fxd Namespace Reference

This is the namespace where the entire library is defined. More...

Namespaces
namespace	down
	Round down.
namespace	except
	Throw on overflow.
namespace	expect
	Return fxd::expect::maybe<...> result.
namespace	saturate
	Clamp on overflow.
namespace	up
	Round up.
namespace	zero
	Round to zero.

Classes
struct	fixed
	The fixed-point class template. More...
struct	is_fixed_point< fixed< Int, Frac, Raw > >
	Test if a type is fxd::fixed. More...
struct	is_signed_fixed_point< fixed< Int, Frac, Raw > >
	Test if a type is signed fxd::fixed. More...
class	uniform_real_distribution
	Analogous to std::uniform_real_distribution. More...

Concepts
concept	fixed_point
	Concept to match any fxd::fixed
concept	unsigned_fixed_point
	Concept to match only unsigned fxd::fixed
concept	signed_fixed_point
	Concept to match only signed fxd::fixed

Typedefs
template<int Int, int Frac>
using	ufixed = fixed< Int, Frac, detail::select_uint_t< Int+Frac > >
	Alias for creating unsigned fxd::fixed.

Enumerations
enum class	error { underflow , overflow , not_a_number }
	Error values reported by fxd::expect function. More...

Functions
template<fixed_point Dst, fixed_point Src>
constexpr Dst	fixed_cast (Src src) noexcept
	Convert a fixed point to a different type of fixed point.
template<int Int, int Frac, typename Raw = detail::select_int_t<Int + Frac>, fixed_point Src>
constexpr fixed< Int, Frac, Raw >	fixed_cast (Src src) noexcept
	Convert a fixed point to a different type of fixed point.
template<int Int, int Frac, typename Raw = detail::select_uint_t<Int + Frac>, fixed_point Src>
constexpr fixed< Int, Frac, Raw >	ufixed_cast (Src src) noexcept
	Convert a fixed point to a different type of fixed point (unsigned version.)
template<fixed_point Fxd>
constexpr bool	operator== (Fxd a, Fxd b) noexcept
	Equality check for two similar fxd::fixed.
template<fixed_point A, fixed_point B>
constexpr bool	operator== (A a, B b) noexcept
	Equality check for dissimilar fxd::fixed.
template<fixed_point Fxd, std::integral I>
constexpr bool	operator== (Fxd a, I b) noexcept
	fxd::fixed == integer.
template<fixed_point Fxd, std::floating_point Flt> requires (requires (Fxd fxd) {to_float(fxd);})
constexpr bool	operator== (Fxd a, Flt b) noexcept
	fxd::fixed == floating-point
template<fixed_point Fxd>
constexpr std::strong_ordering	operator<=> (Fxd a, Fxd b) noexcept
template<fixed_point A, fixed_point B>
constexpr std::strong_ordering	operator<=> (A a, B b) noexcept
template<fixed_point Fxd, std::integral I>
constexpr std::strong_ordering	operator<=> (Fxd a, I b) noexcept
template<fixed_point Fxd, std::floating_point Flt> requires (requires (Fxd a) {to_float(a);})
constexpr std::partial_ordering	operator<=> (Fxd a, Flt b) noexcept
template<std::integral I, fixed_point Fxd>
constexpr I	to_int (Fxd f) noexcept
	Convert to integer.
template<fixed_point Fxd> requires detail::has_int_for<Fxd::int_bits, typename Fxd::raw_type>
constexpr detail::select_int_for< Fxd::int_bits, typename Fxd::raw_type >	to_int (Fxd f) noexcept
	Convert to the "natural integer" for this fixed-point type.
template<std::floating_point Flt, fixed_point Fxd>
constexpr Flt	to_float (Fxd f) noexcept
	Convert a fixed-point to a floating-point type, rounds to zero.
template<fixed_point Fxd>
constexpr std::numeric_limits< Fxd >::float_type	to_float (Fxd f) noexcept
	Converts a fixed-point to its natural floating-point type (with no losses/rounding).
template<fixed_point Fxd>
constexpr Fxd	abs (Fxd f) noexcept
	Same as std::abs().
template<fixed_point Fxd>
constexpr Fxd	fdim (Fxd a, Fxd b) noexcept
	Same as std::fdim().
template<fixed_point Fxd>
constexpr Fxd	fma (Fxd a, Fxd b, Fxd c) noexcept
	Same as std::fma().
template<fixed_point Fxd>
constexpr int	ilogb (Fxd x) noexcept
	Same as std::ilogb().
template<fixed_point Fxd>
constexpr Fxd	midpoint (Fxd a, Fxd b) noexcept
	Same as std::midpoint().
template<fixed_point Fxd>
