Float types and arithmetic, see also and meta-group Math Support. More...

Namespaces
namespace	jau::float_literals

namespace	jau::string_literals

Classes
class	jau::float_ctti

class	jau::string_ctti

Typedefs
typedef jau::uint_bytes_t< sizeof(float64_t)>	jau::double_uint_t

typedef float	jau::float32_t

typedef double	jau::float64_t

typedef jau::uint_bytes_t< sizeof(float)>	jau::float_uint_t

typedef float	jau::si_lengthf32_t
	Length in fractions of meter using float.

typedef float	jau::si_massf32_t
	Mass in fractions of kilograms using float.

typedef float	jau::si_speedf32_t
	Speed in fractions of meter/seconds using float.

typedef float	jau::si_timef32_t
	Time in fractions of seconds using float.

typedef std::basic_ostream< uchar8_t >	jau::u8ostream

typedef std::basic_string< uchar8_t >	jau::u8string

typedef std::basic_string_view< uchar8_t >	jau::u8string_view

typedef uint8_t	jau::uchar8_t

Functions
template<std::floating_point T>
constexpr T	jau::adeg_to_rad (const T arc_degree) noexcept
	Converts arc-degree to radians.

template<std::floating_point T>
constexpr bool	jau::almost_equal (const T &a, const T &b, int ulp=1, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true, if both floating point values are equal in the sense that their potential difference is less or equal `epsilon * \|a+b\| * ulp`, where `\|a+b\|` scales epsilon to the magnitude of used values.

constexpr uint32_t	jau::bit_value (const float a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout.

constexpr uint64_t	jau::bit_value (const float64_t a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) float64_t floating-point bit layout.

constexpr uint32_t	jau::bit_value_raw (const float a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout.

constexpr uint64_t	jau::bit_value_raw (const float64_t a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) float64_t floating-point bit layout.

template<std::floating_point T>
jau::uint_bytes_t< sizeof(T)>	jau::bit_value_raw (const T a) noexcept
	Returns the unsigned integer representation according to IEEE 754 (IEC 559) floating-point bit layout.

template<std::floating_point T>
constexpr int	jau::compare (const T a, const T b) noexcept
	Returns `-1`, `0` or `1` if `a` is less, equal or greater than `b`, disregarding epsilon but considering `NaN`, `-Inf` and `+Inf`.

template<std::floating_point T>
constexpr int	jau::compare (const T a, const T b, const T epsilon) noexcept
	Returns `-1`, `0` or `1` if `a` is less, equal or greater than `b`, considering epsilon and `NaN`, `-Inf` and `+Inf`.

constexpr float64_t	jau::double_value (const uint64_t a) noexcept
	Converting IEEE 754 (IEC 559) float64_t floating-point bit layout to float64_t, see bit_value()

template<std::floating_point T>
constexpr bool	jau::equals (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if both values are equal, i.e.

template<std::floating_point T>
constexpr bool	jau::equals (const T &a, const T &b, int ulp, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true, if both floating point values are equal in the sense that their potential difference is less or equal `epsilon * ulp`.

template<std::floating_point T>
constexpr bool	jau::equals2 (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if both values are equal, i.e.

template<std::floating_point T>
constexpr bool	jau::equals_raw (const T &a, const T &b) noexcept
	Returns true if both values are equal disregarding epsilon but considering `NaN`, `-Inf` and `+Inf`.

constexpr uint32_t	jau::exponent_raw (float32_t a) noexcept
	Extracts the 8-bit exponent from the given IEEE 754 (IEC 559) float32_t.

constexpr uint32_t	jau::exponent_raw (float64_t a) noexcept
	Extracts the 11-bit exponent from the given IEEE 754 (IEC 559) float64_t.

constexpr int32_t	jau::exponent_unbiased (float32_t a) noexcept
	Extracts the unbiased 8-bit exponent from the given IEEE 754 (IEC 559) float64_t and subtracts 127, i.e.

constexpr int32_t	jau::exponent_unbiased (float64_t a) noexcept
	Extracts the unbiased 11-bit exponent from the given IEEE 754 (IEC 559) float64_t and subtracts 1023, i.e.

