Mathematical types, constants, and utilities: fixed-point, vectors, point. More...

Namespaces
namespace	constants
	Variable templates for mathematical constants.

Classes
class	fixed
	Fixed-point numeric type with configurable storage and fractional precision. More...
struct	is_fixed_point
	Unary type trait: `true` if T is an instantiation of toy::math::fixed, `false` otherwise. More...
struct	is_fixed_point< fixed< Base, Intermediate, Fraction, Rounding > >
class	Point
	2D integer point for UI and input coordinates. More...
class	Vector2
	2D vector with floating-point or fixed-point components for positions, movement, and physics. More...

Concepts
concept	FractionalConstantType
	Type that can be used with toy::math::constants variable templates.
concept	ValidFixedPointTypes
	Concept constraining template parameters for toy::math::fixed.
concept	fixed_point
	Concept satisfied when T is an instantiation of toy::math::fixed.
concept	PointScalar
	Concept satisfied when T is a signed integral, floating-point, or fixed-point type.
concept	Vector2Component
	Concept satisfied when T is a component type allowed as toy::math::Vector2 template parameter.

Typedefs
using	real_t = float
	Floating‑point scalar type.

Functions
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator- (const fixed< Base, Intermediate, Fraction, Rounding > &value) noexcept
	Unary minus: returns the negation of a toy::math::fixed value.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator+ (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Returns a + b as a new toy::math::fixed (same type as left operand).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator+ (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Returns a + b as a new toy::math::fixed (fixed plus integral whole units).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator+ (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Returns a + b as a new toy::math::fixed (integral whole units plus fixed).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator- (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Returns a - b as a new toy::math::fixed (same type as left operand).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator- (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Returns a - b as a new toy::math::fixed (fixed minus integral whole units).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator- (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Returns a - b as a new toy::math::fixed (integral whole units minus fixed).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator* (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Returns a * b as a new toy::math::fixed (same type as left toy::math::fixed operand).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator* (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Returns a * b as a new toy::math::fixed (fixed times integral whole units).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator* (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Returns a * b as a new toy::math::fixed (integral whole units times fixed).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator/ (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Returns a / b as a new toy::math::fixed.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator/ (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Returns a / b as a new toy::math::fixed (fixed divided by integral whole units).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	operator/ (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Returns a / b as a new toy::math::fixed (integral whole units divided by fixed).
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr bool	operator== (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Compares two toy::math::fixed values for equality.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>
constexpr bool	operator== (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Compares a toy::math::fixed value with an integral for equality.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>
constexpr bool	operator== (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Compares an integral with a toy::math::fixed value for equality.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>
constexpr strong_ordering	operator<=> (const fixed< Base, Intermediate, Fraction, Rounding > &a, const fixed< Base, Intermediate, Fraction, OtherRounding > &b) noexcept
	Three-way comparison of two toy::math::fixed values.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>
constexpr strong_ordering	operator<=> (const fixed< Base, Intermediate, Fraction, Rounding > &a, const T &b) noexcept
	Three-way comparison of a toy::math::fixed value with an integral.
template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>
constexpr strong_ordering	operator<=> (const T &a, const fixed< Base, Intermediate, Fraction, Rounding > &b) noexcept
	Three-way comparison of an integral with a toy::math::fixed value.
constexpr Point	operator- (const Point &point) noexcept
	Unary minus: negated coordinates.
constexpr Point	operator+ (const Point &left, const Point &right) noexcept
	Addition of two points.
constexpr Point	operator- (const Point &left, const Point &right) noexcept
	Subtraction of two points.
template<PointScalar T>
constexpr Point	operator* (const Point &point, const T &scalar) noexcept
	Point scaled by scalar and truncated to integer.
template<PointScalar T>
constexpr Point	operator* (const T &scalar, const Point &point) noexcept
	Point scaled by scalar (scalar on the left).
template<PointScalar T>
constexpr Point	operator/ (const Point &point, const T &scalar) noexcept
	Point divided by scalar and truncated to integer.
constexpr bool	operator== (const Point &left, const Point &right) noexcept
	Exact equality of two points.
template<typename T>
constexpr T	abs (const T &value) noexcept
	Returns the absolute value of value.
template<typename T>
constexpr bool	isEqual (const T &a, const T &b, T absEpsilon=8 numeric_limits< T >::epsilon(), T relEpsilon=64 numeric_limits< T >::epsilon()) noexcept
	Compares two values for approximate equality.
template<typename T>
constexpr T	deg2rad (const T &angle) noexcept
	Converts angle from degrees to radians.
template<typename T>
constexpr T	rad2deg (const T &angle) noexcept
	Converts angle from radians to degrees.
template<Vector2Component T>
constexpr Vector2< T >	operator- (const Vector2< T > &vector) noexcept
	Unary minus: negated components.
template<Vector2Component T>
constexpr Vector2< T >	operator+ (const Vector2< T > &left, const Vector2< T > &right) noexcept
	Addition of two vectors.
template<Vector2Component T>
constexpr Vector2< T >	operator- (const Vector2< T > &left, const Vector2< T > &right) noexcept
	Subtraction of two vectors.
template<Vector2Component T>
constexpr Vector2< T >	operator* (const Vector2< T > &left, const T &right) noexcept
	Vector scaled by scalar.
template<Vector2Component T>
constexpr Vector2< T >	operator* (const T &left, const Vector2< T > &right) noexcept
	Vector scaled by scalar (scalar on the left).
template<Vector2Component T>
constexpr T	operator* (const Vector2< T > &left, const Vector2< T > &right) noexcept
	Dot product of two vectors.
template<Vector2Component T>
constexpr Vector2< T >	operator/ (const Vector2< T > &left, const T &right) noexcept
	Vector divided by scalar.
template<Vector2Component T>
constexpr bool	operator== (const Vector2< T > &left, const Vector2< T > &right) noexcept
	Exact equality of two vectors.
template<Vector2Component T>
constexpr bool	operator!= (const Vector2< T > &left, const Vector2< T > &right) noexcept
	Inequality of two vectors.
template<Vector2Component T>
constexpr T	cross (const Vector2< T > &left, const Vector2< T > &right) noexcept
	2D cross product (scalar result).
template<Vector2Component T>
	Vector2 (const T &, const T &) -> Vector2< T >
	Deduction guide: enables `Vector2(x, y)` without an explicit template argument when both arguments have the same toy::math::Vector2Component type.

