half_float::detail Namespace Reference

Data Structures
struct	binary_t
	Tag type for binary construction. More...
struct	bits
	Type traits for floating-point bits. More...
struct	bits< const T >
struct	bits< const volatile T >
struct	bits< double >
	Unsigned integer of (at least) 64 bits width. More...
struct	bits< float >
	Unsigned integer of (at least) 32 bits width. More...
struct	bits< volatile T >
struct	bool_type
	Helper for tag dispatching. More...
struct	conditional
	Conditional type. More...
struct	conditional< false, T, F >
struct	f31
	Class for 1.31 unsigned floating-point computation. More...
struct	half_caster
	Helper class for half casts. More...
struct	half_caster< half, half, R >
struct	half_caster< half, U, R >
struct	half_caster< T, half, R >
struct	is_float
	Type traits for floating-point types. More...
struct	is_float< const T >
struct	is_float< const volatile T >
struct	is_float< double >
struct	is_float< float >
struct	is_float< long double >
struct	is_float< volatile T >

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...

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

Definition at line 489 of file includes/half.hpp.

int32

typedef long half_float::detail::int32

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

Definition at line 530 of file includes/half.hpp.

true_type

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

Definition at line 488 of file includes/half.hpp.

uint16

typedef unsigned short half_float::detail::uint16

Unsigned integer of (at least) 16 bits width.

Definition at line 524 of file includes/half.hpp.

uint32

typedef unsigned long half_float::detail::uint32

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

Definition at line 527 of file includes/half.hpp.

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

Definition at line 1621 of file includes/half.hpp.

References half_float::abs(), half_float::exp(), and multiply64().

Referenced by half_float::cos(), half_float::sin(), half_float::sincos(), and half_float::tan().

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

Definition at line 1805 of file includes/half.hpp.

References half_float::abs(), and log2().

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

Definition at line 622 of file includes/half.hpp.

Referenced by atan2(), and sincos().

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

Definition at line 1599 of file includes/half.hpp.

References arithmetic_shift(), and sign_mask().

Referenced by half_float::acos(), half_float::asin(), half_float::atan(), and half_float::atan2().

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

Definition at line 1644 of file includes/half.hpp.

References half_float::abs(), and half_float::exp().

Referenced by half_float::acos(), and half_float::asin().

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 563 of file includes/half.hpp.

References half_float::isinf().

Referenced by float2half_impl().

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 579 of file includes/half.hpp.

References half_float::isnan().

Referenced by float2half_impl(), and half_float::nexttoward().

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 595 of file includes/half.hpp.

References half_float::signbit().

Referenced by float2half_impl(), and half_float::nexttoward().

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

Definition at line 784 of file includes/half.hpp.

References FE_UNDERFLOW.

Referenced by exp2_post(), half_float::hypot(), and half_float::pow().

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

Definition at line 696 of file includes/half.hpp.

References FE_INVALID.

Referenced by half_float::operator!=(), half_float::operator<(), half_float::operator<=(), half_float::operator==(), half_float::operator>(), and half_float::operator>=().

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

Definition at line 1397 of file includes/half.hpp.

Referenced by half_float::atanh(), half_float::cbrt(), exp2_post(), half_float::expm1(), hyperbolic_args(), log2_post(), and tangent_post().

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

Definition at line 1935 of file includes/half.hpp.

References half_float::abs(), half_float::detail::f31::exp, exp2(), and half_float::detail::f31::m.

errflags()

int & half_float::detail::errflags ( )

inline

Internal exception flags.

Returns

reference to global exception flags

Definition at line 637 of file includes/half.hpp.

References HALF_THREAD_LOCAL.

Referenced by half_float::feclearexcept(), half_float::fegetexceptflag(), half_float::feraiseexcept(), half_float::fesetexceptflag(), half_float::fetestexcept(), half_float::fethrowexcept(), and raise().

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

Definition at line 1521 of file includes/half.hpp.

Referenced by half_float::cbrt(), erf(), exp2_post(), half_float::expm1(), gamma(), and hyperbolic_args().

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

Definition at line 1705 of file includes/half.hpp.

References check_underflow(), divide64(), half_float::exp(), and exp2().

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

Definition at line 901 of file includes/half.hpp.