constexpr float	jau::float_value (const uint32_t a) noexcept
	Converting IEEE 754 (IEC 559) single floating-point bit layout to float, see bit_value()

template<std::floating_point T>
constexpr bool	jau::is_zero (const T &a, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if the given value is less than epsilon, w/ epsilon > 0.

template<std::floating_point T>
constexpr bool	jau::is_zero2f (const T &a, const T &b, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a and b are less than epsilon, w/ epsilon > 0.

template<std::floating_point T>
constexpr bool	jau::is_zero3f (const T &a, const T &b, const T &c, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a, b and c are less than epsilon, w/ epsilon > 0.

template<std::floating_point T>
constexpr bool	jau::is_zero4f (const T &a, const T &b, const T &c, const T &d, const T &epsilon=std::numeric_limits< T >::epsilon()) noexcept
	Returns true if all given values a, b, c and d are less than epsilon, w/ epsilon > 0.

template<std::floating_point T>
constexpr bool	jau::is_zero_raw (const T &a) noexcept
	Returns true if the given value is zero, disregarding `epsilon` but considering `NaN`, `-Inf` and `+Inf`.

template<std::floating_point T>
T	jau::machineEpsilon () noexcept
	Calculates the smallest floating point value approximation the given type T can represent, the machine epsilon of T.

template<std::floating_point T>
std::string &	jau::mat_to_string (std::string &sb, const std::string &rowPrefix, const std::string_view f, const T a[], const jau::nsize_t rows, const jau::nsize_t columns, const bool rowMajorOrder) noexcept
	Appends a matrix of floating points to the given string `sb`

template<std::floating_point T>
constexpr T	jau::rad_to_adeg (const T rad) noexcept
	Converts radians to arc-degree.

template<std::floating_point T>
constexpr jau::sint_bytes_t< sizeof(T)>	jau::round_to_int (const T v) noexcept
	Returns the rounded value cast to signed int.

template<std::floating_point T>
constexpr jau::uint_bytes_t< sizeof(T)>	jau::round_to_uint (const T v) noexcept
	Returns the rounded value cast to unsigned int.

template<std::floating_point T>
std::string &	jau::row_to_string (std::string &sb, const std::string_view f, const T a[], const jau::nsize_t rows, const jau::nsize_t columns, const bool rowMajorOrder, const jau::nsize_t row) noexcept
	Appends a row of floating points to the given string `sb`

constexpr uint32_t	jau::significand_raw (float32_t a) noexcept
	Extracts the 23-bit significand (fraction, mantissa) from the given IEEE 754 (IEC 559) float32_t.

constexpr uint64_t	jau::significand_raw (float64_t a) noexcept
	Extracts the 52-bit significand (fraction, mantissa) from the given IEEE 754 (IEC 559) float64_t.

Variables
constexpr uint64_t const	jau::double_iec559_exp_mask = 0x7ff0000000000000_u64
	Exponent mask bits 52-62 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint64_t const	jau::double_iec559_mant_mask = 0x000fffffffffffff_u64
	Mantissa mask bits 0-51 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint64_t const	jau::double_iec559_nan_bitval = 0x7ff8000000000000_u64
	NaN bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint64_t const	jau::double_iec559_negative_inf_bitval = 0xfff0000000000000_u64
	Negative infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint64_t const	jau::double_iec559_positive_inf_bitval = 0x7ff0000000000000_u64
	Positive infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint64_t const	jau::double_iec559_sign_bit = 1_u64 << 63
	Signed bit 63 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_exp_mask = 0x7f800000_u32
	Exponent mask bits 23-30 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_mant_mask = 0x007fffff_u32
	Mantissa mask bits 0-22 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_nan_bitval = 0x7fc00000_u32
	NaN bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_negative_inf_bitval = 0xff800000_u32
	Negative infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_positive_inf_bitval = 0x7f800000_u32
	Positive infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

constexpr uint32_t const	jau::float_iec559_sign_bit = 1_u32 << 31
	Signed bit 31 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

Detailed Description

Float types and arithmetic, see also and meta-group Math Support.

