Mathematical operations and algorithms. More...

Files
file	TrigPolyImpl.inl
	Estrin-based polynomial evaluation for sine and cosine.

Functions
template<typename T>
constexpr T	Crux::Lerp (T a, T b, float t)
	Linear interpolation between a and b by factor t.
template<typename T>
constexpr T	Crux::Min (T a, T b)
	Return the minimum of two values.
template<typename T>
constexpr T	Crux::Max (T a, T b)
	Return the maximum of two values.
template<typename T>
constexpr T	Crux::Clamp (T value, T min, T max)
	Clamp a value between a minimum and maximum.
template<typename T>
constexpr T	Crux::Saturate (T value)
	Clamp a value to the [0,1] range.
template<typename T>
constexpr T	Crux::Sign (T value)
	Signum function: returns -1, 0, or +1.
template<typename T>
constexpr T	Crux::Abs (T value)
	Absolute value.
template<typename T>
constexpr T	Crux::Floor (T value)
	Floor function for floating-point values.
template<typename T>
constexpr T	Crux::Ceil (T value)
	Ceiling function for floating-point values.
template<typename T>
constexpr T	Crux::Fract (T value)
	Fractional part of a value.
template<typename T>
constexpr T	Crux::Square (T value)
	Square of a value.
template<typename T>
constexpr T	Crux::Cube (T value)
	Cube of a value.
constexpr float	Crux::Smoothstep (float edge0, float edge1, float x)
	Smoothstep interpolation between edge0 and edge1.
constexpr float	Crux::CTInverseSqrt (float x)
	Fast compile-time inverse square root (single Newton step).
constexpr float	Crux::CTSqrt (const float x)
	Fast compile-time square root using bit manipulation.
float	Crux::InverseSqrt (const float x)
	Inverse square root using hardware rsqrt.
float	Crux::Sqrt (const float x)
	Standard square root using hardware sqrt.
constexpr float	Crux::Radians (float degrees)
	Convert degrees to radians.
constexpr Vector< float, 3 >	Crux::Radians (Vector< float, 3 > vector)
	Convert a Vector3s components from degrees to radians.
constexpr float	Crux::Degrees (float radians)
	Convert radians to degrees.
constexpr Vector< float, 3 >	Crux::Degrees (Vector< float, 3 > vector)
	Convert a Vector3s components from radians to degrees.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
float	Crux::Sin (float radians)
	Computes the sine of an angle in radians using a fast polynomial approximation.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
float	Crux::Cos (float radians)
	Computes the cosine of an angle in radians using a fast polynomial approximation.

Detailed Description

Mathematical operations and algorithms.

Houses core arithmetic and math utilities.

Function Documentation

◆ Abs()

template<typename T>

T Crux::Abs ( T value )

inlineconstexpr

Absolute value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: Non-negative absolute of value.

◆ Ceil()

template<typename T>

T Crux::Ceil ( T value )

inlineconstexpr

Ceiling function for floating-point values.

Template Parameters

T	Floating-point type.

Parameters

value Input value.

Returns: Smallest integer >= value as T.

◆ Clamp()

template<typename T>

T Crux::Clamp	(	T	value,
		T	min,
		T	max )

inlineconstexpr

Clamp a value between a minimum and maximum.

Template Parameters

T	Arithmetic type.

Parameters

value	Input value.
min	Minimum allowed.
max	Maximum allowed.

Returns: Clamped value in [min, max].

◆ Cos()

template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>

float Crux::Cos ( float radians )

inline

Computes the cosine of an angle in radians using a fast polynomial approximation.

Performs a branchless range-reduction into [-pi/4, pi/4], shifts the quadrant index for the pi/2 phase offset (cos(x)=sin(x+pi/2)), evaluates a minimax polynomial of degree determined by the PrecisionMode template (Standard=7), and applies the correct sign.

Template Parameters

PrecisionMode

Selects the polynomial degree:

UltraFast (degree 5)
Standard (degree 7, default)
High (degree 9) It is recommended to use Standard for most applications.

Parameters

radians Angle in radians.

Returns: Approximation of cos(radians).

Note: This uses the internal Detail::ReduceAngle and Detail::PolyCos<PrecisionMode> routines.

See also: Detail::ReduceAngle, Detail::PolyCos

◆ CTInverseSqrt()

float Crux::CTInverseSqrt ( float x )

inlineconstexpr

Fast compile-time inverse square root (single Newton step).

Note: This is an approximation and may not be accurate for all values. Prefer using the provided Hardware InverseSqrt function. Only use if you need the value at Compile-Time

Warning: Entering 0.0f will result in a really large number.

Parameters

x	Input value.

Returns: Approximate 1/sqrt(x).

◆ CTSqrt()

float Crux::CTSqrt ( const float x )

inlineconstexpr

Fast compile-time square root using bit manipulation.

Note: This is an approximation and may not be accurate for all values. Prefer using the provided Hardware Sqrt function. Only use if you need the value at Compile-Time

Warning: Entering a negative value will result in inf.

Parameters

x	Input value.

Returns: Approximate sqrt(x).

◆ Cube()

template<typename T>

T Crux::Cube ( T value )

inlineconstexpr

Cube of a value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: value * value * value.

