Crux::Detail Namespace Reference

Classes
struct	CosCoeffs
	Polynomial coefficient table for cosine approximations on [-pi/4, pi/4]. More...
struct	CosCoeffs< 5 >
	Degree-5 cosine: cos(x) ~= c0 + c2*x^2 + c4*x^4. More...
struct	CosCoeffs< 7 >
	Degree-7 cosine: cos(x) ~= c0 + c2*x^2 + c4*x^4 + c6*x^6. More...
struct	CosCoeffs< 9 >
	Degree-9 cosine: cos(x) ~= c0 + c2*x^2 + c4*x^4 + c6*x^6 + c8*x^8. More...
struct	SinCoeffs
	Polynomial coefficient table for sine approximations on [-pi/4, pi/4]. More...
struct	SinCoeffs< 5 >
	Degree-5 sine: sin(x) ~= c1*x + c3*x^3 + c5*x^5. More...
struct	SinCoeffs< 7 >
	Degree-7 sine: sin(x) ~= c1*x + c3*x^3 + c5*x^5 + c7*x^7. More...
struct	SinCoeffs< 9 >
	Degree-9 sine: sin(x) ~= c1*x + c3*x^3 + c5*x^5 + c7*x^7 + c9*x^9. More...

Enumerations
enum class	PrecisionMode { Fast , Standard , High }
	Precision modes for selecting polynomial degree. More...

Functions
template<PrecisionMode Mode>
constexpr float	PolySin (float x)
	Dispatch to the appropriate degree-xx sine polynomial.
template<PrecisionMode Mode>
constexpr float	PolyCos (float x)
	Dispatch to the appropriate degree-xx cosine polynomial.
template<int Degree>
constexpr float	PolySinImpl (float x)
	Generic Estrin-based sine polynomial of degree D on x in [-pi/4,pi/4].
template<>
float	PolySinImpl< 5 > (float x)
template<>
float	PolySinImpl< 7 > (float x)
template<>
float	PolySinImpl< 9 > (float x)
template<int Degree>
constexpr float	PolyCosImpl (float x)
	Generic Estrin-based cosine polynomial of degree D on x in [-pi/4,pi/4].
template<>
float	PolyCosImpl< 5 > (float x)
template<>
float	PolyCosImpl< 7 > (float x)
template<>
float	PolyCosImpl< 9 > (float x)

Local constants for range reduction (float)
void	ReduceAngle (float x, float &outXr, unsigned int &outQuad) noexcept
	Reduce angle into [-pi/4, pi/4] and extract quadrant.

Enumeration Type Documentation

PrecisionMode

enum class Crux::Detail::PrecisionMode

strong

Precision modes for selecting polynomial degree.

Enumerator
Fast	degree 5 approximation (lowest accuracy, highest speed)
Standard	degree 7 approximation (default tradeoff)
High	degree 9 approximation (highest accuracy)

Function Documentation

PolyCos()

template<PrecisionMode Mode>

float Crux::Detail::PolyCos ( float x )

inlineconstexpr

Dispatch to the appropriate degree-xx cosine polynomial.

Template Parameters

Mode	Desired precision mode.

Parameters

x	Input in [-pi/4, pi/4].

Returns

Approximated cos(x).

PolyCosImpl()

template<int Degree>

float Crux::Detail::PolyCosImpl ( float x )

inlineconstexpr

Generic Estrin-based cosine polynomial of degree D on x in [-pi/4,pi/4].

Template Parameters

Degree

Polynomial degree (must be even: 5,7,9).

Parameters

x	Reduced input in [-pi/4,pi/4].

Returns

Approximation of cos(x).

PolyCosImpl< 5 >()

template<>

float Crux::Detail::PolyCosImpl< 5 > ( float x )

inline

PolyCosImpl< 7 >()

template<>

float Crux::Detail::PolyCosImpl< 7 > ( float x )

inline

PolyCosImpl< 9 >()

template<>

float Crux::Detail::PolyCosImpl< 9 > ( float x )

inline

PolySin()

template<PrecisionMode Mode>

float Crux::Detail::PolySin ( float x )

inlineconstexpr

Dispatch to the appropriate degree-xx sine polynomial.

Template Parameters

Mode	Desired precision mode.

Parameters

x	Input in [-pi/4, pi/4].

Returns

Approximated sin(x).

PolySinImpl()

template<int Degree>

float Crux::Detail::PolySinImpl ( float x )

inlineconstexpr

Generic Estrin-based sine polynomial of degree D on x in [-pi/4,pi/4].

Template Parameters

Degree

Polynomial degree (must be odd: 5,7,9).

Parameters

x	Reduced input in [-pi/4,pi/4].

Returns

Approximation of sin(x).

PolySinImpl< 5 >()

template<>

float Crux::Detail::PolySinImpl< 5 > ( float x )

inline

PolySinImpl< 7 >()

template<>

float Crux::Detail::PolySinImpl< 7 > ( float x )

inline

PolySinImpl< 9 >()

template<>

float Crux::Detail::PolySinImpl< 9 > ( float x )

inline

ReduceAngle()

void Crux::Detail::ReduceAngle ( float x, float & outXr, unsigned int & outQuad )

inlinenoexcept

Reduce angle into [-pi/4, pi/4] and extract quadrant.

1) Scale x by 2/pi to get k. 2) Round k to nearest int without branches. 3) Subtract k*(pi/2) using two-step FMA (hi then lo). 4) Compute quadrant = k mod 4.

Parameters

x	Input angle in radians.
outXr	[out] Reduced angle in [-pi/4, pi/4].
outQuad	[out] Quadrant index in {0,1,2,3}.

The caller uses outQuad to decide sine vs cosine and sign.