constexpr Fxd	nextafter (Fxd from, Fxd to) noexcept
	Same as std::nextafter().
template<unsigned_fixed_point Fxd> requires (Fxd::int_bits > 0 && Fxd::frac_bits >= 0)
constexpr Fxd	sqrt (Fxd x) noexcept
	Same as std::sqrt().
template<signed_fixed_point Fxd> requires (Fxd::int_bits > 1 && Fxd::frac_bits >= 0)
constexpr Fxd	sqrt (Fxd x) noexcept
template<unsigned_fixed_point Fxd> requires (Fxd::int_bits > 0 && Fxd::frac_bits >= 0)
Fxd	sqrt_bin (Fxd x) noexcept
template<signed_fixed_point Fxd> requires (Fxd::int_bits > 1 && Fxd::frac_bits >= 0)
Fxd	sqrt_bin (Fxd x) noexcept
template<fixed_point Fxd, std::convertible_to< Fxd > T>
constexpr Fxd &	operator+= (Fxd &a, T b) noexcept
	In-place addition.
template<fixed_point Fxd, std::convertible_to< Fxd > T>
constexpr Fxd &	operator-= (Fxd &a, T b) noexcept
	In-place subtraction.
template<fixed_point Fxd, std::convertible_to< Fxd > T> requires (!std::integral<T>)
constexpr Fxd &	operator*= (Fxd &a, T b) noexcept
	In-place multiplication.
template<fixed_point Fxd, std::integral I>
constexpr Fxd &	operator*= (Fxd &a, I b) noexcept
	In-place multiplication by integer.
template<fixed_point Fxd, std::convertible_to< Fxd > T> requires (!std::integral<T>)
constexpr Fxd &	operator/= (Fxd &a, T b) noexcept
	In-place division.
template<fixed_point Fxd, std::integral I>
constexpr Fxd &	operator/= (Fxd &a, I b) noexcept
	In-place division by integer.
template<fixed_point Fxd>
constexpr Fxd &	operator++ (Fxd &a) noexcept
	Pre-increment.
template<fixed_point Fxd>
constexpr Fxd &	operator-- (Fxd &a) noexcept
	Pre-decrement.
template<fixed_point Fxd>
constexpr Fxd	operator++ (Fxd &a, int) noexcept
	Post-increment.
template<fixed_point Fxd>
constexpr Fxd	operator-- (Fxd &a, int) noexcept
	Post-decrement.
template<fixed_point Fxd>
constexpr Fxd	operator+ (Fxd a) noexcept
	Unary +.
template<fixed_point Fxd>
constexpr Fxd	operator- (Fxd a) noexcept
	Negation.
template<typename A , typename B > requires (fixed_point<A> || fixed_point<B>)
constexpr std::common_type_t< A, B >	operator+ (A a, B b) noexcept
	Addition.
template<typename A , typename B > requires (fixed_point<A> || fixed_point<B>)
constexpr std::common_type_t< A, B >	operator- (A a, B b) noexcept
	Subtraction.
template<fixed_point A, fixed_point B>
constexpr std::common_type_t< A, B >	operator* (A a, B b) noexcept
	Multiply: fxd::fixed * fxd::fixed
template<fixed_point Fxd, std::integral I>
constexpr Fxd	operator* (Fxd a, I b) noexcept
	Multiply: fxd::fixed * integer.
template<std::integral I, fixed_point Fxd>
constexpr Fxd	operator* (I a, Fxd b) noexcept
	Multiply: integer * fxd::fixed
template<fixed_point Fxd, std::floating_point Flt>
constexpr Fxd	operator* (Fxd a, Flt b) noexcept
	Multiply: fxd::fixed * floating-point
template<std::floating_point Flt, fixed_point Fxd>
constexpr Fxd	operator* (Flt a, Fxd b) noexcept
	Multiply: floating-point * fxd::fixed
template<fixed_point A, fixed_point B>
constexpr std::common_type_t< A, B >	operator/ (A a, B b) noexcept
	Divide: fxd::fixed / fxd::fixed
template<fixed_point Fxd, std::integral I>
constexpr Fxd	operator/ (Fxd a, I b) noexcept
	Divide: fxd::fixed / integer.
template<std::integral I, fixed_point Fxd>
constexpr Fxd	operator/ (I a, Fxd b) noexcept
	Divide: integer / fxd::fixed
template<fixed_point Fxd, std::floating_point Flt>
constexpr Fxd	operator/ (Fxd a, Flt b) noexcept
	Divide: fxd::fixed / floating-point
template<std::floating_point Flt, fixed_point Fxd>
constexpr Fxd	operator/ (Flt a, Fxd b) noexcept
	Divide: floating-point / fxd::fixed.
template<typename CharT , typename Traits , fixed_point Fxd>
std::basic_ostream< CharT, Traits > &	operator<< (std::basic_ostream< CharT, Traits > &out, Fxd f)
	Output (by converting to a floating-point value).
template<typename CharT , typename Traits , fixed_point Fxd>
std::basic_istream< CharT, Traits > &	operator>> (std::basic_istream< CharT, Traits > &in, Fxd &f)
	Input (by converting from a floatiung-point value).