Variables
template<typename T>
constexpr bool	is_fixed_point_v = is_fixed_point<T>::value
	Helper variable template: `true` if T is toy::math::fixed, `false` otherwise.

Detailed Description

Mathematical types, constants, and utilities: fixed-point, vectors, point.

See also: toy::math::Point, toy::math::Vector2, toy::math::fixed

Typedef Documentation

◆ real_t

using toy::math::real_t = float

Floating‑point scalar type.

Function Documentation

◆ cross()

template<Vector2Component T>

T toy::math::cross	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

2D cross product (scalar result).

Parameters

left	First operand.
right	Second operand.

Returns: left.x * right.y - left.y * right.x.

◆ operator!=()

template<Vector2Component T>

bool toy::math::operator!=	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Inequality of two vectors.

Parameters

left	First operand.
right	Second operand.

Returns: true if !(left == right).

◆ operator*() [1/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator*	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Returns a * b as a new toy::math::fixed (same type as left toy::math::fixed operand).

Parameters

a	Left operand (fixed-point value).
b	Right operand (fixed-point value).

Returns: Product as toy::math::fixed with same type as a.

◆ operator*() [2/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator*	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Returns a * b as a new toy::math::fixed (fixed times integral whole units).

Parameters

a	Fixed-point value.
b	Integral value (whole units).

Returns: Product as toy::math::fixed.

◆ operator*() [3/8]

template<PointScalar T>

Point toy::math::operator*	(	const Point &	point,
		const T &	scalar )

nodiscardconstexprnoexcept

Point scaled by scalar and truncated to integer.

Template Parameters

T	Type satisfying toy::math::PointScalar.

Parameters

point	Point operand.
scalar	Scale factor.

Returns: toy::math::Point with coordinates multiplied by scalar then cast to int32_t.

◆ operator*() [4/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator*	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Returns a * b as a new toy::math::fixed (integral whole units times fixed).

Parameters

a	Integral value (whole units).
b	Fixed-point value.

Returns: Product as toy::math::fixed.

◆ operator*() [5/8]

template<Vector2Component T>

Vector2< T > toy::math::operator*	(	const T &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Vector scaled by scalar (scalar on the left).

Template Parameters

T	Component type satisfy toy::math::Vector2Component.

Parameters

left	Scale factor.
right	Vector operand.

Returns: toy::math::Vector2 with components multiplied by scalar.

◆ operator*() [6/8]

template<PointScalar T>

Point toy::math::operator*	(	const T &	scalar,
		const Point &	point )

nodiscardconstexprnoexcept

Point scaled by scalar (scalar on the left).