Typedef Documentation

◆ si_timef32_t

typedef float jau::si_timef32_t

Time in fractions of seconds using float.

Definition at line 36 of file float_si_types.hpp.

◆ si_lengthf32_t

typedef float jau::si_lengthf32_t

Length in fractions of meter using float.

Definition at line 38 of file float_si_types.hpp.

◆ si_massf32_t

typedef float jau::si_massf32_t

Mass in fractions of kilograms using float.

Definition at line 40 of file float_si_types.hpp.

◆ si_speedf32_t

typedef float jau::si_speedf32_t

Speed in fractions of meter/seconds using float.

Definition at line 42 of file float_si_types.hpp.

◆ float32_t

typedef float jau::float32_t

Definition at line 51 of file float_types.hpp.

◆ float64_t

typedef double jau::float64_t

Definition at line 52 of file float_types.hpp.

◆ float_uint_t

typedef jau::uint_bytes_t<sizeof(float)> jau::float_uint_t

Definition at line 66 of file float_types.hpp.

◆ double_uint_t

typedef jau::uint_bytes_t<sizeof(float64_t)> jau::double_uint_t

Definition at line 67 of file float_types.hpp.

◆ uchar8_t

typedef uint8_t jau::uchar8_t

Definition at line 47 of file string_types.hpp.

◆ u8string

typedef std::basic_string<uchar8_t> jau::u8string

Definition at line 48 of file string_types.hpp.

◆ u8string_view

typedef std::basic_string_view<uchar8_t> jau::u8string_view

Definition at line 49 of file string_types.hpp.

◆ u8ostream

typedef std::basic_ostream<uchar8_t> jau::u8ostream

Definition at line 56 of file string_types.hpp.

Function Documentation

◆ machineEpsilon()

template<std::floating_point T>

T jau::machineEpsilon ( )

noexcept

Calculates the smallest floating point value approximation the given type T can represent, the machine epsilon of T.

Template Parameters

T	a non integer float type

Returns: machine epsilon of T

Definition at line 53 of file float_math.hpp.

◆ is_zero()

template<std::floating_point T>

bool jau::is_zero	(	const T &	a,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if the given value is less than epsilon, w/ epsilon > 0.

Definition at line 66 of file float_math.hpp.

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◆ is_zero2f()

template<std::floating_point T>

bool jau::is_zero2f	(	const T &	a,
		const T &	b,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if all given values a and b are less than epsilon, w/ epsilon > 0.

Definition at line 72 of file float_math.hpp.

◆ is_zero3f()

template<std::floating_point T>

bool jau::is_zero3f	(	const T &	a,
		const T &	b,
		const T &	c,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if all given values a, b and c are less than epsilon, w/ epsilon > 0.

Definition at line 78 of file float_math.hpp.

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◆ is_zero4f()

template<std::floating_point T>

bool jau::is_zero4f	(	const T &	a,
		const T &	b,
		const T &	c,
		const T &	d,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if all given values a, b, c and d are less than epsilon, w/ epsilon > 0.

Definition at line 84 of file float_math.hpp.

◆ is_zero_raw()

template<std::floating_point T>

bool jau::is_zero_raw ( const T & a )

constexprnoexcept

Returns true if the given value is zero, disregarding epsilon but considering NaN, -Inf and +Inf.

Definition at line 93 of file float_math.hpp.

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◆ compare() [1/2]

template<std::floating_point T>

int jau::compare	(	const T	a,
		const T	b )

constexprnoexcept

Returns -1, 0 or 1 if a is less, equal or greater than b, disregarding epsilon but considering NaN, -Inf and +Inf.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf
NaN > 0
+Inf > -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare

Definition at line 113 of file float_math.hpp.

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◆ compare() [2/2]

template<std::floating_point T>

int jau::compare	(	const T	a,
		const T	b,
		const T	epsilon )

constexprnoexcept

Returns -1, 0 or 1 if a is less, equal or greater than b, considering epsilon and NaN, -Inf and +Inf.

epsilon must be > 0.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf
NaN > 0
+Inf > -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare
epsilon	defaults to std::numeric_limits<T>::epsilon(), must be > 0

Definition at line 153 of file float_math.hpp.