Variables
template<typename T >
constexpr bool	is_fixed_point_v = is_fixed_point<T>::value
	Helper template variable for fxd::is_fixed_point
template<typename T >
constexpr bool	is_signed_fixed_point_v = is_signed_fixed_point<T>::value
	Helper template variable for fxd::is_signed_fixed_point

Detailed Description

This is the namespace where the entire library is defined.

Typedef Documentation

ufixed

using ufixed = fixed<Int, Frac, detail::select_uint_t<Int + Frac> >

Alias for creating unsigned fxd::fixed.

Definition at line 131 of file fixed.hpp.

Enumeration Type Documentation

error

enum class error

strong

Error values reported by fxd::expect function.

Enumerator
underflow
overflow
not_a_number

Definition at line 14 of file error.hpp.

Function Documentation

abs()

constexpr Fxd abs ( Fxd  f )

constexprnoexcept

Same as std::abs().

Definition at line 38 of file math.hpp.

fdim()

constexpr Fxd fdim ( Fxd  a, Fxd  b  )

constexprnoexcept

Same as std::fdim().

Definition at line 49 of file math.hpp.

fixed_cast() [1/2]

constexpr Dst fixed_cast ( Src  src )

constexprnoexcept

Convert a fixed point to a different type of fixed point.

Definition at line 28 of file casting.hpp.

fixed_cast() [2/2]

constexpr fixed< Int, Frac, Raw > fixed_cast ( Src  src )

constexprnoexcept

Convert a fixed point to a different type of fixed point.

Definition at line 68 of file casting.hpp.

fma()

constexpr Fxd fma ( Fxd  a, Fxd  b, Fxd  c  )

constexprnoexcept

Same as std::fma().

Definition at line 64 of file math.hpp.

ilogb()

constexpr int ilogb ( Fxd  x )

constexprnoexcept

Same as std::ilogb().

Definition at line 77 of file math.hpp.

midpoint()

constexpr Fxd midpoint ( Fxd  a, Fxd  b  )

constexprnoexcept

Same as std::midpoint().

Definition at line 158 of file math.hpp.

nextafter()

constexpr Fxd nextafter ( Fxd  from, Fxd  to  )

constexprnoexcept

Same as std::nextafter().

Definition at line 171 of file math.hpp.

operator*() [1/5]

constexpr std::common_type_t< A, B > operator* ( A  a, B  b  )

constexprnoexcept

Multiply: fxd::fixed * fxd::fixed

Definition at line 251 of file operators.hpp.

operator*() [2/5]

constexpr Fxd operator* ( Flt  a, Fxd  b  )

constexprnoexcept

Multiply: floating-point * fxd::fixed

Definition at line 304 of file operators.hpp.

operator*() [3/5]

constexpr Fxd operator* ( Fxd  a, Flt  b  )

constexprnoexcept

Multiply: fxd::fixed * floating-point

Definition at line 290 of file operators.hpp.

operator*() [4/5]

constexpr Fxd operator* ( Fxd  a, I  b  )

constexprnoexcept

Multiply: fxd::fixed * integer.