◆ Degrees() [1/2]

float Crux::Degrees ( float radians )

inlineconstexpr

Convert radians to degrees.

Parameters

radians Angle in radians.

Returns: Angle in degrees.

◆ Degrees() [2/2]

Vector< float, 3 > Crux::Degrees ( Vector< float, 3 > vector )

inlineconstexpr

Convert a Vector3s components from radians to degrees.

Parameters

vector The Vector to convert

Returns: A vector with all its components turned from radians to degrees

◆ Floor()

template<typename T>

T Crux::Floor ( T value )

inlineconstexpr

Floor function for floating-point values.

Template Parameters

T	Floating-point type.

Parameters

value Input value.

Returns: Largest integer <= value as T.

◆ Fract()

template<typename T>

T Crux::Fract ( T value )

inlineconstexpr

Fractional part of a value.

Template Parameters

T	Floating-point type.

Parameters

value Input value.

Returns: value - floor(value).

◆ InverseSqrt()

float Crux::InverseSqrt ( const float x )

inline

Inverse square root using hardware rsqrt.

Warning: Entering 0.0f will result in infinity.

Parameters

x	Input value.

Returns: 1.0f / sqrt(x).

◆ Lerp()

template<typename T>

T Crux::Lerp	(	T	a,
		T	b,
		float	t )

inlineconstexpr

Linear interpolation between a and b by factor t.

Template Parameters

T	Arithmetic type of endpoints.

Parameters

a	Start value.
b	End value.
t	Interpolation factor in [0,1].

Returns: Interpolated value.

◆ Max()

template<typename T>

T Crux::Max	(	T	a,
		T	b )

inlineconstexpr

Return the maximum of two values.

Template Parameters

T	Arithmetic type.

Parameters

a	First value.
b	Second value.

Returns: Larger of a and b.

◆ Min()

template<typename T>

T Crux::Min	(	T	a,
		T	b )

inlineconstexpr

Return the minimum of two values.

Template Parameters

T	Arithmetic type.

Parameters

a	First value.
b	Second value.

Returns: Smaller of a and b.

◆ Radians() [1/2]

float Crux::Radians ( float degrees )

inlineconstexpr

Convert degrees to radians.

Parameters

degrees Angle in degrees.

Returns: Angle in radians.

◆ Radians() [2/2]

Vector< float, 3 > Crux::Radians ( Vector< float, 3 > vector )

inlineconstexpr

Convert a Vector3s components from degrees to radians.

Parameters

vector The Vector to convert

Returns: A vector with all its components turned from degress to radians

◆ Saturate()

template<typename T>

T Crux::Saturate ( T value )

inlineconstexpr

Clamp a value to the [0,1] range.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: Saturated value in [0,1].

◆ Sign()

template<typename T>

T Crux::Sign ( T value )

inlineconstexpr

Signum function: returns -1, 0, or +1.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: +1 if value > 0, -1 if value < 0, 0 if value == 0.

◆ Sin()

template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>

float Crux::Sin ( float radians )

inline

Computes the sine of an angle in radians using a fast polynomial approximation.

Performs a branchless range-reduction into [-pi/4, pi/4], evaluates a minimax polynomial of degree determined by the PrecisionMode template (Standard=7), and applies the correct sign based on the original quadrant.

Template Parameters

PrecisionMode

Selects the polynomial degree:

UltraFast (degree 5)
Standard (degree 7, default)
High (degree 9)

It is recommended to use Standard for most applications.

Parameters

radians Angle in radians.

Returns: Approximation of sin(radians).

Note: This uses the internal Detail::ReduceAngle and Detail::PolySin<PrecisionMode> routines.

See also: Detail::ReduceAngle, Detail::PolySin

◆ Smoothstep()

float Crux::Smoothstep	(	float	edge0,
		float	edge1,
		float	x )

inlineconstexpr

Smoothstep interpolation between edge0 and edge1.

Parameters

edge0	Lower edge of interpolation.
edge1	Upper edge of interpolation.
x	Value to interpolate.

Returns: Interpolated result in [0,1].

◆ Sqrt()

float Crux::Sqrt ( const float x )

inline

Standard square root using hardware sqrt.

Warning: Entering a negative value will result in -nan.

Parameters

x	Input value.

Returns: sqrt(x).

◆ Square()

template<typename T>

T Crux::Square ( T value )

inlineconstexpr

Square of a value.

Template Parameters

T	Arithmetic type.

Parameters

value Input value.

Returns: value * value.

Files

Functions

Detailed Description

Function Documentation

◆ Abs()

◆ Ceil()

◆ Clamp()

◆ Cos()

◆ CTInverseSqrt()

◆ CTSqrt()

◆ Cube()

◆ Degrees() [1/2]

◆ Degrees() [2/2]

◆ Floor()

◆ Fract()

◆ InverseSqrt()

◆ Lerp()

◆ Max()

◆ Min()

◆ Radians() [1/2]

◆ Radians() [2/2]

◆ Saturate()

◆ Sign()

◆ Sin()

◆ Smoothstep()

◆ Sqrt()

◆ Square()