Template Parameters

T	Type satisfying toy::math::PointScalar (signed integral, floating-point, or fixed-point).

Parameters

scalar	Scale factor.
point	Point operand.

Returns: toy::math::Point with coordinates multiplied by scalar then cast to int32_t.

◆ operator*() [7/8]

template<Vector2Component T>

Vector2< T > toy::math::operator*	(	const Vector2< T > &	left,
		const T &	right )

nodiscardconstexprnoexcept

Vector scaled by scalar.

Template Parameters

T	Component type satisfy toy::math::Vector2Component.

Parameters

left	Vector operand.
right	Scale factor.

Returns: toy::math::Vector2 with components multiplied by scalar.

◆ operator*() [8/8]

template<Vector2Component T>

T toy::math::operator*	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Dot product of two vectors.

Parameters

left	First operand.
right	Second operand.

Returns: left.x * right.x + left.y * right.y.

◆ operator+() [1/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator+	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Returns a + b as a new toy::math::fixed (same type as left operand).

b may be a toy::math::fixed with different rounding (OtherRounding) or an integral; the result uses Rounding of the toy::math::fixed operand.

Parameters

a	Left operand (fixed-point value).
b	Right operand (fixed-point or integral whole units).

Returns: Sum as toy::math::fixed with same type as a.

◆ operator+() [2/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator+	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Returns a + b as a new toy::math::fixed (fixed plus integral whole units).

Parameters

a	Fixed-point value.
b	Integral value (whole units).

Returns: Sum as toy::math::fixed.

◆ operator+() [3/5]

Point toy::math::operator+	(	const Point &	left,
		const Point &	right )

nodiscardconstexprnoexcept

Addition of two points.

Parameters

left	First operand.
right	Second operand.

Returns: toy::math::Point with (left.x + right.x, left.y + right.y).

◆ operator+() [4/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator+	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Returns a + b as a new toy::math::fixed (integral whole units plus fixed).

Parameters

a	Integral value (whole units).
b	Fixed-point value.

Returns: Sum as toy::math::fixed.

◆ operator+() [5/5]

template<Vector2Component T>

Vector2< T > toy::math::operator+	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Addition of two vectors.

Parameters

left	First operand.
right	Second operand.

Returns: toy::math::Vector2 with (left.x + right.x, left.y + right.y).

◆ operator-() [1/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator-	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Returns a - b as a new toy::math::fixed (same type as left operand).

Parameters

a	Left operand (fixed-point value).
b	Right operand (fixed-point value).

Returns: Difference as toy::math::fixed with same type as a.

◆ operator-() [2/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator-	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Returns a - b as a new toy::math::fixed (fixed minus integral whole units).

Parameters

a	Fixed-point value.
b	Integral value (whole units).

Returns: Difference as toy::math::fixed.

◆ operator-() [3/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator- ( const fixed< Base, Intermediate, Fraction, Rounding > & value )

nodiscardconstexprnoexcept

Unary minus: returns the negation of a toy::math::fixed value.

The result has the same raw storage as value with sign flipped. The operand is not modified.

Parameters

value Fixed-point value to negate.

Returns: A new toy::math::fixed instance representing -value.

◆ operator-() [4/8]

Point toy::math::operator-	(	const Point &	left,
		const Point &	right )

nodiscardconstexprnoexcept

Subtraction of two points.

Parameters

left	First operand.
right	Second operand.

Returns: toy::math::Point with (left.x - right.x, left.y - right.y).

◆ operator-() [5/8]

Point toy::math::operator- ( const Point & point )

nodiscardconstexprnoexcept

Unary minus: negated coordinates.

Parameters

point Operand.

Returns: toy::math::Point with (-point.x, -point.y).

◆ operator-() [6/8]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator-	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Returns a - b as a new toy::math::fixed (integral whole units minus fixed).

Parameters

a	Integral value (whole units).
b	Fixed-point value.

Returns: Difference as toy::math::fixed.

◆ operator-() [7/8]

template<Vector2Component T>

Vector2< T > toy::math::operator-	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Subtraction of two vectors.

Parameters

left	First operand.
right	Second operand.

Returns: toy::math::Vector2 with (left.x - right.x, left.y - right.y).

◆ operator-() [8/8]

template<Vector2Component T>

Vector2< T > toy::math::operator- ( const Vector2< T > & vector )

nodiscardconstexprnoexcept

Unary minus: negated components.

Parameters

vector Operand.

Returns: toy::math::Vector2 with (-vector.x, -vector.y).