Definition at line 265 of file operators.hpp.

operator*() [5/5]

constexpr Fxd operator* ( I  a, Fxd  b  )

constexprnoexcept

Multiply: integer * fxd::fixed

Definition at line 278 of file operators.hpp.

operator*=() [1/2]

constexpr Fxd & operator*= ( Fxd &  a, I  b  )

constexprnoexcept

In-place multiplication by integer.

Definition at line 92 of file operators.hpp.

operator*=() [2/2]

constexpr Fxd & operator*= ( Fxd &  a, T  b  )

constexprnoexcept

In-place multiplication.

Definition at line 79 of file operators.hpp.

operator+() [1/2]

constexpr std::common_type_t< A, B > operator+ ( A  a, B  b  )

constexprnoexcept

Addition.

Definition at line 218 of file operators.hpp.

operator+() [2/2]

constexpr Fxd operator+ ( Fxd  a )

constexprnoexcept

Unary +.

Definition at line 194 of file operators.hpp.

operator++() [1/2]

constexpr Fxd & operator++ ( Fxd &  a )

constexprnoexcept

Pre-increment.

Definition at line 138 of file operators.hpp.

operator++() [2/2]

constexpr Fxd operator++ ( Fxd &  a, int    )

constexprnoexcept

Post-increment.

Definition at line 162 of file operators.hpp.

operator+=()

constexpr Fxd & operator+= ( Fxd &  a, T  b  )

constexprnoexcept

In-place addition.

Definition at line 50 of file operators.hpp.

operator-() [1/2]

constexpr std::common_type_t< A, B > operator- ( A  a, B  b  )

constexprnoexcept

Subtraction.

Definition at line 235 of file operators.hpp.

operator-() [2/2]

constexpr Fxd operator- ( Fxd  a )

constexprnoexcept

Negation.

Definition at line 205 of file operators.hpp.

operator--() [1/2]

constexpr Fxd & operator-- ( Fxd &  a )

constexprnoexcept

Pre-decrement.

Definition at line 150 of file operators.hpp.

operator--() [2/2]

constexpr Fxd operator-- ( Fxd &  a, int    )

constexprnoexcept

Post-decrement.

Definition at line 175 of file operators.hpp.

operator-=()

constexpr Fxd & operator-= ( Fxd &  a, T  b  )

constexprnoexcept

In-place subtraction.

Definition at line 64 of file operators.hpp.

operator/() [1/5]

constexpr std::common_type_t< A, B > operator/ ( A  a, B  b  )

constexprnoexcept

Divide: fxd::fixed / fxd::fixed

Definition at line 319 of file operators.hpp.

operator/() [2/5]

constexpr Fxd operator/ ( Flt  a, Fxd  b  )

constexprnoexcept

Divide: floating-point / fxd::fixed.

Definition at line 372 of file operators.hpp.

operator/() [3/5]

constexpr Fxd operator/ ( Fxd  a, Flt  b  )

constexprnoexcept

Divide: fxd::fixed / floating-point

Definition at line 359 of file operators.hpp.

operator/() [4/5]

constexpr Fxd operator/ ( Fxd  a, I  b  )

constexprnoexcept

Divide: fxd::fixed / integer.

Definition at line 333 of file operators.hpp.

operator/() [5/5]

constexpr Fxd operator/ ( I  a, Fxd  b  )

constexprnoexcept

Divide: integer / fxd::fixed

Definition at line 346 of file operators.hpp.

operator/=() [1/2]

constexpr Fxd & operator/= ( Fxd &  a, I  b  )

constexprnoexcept

In-place division by integer.

Definition at line 120 of file operators.hpp.

operator/=() [2/2]

constexpr Fxd & operator/= ( Fxd &  a, T  b  )

constexprnoexcept

In-place division.

Definition at line 107 of file operators.hpp.

operator<<()

std::basic_ostream< CharT, Traits > & operator<<	(	std::basic_ostream< CharT, Traits > &	out,
		Fxd	f
	)

Output (by converting to a floating-point value).