◆ equals_raw()

template<std::floating_point T>

bool jau::equals_raw	(	const T &	a,
		const T &	b )

constexprnoexcept

Returns true if both values are equal disregarding epsilon but considering NaN, -Inf and +Inf.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare

Definition at line 175 of file float_math.hpp.

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◆ equals() [1/2]

template<std::floating_point T>

bool jau::equals	(	const T &	a,
		const T &	b,
		const T &	allowed_deviation = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if both values are equal, i.e.

their absolute delta < epsilon, considering epsilon and NaN, -Inf and +Inf.

epsilon must be > 0.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare
epsilon	defaults to std::numeric_limits<T>::epsilon(), must be > 0

their absolute delta <= allowed_deviation.

Template Parameters

T	an integral type

Parameters

a	value to compare
b	value to compare
allowed_deviation	allowed deviation

Definition at line 197 of file float_math.hpp.

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◆ equals2()

template<std::floating_point T>

bool jau::equals2	(	const T &	a,
		const T &	b,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true if both values are equal, i.e.

their absolute delta < epsilon, considering epsilon but disregarding NaN, -Inf and +Inf.

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare

Definition at line 215 of file float_math.hpp.

◆ equals() [2/2]

template<std::floating_point T>

bool jau::equals	(	const T &	a,
		const T &	b,
		int	ulp,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true, if both floating point values are equal in the sense that their potential difference is less or equal epsilon * ulp.

epsilon must be > 0.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare
ulp	desired precision in ULPs (units in the last place)
epsilon	the machine epsilon of type T, defaults to `std::numeric_limits<T>::epsilon()`

Definition at line 237 of file float_math.hpp.

◆ almost_equal()

template<std::floating_point T>

bool jau::almost_equal	(	const T &	a,
		const T &	b,
		int	ulp = 1,
		const T &	epsilon = std::numeric_limits<T>::epsilon() )

constexprnoexcept

Returns true, if both floating point values are equal in the sense that their potential difference is less or equal epsilon * |a+b| * ulp, where |a+b| scales epsilon to the magnitude of used values.

epsilon must be > 0.

Implementation considers following corner cases:

NaN == NaN
+Inf == +Inf
-Inf == -Inf

Template Parameters

T	a non integer float type

Parameters

a	value to compare
b	value to compare
ulp	desired precision in ULPs (units in the last place), defaults to 1
epsilon	the machine epsilon of type T, defaults to `std::numeric_limits<T>::epsilon()`

Definition at line 260 of file float_math.hpp.

◆ round_to_int()

template<std::floating_point T>

jau::sint_bytes_t< sizeof(T)> jau::round_to_int ( const T v )

constexprnoexcept

Returns the rounded value cast to signed int.

Definition at line 274 of file float_math.hpp.

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◆ round_to_uint()

template<std::floating_point T>

jau::uint_bytes_t< sizeof(T)> jau::round_to_uint ( const T v )

constexprnoexcept

Returns the rounded value cast to unsigned int.

Definition at line 280 of file float_math.hpp.

◆ adeg_to_rad()

template<std::floating_point T>

T jau::adeg_to_rad ( const T arc_degree )

constexprnoexcept

Converts arc-degree to radians.

Definition at line 286 of file float_math.hpp.

◆ rad_to_adeg()

template<std::floating_point T>

T jau::rad_to_adeg ( const T rad )

constexprnoexcept

Converts radians to arc-degree.

Definition at line 292 of file float_math.hpp.

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◆ row_to_string()

template<std::floating_point T>

std::string & jau::row_to_string	(	std::string &	sb,
		const std::string_view	f,
		const T	a[],
		const jau::nsize_t	rows,
		const jau::nsize_t	columns,
		const bool	rowMajorOrder,
		const jau::nsize_t	row )

noexcept

Appends a row of floating points to the given string sb

Parameters

sb	string buffer to appends to
f	format string for each float element, e.g. "%10.5f"
a	the float data of size rows x columns
rows	float data `a` size row factor
columns	float data `a` size column factor
rowMajorOrder	if true floats are laid out in row-major-order, otherwise column-major-order (OpenGL)
row	selected row of float data `a`

Returns: given string buffer sb for chaining

Definition at line 308 of file float_math.hpp.