◆ operator/() [1/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator/	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Returns a / b as a new toy::math::fixed.

Behavior is undefined if b is zero.

Parameters

a	Dividend (fixed-point value).
b	Divisor (fixed-point value, must not be zero).

Returns: Quotient as toy::math::fixed.

◆ operator/() [2/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator/	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Returns a / b as a new toy::math::fixed (fixed divided by integral whole units).

Behavior is undefined if b is zero.

Parameters

a	Dividend (fixed-point value).
b	Divisor (integral, must not be zero).

Returns: Quotient as toy::math::fixed.

◆ operator/() [3/5]

template<PointScalar T>

Point toy::math::operator/	(	const Point &	point,
		const T &	scalar )

nodiscardconstexprnoexcept

Point divided by scalar and truncated to integer.

Template Parameters

T	Type satisfying toy::math::PointScalar (signed integral, floating-point, or fixed-point).

Parameters

point	Point operand.
scalar	Divisor.

Returns: toy::math::Point with coordinates divided by scalar then cast to int32_t.

Precondition: scalar != 0.

◆ operator/() [4/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, typename T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::operator/	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Returns a / b as a new toy::math::fixed (integral whole units divided by fixed).

Behavior is undefined if b is zero.

Parameters

a	Dividend (integral value).
b	Divisor (fixed-point value, must not be zero).

Returns: Quotient as toy::math::fixed.

◆ operator/() [5/5]

template<Vector2Component T>

Vector2< T > toy::math::operator/	(	const Vector2< T > &	left,
		const T &	right )

nodiscardconstexprnoexcept

Vector divided by scalar.

Template Parameters

T	Component type satisfy toy::math::Vector2Component.

Parameters

left	Vector operand.
right	Divisor.

Returns: toy::math::Vector2 with components divided by scalar.

Precondition: right != 0.

◆ operator<=>() [1/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

strong_ordering toy::math::operator<=>	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Three-way comparison of two toy::math::fixed values.

Compares raw storage values; Rounding of either operand does not affect the result. Enables <, <=, >, >=, and != via the compiler-generated operators.

Template Parameters

Base	Storage type (shared by both operands).
Intermediate	Intermediate type (shared by both operands).
Fraction	Number of fractional bits (shared by both operands).
Rounding	Rounding policy of the left operand.
OtherRounding	Rounding policy of the right operand.

Parameters

a	Left operand.
b	Right operand.

Returns: strong_ordering::less if a is less than b, strong_ordering::equal if equal, strong_ordering::greater if a is greater than b.

◆ operator<=>() [2/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>

strong_ordering toy::math::operator<=>	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Three-way comparison of a toy::math::fixed value with an integral.

Converts b to the same toy::math::fixed type and compares raw storage values. Enables <, <=, >, >=, and != for fixed and integral operands.

Template Parameters

Base	Storage type of the fixed operand.
Intermediate	Intermediate type of the fixed operand.
Fraction	Number of fractional bits of the fixed operand.
Rounding	Rounding policy of the fixed operand.
T	Integral type; must satisfy `integral`.

Parameters

a	Left operand (fixed-point).
b	Right operand (integral whole units).

Returns: strong_ordering::less if a is less than b, strong_ordering::equal if equal, strong_ordering::greater if a is greater than b.

◆ operator<=>() [3/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>

strong_ordering toy::math::operator<=>	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Three-way comparison of an integral with a toy::math::fixed value.

Converts a to the same toy::math::fixed type as b and compares raw storage values. Enables <, <=, >, >=, and != for integral and fixed operands.

Template Parameters

Base	Storage type of the fixed operand.
Intermediate	Intermediate type of the fixed operand.
Fraction	Number of fractional bits of the fixed operand.
Rounding	Rounding policy of the fixed operand.
T	Integral type; must satisfy `integral`.

Parameters

a	Left operand (integral whole units).
b	Right operand (fixed-point).

Returns: strong_ordering::less if a is less than b, strong_ordering::equal if equal, strong_ordering::greater if a is greater than b.

◆ operator==() [1/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, bool OtherRounding>

bool toy::math::operator==	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const fixed< Base, Intermediate, Fraction, OtherRounding > &	b )

nodiscardconstexprnoexcept

Compares two toy::math::fixed values for equality.

Compares raw storage values; Rounding of either operand does not affect the result. Two values are equal if and only if their raw values are equal.