References half_float::exp(), and sign_mask().

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

Definition at line 1081 of file includes/half.hpp.

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

Definition at line 1012 of file includes/half.hpp.

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

Definition at line 924 of file includes/half.hpp.

References half_float::exp().

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

Definition at line 1048 of file includes/half.hpp.

References half_float::abs(), builtin_isinf(), builtin_isnan(), builtin_signbit(), half_float::exp(), half_float::frexp(), half_float::ldexp(), and half_float::modf().

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

Definition at line 1954 of file includes/half.hpp.

References half_float::abs(), half_float::detail::f31::exp, exp2(), log2(), half_float::detail::f31::m, and sincos().

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

Definition at line 1320 of file includes/half.hpp.

References half2float_impl().

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

Definition at line 1276 of file includes/half.hpp.

References half_float::abs().

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

Definition at line 1113 of file includes/half.hpp.

References half_float::abs().

Referenced by half2float().

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

Definition at line 1300 of file includes/half.hpp.

References half_float::abs(), half_float::ldexp(), and max().

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

Definition at line 1334 of file includes/half.hpp.

References half_float::abs(), half_float::exp(), FE_INEXACT, FE_INVALID, max(), and min().

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

Definition at line 1667 of file includes/half.hpp.

References half_float::abs(), divide64(), half_float::exp(), exp2(), and multiply64().

Referenced by half_float::cosh(), half_float::sinh(), and half_float::tanh().

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

Definition at line 1762 of file includes/half.hpp.

References half_float::exp().

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

Definition at line 1093 of file includes/half.hpp.

References half_float::exp().

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

Definition at line 866 of file includes/half.hpp.

References half_float::abs(), half_float::exp(), FE_INEXACT, and signal().

invalid()

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

inline

Raise domain error and return NaN.

return quiet NaN

Exceptions

FE_INVALID

Definition at line 760 of file includes/half.hpp.

References FE_INVALID.

Referenced by half_float::acos(), half_float::acosh(), half_float::asin(), half_float::atanh(), half_float::cos(), half_float::fma(), half_float::fmod(), half_float::log(), half_float::log10(), half_float::log1p(), half_float::log2(), half_float::operator*(), half_float::operator+(), half_float::operator/(), half_float::pow(), half_float::remainder(), half_float::remquo(), half_float::rsqrt(), half_float::sin(), half_float::sincos(), half_float::sqrt(), half_float::tan(), and half_float::tgamma().

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

Definition at line 1548 of file includes/half.hpp.

Referenced by area(), half_float::atanh(), gamma(), half_float::log(), half_float::log10(), and half_float::log1p().

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

Definition at line 1737 of file includes/half.hpp.

References divide64(), half_float::exp(), and sign_mask().

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

Definition at line 1426 of file includes/half.hpp.

References half_float::exp().

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

Definition at line 1372 of file includes/half.hpp.

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

Definition at line 1383 of file includes/half.hpp.

Referenced by angle_arg(), half_float::cbrt(), half_float::exp(), half_float::expm1(), hyperbolic_args(), and half_float::pow().

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

Definition at line 801 of file includes/half.hpp.

References 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

Definition at line 772 of file includes/half.hpp.

References FE_DIVBYZERO.

Referenced by half_float::atanh(), half_float::lgamma(), half_float::log(), half_float::log10(), half_float::log1p(), half_float::log2(), half_float::logb(), half_float::operator/(), half_float::pow(), half_float::rsqrt(), and half_float::tgamma().

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

Definition at line 642 of file includes/half.hpp.

References errflags(), FE_DIVBYZERO, FE_INEXACT, FE_INVALID, FE_OVERFLOW, FE_UNDERFLOW, and half_float::feraiseexcept().

Referenced by half_float::feraiseexcept(), half_float::ilogb(), half_float::nextafter(), and half_float::nexttoward().

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

Definition at line 837 of file includes/half.hpp.

References FE_INEXACT, FE_OVERFLOW, FE_UNDERFLOW, and HALF_ERRHANDLING_UNDERFLOW_TO_INEXACT.

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

Definition at line 748 of file includes/half.hpp.

References signal().

Referenced by half_float::fmax(), half_float::fmin(), half_float::hypot(), and half_float::pow().