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◆ mat_to_string()

template<std::floating_point T>

std::string & jau::mat_to_string	(	std::string &	sb,
		const std::string &	rowPrefix,
		const std::string_view	f,
		const T	a[],
		const jau::nsize_t	rows,
		const jau::nsize_t	columns,
		const bool	rowMajorOrder )

noexcept

Appends a matrix of floating points to the given string sb

Parameters

sb	string buffer to appends to
rowPrefix	prefix for each row
f	format string for each float element, e.g. "%10.5f"
a	the float data of size rows x columns
rows	float data `a` size row factor
columns	float data `a` size column factor
rowMajorOrder	if true floats are laid out in row-major-order, otherwise column-major-order (OpenGL)

Returns: given string buffer sb for chaining

Definition at line 338 of file float_math.hpp.

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◆ bit_value_raw() [1/3]

template<std::floating_point T>

jau::uint_bytes_t< sizeof(T)> jau::bit_value_raw ( const T a )

noexcept

Returns the unsigned integer representation according to IEEE 754 (IEC 559) floating-point bit layout.

Meaningful semantics are only given if true == std::numeric_limits<T>::is_iec559.

This raw method does not collapse all NaN values.

The result is a functional unsigned integer that, i.e. reversible to double via float_value() or double via double_value() depending on type T,

See specific semantics of IEEE 754 (IEC 559) single floating-point bit layout:

float_iec559_sign_bit
float_iec559_exp_mask
float_iec559_mant_mask
float_iec559_positive_inf_bitval
float_iec559_negative_inf_bitval
float_iec559_nan_bitval

See specific semantics of IEEE 754 (IEC 559) double doubleing-point bit layout:

double_iec559_sign_bit
double_iec559_exp_mask
double_iec559_mant_mask
double_iec559_positive_inf_bitval
double_iec559_negative_inf_bitval
double_iec559_nan_bitval

Template Parameters

T	floating point type, e.g. float or double
matching	floating point unsigned integer type, e.g. float_uint_t or double_uint_t

Parameters

a	float value

Returns: unsigned integer representation of IEEE 754 (IEC 559) floating-point bit layout

See also: float_value(); double_value()

Definition at line 141 of file float_types.hpp.

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◆ bit_value_raw() [2/3]

uint32_t jau::bit_value_raw ( const float a )

constexprnoexcept

Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout.

See bit_value() for details.

This raw method does not collapse all NaN values to float_iec559_nan_bitval.

Definition at line 156 of file float_types.hpp.

◆ significand_raw() [1/2]

uint32_t jau::significand_raw ( float32_t a )

constexprnoexcept

Extracts the 23-bit significand (fraction, mantissa) from the given IEEE 754 (IEC 559) float32_t.

Examples: test_stringfmt_format.cpp.

Definition at line 161 of file float_types.hpp.

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◆ exponent_raw() [1/2]

uint32_t jau::exponent_raw ( float32_t a )

constexprnoexcept

Extracts the 8-bit exponent from the given IEEE 754 (IEC 559) float32_t.

Definition at line 165 of file float_types.hpp.

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◆ exponent_unbiased() [1/2]

int32_t jau::exponent_unbiased ( float32_t a )

constexprnoexcept

Extracts the unbiased 8-bit exponent from the given IEEE 754 (IEC 559) float64_t and subtracts 127, i.e.

exponent_raw(a)-127

Examples: test_stringfmt_format.cpp.

Definition at line 170 of file float_types.hpp.

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◆ bit_value() [1/2]

uint32_t jau::bit_value ( const float a )

constexprnoexcept

Returns the unsigned integer representation according to IEEE 754 (IEC 559) single floating-point bit layout.

Meaningful semantics are only given if true == std::numeric_limits<float>::is_iec559.

All NaN values which are represented by float_iec559_nan_bitval.

The result is a functional unsigned integer that, i.e. reversible to double via float_value().