Template Parameters

Base	Storage type (shared by both operands).
Intermediate	Intermediate type (shared by both operands).
Fraction	Number of fractional bits (shared by both operands).
Rounding	Rounding policy of the left operand.
OtherRounding	Rounding policy of the right operand.

Parameters

a	Left operand.
b	Right operand.

Returns: true if a and b represent the same value, false otherwise.

◆ operator==() [2/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>

bool toy::math::operator==	(	const fixed< Base, Intermediate, Fraction, Rounding > &	a,
		const T &	b )

nodiscardconstexprnoexcept

Compares a toy::math::fixed value with an integral for equality.

Converts b to the same toy::math::fixed type and compares raw storage values. Two values are equal if and only if their raw values are equal.

Template Parameters

Base	Storage type of the fixed operand.
Intermediate	Intermediate type (shared).
Fraction	Number of fractional bits.
Rounding	Rounding policy of the fixed operand.
T	Integral type; must satisfy `integral`.

Parameters

a	Left operand (fixed-point).
b	Right operand (integral whole units).

Returns: true if a and b represent the same value, false otherwise.

◆ operator==() [3/5]

bool toy::math::operator==	(	const Point &	left,
		const Point &	right )

nodiscardconstexprnoexcept

Exact equality of two points.

Parameters

left	First operand.
right	Second operand.

Returns: true if left.x == right.x and left.y == right.y, false otherwise.

See also: isEqual() for tolerance-based comparison.

◆ operator==() [4/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding, integral T>

bool toy::math::operator==	(	const T &	a,
		const fixed< Base, Intermediate, Fraction, Rounding > &	b )

nodiscardconstexprnoexcept

Compares an integral with a toy::math::fixed value for equality.

Converts a to the same toy::math::fixed type as b and compares raw storage values. Two values are equal if and only if their raw values are equal.

Template Parameters

Base	Storage type of the fixed operand.
Intermediate	Intermediate type (shared).
Fraction	Number of fractional bits.
Rounding	Rounding policy of the fixed operand.
T	Integral type; must satisfy `integral`.

Parameters

a	Left operand (integral whole units).
b	Right operand (fixed-point).

Returns: true if a and b represent the same value, false otherwise.

◆ operator==() [5/5]

template<Vector2Component T>

bool toy::math::operator==	(	const Vector2< T > &	left,
		const Vector2< T > &	right )

nodiscardconstexprnoexcept

Exact equality of two vectors.

For floating-point T, delegates to isEqual() with default epsilons. For fixed-point T, compares raw storage of both components.

Parameters

left	First operand.
right	Second operand.

Returns: For floating-point T: true if isEqual(right) with default tolerances. For fixed-point T: true if left and right have equal raw component values.

See also: isEqual() for custom tolerances (floating-point).

◆ Vector2()

template<Vector2Component T>

toy::math::Vector2	(	const T &	,
		const T &	) -> Vector2< T >

Deduction guide: enables Vector2(x, y) without an explicit template argument when both arguments have the same toy::math::Vector2Component type.

Template Parameters

T	Component type; must satisfy toy::math::Vector2Component.

Variable Documentation

◆ is_fixed_point_v

template<typename T>

bool toy::math::is_fixed_point_v = is_fixed_point<T>::value

inlineconstexpr

Helper variable template: true if T is toy::math::fixed, false otherwise.

Namespaces

Classes

Concepts

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ real_t

Function Documentation

◆ cross()

◆ operator!=()

◆ operator*() [1/8]

◆ operator*() [2/8]

◆ operator*() [3/8]

◆ operator*() [4/8]

◆ operator*() [5/8]

◆ operator*() [6/8]

◆ operator*() [7/8]

◆ operator*() [8/8]

◆ operator+() [1/5]

◆ operator+() [2/5]

◆ operator+() [3/5]

◆ operator+() [4/5]

◆ operator+() [5/5]

◆ operator-() [1/8]

◆ operator-() [2/8]

◆ operator-() [3/8]

◆ operator-() [4/8]

◆ operator-() [5/8]

◆ operator-() [6/8]

◆ operator-() [7/8]

◆ operator-() [8/8]

◆ operator/() [1/5]

◆ operator/() [2/5]

◆ operator/() [3/5]

◆ operator/() [4/5]

◆ operator/() [5/5]

◆ operator<=>() [1/3]

◆ operator<=>() [2/3]

◆ operator<=>() [3/3]

◆ operator==() [1/5]

◆ operator==() [2/5]

◆ operator==() [3/5]

◆ operator==() [4/5]

◆ operator==() [5/5]

◆ Vector2()

Variable Documentation

◆ is_fixed_point_v