()

◆ exp2()

◆ exp2_post()

◆ fixed2half()

◆ float2half()

◆ float2half_impl() [1/3]

◆ float2half_impl() [2/3]

◆ float2half_impl() [3/3]

◆ gamma()

◆ half2float()

◆ half2float_impl() [1/3]

◆ half2float_impl() [2/3]

◆ half2float_impl() [3/3]

◆ half2int()

◆ hyperbolic_args()

◆ hypot_post()

◆ int2half()

◆ integral()

◆ invalid()

◆ log2()

◆ log2_post()

◆ mod()

◆ mulhi()

◆ multiply64()

◆ overflow()

◆ pole()

◆ raise()

◆ rounded()

◆ select()

◆ sign_mask()

◆ signal() [1/3]

◆ signal() [2/3]

◆ signal() [3/3]

◆ sincos()

◆ sqrt()

◆ tangent_post()

◆ underflow()

Variable Documentation

◆ binary