See specific semantics of IEEE 754 (IEC 559) single floating-point bit layout:

float_iec559_sign_bit
float_iec559_exp_mask
float_iec559_mant_mask
float_iec559_positive_inf_bitval
float_iec559_negative_inf_bitval
float_iec559_nan_bitval

The result is a functional unsigned integer that, i.e. reversible to float via float_value(), except all NaN values which are represented by float_iec559_nan_bitval.

Parameters

a	single float value

Returns: unsigned integer representation of IEEE 754 (IEC 559) single floating-point bit layout

See also: float_value(); bit_value_raw()

Definition at line 199 of file float_types.hpp.

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◆ float_value()

float jau::float_value ( const uint32_t a )

constexprnoexcept

Converting IEEE 754 (IEC 559) single floating-point bit layout to float, see bit_value()

Definition at line 207 of file float_types.hpp.

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◆ bit_value_raw() [3/3]

uint64_t jau::bit_value_raw ( const float64_t a )

constexprnoexcept

Returns the unsigned integer representation according to IEEE 754 (IEC 559) float64_t floating-point bit layout.

See bit_value() for details.

This raw method does not collapse all NaN values to double_iec559_nan_bitval.

Definition at line 219 of file float_types.hpp.

◆ significand_raw() [2/2]

uint64_t jau::significand_raw ( float64_t a )

constexprnoexcept

Extracts the 52-bit significand (fraction, mantissa) from the given IEEE 754 (IEC 559) float64_t.

Definition at line 224 of file float_types.hpp.

◆ exponent_raw() [2/2]

uint32_t jau::exponent_raw ( float64_t a )

constexprnoexcept

Extracts the 11-bit exponent from the given IEEE 754 (IEC 559) float64_t.

Definition at line 228 of file float_types.hpp.

◆ exponent_unbiased() [2/2]

int32_t jau::exponent_unbiased ( float64_t a )

constexprnoexcept

Extracts the unbiased 11-bit exponent from the given IEEE 754 (IEC 559) float64_t and subtracts 1023, i.e.

exponent_raw(a)-1023

Definition at line 233 of file float_types.hpp.

◆ bit_value() [2/2]

uint64_t jau::bit_value ( const float64_t a )

constexprnoexcept

Returns the unsigned integer representation according to IEEE 754 (IEC 559) float64_t floating-point bit layout.

Meaningful semantics are only given if true == std::numeric_limits<float64_t>::is_iec559.

All NaN values which are represented by double_iec559_nan_bitval.

The result is a functional unsigned integer that, i.e. reversible to float64_t via double_value().

See specific semantics of IEEE 754 (IEC 559) float64_t floating-point bit layout:

double_iec559_sign_bit
double_iec559_exp_mask
double_iec559_mant_mask
double_iec559_positive_inf_bitval
double_iec559_negative_inf_bitval
double_iec559_nan_bitval

Parameters

a	float64_t float value

Returns: unsigned integer representation of IEEE 754 (IEC 559) float64_t floating-point bit layout

See also: double_value(); bit_value_raw()

Definition at line 260 of file float_types.hpp.

◆ double_value()

float64_t jau::double_value ( const uint64_t a )

constexprnoexcept

Converting IEEE 754 (IEC 559) float64_t floating-point bit layout to float64_t, see bit_value()

Definition at line 267 of file float_types.hpp.

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Variable Documentation

◆ float_iec559_sign_bit

uint32_t const jau::float_iec559_sign_bit = 1_u32 << 31

constexpr

Signed bit 31 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0x80000000.

Definition at line 70 of file float_types.hpp.

◆ float_iec559_exp_mask

uint32_t const jau::float_iec559_exp_mask = 0x7f800000_u32

constexpr

Exponent mask bits 23-30 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0x7f800000.

Definition at line 73 of file float_types.hpp.

◆ float_iec559_mant_mask

uint32_t const jau::float_iec559_mant_mask = 0x007fffff_u32

constexpr

Mantissa mask bits 0-22 of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0x007fffff.

Definition at line 76 of file float_types.hpp.