Definition at line 372 of file operators.hpp.

operator<=>() [1/4]

constexpr std::strong_ordering operator<=> ( A  a, B  b  )

constexprnoexcept

Definition at line 133 of file compare.hpp.

operator<=>() [2/4]

constexpr std::partial_ordering operator<=> ( Fxd  a, Flt  b  )

constexprnoexcept

Definition at line 215 of file compare.hpp.

operator<=>() [3/4]

constexpr std::strong_ordering operator<=> ( Fxd  a, Fxd  b  )

constexprnoexcept

Definition at line 116 of file compare.hpp.

operator<=>() [4/4]

constexpr std::strong_ordering operator<=> ( Fxd  a, I  b  )

constexprnoexcept

Definition at line 188 of file compare.hpp.

operator==() [1/4]

constexpr bool operator== ( A  a, B  b  )

constexprnoexcept

Equality check for dissimilar fxd::fixed.

Definition at line 39 of file compare.hpp.

operator==() [2/4]

constexpr bool operator== ( Fxd  a, Flt  b  )

constexprnoexcept

fxd::fixed == floating-point

Definition at line 104 of file compare.hpp.

operator==() [3/4]

constexpr bool operator== ( Fxd  a, Fxd  b  )

constexprnoexcept

Equality check for two similar fxd::fixed.

Definition at line 25 of file compare.hpp.

operator==() [4/4]

constexpr bool operator== ( Fxd  a, I  b  )

constexprnoexcept

fxd::fixed == integer.

Definition at line 79 of file compare.hpp.

operator>>()

std::basic_istream< CharT, Traits > & operator>>	(	std::basic_istream< CharT, Traits > &	in,
		Fxd &	f
	)

Input (by converting from a floatiung-point value).

Definition at line 402 of file operators.hpp.

sqrt() [1/2]

constexpr Fxd sqrt ( Fxd  x )

constexprnoexcept

Same as std::sqrt().

Note

If the argument x is negative, errno is set to EDOM.

Examples

square-root.cpp.

Definition at line 194 of file math.hpp.

sqrt() [2/2]

constexpr Fxd sqrt ( Fxd  x )

constexprnoexcept

Definition at line 244 of file math.hpp.

sqrt_bin() [1/2]

Fxd sqrt_bin ( Fxd  x )

noexcept

Examples

square-root.cpp.

Definition at line 261 of file math.hpp.

sqrt_bin() [2/2]

Fxd sqrt_bin ( Fxd  x )

noexcept

Definition at line 352 of file math.hpp.

to_float() [1/2]

constexpr Flt to_float ( Fxd  f )

constexprnoexcept

Convert a fixed-point to a floating-point type, rounds to zero.

Definition at line 98 of file conversions.hpp.

to_float() [2/2]

constexpr std::numeric_limits< Fxd >::float_type to_float ( Fxd  f )

constexprnoexcept

Converts a fixed-point to its natural floating-point type (with no losses/rounding).

Definition at line 112 of file conversions.hpp.

to_int() [1/2]

constexpr I to_int ( Fxd  f )

constexprnoexcept

Convert to integer.

Definition at line 45 of file conversions.hpp.

to_int() [2/2]

constexpr detail::select_int_for< Fxd::int_bits, typename Fxd::raw_type > to_int ( Fxd  f )

constexprnoexcept

Convert to the "natural integer" for this fixed-point type.

Definition at line 72 of file conversions.hpp.

ufixed_cast()

constexpr fixed< Int, Frac, Raw > ufixed_cast ( Src  src )

constexprnoexcept

Convert a fixed point to a different type of fixed point (unsigned version.)

Definition at line 83 of file casting.hpp.

Variable Documentation

is_fixed_point_v

constexpr bool is_fixed_point_v = is_fixed_point<T>::value

inlineconstexpr

Helper template variable for fxd::is_fixed_point

Definition at line 35 of file traits.hpp.

is_signed_fixed_point_v

constexpr bool is_signed_fixed_point_v = is_signed_fixed_point<T>::value

inlineconstexpr

Helper template variable for fxd::is_signed_fixed_point

Definition at line 51 of file traits.hpp.