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

Definition at line 608 of file includes/half.hpp.

Referenced by atan2(), half_float::cbrt(), fixed2half(), half_float::log2(), log2_post(), half_float::pow(), sincos(), and half_float::tan().

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

Definition at line 708 of file includes/half.hpp.

References FE_INVALID.

Referenced by half_float::acos(), half_float::acosh(), half_float::asin(), half_float::asinh(), half_float::atan(), half_float::atan2(), half_float::atanh(), Node::attach(), half_float::cbrt(), half_float::cos(), half_float::cosh(), half_float::erf(), half_float::erfc(), half_float::exp(), half_float::exp2(), half_float::expm1(), half_float::fdim(), half_float::fma(), half_float::fmod(), half_float::frexp(), half_float::hypot(), integral(), half_float::lgamma(), half_float::log(), half_float::log10(), half_float::log1p(), half_float::log2(), half_float::logb(), half_float::modf(), half_float::nextafter(), half_float::nexttoward(), half_float::operator*(), half_float::operator+(), half_float::operator/(), half_float::pow(), half_float::remainder(), half_float::remquo(), half_float::rsqrt(), half_float::scalbln(), select(), half_float::sin(), half_float::sincos(), half_float::sinh(), half_float::sqrt(), half_float::tan(), half_float::tanh(), and half_float::tgamma().

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

Definition at line 721 of file includes/half.hpp.

References FE_INVALID.

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

Definition at line 735 of file includes/half.hpp.

References FE_INVALID.

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

Definition at line 1575 of file includes/half.hpp.

References arithmetic_shift(), and sign_mask().

Referenced by half_float::cos(), gamma(), half_float::sin(), half_float::sincos(), and half_float::tan().

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

Definition at line 1497 of file includes/half.hpp.

References half_float::exp().

Referenced by CV_FUNCS::computeSearchRegion(), TrackerVizOutput::drawUncertaintyEllipse(), and rs2::vec3d::length().

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

Definition at line 1784 of file includes/half.hpp.

References divide64(), and half_float::exp().

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

Definition at line 817 of file includes/half.hpp.

References FE_UNDERFLOW.

Variable Documentation

binary

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

Tag for binary construction.

Definition at line 553 of file includes/half.hpp.

Referenced by half_float::acos(), half_float::acosh(), half_float::asin(), half_float::asinh(), half_float::atan(), half_float::atan2(), half_float::atanh(), half_float::cbrt(), half_float::ceil(), half_float::copysign(), half_float::cos(), half_float::cosh(), std::numeric_limits< half_float::half >::denorm_min(), std::numeric_limits< half_float::half >::epsilon(), half_float::erf(), half_float::erfc(), half_float::exp(), half_float::exp2(), half_float::expm1(), half_float::fabs(), half_float::fdim(), half_float::floor(), half_float::fma(), half_float::fmax(), half_float::fmin(), half_float::fmod(), half_float::frexp(), half_float::hypot(), std::numeric_limits< half_float::half >::infinity(), half_float::lgamma(), half_float::log(), half_float::log10(), half_float::log1p(), half_float::log2(), half_float::logb(), std::numeric_limits< half_float::half >::lowest(), std::numeric_limits< half_float::half >::max(), std::numeric_limits< half_float::half >::min(), half_float::modf(), half_float::nanh(), half_float::nearbyint(), half_float::nextafter(), half_float::nexttoward(), half_float::operator*(), half_float::operator+(), half_float::half::operator++(), half_float::operator-(), half_float::half::operator--(), half_float::operator/(), half_float::pow(), std::numeric_limits< half_float::half >::quiet_NaN(), read_tensor_from_file(), TrackerInt8EntropyCalibrator::readCalibrationCache(), ds3d::readFile(), half_float::remainder(), half_float::remquo(), half_float::rint(), half_float::round(), std::numeric_limits< half_float::half >::round_error(), half_float::rsqrt(), half_float::scalbln(), std::numeric_limits< half_float::half >::signaling_NaN(), half_float::sin(), half_float::sincos(), half_float::sinh(), half_float::sqrt(), half_float::tan(), half_float::tanh(), half_float::tgamma(), and half_float::trunc().