◆ float_iec559_positive_inf_bitval

uint32_t const jau::float_iec559_positive_inf_bitval = 0x7f800000_u32

constexpr

Positive infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0x7f800000.

Definition at line 79 of file float_types.hpp.

◆ float_iec559_negative_inf_bitval

uint32_t const jau::float_iec559_negative_inf_bitval = 0xff800000_u32

constexpr

Negative infinity bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0xff800000.

Definition at line 82 of file float_types.hpp.

◆ float_iec559_nan_bitval

uint32_t const jau::float_iec559_nan_bitval = 0x7fc00000_u32

constexpr

NaN bit-value of IEEE 754 (IEC 559) single float-point bit layout, i.e.

0x7fc00000.

Definition at line 85 of file float_types.hpp.

◆ double_iec559_sign_bit

uint64_t const jau::double_iec559_sign_bit = 1_u64 << 63

constexpr

Signed bit 63 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0x8000000000000000.

Definition at line 88 of file float_types.hpp.

◆ double_iec559_exp_mask

uint64_t const jau::double_iec559_exp_mask = 0x7ff0000000000000_u64

constexpr

Exponent mask bits 52-62 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0x7ff0000000000000.

Definition at line 91 of file float_types.hpp.

◆ double_iec559_mant_mask

uint64_t const jau::double_iec559_mant_mask = 0x000fffffffffffff_u64

constexpr

Mantissa mask bits 0-51 of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0x000fffffffffffff.

Definition at line 94 of file float_types.hpp.

◆ double_iec559_positive_inf_bitval

uint64_t const jau::double_iec559_positive_inf_bitval = 0x7ff0000000000000_u64

constexpr

Positive infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0x7ff0000000000000.

Definition at line 97 of file float_types.hpp.

◆ double_iec559_negative_inf_bitval

uint64_t const jau::double_iec559_negative_inf_bitval = 0xfff0000000000000_u64

constexpr

Negative infinity bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0xfff0000000000000.

Definition at line 100 of file float_types.hpp.

◆ double_iec559_nan_bitval

uint64_t const jau::double_iec559_nan_bitval = 0x7ff8000000000000_u64

constexpr

NaN bit-value of IEEE 754 (IEC 559) double double-point bit layout, i.e.

0x7ff8000000000000.

Definition at line 103 of file float_types.hpp.

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ si_timef32_t

◆ si_lengthf32_t

◆ si_massf32_t

◆ si_speedf32_t

◆ float32_t

◆ float64_t

◆ float_uint_t

◆ double_uint_t

◆ uchar8_t

◆ u8string

◆ u8string_view

◆ u8ostream

Function Documentation

◆ machineEpsilon()

◆ is_zero()

◆ is_zero2f()

◆ is_zero3f()

◆ is_zero4f()

◆ is_zero_raw()

◆ compare() [1/2]

◆ compare() [2/2]

◆ equals_raw()

◆ equals() [1/2]

◆ equals2()

◆ equals() [2/2]

◆ almost_equal()

◆ round_to_int()

◆ round_to_uint()

◆ adeg_to_rad()

◆ rad_to_adeg()

◆ row_to_string()

◆ mat_to_string()

◆ bit_value_raw() [1/3]

◆ bit_value_raw() [2/3]

◆ significand_raw() [1/2]

◆ exponent_raw() [1/2]

◆ exponent_unbiased() [1/2]

◆ bit_value() [1/2]

◆ float_value()

◆ bit_value_raw() [3/3]

◆ significand_raw() [2/2]

◆ exponent_raw() [2/2]

◆ exponent_unbiased() [2/2]

◆ bit_value() [2/2]

◆ double_value()

Variable Documentation

◆ float_iec559_sign_bit

◆ float_iec559_exp_mask

◆ float_iec559_mant_mask

◆ float_iec559_positive_inf_bitval

◆ float_iec559_negative_inf_bitval

◆ float_iec559_nan_bitval

◆ double_iec559_sign_bit

◆ double_iec559_exp_mask

◆ double_iec559_mant_mask

◆ double_iec559_positive_inf_bitval

◆ double_iec559_negative_inf_bitval

◆ double_iec559_nan_bitval